<%BANNER%>

On the Modeling and Design of Zero-Net Mass Flux Actuators

xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID E20110115_AAAACJ INGEST_TIME 2011-01-15T15:01:36Z PACKAGE UFE0008338_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES
FILE SIZE 1976 DFID F20110115_AABQVA ORIGIN DEPOSITOR PATH gallas_q_Page_055.txt GLOBAL false PRESERVATION BIT MESSAGE_DIGEST ALGORITHM MD5
8dcee6a3806691a4054e76d69203962c
SHA-1
a5a0d990607fb6a1e710cb85f3a52afbfef873bc
1053954 F20110115_AABQCX gallas_q_Page_249.tif
2f2f6ebeee02239d778d8af0b54f2bbc
97e210805dc41080643382c7b99120cd5f7c6a8b
44308 F20110115_AABOWN gallas_q_Page_294.pro
eb940af43b01ab47151c101c3f746ab3
28eb23b01fe72609656e80c3d0c9e41a5d083f89
55413 F20110115_AABPTG gallas_q_Page_325.jp2
54ac72df4ec5ee792f5a2931c5ff80e5
f61ac71a3122f8dc10fe3011929f90d680a4abd4
22091 F20110115_AABOJC gallas_q_Page_180.pro
21326c61c82a703bf72f63b988b73dfa
20353d6b3e45e5f556ff24ea7ec5e58c8a148669
497 F20110115_AABQVB gallas_q_Page_056.txt
149dd38c6dfb52f3042ffd7c2d2d9f4b
9d136624b1f8c1e0e4767210a6bf8383d89d3c79
F20110115_AABQCY gallas_q_Page_250.tif
e64b4d3bdcbdbfbcb9ff88bb4ff62838
c38b4df381643ecafc06bbaca9d9ee1b212eba73
83966 F20110115_AABOWO gallas_q_Page_128.jpg
c03ca3ae4cc13e18cfe29ee27e347646
ded61d861e699326bd79bd7e2c84e2cd16757244
47856 F20110115_AABPTH gallas_q_Page_326.jp2
9826eed3a89f9301ba112f77f9ef7d35
cfc177ffa1e24d32bd92fa90f2df80ce2f0f7d7f
2021 F20110115_AABOJD gallas_q_Page_041.txt
8740154eab3c5612a853ea6955371826
aa63f21e49c6a73ec9e2925e866540490ba8a46c
1785 F20110115_AABQVC gallas_q_Page_058.txt
2302d7f2f1ecb6692ac7502a347eb69f
818de9c32ec61cdb9e5e9acb54961fbe17fdf350
F20110115_AABQCZ gallas_q_Page_252.tif
004ce67b9a51d74852caad79095d43f8
ef43e78380d055a85e344bcfd51c7dcc94c5a93f
56355 F20110115_AABOWP gallas_q_Page_384.pro
eae52b3edd34370222590f90a2e62e22
c552f558ca7a564f3bd7e9f3cde054a908e707fc
57849 F20110115_AABPTI gallas_q_Page_327.jp2
1936313cecde7ae8e276b7f1ccfe88d4
8dc07333b711272e6e28ea9e3c8e50f9794717ff
43729 F20110115_AABOJE gallas_q_Page_010.jpg
8da18c088a70468fa41799da1f569c67
f589e92b1a05ffbd0fadd21719213022d7cdcf6a
1595 F20110115_AABQVD gallas_q_Page_059.txt
444e1e38026f75b5677cbb7b39874326
878e1c16877ac00703b037c206002bb1f88fcf5c
25271604 F20110115_AABOWQ gallas_q_Page_147.tif
fec6f6775a619666714ab360bad81c0d
61e5352b8c30385fcb684d9f376a1bb3ff56004f
67495 F20110115_AABPTJ gallas_q_Page_328.jp2
d0e87ac095c8edefb4af0d4f07c4d129
638d23bbcbb71921444399a56f3b56da71934923
30546 F20110115_AABOJF gallas_q_Page_223.pro
35d5d57c60f41483c019324bcc717dbe
de761506573eb1c26acdb14dbf023ce53f8f0d38
1853 F20110115_AABQVE gallas_q_Page_060.txt
208c29a11e6f9c5a9c75dde67397120f
01715b6fb91664099564666c620a476e6182d9ef
6164 F20110115_AABOWR gallas_q_Page_291thm.jpg
bd67168eabb5d87b081a0a774743d80f
4deae6a119a06b60306b43dc615231d31e7fb7f7
48489 F20110115_AABPTK gallas_q_Page_329.jp2
420a21851c46531a7fe4476373b54fc9
8d4c50f1243931fcc8b5cded939e7cd53f8c0feb
1817 F20110115_AABQVF gallas_q_Page_063.txt
b728d408c4cc0e6d21692d64d1330180
e3fdf5790df2e84f88436640ccf9481d5fdd96da
58140 F20110115_AABPGA gallas_q_Page_285.jpg
2b98c39ef4dc97b285c7af8df8ad2075
c4136afa5c420b812f4a51976ba5f3b23b24c0c8
56926 F20110115_AABOWS gallas_q_Page_349.jp2
3392f3e3e1c63852ab735052ba4f82ac
bc97a7d672788a1a203223c795c001c61769bc8a
54150 F20110115_AABPTL gallas_q_Page_330.jp2
bb3cd79c551c6d01db88b17828b47733
01e62208030475488c36a508f2cd4d546736fe3e
24911 F20110115_AABOJG gallas_q_Page_029.QC.jpg
a573965d6348808486c56b326a026fe9
32a146fd2a66d6ea7501f2440314bae4e2a04f5f
1762 F20110115_AABQVG gallas_q_Page_065.txt
c059a3baaad2e0e4177b6ed2fd1fb1b3
8db326e99a6fb7fc912b05c58b8f0259959e2a54
73065 F20110115_AABPGB gallas_q_Page_286.jpg
f7e5d96d44b987ff197eeb97a37cc86f
041250628d1b5515cc978250934ff7ec02f348d0
49273 F20110115_AABPTM gallas_q_Page_331.jp2
786300b99ef3ab631bef112928df0141
3207d662a7eb59fa461103be5a7af5660d4033a9
19952 F20110115_AABOJH gallas_q_Page_250.QC.jpg
c6b773af6915e8d76370118d8a6917a8
e7ea5d00b5870c28c457214228d1730e54b5a10f
6058 F20110115_AABRSA gallas_q_Page_198thm.jpg
153a387fe769f88747071dc12df7899b
1a70d636dfddc75834b24836d67ece353d3eec49
2022 F20110115_AABQVH gallas_q_Page_066.txt
374bc1f7687a41a4ad57d2ae4283b78e
5267068fc64ab34bd050360d03de2ac08cc69a02
571140 F20110115_AABOWT UFE0008338_00001.xml FULL
32ff20ef988b97ed0eda15bf1cef15c2
411ae831633b92e5dd4001ab8b44c0150fbe8914
68791 F20110115_AABPTN gallas_q_Page_333.jp2
aa33241644346d2dd4b0efdb71d4e73a
fc43163a8238a608fa7b75c5b0ab255b41db414e
F20110115_AABOJI gallas_q_Page_222.tif
1d11949a41c41bb7010612e4e279e8ef
93a87e9104c999d7bfc3ca8ba33106b1976b1bc7
5452 F20110115_AABRSB gallas_q_Page_199thm.jpg
1e97d4aa91052be4c474022fc94f3acd
9b76e76afd521b19014096ab0741cc29e1ca185b
1914 F20110115_AABQVI gallas_q_Page_067.txt
2136e187c679ef6553a6b18d3a4926a9
c5abd3c271056f496c4c4c0326d2fb4dc70e4496
58504 F20110115_AABPGC gallas_q_Page_287.jpg
7531c9e8203b65693243af08ca6d4d5d
1c572ce3bc82212adfd432beb15d0311334bcba8
98037 F20110115_AABPTO gallas_q_Page_334.jp2
8bf32bb8ccb70a783428c0cdac469e72
0b28af7f0b2e8e76b8e7e4d5ab30a794a8744d07
2407 F20110115_AABOJJ gallas_q_Page_211.txt
872f75e2199cf4fc2bd00085c12c6730
e7ae7b083c48adf08d8e0a8e5f0f3e8ce96ea7e9
13424 F20110115_AABRSC gallas_q_Page_200.QC.jpg
570400deb7344a9f1e65bab904e05b64
4cf864dfc9287ea51e515263f233272044ac273c
2153 F20110115_AABQVJ gallas_q_Page_068.txt
c5e46cb5df4fe958f559c53626393d02
a5f32ed6e9709516db413b2321b4fb7d3dbe5b88
57898 F20110115_AABPGD gallas_q_Page_288.jpg
bc9d5e6d3dbb67f44c833af3ef4b3193
e490c01631ae793a6861730421bfc17ba003bb5e
45297 F20110115_AABOJK gallas_q_Page_200.jpg
824bd93632829cb892a9b7ad474cff64
7f2a1257e2df7eb80eb9fe11153d515530ee826e
15795 F20110115_AABRSD gallas_q_Page_201.QC.jpg
4a0e77d8609c4974b4112a1c020dfca2
8ab64e6ce237761dc193a46a1f5cef5528c19424
1728 F20110115_AABQVK gallas_q_Page_070.txt
9710d0ccb1d7f3482daabfffa810c93d
dc67a2c8882db8add982cc720fd71a910f91d383
45843 F20110115_AABPGE gallas_q_Page_290.jpg
b6efc6884d22db0503c52ca778549b74
12c78d1736f544bfd2607a618cc9e4f4643e8b3e
21996 F20110115_AABOWW gallas_q_Page_001.jpg
4f93dc1c13cf03c8abfa7e6fe561b03e
adac1bb4a1a29520087448baf0f14878f502f05c
56282 F20110115_AABPTP gallas_q_Page_335.jp2
81f0406b8e2170bd86f0fabdf6e85a7e
4c2c558734cdcf4fb8f8b7fefc197e22d2408554
F20110115_AABOJL gallas_q_Page_065.tif
fa87c8f5221f1ea53fb67c52eb3354f4
a255976090a8e66c030e07a30b347ad3a74e7f2e
4822 F20110115_AABRSE gallas_q_Page_201thm.jpg
6fa5f06683e59a756b938138d92b9f10
119d33761d337d66f7d79a34f6631a7ef690f6f3
1847 F20110115_AABQVL gallas_q_Page_071.txt
12371bbf8175e0b6c654908b55ad91b1
8f047609d5ca29c7ce5a69b44ec31a52779ad92f
24831 F20110115_AABQIA gallas_q_Page_025.pro
a189b3d50393beef6f5e91cb21cb3e10
8490267a28c3da16c5d0e901d1833cb905d1899b
64744 F20110115_AABPGF gallas_q_Page_291.jpg
90f3400b13f21ef74b2d61b14612ad97
0dc66cc4fcc8e3467bc244ad2e724e30dc57d910
10250 F20110115_AABOWX gallas_q_Page_002.jpg
28f852afcd7b39ca208f83cbfbfd1c38
55bcefc46088dd5a509cbb4660e8050559b2b246
53376 F20110115_AABPTQ gallas_q_Page_336.jp2
4e4cda93b830964f8dde4a6d1e657ced
4e32a3c8b2e03a899a12814119b5d5ede4b8a7dd
48278 F20110115_AABOJM gallas_q_Page_160.pro
b59c59e4830e58c3e99741b3e2d255dd
a46e630da04d1280a18e3b0199da045f93726834
25018 F20110115_AABRSF gallas_q_Page_202.QC.jpg
d10b93675290f06eb7d8dbdbfe6117d9
491b8d925fe63b719c20dcc9289715661d45d32e
1889 F20110115_AABQVM gallas_q_Page_072.txt
4af0f2bd82648ef325e1d96ca9e4c972
a8b841b0532471c205221ad07511d1e3faa6e7ac
39098 F20110115_AABQIB gallas_q_Page_026.pro
c118edf0324647eb83d4c883a14544ee
c7c8e53bca44b8ca7cbcba042bb2040c3d8b705c
72851 F20110115_AABPGG gallas_q_Page_292.jpg
323958731f38aa9e434bedef9ac83554
f5a403d9d69eef488976c19d264016997881caa3
12680 F20110115_AABOWY gallas_q_Page_003.jpg
567e0205366ba85a117e592805044cb4
ed6e2c6dca74b1d16fe0d1bd5c2b750a14c8792c
71089 F20110115_AABPTR gallas_q_Page_337.jp2
4068ed40f8fbf8b8af4176ea54c3cc8d
b6fd47d67d5db72c9bb9100eb7ec786976cd8a75
F20110115_AABOJN gallas_q_Page_105.tif
3cffe2162d185e29cc9ad8de057ed7e8
301c4c4e76af5b9833ec6aad3a953866df620fc8
6912 F20110115_AABRSG gallas_q_Page_202thm.jpg
558f769b8713211b5228a0348f06f3a4
094ec081a468773080d06b526e20e07d6d71986b
1895 F20110115_AABQVN gallas_q_Page_073.txt
f010222fea257c9996fd0fcded023084
76cebbd581760d962636025c82d140e6a4553de8
31270 F20110115_AABQIC gallas_q_Page_027.pro
90e76847c96b44d0a3d255398ecdb5e8
3ee55295d4f096a807cb213226d074a654d0faa6
65493 F20110115_AABPGH gallas_q_Page_294.jpg
38d68f675e73075ca2398dde755d9f79
c4a03fb749f709ba42ef808362c27a6c663a2041
50853 F20110115_AABOWZ gallas_q_Page_004.jpg
bd4dbe8271078af598aa317fb26a69fe
ac1df2e5f169dc7bf3496023fde24f4cd4e05c66
54555 F20110115_AABPTS gallas_q_Page_338.jp2
2cdaab1cd685a1c8f77a2504346af6ad
8c533bda4cb37bf85e097d34f6eaef8cbc840acd
42924 F20110115_AABOJO gallas_q_Page_239.pro
a8d49e301577fa2de35c2ea3088bc38d
27d3d65304eba96cc22072f519d48f1894d14cf7
17941 F20110115_AABRSH gallas_q_Page_203.QC.jpg
4d875c1eeb612ab5562bf221814cb945
45ef962960bca63f7fc9359d0678bdc64dab22c2
2345 F20110115_AABQVO gallas_q_Page_075.txt
52f3b92f6960e0b945e8b465871c8d1d
318350854b4f1322e439b503f45511cb3f2692c3
70637 F20110115_AABPGI gallas_q_Page_297.jpg
ad1922ad95636417a2e1d7fe8c2c1b33
81b4f6b7bb5fb13e608c0d1dc7ac1d6972dd495b
77767 F20110115_AABPTT gallas_q_Page_339.jp2
e9af72ca7217cbc0cbfce8e791391743
e73be04724f85fbce23ed7cf151caa3508234ef4
F20110115_AABOJP gallas_q_Page_298.tif
b01d880c9dfa2ab854bf71b15583996e
1a9128e2c7ef5a1b5800e6d5af6dd98e1a399b3b
4956 F20110115_AABRSI gallas_q_Page_203thm.jpg
9b0ee6c2ff09e2e2babfef3257a96909
ba01d5ec498dd53c3490ec54f09842f3fc8a81ae
F20110115_AABQVP gallas_q_Page_077.txt
6efb1d3d4f2e1264950a95484f82fc81
8da84dadb6e394360797954124bf1943918ce49c
40553 F20110115_AABQID gallas_q_Page_028.pro
fc6248edac411604baa891544ec7d78b
54144425a6629b10a87e0fc2042c8eccffe9e473
70392 F20110115_AABPGJ gallas_q_Page_298.jpg
3f1443c8a774a8bee6dd265812d62545
e693d1c3fb19480b9ee611633c18b2d9db9ed9c3
89936 F20110115_AABPTU gallas_q_Page_340.jp2
3839b58041559f3982331566d7e5e48e
2f50e46a6ca2b632dc67ef779d169db02c55996e
46576 F20110115_AABOJQ gallas_q_Page_229.pro
bc82cebdd87dff165bb4029a3f36619f
72c460824c74fed1a1d32655eb268a023478ad5c
4481 F20110115_AABRSJ gallas_q_Page_204thm.jpg
faeed519f5f857ca5e617d934023f2a7
47bdbfc07117eb0e903fef91aa282c2f53ff866e
51081 F20110115_AABQIE gallas_q_Page_029.pro
59fc06613f7e55be924ccaf7fdf6c38f
ffb69cd2bad68a95817676222f79d244f8789f29
68124 F20110115_AABPGK gallas_q_Page_299.jpg
366b86f869bb001b0e8b7abad5d6880e
a743b4231e3fb3ab36f4b25823e074ab8a16101f
66131 F20110115_AABPTV gallas_q_Page_342.jp2
4070dd529537f0b14c2bd7b8b7ecb2b1
e782e66bf08ac8b79b38a3c6512be2bf7f225ef7
26580 F20110115_AABOJR gallas_q_Page_074.pro
a434566d56694f0ffa5e1dddd49b6a4a
b9e98d544275aa4995bd8c1c84971edb5ccd1824
21004 F20110115_AABRSK gallas_q_Page_205.QC.jpg
e4262a1494563ce6dfe4492641c6d5d9
00e93a2aef8171def6581087756e6371c092a043
1896 F20110115_AABQVQ gallas_q_Page_078.txt
71f91a378b81a9e1ee25add0bad2f487
987859332296fa6dd8a7586d2b27df5c98fa7011
48780 F20110115_AABQIF gallas_q_Page_030.pro
96fabd9313ebeb9c2e8a52b99727c47d
5b63930b9067730765ceb9b98cb3fb6ebab3199d
67915 F20110115_AABPGL gallas_q_Page_301.jpg
19396e90ba6aa4610ad40266165c2c1d
0b4af2eb7e6bbe8f4f4f4b288343113ce91b8ee5
67786 F20110115_AABPTW gallas_q_Page_343.jp2
a68f2833656e665ffa7029c73c453df7
36f12b3582b255718fce638f7a80616535a78624
60505 F20110115_AABOJS gallas_q_Page_075.jpg
83f98e92af3246e07e5c2f34166f2286
a1a72f1817594a6310ad22853b56df45bcb52c24
18782 F20110115_AABRSL gallas_q_Page_206.QC.jpg
aa48a0564d50d02c86f1292ca8468d14
5655ff9497eb1a502f5f81aef0343bcab55e4462
1710 F20110115_AABQVR gallas_q_Page_079.txt
7abe374eeaaa890ea54bb231d5008250
828ab141c9b8bacd8470aef5088e58fd75d21600
26592 F20110115_AABQIG gallas_q_Page_031.pro
02b3b7b819fdeab255a8f162e5f9cd6f
1bbd66addb39350ed42b9fff40b0731730c298c3
68260 F20110115_AABPGM gallas_q_Page_302.jpg
60d1362a19dfeddb26a705bf2047df3b
0ee5ad887ee1c5363e5c9c3eb2839a800031cf7a
63108 F20110115_AABPTX gallas_q_Page_344.jp2
745b3a5974275f96f3208050f58d80f5
c0b12bb749c95a857492c4853ceefa0a59203a88
1051982 F20110115_AABOJT gallas_q_Page_371.jp2
580f8bf2d3cdd99bb2d1d6d37e7724e2
c7c135707cef6248cc668b1fad3dfca4ab3fc788
5116 F20110115_AABRFA gallas_q_Page_370.txt
8ac1374e0e80f2c8f7239d5b8bb31b0d
14eb7d0d14320092f6be2261498290a05e3f6e2d
2178 F20110115_AABQVS gallas_q_Page_080.txt
6d131365c204d4138884a26d42bfe9db
97d87cd98a8aed984da6b888d4c365c5c462878c
40784 F20110115_AABQIH gallas_q_Page_032.pro
0078f9e37099e826a954788630e1f0bb
b2f17c0451460466916d0618499dea36bc47f32e
69733 F20110115_AABPGN gallas_q_Page_303.jpg
188b519054f652f70dd9ebd49de73fda
79e451cce4a196b73880ed7413cf568edf6ea9d8
57511 F20110115_AABPTY gallas_q_Page_345.jp2
cfdb46cefdcf168d709f90e184caad0a
589da4789fcb4d7942cba3a948b15a08ec9aff95
4779 F20110115_AABOJU gallas_q_Page_022thm.jpg
7cd9228ae0fe658635b3e556b57cb091
a2add0f3ad334f9044d51da470584e95dcf35bbb
5522 F20110115_AABRSM gallas_q_Page_206thm.jpg
be73280fb9c81eb08c687dca6c2f04c1
c0b57116be194004500a822d2b74e95a0af8489b
4664 F20110115_AABRFB gallas_q_Page_371.txt
72c66f9fd4b893bee156137c68c02383
9bbc37230959355662d2578a4ca1ff44c56fb037
1707 F20110115_AABQVT gallas_q_Page_081.txt
10a2fe0e7c0c2f281dcb869641afb439
b9ad86696a8bd38604a35a80d869007ce1cee14d
49543 F20110115_AABQII gallas_q_Page_033.pro
a6041d5cc53eb6f068cfb3d5ec88d10b
f3cd130c167693efc6ec11f3e92a76a480dbf090
69410 F20110115_AABPGO gallas_q_Page_305.jpg
f641346aff4dbf2d217a85869996c780
90644d95c563bc144b18f858903543104549751b
66795 F20110115_AABPTZ gallas_q_Page_346.jp2
b94ed7b8dec852ce194af339643d5685
f98f0bf69a1c44f5579afa9a08fff3d7e71b65f7
F20110115_AABOJV gallas_q_Page_194.tif
0986b2e41a2f9befe2d788e9c51d0759
7d168b7f31c33c79886567581932f2d52b5e179c
5825 F20110115_AABRSN gallas_q_Page_207thm.jpg
384ccaabbd7645f2f4cb9362969fe612
3e123f861cd2e00084fbb691f77c5b078366d147
4693 F20110115_AABRFC gallas_q_Page_372.txt
32580160df41647a2c67488f020be25f
456ca8903c7cadac41cf2855f6197ad3c71505d4
1615 F20110115_AABQVU gallas_q_Page_082.txt
839d30558941f8fc699f14ff8f468b2f
9dbd907fd75990d8edceb2050b47a1a1b3b2112f
46999 F20110115_AABQIJ gallas_q_Page_035.pro
ca04eee2d9c524ccad305bf704634115
86741e8b6d6ab9c875eb7ef2c6815baa6c34c905
68688 F20110115_AABPGP gallas_q_Page_306.jpg
e89ffe7f2e911d920fdfe4a50059c46d
1cca40735f45d1a6ed668aebf783193c8f473da4
F20110115_AABOJW gallas_q_Page_125.tif
b2b8aa22238ac7346db85b378afb9ac9
7a061d61f7ac5082af586f78f05804a060a4fba5
14884 F20110115_AABRSO gallas_q_Page_208.QC.jpg
d9fd2b554ad90728eb55c80a3e749eb3
4ded0673025c08d73095e146efd665b4d8dfa8a5
4460 F20110115_AABRFD gallas_q_Page_373.txt
ad7d9e2d38d2bd9d313d35d9d783251c
d6f4bd0c6c3068d45a28f03d41e7408776850fee
1758 F20110115_AABQVV gallas_q_Page_083.txt
2981b7aef29c55838296226263d000da
783f7650292d6d8210b516cb70a2bc33ec19eb88
47274 F20110115_AABQIK gallas_q_Page_036.pro
dbf27cb42877c1c299bc9d1c36d20276
a49caff8e6233b5a253fc9db96890d93ca3e76d4
54954 F20110115_AABPGQ gallas_q_Page_308.jpg
336027c52b42fddae4f06f6b01f7b949
f9fada86c0554411e741cbf9da1b1c25819c1d87
90777 F20110115_AABOJX gallas_q_Page_248.jp2
f7b8110a2a1badae0f3c1e1d2d9d69f4
c2d1a09d559b76e2c0f403e02ed8c2ffb67c5fc9
19482 F20110115_AABRSP gallas_q_Page_209.QC.jpg
08e7bac5da6947bac4ae46a5937bc1e6
720e0b7012d42ec50122eecae2b63072af8978c4
2272 F20110115_AABRFE gallas_q_Page_374.txt
85a660a04e24e15f41804deb453fd705
36d27712a599e88740f6b943264a9208c90e7bc8
2385 F20110115_AABQVW gallas_q_Page_084.txt
2d5f64d01d20bbc9a275c824055d1d34
c9b7ac60b4c939c97b89fff3c0103b3fbaa2949d
46271 F20110115_AABQIL gallas_q_Page_037.pro
76c075bd99362e35eaf66e29f9df7ccf
16bc5191c7a5d30e3832030f3cd20c579af62e22
50305 F20110115_AABPGR gallas_q_Page_309.jpg
9f88b8de2c220a2fef5c0da99a14d2dc
e3521820b86a12ae43998142506a32cbc5d3495c
21828 F20110115_AABOJY gallas_q_Page_077.QC.jpg
5150ecc6e9e00c1719a94b488e27493a
6070ba81feaf6daad8f6f9cc82304d842f0d34c8
5888 F20110115_AABRSQ gallas_q_Page_209thm.jpg
1e7b10bd8be97ee81dd1e4202b322b9c
d19464175a9d75a19b63d726eb2cb9b862bde9e2
2006 F20110115_AABRFF gallas_q_Page_375.txt
2e7b41c6e4630e2efaed9b7eba4384cd
3cc2e06665753695033288c1482439ae942051a7
1739 F20110115_AABQVX gallas_q_Page_087.txt
b54943d50d2e97ab6f18d3538c00463f
73e1b248195cedcde061f980ea24ff1abbd6acb1
51851 F20110115_AABQIM gallas_q_Page_038.pro
294aad0c15ca60685578aa888bf19e81
b54d6c48e0f0482b0e383bea621459b3388ccfc7
53732 F20110115_AABPGS gallas_q_Page_310.jpg
5a70e3136aa7babae5dd2f5b0fa0a140
97f6c8467f0be82179ee204c62ed3bf2d1d33e34
4027 F20110115_AABOJZ gallas_q_Page_331thm.jpg
13fe82a3e79fb72424d5c1e2c0b2caf8
bc2dddc12edfd5101b38e3a260d82a65024ed9b2
21398 F20110115_AABRSR gallas_q_Page_210.QC.jpg
63516f81ea5e0a3905753e97204222aa
3352307a7e6d3e8450ca8cddec986065dc55412f
2392 F20110115_AABRFG gallas_q_Page_376.txt
2af7d5fd7fba9718aa4fd5154c955d58
bc3b7fe41223551deaa1e1d83a405462a9c99d42
1813 F20110115_AABQVY gallas_q_Page_089.txt
83e67ef3cccceffa21f681d3956a2911
0d3b6249983a9a2bdcecfb47640575b5e7209f76
49072 F20110115_AABQIN gallas_q_Page_039.pro
6165630a4e0647c26c1ec33bfc2b85a0
4e5a5f7c65a4637e8dc35a384414a47658e9a06e
54949 F20110115_AABPGT gallas_q_Page_311.jpg
cbb0f3c9f215b7e6de4a050940186cae
d15d5bfa72274ca665b1d8c34fb14ced42afcd6a
4583 F20110115_AABSCA gallas_q_Page_352thm.jpg
35e012f0d39165bc71fca66ae861f5c3
c69d7e99fa199d5069852ebe046e40cfe965c093
6264 F20110115_AABRSS gallas_q_Page_210thm.jpg
4f4fff3b497641ac279a92b3b318760f
4fcdfab2a254fbf2674cbd725e0df7fa990b0e1d
2283 F20110115_AABRFH gallas_q_Page_377.txt
6fced2645bce50d517b4a6bd84d916ed
ff90ed86a39a5d5ef1019e65f9ad270132fa0e40
1989 F20110115_AABQVZ gallas_q_Page_090.txt
91f2f1fcb086b78df26ae78ccc41a0be
6e3e29be731dafe8ff6658dfcda67fd8ede90726
47477 F20110115_AABQIO gallas_q_Page_040.pro
983d16a566cd0382b5e0e512be0f8b32
d3cf32a960f630b9c72ed6d983a4d7d77e9966d2
63169 F20110115_AABPGU gallas_q_Page_312.jpg
803b180801f4d30fe5123d674dc1f50d
5fb49625cb8974c200bd80f3dff66e2fe45e56ae
19240 F20110115_AABSCB gallas_q_Page_353.QC.jpg
7e2fd6e3a24597c6ffc44be3a40d9c88
79aa89c72d7685bb0a53db1038ef51dce79f5c19
19954 F20110115_AABRST gallas_q_Page_211.QC.jpg
2298c468bc69253ddf46dcb1211afe0b
78b7f94f8252934e316d1a0847c026069694915a
2438 F20110115_AABRFI gallas_q_Page_378.txt
28fadc17c3c12d05dfb695b1b61089f7
423b2f6638a610df0554594eb3ffa01bee3d7875
51398 F20110115_AABQIP gallas_q_Page_041.pro
1df3124e298d886f9902709b71028ad6
f11c8d18a4b3eec644cca487c2a0a65c03d42efb
52945 F20110115_AABPGV gallas_q_Page_313.jpg
55762f10eabf1f163a8f9ef809e25e08
c68c63f8be4a10d733b90ddc12d3fc8478673ba0
5919 F20110115_AABSCC gallas_q_Page_353thm.jpg
681c7b70d09e189c2a5137c2f94befcd
d4fc72c80094621af51e02eda655bbb95b578fa2
5680 F20110115_AABRSU gallas_q_Page_211thm.jpg
650c49e5409fa037c2df8c111389f917
58dd050c62c1a0b610cdef35690264d63e7485c8
F20110115_AABRFJ gallas_q_Page_379.txt
d88400bdde1299cfd9ed0298be5b9beb
8f04672272d9bb748e1bfdd050a8ebc56a86e84c
50680 F20110115_AABQIQ gallas_q_Page_042.pro
b3bdae076822d2b8f5dd5b9f71bd59a1
1a46c0e42d972d61685f08a3fc33f843538eb6b2
29989 F20110115_AABPGW gallas_q_Page_315.jpg
b18b60421afcde3db12f59dc9ea67020
c3e3319c8595c9c525c1468b80f71cb5f265aa1b
24798 F20110115_AABSCD gallas_q_Page_354.QC.jpg
9dc8210a2ff9d273d76ff087a12f73ca
6ad98d3632b42467e4458250a502be5a574a033b
21852 F20110115_AABRSV gallas_q_Page_212.QC.jpg
035bc06de856501f7c9917e0d0fa82c4
354366a971493947107933af9525ac94358dfe59
2254 F20110115_AABRFK gallas_q_Page_380.txt
3bd17e51b615e19198f8992244808058
c3c73e0c49580d1bc9754d1ae76251a84e4bc501
49689 F20110115_AABQIR gallas_q_Page_044.pro
d567ac8626c69f71ce196382104194bd
6e39109f1a8cf19ff5bf8fe4b9e7a03034ab9835
38521 F20110115_AABPGX gallas_q_Page_318.jpg
e77059de986ae9d3394df2d7e1076149
cca460bdfca7e139ef21034f6cf010ac3219ace5
F20110115_AABPZA gallas_q_Page_122.tif
5489dfb25dcfa888942a205a84d44d80
246c3a2420a0cec26b897679f4d1c3f3376cc926
6850 F20110115_AABSCE gallas_q_Page_354thm.jpg
ff1180d320c5287a7bc72312cac3908e
1115b9ad9574d5a239b069c08d0da4a235dd5fce
20519 F20110115_AABRSW gallas_q_Page_213.QC.jpg
9a5cd81a5b2627fdc2c2bf11b3ae076f
5446eeea1f88a907e99203c32e77a35bc4a1b98d
2445 F20110115_AABRFL gallas_q_Page_381.txt
0e29d9086d39937dfd4a2138d60aaa06
ed15a50211fa619c5505e359aab67890da666cb5
51777 F20110115_AABQIS gallas_q_Page_045.pro
bb38b09e6e6afaa51e5968207bcf84c8
b573d33a17b5f51c3a2510f1eb376003a814f017
65537 F20110115_AABPGY gallas_q_Page_319.jpg
7b30d4b4c19601c042ddbd3328010ebc
66aaa513c6c2421521282f4681de9cfd82fdcd66
F20110115_AABPZB gallas_q_Page_123.tif
110f216d69451cb27711f7124c88ae2c
77edfa3a45e303e0f001ced1caa81035aa698557
19764 F20110115_AABSCF gallas_q_Page_355.QC.jpg
c5bd3c7d1a72245959550232df814c74
6fa7873465f398c17accb189eb6ea87f19c2dcf2
6009 F20110115_AABRSX gallas_q_Page_213thm.jpg
9d0dd423e53ae570ce2b2c6e489ddb1d
dcfcf06159409876021adce7c2a4650d9a6e8d38
2389 F20110115_AABRFM gallas_q_Page_382.txt
5b32acbf532ebd50f54ad58db247d9c4
4405428d6401d1f03ec365006ca2b369831dfa4b
50936 F20110115_AABQIT gallas_q_Page_046.pro
6ef055f6e672ff36a7b33f24eac28439
bf7d457ba175823437c63b20ea0d6089eebba597
45006 F20110115_AABPGZ gallas_q_Page_320.jpg
90c5c654b925c90dcbc2077a413f735b
693cb9da38352a449668fd82a1e973f8de97949a
F20110115_AABPZC gallas_q_Page_124.tif
46b8c54b254671b933b40d545246a44d
90146ec5bfea7196b8f594c644936ce5d22c8d28
6511 F20110115_AABSCG gallas_q_Page_355thm.jpg
1a9eaddb6a9de80516d25a49d8b5751d
dd23bbacfdedd403883c1116f6659aeed3e59037
7196 F20110115_AABRSY gallas_q_Page_214thm.jpg
f1d4e10d5b982b23032b0c4d75061bce
445182da4cc52ae56ecaf69d7b782d3a44686453
2281 F20110115_AABRFN gallas_q_Page_383.txt
5f00bef20c65ac38bd2e4173e856d37a
5459ced3a49f552a60a325aca0e3daccff3fb6dd
49315 F20110115_AABQIU gallas_q_Page_047.pro
8701f13586491d16bed1d7d7b5815543
0d8c152a62cb5e374ec96c182d81f285c84200b5
F20110115_AABPZD gallas_q_Page_127.tif
cb66ae62030f623738d6a60937179406
846634385127b5584574d0b34f7a16b149fea315
18698 F20110115_AABSCH gallas_q_Page_356.QC.jpg
781e7a31789b676ac501d39964652f36
25f4efbc1945f38a812614f0135298859889cdb8
22753 F20110115_AABRSZ gallas_q_Page_215.QC.jpg
c5c462df9fb18da3e4c13400987dca44
47fb91637a0a353d8f17c6ed74594602d9354b0d
2282 F20110115_AABRFO gallas_q_Page_384.txt
b17d748a2faff6d18f24bb5dc7f80b22
4910bc371c8da807834d5037bf1a6ae252f9b223
53432 F20110115_AABQIV gallas_q_Page_048.pro
5be0ef5f1785bc769415d3e8253c410c
0cf3d1e076fc8152ef43aaec253f329e3a193448
F20110115_AABPZE gallas_q_Page_128.tif
7b7d2e12a1bbd208c1dc55c828d6edf0
c72cb2b80dd56b82967f3af9653ae39db5583543
33300 F20110115_AABOPA gallas_q_Page_348.pro
ace57dea9fcb3712397a659689d2159c
f3a301633402fa62455f634410407e3c113b69cf
6101 F20110115_AABSCI gallas_q_Page_356thm.jpg
9b14fc9f6b339fbc51e7ff519c2b8eb9
66ec229b8c2f8b360efa5b465fa917299903acce
1125 F20110115_AABRFP gallas_q_Page_385.txt
383000a8330c6984cc6516c1f9a3c1cb
ccd3bfe2bafa78d1a845afe151b3c72a65a163da
F20110115_AABPZF gallas_q_Page_129.tif
3333d29bca74e9c390cea6730ca067ba
fbcafea2c54a996f493c7ab1323ed9cf728bdde3
53992 F20110115_AABOPB gallas_q_Page_121.jpg
ec85ffa78873506212e8961336a4db66
52ff035b469e4633dce8f0f1fef02841ce838779
51332 F20110115_AABQIW gallas_q_Page_049.pro
6a7771f7586aef2f9b5a5606abc7e569
d2ee4fc8c08536d2be9a8f5834a8f9a720f09d8e
3431 F20110115_AABSCJ gallas_q_Page_357thm.jpg
d737e8be99697907e6f8238de9e5b7f1
24d06d6ec19cb5ff7dd9d4f96b218ea5f8ff70ed
1101 F20110115_AABRFQ gallas_q_Page_386.txt
d381468956468b90c8670f1eecd35427
ab5a2b6a5145c9b9d530b221294a513e7fb5aba3
F20110115_AABPZG gallas_q_Page_130.tif
5129a948496d4b2905895c34a76080f7
e5034c9f3b9145e81963217d887ba88ea9ef68d2
4330 F20110115_AABOPC gallas_q_Page_336thm.jpg
42aa88b926ae22fa1480c3ac2ee62fd9
881a21c6b5186911a9a1d929d580ee0a428603ed
49066 F20110115_AABQIX gallas_q_Page_050.pro
611b546212d35458ad57032403e551f7
b910b51e5442de7754334363a7ff90434146b8b4
16635 F20110115_AABSCK gallas_q_Page_358.QC.jpg
07de0c03ae7470ee855bd56b21e9f434
f954979249cf5691e6096f9d545082cc86bc0ac4
6875 F20110115_AABRFR gallas_q_Page_001.QC.jpg
c2ac032d73d24ad53199fb9e821afa91
4f935a09848c8c20ea2b0f130277803770bd978e
F20110115_AABPZH gallas_q_Page_131.tif
b112ebe9be171c296d087e7c35b8238d
df1355b3eb435aa169e1eeb11fe8096745c7382f
4882 F20110115_AABOPD gallas_q_Page_273thm.jpg
a8eec329436133377f538c11ca647f88
af5d03e00070e10b66aae6ac19dd66fc28827ca1
47332 F20110115_AABQIY gallas_q_Page_052.pro
d24011ef35323ff8aed3ee62a3b84fd4
9ad17e4277300e4c6098463e3d3715b0b761e99d
4784 F20110115_AABSCL gallas_q_Page_358thm.jpg
2a99671a9aa990ab2dd20dd2bcc15d13
908f5271bdc58532aec514124234146e510b16d7
2300 F20110115_AABRFS gallas_q_Page_001thm.jpg
78d0deae850e3e1704c8c865547d423e
bf8509d2b48620845bc51677750fcd9364576e79
F20110115_AABPZI gallas_q_Page_132.tif
778874e45b11075ef9854ea0de860a11
5c94b1c535329a4284c9cdeaa6ff88a3fadc95b8
9143 F20110115_AABOPE gallas_q_Page_003.jp2
1062e573ffe6367759456bdc68e46888
7d14e5284a3d55f2f8ab8b1f15a7cf46e8d7d53c
47621 F20110115_AABQIZ gallas_q_Page_053.pro
e3d32e283acf2bf3239b5d0dbc13407f
0a89326ed1d31baa1b9804bc18ee78ad038b9da9
29987 F20110115_AABSCM gallas_q_Page_359.QC.jpg
9ffea759aa8fec0f5dfe8a6fbf8ffff3
25f0302b773b635086e3bb3eb93f51a6497c9132
3276 F20110115_AABRFT gallas_q_Page_002.QC.jpg
f6d9163ce2cc5fbbddb584bbeb9ad8da
352f811a34c0bc2a82fc0aa63a0057dffa529c77
F20110115_AABPZJ gallas_q_Page_133.tif
85ecd9ee49e50c8f7df7c153dd366648
0c89152fa538bed5bfeb5dcdea0232ca9ef88da5
974 F20110115_AABOPF gallas_q_Page_020.txt
0ffb2660af32381bb71631dac39a4d5a
0acab969432780c3bc2175bec222175273988bef
7748 F20110115_AABSCN gallas_q_Page_359thm.jpg
0032e4ad2f650b724d63c214862168e1
7fb68538004ad99e16fae7e376ebafc4452837e9
1364 F20110115_AABRFU gallas_q_Page_002thm.jpg
8f3e7fbfcf5157d017b0fd9cd4b1a92e
402700069550c2b048e2262a0f9599fbbffd87e0
F20110115_AABPZK gallas_q_Page_134.tif
abcaf0c3f663341be7a261bd33b852d9
649fbb2b4ac0a0a8172e507a29864b4277c39a18
48765 F20110115_AABOPG gallas_q_Page_268.pro
17372fa085462059706d18f5e9200b89
d363585073d4e6bc439d3a1ee1759b69a8adb2fb
29197 F20110115_AABSCO gallas_q_Page_360.QC.jpg
6f0b3214c9a99af179fd082317f6f36a
62721753e9814def55dd46b6f2501eae01300bca
1567 F20110115_AABRFV gallas_q_Page_003thm.jpg
d5a8b106deee1916cb1bbdb0d47b8c50
70c63bcf0f5d7dacf1d88d65dff7733a9a9d176d
F20110115_AABPZL gallas_q_Page_135.tif
89258bc7225c2034a24a1e08b18559c0
562de71146ff27c9f691e1197a4414b979d3c670
82454 F20110115_AABOPH gallas_q_Page_373.pro
e6510d8dc2477271916592fc5656660b
ea03bceb032895387201d65b4c7f5da6e07c9ce6
1051970 F20110115_AABPMA gallas_q_Page_096.jp2
456dc4274228844949b76079b15dd620
c6426fb82bd27ab4c41c53f880c5898c257bbee8
7251 F20110115_AABSCP gallas_q_Page_360thm.jpg
31f6c3a1a34602feffb4af730259589c
ab12813a96e66cf0a9198c31b05d98234f39251e
16926 F20110115_AABRFW gallas_q_Page_004.QC.jpg
cd9aa8cc8687361b06d2bcf07ea9a8dc
5e06d2ffac115a90f7f258365a59e4f268001ec2
F20110115_AABPZM gallas_q_Page_136.tif
dc3b2987daee5c0b64eed93eb75f76b0
c64a92ef4dee57dec5a9d5978f13e2274d36cbfa
1051979 F20110115_AABOPI gallas_q_Page_085.jp2
be311412ad5be1005c4f602492b4979d
76437b379f4ad7b4aa1cd8ec663c12cbb639e2a1
1051966 F20110115_AABPMB gallas_q_Page_098.jp2
ee3ea5eb248bba6122ebd1fbfb6d4b74
0a3e09bf9905b90f75d68e3d33590e09fbc1697a
28355 F20110115_AABSCQ gallas_q_Page_361.QC.jpg
79758dec872ae13efb955942e2d52679
36a496e9240a6c63f00b5bde7822c6ee6096e50c
22657 F20110115_AABRYA gallas_q_Page_292.QC.jpg
569bf1c42384a1b4a94e5a40b48924fa
3f87cb8480e75d258bb14f28a859a80570100272
4937 F20110115_AABRFX gallas_q_Page_004thm.jpg
b0f55333cff675f381081281ad3c7dd0
bfedaaf007db5aa5a04f31d601dd6c26f97afb3d
F20110115_AABPZN gallas_q_Page_138.tif
245fb117c2741ddfcb521ab844ba35b3
a5719cb59b69f5dad7cf7fcbe64595f8f1b83a24
F20110115_AABOPJ gallas_q_Page_139.tif
e62b6224fae3ca70bb540b42e95feaba
d68950c8f5610047143281a16904ff9eb56bfc3e
90067 F20110115_AABPMC gallas_q_Page_099.jp2
976f15492d5c63e721d257f0e4dfb958
e2919c4e8eefa92597b90e46af0bad95c7efcf55
7058 F20110115_AABSCR gallas_q_Page_361thm.jpg
dc5e37c80e922322563754ce1a979a47
1e8d2f578e1a0fc36ef50a1dd3e05537e85c5293
6459 F20110115_AABRYB gallas_q_Page_292thm.jpg
7791c03d9a81cd1b39f4ac66831e041e
0dbbc99ed9c388f33cf2fa2b463b05b835a52084
4799 F20110115_AABRFY gallas_q_Page_005thm.jpg
afdffbdf17702725618548b8d4dc05ee
7f633d42b4a1db90ba8b6b60fe27d9cb2aee9851
F20110115_AABPZO gallas_q_Page_142.tif
03e63666ddd1744e2ed6e2a7a8ed0a62
f40b31901d38645a872af88c043fbf9877b442ac
6414 F20110115_AABOPK gallas_q_Page_007thm.jpg
a75328071bdf6aa0bcd370d6236f5fc1
8413cab004f317140cb1ac043044610137d2fae5
711136 F20110115_AABPMD gallas_q_Page_100.jp2
3f4da675bcfbd271079fbb449fa83cbf
4c1e0f2a30a5623cf40452e8e66ea33c7a9c05fb
28837 F20110115_AABSCS gallas_q_Page_362.QC.jpg
3b129136efdc3ce86b4036f4d7240c89
65f0abdcb5b8c4d77f908ffb321c9a8b7a76fab5
24929 F20110115_AABRYC gallas_q_Page_293.QC.jpg
fdbc38992aad043173efd5d9b99b57c3
1d2af79a7b9e2141bb53460bdb766fb4c633dc38
22561 F20110115_AABRFZ gallas_q_Page_006.QC.jpg
b37fa5617eb2201bba816cf918a18693
e0ef63511380c4df3e72c5e7402e557cf75a8241
F20110115_AABPZP gallas_q_Page_143.tif
2587e605732ffbe47b0a8730e3eb661c
1579e1827322df493bbb2646635f0b8b2711dcf6
56680 F20110115_AABOPL gallas_q_Page_383.pro
41a03f91867e5d2f2082a2441cefc36b
623e683e090ff6e7f58c700aa75b915d3b26b096
110510 F20110115_AABPME gallas_q_Page_101.jp2
09ced7e17e246edb125155c75d11ece9
7f841032b98a172817d889d71e2445d723451d13
7232 F20110115_AABSCT gallas_q_Page_362thm.jpg
1ab1151125523d34a061a8b050a2203b
794ca84f2a89fbde0c17965f8f62f50e508b8aea
6369 F20110115_AABRYD gallas_q_Page_293thm.jpg
77bddb2edd059af548da6c493af5b95f
c39712647b5ebec54f9f5859c80541e091454612
F20110115_AABPZQ gallas_q_Page_145.tif
0d7d29eb2581e693283977ca0663974d
30cc72fbd111a436c0d047b1ef455d01ea7f5943
81002 F20110115_AABPMF gallas_q_Page_102.jp2
85b6fad9c720f8a5d42d2674d227c638
3d30a7114de253546d24094fb283450fa6323072
29553 F20110115_AABSCU gallas_q_Page_363.QC.jpg
9a28f214e2831abeb5fbd72e842683e1
38ff02ee55b4bd8b4c422c08f8ddbf65dc07f781
20562 F20110115_AABRYE gallas_q_Page_294.QC.jpg
bd1503a3b71315d701905f4a5a27bea3
c6a0df6e9e676bb376001023e1fc48b9dd2940f5
F20110115_AABPZR gallas_q_Page_150.tif
6bcb8f6f1e1925ad79a6b1415aaf00e9
6812137cefc9fbe4795c68316f1866114cd95878
109833 F20110115_AABOPM gallas_q_Page_046.jp2
7d156fc65efa2e506f5bf50fdffcc182
48312266d79e804340c4a94e50ba10b4402644f4
38327 F20110115_AABQOA gallas_q_Page_207.pro
2126c000e5837d151c6a9c38bf29911a
6e735b9435a91d379ce7f7157f18758b026d13c5
896631 F20110115_AABPMG gallas_q_Page_103.jp2
4e890fed71ba7e740d2889f63a2ae2b7
c8593c50fa423bfbeda8d48531623b0a4dc9f9a5
7474 F20110115_AABSCV gallas_q_Page_363thm.jpg
8c22d0fc1ab1dbd890f8d744d68eb0a5
771c61e01b5df5d32944e964272080a28731210d
6260 F20110115_AABRYF gallas_q_Page_294thm.jpg
ec366badf27c91ec25a1bb7d8413a7a1
9b95a30a5c1c1cccdf34421f0d153fba5c2b4d17
F20110115_AABPZS gallas_q_Page_151.tif
b409c377de2c9fd885a6d84b101dfcf5
b759e31cfadcd0703432baa28f2eccf47ee1a060
F20110115_AABOPN gallas_q_Page_039.tif
8410e1b6cc20bbc3f63b073cae15489f
c8e35bf2aa9a93b61fdc5f3c190571ed901a04b9
15139 F20110115_AABQOB gallas_q_Page_208.pro
7ec8033660ed85ec1449528f538b0e3f
45d490c8913fb39b3d20b865fe1bb00e234ce003
851005 F20110115_AABPMH gallas_q_Page_104.jp2
2eeef23b741b9f7b293a68f867584c10
7179fcff296c7f70aaad4de78b0d6ad97f2d8cd6
30338 F20110115_AABSCW gallas_q_Page_364.QC.jpg
c4e7d61b4ab3af88764e0a2f71d34367
abddbfe326565d84b823d4f4173bb0cbec3992a1
16766 F20110115_AABRYG gallas_q_Page_295.QC.jpg
2644ea86d24a734017135c7cbfe71ff0
9f46da0f9285be11d10ba1156c780bcfe4958b7f
F20110115_AABPZT gallas_q_Page_152.tif
ce621e3c0d2a5664cc10b035b3855062
dfd6c064c37348e424edb8d46790278a22fd87e6
39522 F20110115_AABOPO gallas_q_Page_102.pro
619f74a2d5965a28364b28115b5ae300
2c2b5dc527315487ac1ace11b1a68013a5933072
40276 F20110115_AABQOC gallas_q_Page_209.pro
f65ee81742361ac7c1441e236c22503e
d504c87e866f8581d7bd7c5b7de961c6788e7932
7496 F20110115_AABSCX gallas_q_Page_364thm.jpg
66f1ddff5078a947b114426d8cb673e7
ae36a8cf58a6e377883b4f3cc75a49a080fdcb15
5369 F20110115_AABRYH gallas_q_Page_295thm.jpg
ae584d7f23bb3e3f1c06bfcc69791f78
3e9f773f86e77690178048a39d8e408e38232c81
F20110115_AABPZU gallas_q_Page_153.tif
c114f6282c479d40899f20f1c2d0da67
78950313a8e5fa39de990256f62a5f2087cc164a
42586 F20110115_AABOPP gallas_q_Page_075.pro
bd618925536ea199d72ecc0b0b7757cb
a6b3c805467d119203f013bac93056e173ea8a19
49838 F20110115_AABQOD gallas_q_Page_210.pro
ed8c94c4d864989274e220eda2c18920
626b5f5ad8340e4bae1fa1425cb820320a84aa2b
105291 F20110115_AABPMI gallas_q_Page_105.jp2
94f1ecd41f887fdba13f7c87be1c96de
d05d967e872e1d0aea556a9f854b29992c6502b3
29284 F20110115_AABSCY gallas_q_Page_365.QC.jpg
b0ff0301c19d946232e2f5dedb6d15ff
93c9e493b6a54fe7ab39fb8e083abe690b0c9952
25409 F20110115_AABRYI gallas_q_Page_296.QC.jpg
0500fdee8bee2152422c4343ac82eaa9
b08e641e951f72deeec77471dc27871d7b070514
38389 F20110115_AABOPQ gallas_q_Page_330.jpg
3589577657838de2f44c351f8e76fe9e
9dff44633f10cc6914ef10fccd8195cec0e31eb1
42465 F20110115_AABQOE gallas_q_Page_212.pro
bc20eb4cc4a08d0749a61a028118279e
af381fa6ec9d541a102f4d479f243bb3bfbf96b1
1031041 F20110115_AABPMJ gallas_q_Page_106.jp2
ac1d86728ce7337521e5b5384106e825
42bbba7fdb800741db5f60280f4dcaa2c967ac50
7191 F20110115_AABSCZ gallas_q_Page_365thm.jpg
e8a1e26cae9f1c689753870136736d3a
ba853085c8de48e7a4ef27fd5ada38a421b283df
23499 F20110115_AABRYJ gallas_q_Page_297.QC.jpg
8be4acb866aa3a5880674679b69bf9fe
84c31f44def39e0e3cbb08dfaa570dd70bf3da69
F20110115_AABPZV gallas_q_Page_154.tif
f9a7d211873c88f612cfad4c0a5a6308
00930e44981baa3fa37ad68c016d4ccb88e5f5a0
F20110115_AABOPR gallas_q_Page_114.tif
8624820dc8d8fd6048e8ace61241aa97
74262dabc4ace2888c00c15916eabb29cb8353da
42493 F20110115_AABQOF gallas_q_Page_213.pro
9f369e9ad3f2103941c8e96d89b1879c
a29c0bcf35274ffb70aae06735d2c7fa391c5e15
866991 F20110115_AABPMK gallas_q_Page_107.jp2
ff8ef1305e60da1c516ef4b0a724727f
2ef586d294f4ac8ff70dcddf39c6f1be8c819356
6620 F20110115_AABRYK gallas_q_Page_297thm.jpg
7890f12185f5e2d841bb382ed4e7424f
c03db1d48f12fa26405c936a26712dba749fd8f8
F20110115_AABPZW gallas_q_Page_155.tif
3aed2da58b1a29b4aa16351b23fcff40
d56d3be72319677aa99f34eec0cdfa292c059487
6825 F20110115_AABOPS gallas_q_Page_220thm.jpg
54ce741b0ed209f67d50ff284c47fc86
ba661eab39c22d172b1929c74d9743faa8ecaaea
53310 F20110115_AABQOG gallas_q_Page_214.pro
849c4b777187ad92259c20baee7a2969
07e0bc7239ac7c27e1101b3eb2b8f4d317106108
100390 F20110115_AABPML gallas_q_Page_109.jp2
c59854cf3b8288bd557ddb92e7590cc2
ec0a2c2eb8a3306807734300b02513fcac37f017
F20110115_AABRYL gallas_q_Page_298.QC.jpg
e2e2265d56f2b282ba69a7161355b3f2
bfeedd44cbdeb38117ef08e842fbc31292872f92
6501 F20110115_AABRLA gallas_q_Page_088thm.jpg
b73bb3cf6daf2a9b9a44b0fafdd597c9
ce0da027ba8368c06c93cd471e1477b399baabea
F20110115_AABPZX gallas_q_Page_156.tif
4df08516a2537ffc99b51d8997b69175
7596aae38f443a8b3e18f4a3487feba6a1fdd91d
F20110115_AABOPT gallas_q_Page_149.tif
783b85383cdcd1f32a731a03acf29932
fc9f66c22a1453bc4deab0598686f783fb4649a9
32478 F20110115_AABQOH gallas_q_Page_215.pro
35f1d61b2e1a0b0e93155a8ba9227b4a
0a74d50543d3c214e30ff85f5dd613ac26a70f75
108414 F20110115_AABPMM gallas_q_Page_112.jp2
65b756a719d9037da2c2e2beec31ace9
baf784bc4ce8566b2d065e599d45226b6db31d86
6137 F20110115_AABRYM gallas_q_Page_298thm.jpg
16aa3b3bd0daed076ab1d891126521cd
947ba904c3099464964b5368052b78245c55f4a6
22188 F20110115_AABRLB gallas_q_Page_089.QC.jpg
d02254af054340cebf30cfc3d07663db
77935c306d51882d51cd17c56bb17d4108d5e868
F20110115_AABPZY gallas_q_Page_157.tif
784f3a00615105834fc2194e7235811d
2539f3a7780467317301886c6258fe57a6d8a10f
79162 F20110115_AABOPU gallas_q_Page_016.pro
5424a64f8fd1130ca3589628373e40b8
25816a9d12ad8cd174e125604f71c6925fae9d08
43101 F20110115_AABQOI gallas_q_Page_217.pro
35a5ef1437e4e0f3a36caaeb562eb93c
fbe7984ea6d01b062427afae91ad62c029a31b8c
88345 F20110115_AABPMN gallas_q_Page_113.jp2
a2d2fe712faf6e912864203e754bf186
942ce75d257bb10ce4cfb640be69daec0dd18337
21495 F20110115_AABRYN gallas_q_Page_299.QC.jpg
4bd56638577785ab3f4457d322dfda44
35bc1bc8b3dd2fddfb6c58f72c9ba2535696ed44
6576 F20110115_AABRLC gallas_q_Page_089thm.jpg
e139281b639f14e13508cae0f5b6b579
1291c977fbc53e5bac466da517d4c111bb336cbc
F20110115_AABPZZ gallas_q_Page_158.tif
4afc71e9c990a2dadaf4ca7bd3f92c5d
7ccece04ef1e24d3942a7ace1e4ef5078e8a1882
4630 F20110115_AABOPV gallas_q_Page_143thm.jpg
f4f0f38a671debf5173a916ec3d287d5
f1cb2dee93b283a8c33e3e00eda050b4e24148bd
895999 F20110115_AABPMO gallas_q_Page_114.jp2
e7c09b02e8c482c3472e7db0f90d8dcd
18148d3013df1b73cff9c453888aa266ea2cffa8
6650 F20110115_AABRYO gallas_q_Page_299thm.jpg
41e569d8407e6d259793520ae95670d5
d9478e839719af62227f3502d4b0adcfc79e1fd5
23776 F20110115_AABRLD gallas_q_Page_090.QC.jpg
fc7f93bb517c8fffdacd857535da746f
f9a0f2e9272d9aa43013dbabb43f1990b0d93179
1550 F20110115_AABOPW gallas_q_Page_134.txt
752936743b919f44c9de97070ed225d2
2102be11613c8a9521d22d1108d53073dd562f27
39159 F20110115_AABQOJ gallas_q_Page_218.pro
1d704de0fbcdea954bf5451ceff0e4ba
268c0bcf0a51e41b880875b221b60fa5ccea9fd3
100324 F20110115_AABPMP gallas_q_Page_115.jp2
be0396b40d3cca63aacac794c7f375f2
6afa22cbcb2d42c3cbe1fa31dd1b86795558f1b2
5595 F20110115_AABRYP gallas_q_Page_300thm.jpg
c602a4fdd7ebe28b0bd683c59b386ca9
1854c83e6f455ad74da360933fa6d2776c991774
6826 F20110115_AABRLE gallas_q_Page_090thm.jpg
d7d860f6bf02d30726cb5dcf4f2a9337
172c331f0b4de95c3140c674ecd8849103a9ac28
1980 F20110115_AABOPX gallas_q_Page_091.txt
7108d806a283bbdb21c07aa9bb81fae9
04c85db92ee83605a911d0af1cb306a0b9159f04
33224 F20110115_AABQOK gallas_q_Page_219.pro
3822b79aef022473a8ad0fb78a9d16c2
214ed1b1ab99c01c476546f61cf36e8ad9c9701f
1043466 F20110115_AABPMQ gallas_q_Page_116.jp2
4eb8153bb67685eb98fb9aeb8609b17f
bcff82a536845609f2d26f75d5db0e7c1f3656da
22877 F20110115_AABRYQ gallas_q_Page_301.QC.jpg
2ad5613893cd27c49e632bc04a5644c6
eebb4b21668e7858d21f3f0e6b7450c893ad045f
F20110115_AABQBA gallas_q_Page_191.tif
0eef9d13930936df4147e1c2554400e2
afb7248e5a5c1e20c546228af7ff5ce785779018
51029 F20110115_AABOPY gallas_q_Page_295.jpg
793964e43c5af35ee71d1c0525806d04
a5e72e7b24a4a613433ca8333e3b72fe1bdd16e1
40483 F20110115_AABQOL gallas_q_Page_220.pro
eeba9b7af13e7a184a188059b6e87303
6f025ff088a896e8196462405f1529135a6c000c
89280 F20110115_AABPMR gallas_q_Page_117.jp2
a7db3e8e2c16825a0b95ea74cce11b1d
8ec04276fe80fb70ed0fd0084e323f0ddca5bdf5
6606 F20110115_AABRYR gallas_q_Page_301thm.jpg
b33f6815322d8d371309449d67ed8fc1
1e39b5cc023bf25e6888be44181bd3c42ba82c97
22209 F20110115_AABRLF gallas_q_Page_091.QC.jpg
127f0f6c26e0c1ecefead096dfc79564
ff39c789aefd7c8113a812faf0430bde792dba2a
F20110115_AABQBB gallas_q_Page_193.tif
746c1b5341c0032c1aefb0293453d577
2b77c882e888ddac2a22582ffcd4c64b7c2fb300
35941 F20110115_AABOPZ gallas_q_Page_154.pro
1e5bb8a7a601257faa30172a49ad5319
7fa75250ccd871db723a2905b0e10c895f12dbe2
47741 F20110115_AABQOM gallas_q_Page_221.pro
21c8f5bcac27acfbaac52cbabae7d359
406c8df801d1cefa1b4984724d11290c5e3f379f
1051916 F20110115_AABPMS gallas_q_Page_118.jp2
a1fcecca59fb9e0a2eeeec72cc282109
7ad54758a6434c43d1f51f37fe84304d2c5beb52
6540 F20110115_AABRLG gallas_q_Page_091thm.jpg
0c44f224d169ff26b23be77aef7da9bb
e333b57a60d75635464686c5ca8d4fe0cd2d8f10
F20110115_AABQBC gallas_q_Page_195.tif
6c6027a4f2e7b8dc9e2e10fca7fbd5dd
31600b9f36f372509ccc49dc749b0c287dcfd985
39443 F20110115_AABQON gallas_q_Page_222.pro
a399be1866f388bec5afebf424ca68c4
ee6820444ae7f547fe4e933b8b8e09e4ead4eb14
97384 F20110115_AABPMT gallas_q_Page_119.jp2
0b027c86d77ce76096bb84222aa19984
b073fb38339af3a66450e375d40ed32b0c950978
22803 F20110115_AABRYS gallas_q_Page_302.QC.jpg
1c96931f82154d6e3c65b22773d02631
7df151242aa15efa9cc3ecefd3e1c5803fb5ad63
23628 F20110115_AABRLH gallas_q_Page_092.QC.jpg
b0ec4081c2697e8b0653f682e062ee6e
010d883ae9c723f8aafff4c228ee2a6168518ada
F20110115_AABQBD gallas_q_Page_196.tif
60b5be762136159d3bed26bc34df9392
ab0eee20f96a8ebbf33f31ea8eae3e4c6d4044a2
32048 F20110115_AABQOO gallas_q_Page_224.pro
afec38b222192508656d047d713b08ba
5288b2156de8d8db349552d3b6aab6ce04f2b2e5
964583 F20110115_AABPMU gallas_q_Page_120.jp2
14e64e9d3980686015eca5eb314c1a04
c9eb667c6eace8a63d57dc12226ae4187fb4b608
6514 F20110115_AABRYT gallas_q_Page_302thm.jpg
d02ab4705b5a895a64d1b85f99d6e66c
d81eb1610734a8d143a7d77709749f6908572bbe
F20110115_AABRLI gallas_q_Page_092thm.jpg
4c100b4173246876a83445db870cddf6
0e65f97a69a6e8271d10103c616998b9ba56a68f
F20110115_AABQBE gallas_q_Page_197.tif
b3871520fe59b4695c5a42aefdc9a278
702e8e2745afbbed1acf8966adacb9a868f6f61e
35095 F20110115_AABQOP gallas_q_Page_225.pro
56f40e3b614b3422ae02223fb361bfb1
da45de4f7761176e143445671e0a458475066a14
926094 F20110115_AABPMV gallas_q_Page_122.jp2
8b9b7aeb69e57fecf9c9035ee8c08ce5
92b22330bef0f46c5353e4f7d88388008864212d
23615 F20110115_AABRYU gallas_q_Page_303.QC.jpg
87285f99a50c334edaec8b7eca41a000
ae5917764f22ff125ff70627e8483b570d0a5540
23588 F20110115_AABRLJ gallas_q_Page_093.QC.jpg
e4508d24862019d83cda25d93edde575
e42054aeaea191e3f20b0f5c365b5a632c9129bd
F20110115_AABQBF gallas_q_Page_198.tif
178ff4bc03e94bf68a7eb9509daacccd
bb12e5f80935a23c42f746e7c327e66d8a3a353d
33592 F20110115_AABQOQ gallas_q_Page_226.pro
876fe633b922b362596a224ba8b9c4d1
de77d9aa396bad0f75bad4bfbc46efdbb365cb6e
502690 F20110115_AABPMW gallas_q_Page_123.jp2
5871521c0d657b4ef217083509e603ab
4bedf638ece89a76852e38b14d7112d0cdd85cb4
6651 F20110115_AABRYV gallas_q_Page_303thm.jpg
31088703b88469aaa838bda57845154e
d0516bbb22fbb2bb124f8e78db2fe704e07ab064
6953 F20110115_AABRLK gallas_q_Page_093thm.jpg
6ef4758f761060fe1afd69281955cc4e
adad7e1bf626be7ff99a32cd90b78dea5a316c5b
F20110115_AABQBG gallas_q_Page_200.tif
c86fec46f15c9df4195aee64631b8576
3fa552ecaa6bd9c978a2e30b6dcc6ad3128dad62
5630 F20110115_AABQOR gallas_q_Page_228.pro
642e0c486702a51d1ad31c4fd40ef6d2
f67b4ef5f813ac3b2148dc01f148b3795730fc96
676455 F20110115_AABPMX gallas_q_Page_124.jp2
ed475a9c4497131b13441a17cdca41c8
d64b95190f39471d2a62c00dc16131ff594d1a85
24335 F20110115_AABRYW gallas_q_Page_304.QC.jpg
8b3750d6e8d2f7881d0fe621499ff6df
43f622ad4a760dba6f87988de7bddda875ed5a2f
24460 F20110115_AABRLL gallas_q_Page_094.QC.jpg
f3f310205ffabe6ba10549090e8da6c4
a6e603f99615fc500064ceb9339a81820a054923
F20110115_AABQBH gallas_q_Page_201.tif
fe44c962afa6c7e18ddae4ab14252974
bb66a4b087fe5678b119069475a6d160c108e54f
37195 F20110115_AABQOS gallas_q_Page_230.pro
db4253f1b937fbb0c255ccad948ed2bd
4fbd30d206369a8129eee5c4759a7a23341214cb
86428 F20110115_AABPMY gallas_q_Page_125.jp2
116de7001ee1aa9cdfef288fc2d3e25f
7e486827f02c0652919d08f9e0ee0989c2c5be01
21005 F20110115_AABRYX gallas_q_Page_305.QC.jpg
f2d5fc3109ab153d1ffa14b015a34c16
4eeeae6da75f5458ab1b750426512bd66e427161
22326 F20110115_AABRLM gallas_q_Page_095.QC.jpg
be09014241cdab8c341a5282b08191d4
4ae0492ad2be4dd33b77621f325067cf656f97cb
F20110115_AABQBI gallas_q_Page_202.tif
53d4f38c49594e109c5638d68a2f8e09
20bc1b807754d42a7950422501b393ffa50a03fa
17636 F20110115_AABQOT gallas_q_Page_231.pro
6a5150373a9742e9248638172c1886b3
e379bc1ed1488b7cabf1aac2085b97156bc5f05b
95972 F20110115_AABPMZ gallas_q_Page_126.jp2
662af0e41267a54262a03ffdd5059984
622df6ef256e050fc90342dcff2ace423fd7c409
6115 F20110115_AABRYY gallas_q_Page_305thm.jpg
ca742161354809a43ff7ac6818545f91
c222970ab98476d454c36a045f34d2552df1893d
6257 F20110115_AABRLN gallas_q_Page_095thm.jpg
c1711ac968c85efe7197086103a31457
91d329af4f1c7b2fc7036ca1b5e9c47cfdc0a74b
F20110115_AABQBJ gallas_q_Page_203.tif
c38baa3be7566d0c9fe6d158141e04f5
a13f4d4a81d5c60ea89d0c247089ad5ea123ffb1
23222 F20110115_AABQOU gallas_q_Page_232.pro
55927053d60477cd9c0305b944c583c3
94c3848cdbbc6e1108eaed646eb41a8a7a668801
23169 F20110115_AABRYZ gallas_q_Page_306.QC.jpg
b2ad577cd5dc0e13fc201c5bc87d6d0e
d0c45e45c3fa4140c7230b5548b2f134d37bb3e6
7361 F20110115_AABRLO gallas_q_Page_096thm.jpg
403115922990b0814f61824df95b425e
65a18b0388d5eb9a2fe0da170e78b02e8ef4aa15
F20110115_AABQBK gallas_q_Page_204.tif
fc5b54e190d2152c31108975cec9b4ee
9031c6b6f7eca4562fa4e12a7c4995e8d3f49cd3
2042 F20110115_AABOVA gallas_q_Page_038.txt
a68c1aca3011e1d432cfeeb95ee657bc
54dd0cf14cd2422b56415ca9344676fb17511c5e
46909 F20110115_AABQOV gallas_q_Page_234.pro
fa92196571efe984663c92fb3009d4ce
ff65b7012b77f46f0e16511f2c1aa010beac18ae
33058 F20110115_AABRLP gallas_q_Page_097.QC.jpg
7ccc1917ed1f69f17ec050fe46bc6dd3
0decaa31ed1ca7405a0914791fa131acb888c1b3
F20110115_AABQBL gallas_q_Page_205.tif
f85596df0932752a145bfb2c8fcfc351
c2689f8ed7ea68ff925c3c274954d6b9b948392e
1928 F20110115_AABOVB gallas_q_Page_194.txt
97a469e313652c7e0441ddcb1ceeb49a
8f7d5127451d4375fa4a56ab938f1eb30d593527
49731 F20110115_AABQOW gallas_q_Page_235.pro
cd86cca2b58617d09f75d483cf7372cf
86a84f65c1f349d1c4b45db674fafc2b42322b5c
7995 F20110115_AABRLQ gallas_q_Page_097thm.jpg
8cc39a6d15b0da5caed2073abd246ad8
f1484b872ae68a0a002ba151cba7f19d8ca31fc0
F20110115_AABQBM gallas_q_Page_206.tif
e318a5cf494c850c3372ddf6465e2b5c
f96ff67404b07ffe33bbdc73c7f4eb426fc77730
F20110115_AABOVC gallas_q_Page_117.tif
593ee99037144d78faacfa505d766aff
c5104b0e7a9bf4c9275255eaf1733a2b54dcb243
24526 F20110115_AABQOX gallas_q_Page_236.pro
83a239daa138f3545aa286ef977d24ab
3dd9c6fca0748cbd1d7024f3af71785360aba806
26376 F20110115_AABRLR gallas_q_Page_098.QC.jpg
83fbb8c96e6b3a65a0e0f9d77c89a339
c7e96221b351cf0ece693f448b1eac758b921863
F20110115_AABQBN gallas_q_Page_207.tif
ac77446cd0c0dfb1fae99dcab864f824
dc5cc44f23e342255e83dabff6cb81748311d7cc
F20110115_AABOVD gallas_q_Page_106.tif
f7c88fb6fae1b1720997fd1b8f0aff0f
63248b3c2c4ea1ac09ab3b85a6bfa49dc88488aa
32546 F20110115_AABQOY gallas_q_Page_237.pro
91b1bc8c6e37f8ac6b3341420b2210a3
058d526dc0d82284106b67d5466a8847ced580fd
6807 F20110115_AABRLS gallas_q_Page_098thm.jpg
e4de372bbaa5a1ffcb70e9181280e9da
cd7e57ba15b27964ceb3cfd73c719adea95988a4
F20110115_AABQBO gallas_q_Page_209.tif
2b0a1436589cac0c593a566d5a9e6bd8
35e04d1fe71fb00cf04bd78c84b99a5d9b15bef1
F20110115_AABOVE gallas_q_Page_347.tif
5e397d3d352b3ce3df0009128dc9c71e
5756cc669acafffd9b0ba9fabf7e522ca21e7dfe
42574 F20110115_AABQOZ gallas_q_Page_238.pro
a9ed606acc2b6cedee41f6721390cbb1
c14d2a69ae2b0455c2f4460f22d578466093db72
19844 F20110115_AABRLT gallas_q_Page_099.QC.jpg
1e71f2f8d38be09909e7c763ff031981
a7ab15d5929b5f6881b7443a7d31be35fc254d78
F20110115_AABQBP gallas_q_Page_210.tif
7201ea530aee2f3201a12cb18a302e72
0d3d5eca28cc0434cc4d54c88f04381c0c332399
18860 F20110115_AABOVF gallas_q_Page_289.pro
725b4f7b52097dc8b47095df461440c6
1daa34332eb028e519b4cf5875325efb228df8ef
F20110115_AABRLU gallas_q_Page_100.QC.jpg
5daa7ff9df5ca5fec5a5fb0fdc434d00
f58b7c2444e8dc484ea0f418f62559c364cfa3ab
F20110115_AABQBQ gallas_q_Page_211.tif
a5fdef9e42b40e16c9949969fb5fbcf7
b87fa7baefe6b0f0f2461a85fa5d615a3e76a288
F20110115_AABOVG gallas_q_Page_126.tif
25eb5c105539a22df26d46f11960e743
8eb910b39199c969d098ca3e1422d780b423010d
4498 F20110115_AABRLV gallas_q_Page_100thm.jpg
7856ea94996c83cbb129e5face3132fa
589f859f95f594949afdc7b056508c6246d98f12
F20110115_AABQBR gallas_q_Page_213.tif
4e517e8b343a6d6f86e11fc05efda473
461f4e6ff0112db0f4b35a34c688cf287917e674
70999 F20110115_AABOVH gallas_q_Page_220.jpg
cd40337a3aec19d016590915106a4959
daf38f9efc9d99d4f64c2b4a86add26fff00447c
86300 F20110115_AABPSA gallas_q_Page_288.jp2
4d89ae311d3fc4f3f1f42daea346b399
a0039b5d696986e1368fe0e785f7e19892e77af1
6857 F20110115_AABRLW gallas_q_Page_101thm.jpg
4477fe22183788f08642997a229f2ce5
aa16a2e4cb2ca83644079477d816f0bc44201273
F20110115_AABQBS gallas_q_Page_214.tif
9a899c730b24f5d893fbe9e2ceffed5b
d5281ebe4c7cff3f8ea1c0e77ded374701427337
F20110115_AABOVI gallas_q_Page_262thm.jpg
2d64a7971108321963ab9f09e532098b
ba98be06f9f69f8079c44327203c81d70ef601a4
43915 F20110115_AABPSB gallas_q_Page_289.jp2
97877613dfeeaeec11fc0ef9279ab21d
ebfb8fd4432017bbf94de06d2b05f880f7587ede
19040 F20110115_AABRLX gallas_q_Page_102.QC.jpg
265eddfb2cd23a59e39b6e16797ba5c0
4ea35565f4ef42f7d14391cdd16d5f97ff6d68cc
F20110115_AABQBT gallas_q_Page_215.tif
f8dd31bfb9cad92327fd8d6a7d53b327
cafa933adc4a1325fa26ced09dad259969f99388
6492 F20110115_AABOVJ gallas_q_Page_268thm.jpg
e7f9aaa5721dffdb24a5af1649cc4c0d
0fac9bf19be8caae8eac448f71dd1c0696cb7f9a
105612 F20110115_AABPSC gallas_q_Page_292.jp2
980b99301887cd6adba089558e86782b
f1a1111f2be90604384211be14c8cba74702b669
21162 F20110115_AABRLY gallas_q_Page_103.QC.jpg
13027fc8fe62457d19be78d8f1e23a0f
bd0b3bbceee07d8396792e239fbcfba172ed7128
F20110115_AABQBU gallas_q_Page_216.tif
35a29be86713cb8784e6fc40da32ce0a
a33d987b14d2ceeb823dcc18503a79f119fb5fbb
103155 F20110115_AABOVK gallas_q_Page_160.jp2
aaf9cd528e656cc4285f2fc8984457c2
b65e38c1af615d74d0f61d1f7959e0487115f4ca
117721 F20110115_AABPSD gallas_q_Page_293.jp2
961a607d0d6851161d2c60d6a6e4112b
8bb4c3f13105e346b43a72af1372da13d55d5c7d
F20110115_AABRLZ gallas_q_Page_103thm.jpg
293f0fa62c9e56ce2b1eac8a635417b6
673f6f059c3b54569b28b2645054de13656c08e7
F20110115_AABQBV gallas_q_Page_217.tif
2f81eb3780e922dfa61ab6f5e814d7ff
eae6f16145c807f331ed509bb7111710c42f33ed
73804 F20110115_AABOVL gallas_q_Page_049.jpg
3d81a64a212c6163fb5f71548172267a
1decfa7151e051cf76ca42a28763a8ed5c55e4df
93914 F20110115_AABPSE gallas_q_Page_294.jp2
05dedfb73e17044b6f3bc496f6850ed7
78024a21ba302f1a6fa273da222a8fd8c6adac3c
28603 F20110115_AABOIA gallas_q_Page_338.pro
cc913a74bf0fcc5578d18ee0660105ef
f4d71ac625d0f2c649d1fc1007b4c0873d8c7ba6
F20110115_AABQBW gallas_q_Page_218.tif
12c980a9e569207321ca408e07407c5d
c669543ab34e7086afe05d44418dc7d34fe36074
23739 F20110115_AABOVM gallas_q_Page_050.QC.jpg
cff7c825ae2a9077aefcd3edfd2d89af
8fbf74d1422dcf0bcb49171b500aaa1e0a384fc3
606229 F20110115_AABPSF gallas_q_Page_295.jp2
2d52e57c6ce8dfd1c26cf8de881cf8ed
c89719225e8744e774b5a8b21e6b9e80b589e996
75535 F20110115_AABOIB gallas_q_Page_029.jpg
29a360472482ea57a2c2e5061b333eea
5712d6159261cb57fbbb46a1de694ffabe48bd8d
985 F20110115_AABQUA gallas_q_Page_021.txt
a15468c11a6416a45aaf742c102d6f17
838e28f077ce8c91c9fdb922d1408203da4f368f
F20110115_AABQBX gallas_q_Page_219.tif
4414fa5f76e4cc1c6626b9f624c6cc45
b3f4018dc1a054842a8ebb927dd6821219d50e29
F20110115_AABOVN gallas_q_Page_171.tif
9ef76997d2061a85067f4720f91cfc6a
0424074be638872ec47bad02a06abdb966aba330
110074 F20110115_AABPSG gallas_q_Page_296.jp2
9f0988ce47d7219c5e9bc882edbad553
0cda3549d12c0a2d1540ab61be946e2df3905da9
3919 F20110115_AABOIC gallas_q_Page_385thm.jpg
709b096891ea9b0ce2aaac63cd87affa
50c1bef7fb7ab7f3321d9465db42a0f1d0233a72
1153 F20110115_AABQUB gallas_q_Page_022.txt
1d910925bea2672df56380793e9941fd
88009c3db94fbb05f5f7884abaa006163eb278fd
F20110115_AABQBY gallas_q_Page_220.tif
0da96885d319036515c0eaa42c90b7f3
a8400452b49132e86c4b831019e1e5249a359c7c
2012 F20110115_AABOVO gallas_q_Page_046.txt
48c6762ad87f45622caa0b3d1d235421
d8aec2b1a0915aff6b9527409abf5ef6fef96e5d
106242 F20110115_AABPSH gallas_q_Page_297.jp2
4bb434fce9a234fb598b81c6becd4793
b104c16649f1d876d0b71da81da105c0dd378d1a
63937 F20110115_AABOID gallas_q_Page_212.jpg
4e1daefd7eeb14193b4e0f9d4b61350d
1c4bd29828c4de51d63c5ca8312fe60dd811b20e
1091 F20110115_AABQUC gallas_q_Page_023.txt
3c251d5038d5d236b987fdfbdb50ca0c
63a031b1f4b24224928c91056f696a2ce6be0ed9
F20110115_AABQBZ gallas_q_Page_223.tif
bf00a5c211e57054bf83f2df21157db6
7f48e3bd786c1b9bd82195e8bb428d917b93c80a
31614 F20110115_AABOVP gallas_q_Page_346.pro
16001f08f8457a83043092d1aed738cd
fe756e14c0a75dc1cc359beeb7c4fbc3c05f33ca
1051965 F20110115_AABPSI gallas_q_Page_298.jp2
9171db256223d0db39e466e3ebb886b1
3569320a625e965d2b60e1b248f7b947d2fba0dd
1790 F20110115_AABOIE gallas_q_Page_225.txt
3f8068526e616ca3e0903bd8a455dd1a
e63f27ada947c13e834aea014ec69c5f553fc554
691 F20110115_AABQUD gallas_q_Page_024.txt
d3f0041fdac866965f458517a161eaa6
f75ef539c194e0bde7b261a3974b088c49616398
F20110115_AABOVQ gallas_q_Page_187.tif
79e15ceeb4b7c79d42f44e8184b44ad0
7eaaf2e20de31308334cda909c1fe19567d08598
102858 F20110115_AABPSJ gallas_q_Page_299.jp2
7c61ef291c5af62216e75389f86f2568
fedccf21371ed0b4605b922c489a11e50f077f5a
1064 F20110115_AABQUE gallas_q_Page_025.txt
cd0c4387c4f906192f7b52a368bb80ce
b525ae5644ff991e8348d554021b0ac25da4ebd0
F20110115_AABOVR gallas_q_Page_208.tif
29cd20103410a87e4b680fa9a479bbbb
28fec1638e0383499d9320a46171b872ab11cac6
87478 F20110115_AABPSK gallas_q_Page_300.jp2
87708b16337bc688afbce642a2c05752
80b313cfb0b379e7f9a6331c6b10df90203e3553
75914 F20110115_AABOIF gallas_q_Page_202.jpg
5b4bda190e38be4a334908bf5dd24245
1eb7b6a864f4c14f280f8a796a7c84099542e0b7
1705 F20110115_AABQUF gallas_q_Page_026.txt
cccd5ec050bb1b1ef715d7e9037c7166
f6e95b4882a0f7ba1b31aacf757d66a4de7f674c
67750 F20110115_AABPFA gallas_q_Page_256.jpg
a4ca86eb77d2ce847f1303e2a86f642c
c8a1ede1c5c270a2051234232ffc17c90a8d9196
101126 F20110115_AABPSL gallas_q_Page_301.jp2
f2bcdcdc904a9a9cbcde7660702613af
6872c15242845ce29808ff65ea95c914e274d5be
12182 F20110115_AABOIG gallas_q_Page_318.QC.jpg
e3944039f8987a6556111559b5997c58
93c9ac5b8e3dee26dc5eead1444865562af25851
1250 F20110115_AABQUG gallas_q_Page_027.txt
02cdc378c8446b6342e5b38f7362ad9f
4ba02b20b21071971643b206d1bb59db2d2b60c7
3624 F20110115_AABOVS gallas_q_Page_351thm.jpg
33165cb3bb07147467769c5788dee846
d02c24634b999e0f32f59b8e5970ca5d784f508c
103317 F20110115_AABPSM gallas_q_Page_302.jp2
2830c382a03c6310a6f2a639a67d9bcc
02590048a8d83405d8c01d5f102564eae54cd6f7
25788 F20110115_AABOIH gallas_q_Page_239.QC.jpg
80cd5f6cbcbbea8c1580574da5a4e67f
2399288582effaeecdd2b2b7606b595208b403e4
4379 F20110115_AABRRA gallas_q_Page_181thm.jpg
ab789e8356e0a59d5538c649c52841a9
2b086f05a13d67cae333da7f7c7fb36a828043a5
2011 F20110115_AABQUH gallas_q_Page_029.txt
e09f4e9febdf6b65f234d19b6cbc0f15
de4f9a85bda3b8db4e317701f1a37a4b69d18236
53144 F20110115_AABPFB gallas_q_Page_257.jpg
8e0f8d9a40603ce8b0bfcaaf8782ffca
4ab60a6d8e46bcb6db7794e20117c52365a0d1f1
6804 F20110115_AABOVT gallas_q_Page_055thm.jpg
c1eca49d29dbbcf4e8d25069c77b7f86
7f19e9f038aeab05943530b5a8be6dc23966d24a
105697 F20110115_AABPSN gallas_q_Page_303.jp2
dad96799c6406ee5b3eb08b409160c75
dcbeda3709fe1375173553e1c9ce1a48e846b794
52649 F20110115_AABOII gallas_q_Page_195.jpg
c956dfce2d98a7eb45270d646f9cc931
6f3e9571540a6534f2d41de95c15595f0e071c50
19465 F20110115_AABRRB gallas_q_Page_182.QC.jpg
a885ee1da9c5b7045e9d92f12a120328
3505ba4139ace0ca6e630ac480665cfe1c044b67
1956 F20110115_AABQUI gallas_q_Page_030.txt
5b9dc72d691cd1ef3534771fc0281c14
3c79624c1ce9497637c5706d5ccb9999baaace58
49906 F20110115_AABPFC gallas_q_Page_258.jpg
2e32b5f2d2fda9f45065e70dc0a2a04a
943845cda1ebdb43b9ecf198f513d75e91079faf
24752 F20110115_AABOVU gallas_q_Page_384.QC.jpg
094d718578a127c35869e1d23727a637
08df8d31992f893a4604bdca3e793d242a16f567
1051975 F20110115_AABOIJ gallas_q_Page_230.jp2
42b57e81824fc5428688eee3fa24923d
d63dcc3080c518c81e99302db06d41224bfd4fac
6232 F20110115_AABRRC gallas_q_Page_183thm.jpg
3d81c9dedf20ef4c4f97798ad039f70e
962677c02c5f947931f22eb466d88101adc5d927
1246 F20110115_AABQUJ gallas_q_Page_031.txt
f0af28d4d5c472f67f424e3b5f2d6c6d
cc615b6886a08e251623ee78f8f5c5e7475f5f80
58112 F20110115_AABPFD gallas_q_Page_259.jpg
df43cb6c646947b1ae26e9873289721b
375176d056a338bdab35ab3e3821f5fdafabb30f
1891 F20110115_AABOVV gallas_q_Page_162.txt
b7dccdc0721a3aa481c64a7d604dcbf0
b28cf170d94089818e9c57a865b9aae98f5d7ec7
111771 F20110115_AABPSO gallas_q_Page_304.jp2
675ec8640f023f6077856c87e40278e8
1b3104843b598c90f77289ce1798195d91a26f23
6656 F20110115_AABOIK gallas_q_Page_306thm.jpg
fcdd17a038df5f87ae8778d592687a1d
77a03bcc28bc098e1f8cb997aeb6a7333bf05908
20913 F20110115_AABRRD gallas_q_Page_184.QC.jpg
9ee476605d806907b97a1cdcfd26ff6a
60a2380b422bb4f35f94a1dbaba76dd9f11b97b6
1851 F20110115_AABQUK gallas_q_Page_032.txt
10dad493cd3b61bc63735bdd9926f5ec
ae26dd3d9808d78cf85e0637664164965caf67ba
61711 F20110115_AABPFE gallas_q_Page_260.jpg
7eaeed1abef307c5eace13aac2476a3a
c51a59756e77440ea2e75ac1d8681662aa84fc22
29014 F20110115_AABOVW gallas_q_Page_320.pro
b7d3dd06d9b77a7384b75e480471c7ca
0a66db684d39dc8f3b33fecb544b3074b32fe058
1051985 F20110115_AABPSP gallas_q_Page_305.jp2
0c340893641d820712ec45004c2ff142
cbbe7eb246ffb067028ab71e3068b257c55f572f
99646 F20110115_AABOIL gallas_q_Page_013.jpg
12c30564d8eff9d9ee80701e4131216b
febbd5b9a47267f4472bc267d9557504291af753
5993 F20110115_AABRRE gallas_q_Page_184thm.jpg
7ad2ca84cfcbe5bd13cd436aa48bf70f
4c5d53e36c9e2df2cbbea07fb7f9721f33e6a1b7
2146 F20110115_AABQUL gallas_q_Page_033.txt
0c567861034e1d5ebac2e268106a789e
2ddc56e9f13f41a5c78f6f68bacf86b9e4255fe1
F20110115_AABQHA gallas_q_Page_377.tif
9e5e2dc59b94840e2384d7c1b204dd41
e12ac9c738cc7f891ae9065bbd754a20c5bedd5f
41438 F20110115_AABPFF gallas_q_Page_261.jpg
d178b7ea0c82c863c4b4049370202804
2b9dda4379d319eb9b1525e90a59245d5ccca5be
5240 F20110115_AABOVX gallas_q_Page_158thm.jpg
8f872a3bcdebeff11858cd2de270ab6a
31d397f48d620096957772895aae16ac865674f7
100622 F20110115_AABPSQ gallas_q_Page_306.jp2
7256f9114b6922735bccd7af428aa32c
15708a40ac799f4b09b7f42e703549804fe7cdac
1543 F20110115_AABOIM gallas_q_Page_074.txt
aa9f78f7e0355530669eccaa484e4bc7
d54fc8a9c0e463f1864af5acbcf55bb9a195195f
4276 F20110115_AABRRF gallas_q_Page_185thm.jpg
45e5efe7dc2c951622947e89caed7346
cefec6b1ebc7fb6789e6d8c11a9e241f41063091
1948 F20110115_AABQUM gallas_q_Page_034.txt
caae9aa00fb006c6e1c9a91941197bd8
7d236352490101a4c89f1cc3b560d9b896d786d9
F20110115_AABQHB gallas_q_Page_378.tif
42cafd98a61113b935f118817218fbb8
5f2aafacaf35786e39e7f9b6a8f060aad858f0c7
69782 F20110115_AABPFG gallas_q_Page_262.jpg
baed16b63980cebfcb995e1b12140acd
128a95ab0b88753dc5175ab3c91659b3a5d141f5
45773 F20110115_AABOVY gallas_q_Page_269.pro
f531998d8f9d47aad3396dac0f1c665d
4ad586ce815c7332430b81eef91fc97a839d6c8c
89277 F20110115_AABPSR gallas_q_Page_307.jp2
5db570f50a3597fdc7b50cfe7f5b0cbe
455d62d45e2cbf24a4a29506f276e7a99046730f
6923 F20110115_AABOIN gallas_q_Page_141thm.jpg
6db651c2b06308d7e2a9438ea97dd1db
0c8b5be0cd720a077cbf18173a4b0fa0d07bde4c
24143 F20110115_AABRRG gallas_q_Page_186.QC.jpg
b419ba8cf995eca46782b8c5588178c1
158b2c5d063459b615955ab7395b4e0253b6f184
1869 F20110115_AABQUN gallas_q_Page_035.txt
35e289a293b908b7e0cfbd3f91539b11
b6aedce1a2db546af553ff9272d3196e7438dc9d
51614 F20110115_AABPFH gallas_q_Page_263.jpg
fbf8bc85a812f7d79d01bdaeabdb8284
dc98ede293d67635be6bb1951ced280760a8879d
6513 F20110115_AABOVZ gallas_q_Page_127thm.jpg
817be968f613a078ea1a360e7d2bc43e
dac03aa5c1b6252b645c8d5e964348484c6700c7
717150 F20110115_AABPSS gallas_q_Page_308.jp2
a3116a82fa2066fd35d7d56270cdc0a8
1724a502336e01a99932c8ce2b0630c4a8ad0c33
1051974 F20110115_AABOIO gallas_q_Page_010.jp2
1ab51c1bbe61d7d4bf75e6ae7ab2a15e
3e0aa5a245ed72928de14eab8418c1e5b5d3b101
24348 F20110115_AABRRH gallas_q_Page_187.QC.jpg
b165284dea5ae1a0e9b5b2382c24fa6c
614a9f0f11ecb728a71f4885beb0b41c77ecfc61
1882 F20110115_AABQUO gallas_q_Page_040.txt
1015508f3a47362ae2ccea6d3136d122
4780f52161491c75e95c3b114e64f059d3593c49
F20110115_AABQHC gallas_q_Page_379.tif
20bc17dcd4e720cb59a32fbe55dddf21
4160b8b45565c83300ee5df418ea23a92f19dc38
61141 F20110115_AABPFI gallas_q_Page_264.jpg
8268b3ee372d25d109a018b07a8c2d3a
f313dbebf9b8891091b2573241dd1c88e7c9749f
72662 F20110115_AABPST gallas_q_Page_309.jp2
5b9288006ff7425632a59984a50a3f70
2713ef3c1aa8f153cd977e8f9e144d7ba63aa876
75063 F20110115_AABOIP gallas_q_Page_296.jpg
02336630741475b4b9be413fea1f16b5
65f7b5923a0d1f92ba8de3b16f19fd943071b70f
6823 F20110115_AABRRI gallas_q_Page_187thm.jpg
7c88800a81de2ab2761c639296cee5e8
19643ee063e279ce37492dfcbcd2ad0c1f5f0069
F20110115_AABQHD gallas_q_Page_381.tif
ab5c2ac79080c92338ea58c82452977e
b5452194c8c63a02caaa483120c1c09b7f032eb2
71541 F20110115_AABPFJ gallas_q_Page_265.jpg
c6cf7c70c83aa2f96ffd5a3ab148c1d6
ae242cb72b7b24036850456827ab6616156a3ca1
74996 F20110115_AABPSU gallas_q_Page_310.jp2
2f91bb6bcc191dba0a2dc536389adb5d
628f03c591dc7747876f5be027ede5c8e2968921
1964 F20110115_AABOIQ gallas_q_Page_108.txt
1fb5932620cf57710d2667063aefab8f
5ad13b78715135bb0d261b095d0f816d5986fe5d
20152 F20110115_AABRRJ gallas_q_Page_188.QC.jpg
d130615b4581776298332a01d2f790fe
5ef565392cde7f33246e3c2c305953fae43d7a6b
F20110115_AABQUP gallas_q_Page_042.txt
0b89584c26dee5058bea0dbb6e58e36e
3593ca609c653bf00b1af6640a2a4c5a4263698b
F20110115_AABQHE gallas_q_Page_382.tif
b33462676aadf7a42a91f094aa8d8c78
4f4abbaa55f4aa58b4b29180e3616a109f39f1f4
62074 F20110115_AABPFK gallas_q_Page_266.jpg
52b04a3c9865bec73332a6fae267c088
3ff73e74635bc0a94bc0b63a6a91e990a37bc548
855599 F20110115_AABPSV gallas_q_Page_312.jp2
e960c822bd005638d0420fe7e90a6195
e0848ed18b256d67e24dee0b8cdd4dbcd6aef835
15074 F20110115_AABOIR gallas_q_Page_290.QC.jpg
a4f07fe672dc6f5697e003023220342d
56de6e43d3a23015cfe2e675dddf8d82bb060c25
6171 F20110115_AABRRK gallas_q_Page_188thm.jpg
045b8fc7adaa3d21cf07c04d0d3f62d7
2a46d6fff12c9f4bf6f29eae4050f90ea5dad6d3
1916 F20110115_AABQUQ gallas_q_Page_043.txt
646c6d2ddc1edac8bacd28deb87b6b6e
87aaac441eaa50699ebcd737a43f40e260950524
F20110115_AABQHF gallas_q_Page_383.tif
01051c8a5ef8ad9746b75984988921b7
f8652af1d3550f2bc49f6fdaf579bc34860d08dd
69296 F20110115_AABPFL gallas_q_Page_267.jpg
a6ed9e3f988d08fa60f26754be1eea94
22b198fd5e5265021f4e5b15070283846e98761a
712552 F20110115_AABPSW gallas_q_Page_313.jp2
4e44a0803e1ee7c047603bfbf268d114
e753fe788f115d6c5d1e403ffe8b709bbc83da12
6462 F20110115_AABOIS gallas_q_Page_186thm.jpg
b22d430a3219c77f6f9cab78e911f00e
e2205065a1087f41751c877886dc45c7240131c0
1953 F20110115_AABQUR gallas_q_Page_044.txt
35a35e7a7c49b8107072f350433213ac
d3be08f30fc0df3129fae45e725449d7b94a1219
F20110115_AABQHG gallas_q_Page_384.tif
935e2a994356b6155aa46ad1ac7a3444
79602926404a24e1733ed56dfe65803432f5eaf0
69568 F20110115_AABPFM gallas_q_Page_268.jpg
0d2700b45641e136339b592b0117da54
4abfbcb9365e6e934b93611bcd967e662e0df404
321024 F20110115_AABPSX gallas_q_Page_315.jp2
f1582632c15f705145d3e7fbbdbdfa00
a14c4ac7e85b12a19ce18fc639255a5e5c6167c0
46106 F20110115_AABOIT gallas_q_Page_144.pro
7e4da28f824a8b26774653b859eebd39
58cce91ff7390f8b68b35e20addccf5ca2024ab5
19693 F20110115_AABRRL gallas_q_Page_189.QC.jpg
804a8d770d1a80fd47256eb07ca55170
02cc8c3e64a76454ea6343ddee01e0cd47df36a8
1769 F20110115_AABREA gallas_q_Page_337.txt
70d3d6594f8f60125ddea4317f0c3ed6
5029eaa4760de0b3cfe8e2fe700fcdccd41d4617
2039 F20110115_AABQUS gallas_q_Page_045.txt
0d20632f02d17466c615bf8df635a2f8
af363b6ced27023a9e5e47134320e501b1615254
F20110115_AABQHH gallas_q_Page_385.tif
6aa3dfaa0fd96d56f1f34eff3f3413bc
583902d75fccd75808940d6241918deba21ccb6e
67931 F20110115_AABPFN gallas_q_Page_269.jpg
2fe8196a3c24f350db272f8e91b00157
eb1e2b83dc5e3cdd9715655c9396ed3a39d92c08
99659 F20110115_AABPSY gallas_q_Page_316.jp2
de0de3ea9c7ca8e46067ea3f02b0f4ad
76dfe6a6f213cbb4af7e47bcb56bf646225e3870
2116 F20110115_AABOIU gallas_q_Page_018.txt
8a7f2c014463ca0d7758275bf9985cb6
b83a285d4921aed7b4fb4df408aab6cfd062f663
6102 F20110115_AABRRM gallas_q_Page_190thm.jpg
9114c009e53e4794ab1aef17316e8601
9c8090b903e94086b98b37be78e45c3daea83785
1468 F20110115_AABREB gallas_q_Page_338.txt
8c750b1d41489409250add0b8588bd09
bf3f194eafe49a867019794ab938a249aca55092
1954 F20110115_AABQUT gallas_q_Page_047.txt
1f6d0d4c86671518c5005b1ef0343916
e368adf59b81a54337decb4a984c791bf393baf6
F20110115_AABQHI gallas_q_Page_386.tif
df345cde25eb78cb41baf8b7c2b461f2
d6dded1255ebea1148d0bdd8737f9c1062912f11
62446 F20110115_AABPFO gallas_q_Page_270.jpg
c173aad919e5ced8237c7274ba516ea4
0f8db0001d349550e6da25f3889f8c4c388c8663
775054 F20110115_AABPSZ gallas_q_Page_317.jp2
80b94025be2108b7f545f5a64df1d00a
361f5ac7c813c951a6f7502eb06bffe648b91515
21937 F20110115_AABOIV gallas_q_Page_318.pro
ff4a5f17e54c0c9f15fa951884dddc42
163bffa9b507f899bbd7316ac3994dc647629990
19127 F20110115_AABRRN gallas_q_Page_191.QC.jpg
4f0367497b148b0b4080ed8cfb850d0c
65659bf5e3fb22999bc039ae9487d2b823d9661a
1636 F20110115_AABREC gallas_q_Page_339.txt
9c76f40eb98c6ff607d4a20a42ae2d1b
c1ea00036e6169b05d594c8d3ac74ac395cc38ab
2088 F20110115_AABQUU gallas_q_Page_048.txt
eeb234f00ea820a184b4a0bc032fd922
be7744b7d63bf13856a30dc7194d026dd1ec95be
7728 F20110115_AABQHJ gallas_q_Page_001.pro
24bfc58aeb72047667601201217a4b12
e8054120e77673e2dcebdab6e123f96d65e80956
52910 F20110115_AABPFP gallas_q_Page_271.jpg
0cb43162e39d2d4bf7df9079fe858010
6b29cad1c48a12a30ebb2e188f343c05a918c74a
4256 F20110115_AABOIW gallas_q_Page_362.txt
f3851ecdef0bb287c64df7c453777835
fe0ca4e5a72fff129abcd744b8b111c0d1e96c1a
5465 F20110115_AABRRO gallas_q_Page_191thm.jpg
e5bb5be9311ab67ad00d6662f85c2320
3b2393857631cd1045c487389b6305ceca866a58
1653 F20110115_AABRED gallas_q_Page_340.txt
748935e7ed72e503910d958e641b2d40
2e3fca62f6f8990d9c76ee1a5e0cab21bcb8b3bd
1932 F20110115_AABQUV gallas_q_Page_050.txt
f440df5a5a3373e70405aa88d714bd18
57df5a6d37e1dfe5dda09bc279033a69e2db78a4
1149 F20110115_AABQHK gallas_q_Page_002.pro
fbaafe841d4e7ca0120171d59fa555f8
c6e8f1128c824b7824e7c00963c86ba07762d8a7
39064 F20110115_AABPFQ gallas_q_Page_272.jpg
ada1ae0e7fd4c25cdd59621a783c4743
04d17faa646060419110786d511ed4f6df6cf48f
16924 F20110115_AABOIX gallas_q_Page_356.pro
6907cde9920f096286cdee7fcf7065cc
d8972fcfcffe76115c3b0761ed29b695c9814583
5743 F20110115_AABRRP gallas_q_Page_192thm.jpg
7871acadf1753b0d1a26a02059e09e4d
e2db436f79ef5bc42490d0245ea517889da8baf6
1184 F20110115_AABREE gallas_q_Page_341.txt
896560146d58847d98809b3d0e8cb414
b13a4bcb73309e83234ee7e323ef0da9228cf58d
1990 F20110115_AABQUW gallas_q_Page_051.txt
1735026dfebe1c5144dfb93524cf9101
52403a6248b3fcf0f9e93d3f305708c37dbebcde
31011 F20110115_AABQHL gallas_q_Page_004.pro
6e6a3881b7f5807f5a6ef1b6671260e2
2262e7c5ef9bdb0c3e87520c14acc69f75a3b597
52131 F20110115_AABPFR gallas_q_Page_273.jpg
1b6b0aff01f9f13de694ff33e65f1686
1f2adf615c8fafa719404abd8b8cbde719992dd4
1874 F20110115_AABOIY gallas_q_Page_036.txt
3bf5fe226ae532f252a7d83552b822c0
7c1395b2dcaaaca75e3cb679afb1580f1277d9f3
15646 F20110115_AABRRQ gallas_q_Page_193.QC.jpg
aefb5b7ceb87b97b41e0ed0ee945749c
08efd2069b52b546ccb948816236e65889672e03
1467 F20110115_AABREF gallas_q_Page_342.txt
266ba8d2cee785e87585ab3b114e1579
b70c9e50e9791ad951ee78c4443f18d4001ff806
1880 F20110115_AABQUX gallas_q_Page_052.txt
74a5a303fce69f99281b5a6b374e602e
25802b764a0a482f0c8dac15de238999db5925a3
73171 F20110115_AABQHM gallas_q_Page_005.pro
d88a93bcb40415e8eee68126ead5e7cf
49ff65847c9caa8e3f8c7c9b4a5759a5a6c6d0d4
44520 F20110115_AABPFS gallas_q_Page_274.jpg
71c1a2a7c6b173e442629bf4bf4e00d2
e789ead30c9300fd09d0916db171a834e25466fe
1421 F20110115_AABOIZ gallas_q_Page_358.txt
99fed7a7542e39409fd077cd92f52305
0571f3f92c0318ee87ba208fffd8ea110a883cf6
4747 F20110115_AABRRR gallas_q_Page_193thm.jpg
26187388b9dfa742fd1d8cae3ff92668
7ac7a8dc930ab784b701191055d5229910557224
1748 F20110115_AABREG gallas_q_Page_343.txt
3dd10ecf323cf3a0dcb82b2fb78aa0cc
a1e238af6bcd05bffa4bad32961b8b090c39a118
1894 F20110115_AABQUY gallas_q_Page_053.txt
e24ea96229db9ef2dbfe5de56d2aed85
b7639b87c086fbcd69c372fd27b299deeeefd62a
108226 F20110115_AABQHN gallas_q_Page_006.pro
4862c85f76e69684534ac05a2d04f847
577c139d26ef5c46f9238520bb517baec22ce999
45421 F20110115_AABPFT gallas_q_Page_275.jpg
500d73b6d9c0c4f693466b6338c5ba09
5f3b4832f78f9b4b2a5c4a712fc3f0c144dc88bb
4234 F20110115_AABSBA gallas_q_Page_338thm.jpg
04396878ebb09da194cea3f4565cd377
546a6de8dd4472980de67a942abea035c92a3130
21717 F20110115_AABRRS gallas_q_Page_194.QC.jpg
a28a20068eeeedb53ede50d9199371db
836c0e56ca6ede832734e1efd13192516226e9af
1375 F20110115_AABREH gallas_q_Page_344.txt
8c26f6e49631c64da6605c70f6ef23b0
4ad1147e3a0ea27213b5fea6b499f4950229c415
1986 F20110115_AABQUZ gallas_q_Page_054.txt
4a3d3dfc5cb2d07931adfb07bc8aaa6d
f801232f03ae70ae21f19002e665b82166301566
11848 F20110115_AABQHO gallas_q_Page_008.pro
5717adf8e00cb81c0a605e513377f728
6f765c6c2688b3b136f3388c9402fb3533db617c
45550 F20110115_AABPFU gallas_q_Page_278.jpg
4c0d30cdd312b1a672185457ab996dc9
cb8c15de3f050da14877db2bba3408e91a65d602
17800 F20110115_AABSBB gallas_q_Page_339.QC.jpg
ef7ae3c472f85ff15db697d3c4213d96
ca2bd7ab5b81f51fb372bd0c5a5c19018685340c
6672 F20110115_AABRRT gallas_q_Page_194thm.jpg
b7a01a769b1bb23b2b4fcd57edb0aed3
ed5219d0a7787a7c01ba5c0f4e381ba9fc642d3c
1243 F20110115_AABREI gallas_q_Page_345.txt
e20eef6f1c3df70565ed4146188ba98a
cf259826ef93000731895909c5a12dcb6d239b88
32265 F20110115_AABQHP gallas_q_Page_010.pro
6f5b34a4c4c8b8d7fb6bd2213945d04d
a08172afb072de01334d27d36068c46d4d48c126
45058 F20110115_AABPFV gallas_q_Page_279.jpg
a1a534158caa3ddabba82667e0cbdc72
cb94472d7508a0aee1c7212841cf8b24d8c1f534
5328 F20110115_AABSBC gallas_q_Page_339thm.jpg
159bf8100828b5f4b70e0786598d3276
e9575ccd707b056c54862e8794bfc37cd6cd4906
17677 F20110115_AABRRU gallas_q_Page_195.QC.jpg
54a6ad43abd71a5423f05027f555e2e7
495ca9472ff234c990e1162d233fe2a15a3a3fc2
1884 F20110115_AABREJ gallas_q_Page_346.txt
9fc11355e9970b6a88127ed77868163b
d278d946d3ec3e4213ef56bef48649b22d28d077
76814 F20110115_AABQHQ gallas_q_Page_013.pro
72db7e2a09bedfe08144f34879b8d2e8
f3adacfd14bc64f8e54d8727b0023208df25f2fb
73583 F20110115_AABPFW gallas_q_Page_281.jpg
78451f3b271d7aaa31bef86b4983bf9b
25eb6701d1e15e3155382b47481c7878d7f01267
18879 F20110115_AABSBD gallas_q_Page_340.QC.jpg
24813980dfad69b80be92a7e7893aa10
2c66a2dd3dd26261506db58a4b40589a5d0004f2
5414 F20110115_AABRRV gallas_q_Page_195thm.jpg
2c241baacd3507dca4d71258b6c871db
60fa98858332901fbac1c30fcb98d7b7c8a751f5
F20110115_AABREK gallas_q_Page_348.txt
34b04e4dad0a5dd62ec6c259e93af74a
73e6160273a1505f63640a308b071c8f9d5fa808
71062 F20110115_AABQHR gallas_q_Page_014.pro
e9b5aa8806e6e3451768a5af1479e4c6
b06292d7c0ac1a70a3c3c6545b9a28b46e4f95f1
65484 F20110115_AABPFX gallas_q_Page_282.jpg
d51a84560a5f6a614bddf7cb30b28cfe
be1ae892c65794924ec6967c4a5199f437dab082
F20110115_AABPYA gallas_q_Page_089.tif
52e9b6bd81dbd9e45049175e7404f079
6127acc75bbe8b547b1fb5b91f60097dff9b55b3
6011 F20110115_AABSBE gallas_q_Page_340thm.jpg
f778e7acf5e714447754a1cfd4073e7e
99326787dccfecef7ab8c923d5ec44a9688dfd3a
20435 F20110115_AABRRW gallas_q_Page_196.QC.jpg
8c077d932b6b6930828967c6d15b7dba
12c1677403941c62a8ae7a2583173202e41e3621
1905 F20110115_AABREL gallas_q_Page_350.txt
fe81fb959fb49d52d369a9e39ed36880
9feb2e8cfbf4c5fce7e59a8aa947521f0c610ced
76790 F20110115_AABQHS gallas_q_Page_015.pro
8c8406f984b12c67c162c8517d3e85b0
a79c2865b6f626aef921465241fb35027da53e1a
73634 F20110115_AABPFY gallas_q_Page_283.jpg
b06a19b666f7acb6b03441dad9df5614
386061c8d779286a2cfd5434048a514b62f3ad02
F20110115_AABPYB gallas_q_Page_090.tif
d007521ae7588390679e76bb26a5b56c
f8f8b30bfbc666514d06156d1f6f8483951d863a
8423 F20110115_AABSBF gallas_q_Page_341.QC.jpg
1c60ba99631ef257c55e4361aaa04898
ffcb03ea106789133f77d1c3bf621685415d2467
6000 F20110115_AABRRX gallas_q_Page_196thm.jpg
c0ae809ffa2476513aca095d4c312b49
7492170ab6beab7dd7f02dba35ba89fdf703474f
937 F20110115_AABREM gallas_q_Page_351.txt
30ca9eeb42ac4ad16f01f1147acbc61e
958a79fb8e57b8c1331040c08b6f093633e138bd
78272 F20110115_AABQHT gallas_q_Page_017.pro
59b771575741aaedb6413634fef3932b
fcde07a10255d86a700b025d531c2c548cf0e500
73184 F20110115_AABPFZ gallas_q_Page_284.jpg
1c138c05e6e166fade912b6bf03294b6
ead692bb45ae184385495aa864f029f2d9db5787
F20110115_AABPYC gallas_q_Page_091.tif
fd63e4caa3929d3c6214ca4f589e8a1b
26000c638dd9c142e2321c866b02a35e6e36baae
3111 F20110115_AABSBG gallas_q_Page_341thm.jpg
698d73f9c6fa9cc038a53099c1221481
0f582b4bdb56b1c2a1f26ebdaab70ff4d5853aac
21341 F20110115_AABRRY gallas_q_Page_197.QC.jpg
46d92c9fdc75c885fc2f4ef92c83a7b6
eeadfa7e4bd9be1792f0c49cbea185900ab254ec
1640 F20110115_AABREN gallas_q_Page_352.txt
4d522237b9ce77e62a1f994940f8c617
a669215907b809f5872385ca774e2f8c755d1799
53164 F20110115_AABQHU gallas_q_Page_018.pro
783d64ca392a1f30541d6c22a2aec5bd
ddbe90de6aca9541bb3dab2bbc5d9db82afef274
F20110115_AABPYD gallas_q_Page_093.tif
93fbd4cf47bd0b12f73337674636cbd5
7ed8a96691d2764ca691ae478762dda9fd95b316
15963 F20110115_AABSBH gallas_q_Page_342.QC.jpg
5beb16f298a04b033b8c4dc6346900a7
312afc44cbcd7f4038c36e5bf83e8d51a58b316b
6455 F20110115_AABRRZ gallas_q_Page_197thm.jpg
df4615278a9b9d49b8dc303719c47bab
c01322ea2c4505878d30ba9f79e157c002247a27
1757 F20110115_AABREO gallas_q_Page_353.txt
15e68deb65b3a79291ff61ebf610859a
e09f60c11e4173c63a571d0fa8ca657ef36e9b24
22956 F20110115_AABQHV gallas_q_Page_020.pro
c36a889052116779ba9267d9f09afd6e
e83a3e3a89dcb4d12f0037542447e5667e0caf69
F20110115_AABPYE gallas_q_Page_094.tif
f3c7eb5abff425cce8530f78acb86b70
56321007c59b76eff08c07530a596796aba403a1
103265 F20110115_AABOOA gallas_q_Page_035.jp2
3ae967f9f0f71cc9fb051b27deaccb03
c251baf710767dde920992e13267b950546f2521
5007 F20110115_AABSBI gallas_q_Page_342thm.jpg
6bcf47c2f1aaa8f890ad8a7079890e53
4e0903a5ca0c0f8b1da666fbb32db991dd8a9a38
F20110115_AABREP gallas_q_Page_354.txt
36e6023c348b9d7a8fea688469aadfe8
73f2c8db6b26d4973ebbc4378a62a36bee3d2ecf
23208 F20110115_AABQHW gallas_q_Page_021.pro
75a6e327636c4131e7c4b15c60236818
0f0a32fdcdd0c4e27a51097dd8be476d89655bfb
F20110115_AABPYF gallas_q_Page_095.tif
55f33bb80a1753811d38a41321077b0b
a810cc7f0f58bf9208a7d55ee48bb925fb146534
F20110115_AABOOB gallas_q_Page_267.tif
842c47c891478e3fe2b0e72d0b10630b
1c0ede9d703b85af4740b9a09b0cf91d5b180e08
16160 F20110115_AABSBJ gallas_q_Page_343.QC.jpg
19ee010e4ff71590694e6147af5e64e4
203364b52c1464ef6d8e6cc2b73fbbe19f098d62
1576 F20110115_AABREQ gallas_q_Page_355.txt
dfb896673d89433c5d3768573e9a2184
c38dd2697c288c1f4624e3d68fdbcb1ee69345d8
27856 F20110115_AABQHX gallas_q_Page_022.pro
3630d2273a3d604c2a19b0a759eee64f
1a14fa083c1c9d92bd9f863fdd35a44f5a923058
F20110115_AABPYG gallas_q_Page_097.tif
f1b7044f9ea62051247ae233df1e999c
cb1eec034d703f3773757b5e26777906b3c26596
107434 F20110115_AABOOC gallas_q_Page_054.jp2
6745bf6154c2d422d3ce9dc979652f59
bd8c26c419b9d9e38264fe7f9b73979f84848c9d
4948 F20110115_AABSBK gallas_q_Page_343thm.jpg
33981c47a9c19615914ea1643e35477e
dbd050f2fead5d863860292cfdff56c1d3c99bce
806 F20110115_AABRER gallas_q_Page_357.txt
e780a68950dc09013a161cb45db0c5db
5edac276b94fd933e212f317598213285b95c5d4
26021 F20110115_AABQHY gallas_q_Page_023.pro
9a70ac29d2a51e06df43bb038243f0a5
96d05b2abc3b10fdb5abac91e95b758779015d6f
F20110115_AABPYH gallas_q_Page_099.tif
ac42242a7f3873913bc6f451437085f5
320a664f93e691c467e9f2737f24747d6796233c
19041 F20110115_AABOOD gallas_q_Page_199.QC.jpg
4c023661bcb46bb30dbca8c4d36df872
0d4966c9138114664edad9189fe92e41a561b247
13787 F20110115_AABSBL gallas_q_Page_344.QC.jpg
5e9ddcc25f8bb32c3f39d8746a0bd330
a6761a46d40821a3e679efdc35891981998f1939
3295 F20110115_AABRES gallas_q_Page_360.txt
287205b4d4a47d4cc04e2916667252de
ad4604310cfb69b91cc3b598ef3f3852e07cd766
15082 F20110115_AABQHZ gallas_q_Page_024.pro
f8c92235892259956dc88c0401930148
7891be6a6113a52de7fba4e59e1723f5b41b90fa
F20110115_AABPYI gallas_q_Page_100.tif
f7d13c6a13b64f60b77f3fa5e0bf7ea1
2271163b0625b04d9fe6bdb80390d123b119c3d7
26750 F20110115_AABOOE gallas_q_Page_007.QC.jpg
6385cf7ae84fb8d63bb9ad8e63e19692
6cd241412fb900cb6e4c4163ae8b1ea800c7757f
4580 F20110115_AABSBM gallas_q_Page_344thm.jpg
ec51c7eb5178045abbe08745ca66f15e
c7dfe0603ede9ce3e485879477462c02b2cedbcd
4716 F20110115_AABRET gallas_q_Page_363.txt
5fe573bc7bf312ff18a992656b2e099b
f0ee24daa5d60c2d9b32d85864c5b38528706de9
F20110115_AABPYJ gallas_q_Page_101.tif
ce69b152204e7d0b2c3c13bc51b15589
5cc7f5f5ac367926cce24ec6474cf07560bb5293
36873 F20110115_AABOOF gallas_q_Page_192.pro
a6e021f77ba332eb412c925b0ca79046
9b4787125b7c99827fd277353fc89d799940e977
13485 F20110115_AABSBN gallas_q_Page_345.QC.jpg
e811ab79652af936efde48b54d326614
b44572001e6e4710efa89b9b894849c0932df30d
F20110115_AABREU gallas_q_Page_364.txt
79e49b0d50caeaefe236d2fb838f3a1a
7d26645a54087f07d3d802a744dbb3207d8d096f
F20110115_AABPYK gallas_q_Page_102.tif
2f58d526d07fbfdfd7a3edf7b26d8cd2
e7460f4446110ccfae0097b23bef36b2508fd534
1913 F20110115_AABOOG gallas_q_Page_135.txt
9c7591e1dcf53cbd51cc601625312acc
422901e2af7a75a7f708687940cf1a3560bf37d1
4305 F20110115_AABSBO gallas_q_Page_345thm.jpg
adbce4afd934e99b50092749fa869cce
f601a8175f742d86485d6bdd2f1c4301d260a179
4690 F20110115_AABREV gallas_q_Page_365.txt
b979b7f49050a591f69c16e9b5200555
ac21b228187a1e8d66cbfa8f4ebd1441c2a64fff
F20110115_AABPYL gallas_q_Page_103.tif
a43cadc2deab7782326fc8e2eca46963
0f46bb551ae6120d02579ad4240c1b299c56b77f
1831 F20110115_AABOOH gallas_q_Page_037.txt
faee8a74a66b60361ea7c9b296fd5fe6
d16b8c7563324498e6cbaeb2af15bd651f9a9f74
99776 F20110115_AABPLA gallas_q_Page_061.jp2
d253d518e29be96b4bf866f4dcd5d850
840ff79d85ebe29bbcd0095b02b787fd0cb4cfb4
15163 F20110115_AABSBP gallas_q_Page_346.QC.jpg
12f7b67dd3a4cc418dd05aca061b310a
5dd85dab4d70e3c66388f97ddb553dee7b413c16
4860 F20110115_AABREW gallas_q_Page_366.txt
0969ee2966a0d86aebcf2ae9150a2be6
7b16aa19748cc6d1993f2c4d75dd20919c2864d9
F20110115_AABPYM gallas_q_Page_104.tif
71f439f9a861bf9450ac61cae3f698de
8671a2c88bfc8e3e7c281643dfcc43aa63788afd
16524 F20110115_AABOOI gallas_q_Page_157.QC.jpg
8f0e80e041fd7a5bb300fd17224a7883
8c2ec2fe7e9867f76990f42906ab41d93f2d6551
945709 F20110115_AABPLB gallas_q_Page_062.jp2
82b9f906df903beec445e045c040430a
5b6e4dc8e89fc244e3083eb053801d5ab4189c8d
17182 F20110115_AABSBQ gallas_q_Page_347.QC.jpg
fc0ef54d8cd7e1adac8215965e20f95b
68ff6b8e64b6d0159f5c7619a3eefa81a49ab6ca
14237 F20110115_AABRXA gallas_q_Page_277.QC.jpg
b1ac896b45eff0822e77813ce1ca3d67
702006edbc6766f1831fd933ceba86fc0f9c4e9d
4884 F20110115_AABREX gallas_q_Page_367.txt
df965ba8c651a9b328dc21b332dfa06a
ea73d9c2c5c5277eef54042c300c70365aafb5cc
F20110115_AABPYN gallas_q_Page_107.tif
e8a2e571a255589b1678996b9de47f9a
bbcc094c63978af8aa56bb8753bd8c59b7291ec1
1051980 F20110115_AABOOJ gallas_q_Page_239.jp2
f8b5568e39926b4e04fee63d2faa4700
2ce149beb2324defbe9b0c565ed23e926c314bdd
90293 F20110115_AABPLC gallas_q_Page_063.jp2
f819a6a1feafd9a60ba04037f4f1043e
f2fdad92bdafea5eabc65cba5d6059a944f8c8c6
5456 F20110115_AABSBR gallas_q_Page_347thm.jpg
47313692351499d28e6830d3f154f0c6
5e31c3753c2ad81ef91850800674dd5b650dfba5
4142 F20110115_AABRXB gallas_q_Page_277thm.jpg
23dd13faa6afc7943bbaeb774265bda4
44ae0c4567a5ce872d78174e1914ab62a78c013f
4650 F20110115_AABREY gallas_q_Page_368.txt
319b0d5069b4f54d18d2fc56f472aca3
ba39345dc7369c82627372a5eb9282178635922f
F20110115_AABPYO gallas_q_Page_108.tif
12f34d494b9a5b333ee225a1497f675d
549775278f224ade3d0032d4b25fbf626bcd9360
1123 F20110115_AABOOK gallas_q_Page_116.txt
923a42fa13696ce143842ad8418332c5
ebc0421f0619e55829c2d66e88ea431a84f476a2
86145 F20110115_AABPLD gallas_q_Page_065.jp2
aa01026891192db8302fd8b902b2b434
a4b43413ab0aab84ef835b45b918e06045305b4d
17491 F20110115_AABSBS gallas_q_Page_348.QC.jpg
fd80cd20fa948a7b2796f05522e5597e
4d4e313591884234eabbf5b57927b928c312fc3a
4094 F20110115_AABRXC gallas_q_Page_278thm.jpg
4018bf1b9963d3947e06a62624e2ece6
7dc0a60ad2640cee4616d650b5ef823ae95ad6c2
4614 F20110115_AABREZ gallas_q_Page_369.txt
218bcfa6fb5b51c6ca07c7612c757578
410ee3a4d472743aee6f1b232cf19ab1485799cd
F20110115_AABPYP gallas_q_Page_109.tif
6638c9bafd20739649668f60c87ddc91
bbe0859dcdeff625f478c14a02ddaffdb6e48d39
107129 F20110115_AABPLE gallas_q_Page_067.jp2
4e764fd6385f7073829259feb537c93b
f5edf04432a3e9acb6b91ecfc513e2212b8753df
5172 F20110115_AABSBT gallas_q_Page_348thm.jpg
4477a6455ef9916e9d41e54d5264222f
fbb6b0243513b43bfc5122bdd7043bb1092038fe
13707 F20110115_AABRXD gallas_q_Page_279.QC.jpg
63758ec4fa35bbe87c2c04a83cd6bdd8
c3be56f16a3017daa63457380d73dabeba8ed30f
F20110115_AABPYQ gallas_q_Page_110.tif
405cae012cd0ed9f728f67cb675c6167
e2ad2bd5bf24aa092394018a5a4681d5efbd255a
872336 F20110115_AABOOL gallas_q_Page_236.jp2
6ee77acb5b936ada21eb4625b30eac1e
7a97a1b9611d7881904ae4d0b7cd7c16663a4b39
1051981 F20110115_AABPLF gallas_q_Page_068.jp2
35b377778c2257b940b95d4a44c73d46
0b16c218d6c4649ce1a6e6021109ce04e659847a
14247 F20110115_AABSBU gallas_q_Page_349.QC.jpg
5f316fa61cd8fbc4f26774c841704a3c
064c88635cc204c1a8eee9754d2bc6751a002fef
4101 F20110115_AABRXE gallas_q_Page_279thm.jpg
15fd7b12d8a192fcfb474e01147bbaf2
ecec59cb9287a40a435bb234bec3e6614de465d4
F20110115_AABPYR gallas_q_Page_111.tif
035b90b8256fb0e82b1bfd8b717ab506
fbb51eb1a41ee1756de19f2894c70bead48dc136
F20110115_AABOOM gallas_q_Page_281.tif
6fb91d17b3a3e721f7deaeb0141b0f9e
4b6b165e6869efb27f7f24caafd966b70a0a7a92
50127 F20110115_AABQNA gallas_q_Page_177.pro
a931843d530428cd24498379ca37c33a
b8978c9e1f91900a7942e95954d3751c68e67711
1026612 F20110115_AABPLG gallas_q_Page_069.jp2
e664b6854ab90efe130f71d0843ed0d4
d3a33bbb17b09a357abef7a227103da16c757d1a
4212 F20110115_AABSBV gallas_q_Page_349thm.jpg
ae3e20cc8ba4c796fc31fe21c5a31f90
0ff7019a75060fdf3d4db30fa1067d32a61c2fff
13857 F20110115_AABRXF gallas_q_Page_280.QC.jpg
f658eddaecc8504e82af5e6b91b15f5c
2eb737568481fe90f4312b5a6f73fcb428f22e18
F20110115_AABPYS gallas_q_Page_112.tif
6e406d1b5b5d7ab13fc336e280868f25
318e74d6c48b134a6ff28cc40436ea06dba07a9e
2850 F20110115_AABOON gallas_q_Page_014.txt
6ab6188ac02d1a28f96fc80d3dc78f50
011533b144795fd80c2b6338c7b181b3784be85f
34675 F20110115_AABQNB gallas_q_Page_178.pro
2302a329791f45da011fa525a8696833
a94951261981466a42675d350ecb4f94643864d6
20153 F20110115_AABSBW gallas_q_Page_350.QC.jpg
85c0507688a45491b5622fb29e2ffb55
43048e64312abec3079de4e4f1d1d7325a0f0ba9
4042 F20110115_AABRXG gallas_q_Page_280thm.jpg
5c89ba63ddab6115341ae3c76f253a98
01f625d1c04077d2bd6c210b6aff50feb96fd4e0
F20110115_AABPYT gallas_q_Page_113.tif
b41e464f7d959dcbf15384f9df5e21e0
2ec70d02c335807f7ff247ae4db9cff92ab54ebc
57257 F20110115_AABOOO gallas_q_Page_317.jpg
034cf789f2868e63cff6110808cafd7b
c8ae48afcd079030bfd277d045acd6c140eb08e8
36552 F20110115_AABQNC gallas_q_Page_179.pro
9781a111c040c0b6f5237ff858522ee9
b922784cc10dcb812c5048eb2d416f2c2c2467c8
904782 F20110115_AABPLH gallas_q_Page_070.jp2
d05166d7ab79a2090120c7913cbf42e6
38051d911a10213154df4a9a0f5c6c5d23058286
6071 F20110115_AABSBX gallas_q_Page_350thm.jpg
8f389cb993860b65ed590734f4e54ee0
837994cf5d04c7971d88daee7ad6b1e36a179d92
24099 F20110115_AABRXH gallas_q_Page_281.QC.jpg
d42cf36c187ce77f1dcb8471fa3ba3a2
2807f120b49c384dba6cba412b701ff075dd112b
43486 F20110115_AABOOP gallas_q_Page_385.jpg
0500169ad84d392c8aa1c5c0fc64057c
acdf934ae66275a756d535ed2749f92bdd583541
26130 F20110115_AABQND gallas_q_Page_181.pro
09d6dc6261d7f372d9c0cee48aa28d27
89ccfc55429cfb1deafdb055ca5931b573487752
92157 F20110115_AABPLI gallas_q_Page_071.jp2
f8f450576643fb57ff710426a650bcc0
869949ae52701b63a9827e4a8681f3b4894c0fe1
11038 F20110115_AABSBY gallas_q_Page_351.QC.jpg
7282f313cc281dc57c779cd92e4fd9a2
ee7923dcaba7fc43dc2ba813af62461623737ec7
6702 F20110115_AABRXI gallas_q_Page_281thm.jpg
3cea9eb2d77ac2f063b415c01d37b585
0f6bba047cc81ff7101456a8943a0fd9a90c51b4
F20110115_AABPYU gallas_q_Page_115.tif
79a96b65491ca8c17246b8e5ea046a73
8a85543782954bf8869b0105952139a994aa92b8
5502 F20110115_AABOOQ gallas_q_Page_102thm.jpg
8fb95364da4c74efffa4c18fd1b0e65b
b5fcad442fa47c3a1fc8a7a1d1f50ab6b2e8bf04
39755 F20110115_AABQNE gallas_q_Page_182.pro
e7ab45e9a8c394c37c4a5d2bdfa37ee9
d0715ef58e3ca270c6a2558df5ae7733c6a05f0d
85712 F20110115_AABPLJ gallas_q_Page_072.jp2
d0e00b6c93431d9bde89339b1374f4b4
c1cf1fcf0246aad9a0a04848bd832435ac17308f
16035 F20110115_AABSBZ gallas_q_Page_352.QC.jpg
7f6cdbe9edb72803587d28cdc42e088d
78c4fcb549a323d1d1c8524cb97aeb5e55ec8e72
5686 F20110115_AABRXJ gallas_q_Page_282thm.jpg
b692cd288e42d31779e321b90d3a06c2
bb59bd51a852be7dc8636232d4bb955341ec2ae1
F20110115_AABPYV gallas_q_Page_116.tif
81c5ccd055c09acd9bf2a8e8ea54619d
e7e4a5b485290d96e3f9dcaf54c444a925f738e3
23385 F20110115_AABOOR gallas_q_Page_221.QC.jpg
23e04a44416944aeaf25da2e00380a93
359a70a311f9b461176df6d407fe08c85996377c
48532 F20110115_AABQNF gallas_q_Page_183.pro
d6ac48c0e583202e46037132d964afef
cdd75928d328eccf3b2cae036e8dd246adf5dc98
102883 F20110115_AABPLK gallas_q_Page_073.jp2
a9da0508e9186f78d342c19e3191a078
7aaf51a5233da71c084caf34803a97008c954128
22848 F20110115_AABRXK gallas_q_Page_283.QC.jpg
b59778163b8c90743dfb1e8d8afb2483
6807d9b3c731a5ab8cbd2553ebfc411d5cf01a45
F20110115_AABPYW gallas_q_Page_118.tif
59fe4dfe8461007afb72b0eb2ee9bfc8
4e48406d6f163c84193cecccefe3a49b5c8a195e
2035 F20110115_AABOOS gallas_q_Page_167.txt
02f1f82f0130d5c719179a8f1a4874ef
dc29c5457b3db30b931acc9eb1f9f742be6d6d14
41279 F20110115_AABQNG gallas_q_Page_184.pro
e5b6d31925167c2d2a2658de79ac8d33
f84e063ecdf69ab638c420713924e31c37b5cc48
623047 F20110115_AABPLL gallas_q_Page_074.jp2
79545538c8399b43ad76b8715a6767ea
60c0adc58c0e641085bec57f808c1eab3c1a475f
6762 F20110115_AABRXL gallas_q_Page_283thm.jpg
d4409ac48e2576dfdee3ea0d399b9d99
b8912027c4baefa7961d4d2bd1ac44f4b34f940a
6213 F20110115_AABRKA gallas_q_Page_071thm.jpg
0dc8e7bffc442ad0567f10b1755f8a59
0fd090dfbc0b371c974ab542f6ec67d3a969eb6e
F20110115_AABPYX gallas_q_Page_119.tif
f540c9f24ed47e8ef078982a81adcaef
26ecfc2cc1bfe16ada26c3b7aab7b708f6de2414
629606 F20110115_AABOOT gallas_q_Page_180.jp2
8132a125ce1cdcf26ca974930eeb6fee
44372b4d4f29448ef34c663995153fc169bc9d3b
22071 F20110115_AABQNH gallas_q_Page_185.pro
147acf895dfe2af410f2e7bb1cce08f0
af0bd78fbc237f357f85ae4fc9ef6285495dfe58
938712 F20110115_AABPLM gallas_q_Page_075.jp2
5fd3d79522422dad01af6c63ff227f8b
a8b86dc32872d66e11e4570472d82de08bc73673
22050 F20110115_AABRXM gallas_q_Page_284.QC.jpg
16f9da8979d7ad7ff712d944d9211f9c
54931e5997fedd3ee647ef9b1d2601290042db45
19322 F20110115_AABRKB gallas_q_Page_072.QC.jpg
34406ff5fe2af443a8cff21d9d34ddea
52b382b2eadb88a1fd291759689f24446aaee51d
F20110115_AABPYY gallas_q_Page_120.tif
1d59dd70ab2ba50f3ae17ef0987c8fa9
187f0d374c9bca6d7445bac42d8fc5be5ef510a7
20749 F20110115_AABOOU gallas_q_Page_087.QC.jpg
3283fa92d44f55c981484463ff2a71ba
bb676327a414f57e328d90b8793bf53f40ba7d53
63914 F20110115_AABPLN gallas_q_Page_076.jp2
b32a7c66c95043474458517789fe303d
c6528f02b3af90ec2021717a820691fd0c8cf29f
6777 F20110115_AABRXN gallas_q_Page_284thm.jpg
4c6693e0b9261093e65beaf79006c003
5c4f6762b65a0108a0e94073f127b7746a9e5fc9
5730 F20110115_AABRKC gallas_q_Page_072thm.jpg
0841da2d5b0a032f1c3bc7556db3f916
3036b38b8337a805843a189c97b6d2a8fa9360f6
F20110115_AABPYZ gallas_q_Page_121.tif
0512d201eff01830c2a5397812aab3e9
e416ae7810e94f25c50d6b2472857d9f8f79b427
45240 F20110115_AABOOV gallas_q_Page_277.jpg
dd5498550a701fa72fad679a574429e4
e9cad18bbb618716f751ecbbde251df401eed48f
46003 F20110115_AABQNI gallas_q_Page_186.pro
7a0a0c54abe82f0899c532062fd8ee1e
d14d487cc398397568ef7edbe93bfc7c52387f41
97236 F20110115_AABPLO gallas_q_Page_077.jp2
dbaadb691cb11675af67f64fcf1cdbf7
f13a785e7d691bb1ac45cf849807adaee32fb027
20166 F20110115_AABRXO gallas_q_Page_285.QC.jpg
dab747966668d41dbc6bbc02fe37fb4d
2552c37560fe6954664783dab196188bf063503c
22399 F20110115_AABRKD gallas_q_Page_073.QC.jpg
3b1019fad2dd3d1020acb888950ec438
e2a92d54f47298277ef98a82251f832ff453b6bb
3365 F20110115_AABOOW gallas_q_Page_228thm.jpg
56789f42608a1db0bd5a9eb92a0462bc
71c2dca724372987a96a30c631d7a7b59d3ac5d5
43738 F20110115_AABQNJ gallas_q_Page_187.pro
bdb68b09521d83b324e603f407063491
c44a0de29f6ae0f9757eba059455cff76eb58c9e
101604 F20110115_AABPLP gallas_q_Page_078.jp2
6715aed5de283ae9eaede0733484a389
950467a1378addc18d81ae744b7d0c727dd6b16f
F20110115_AABRXP gallas_q_Page_285thm.jpg
0bd63858312b5533dc89a7d91557d96c
669b25be0991e3c72035cade9dba3f34e7204f41
6811 F20110115_AABOOX gallas_q_Page_296thm.jpg
275de7c11612bf41d3e9dff702c5b5b0
c33a9e73b57ce297ff280f03a95faba84230fe27
43661 F20110115_AABQNK gallas_q_Page_188.pro
696d22de26029d5303531e5bdf6a2b04
23e6cf2046110df83bba754da1ac274de521de6c
89718 F20110115_AABPLQ gallas_q_Page_079.jp2
633f5daf88db3b544e0e9376482311b6
20a450fcd83e98d10816c1e928a753570745dd60
24133 F20110115_AABRXQ gallas_q_Page_286.QC.jpg
2e281c9bf81923dad63371f65a5cb550
d2efb8510e1bdb4c43565ce14534a65df5dee946
6646 F20110115_AABRKE gallas_q_Page_073thm.jpg
b36c8af027ee65b31794ec39d48be7d9
3ab1c0d6394fc5874c64c1244c8cba961bbe3fb5
F20110115_AABQAA gallas_q_Page_159.tif
7b291b3cfeeaaaaa9e6df493826b96d4
a2305899fa22d94dfde12cdc0476f41e85716027
5901 F20110115_AABOOY gallas_q_Page_205thm.jpg
d4957e93927187048e969fbecb18847b
b74fdb728880b0221ace4bb4d5fe4f2227219702
41257 F20110115_AABQNL gallas_q_Page_189.pro
91aab98a6003c6fb9ddd20a1390014ff
50d6ecd6230dbf92b0e8d51ab83928a9a8713052
895549 F20110115_AABPLR gallas_q_Page_080.jp2
bb4c240f9b814f5401321150073b27b0
bc1b1a6c6b84308070d5560b274a966a1286aabc
15298 F20110115_AABRKF gallas_q_Page_074.QC.jpg
9f00fe42c7e1aa6dab186224bbbc8381
822cebedc4d0d77880e484fb308ea7d5d8df9c06
F20110115_AABQAB gallas_q_Page_160.tif
7e05e6b0b04ce2dc517289a6e9a94a9b
4e79c4823bd3614259445a0c7de33423b23d5426
6993 F20110115_AABOOZ gallas_q_Page_140thm.jpg
de76736727afad7d2a36f91ac0656e59
82b578d5128f15884c0ef625e743b3123463aa52
43386 F20110115_AABQNM gallas_q_Page_190.pro
e6e381143e9a989f6570720b8f0ef889
c9d94f33203f778ca3605bd5d22aa3b795f84804
75939 F20110115_AABPLS gallas_q_Page_081.jp2
846d3e235d81b0e049b6b6d9ecd6ebe1
7e35c40aa31fb2ad375365c4b9d3d8d993abd706
6595 F20110115_AABRXR gallas_q_Page_286thm.jpg
d0e8d3bb8448a248edf68449894a2099
92735ea40603523663839f7b12dbe90c6b76e6db
4592 F20110115_AABRKG gallas_q_Page_074thm.jpg
7dff602756d466be587916ad1955b5dc
b8484a2173624a3bfe9a2c61ab2311cc6006b436
F20110115_AABQAC gallas_q_Page_161.tif
4cd11d8c8a3554beb3f4295d5daa817b
6a02e154dd16fd40683c980e01910973ee1b85a8
35705 F20110115_AABQNN gallas_q_Page_191.pro
e1d694e87e3a4784f2c65b5f147f69a1
63d134508d9fb4db381208c5689c3c04c8df2d13
1051977 F20110115_AABPLT gallas_q_Page_082.jp2
a7b45792ba61a9614832bac618768060
5a09559620bd4cbe9dd0a5a330f1f670f2ce2bd9
18779 F20110115_AABRXS gallas_q_Page_287.QC.jpg
3dd70e5b4f3a4a78c97f2523e4c7053f
ba3eb8f282daccfd8bd3666d3a2f39018b87c2d0
18514 F20110115_AABRKH gallas_q_Page_075.QC.jpg
4cd1e18e0c77db167e70ed785bc7448e
a4508a6cdbdbdadf1b62cc541442126bb8487dd3
F20110115_AABQAD gallas_q_Page_162.tif
7aabbd16fd087b7574bf40980b3cb16d
d006483c4ff00b4f012f30d1cedfe65770b21e87
47870 F20110115_AABQNO gallas_q_Page_194.pro
7da462a144c0e893008be8081631b758
f7094a58b65490488d465da4de1f23255e196caf
92150 F20110115_AABPLU gallas_q_Page_083.jp2
20bdfcbedbd2ed69548785706d676494
468ef27fbf65f12448f9408d6eabfbea2500bd72
5519 F20110115_AABRXT gallas_q_Page_287thm.jpg
6b9ba4f9bf7206e8dd2f0f9dd74a1643
3ddea5adb8b195a1a35ef44edde499c6d394a356
5389 F20110115_AABRKI gallas_q_Page_075thm.jpg
1ffa0b7f2cf770ba86d1c280a6be0cbc
de159b0f577f5ee22b0bf62a73f464b23c97147d
F20110115_AABQAE gallas_q_Page_163.tif
e1dc9af74ca1b25cadfc8bcc5b3e1d95
3e0f5d74b3d8fda7b40defdc86751ec5320fd129
33085 F20110115_AABQNP gallas_q_Page_195.pro
9f9025aedfefd73f7476c1041c779f2d
fb74a9df891e2d0953a0119b54c1af134c513390
1008683 F20110115_AABPLV gallas_q_Page_084.jp2
7a409577a0430beb9715055131cf68df
b0858d91a691e6016b2df5d4afcd0e9b5a4a5733
19326 F20110115_AABRXU gallas_q_Page_288.QC.jpg
8633d0493f97d8e59ae8c55d1a10f063
f71db29bbfaa55238ec2605555eaa0835135d689
15008 F20110115_AABRKJ gallas_q_Page_076.QC.jpg
9a9d10ee1faf8609985bdd8ba760a0a0
e04a6f799cfae991178bbdc99a35cf690413754c
F20110115_AABQAF gallas_q_Page_164.tif
74741b886606021833daa23bde268336
f5e4af7cbfbf0baf1f4d89da44958244ac9687db
41290 F20110115_AABQNQ gallas_q_Page_196.pro
617065583fe3349c69146db9f5b44052
f1facca6220f7eee09a0e20960d0e6ad4a0154b8
F20110115_AABPLW gallas_q_Page_086.jp2
b5f19362d0165934ba018d188c7a21d9
edf0745f2fab1c80c1c5034b0fcf6d1171dad6fe
5634 F20110115_AABRXV gallas_q_Page_288thm.jpg
118040057f528aa074f0413b5052275c
7d4dc9d1cb8624e7b1341ec7924ecaf26aacfa0a
22098 F20110115_AABRKK gallas_q_Page_078.QC.jpg
5cce3ed7e8b04f17fc7a93c3e037cf62
ef72decffacfb006752576531480a354280b0319
F20110115_AABQAG gallas_q_Page_166.tif
3db34fd1efae4ded86f398cc02066c3f
252dd0a1b280bc5d4b60da9c8db22f7c2901a8f4
45404 F20110115_AABQNR gallas_q_Page_197.pro
cebcd7dc809bfe98a302656d101ce022
fb4f7576e37c92da941cc6af43cb6bcf32cc4464
95502 F20110115_AABPLX gallas_q_Page_087.jp2
f637db95f2053319c7fafb9d73452f82
7269a60deb22f662a7781756ec03f3fb079f14c5
11715 F20110115_AABRXW gallas_q_Page_289.QC.jpg
2f0477570c2d43a0bd13190cbe3d9d87
eda86f4db53bb0bec7366f0305a9fc648950d480
19819 F20110115_AABRKL gallas_q_Page_079.QC.jpg
aba2ee1e081b9dc5315ba683759f1768
c1822781dbef913daf0980e0bc5b1cdfb6518ddf
F20110115_AABQAH gallas_q_Page_167.tif
b8ad5cc895988b682c3beedc3006d3ab
b938e2b7824b5fa215ca769a9623ed31c5595e23
42383 F20110115_AABQNS gallas_q_Page_198.pro
1fbd005bb3afe3e492fdbb7e30c5bfa7
34d80c017d5174d181a4ca8ba3c05eb1b48f18fa
109631 F20110115_AABPLY gallas_q_Page_090.jp2
cf8ec4c078c4c9e6629ad297efcf6990
fac0388aeeaecf92dd48ac4f231cf9ea617fd542
3783 F20110115_AABRXX gallas_q_Page_289thm.jpg
fa37eedb7c2961491fe200ffd0874025
720d8cce4eea87443483efb38d8f8a5a7caa472f
5879 F20110115_AABRKM gallas_q_Page_079thm.jpg
74bcfaf2a11ca37140e09a0183f054b9
5ac273cb7bd2c86c5fb44e55a85c9a4e92d2841b
F20110115_AABQAI gallas_q_Page_168.tif
39ac7822d4e70ab0f9692d4d9615469b
a6dc76ef24ae963e5baa927cfbc2dd8f8c070389
32146 F20110115_AABQNT gallas_q_Page_199.pro
b2194443b6120604c8d660c6ee133c6c
ac44a959c6dbac758099f553f6b778e702f7c82f
1051973 F20110115_AABPLZ gallas_q_Page_094.jp2
76f2abd1b472c2167f3383d056cdb4bf
542bb78737ab4801a8246e64a97003a7c707f72c
4857 F20110115_AABRXY gallas_q_Page_290thm.jpg
0116ab6ed55bf9b4d6ee73568169e334
ddc745f65d4fed8231358aa4d73e2708d978ca5b
21721 F20110115_AABRKN gallas_q_Page_080.QC.jpg
d73a8acd2738fe5354d59346cc38a4eb
ffcfabe45a3b4024b7cdc85d6f8c50dc6eb450ec
F20110115_AABQAJ gallas_q_Page_169.tif
242ca305ac67f916a3b63db14c691f02
11d274262ea0dd8061ccee2431a6deafe2b0b3a6
30150 F20110115_AABQNU gallas_q_Page_200.pro
080fb10f860c327e6a0f80a17fef7272
96603de9cddcdf39cf6affc59fc2a6ad016f7885
21834 F20110115_AABRXZ gallas_q_Page_291.QC.jpg
5136cecb4ab7d88f6b0633b9819f2373
e3b0295a96cf17040005f76df8bba61ce3235057
6692 F20110115_AABRKO gallas_q_Page_080thm.jpg
ad72d093bdddcd5ac4c80990a7c2c10d
491ef57f286b2e08fd2965a3efc3d202db110870
F20110115_AABQAK gallas_q_Page_170.tif
672d0c6cfdd743e6f9dc0c9bf045c230
2169f184e5d57666dd592dac648214034a35ea11
24313 F20110115_AABOUA gallas_q_Page_220.QC.jpg
e6af28ee16064050cc1058b2026595b5
21e8f67fbffd2aa68adadf4d1e0bbdff5ee3c98b
32905 F20110115_AABQNV gallas_q_Page_201.pro
2bbf100b8f7013ab181340ab1b6f5777
70b93849fd4e014faf19d035c0b453c7ed197c42
16871 F20110115_AABRKP gallas_q_Page_081.QC.jpg
54da028163cf9b2bf9694c2d4448644e
b3c630aa6c1ca2279e7d1d59274d1760543f2dba
F20110115_AABQAL gallas_q_Page_172.tif
d41fc7b102d547b678abb1d00ad94131
c81023f29f3a1833e0658137551b1e40fec89328
2250 F20110115_AABOUB gallas_q_Page_064.txt
c43c9cd2f2284c8a383a7ea293634e07
58f90d32a9fbf808827feca4f9756789a80fd4bb
53222 F20110115_AABQNW gallas_q_Page_202.pro
16c2b66dd7c4135a8f95a33ab2dd811b
1ef7fcecfb4cf2c8d185d9b56624d9d81d537fd0
5283 F20110115_AABRKQ gallas_q_Page_081thm.jpg
70f4ebe9952f2f27c888f85732f42ae7
f3159f48bb81bebab3082d0faf235183ad2aad1f
F20110115_AABQAM gallas_q_Page_173.tif
db9b07974ec35e9e753a96cb546feba7
34be86d98913e31bc800b922e0a49272ad1f11cc
1051984 F20110115_AABOUC gallas_q_Page_128.jp2
317790cb5f18e6543ba966ea543b3e90
3231d8d5e6f73f84739f3b07181b9e7aee8f146d
19467 F20110115_AABQNX gallas_q_Page_204.pro
ab733f4876c77076ac1e6e27a641d8ec
89e00497be80ac343d719b02ba52381be487539b
20917 F20110115_AABRKR gallas_q_Page_082.QC.jpg
b3e63c48a35551dddab139a695282a2c
369ca5aa7800988c13f948356d99f7b56cc76a60
F20110115_AABQAN gallas_q_Page_174.tif
09166a7e51cbd2b2b0528a7428c44f58
47c4cea51a296de0cb4ed19ca02148f48cf8d61a
F20110115_AABOUD gallas_q_Page_330.tif
4c7d5691e3bb03940fdd3591a4574f2a
aea24467940474c03157e3a1769a3cfd288937a6
38162 F20110115_AABQNY gallas_q_Page_205.pro
a6b3d68762fbeb189231dfdbbd4e5238
209e71b944fd458314248a31e3963e1e73b7341e
6047 F20110115_AABRKS gallas_q_Page_082thm.jpg
9eadc9b21061aeef671540a97de9d8d9
3ec69555a71095d945663fb0cc15d9c22f292b7e
F20110115_AABQAO gallas_q_Page_175.tif
49c275b1b985c55e8cf3844981d52b17
3ebbf97a7e0f6a73d019f99880b685a7d591a1ce
60942 F20110115_AABOUE gallas_q_Page_307.jpg
331eb4706221731c9459b5e24b7dfa82
26dbaba00d192077bc2b6962b5ac37e2de3311d9
29286 F20110115_AABQNZ gallas_q_Page_206.pro
3930f965f5c65897d80c402fe11db0a1
1622e8e684854d7f69d68cfc1cce0b76e35a8e64
20586 F20110115_AABRKT gallas_q_Page_083.QC.jpg
ef2c06a138c7b95b46c8a16666d5b2da
366b07c75c6442b7aabdc37a0e2cad2a6e4fc79c
F20110115_AABQAP gallas_q_Page_176.tif
f933614d45d347a0ce844bd71a1ffc68
ab6cb900b6f593d0cf6b377c749141b54c5ab9e2
46691 F20110115_AABOUF gallas_q_Page_351.jp2
452deae429256a798d64e693da618843
d35712f00b7bace7d0b7187f490449550e444476
21176 F20110115_AABRKU gallas_q_Page_084.QC.jpg
91130efe320e3983162cd4f8a8f212d9
b726031de0819303f2423b8d950cdc45581234c9
F20110115_AABQAQ gallas_q_Page_177.tif
7e7d0f657df08e2ce6f355dc589c3866
ed127bde9a941818c20c9dbac8a0c568e191841c
1756 F20110115_AABOUG gallas_q_Page_076.txt
a232ad8383a2c3782cc4312f2f959fcc
b31ebe3ac68f3767670c8d218aef04f2037e2d1e
25569 F20110115_AABRKV gallas_q_Page_085.QC.jpg
969274ce62f185b03f7b8da43a96ffce
4a4115d9ea1024bbf08fd0f94d3ff1896c48b687
F20110115_AABQAR gallas_q_Page_178.tif
cb7988de68c353fafa4756009f9b6f46
1a3bb69c4c44adb7d619c14addd043ea06fe1dfa
107048 F20110115_AABOUH gallas_q_Page_088.jp2
7421a9a08e8601e2302faffd9375c123
684faab59b7ef34b2baebbd42c4966939e6175f6
102051 F20110115_AABPRA gallas_q_Page_256.jp2
5e3e864121f705aab0828b501cd461ed
cce913e5c366cf3ea3b8d4dde4aa0242f045f7bc
7230 F20110115_AABRKW gallas_q_Page_085thm.jpg
d98b894db303370a097f42ecfe6b3c3d
53b51210a35dd8eb2c043051ed1f8ccbe238baaf
F20110115_AABQAS gallas_q_Page_179.tif
ee1d4f829d2f920ee3ac12f882d76f99
763cf5981259b5f49b92df0ac587318b2521b635
1220 F20110115_AABOUI gallas_q_Page_166.txt
507880c9d657074271597dc4d502219d
107138cbc86f480a2d2799cc44a5e5be4e8c8ce4
71364 F20110115_AABPRB gallas_q_Page_257.jp2
f04f9753136119b8f2f2de8f1296ae4f
cd37dbeac1461f51703c81e0362e0d25cd354db4
26517 F20110115_AABRKX gallas_q_Page_086.QC.jpg
4cf0cf078dcac27cca70d0e91b4b5896
c428ac2dacb2081b7b0ddb6b408af903fae8b925
F20110115_AABQAT gallas_q_Page_180.tif
e189855719b9f820a87214d47a37d418
665370f52729e5e37750411d0919eac3fa2d6fd7
6789 F20110115_AABOUJ gallas_q_Page_177thm.jpg
1b73c35f15ff13512a3ea2105ff1df5d
aed4d89f8967d333f33877b19bfa132fb0bbb761
1051976 F20110115_AABPRC gallas_q_Page_260.jp2
2ad6517e831913853063550112e4e619
a86c8d4b5906638d0c6484ed761ab8d5c95f9de4
6225 F20110115_AABRKY gallas_q_Page_087thm.jpg
0e76cd707d6b34406c1cc41920f0dc68
c1c63154483e992949ef7b7092df5aae5e17b3c2
F20110115_AABQAU gallas_q_Page_182.tif
146c4c9e25f0128723e4ce9b8c0c7cd6
229f8393764458d22b6ce1ec450dd93849ab3ba8
67662 F20110115_AABOUK gallas_q_Page_091.jpg
138f5b95c9aa852f653d65a469d0a986
e255c6753d361a036587335668667b0e175043a5
746870 F20110115_AABPRD gallas_q_Page_261.jp2
801d97fe213fd9f474be5270fe12691f
0950cfb62442dcd23548200463d6ab68e20c3147
23372 F20110115_AABRKZ gallas_q_Page_088.QC.jpg
b570d9bc37e978128b5703a5d0ae01a7
c7f0e037e48d7d2474264ba4602bedcea6a0a35d
F20110115_AABQAV gallas_q_Page_183.tif
2e63bde3659a3fbad79f2662c27529a2
4ee35083a5c4f588bcb26fdfb64785af789c743b
F20110115_AABOUL gallas_q_Page_037thm.jpg
9668ee2a551883abe84bde14643c6716
a2f36d8789cde58a5dd89fe2f1ef5515682904d9
1047828 F20110115_AABPRE gallas_q_Page_262.jp2
212e3f32042cad39cdf2ee14d601a8a8
d5325fa7771cdbd4bebf8e67c51898faadcc47af
6683 F20110115_AABOHA gallas_q_Page_047thm.jpg
b0184f2e92078981065b6a5bf8a6846d
ad2c04a2b5e1d3c3f53c824c9135b70acabfdeae
F20110115_AABQAW gallas_q_Page_184.tif
660f795d053cb46b34191678cf2fd9d5
c2ad7255b5856f830a2ef9ea13089738e4033969
16429 F20110115_AABOUM gallas_q_Page_027.QC.jpg
a5f6fa1b7b276e6a966d44609776c951
ed51f04b74b36a9d637b23adb09982c0dd28d81f
683329 F20110115_AABPRF gallas_q_Page_263.jp2
cb5ce852b83d2ac33799ee51f2e49904
9b4f46195b5aa94d865a9f6b1146cfb2a7d1fce4
21844 F20110115_AABOHB gallas_q_Page_126.QC.jpg
ce9cf8fe0847ae002a7cb5e841ebf197
2d529f1841741ae530c33962e643398eb3162a8c
86444 F20110115_AABQTA gallas_q_Page_371.pro
677d26db0ddfeaf793dfae3e8a52e103
02d36273ef27e1464f48da3979efaaf065d652dd
F20110115_AABQAX gallas_q_Page_185.tif
8bfd04ade6827ce3786e227c2e1c9ef7
bc1af460fab763dd87450f5494013bb54ccc1421
5806 F20110115_AABOUN gallas_q_Page_028thm.jpg
92de660e67f9593fdd8fdbe468a7e7ea
851f986d0d79cbfe3ea29bbdb89a1973a2cd6033
841984 F20110115_AABPRG gallas_q_Page_264.jp2
84cb8ffeb945ebd81002a6fadf16a75b
4065b032ea19cc4e366621440c7e57e0da34cea2
F20110115_AABOHC gallas_q_Page_256.tif
a5d2a0ee2cb38ae5364ca2614779efb7
246f7ad7b3ab853f9e39c0c540aea079789ac558
83503 F20110115_AABQTB gallas_q_Page_372.pro
7e111c66ce7096af24910a989d13d34f
0d20536083772cb04a5f8daf4878fe5235a85119
F20110115_AABQAY gallas_q_Page_186.tif
77edf1a7d517c5d35b3e6ac48b66cd2f
c659323dbf38e1de50c7ba4ac3d76cae726fbec9
F20110115_AABOUO gallas_q_Page_282.tif
1695234a7eed3c53d3cdd0a09524ab8d
ffc4a5ca7b46066b2f06e637533fee5c44483844
918528 F20110115_AABPRH gallas_q_Page_266.jp2
fb896167eb10702f893cfe75bfe1123d
26e54fa212daffe10eb84154636c3150ca06d144
F20110115_AABOHD gallas_q_Page_187.jp2
8ddc1bcc12c5b8fd8f3e9bd33fde9748
e45b615b589b0fd0f6c75ed60c7014a9880d6d91
38606 F20110115_AABQTC gallas_q_Page_374.pro
ce8118cda832cee566e9859bdaca80ff
5b7396d8ed61715ef5bf3ad8877b9562ebf9590e
F20110115_AABQAZ gallas_q_Page_190.tif
d87bc407b2ac1cf58f21d91a2d62f243
aabf0808ee71ac839a9eba321bca6ea9f910667a
F20110115_AABOUP gallas_q_Page_098.tif
0dd6ef1680892011919b2dada59a55b7
994549ad92db68d4feaab1be9fc58aec8e3267ea
1051958 F20110115_AABPRI gallas_q_Page_267.jp2
b7a964d55d5e3f328807e8bbbf82b2a9
d0189ef74d138ac1c6ba22d46608135f9ef0653f
49305 F20110115_AABQTD gallas_q_Page_375.pro
359fec31638c2500bf9ba2ddee4c6ac1
80d0fa278a921012b04842553292ded6ef7aa309
5882 F20110115_AABOUQ gallas_q_Page_254thm.jpg
8bc1b99e49c878700b48e950cef149b7
1b28053311a0cc7de2be4fcc12ed9371db3ca05c
104849 F20110115_AABPRJ gallas_q_Page_268.jp2
0b3451b94cd35fd66ccfe5e66086ca3b
4e2b2c9551687570639aa26ac86d749190c8ddf5
6287 F20110115_AABOHE gallas_q_Page_243thm.jpg
ff5648e0f696294f5fbd9d12c6740491
d98a3c50832ef3b9c6fb343a8fc2b2184632dcd7
59241 F20110115_AABQTE gallas_q_Page_376.pro
37aa2c35e6827cf3a16fec5b6303152d
1fb4123a0b9855e62295f6d0056f8ec78237bf30
96947 F20110115_AABPRK gallas_q_Page_269.jp2
e6c55a5324e8738ffc9023d1119ddcb4
7dfe53c1af39aa8cb14574374ddd32959179a375
94474 F20110115_AABOHF gallas_q_Page_291.jp2
418a12c3ecdda1edf4362b554732fe9b
0c20d511d9e3b06c11a785c56608d2339476d327
60465 F20110115_AABQTF gallas_q_Page_378.pro
5df1108a305daa1642d2410b5f06f327
62894b672780734b9eef4afc84db13d0eaab20ea
34014 F20110115_AABOUR gallas_q_Page_357.jpg
3a7b6a35f3afc8f4bea1ced5f8cb47a1
def808e62283d9de12489176b07443c5aee7ddaf
92879 F20110115_AABPRL gallas_q_Page_270.jp2
4f434856a63f288776e33edf4b228854
859f0c30f473532e058625edb7382a1154595b0d
5849 F20110115_AABOHG gallas_q_Page_008.QC.jpg
21e005bb90a5f1339e28303640dc94d8
a84497d5ab66f5e8c0e32731fa17244baf8c3edd
59136 F20110115_AABQTG gallas_q_Page_379.pro
d1e9a4846e5f094e64933385b9a72e4d
3666e7d86e6c2fa3a3573fb43504c79133f5887b
55348 F20110115_AABPEA gallas_q_Page_225.jpg
ac3d9f999363971e7ffd50b4f472f301
dfb1892002a73380feb1b4b16fb530aabbe436de
33480 F20110115_AABOUS gallas_q_Page_203.pro
cdcc579b29785e4430c5f30bd200b839
10dcce6fa988cf0b7176de7b4a30223c44193f56
71531 F20110115_AABPRM gallas_q_Page_271.jp2
176c6edaa145e8e0bf166c718a53716a
3caf8713300361b10e339c4ccf07330deaad0992
6820 F20110115_AABOHH gallas_q_Page_176thm.jpg
f2c742ba3e375d5e93891304c1e65232
b3d995d3921583fc40c222d8b2175355065b7572
22872 F20110115_AABRQA gallas_q_Page_166.QC.jpg
39e9954ecc64b7f120f408b17a4ec964
2dea1522d2b34c4e73520a8d30e41f9f5b6066f7
54572 F20110115_AABQTH gallas_q_Page_380.pro
3a8110844578cb832188bdb54e4a9e98
b4215b01a02e0ef5cd2739dc02b496d6ba51c338
33741 F20110115_AABPEB gallas_q_Page_228.jpg
aaa2f2516088b7de6540166712f4a924
386cab57a3cbb123746581d1a23ad91341da21c4
1974 F20110115_AABOUT gallas_q_Page_088.txt
7688e2b879ec38fc3b6c4ee894a7499c
8e1e4e24f4c37b639d0a03e94f0b981dbb39fef3
4813 F20110115_AABOHI gallas_q_Page_200thm.jpg
8386ecde1566a5060ab72ba2305fc638
b087137bd17d9375595f3e6d089b0da022ce4bc8
6644 F20110115_AABRQB gallas_q_Page_166thm.jpg
8cf72924e7016b3f648865b28390336a
8633aa4e0f5b8f24de37e6ffc45d0fe001dcdc20
59740 F20110115_AABQTI gallas_q_Page_381.pro
3405a0108b4adf45d803ad5970e80ff4
01ce1a749db81a04be258f534ea872f9f93ff53f
70551 F20110115_AABPEC gallas_q_Page_229.jpg
6fc19be9be5bae2cdfa484b2dbd302c2
68dd8e6993332470d415b528661dde3637dd92da
16366 F20110115_AABOUU gallas_q_Page_143.QC.jpg
15a9f541758aec067ef901672d8c8299
1da7e783d029844db7cbad9ce64902af1e83c7e2
73397 F20110115_AABPRN gallas_q_Page_273.jp2
e46e76be4f513d8d1d6022e1d42e4cbd
ede88018d6b78837c98daef24ae50bdc20ee71f4
63978 F20110115_AABOHJ gallas_q_Page_332.jp2
dbefcf720eed0b17e0d1f94fb0b0d513
e731a600833d878e1fc7dcf56bc096686d67f993
6420 F20110115_AABRQC gallas_q_Page_167thm.jpg
fee5d4507b82d5639c91cc8793ce7c72
a3e93657cf22b5fdee21ac88e501c56d225820a0
59103 F20110115_AABQTJ gallas_q_Page_382.pro
2814dd7ce7e9c26e9a8015adfbb8278e
b186488478d4946aa7fce8b8fda22ffc73a69493
46645 F20110115_AABPED gallas_q_Page_231.jpg
fbfdfee759ed82146279381f53349eda
0a1c57a346de5398d87878e8286de512bdb82356
103003 F20110115_AABOUV gallas_q_Page_366.jpg
fd08b5f82a5e5df3e4392909f5fe544a
5ac1be52b131d097d5ec3307233fc54cfb32b3ea
762287 F20110115_AABPRO gallas_q_Page_274.jp2
9997748f607dcfe1d877d3a57c3f3b61
58bd053f74a2bb24b02ee7314ebffc6c3d7d7ae6
102485 F20110115_AABOHK gallas_q_Page_373.jpg
c09c49cf8b59cdc84876226f592968b0
2c06e495159b3d45dd54cc4c9b14c7405c08d87b
19572 F20110115_AABRQD gallas_q_Page_168.QC.jpg
e58bb16d786f798c7d4c81328329c105
73436ebfec5217263b1accd25bae291d0a21d56d
27590 F20110115_AABQTK gallas_q_Page_385.pro
01e9c76cfba2c0c8137f651e4b1b28d3
aa05055cb2195a194d6d99b907832e723b36000a
57857 F20110115_AABPEE gallas_q_Page_232.jpg
57b2435adf5ff43e9561392562a3f014
5381e5939c642bf3fa8b57fe473226fb801a3f31
F20110115_AABOUW gallas_q_Page_080.tif
e827ee96a1f1c3af4515e2bed3761ec7
4c375706cf73b74108651fb35e1813cf4e61acc9
787233 F20110115_AABPRP gallas_q_Page_275.jp2
4cf7594535e5d41e4b459bac18c78b37
c9dfbac3b245d86140c3ae17f77c61e523fbc47c
2383 F20110115_AABOHL gallas_q_Page_009.txt
3e4e6cb2aad61e4f917a5d3bbdc8bf5b
7abbf25a8db5df37cbdd171380758b41b4a81ce2
5539 F20110115_AABRQE gallas_q_Page_168thm.jpg
78d68c46467a5fc549c60cc0c7e4a648
260a063b9a0ee7ebf08a6706fab23b902c597ac8
26478 F20110115_AABQTL gallas_q_Page_386.pro
d6979250534a5901028580ddd961ca2d
f503884a13109620434344173d7ceb683586f738
F20110115_AABQGA gallas_q_Page_345.tif
d7916c52bb2a361bc025df4a7930275b
93f0067247c17920bedbf342d6fd550223b2e3d5
62118 F20110115_AABPEF gallas_q_Page_233.jpg
5b9fb76ebad2e32536a3b6dee83c616f
2ff87faff80db7af01b5dc7408a075a2e5af0088
51320 F20110115_AABOUX gallas_q_Page_081.jpg
bb37864ba9811503f28d09b446828a3c
748f7962337e3f596fdffb95a2534d64fc794aef
768176 F20110115_AABPRQ gallas_q_Page_276.jp2
9a15211480e57fd3e08acf7338dce048
c6e7c43cead5d928513f2bf74eded37e2529c376
4710020 F20110115_AABOHM gallas_q.pdf
1ce6802759a5a0337d6fd0e17e79ec2a
406a15f6f853943542cb5c2d564e33e9d258342a
24247 F20110115_AABRQF gallas_q_Page_169.QC.jpg
67c7db8511272e05b506a9b867efc4b5
a502bd30579d0ac33e2a99c63365540d32326b3c
420 F20110115_AABQTM gallas_q_Page_001.txt
d54761498cc2efec8869cb3c48860bab
6d7e3bf6f77e607bda0b5f7266ca464f8fc7b08b
75125 F20110115_AABPEG gallas_q_Page_234.jpg
0904516aba6bb69663e86e5ee9c90ac0
947baf0e19740aa6b794dd6732cd9aebcc8c53b7
7193 F20110115_AABOUY gallas_q_Page_240thm.jpg
0a954fab4063af70ca9fc27b16c14e2a
bf41429edfad9e3ef9d6bd27f6da3e917900d986
776718 F20110115_AABPRR gallas_q_Page_278.jp2
f37d6b0eba9f2f744bc934dbad8958d5
0562454fbaf3436618f8a845b7db651f649b5774
709 F20110115_AABOHN gallas_q_Page_313.txt
ef587ccb10a7e087ca68f4f8f557f8f2
a2153abc7edd219da74fbcfae6d1a1b733c9524a
F20110115_AABRQG gallas_q_Page_169thm.jpg
bee21915393ded0e123c628ad3b375cd
4eaeee45c86b444a1c2d4380053cb58f335ee6c4
177 F20110115_AABQTN gallas_q_Page_003.txt
39f63fa056a8e7763e5f9efe7687b35b
99fc366dbefae5f9e9356fb6a2229ce4d9c42ad9
F20110115_AABQGB gallas_q_Page_346.tif
5a04fbc08b5e6794f32ccddd592a8502
f7c2a3c2c7be0bae89e780c8cae1161036f0221b
71104 F20110115_AABPEH gallas_q_Page_235.jpg
81dc7350bf5b562864226664561a4bd3
fe00dff70b97413948d9ac2ea14d815111805ebb
100843 F20110115_AABOUZ gallas_q_Page_370.jpg
0af8f72a70aa3515dddd8113e143f147
275d9f0a95037e69b80ca50731b8c6c33c994877
776210 F20110115_AABPRS gallas_q_Page_279.jp2
bf999d8eba1bc0670981a01ff5c41f32
23a00a20002a990adb47404250bf557572deabf8
28012 F20110115_AABOHO gallas_q_Page_290.pro
392276515df803b3fbb0adb13eb6dea9
662f3e367506f7b4342cf65ae63c5a847d5ab6c0
15111 F20110115_AABRQH gallas_q_Page_170.QC.jpg
68c7b3cf251a80088270ca0a14ff00e6
4fe349e71503faa112d1882b7c0166981470b4f7
F20110115_AABQGC gallas_q_Page_349.tif
298ae9f1ec8c28229364860f30678c7a
2264dfceaf49c5e1be9b648970dfbce349efffe9
52106 F20110115_AABPEI gallas_q_Page_236.jpg
2b1ee8d15c883fc4c57007a2bbd86c90
ca0a7cd83507476f95bde16f38f4129defa38853
794620 F20110115_AABPRT gallas_q_Page_280.jp2
ffc2127404411c87371f4492b3163e8c
a4075aaa0705809bb68a0621b66da727ec9acc8d
20194 F20110115_AABOHP gallas_q_Page_282.QC.jpg
10c1ce43b18c263cf6a83a5040e81e7e
3ec66914d1f9c7775c29128cb12cc320a7a8bb34
4524 F20110115_AABRQI gallas_q_Page_170thm.jpg
0a2fbc7b67c7ce0fd75621efdb94c0c7
da80a1ee34f2b12c195bd13df2f342c81e18119d
1285 F20110115_AABQTO gallas_q_Page_004.txt
099e62e7b38ced78ff4d131713e1f806
4513bf4a42c410c02804d84ba90de85007910cd7
F20110115_AABQGD gallas_q_Page_351.tif
aa190f7c785a79f7889239176394f564
b9220b46ddb4a54e95e15e9026df490b32bde2ce
50136 F20110115_AABPEJ gallas_q_Page_237.jpg
2b07f15f642b7e70efccce566eb4fb22
358459600fa0f71e30916cf595e5611b0a300eec
107492 F20110115_AABPRU gallas_q_Page_281.jp2
8466ec38945c38834439562e194ac3fe
ec116a0074830862e57f89b6c731397cdfa2b7f6
103104 F20110115_AABOHQ gallas_q_Page_221.jp2
b62be5681802c3ae4eede86680274ff8
8aaf1a761e1c867c254d0af88d7299ed41a8aa47
17839 F20110115_AABRQJ gallas_q_Page_171.QC.jpg
c62d724010e09dac9d3d81950c309ea7
2be649a9cf8167f405c52ddb698907682fe90ef1
3098 F20110115_AABQTP gallas_q_Page_005.txt
5e1f3ebd975579e1cb406dbbd0493010
c76dea7125604080446ab8f325dde4e48a100ff8
F20110115_AABQGE gallas_q_Page_352.tif
18b2e4d88e9888c6dde1df48ae5dd965
09ea267a625aeb0561dc1529e5a8cd8bfe31c907
65748 F20110115_AABPEK gallas_q_Page_238.jpg
63fd76c0ec7f883a7f0dbd6d6e64b716
5fbe8d947b3ac0146cfde9fc003517f10e617446
1051920 F20110115_AABPRV gallas_q_Page_282.jp2
5caebaa46fd828665c8a9d875c64adbe
644d63f46966e02e4b87f82be548d0f7c3ce8476
1815 F20110115_AABOHR gallas_q_Page_186.txt
17731a4bd58aa787e0dd86897012c5ac
d47ea928e825acc12e14e19adb2db6c4c5bf2e01
4389 F20110115_AABQTQ gallas_q_Page_006.txt
de35a0b0c2ceeac9832b4db7d6cdebd6
978afc6202d308f99be321f033daa010ecb812e8
F20110115_AABQGF gallas_q_Page_353.tif
e5e82a524295e28ba43ecb742cf7158f
d45d878a64df5171089fbfd2121cf96476fa2d2f
77379 F20110115_AABPEL gallas_q_Page_239.jpg
fefd7bd4c08d1a913242a56463fdc882
fcf9637544ece8c4a2754bd97462d576e708afd4
1051960 F20110115_AABPRW gallas_q_Page_284.jp2
5e2292c492aa4075b8100382064967c6
aedf1b3019fd14b8ebb2df0dd2c8886ddfb510cb
45553 F20110115_AABOHS gallas_q_Page_357.jp2
19ddcbb91b24465ff748018d14f25930
cacdb11c93bb2b1d7538861db3459ab8105dcda6
5269 F20110115_AABRQK gallas_q_Page_171thm.jpg
af0cfab0fbaad3e4143842f5e3147a58
ffe3f22abaab7fef53c6490929b3d9b4b2d051c0
3612 F20110115_AABQTR gallas_q_Page_007.txt
c8bd7f285e26afaebb965a93223399d2
6e3cb9f6b9d4e36fdf5cffe22350a7aaeb9b0950
F20110115_AABQGG gallas_q_Page_354.tif
aa1ed49686a2b07ec27bf5b88dd2bf27
b6850ade68a081e21b3e0524192d70b2e79a4571
69413 F20110115_AABPEM gallas_q_Page_241.jpg
0e9e5be09a00effc87440c7630fba3ce
6537ed559a268afe1f8af1627948705a69e9e17b
84941 F20110115_AABPRX gallas_q_Page_285.jp2
7d829ca4bb0f9ae14cfb99aab2406c75
fe5d1b774dae800e74a1b097faffd88b2c921bc0
F20110115_AABOHT gallas_q_Page_078.tif
f29ddaefd178a47383554e3117237035
05f362987724b56990d77b62ec9e82bf37d27315
21584 F20110115_AABRQL gallas_q_Page_172.QC.jpg
1e15fa84b36eaa93d64d001ea08cdb9a
dbfb86353a5f9e483ce9e16a5917f55e328154a7
1301 F20110115_AABRDA gallas_q_Page_309.txt
4db777c729f27b248f96f736051b1a72
d6a2adb6d2450293a981d612ee39a21ee076f547
1281 F20110115_AABQTS gallas_q_Page_010.txt
9b5e1ee8996ad34ff6c69f6aeb6690d8
868827f29f321d3eb2f8df9963400db1ac729016
F20110115_AABQGH gallas_q_Page_355.tif
821f9e10346a356120a459b9b629d771
315cea614d73228c9bdcb4e9fd20e49d43ae923a
71733 F20110115_AABPEN gallas_q_Page_242.jpg
44987d9f7b0beaaf2836b22447e38db7
0a7f77fbd97e725084faf32c0545960bb179abda
105919 F20110115_AABPRY gallas_q_Page_286.jp2
b78eba3359877ffd8db437b6e5fac309
29766aaecee8a61b4b1f033db3172c15f09918a7
23735 F20110115_AABOHU gallas_q_Page_047.QC.jpg
cb0749698beeee55c6d6fe6cb03bd91d
f1e32d49f9a5ed885f8a1605b74766a6de4e0e0a
13920 F20110115_AABRQM gallas_q_Page_173.QC.jpg
4326985e76fed9cb4055a3c0b4c11135
4b33722374a3df735be41848fd8d8cf1cf6354c9
1656 F20110115_AABRDB gallas_q_Page_310.txt
101b3f22e253db6f006702530fb9da3d
c07925648f10cfb47b0371199daa56e0d3915f4a
2406 F20110115_AABQTT gallas_q_Page_011.txt
360a6de93dff3a263e7873e024a5d616
1ff17d1eb5c45a32fc961b07e4a395135e6acded
F20110115_AABQGI gallas_q_Page_356.tif
87dbd27c38c8c552ed1869213bcc1c22
272bdc9394846968d073b8668b0b613aa532ac33
67078 F20110115_AABPEO gallas_q_Page_243.jpg
2d941d06470f88923ff005b42a86f0f5
b325446269610b19b75268fb9a13befdfe84afa1
940925 F20110115_AABPRZ gallas_q_Page_287.jp2
f67c45243569b27cd7a6f932da1ff235
bc55d62ae9e5bd9b38e427eefd4d24b7f511ae33
98365 F20110115_AABOHV gallas_q_Page_243.jp2
f4a8624c833ba91482bc7c41289124f8
347afe3fd132f026119564e1d749f12470f0852a
4149 F20110115_AABRQN gallas_q_Page_173thm.jpg
0a107e21527c927ef19958e952a8b74f
ec15e5f375c69e7c2f7c2771c1770b1da3122a15
1574 F20110115_AABRDC gallas_q_Page_311.txt
7242073ba4e67b1f4daf85e3342621b9
a9a55d4acefcb5e18bbc79641a2b2465518ef3a7
2940 F20110115_AABQTU gallas_q_Page_012.txt
6d5add41a4aec0a5854aea6763c9445d
3c5d685d2d443160c1a5000e616ec023ae81c947
F20110115_AABQGJ gallas_q_Page_357.tif
6d28c1b7739370768f74119df277eb1e
8abae4248fa2a7224aec7348ebb0797f2052d8c2
71954 F20110115_AABPEP gallas_q_Page_244.jpg
1a4887235c7d9f0af4f618834529991c
0348101458e4c44eaccad7a16f40cb8874c37d7c
4525 F20110115_AABOHW gallas_q_Page_076thm.jpg
2b94d8d4a0bc61e35496b39af59bd749
d2cd5bb9bd2b98b2aeef0ee45de431a3e9d920e2
22125 F20110115_AABRQO gallas_q_Page_174.QC.jpg
cff3785fe3d479233650b95a17e2821f
bd7cf8eacd0b58f1bd5ab4c22afcd4fdc40715e5
1625 F20110115_AABRDD gallas_q_Page_312.txt
edba7d5122c7a9e565fcc82bf58d7305
f8192ede7fc3bdbbd8ea887a4ca8e6fdbe32487b
3033 F20110115_AABQTV gallas_q_Page_013.txt
266acc7353565495469956038c89c336
c97feed457166d4cfc6b8dd31010605cb4876a7b
F20110115_AABQGK gallas_q_Page_358.tif
9372f8122b410b18e85705d99bb28b98
712ed9f0b023f0127ded7c1f089ce4f6560a4b6f
77809 F20110115_AABPEQ gallas_q_Page_245.jpg
65bc4fdbce84c6fc9f4276cbb7086397
578ba812d13cba555f89b2b6a48f1ba5e9f783c3
25740 F20110115_AABOHX gallas_q_Page_101.QC.jpg
fcef9764a6899ea060bfab5d83384d81
a7bd3de5392a1596c40b152e35ce2315dc66f05d
6408 F20110115_AABRQP gallas_q_Page_174thm.jpg
d2d9fd907799da2d0f51e40efb7dd459
4ac4d61ef38896935dd3bca870ed334b487f00a7
1635 F20110115_AABRDE gallas_q_Page_314.txt
6b55c5986840fc6ed8e53988434115b3
4e762e271c46d4dd032398157cd3b8713c207da4
3047 F20110115_AABQTW gallas_q_Page_015.txt
23b8e6c40ef87b93545b5d5963e9f9a0
7c9c890cefa08f3316fc3d5684fc9024db117356
F20110115_AABQGL gallas_q_Page_359.tif
e6bbf9a800f82f3ea39d5adddb0c02ce
182cadfdb2d8015f9ccf7beb5c3129565853b314
60487 F20110115_AABPER gallas_q_Page_246.jpg
c60c8e70e3791b28e9f0a08687278445
680a62c20807d206ccf958e1be30abf3f0f0410f
25939 F20110115_AABOHY gallas_q_Page_214.QC.jpg
da884993813e88fd41f8c83441e92984
4efec2c9d9bcf5462bb8705a53143c47b42788b9
F20110115_AABRQQ gallas_q_Page_175.QC.jpg
961cfbedfe5fb7ed06f8e216aeae38ac
a074b5bbeb7a9add24668e21e0fe43b80a7a9173
387 F20110115_AABRDF gallas_q_Page_315.txt
8ffb153ebce2bf60c630f2e19c943535
7cc25478fb99e96f1b18a1f7b252597a877757c7
3142 F20110115_AABQTX gallas_q_Page_016.txt
f548bbdf08c267c5e44dd9064fc123f8
8980bdbe4ac2063b18307808a703a7584d41697c
F20110115_AABQGM gallas_q_Page_360.tif
f2cd15a2b57057adb1907913f6a817e9
4436ef759f862d66658d72c1e28312a5e3150da8
57455 F20110115_AABPES gallas_q_Page_247.jpg
a647e30d9d1f2798b999a8e956ee469f
d37471857b16009ef4941264c58e11928be23f97
58202 F20110115_AABOHZ gallas_q_Page_085.pro
08806a09c48868e1debfc020a897bb3f
542c8c59e24eb16278039e979ae76e784feef7f6
23937 F20110115_AABRQR gallas_q_Page_176.QC.jpg
a7f183f9d242429c60ec46db11620730
879675d1d8149ddbba9253a46fccadb86d05afa2
1981 F20110115_AABRDG gallas_q_Page_316.txt
05522ff2b8a05df2387858c4c2829d6f
80e9a1d12b088bab00528a01df2fefb6f919d2d7
3093 F20110115_AABQTY gallas_q_Page_017.txt
734305790b209425d1f4b86f5305893a
5daf83fc38000f9c16ba764f8c6702fd30531197
F20110115_AABQGN gallas_q_Page_361.tif
6e85feedc97a785e7449604912e29df1
88f897da3693aa5755a27bacb2fab238a3d71184
60738 F20110115_AABPET gallas_q_Page_248.jpg
0da242968f7de6b3c710b8cf0a6b5fcb
4016ac96279e1a1c8a544c546523d4c4cde3660d
2289 F20110115_AABSAA gallas_q_Page_321thm.jpg
353a48d5fdbb271186fa016dac0ada89
b0e7b2c9f798b678ec3f7e84d3843f8cb0363b6b
24181 F20110115_AABRQS gallas_q_Page_177.QC.jpg
984722a1619b637923f35c60df9ff799
f407a63bd392b0f4a953517a7c25d70bb6d442f8
1856 F20110115_AABRDH gallas_q_Page_317.txt
8c87427b19964d0474fefe7774df6f2c
cf8af0f7328852538e3a17be1979be82d7aa8389
1009 F20110115_AABQTZ gallas_q_Page_019.txt
53f921041280d91b930f6c6aed37512e
3e90d3a4b4f4fa33c0c2c8ae2f61159bb8586d15
F20110115_AABQGO gallas_q_Page_362.tif
c682ddd69c2cd942939bc6e503200d32
de7d3a860e8270d5701424365906e036c471efa8
58127 F20110115_AABPEU gallas_q_Page_249.jpg
9d8aa6a4edde362ea29e2e3fd49cf8d7
8ae71f5ae1d23cd7efce631c8f88bcd3d9964872
12472 F20110115_AABSAB gallas_q_Page_322.QC.jpg
a9028848745603ee2032e0fa62f09ce4
7cf6e60bf6d3a5ddc478e67c188b4f6096909f48
16422 F20110115_AABRQT gallas_q_Page_178.QC.jpg
ceb44f4ebf789abd2a4397455f0a0291
2a46611d987e0f5d57c4df351833cfce77126d21
1034 F20110115_AABRDI gallas_q_Page_318.txt
ba5039a70cf28ddfa3426490d8276aac
79d13908b4155a18410d9b6be285e2340f5bb4ad
F20110115_AABQGP gallas_q_Page_364.tif
06ae08785e11f640bc0ab62b55f3c194
8a811070cab6598196b85a4cbc76e1bc7ba3138a
64030 F20110115_AABPEV gallas_q_Page_251.jpg
acd7dc33e7ac98f4518eecd2aa26e782
b1b31e6f20dca22b761d641b209afc669bf98476
3928 F20110115_AABSAC gallas_q_Page_322thm.jpg
d27d513b98a953b2a92aef1f68a1ddaa
3456a1a743bc1734f345d8be88ae332975d348ac
5386 F20110115_AABRQU gallas_q_Page_178thm.jpg
b751b4bff7d2f42a337b3605035e9bba
136a25b615c0533c4e4ae0a7824a8c244bc47c20
2031 F20110115_AABRDJ gallas_q_Page_319.txt
433240666cc9655fafc3638337ecc61e
00e20a1de89947690dc81fe7202a84b00e18e2db
F20110115_AABQGQ gallas_q_Page_365.tif
a74a0c2874c626e801b2167f104bba63
63bc1ee3fe8a064e7607701d87d14975414a0c87
45944 F20110115_AABPEW gallas_q_Page_252.jpg
d6a46c80d0168aee723eb95efe1330ce
a7950a071de750052e2dd3f0b01ed16c27efb8a4
14539 F20110115_AABSAD gallas_q_Page_323.QC.jpg
fb36ed8708abcbd2630bf440f5baaaa5
2d2255e4ade9442d0b3ba03c3d53ccf6d3fa76bb
18880 F20110115_AABRQV gallas_q_Page_179.QC.jpg
6e8e0851f269ddc4b1e8085ca7428099
3a3d05fbddad3bd18e6f266f6f11829d941fb7fe
1651 F20110115_AABRDK gallas_q_Page_320.txt
c68d60a8f7971a77ab4a60a93acfa46d
9572a6c6b41af86bb5576f8b2274464a24a83547
F20110115_AABQGR gallas_q_Page_366.tif
438e4e2f4683970766a1e2cfdcae8b5e
234bc2eace090fe2e40ceeef876c5319703468b6
64542 F20110115_AABPEX gallas_q_Page_253.jpg
e9161fb3c6d124adbc300d90f5936f3f
581dafad6fab894430818fb2ebbe82c1339d92bb
F20110115_AABPXA gallas_q_Page_056.tif
15f21c1b56dfa17db720009f2e7a5a03
bbba08a99bf44dc9afb9030a3f86c557fea53d51
4538 F20110115_AABSAE gallas_q_Page_323thm.jpg
607ba68d010b8e7f23c3d13b686693a9
21abf0f5cf5799af743417d0fbab619ebeb27123
5302 F20110115_AABRQW gallas_q_Page_179thm.jpg
80347e0b0ebda26ea704f2795471c82a
125549c12858d95f767aa746c7c0389adc173f80
830 F20110115_AABRDL gallas_q_Page_322.txt
9f456fbe2e20a814bfbcb8d60ae09941
0d502c834dee51ce7f8ba41dd230d33a0c5f5ae3
F20110115_AABQGS gallas_q_Page_367.tif
958fdcb7a9f3010f5aa4edf73a8933d7
11e80467feac90ad180cdb82d352840d4566cea9
60700 F20110115_AABPEY gallas_q_Page_254.jpg
8262c0b251dd591a072381b51ab635c0
c2b3f29ac5fd504161258c11439e40c964ce4669
F20110115_AABPXB gallas_q_Page_057.tif
e1fe5a667efa1020dd94344b81c3d84f
400462121ae9b012f7602aad6ece94bfd19105ef
12746 F20110115_AABSAF gallas_q_Page_324.QC.jpg
c0c8bc60832f25d9edd92406cdd98735
2af16289a4f361ccf5ad8ee5bd2b50609b660fd5
13706 F20110115_AABRQX gallas_q_Page_180.QC.jpg
9c944e0574accc22df8150bafac276b4
83e1373a266f40b7444bc62a06f3e335ad4367b1
1687 F20110115_AABRDM gallas_q_Page_323.txt
d209cc18a28479ef34260e266b2d1d48
535b99e12b934cb246148c68a3c03939dd4d4396
F20110115_AABQGT gallas_q_Page_368.tif
8dd24a845e0ff3314ed260d07d2f11f8
fcb5742a061db0a2a2643679bb3133f49b5c5c17
61738 F20110115_AABPEZ gallas_q_Page_255.jpg
3d053a95447614e0bc460e9743542efc
4547d6c6ef9f2e735894c0745d826647c35c9961
F20110115_AABPXC gallas_q_Page_060.tif
ac363aa2e1597e375f5cd2c811d48af0
7af0df3ce6abb2cfddb3b7fe85dc7c6fd450743e
3967 F20110115_AABSAG gallas_q_Page_324thm.jpg
02725b20858362948bc91391cb273ce9
68c0f758ccf40880b0578238941ad33a3effa7f2
4269 F20110115_AABRQY gallas_q_Page_180thm.jpg
4b97333fffec703ab01266eea8935b4f
7619f84886dc0b5f1444a7859082ad3a81095f35
1392 F20110115_AABRDN gallas_q_Page_324.txt
bbbb558f2e8cd9dfeacb59381f7a8089
b07647267ab4f205c7a985b5956b1448d930dc76
F20110115_AABQGU gallas_q_Page_370.tif
799dc468b6cac2d8921b8e83a78f28c4
33f048b0ca24fcee996f69e44abf92c17f0eb00c
F20110115_AABPXD gallas_q_Page_061.tif
a2966d995d663327629680b5945b1716
a064bf461bcfd383e4e697b83a0edccbd8388ea9
11704 F20110115_AABSAH gallas_q_Page_325.QC.jpg
762439443ca3860fbed0202820b70127
c85adb82672a326c79288b7ef839593f11632e4b
13751 F20110115_AABRQZ gallas_q_Page_181.QC.jpg
4502bd03ec7d17c2cfbce469fb8ff976
d86807cd2e675a52802c0294d072b1d589d913ed
1672 F20110115_AABRDO gallas_q_Page_325.txt
b9fc776eb24dfb86444fe647100cb76d
342517047dd76ccffed5f704b80b5d50b97ab7cf
F20110115_AABQGV gallas_q_Page_371.tif
1a88632ba1b574dbd716ec22ffb02bfa
e0532497eb89383d75344adae518eda31428800b
F20110115_AABPXE gallas_q_Page_062.tif
3765a261213f46f350038716ada4d881
68fa67ce89462c5235c417e4dff0fcb157cf2a4b
60296 F20110115_AABONA gallas_q_Page_250.jpg
2a961238c43df717c0c0cdcb6444f65f
d1d1ef84bcb4da7480965e0844024a2603d75b76
4138 F20110115_AABSAI gallas_q_Page_325thm.jpg
2aef1d00940a0502fa2c798c0ac692ae
adbc378ca4f633a68d59964189455d2490fa2ee2
1535 F20110115_AABRDP gallas_q_Page_326.txt
ce8f5881ac3bf8fddf192feb3fc1bdd3
4fa39d5ada9b02edafc6cdd661ccf75c12be5ab9
F20110115_AABQGW gallas_q_Page_372.tif
f9c8ac5f1f7307d22cc5e9c21de6aad3
52fa3bc16234ded18de53f63554ba6e91e2bd51b
F20110115_AABPXF gallas_q_Page_063.tif
cfbf4699f801aae9534d1596f96be8f1
0b73f1c1dcd54701b1ff2b779561c98d3b8fb652
15964 F20110115_AABONB gallas_q_Page_333.QC.jpg
57de6d85918ae2717e96ed20c38019d6
6be485a5ce953728fa4ad0f262fa02e9e1b6963f
3778 F20110115_AABSAJ gallas_q_Page_326thm.jpg
6ee9e7a317db20fc4638efe39388fe91
af70a3ec7c619620a96d99e2b32ae9c32cca2402
1419 F20110115_AABRDQ gallas_q_Page_327.txt
a9080728b645888779759218a6a23c3f
a459543cb715e96ad482b731b727b91dffd4727a
F20110115_AABQZA gallas_q_Page_184.txt
96003cb36203ad287c78813a8e75f4bf
7bc697384160b745e93b0f5b0320b097057a4f7c
F20110115_AABQGX gallas_q_Page_373.tif
35f1916efa43345336a179089ea4f121
abe1e6fd7f1606a2e2f3d220300552cc27da7798
F20110115_AABPXG gallas_q_Page_064.tif
1ce5b74c4f6068554b661cea1bb579b7
6dfb6ad639e7462ea2a11995e45a48a0af316db2
7258 F20110115_AABONC gallas_q_Page_370thm.jpg
69c71338e5262c353e1b02685eef3620
c5063f65ff33f538fd70a63153416434dd693891
14541 F20110115_AABSAK gallas_q_Page_327.QC.jpg
d5201cbd2353f1df843709a0d15dd8dc
bcdb9c8484b3d4b0beb18f229f49a7749eb6dabf
1353 F20110115_AABRDR gallas_q_Page_328.txt
2834fe5732b7aaf685c13649cccdd161
da073a42ebc6ea8c5c950825847b9beee76462b0
1127 F20110115_AABQZB gallas_q_Page_185.txt
331c036d524d95f8245dab35abe2e2f0
668790f30013a455a785df9c45e951faf9904560
F20110115_AABQGY gallas_q_Page_374.tif
7eb91a615edf694d02a24205bc1540f4
0d46442a966a618536dbb76efb602cd50a72c876
F20110115_AABPXH gallas_q_Page_066.tif
a8cabe7c958fad1cba50fc4f33aadb4e
45faaeea290e80dc2109a78b06dcbc0eff8dc532
F20110115_AABOND gallas_q_Page_273.tif
4dead8489a7536f4eda3aeb3fda197ce
2b6860c3e6d238b3243184a95942012c40ec7746
4378 F20110115_AABSAL gallas_q_Page_327thm.jpg
dca721ad4dccfe1e276ae5ecf7784cfa
a9d71f7de582e067f63639d01d7a9dd9ad947892
1309 F20110115_AABRDS gallas_q_Page_329.txt
4b890481e9cc114f9e2522b412456084
b358bc01413c72e52a84d6e15f3b01fdc7611be1
2397 F20110115_AABQZC gallas_q_Page_187.txt
c2a31bce352dc0804df99378258fd5da
0a22bd0c3626ca030406b7a93fe871400712890a
F20110115_AABQGZ gallas_q_Page_375.tif
90e767225e1f69376972576014c9abb8
0e286bc4c8b8bc59cbaa5e48a2bcb68d3c1af1ec
F20110115_AABPXI gallas_q_Page_067.tif
de1944a517e20cf7e172dbf78b3940f2
7109a935274475ec7cfcf568108cccc7a5391f93
29960 F20110115_AABONE gallas_q_Page_193.pro
1c14ba3e4fd9a15e4655552259cacf01
e1d3f17937e635cd9379edc164997cf343cdd332
16897 F20110115_AABSAM gallas_q_Page_328.QC.jpg
ddfced4ce0e5a3edaea3956a4a2cf45d
71a23cabdd55ba8f16dd74df0db7f60165548b4e
1188 F20110115_AABRDT gallas_q_Page_330.txt
4629a6704fa215a869ca07cab7b23274
6fec0b5954384195dcfec67195037e65fc7ac3d7
1841 F20110115_AABQZD gallas_q_Page_188.txt
9e68d5adad78d761d7e1cd7a230c41ea
5f7f6e7e98e40387814c8a85325eb770a6549898
F20110115_AABPXJ gallas_q_Page_069.tif
bb34e77b600cd30352b64ce47424f226
21c5c4951b9d2ce6ff158dfb3416689fce9782de
1051933 F20110115_AABONF gallas_q_Page_134.jp2
4d21f105ec4fd774ce40a2981267967f
bdef58510af0a33bd6ff07deecb5578291281167
5087 F20110115_AABSAN gallas_q_Page_328thm.jpg
5419090c4542583b2cc00338d73ae002
c6bf19c202b3fd1ac0693b799f84852969a59114
1515 F20110115_AABRDU gallas_q_Page_331.txt
9b08e47b4997d359a0713e46f0a7ec4f
87c3cfb084d746c12610d991569308a64eb67341
1719 F20110115_AABQZE gallas_q_Page_189.txt
b6cfd153136017a99a180e3db3285c20
8a70f27fa1921250fa59bab5378fc915bdbefb6e
F20110115_AABPXK gallas_q_Page_070.tif
309002f214b4814dbf776079a45170d9
9de3d1a5ad719ceb69138cb3495fad09671f56d2
5956 F20110115_AABONG gallas_q_Page_084thm.jpg
8e8e757b3e084aeb1435947a782d03af
e6728dc6514664a9fd5ae73b51b6acfbd33d12bd
11993 F20110115_AABSAO gallas_q_Page_329.QC.jpg
f51b943a510e6be5bf139fd4888dfab9
3ceb8672e8d336523b216d6c540148f399f43d92
1485 F20110115_AABRDV gallas_q_Page_332.txt
e224b3249aec8a68b439c3245a1ff8de
c0c0bc85cce7f43f48f416fcee434ce0b3d769bf
1766 F20110115_AABQZF gallas_q_Page_190.txt
c122fd31da7dc40f3b72a689e120b816
b93efd77dda837931a799af4e4f76dd6e92fcf65
F20110115_AABPXL gallas_q_Page_071.tif
321269917a1558b89a98fb327ffa2d90
cb7e0a5df98541065342740d890e1f2bf80825bc
1527 F20110115_AABONH gallas_q_Page_226.txt
30ebf3442227eb06144dc33f3323c5d3
ef5d8acc373ef0d319ce06b45b5fa3cbcd6fcca8
113742 F20110115_AABPKA gallas_q_Page_029.jp2
8940a2508f8c4d2194ca73280876a74e
d6de8fea8031dcf1e3089dacecf010f8da13267b
3955 F20110115_AABSAP gallas_q_Page_329thm.jpg
1d79f1daadfd8ac0b9eb0bd7a3c41727
2f96e786b8345f70ead8f679367a8b1eb522fe6b
1711 F20110115_AABRDW gallas_q_Page_333.txt
1652c75d40b6d030bdb4813e0b0bc0d7
8cacd17963c74699b16e0d3fc50f8bc31b51c7de
1804 F20110115_AABQZG gallas_q_Page_191.txt
26f5b197d13e245c6ff0a84f4540c4b5
e9b050f19e6179e0436b32a5bcfb10b842e88090
F20110115_AABPXM gallas_q_Page_072.tif
6224301486e96458fcc5947b9db9a5b9
0e38e67812955e3ce0019ed2e589c4a6dd0d0ff9
3712 F20110115_AABONI gallas_q_Page_003.QC.jpg
a0e9c7d82ad84a51e755bf999f7bd063
09fbec0ceb44e142fc25e34724960a9d902ce012
107277 F20110115_AABPKB gallas_q_Page_030.jp2
704c8414068846f8598f05d61d0ce8cb
1a9b248abe1ff7a6db967898e2e393ee7231a54d
12365 F20110115_AABSAQ gallas_q_Page_330.QC.jpg
27703bfc75213bc88980d88c7969a430
1638c71386bc47dfb023462faee3ac624094b027
21866 F20110115_AABRWA gallas_q_Page_262.QC.jpg
b05f48f7a7d20e4c4a69430723eb51b7
128b08488f2bb404307aa5e60945f3dbf9a16505
F20110115_AABRDX gallas_q_Page_334.txt
cb61a2a6a6dc79f7f6ac3b6f16bea05f
e145f4ae3ea549edf0d5ae781c40ac5596554f57
1909 F20110115_AABQZH gallas_q_Page_192.txt
6f1aa1ea35d87cc435b28719a47931ca
5a212a91787aa49ff94040e2c60512743c7cfcd0
F20110115_AABPXN gallas_q_Page_073.tif
59dc39f6f032d2d88c771ce7add6a4fe
1c3147b804d2b9e4feffa1c2de34aab48b59ff67
1030033 F20110115_AABONJ gallas_q_Page_093.jp2
e6a78301c2ac85b48aa9455f4ab328ad
58d9c58f9569d7faaf20962d2f19b2b61a311fdc
878310 F20110115_AABPKC gallas_q_Page_031.jp2
48dc7bf390822571bc129f8097424f8d
12121eef30c98857cbff874a8ccfd28bc0302bdd
4374 F20110115_AABSAR gallas_q_Page_330thm.jpg
6cb12ed187e30591ebee2bdcd560e4de
0c909da751b0a859d5df2b00997df4195e31e8fc
16184 F20110115_AABRWB gallas_q_Page_263.QC.jpg
c917fd67196dd1b7a5dff9758f11dccb
eae4f2133ddc6284e6ca976afaf84c1b1b2e6775
1961 F20110115_AABRDY gallas_q_Page_335.txt
0b6c3bf507ce32c962bc6f05235c0bf2
4e7092f7fade25bc4227ea899ec6678bd6b1641f
1646 F20110115_AABQZI gallas_q_Page_193.txt
c41312f83f498d37e5218440c70bebfe
28421427d9feccef05ab6a4f7c8997ae527511fd
F20110115_AABPXO gallas_q_Page_074.tif
8d7b1026aac68d38717d64860ce29486
6a2e4d46bdf002a8adcc6a7ccecaf5ef5a1b275e
956896 F20110115_AABPKD gallas_q_Page_032.jp2
05141dd0dc0fa8b5bf4dda5d2bf52ff4
dfd6524a3ccf7e26e10eabb4f2c1c86757fa7d13
15769 F20110115_AABSAS gallas_q_Page_332.QC.jpg
10dc0f875477bf2096b9162374982453
b8b7d12a792edeeda1818229916387bda1c9f334
4787 F20110115_AABRWC gallas_q_Page_263thm.jpg
36e349bad402f2916e96ccb58b3956d1
f0dd2d9d440a0f8930bd76eb1c42926229a08005
1216 F20110115_AABRDZ gallas_q_Page_336.txt
0a9585ccff3eb2ec368382a1e22e40c5
324fd7d701dd33c62097e8e9e7d1d1f20171357d
1547 F20110115_AABQZJ gallas_q_Page_195.txt
b0bac2aa194ab99751d7ca8dd09f4b7c
a32d5463609525e15758ce3e2c61385bd9e41ea9
F20110115_AABPXP gallas_q_Page_075.tif
5a39b48fa06345aad1cf44859f07f4ae
a0ecb964296674d3696a8b230ac47c8316c16f7c
F20110115_AABONK gallas_q_Page_058.tif
512edf47281ab97d1ca9f619ec854d08
d2cc6b0932a768c4e6c5366eb029bf6030395523
F20110115_AABPKE gallas_q_Page_033.jp2
2a9a7c89d6a8259060c17f3eedaa684c
f778295916cb157c8ffb07906e668f8c0c8ec7bf
5008 F20110115_AABSAT gallas_q_Page_332thm.jpg
c7aa88f1ebd01a1fdfb36285c81fd7a5
5ae22c7d5151def85581af6caf0db14799acb0f2
19723 F20110115_AABRWD gallas_q_Page_264.QC.jpg
2e99bb43dc6e0cd727aa8ba53d549081
b45529a9eef0f576c5ea2befd1e03ee6d73bbb5e
2197 F20110115_AABQZK gallas_q_Page_196.txt
f56e6830d50db38121a38feb90f9dc4f
6b77e158e07e1e4aeb8961ae2a348b1c484e90b9
F20110115_AABPXQ gallas_q_Page_076.tif
ed2a021fed840437a8d554a59f4651eb
1e60eb65f55d589cae32169a39df00f7511cea70
18113 F20110115_AABONL gallas_q_Page_192.QC.jpg
deb059bb1e8680b048983f24a5a43715
b5c40437ef7495fd15a26dce22b436949f1b3431
105578 F20110115_AABPKF gallas_q_Page_034.jp2
55840545bcaf7e30ec9d9ed9825894f3
f0b36938852bf13d31ab0fa73b4a6c5b4b2c4a63
22876 F20110115_AABSAU gallas_q_Page_334.QC.jpg
93d12068428b3507a6fd6d8a7e79c0d4
1b013dfe1ee77e9f3c851dfcd39d3e005c86506a
5812 F20110115_AABRWE gallas_q_Page_264thm.jpg
51b9ee09e0606cd510834af9179c3219
b8b27b9258a52f146eb817debc60f4fe3a2fca2d
1887 F20110115_AABQZL gallas_q_Page_198.txt
6291356848a1b93eaad0a0a3dbc56585
d85cd38271c7d7a023e0c6ef9dc66670f977a622
F20110115_AABPXR gallas_q_Page_077.tif
5937ebcae3e6123a436007aa7e3f25b9
1f34dbd536d4489fbed959d10e93daf337f36c19
4569 F20110115_AABONM gallas_q_Page_208thm.jpg
64761b899262124a805988c4fdf2bdd4
9c1e2e89d24d4b35cec19348f7e5962cd47b14a7
32225 F20110115_AABQMA gallas_q_Page_143.pro
06e801864d4575626dcbca588e6810a8
84253014fab7f7196a9b801a02ed0de4befb8396
F20110115_AABSAV gallas_q_Page_334thm.jpg
0dc306f76db41e42cf811ccaea027986
5758a2182094b9adc471e8fa45682ff9c143ceb8
23429 F20110115_AABRWF gallas_q_Page_265.QC.jpg
9a1242748f6a2c6d5185a6fc9aedbf13
e2395faf4b715dd28cc4582493c36b213299edcf
1723 F20110115_AABQZM gallas_q_Page_199.txt
637356137ccc558c77e60530a2fecb17
e9925522821407c7eb4d7ca005e2d0e3ffbd603d
F20110115_AABPXS gallas_q_Page_079.tif
bbcec3087e1f3f1a29771f4b9934c827
8f58aaa16a272703b3420fef4290352a4637ebe2
85522 F20110115_AABONN gallas_q_Page_138.jpg
b63b91e1652c92bc5cc9ee58b9f6508f
6d47dc5d166f3313d7a6432429f6e14363a3b3f5
32437 F20110115_AABQMB gallas_q_Page_147.pro
0ff80385036af1be78cb8665bf93df10
6b04538a276162428943c62fd081d42271f72f15
105142 F20110115_AABPKG gallas_q_Page_036.jp2
b62a039f6e7b026ab208f8a8e22391df
e70f1bfaac2f7349d221e6eead52f055d4793bc1
14128 F20110115_AABSAW gallas_q_Page_335.QC.jpg
b008828a6e5fbb802a13aad5b65fe6b6
eba8f8295d85c5fdbaf8fb0562fa33debd5c4282
6936 F20110115_AABRWG gallas_q_Page_265thm.jpg
7cd391be432c02e62f3332b453a20c9f
94a5d5a1d4294550c2add57f680f33c2dfb6c41c
1561 F20110115_AABQZN gallas_q_Page_200.txt
20f076e85505b6fb876457667494abf6
d32a377ba7af5be1b210e6f82cad01e27b9af5e2
22435 F20110115_AABONO gallas_q_Page_056.jpg
272693c506cb4f2ee22da38f48a9eeb6
3a96196b028c0590eaf019367124c84084c9c8e7
47191 F20110115_AABQMC gallas_q_Page_148.pro
618e35ff195466dc02a4b55dd5ca6008
31ec085b8deb92d7caad8cf6d6e4c6d858585b8e
111061 F20110115_AABPKH gallas_q_Page_038.jp2
1ad28b0890f01949b478e3f2d9e852d1
775c3162d695f775ad1c313e17cc6d477bdba204
4568 F20110115_AABSAX gallas_q_Page_335thm.jpg
edccd4b10f6a87680666595070f8c439
4ddd3e53cdf6578981153bdee3ec55116ea55511
18818 F20110115_AABRWH gallas_q_Page_266.QC.jpg
1635e2937422201bfb40d1699a3dd1a9
a8f1af01bfa3a3983a86453d88b3c283e4054faf
1552 F20110115_AABQZO gallas_q_Page_201.txt
575cf93617f51b85b58c4a91dd0de8d8
55ab214383ccf96eb574d67d9fe8d945996263f0
F20110115_AABPXT gallas_q_Page_081.tif
bcc0ef556a0ec319feb83266ce755e62
256266ff3905f34252db9bacdff3bd36066881aa
7260 F20110115_AABONP gallas_q_Page_086thm.jpg
9eb8b5f43c7666d810a3162695207bb1
bbf23d8f7b4e1021fdaf145d341e59aaf21e2120
31732 F20110115_AABQMD gallas_q_Page_149.pro
5d3ae1f383bd04fd3f3e045b13656096
a74bb24128ab9efc749948d3609decbe52a8f046
107420 F20110115_AABPKI gallas_q_Page_039.jp2
4647c7919f2c99bc537be44301dfde8b
03a5ac1c9009e489df12e7a49b63714689015e64
17297 F20110115_AABSAY gallas_q_Page_337.QC.jpg
6587ad27c61c7e78ceadc986494050c3
f176e8e90b765d6d831d6f5a5fed200c338600c7
5581 F20110115_AABRWI gallas_q_Page_266thm.jpg
7db350ee2a6b41d9c59a9015f5c58e36
43cbea9399ddf49743e717866c53ac3cbff565fc
2094 F20110115_AABQZP gallas_q_Page_202.txt
0f37331a7bfcdbe7f74a1785ffb56b85
b260ed34a63ed4f090cfe2a751ea29f96420e2ed
F20110115_AABPXU gallas_q_Page_083.tif
7c7a1bbce09bf4faf88ff7bb740100f7
963ea86a4283f5068db1bf6367d368b79b257a4e
69021 F20110115_AABONQ gallas_q_Page_095.jpg
702680dcf2fb0af3c3ec3dccb370b6e9
f8476f99957f33965cbae22d39c63219b7b09754
25844 F20110115_AABQME gallas_q_Page_150.pro
c664bd913e2683c94711c7ec9646ca7e
3522e0039833f079c47cd4cd9ef25535383f95b9
105500 F20110115_AABPKJ gallas_q_Page_040.jp2
1874d15b03f15974487c04c8c3e90367
02be0740f14871ad21869f2641935cc3dea797cc
22338 F20110115_AABRWJ gallas_q_Page_267.QC.jpg
3990c8738a87c08c72f39c830bb5f7b5
2e9261540d76f074968f9812488df6d0efbc6c14
1816 F20110115_AABQZQ gallas_q_Page_203.txt
a1cf428d91c19a76456635588e0a5176
41ae6e39a1ed84bfb6421cdda120de98b503745a
F20110115_AABPXV gallas_q_Page_084.tif
9c589582597a91297ec7c2f14444cfcf
9a1142337d76ce2e98277fc0f617238e358bb378
6546 F20110115_AABONR gallas_q_Page_172thm.jpg
96026f6d41383af8c019c7c2b92dcb09
8cc51bb441c541a29cc6e307ca9ec6b571e5dd21
30156 F20110115_AABQMF gallas_q_Page_151.pro
3c410ded5442404f9da8e85238afb7fc
1635c0b527dd957cb2e3d2542d06f53c09f35c46
111164 F20110115_AABPKK gallas_q_Page_041.jp2
bed0e994e95eae488c63b555294f6c4d
664f3f55274a14c87bacc3df1637a866bb4dd393
12676 F20110115_AABSAZ gallas_q_Page_338.QC.jpg
41b5b8cbe241565d533fa4e4a3e34e6d
7121d360525f9c367d7ca892d03cf22bec8b61c1
6309 F20110115_AABRWK gallas_q_Page_267thm.jpg
d83d6d47bb1c907318cd20750afce23c
7d2544c58e5bc620d49cbf6ae66817c1348454e4
964 F20110115_AABQZR gallas_q_Page_204.txt
e487617a8581192ef891115aecf3a81e
fb468f220fad992409119eac3a775f75a3f4ad13
F20110115_AABPXW gallas_q_Page_085.tif
27f362adfeed6728be61402b16daec21
7ab6a0bb30cbeee33afd5c6611d58fdedd8efe85
F20110115_AABONS gallas_q_Page_199.tif
d758348195f2aab876ea9ed3eb878a21
07809437d8d7cc621694987b212c24e21832eef8
37798 F20110115_AABQMG gallas_q_Page_152.pro
27627165d15a60ae41105ac74a6880e5
3eb49a9c814b5fa2c23210b43ca26937dafdc4fc
111974 F20110115_AABPKL gallas_q_Page_042.jp2
bb32afaaf14f534ef766b021126bd4e6
d37c094308064ae79059b55c79cf011d922c7ff4
23105 F20110115_AABRWL gallas_q_Page_268.QC.jpg
ffb358fa43a737e8a222fe2344b7085c
4d7582df6c00cf5738b4c74cfaa085d02504891c
2423 F20110115_AABRJA gallas_q_Page_056thm.jpg
662235f66e4acd952191c8b9307333a6
a3650a72d69193bf81d40e287a46930510c420a8
1915 F20110115_AABQZS gallas_q_Page_205.txt
330eceaca95307120afb3379e02f7172
25309342f30e414aca1a1e8c81c3e0d933311479
F20110115_AABPXX gallas_q_Page_086.tif
6ceffdfa76d18b07952eed1c6f9f17d8
3be9cb292d123975953439123e00778e2a2aa766
7039 F20110115_AABONT gallas_q_Page_379thm.jpg
5f3791cf1201be08c0dcbc13f6897b12
47d785972f65540696339b104553248dc2f8a2be
107308 F20110115_AABPKM gallas_q_Page_043.jp2
ab5ab41197fdfe95a5fdb13b742fc4ca
fb5b371a395440a3113ef124ca38220ab5ffdc05
22712 F20110115_AABRWM gallas_q_Page_269.QC.jpg
0fcc19b30f29216d0ac7ea879de02cd3
72b784d3e7b47cade6876f0050f184101f195d0e
22629 F20110115_AABRJB gallas_q_Page_057.QC.jpg
231c92de6e38c9408dc18ab7dd397857
0bfa0d0123cf2ba22641208e7ae0f490d6a26d02
1641 F20110115_AABQZT gallas_q_Page_207.txt
4203be363bf6cbd23967d03828d1bafa
019bb2ca3c76a2c3f0ce769175f2b25a04153951
F20110115_AABPXY gallas_q_Page_087.tif
6b52efe9b7a60548b703cc99135a7b07
76478856ce0d3ec24bac39b250099343cd6cefe8
748 F20110115_AABONU gallas_q_Page_356.txt
97d6462e543c313d131f7aa76ecd81eb
ec93c42a98e2d41a09be9c470f8a73b0f8a87992
31536 F20110115_AABQMH gallas_q_Page_153.pro
512ea11dcb4eeff6ebc9e2dadc34e32e
cdb346a0d609492b687b1369b3b33225e514f885
108247 F20110115_AABPKN gallas_q_Page_044.jp2
7416f24e5476676550bb8927eb30ccf6
546aab1bf40165092d5262f4e75447ae641c127c
6396 F20110115_AABRWN gallas_q_Page_269thm.jpg
e030e1206b372cd818a1e5bd88e88769
1f1dd4c58fb180e29f6c1f5df5c768d5b667ea31
6430 F20110115_AABRJC gallas_q_Page_057thm.jpg
5f169be8ccd0d7d579687719d8d45b78
9433ea699a8b2d1115927082216f1899f78a9be3
F20110115_AABPXZ gallas_q_Page_088.tif
53119842c3af3ec27f1478004a8d732f
7157c1d2987b177baba78840c83ff01153a45309
74015 F20110115_AABONV gallas_q_Page_304.jpg
07bdcc11d608fb3c7c14132bb66ef508
c73a4118a07f654954c7bdaeb3a8ad3d43fb543a
32648 F20110115_AABQMI gallas_q_Page_155.pro
462b321cd50b6ee232aa4c33754da902
165ee96446af0a8eb112ed89d1b37e4bd00c2242
111660 F20110115_AABPKO gallas_q_Page_045.jp2
0a640f1d1bb2c35047bbed19a7495419
8f346784de3a3a1baf12608d8015b2d27ef0ffc7
21621 F20110115_AABRWO gallas_q_Page_270.QC.jpg
b28461d740ce794ad9953032c12f62f5
14888f635eb2e94148a34e28b5ef92cd9d024bcb
778 F20110115_AABQZU gallas_q_Page_208.txt
8e66e1e6bd854654b565fb2e022f859f
dbd3a9243b4b5e64c8805fb0c88371c70456a28a
F20110115_AABONW gallas_q_Page_251.tif
89a13df1478cdad171dc840a92d46a5d
f9f38c5ef6b0898396c5d410898a2edc727e33d8
42508 F20110115_AABQMJ gallas_q_Page_156.pro
8c7f2679a9f2e18f2d53394289c58028
36f1773a13d8ed2c9232fa2733a50b7e08d6245e
106793 F20110115_AABPKP gallas_q_Page_047.jp2
d3e714ad140035e89c739814b4b0dd98
3f68055efcddbdf91e8f08eb64ee94d35a030258
F20110115_AABRWP gallas_q_Page_270thm.jpg
667c10ed1f527dd6d9853cc05c07a68a
cd02a0c37314a4ad84dd65c67194a863d5646625
20672 F20110115_AABRJD gallas_q_Page_058.QC.jpg
844b1e62439d1823772d5e5748e052e5
ea00763c3abff40b923d09231d61f67dbcd4dd2d
F20110115_AABQZV gallas_q_Page_209.txt
8dcbd558724abd9dec75c0b2fc5e32f5
fe9d6b4c61e9cc8c7e64f2ac758a1efdac1271b5
1718 F20110115_AABONX gallas_q_Page_028.txt
e0bbe946359ce9d17e0d4748ff47a958
571ae293911381ab0366cfee885e7c976eb9164f
34315 F20110115_AABQMK gallas_q_Page_157.pro
5cbbc8e4c6d7b42aa8347df5ef0180f8
1092111d5f0117cb2b68a2f444e62be178474cd5
115586 F20110115_AABPKQ gallas_q_Page_048.jp2
b893e63b5cf4629e1d4ab31366575ffe
61da7f92fb789f12ab1b3278e6c9cc3aea3f50c2
6226 F20110115_AABRJE gallas_q_Page_058thm.jpg
387b02436585ef2c00e0d5065676ca02
80e8f50509fc631314e2a6f47117c2c4f90783fa
2414 F20110115_AABQZW gallas_q_Page_210.txt
5499480d3c7ba87080ee0a8401d8e61b
ba7c1c4c630d5b6d5ed3e4bdd042eb14422d3a6c
59788 F20110115_AABONY gallas_q_Page_011.pro
8ec1223285aff2370ac7ffdbd13483fb
6545198de65030cb21dcd153f62530d873188660
21850 F20110115_AABQML gallas_q_Page_159.pro
7c63eaf36a44ebcab310dd5b586363b6
b35b7daceb84908b9851b6ebc44f1b20e4420676
112646 F20110115_AABPKR gallas_q_Page_049.jp2
6788e93f6497f87b3a3b8b30c6d52ddc
3735b313d113c3db895fee6cc6f897ff50bab9cf
18502 F20110115_AABRWQ gallas_q_Page_271.QC.jpg
4f64ac534c20de79cecddcced4ad77f9
283c7ab9898582105e19d3fa116818d1492d82fb
16177 F20110115_AABRJF gallas_q_Page_059.QC.jpg
191cca9a99cce9368735b326728549b7
b13a647ff53513e896d5429c7b63a1dc95b9d2f0
1768 F20110115_AABQZX gallas_q_Page_212.txt
6fe2e50a9e02c693eaafca6bf706ef41
76f7bd944d6c4db113f8fbb4a6b6c4a8cd7854ed
59638 F20110115_AABONZ gallas_q_Page_206.jpg
1b077ab0d12371516ad0805ede36d845
5c3e258f5f6f480623ac1fdb6a16b188a5128e07
30013 F20110115_AABQMM gallas_q_Page_161.pro
226cbf142918aff02282cbe3f9e09dd3
210fe0f27bd9ae3ab846cdf0c6d7b77e3c71ced9
108197 F20110115_AABPKS gallas_q_Page_050.jp2
a8ee5ef52c15f437f799244e34a0b0d6
098030c309e5bdf94e882f4360a2aec4d9df757e
5207 F20110115_AABRWR gallas_q_Page_271thm.jpg
fa9d955d73c5091090c8576a684d59e5
1b12fd7c591fd272846a8b0a49300464ab86c885
5026 F20110115_AABRJG gallas_q_Page_059thm.jpg
4c3285c8ff6e25114fb21f9f31fcdef4
e9753a1049e8538149433a1f6fc0f3657fc91837
2451 F20110115_AABQZY gallas_q_Page_214.txt
95e0fa4c6e357340a224f454a96eb137
982aabc918369d84927c610475680f3888c1b147
37051 F20110115_AABQMN gallas_q_Page_162.pro
4bdaa3f4febcbd29a4f0318b2c27be1d
c0fc05cd9e45f8c6e77ca1aa71a4da10f78bad85
107955 F20110115_AABPKT gallas_q_Page_051.jp2
fe2cd93f41bad97c3c1eb3f3671b7d00
2de08c4693fe67f27d9794aeaf9089f90bf80e9a
3808 F20110115_AABRWS gallas_q_Page_272thm.jpg
d98f1cfcedbebe51ab96238eb87b7ead
d9f62f8fa3c523586141a40dd21d5079457d8698
16258 F20110115_AABRJH gallas_q_Page_060.QC.jpg
44085202ec698bedc3ce301362cb450a
b0e5b7d23f0dcf903071136141727914396288bc
1958 F20110115_AABQZZ gallas_q_Page_216.txt
b7dc0c2cc3f79531ce2ef82ce4aeaca8
629b0a1220b2df2c5acc012e79f66bfc884fa699
30481 F20110115_AABQMO gallas_q_Page_165.pro
6c770944bf12c61f0b4e6a09648fe346
e136066aefecb93033dd23c6cf71c42c3e6a42c7
103520 F20110115_AABPKU gallas_q_Page_052.jp2
d50b85cbfaa0f936a070d639f3d3847d
b735a942a39d93c4dbf761e30de2e5268d65ede5
15947 F20110115_AABRWT gallas_q_Page_273.QC.jpg
2af25ce6442c096dc7e4b02bac594370
a8ac1a94c3e9ecd7e6e95be1b7a28bfefb96da7c
5500 F20110115_AABRJI gallas_q_Page_060thm.jpg
a8140964ef9e92f0c22ff6a6c893d2b8
d657ce50cc7d2ed40b87a1a82aff9106d8f8886f
29723 F20110115_AABQMP gallas_q_Page_166.pro
9bee521c589dde5b5346efa4134223f2
b422a775f2ad46956af816f10aaf892a24789804
102620 F20110115_AABPKV gallas_q_Page_053.jp2
6ff8719664c4281e21b87b92645d18d4
a150df26a7ad2021d4fdaedd88fa03ce09feb094
13516 F20110115_AABRWU gallas_q_Page_274.QC.jpg
788f293d30e3b58e3a036238ed35a1c5
c866f90c94c7027f1de0f7b30cf6b9ecb3fead54
21630 F20110115_AABRJJ gallas_q_Page_061.QC.jpg
cb52bfbddd28dfb218b03437a5d93fb5
b2272d385177806aea8b92d8ba28876e1fce6e01
45397 F20110115_AABQMQ gallas_q_Page_167.pro
3868a691c2230897db50b585211c5c6b
d8c2469a337f41323883737fb60fc76b2c64d687
28265 F20110115_AABPKW gallas_q_Page_056.jp2
f92bc4ea61cfa338771bf29df1dff83a
ab1beabd896760cf38a0479c634956e119d1169f
4091 F20110115_AABRWV gallas_q_Page_274thm.jpg
b52b0d46f81e4c7e9fcf8cc18f901e95
43eb67d5c44d88d63eec2d7625f19c1bcf58cef7
6451 F20110115_AABRJK gallas_q_Page_061thm.jpg
d7e64af68de548bb70d0bd55b8e87bd5
a7f65ef6c959a3290fe9ff8f53608dc48fb50418
35726 F20110115_AABQMR gallas_q_Page_168.pro
f2e312b4e9af50853895dcfc1511e3d7
78351689607f3e8241da9a275705fb6bd63c56e1
94631 F20110115_AABPKX gallas_q_Page_058.jp2
30eaa11c5f6cf2eb2b0041bba5ad7bca
e9839d437b645e7ff94e49cd133afe95e709bb6e
13512 F20110115_AABRWW gallas_q_Page_275.QC.jpg
ea6b778cf7e0c6494239a940538f094e
23253d28a6afc5d0fd9de42484a376af58692e46
19720 F20110115_AABRJL gallas_q_Page_062.QC.jpg
ed91c072e050535e56d570f91159f925
fd0e5e2c4c585899a3c361a206a7223fe1f39587
51776 F20110115_AABQMS gallas_q_Page_169.pro
83921c0327709f2ef3e65b039070f2a9
002534a7d02ccf4f18172fd71d2760044f20f753
72651 F20110115_AABPKY gallas_q_Page_059.jp2
a5bf8aca93b284444d7ce5ecfa662729
b36d387eeafaa6c41e78eb49961f447058efb46a
4106 F20110115_AABRWX gallas_q_Page_275thm.jpg
0657f667034aa34a7720c43cd8855c73
50734c44ffce5712c9f0c05527cf4dd2b426d60f
5920 F20110115_AABRJM gallas_q_Page_062thm.jpg
3997b61604c901803f172bf92d24ed02
6a7d086b55d7d2e543daeeab0dd19bd140b47789
18528 F20110115_AABQMT gallas_q_Page_170.pro
675ae722d384b27655abec01201255a5
e39e322860778f2b7614cfdecf657ddbc2cabc50
72939 F20110115_AABPKZ gallas_q_Page_060.jp2
4a5befbd7d040588efc50449777fba83
080d1e9d6971bc0c3cce9f193a960ab3edea4748
13173 F20110115_AABRWY gallas_q_Page_276.QC.jpg
0c0765ced62321c384834f3fbcdbf267
11368b02a5f816629e5fe09a77731529d123eaf3
19803 F20110115_AABRJN gallas_q_Page_063.QC.jpg
be16a7ee4dbaf03e14215db8e00dce0e
d464852d996dca4b885dd0eefd2aec91913c48b3
15933 F20110115_AABQMU gallas_q_Page_171.pro
e2c70845589faff46a21d1d0c554fe48
9248fcf7e671c180fe8974ce948cac2bdb9ee2a5
3952 F20110115_AABRWZ gallas_q_Page_276thm.jpg
21c0730b14d2920c881c56cf92089dac
f9c61b7374f3c12d9e040e842138398424d1c6cf
21540 F20110115_AABRJO gallas_q_Page_064.QC.jpg
0e857c8ab2c32a9a22f62a3d970aadf0
e44da4be9b355bf3e20bdaa665adf24a453c56e1
20438 F20110115_AABOTA gallas_q_Page_276.pro
919d5199fb212566644ffc6a722b86e7
de11bbcdc74d3fbf51bdc892a2d1b9fa748b92a2
40437 F20110115_AABQMV gallas_q_Page_172.pro
4f5cd4b6b21d846efc75b7abe54b131b
e471beefa96b7e046e1037c8130358fbfc98164b
6092 F20110115_AABRJP gallas_q_Page_064thm.jpg
8b1ed065beb3869c0b59fc2a0c52d322
c3f390f33df5b35b667d3245659df7bccf95f5a5
4981 F20110115_AABOTB gallas_q_Page_361.txt
a3cd6b091ef408b68904e5c9c54f6031
8cdd230f86da6ce4b551c6b4fb5ecf1547b5034e
13950 F20110115_AABQMW gallas_q_Page_173.pro
9068a39d10890b5d13df51ba6ade2854
359264fa5467b9a98f5647d7261295b0f46d02d7
19456 F20110115_AABRJQ gallas_q_Page_065.QC.jpg
c8379b0b954c1705c47e180c6f621b58
262d3b736ee1921653cab502c7b4a874959f7cb2
52073 F20110115_AABOTC gallas_q_Page_226.jpg
0fe87054a78b74642793d760df6d58ff
7bd43c6398fda3d6638ab84fa47db3a45aedc577
41800 F20110115_AABQMX gallas_q_Page_174.pro
70317a638b4d64352916693324a64f4b
f62ccd2d628bdec69b25af31eb08773dc171fbf2
5768 F20110115_AABRJR gallas_q_Page_065thm.jpg
1ad9d7dfde7d6adf9cfe5bc5dac0dba9
c1203630291fc698db72fad91c19969025127a71
49270 F20110115_AABOTD gallas_q_Page_265.pro
9487680075c6fabb397c038b38e3996b
253ae7c8057f0512901c27b4923aebf584917164
39008 F20110115_AABQMY gallas_q_Page_175.pro
405c771ac7c5faee74f49914a6c26839
958b8f7557422dd2773b4c1d2893d96567817fb6
22506 F20110115_AABRJS gallas_q_Page_066.QC.jpg
eb5afd84048ed1939a254fe858801067
0e8bf7c914c1ad003b65bb7992f8ec9792218fb4
87872 F20110115_AABOTE gallas_q_Page_007.pro
cfdf0fbcef3c247d87121cf4bec27675
6783228d55fd0075ed4330b06aca3ed5f233dc89
52319 F20110115_AABQMZ gallas_q_Page_176.pro
f89587d1c3eb9eac3778e393a9ff319f
9503aaf4cf8b6f86676ce0fb0d26214e36ebc3e2
23504 F20110115_AABRJT gallas_q_Page_067.QC.jpg
6390ae5e6c1874bb5de57bc42cdf6af2
b04a5354603bc072dfc42cc8648afc649dd939dc
101187 F20110115_AABOTF gallas_q_Page_037.jp2
e89c26c16687c57b73f9f6f08d19128c
bc920111f46c676ad410a65bc97307a0d474af4e
6756 F20110115_AABRJU gallas_q_Page_067thm.jpg
f9245675628c8a267710ba48bab73204
4e59a25a8fd1a92418b104c5521356897748e322
1435 F20110115_AABOTG gallas_q_Page_349.txt
3919f730a88f4783fd942baedd7e71b7
d22e88976cb5492605998a108769893c895dd982
6311 F20110115_AABRJV gallas_q_Page_068thm.jpg
e774579e0d0e40d2130ba74ce485aac6
52116f75c4cf0e5a351646c19b3ce0670530c252
73295 F20110115_AABOTH gallas_q_Page_157.jp2
2bc2b203034020184f317f81721fc05d
cf220e32fef9da56489fa6ad6a67bfe0d5a78330
86309 F20110115_AABPQA gallas_q_Page_222.jp2
0ce18cf5b809295d9b24d4e114cfbe24
edc23403fd011a5c780230ecdec6f340e23a6627
22100 F20110115_AABRJW gallas_q_Page_069.QC.jpg
d0311784072cce19561a8b5957a39ff5
62dd29f04f449ddde2e15e6f1b47d53bf729424b
382 F20110115_AABOTI gallas_q_Page_321.txt
56f27e5562644ac12d60b4b6d4f31252
4de40c88ac17f5c53d5c9fe68496ed93e0d58bc2
957495 F20110115_AABPQB gallas_q_Page_223.jp2
b6d812a278915ad2f3187b85a3f047e5
62873fc0f69cd7246ab168917c92e4e9d3abe0cb
6207 F20110115_AABRJX gallas_q_Page_069thm.jpg
703ca6edc57f1d8dcfe07c37f5f8c3c6
14ad30c03734db422cd0a9ca17a892f243e7da49
F20110115_AABOTJ gallas_q_Page_359.txt
c64893f4a6110ca1ed4121808819b4eb
051292232b272dd4a5741b7613143316af0b3f9a
786778 F20110115_AABPQC gallas_q_Page_224.jp2
39c948841579bcb3cbc7dbf14c3ff804
fc22449e4d57c3a0af39d68fc243a582df4f9c1c
5900 F20110115_AABRJY gallas_q_Page_070thm.jpg
888a00088bdcd48eeb814e18933379e7
0a32874559165f3ddee8b734666360608ee22ad0
F20110115_AABOTK gallas_q_Page_082.tif
c249d2fb2d76e7e810a62ad84f8a9484
9481f991c52e71332533c3ced3e0952558829704
79177 F20110115_AABPQD gallas_q_Page_225.jp2
e8b1e47ed49b2daace4b7a0c928eed10
f2d23db5d996507b2a638804c16ca5ef3ea63544
19989 F20110115_AABRJZ gallas_q_Page_071.QC.jpg
cc84461f709a4a1cae6d710e4ad1aeea
520e8ff58317bc15f289a4c4f0f9edf04d7d3176
31474 F20110115_AABOGA gallas_q_Page_158.pro
650d79d6d24468b0816ccab5371a30de
4d20cb713c138c690d9919b0e617950cc5b00ac3
39349 F20110115_AABOTL gallas_q_Page_065.pro
070846dc97c3aa1f023f2d709762b9bf
dd9e77aa3826fb2055fa1e47b3f5b8b7add4f9da
76428 F20110115_AABPQE gallas_q_Page_226.jp2
69af5453986f0dd96b202e2f8a7a0841
d225dd6a6c1ebf545a038bf6791751097b9e6317
6853 F20110115_AABOGB gallas_q_Page_175thm.jpg
ab2992410384fe588b1105d355e38323
0bbbf9f302058f6ec492b55c24c43927b8e083fd
22860 F20110115_AABOTM gallas_q_Page_148.QC.jpg
42ad4486b17a1f6242451f3e2ed90bb5
aa2f58a613acb9a4e53ba9f34050c544a02bf8ed
37797 F20110115_AABPQF gallas_q_Page_228.jp2
2692592a5cb7c11b098bdeba2e0913d4
935e3a26a3bdd1510ed4d86faa037bb698fb6e2a
34359 F20110115_AABQSA gallas_q_Page_339.pro
84c18dfc9cc6301aa31b372f094d754a
261713e99e4c0d52de2c42cc63a169fac6cb61de
75811 F20110115_AABOGC gallas_q_Page_139.jpg
e5e2dae5b8b73b8ea14672277e4bdd1e
8ce960270b95af417efbabe3765bf7b27426c3f9
36516 F20110115_AABOTN gallas_q_Page_233.pro
267825755a6193adc59ba63eddb31d8c
59cfb0e0d8a03e3df80993792f3de795af8d080e
102280 F20110115_AABPQG gallas_q_Page_229.jp2
a83abe5e1dcb5b10ef9a870eaeca2e0e
440da58489b803a0b7a7348a4ac763667ee43c9e
39557 F20110115_AABQSB gallas_q_Page_340.pro
484e596ea64319475d0d7e279046e6a9
1b3335c9eff364eb31a7c3d7ace440a58e1bbe8d
61535 F20110115_AABOTO gallas_q_Page_190.jpg
9b8499f33f467544016e5672ac2afdd5
03d75a9576749df2aafb56fc622d0e694c92903f
716958 F20110115_AABPQH gallas_q_Page_231.jp2
48803feefd0482f4c451cee6f366a759
4f747237bbac1acc830c5d2a01b33f21613a46c5
28872 F20110115_AABQSC gallas_q_Page_342.pro
941f5b85bd3efacf5548757112b5beee
f35a0026773121aee125f5cfb73d5f217b04b418
F20110115_AABOTP gallas_q_Page_337thm.jpg
ea76589c0692bf9cd253a0ef0955b356
c4c68d46d131f64ce820d314e81d28c644e0fb5a
991542 F20110115_AABPQI gallas_q_Page_232.jp2
eb5a8cc5d644b4031c50a30b08947df1
51a9393cc948cee979c3805be9929c6fe42b47a7
F20110115_AABOGD gallas_q_Page_010.tif
caafed493f9cada8f3b581b09a67911c
0f49a937a85ac76c1c2758951efa7172585135e1
32571 F20110115_AABQSD gallas_q_Page_343.pro
bb958f791c539c68f87a0624e45c4f27
d3fbd6024ed5379acfb327c1d5f14284db323085
866667 F20110115_AABPQJ gallas_q_Page_233.jp2
48103b8360e906304faa45c0b6ef3538
5d15b49707130d205f6bb73f04e5a7c1b44f0e7f
68497 F20110115_AABOGE gallas_q_Page_129.jpg
9792066a3015f47ec488a123161a4cc0
ac67b8340a638bddc5537e8619f9dd13e28a0c9c
27519 F20110115_AABQSE gallas_q_Page_344.pro
d46987969eb0e242e5258e642581f6d3
c203b5551866f3d9daa38b71ca6a4912918b4d03
F20110115_AABOTQ gallas_q_Page_364.jp2
f085c750753c2aa17151c79b7a782e78
8778c3dd2675ee08627dc909a75054812dbe5df6
1051955 F20110115_AABPQK gallas_q_Page_234.jp2
588efc8d77cf0c2cebd96240492b6ef0
d436a8f1133549b1d5d6d80da1e18b7bba444976
F20110115_AABOGF gallas_q_Page_068.tif
f25cfa05d224a08e5de22f344b9061df
51b56b69718f0a6bfc9f1644d4ee5eb7ed2487b4
26927 F20110115_AABQSF gallas_q_Page_345.pro
969bf4e7f092f0edcc5a2bbb4e9053d9
d533e453336ee1e509184e0193827ddf2f79f336
47468 F20110115_AABOTR gallas_q_Page_280.jpg
39082aec4ab82955c1764277312ef36f
fb09c9ba3a3a17eec5538129cb089305198604cf
105381 F20110115_AABPQL gallas_q_Page_235.jp2
edca77ca997b169157d4078ff0d8f930
69920d5c4fee1da889016134702cb17e06866e25
2673 F20110115_AABOGG gallas_q_Page_133.txt
3471a9ed46c8ea8886fcc8ba78f96dc5
460c5a2a7c9dd23637dab84d792dc9d07d02eb39
34224 F20110115_AABQSG gallas_q_Page_347.pro
704959969cc7b3eaeaa193dff2a38d24
79355b35c5c43b91c5e3612cee9912b5085b8179
81804 F20110115_AABPDA gallas_q_Page_187.jpg
60cb4c94b0deaa10b094d1bfb709364b
5ddd5b559e97295680967c8de3e64b2c6d36af89
81871 F20110115_AABOTS gallas_q_Page_293.jpg
489ec9cbbb810f2a061a35f6e2120802
21d7c5d2b1a687cfdc9131bef2cdb46d9929381d
42967 F20110115_AABOGH gallas_q_Page_240.pro
76ef7313a8b20862b97325eda435bc69
5394a65c1d0cc1a071eb44fae339fbb192a275c7
F20110115_AABRPA gallas_q_Page_150thm.jpg
0c7e85fb266117fb77e594cd60bb1b05
dd97438c0299c095a9251f6f7f99ba285b170f28
26790 F20110115_AABQSH gallas_q_Page_349.pro
1472b10b93ff5e840335d54d40ea3442
0eca075d022c0fd99f77690b111d658d5c843390
62897 F20110115_AABPDB gallas_q_Page_188.jpg
160d23bfe662770fcaf71ac4eab86df9
09d419d46f1d0bb7cf306c1690847b17f5068675
874785 F20110115_AABOTT gallas_q_Page_185.jp2
b47eff84633d9f9993ee1ce3b32fa185
9e4aff17e735059c7991503ee2ec02c36ba527e0
72672 F20110115_AABPQM gallas_q_Page_237.jp2
d6dd50f58532c7f5e91218c6e2775354
f919d782d6ba00247611e285db996950bed8ed47
F20110115_AABOGI gallas_q_Page_217.txt
b0a8090e9596876f4cfdde6059b40cf0
ea3a7fee05cbf091a953c00233a68dba540d6a82
20714 F20110115_AABRPB gallas_q_Page_151.QC.jpg
f9815b987ba388fb9e6adb736ca77ca7
1450f62a8e48784a216997e9113555140830144a
41845 F20110115_AABQSI gallas_q_Page_350.pro
5070fbc3b15eb23314dabac4e1a2b722
57c878f6c7edb6a3eb1d7dc17254b1bf59f4049b
63811 F20110115_AABPDC gallas_q_Page_189.jpg
7cbff07201eca096d7204c01d986d45a
61620f996dec22bd33a85caeb03d65297d798415
93580 F20110115_AABOTU gallas_q_Page_188.jp2
99334abc50d2e5a152ba8d5af6f9389c
8b36aca430e7ecd7c8e0bfe35f53acab870371ff
95466 F20110115_AABPQN gallas_q_Page_238.jp2
98c1744cf602d0c7d3824bacc890af96
6695791a91665d49f8ff074977b47ce9537104d3
78937 F20110115_AABOGJ gallas_q_Page_311.jp2
fa25856fb49840c57bbaf9a1402aeb2c
b3070b1cfa6378278b17c610717e6affdfe43fa7
6468 F20110115_AABRPC gallas_q_Page_151thm.jpg
0bd848450210866e84735a7a9f11d314
16cfeefedac1ce6c4a7845aa6615584ed002e6a1
18016 F20110115_AABQSJ gallas_q_Page_351.pro
4d3d3cc79bf0be22bc9ed572c4189dcc
0e603680b7c826e2e9fa5a6131497c0723c76d5c
59219 F20110115_AABPDD gallas_q_Page_191.jpg
fdad54d5cd689c913ee42614cd8c7dd7
e8ec8571b01d7c10b9b9c188fd4f104ef878a31b
101846 F20110115_AABOTV gallas_q_Page_129.jp2
d3e2e32fb5a789d9d28acc915f0219db
66f4bdcfb4d08240ba00a4d5cd47da360957e818
1033711 F20110115_AABPQO gallas_q_Page_240.jp2
465ad0850496523f7d08ae44607749f6
c0669b8e64c039f20c6297d93a9222a0006816ee
51829 F20110115_AABOGK gallas_q_Page_292.pro
94382d240235a1dff82cb8908962da26
0718a302e07e51227fe4e020a48fa2c10911a87c
19265 F20110115_AABRPD gallas_q_Page_152.QC.jpg
0b1e409913409ed827a93fc366baf431
ac7bbc6c3f33c1ab5d6e45f23a657bda04eab1ad
40152 F20110115_AABQSK gallas_q_Page_353.pro
21e488ca60042dc31af2a50dd5734323
be6fec27df23a03d85766c8855aa7de2896c8818
48115 F20110115_AABPDE gallas_q_Page_193.jpg
08cb812c883f6a881f03d9f19c9b9a27
a14025c228ca06d4dfbc4f25d8f43d56d61e52b7
16324 F20110115_AABOTW gallas_q_Page_252.QC.jpg
e251b7e95418b65525317bc402300f8b
77fb2944dbd468975bad688a1621b13bc39116a1
98154 F20110115_AABPQP gallas_q_Page_241.jp2
ae61d93576b4994bbf7b08d9c1247c48
35e361e660e4b7ca2b127260bbf7954702f5c2c3
26717 F20110115_AABOGL gallas_q_Page_096.QC.jpg
cf5fdc5e12608eeefab58e185e9aa45a
6f5a0dd5ac673122a9f3069967f9fe8e375697bf
5899 F20110115_AABRPE gallas_q_Page_152thm.jpg
e5d7af26b3ecbafe027db4e02c7eedb6
748c46de272f534551572dc4bdc59164dd64b954
52045 F20110115_AABQSL gallas_q_Page_354.pro
32e06d5ac1dbd6b91052128d1e65bbfc
0c2acf1c29b9a3e617a976561721ea1b707d6419
70512 F20110115_AABPDF gallas_q_Page_194.jpg
8b3f1e952ec3327e418ecedac2eb19bd
22ca718b0eef03b47d9d313fa4d0b09ec270be7e
1803 F20110115_AABOTX gallas_q_Page_069.txt
becaf4215531e82232509b3a58342473
a1ce380a194a3c964c6f8381235c394741c6facb
106701 F20110115_AABPQQ gallas_q_Page_242.jp2
60deef3e0ea388f3dbcf248b09bd10d8
53ec0f2a9c5e5d6a298d09fbdca6eaed5967f941
7011 F20110115_AABOGM gallas_q_Page_304thm.jpg
466e5a8486d62b44d531f093eccb80b9
211319e8eccd53f5f780b7a403aba414ee1b6462
6298 F20110115_AABRPF gallas_q_Page_153thm.jpg
38e27d4158e45fc9fd25aeec12297ccc
10014271eab32d968049cff77dc96196de88987c
35418 F20110115_AABQSM gallas_q_Page_355.pro
58da60250969ae2263709e2ab80f5403
4d828b1375d39adadd35159aef09265cf65f4517
8423998 F20110115_AABQFA gallas_q_Page_315.tif
4f558c970fc24d2d467d63f65a3c97f6
3dff6c814e075874242568d61ee0afd0c3430981
63755 F20110115_AABPDG gallas_q_Page_196.jpg
e09ffa23279f41974809edd7c09407ae
e1c92ef559caa8723eaf7ae879ee524c36d0f73e
F20110115_AABOTY gallas_q_Page_363.tif
72054a859ae409252332c421d45197f1
2bd40067f49ac82845ed81a5381f97c1c1afe0d9
108220 F20110115_AABPQR gallas_q_Page_244.jp2
2c3f2146eef06b0f20a06c68262726ed
ba252b92fa6656549bfd5ed1b2c6bf282d546cd7
1637 F20110115_AABOGN gallas_q_Page_287.txt
740720e9afa48e0a19689c6786df3ffc
eac8754dd9714838ed0a21d70411f7f3b2da797a
24855 F20110115_AABRPG gallas_q_Page_154.QC.jpg
d3d7bc918bcc44977ebf6914225c31b7
f41267fd47a5da3b4ea0d3ec3a22968ed384e6b7
F20110115_AABQFB gallas_q_Page_317.tif
a7e8a81a4242193ef256c1d6605a6040
3407ff4ece60e5e4c19145765a29170326415775
66138 F20110115_AABPDH gallas_q_Page_197.jpg
5f81677dcaaa03fba62083e53adf2f82
4d86e44a01400166c382b042aab191a46dad1ba4
F20110115_AABOTZ gallas_q_Page_148.tif
a91156f211f97d20244d95e19753ad85
d187dc76a77cbde601750483d7c530d68bd68cc0
1051935 F20110115_AABPQS gallas_q_Page_245.jp2
ea539422c413279e5a6122b8ac672a5a
09cc465cfdcb14284d1a7929af778743a3b58516
F20110115_AABOGO gallas_q_Page_155.jp2
0da34d18e2843b36d4fe1c7ae89849c2
6c77ae41f3347fcf1ac942410cca95b31adb5088
7125 F20110115_AABRPH gallas_q_Page_154thm.jpg
4e2b269dcd25953ff1421f4feb7b95d6
f985ba24fa15f14aaf713ff08010a800eb0c34a6
20235 F20110115_AABQSN gallas_q_Page_357.pro
1dfad988f72d259ec0f80a706e306dc5
786f987507357d6df227920cf4b3ec8a8c8fd72f
F20110115_AABQFC gallas_q_Page_318.tif
a6833da3b692dea99ce8ded70d81a01a
b170ece2657a6d70f0b1d5de7ac31aad171c43b0
63421 F20110115_AABPDI gallas_q_Page_198.jpg
c60e67dd6291525801a13fb989feceda
367f6c103dcb7483d50c52d2c5d48da68f25db46
89053 F20110115_AABPQT gallas_q_Page_246.jp2
dc1695d1f2b0ffcf0d4fd68b38e1ff40
5d3eaf0f19afa6cb9274229dddc975b0175ab7b3
96889 F20110115_AABOGP gallas_q_Page_064.jp2
04d9ca9731892ed0da9111ddcbbcf880
f090aa4d1d84cba58983767849bf1c1219bab75f
22362 F20110115_AABRPI gallas_q_Page_155.QC.jpg
b27fd43b0d5981ac3a0e995093e8ae60
539c42a689bd7ba4c0d81d1f8d3b5606380ab185
31007 F20110115_AABQSO gallas_q_Page_358.pro
5fc32bd17cdc1a37bb4f4cedff35cb43
7dd08e7cf001d928c621d2b36e03f0d83373afbd
F20110115_AABQFD gallas_q_Page_319.tif
a007f62e7d056ca5639bb1bbec447c69
fdd5320699592fc09ce5b2ee22c7d931852b7a35
57504 F20110115_AABPDJ gallas_q_Page_203.jpg
70d8266e81d07b8753985f2eb7574225
f75df7a3c7dece7ce52cbb412422944fab955582
88146 F20110115_AABPQU gallas_q_Page_250.jp2
455ba3d449da49c9d43833c8dfebd855
610382b4313670442c44a111261e4d358cb734a9
2188 F20110115_AABOGQ gallas_q_Page_291.txt
a6de4bedcd6a4624a4200466aa009981
07802946504fc453fdf8d7e5bd5d04a3b0a25924
68589 F20110115_AABQSP gallas_q_Page_360.pro
82d17f4471b36925f173a0ca734c0cfc
d14328b661fbea801c79992bc8b038ce4b76f810
F20110115_AABQFE gallas_q_Page_320.tif
ba4b1776d49fe245000c9da143a08455
81aec1a77401e33c80771b625bc54ab556d09d15
53058 F20110115_AABPDK gallas_q_Page_204.jpg
bfcc8dac7f4a5287bcaa1389fa7482d9
67826e699faf8bcea5cb0a02722c88ca9fac2760
854324 F20110115_AABPQV gallas_q_Page_251.jp2
076f05430259341575007c591bbe4cb2
44eaa97f3179511d3b235b0b83ce0b295c3733a6
38577 F20110115_AABOGR gallas_q_Page_069.pro
d707afee302230c241b94ca7aa81cb05
bf437da858dac7315cc11e794779e88325dd1550
6273 F20110115_AABRPJ gallas_q_Page_155thm.jpg
64fbe9f2d6331a0f5f36d0936d21bf52
e87777244204bd63027d5c9f54565a0c9a5d4b3a
90812 F20110115_AABQSQ gallas_q_Page_361.pro
55523bf2b870fd9ed0fe58418afbcd47
8a1b6cdae41eafcf7d20dd6c4cf6ba6f2ad4314d
F20110115_AABQFF gallas_q_Page_321.tif
22eab5ba819bfafa41d090032fdde60c
94507a4360f86367ce6aa5fa4afeb4843cb9d78a
64441 F20110115_AABPDL gallas_q_Page_205.jpg
4178517e0f7ab06b757df3c8756a90a9
3fd5d3b8f91388a07c4d272a7e27b0a291d4e42d
68360 F20110115_AABPQW gallas_q_Page_252.jp2
0986a3755abeb7a5b4e3430bbd7d9d57
99d6da8356be4180d5105eadc846a7ba4a9eb4c2
F20110115_AABOGS gallas_q_Page_192.tif
1bcc7391aeff3583ecb52effd1a9c688
507955dc47515b8a1b8ae70f752f3bef59fda305
20187 F20110115_AABRPK gallas_q_Page_156.QC.jpg
c709099e77bb18b2632321ba0e618563
f73b5e17be50b0ef3068746023a10769131c8e88
81081 F20110115_AABQSR gallas_q_Page_362.pro
3ad52b12be6ae9f418f9c19c7e7556e2
49a1c0add03fc706e15466da1a0b870a5700fae9
F20110115_AABQFG gallas_q_Page_322.tif
8e21b272f27480dc1e9564a68abc33e8
c5af2a71a147b2fb7331babe1cd2533f2b4c952d
58438 F20110115_AABPDM gallas_q_Page_207.jpg
af163a2a60c1550cfffc20233a835589
f16d2913e3f4f5fee3c09585833c77929a7458b5
95752 F20110115_AABPQX gallas_q_Page_253.jp2
183070ed60616710af51d227206a2383
6b88d1b3bc390155b591335de809b12dda08f695
19441 F20110115_AABOGT gallas_q_Page_162.QC.jpg
78920fa09b402c74492c0fc51dcf5062
b9be5bb8bb29fbbca357fe8cce3d33caa9d41073
5870 F20110115_AABRPL gallas_q_Page_156thm.jpg
55887fb41d16d9a2c3891ffe1aabd0f0
acc716bd53bc6c229e8fc886607049f167879cf8
1145 F20110115_AABRCA gallas_q_Page_278.txt
6aaec49cfd9fe6a255a45cd032623479
084aefd7503b663b23296b6dd1576859bbf4f96c
86181 F20110115_AABQSS gallas_q_Page_363.pro
7ae11e62f647f07271ef40de8f73c2e3
1a0dc2869e2e028dc2b6a32a693bf88b5d7f2f7a
F20110115_AABQFH gallas_q_Page_324.tif
e52c7fc99c561b8bb2cc71785e7c5854
af1e650ed3efcdc6dbd0a89e5c0e7bd4c757f27e
49209 F20110115_AABPDN gallas_q_Page_208.jpg
1788dbef8de121f8fe575a41ec860ed0
7ec94cc57e2aeae1cccc567cc766dc86d2bea9f3
88402 F20110115_AABPQY gallas_q_Page_254.jp2
645a2a9e89731651bf1f1eb43578c89e
5881373e2d0258688217b71da069240bacd18fba
12809 F20110115_AABOGU gallas_q_Page_272.QC.jpg
44b5c1423dae16038429116eaace0ba8
e0fc152f76061b33eb52ac5d9e8679263cc17417
5194 F20110115_AABRPM gallas_q_Page_157thm.jpg
5a11d9137d3bc426ad1c186bdbd2b0ba
bd43e4a193c1dd88f5139aec7d1f76f9f5f89228
936 F20110115_AABRCB gallas_q_Page_279.txt
e52a763c0f77289ec6b86ff8c6fd9d9c
b3c2abdf9b285796b8bf068252d279b7f5e915ca
85122 F20110115_AABQST gallas_q_Page_364.pro
9572510fc59fe0625f8b204aa97727d0
cf779e0fedad85c5cd36d3f23e1697ef6206b3d3
F20110115_AABQFI gallas_q_Page_325.tif
b072adaa0a87f5c5de5d2b43f41acddc
df3510bd04e017d6f6cfabebe8bfa40583d35c97
57702 F20110115_AABPDO gallas_q_Page_209.jpg
4e39c49ca599e7a8aebd22f99f29572d
ea4f5b987ab0d675f235778240955c9c93d57b66
89995 F20110115_AABPQZ gallas_q_Page_255.jp2
f2872b1e77fea366644f112ce1bead37
141f4f42afb29171270d7069491c9567a14c0d89
13999 F20110115_AABOGV gallas_q_Page_278.QC.jpg
946ac21f62c186df3d91105c720ce6b6
0f50b30ab30e559908cc71dbea5407881cd2165c
17247 F20110115_AABRPN gallas_q_Page_158.QC.jpg
d2aa93c45fa46caa34fad3fef37df4ac
4f6ed220d0413764592928202c72d28346d337b0
1886 F20110115_AABRCC gallas_q_Page_280.txt
76d6e491c242a3e8b47a4dd7a153d3eb
a56811518967e3c9146f11ad4535cf8b1d8dd3d1
85424 F20110115_AABQSU gallas_q_Page_365.pro
9d3b8e83f1d0550ea5693edee07517cc
dad6e8133587b7fe7901d3a3051bd508630ed1bc
F20110115_AABQFJ gallas_q_Page_326.tif
a893197000cedcf72d64f8c2387b7bff
3a2ce756dfa49b158e8f39fafb85e1ec38cabea9
73379 F20110115_AABPDP gallas_q_Page_210.jpg
d626f4dd1959d17c59a0fc7d1826d128
47665f9f80acdfc7cbaef33754a5a2062b05be18
66347 F20110115_AABOGW gallas_q_Page_290.jp2
3313dfa9d200e050990453fb58abefca
139e7b1ceee54f6e76590c7a5038578ab77c98e5
14841 F20110115_AABRPO gallas_q_Page_159.QC.jpg
bfa382328b7d306eb4dbf6683c844c12
6193d4b2f35ef1fbfe8dd544ab199a3e9bc61854
2450 F20110115_AABRCD gallas_q_Page_281.txt
4e53ac43235e6d8484a096a59d556125
245f85bf72711de1a64f497b7e127a1e9e7c44a4
88234 F20110115_AABQSV gallas_q_Page_366.pro
de5dfe5ff882b7dd5210b772801ff049
51b61008f2128c6f5ff9bd533fed0ba4df676189
F20110115_AABQFK gallas_q_Page_327.tif
07d8dfdc0690e9aabbdbf8f598d7a718
9b7ba1672bbbd1afe46cb6351936890e4a3806a9
68145 F20110115_AABOZA gallas_q_Page_064.jpg
8be45b8780c60df19ecff16f03d39696
87552e94f9c1ebcae571fda1bb774e2842a04466
62737 F20110115_AABPDQ gallas_q_Page_211.jpg
b4f1167a20a792650822cb521f4bca06
327d86f4c7b3f565b560e3d44a1f1eb37e5af01b
125374 F20110115_AABOGX gallas_q_Page_376.jp2
6d439391db0ad7038fe34e7142302872
6c7020fba5046ef8b16e08435b44688d1445bbdb
4633 F20110115_AABRPP gallas_q_Page_159thm.jpg
8c8bc710d1290565abb0d37a3d9f210e
f673d69553793bb6ac290a067daf8f1607e0e916
1797 F20110115_AABRCE gallas_q_Page_282.txt
1dfb6dfe237dcff489fdaeb3944a1562
617e189f5b5325049e941f4650607694b59fb898
90877 F20110115_AABQSW gallas_q_Page_367.pro
146e6ea3865a03dbc4006ba606747f55
e55a670557e7c8aedee612d6af2f51fc3ca2c590
F20110115_AABQFL gallas_q_Page_329.tif
21def1cee4f6aac59a0320fd81a6f109
8d96f65761e2db1a77fea764d0af4e7b072c29b2
57272 F20110115_AABOZB gallas_q_Page_065.jpg
85b690aa757acbf9eedc53c9e3b80d69
1b6f8ea4dc3a50ba5418f6ed4aeefdbc5cbb6796
60562 F20110115_AABPDR gallas_q_Page_213.jpg
0dc388b99dc1c62c8d89ae1dd4b3ab56
1ac4d930b0cf4d0771deeb00e69dffa389af9f87
103430 F20110115_AABOGY gallas_q_Page_066.jp2
210cb120b00d3e0e4225dea6842d10aa
b1ba4d00fefb3308649daec61d90b8cdbd58e9b8
22880 F20110115_AABRPQ gallas_q_Page_160.QC.jpg
cd7faf2dc2d40397e14f8841cbd15be3
32cfc3989081ab91d7d85b003479d6a9b5900805
739 F20110115_AABRCF gallas_q_Page_283.txt
72c90d5c989055975c552dec3d689d8c
f66576f10c4517aa01b9a3cbcc42afe501cb4575
82069 F20110115_AABQSX gallas_q_Page_368.pro
acd51cbd0cd04cf5141996d76a4fcf02
a2fbafe8520a6fb0e7348cb0f72adfde9e167c8b
F20110115_AABQFM gallas_q_Page_331.tif
d87b6eb12c4ad4ff8b82cf714db4b0e4
2cacb7774c63805e437387439cb4727d6dfaf44a
70762 F20110115_AABOZC gallas_q_Page_066.jpg
2357b6260e91cd3dd8e559dfe8f76749
0ebfc44530ee548cd4261ea0cda98f70a0b9e2f1
85082 F20110115_AABPDS gallas_q_Page_214.jpg
67a4b1d1eb50333e025fc27e63e82d4d
112379e97b49047e3a69aaee06dab1267278f56d
F20110115_AABOGZ gallas_q_Page_215.txt
e6d552d5ee968947b87cd856ea35e8f8
45a0249de02daf6a63039e1e7c1fa3254acad43c
6587 F20110115_AABRPR gallas_q_Page_160thm.jpg
dd0e2e78be3b95a83b05929b29376b8a
84d5e747103118914dd02d12d4abab9a666e8bd6
F20110115_AABRCG gallas_q_Page_285.txt
56e25456cdccc707ed1272be6ae191ba
d0780a794591db0cabaf00d0e6d71a24c2777d20
86915 F20110115_AABQSY gallas_q_Page_369.pro
9f99147c59a947d0f961c73b640cefb9
fb24a377976c86ee5243c3b63377d5bcab7b437e
F20110115_AABQFN gallas_q_Page_332.tif
b0422643aff5c63d743d401fb52ede61
995df717139b785854c4e1e506df5b2a06cc1c53
69567 F20110115_AABOZD gallas_q_Page_068.jpg
91105138dc3bf13c7d5afcc64a68b1d0
cb31d26434e7f505a94324ebecffa0b3c13d6d7b
70790 F20110115_AABPDT gallas_q_Page_215.jpg
34efdfeb7849fd6cc023b2836b6b3c3d
c81cddefe0500862c9bce0af945f5b8499ccec73
14394 F20110115_AABRPS gallas_q_Page_161.QC.jpg
227200d0abf10b6d7266a35cd5a0b721
a6a73a2282f6d285d18eb15be766db24db900f1f
F20110115_AABRCH gallas_q_Page_288.txt
8de88285471122a9edfd7a91de44b888
1bd36234a94354b36bdae927a5ab1b693040161f
95423 F20110115_AABQSZ gallas_q_Page_370.pro
b0de5225a8fba7c97489e99dafafc321
4d2ebef8de11e294167c783df158a3926f271f56
F20110115_AABQFO gallas_q_Page_333.tif
04b526942ec2747590a71ec8a38fb3d8
f508fb2deae15e253c4a50ff335c3dcaafddfde8
73010 F20110115_AABOZE gallas_q_Page_069.jpg
38864047d721af3dbd9e661ef2536914
424de079cad1c5afa789b3275c5477b7d94d832e
63703 F20110115_AABPDU gallas_q_Page_217.jpg
4273bfefbcedb2236f92edf835ea386c
1e6bc504f9392f4520c9e3df24b508296288ea8f
4547 F20110115_AABRPT gallas_q_Page_161thm.jpg
c3c635d38794da39c72aa34966e39700
b5a9daa729d5146b2752ec55d69dc0d092a8ee1d
1480 F20110115_AABRCI gallas_q_Page_289.txt
1885af63402349ab948232cedcaf5f71
f9158bba7b478d5890adfad85bb25926be94efdc
F20110115_AABQFP gallas_q_Page_334.tif
fe8e963d5ab6434911820824e4b03b02
187c7b3c544974400711dd509fee3c153f5d782e
63461 F20110115_AABOZF gallas_q_Page_070.jpg
9c2f000e34f3cee352a57d288c52ba6c
00b86cc47c58c863dd1657cd294f4c2cdb967a67
66283 F20110115_AABPDV gallas_q_Page_218.jpg
97ff3b0233577c7ca9d02a521e088ab3
06866da6b43501ff2d07a170bdc80339d725ede7
5829 F20110115_AABRPU gallas_q_Page_162thm.jpg
c61393842bb5df018e37b9bbba1dc228
696b04217b57da2ff4b215da5cf28ed6e288888f
1351 F20110115_AABRCJ gallas_q_Page_290.txt
6bb27f93d352143304ee98b7987d32e0
0c8c604959e1bab978719853583a0d6f0b4debb9
F20110115_AABQFQ gallas_q_Page_335.tif
b8b28f037dee28fbba0a50fcd19076d1
ae76daf0f65d597bb635e3cb9f8b485176f3f58a
64305 F20110115_AABOZG gallas_q_Page_071.jpg
7b5739203f835543ccfa52e20e9370bd
92da6dec15cad5beb38709f4faad6f71b9916cdf
62743 F20110115_AABPDW gallas_q_Page_219.jpg
b8e062ba24896be6249faeb6b3273e63
e17a764c8efc4a761dc94335e27668a00b0c995e
6787 F20110115_AABRPV gallas_q_Page_163.QC.jpg
b271e42baa10348aca51911f10b57443
ffe19bc4f926c6f1d630a1c63c89f9acd4b73b3b
2152 F20110115_AABRCK gallas_q_Page_292.txt
a075d7fba59a4594cf9d8aada9790d5d
2f35ae61ddf1f2dc7794af9a37df0fec1d418b5a
F20110115_AABQFR gallas_q_Page_336.tif
f94589c7c257ff6b3056a16d69ec9fd3
8956abf55503de4e556001f4c3c0671ae47fad89
57715 F20110115_AABOZH gallas_q_Page_072.jpg
37b86fb928f612ed7baec5b3e8d0b9e0
e52417c6b4f186638a09de240289fd6a34fc1ae0
69171 F20110115_AABPDX gallas_q_Page_221.jpg
8998e0d10d3c2a07cbae7933c3c8e00a
92f689a6fd70cef2769f1d6a877ec52c063f5196
F20110115_AABPWA gallas_q_Page_025.tif
f031245b073a2941f253961fabccaba7
936b1ad2b3d07d5d7b9c0ee0e70f7fdc83a99769
2377 F20110115_AABRPW gallas_q_Page_163thm.jpg
f164add4327ea78e01b057729a102845
8ede34e1d34e26adf6f478b9adc4ed5cb3d68eee
2874 F20110115_AABRCL gallas_q_Page_293.txt
5169bef9fca5d6bbdc985574da814045
8389c58daf62c4047716cbe49fc6a55e57e6219c
F20110115_AABQFS gallas_q_Page_337.tif
53fdcfbb38eb7b0c92e85e34df62709d
e492a0dc76bd8c658db87975ec77139f0e692cd1
70545 F20110115_AABOZI gallas_q_Page_073.jpg
4c6ef340fc1e9d109755eb19803cfaa8
e916894bf9e11ea44e1ab8b7089e4d2beb85f7bc
56562 F20110115_AABPDY gallas_q_Page_222.jpg
b364e326cb1cb7add205f230506f8d1a
b1c39964dd3704882b6424b0f78e3a38f4fc22a0
F20110115_AABPWB gallas_q_Page_026.tif
563b778628fce8ff8de68b6129bd8d8b
993f5b88727b9ab32ec246ccf43550e2c7a317b7
6337 F20110115_AABRPX gallas_q_Page_164thm.jpg
9d82139cbd1864b9699b51a060fc3ba4
b358858758fe8083466629b5a75bedfa8125585c
2004 F20110115_AABRCM gallas_q_Page_294.txt
a9a21ff474da84637f0eac7d62230289
1936c95f126119cf372f24c5143336a3da0390da
F20110115_AABQFT gallas_q_Page_338.tif
dd1cd127b86c167a817cedd6f023de0f
bfcfe2003a0242348b3ababf7ed932014e48a784
46853 F20110115_AABOZJ gallas_q_Page_074.jpg
e90950375c91bbd25d29fd86370e552d
512b78a28094b0d0d467a59ccc9fd3d9bfc8eb20
57623 F20110115_AABPDZ gallas_q_Page_223.jpg
0e889b6a30f233d863a1d5f463dc9ffb
39721804f73f365b41630bbf0866ab1c04c4b728
F20110115_AABPWC gallas_q_Page_027.tif
2ae9b0abe2910eda0609909311e52b52
fb747722b31267d52a600477ae068e87927b78b7
21159 F20110115_AABRPY gallas_q_Page_165.QC.jpg
b7af824e6f7133494d121676e3095a71
57f4987178b13fd1e1af9b80b352c960764f7fec
1165 F20110115_AABRCN gallas_q_Page_295.txt
e12de6ba222d07dc258c98dc512c811e
0a75fe65465bf4976554fcec77e3b5d58e1534ce
F20110115_AABQFU gallas_q_Page_339.tif
0d73ab73f937bc3d2e459cf00fcdf3f0
eabd22f24334c7794c59bf440444ef5f4f12c66e
46332 F20110115_AABOZK gallas_q_Page_076.jpg
5ba0a833cefd1271ce259409213cb9e7
0bdd5fb963596472c28602c5123b488d7120ba8a
F20110115_AABPWD gallas_q_Page_028.tif
a7390bbdf0e68788e98e0a45ae738927
76e21acb7f3af489c605901210ad4e829fe72702
6269 F20110115_AABRPZ gallas_q_Page_165thm.jpg
f7ade4f0f3e5c1b250bfca1aab965765
83d03fd06136cdb3347496525bb7bc14ee69dd30
2038 F20110115_AABRCO gallas_q_Page_296.txt
ea1878612b8138e109d3e28c69f87481
b6245f4c6ff2e13d4733228665279cf05f158c1f
F20110115_AABQFV gallas_q_Page_340.tif
b2bd02f7852cb60b7993ebf62e21acf8
f3fb226316e8ef2a4444066013f18218ee153db8
68394 F20110115_AABOZL gallas_q_Page_078.jpg
42621a9c795d0e68c03fb27ca4202a66
bd7df0466ea0b0e99354fd87982359984ddaa6b0
F20110115_AABPWE gallas_q_Page_029.tif
ad5cf40d4d847b95ef11a4a031f552d9
93d177f5054aa0a642eeefeedc9b7efcef158cb8
46558 F20110115_AABOMA gallas_q_Page_316.pro
4c842f094854769db659dd2340b95d54
f0698a88fd155a30317cdf0b1c69368fda5db0a6
F20110115_AABRCP gallas_q_Page_297.txt
1ad198ab31fd39e9a0f440ba8aada79d
b92e3a61b42c1d1ef3596c1096223383f3f85aa3
F20110115_AABQFW gallas_q_Page_341.tif
0c8c44d3700444b74370451bd92470b9
ee1a0650105ef45b3ce80557e8f7762c7f08e2d7
61027 F20110115_AABOZM gallas_q_Page_079.jpg
27b49a94f0f62bf0c45740140b903a47
0c82f367083fab7c49905bd7b82d2bc88cb7103b
F20110115_AABPWF gallas_q_Page_030.tif
a2a34cd82f8952d3e58d0b9e033cffd4
f12db74bc083af3c716c3eb9c1e7b5a9e52c6d84
23929 F20110115_AABOMB gallas_q_Page_336.pro
adbccf019bd6787c424aecf6ae1b5cf8
7dc980136a82b192820a9597e40e46e0b835f9c9
1770 F20110115_AABRCQ gallas_q_Page_298.txt
a3fa08ab372eda09fb15c983d91d9a90
21121c8a6f2f78dd4c1120f142bc82823dcd1616
1491 F20110115_AABQYA gallas_q_Page_154.txt
43e436708eed29be7df1c411be06fadb
ab352561206571a56c81f3944e9278b2ea5dc777
F20110115_AABQFX gallas_q_Page_342.tif
aaeb243f5b48b8a8ff9cb2a550f0a13c
ce65d4ccac3f161986d906a9b6b628ca3b9fdec8
67238 F20110115_AABOZN gallas_q_Page_080.jpg
118d1025162b3f6cd393986a55bdffb5
74687eebd684dd1ba3cb1530ec317f0cd89b666f
F20110115_AABPWG gallas_q_Page_031.tif
70ea3b6beab3c5e0b73192b872cf36ca
803d241f29af288009983fd5ca38f0bf8c7998a2
32556 F20110115_AABOMC gallas_q_Page_333.pro
14b1e48d8d567251f2df9037dc9b94f5
a927b0b8895fd8156627c3b341bb523091b29700
1850 F20110115_AABRCR gallas_q_Page_299.txt
9f6d7ebaf05ac9552522f4c632720d99
1f3f1cde35ef98f2a3a347625993bbbcbf25090a
1579 F20110115_AABQYB gallas_q_Page_155.txt
f62624fcf365e3f5269d21832f6521ce
ee8aaeabb53a566ec4b4dc46cb6e80161989b5db
F20110115_AABQFY gallas_q_Page_343.tif
bbeaff7e035129f59d2b34b5043b7680
6212e375344c5e7ea6cdeeb85df956dc87966bc7
67540 F20110115_AABOZO gallas_q_Page_082.jpg
a326d762814b903af9d11b5f64c262f5
a6081b7f981e4e5c52c5ad599677a6eabc4b6acc
F20110115_AABPWH gallas_q_Page_032.tif
a2a5c365506cbcb3035221fdd690a8e8
ee92097751c7c02600863bc92328a3dde0092dd4
36275 F20110115_AABOMD gallas_q_Page_311.pro
02ac02614f6885f90be9d88df1c88f7f
06989dd99d59d6da6244ddf1f3daf1adc0148666
1620 F20110115_AABRCS gallas_q_Page_300.txt
a6961300374a8dfa1072e08aa8c4eb0b
0d1ed5b0922103ec7423c1b886cf9728934e404e
1773 F20110115_AABQYC gallas_q_Page_156.txt
d2a1ec16e49b85a8d1c6ad12d2208d41
5deda72e5ffc048e4568c63b791b24464a992206
F20110115_AABQFZ gallas_q_Page_344.tif
d96d9ad9d7e737c32e1644d6f538f8cd
4fc63cee813bcfaa3fa01641cdb3728219fc09a2
63030 F20110115_AABOZP gallas_q_Page_083.jpg
bee1c63d8d9967cf1d075c908b393f4e
141aa45ba4ad83811dedcfd88cdcc57a95726d85
F20110115_AABPWI gallas_q_Page_033.tif
858be3897a6f62bd58b495f690832525
cc2b5d14969ad0fbd3626f7d1631772afa45adcf
6452 F20110115_AABOME gallas_q_Page_234thm.jpg
b917c5f16834b001333d74d3b7ebb297
d5b4b272da692d20b6ad9cc0346e69955e3f4074
1870 F20110115_AABRCT gallas_q_Page_302.txt
edcbb9453be1f6faf1648bd50e981962
300fe2950082782aa1a769de9d505c6b1024b502
F20110115_AABQYD gallas_q_Page_157.txt
51336fbf0ad36a423fa7e91bd7a3a7fa
de6fba9b0a0d29197fce00e6aece89bd1efe62d9
66417 F20110115_AABOZQ gallas_q_Page_084.jpg
62396b71a9298341a11e7da16f0b2c28
6d29d67235fb2e90cbbb7d0bdbe24066a031c92f
F20110115_AABPWJ gallas_q_Page_034.tif
9c2c120393e2e4f529e2cab3dd72ac9d
995cd3c4432701a36b1da35fdff95d36327cd302
4837 F20110115_AABOMF gallas_q_Page_027thm.jpg
e34af2bd3c8058ba188578a99a939e2b
740c5f5c5145ea408b1cf840ac6b1a601429d5f5
1906 F20110115_AABRCU gallas_q_Page_303.txt
d9ae9908a5d2283ebc148eca89707181
620dc7b722d7fb4fad07871af51855e8e3769db6
1537 F20110115_AABQYE gallas_q_Page_158.txt
f57e96949e1fb23369df4765e096c161
6318e43f43fc9b80412c6a87d8cc668d7efbe6a5
82929 F20110115_AABOZR gallas_q_Page_085.jpg
753e89afc14837ce7c0fe77f50ec5001
bf3fa9850e3a69949ae5adb5e67758930a4c63b3
F20110115_AABPWK gallas_q_Page_035.tif
17a55a69a1e93a136a0845bd1621b09f
1a03c6a33f3fe09109a4ea6a38bd59bf53e486a4
50389 F20110115_AABOMG gallas_q_Page_051.pro
88fcbf366d8450e26ec251c111c724aa
0328faf84df503c3586f80e71bafa01b56bc4519
2016 F20110115_AABRCV gallas_q_Page_304.txt
867bb83a2ec974f76f59111aa3c55d16
d30657ec709846f2142f00b4f86528216e93a21e
984 F20110115_AABQYF gallas_q_Page_159.txt
970147da31c7154c3aa412444a4a5cea
6aa25b1360d1b5fa12ddfb53dfbc3a969adf4953
44160 F20110115_AABPJA gallas_q_Page_386.jpg
bbe023672c35a9ced74e7a517479f02d
1a7ba2649aebc41d543b9f50d397b68dfc547f25
86126 F20110115_AABOZS gallas_q_Page_086.jpg
3215e27f41ba526f7f098363dd6e3dda
49dd3d30728621c8c75c2b167f003f9ad0b5d946
F20110115_AABPWL gallas_q_Page_036.tif
c76b8bdb00a5c33957d231495b312442
92e9b49b6a7c208e204b0e2792cc1a5090191769
69986 F20110115_AABOMH gallas_q_Page_375.jpg
c167399472a322cb49ecdcd98c82148e
ec24f198864749ed4b8a6feb0cae77dc5ca88246
F20110115_AABRCW gallas_q_Page_305.txt
1fc67f6c1008b1a29cb09fa2bad9089e
118e0013c2697cb02c6a17bc50b6c790523a801e
1979 F20110115_AABQYG gallas_q_Page_160.txt
a4cd0bf5d314be3a61baeeafcf108403
fb909ed507e5797b5af9cf76117f3ee0fc49c5f4
23325 F20110115_AABPJB gallas_q_Page_001.jp2
d8249a9e62b2f7a99b21305f49421c66
acfaae3427b88161bbebe1f8a6062e26d42236d3
64312 F20110115_AABOZT gallas_q_Page_087.jpg
505c13787b83029f2df09cb3b68630fc
f8e102af8b9a341718a34ad023ab12b8e1315752
F20110115_AABPWM gallas_q_Page_037.tif
552f18d6e76b17b4572f2f17c639ad34
0f8db62ca264a3af4be3cc6a4bdf802388948d71
F20110115_AABOMI gallas_q_Page_033.QC.jpg
640c5b1b7f016b61fbea042a32d4b80c
e9fc68e211a1dc062357e4bf9f558d9c88edca0e
19236 F20110115_AABRVA gallas_q_Page_247.QC.jpg
832157049dd528ae8d981be42604485e
602cb7c666de9da761b935d539af09586daa613b
1897 F20110115_AABRCX gallas_q_Page_306.txt
434400d55eda6cd437fb3549568c5515
5559020854dbe24b13b242ddd98bf0fe1f582b8c
2139 F20110115_AABQYH gallas_q_Page_161.txt
2b8ebfaee6b183b1248a470b37c2c6db
88a721dadc702542f4464d3e15eb541329776268
5555 F20110115_AABPJC gallas_q_Page_002.jp2
b378e76c4227c06e8e69169cb63d613a
88be736c857ef4f2177d662adfdb373f4adaef4a
71706 F20110115_AABOZU gallas_q_Page_088.jpg
d0b0a409f9b9d4fcaa21945674e598c0
700aacc68cd4892b10c42d25cfd62d88abe7b533
F20110115_AABPWN gallas_q_Page_038.tif
4f7d82ad4d3674f82dfe9eb96ec83ce8
bd4fcc76666975b9fb6c00a44fedbe11b8819889
5545 F20110115_AABRVB gallas_q_Page_247thm.jpg
a920c7b7e3a93b0d20503fc7f578f321
e08a4344ca52435f15f8576c54e8e3ea779877dd
1699 F20110115_AABRCY gallas_q_Page_307.txt
07da30146e582e36e219bd5fa5b566ef
24cc27d4d21f0ee4704e30d3a45da5b6dc1436b2
F20110115_AABQYI gallas_q_Page_164.txt
bbdf7fa44e0abee2101aaf78fbf51c42
a211ed9d43e4a41f3f171b0cc6e23e6edd480787
70995 F20110115_AABPJD gallas_q_Page_004.jp2
d3fd826493e343a3865e9ea333362535
b8141c6100bf88800e907a3953499c2f1ad46d49
71867 F20110115_AABOZV gallas_q_Page_089.jpg
08f9fe3f1cb598d4b82a3fd17fa83aa8
114ff7dc020c9db98abddcf2c606c199abc156a0
F20110115_AABPWO gallas_q_Page_040.tif
dd1f8b41a033a6b959e2762d5be0c493
470c4060d299223bcb6b0e68f6950b0f6c0baa4c
432 F20110115_AABOMJ gallas_q_Page_163.txt
699b3fdee5f33696c584f7344ed8e15f
825a409c4ee68d0b2ede1ae176420a98626e25c5
21780 F20110115_AABRVC gallas_q_Page_248.QC.jpg
9526b5bdba7a45f647efeb823bc72b16
0383dfc1947e0089b31e843bd2401e847d800689
1602 F20110115_AABRCZ gallas_q_Page_308.txt
0ef0b7effee6feb622580cfd7d1b9bbb
78b745bbea1ae3c5e38d398eabc422133409d2fd
1390 F20110115_AABQYJ gallas_q_Page_165.txt
2e66c26ccc98aff9edd6704357b04da5
ed374837b87abd3a372454302aa665819f4e729d
1051978 F20110115_AABPJE gallas_q_Page_005.jp2
68a6e83d93211c16c8c18d91daf9c17d
b97e5cc7d139a3b30dd8fad64293cf5a92c2ca96
F20110115_AABPWP gallas_q_Page_041.tif
9674f517781248ffd6b286b15fbfa647
72a191241f5149bed695afc49d3a245a73acfa2d
75705 F20110115_AABOMK gallas_q_Page_195.jp2
f1862a6c1cbed97bb40170f2e21e88cb
12a490e6c1b0070061829d7620f6f8381a8be792
6268 F20110115_AABRVD gallas_q_Page_248thm.jpg
0e0146d0d27327baca487c6295531279
736dc3aa8f5839bd27d4e2d4fb1fe2cd71451efd
F20110115_AABQYK gallas_q_Page_168.txt
2035682c1098588ce577ce7051ba185a
e4c7f9a4453ed849fb7c55d4ba562dee66b779e1
72820 F20110115_AABOZW gallas_q_Page_090.jpg
b81ce4005ebc9b4716c3e852cbee25bb
4866e7f604c05d30b019bb86738bb4781e00ee15
F20110115_AABPWQ gallas_q_Page_042.tif
228607e8c98525f572919d90c64dbece
fc7db447275e718e8865248963a895a481f53ffd
73768 F20110115_AABOML gallas_q_Page_101.jpg
5b36e248e3f42814233879cd31ed2892
3ca98b87a65b54f25a773b855cb64e56ecf28501
17481 F20110115_AABRVE gallas_q_Page_249.QC.jpg
4aca3e608e01db9afcb47883f6789a44
95d8b242984f2680531cc76a7ff4cb815fb37091
2037 F20110115_AABQYL gallas_q_Page_169.txt
24614a1880f2ba47b749ed3b2357cb10
7d08e2c251fbdaeee0ca1d0cecc2ad807ef8fad2
71179 F20110115_AABOZX gallas_q_Page_092.jpg
f56a1bc89bf9abe204fc3d454c65cc1f
1154945587a4ae0db9087ceef9613d22d07f14a6
F20110115_AABPWR gallas_q_Page_043.tif
d0a43509b2e3f16c707b77a22c44a83a
799c712458641f85c708ae05ff3a0fcebd2b5f18
28307 F20110115_AABOMM gallas_q_Page_016.QC.jpg
a4e3f6606359d979d26eeb10925c7e72
287517dce4c00e416b5898413a79f90456bfe8dc
46461 F20110115_AABQLA gallas_q_Page_115.pro
2469c1660132586b32160fe5c1d6694b
b372020c26a2b86c10bb90526ee7641f2dc00285
F20110115_AABPJF gallas_q_Page_006.jp2
d3cdbd144b0f9e4f22e7e4766ff5fd3a
4434aaa81937e6e6c503b2af50909b210ef0ebb3
5699 F20110115_AABRVF gallas_q_Page_249thm.jpg
6b77c460d30ebaf065bb14d2ab054cc7
e20400dc1ed62f966f454c28db20dde9ee1a39a5
1388 F20110115_AABQYM gallas_q_Page_170.txt
7070e138cb3f340bf44159e774b6f313
03578332da81cb2e69ce4fc5eeb16d216c6ded35
76963 F20110115_AABOZY gallas_q_Page_093.jpg
b8273e3b27b1cc4a8186d0f4596249a1
c33ce9207704237c772929a5e86e8118d330448a
2157 F20110115_AABOMN gallas_q_Page_143.txt
dc753d2ca8712a85a155588c44a3370c
ce711003a23dcc3adf700642a8d8166bfa5d9ef2
23009 F20110115_AABQLB gallas_q_Page_116.pro
5685a4ec87ca673d3ee31c8361ff0e6b
1be4337f10bd61975d1198e8bdaf5b8093c70abd
1051942 F20110115_AABPJG gallas_q_Page_007.jp2
c72678ca2fec4fafce626af62a6db9c4
f8d4d65288bd45668705b63ee8b82a7095a9310c
5742 F20110115_AABRVG gallas_q_Page_250thm.jpg
7918dfd5756d5d9f29f167f94ef3cbb0
359e6b1a3149b9969720f2f71c5d5ce2edb8b9d5
754 F20110115_AABQYN gallas_q_Page_171.txt
356cb98b1a9fab541ecdb73d4373737f
2566bb17f2d5f797fb593a5e371436d69d1b5cad
86253 F20110115_AABOZZ gallas_q_Page_096.jpg
6f14fdedd2c2d18ad990f50e0762e5ed
ccd0f86411f9148f3c42f629c56eafeb724ff885
F20110115_AABPWS gallas_q_Page_044.tif
dc36ffb5e70bef7ea89c134aade238fc
17be1f8577cc0b83b4c0cb71fb8c52dd97a262b4
5096 F20110115_AABOMO gallas_q_Page_333thm.jpg
d20790460d9489f72b414d574b432ede
3aea806bf06742aaa30538e806ffe2253d5833cd
42637 F20110115_AABQLC gallas_q_Page_117.pro
986303086e863b2a13485a30f2a9c708
b15496599b03aaa0ebce0ca9a8527ad58ac502b7
336392 F20110115_AABPJH gallas_q_Page_008.jp2
0a49423c4a7cedf24614c8bc5c611b6d
7469e1ba0b83ac6acc36022efcf1dc2b5a37d56a
20204 F20110115_AABRVH gallas_q_Page_251.QC.jpg
3f7215f7176ba1723ad8ddcf06efa544
ca59df077da2fe3ba30d751be0c1c7c0836d7d80
1852 F20110115_AABQYO gallas_q_Page_172.txt
a842e3a4a6abfb908c17f3f63ebecbdd
cadd8cbd5cba16649d4e96569631b56dc597f560
F20110115_AABPWT gallas_q_Page_047.tif
7fec28acc24db70ab56103f0ea9e649c
9f923f67484ad3e90f85cdde9d8c9408bb674862
17576 F20110115_AABOMP gallas_q_Page_259.QC.jpg
d6643283f22178b1d5032f60027a671d
ad7fec236d597590374600654663f26b8dc1dc11
43775 F20110115_AABQLD gallas_q_Page_119.pro
d74da31c6e72f8a52150103aa97eafe7
96837c32ad6a84920a8e9d348ec5c557034424c1
1051940 F20110115_AABPJI gallas_q_Page_009.jp2
550eb89c33d09ddf6f991d650fbdcb22
4e7f51272c2b2ac2d3578a4cf04637463138d397
5822 F20110115_AABRVI gallas_q_Page_251thm.jpg
9c14e404d1e366d7a53f5241ec7e15f3
f7dec5021646290829ccb554d32c3b59f605d8c9
1108 F20110115_AABQYP gallas_q_Page_173.txt
dcb686c4ad5199cefb9ce146706c971e
5d6d804bcfe4a6a303abbec370caaf521b33c5f3
F20110115_AABPWU gallas_q_Page_049.tif
13eb3f48b824ddcccf3a1c157ac9b3a6
19b3df745d5a8a016cbdfb9a7c018b537cb175e7
F20110115_AABOMQ gallas_q_Page_212.tif
9a70dd1465cf8f54bdc028eda7033886
76d959225abfecaad6b942ccf301571c7ca25104
F20110115_AABQLE gallas_q_Page_120.pro
ff7ed81e249b9b4c757793cd33ba9828
aa7e7cac28bbaaaf8de0f49337c07e6bf27a3afb
F20110115_AABPJJ gallas_q_Page_011.jp2
86babe94fcb3f493ac60965bcce98bc6
f6e84f8d960a1be09a711244bd76fa2a7d8bf424
5048 F20110115_AABRVJ gallas_q_Page_252thm.jpg
21e379335132243bd9887d6912f86441
f1399b5c7d792d5ac2eae957594721839cdb5532
2164 F20110115_AABQYQ gallas_q_Page_174.txt
fc6b95a6ec6814bca10e3dd46b11f548
6d2c1a615fe60433c1edc23c00aadfc3852c223e
F20110115_AABPWV gallas_q_Page_050.tif
665bcc7018657999b422f00a92e6286a
ff6a4a195679d1e678f4e8f92b5e97acec9d9e94
4864 F20110115_AABOMR gallas_q_Page_308thm.jpg
40ab8e1f418570c1904279491cda9bee
c731edef862f8709672d99077f46ea56f7824842
20124 F20110115_AABQLF gallas_q_Page_121.pro
3918c141ebbf093d83581a526424c4f4
b2f374c40b9e87c9858bee802dd1bd16ca59bb2d
F20110115_AABPJK gallas_q_Page_012.jp2
f759cdfb2e0eb4eccf59e4f60b04b365
14528016fc93a5ad0a3edfeaed64faa737e8aaa9
21337 F20110115_AABRVK gallas_q_Page_253.QC.jpg
bf354f056a4daf4c9c6a0179cf8d0e90
c0564028b83d01d4c4b72ed55e37e6e57d0fa89f
1810 F20110115_AABQYR gallas_q_Page_175.txt
92e9d6b0ab25a1ea6e1632f4bc2b2bf8
ff98bd69a40fa0bccb5f86b4fa2c741b44a534c7
F20110115_AABPWW gallas_q_Page_052.tif
77f13bac0ea778376f5312afbdfed61e
87bf7b497e56480095f4c2134b20d756ff55dc31
F20110115_AABOMS gallas_q_Page_348.tif
a8d18322830161c9218ec15e28f4a63b
5a433efbd170ca787eb4a2b34a346ae0621c9b06
F20110115_AABPJL gallas_q_Page_013.jp2
6ca545066d704a644c43f21c5d6658bc
389b76c147ae1133fc0f1a120c2893940a2ee612
6156 F20110115_AABRVL gallas_q_Page_253thm.jpg
6c7843f7e0eeb540123a1f4175a6e6ae
4b477027dd0ad74a581583b0ecdb0e75e2f1c0e2
6568 F20110115_AABRIA gallas_q_Page_040thm.jpg
f608872f6f12797490332766eb3467a7
e5ee270facef341882b83dc37ae7dbe2ff632333
2590 F20110115_AABQYS gallas_q_Page_176.txt
d6207c4ee1358214fb783991c5630a49
121d8c00797909d4126a809b8b3abb24df02569d
F20110115_AABPWX gallas_q_Page_053.tif
3afad56164883640441c9abce1026fe7
2b99ae1a06bfe883923cb5099c669dd7494c639a
F20110115_AABOMT gallas_q_Page_057.txt
9c35a617bad1dc8e3b4bbc3e661b86f8
c1c353f871b3a6ac3d5da19db5add2f04592a645
38231 F20110115_AABQLG gallas_q_Page_122.pro
ceb031e799d4a5ba4407f5d3868ba827
93962cf35cb74d5f53a475fefc086ae39a9f4ed0
F20110115_AABPJM gallas_q_Page_014.jp2
de6b1751240ebbf7fc1298f5484c4892
ac994f8e5e7aa1d7b6e6ec441171ff5b596e1645
20510 F20110115_AABRVM gallas_q_Page_254.QC.jpg
12f7213a87a0819e74cfd637bd342ae8
606314cbca0adb138a6c61fdf87483690fc1d91a
24299 F20110115_AABRIB gallas_q_Page_041.QC.jpg
ef13ac2fe1f6412642da7dcc10d84445
572f43fd4ae631ea08227d8b0fde425012935c4c
F20110115_AABPWY gallas_q_Page_054.tif
41446a68a659f4dfa2a2e80c8b1fffaf
016a649cb758ab0f155d09d1999f2f04ec2a04f5
39715 F20110115_AABOMU gallas_q_Page_211.pro
93f28e59e98e81b5e9fe64d82b6c59c1
9cb0d30499a0fc3d8573a7c46e225ea78faf6887
9042 F20110115_AABQLH gallas_q_Page_123.pro
33b310cbc5a55c59bb56c6a30b6f1313
ecd4bd2997e63b3ec96ad2e252da9a066ecb21ec
F20110115_AABPJN gallas_q_Page_015.jp2
c62a748d79534ac68de86b6d54ae31bf
95fac49c0c1c16d09b201e68553a75fe485a907d
19962 F20110115_AABRVN gallas_q_Page_255.QC.jpg
edc8d36569c1fa839ea1c86f5bea6f8e
336f542cc765f6502c8836383cc6c2842aadc0cb
1999 F20110115_AABQYT gallas_q_Page_177.txt
038dcb4270099c1263264e277b04ba51
b932b91595cb49490f03188ac5375eacafb6fc24
F20110115_AABPWZ gallas_q_Page_055.tif
b1463330bbb0d01a042c7badf59d3b86
f596a221b7e53720146cc7ca107643e63c62b661
36494 F20110115_AABOMV gallas_q_Page_289.jpg
802790f5d90493b8c00709c518a3537c
ff8a497a6089462e16ba2fcb88f49a3d016cfd80
19342 F20110115_AABQLI gallas_q_Page_124.pro
cd910a5159f619d1fa293c8f4af8b034
6005cda9c43239e82a3b80edcf3ba44d437f506e
1051983 F20110115_AABPJO gallas_q_Page_016.jp2
011abcf6375fb717bd6c7a5d38faf701
e4d5bae953b9e5d65dcd7757861aaa8d7272edb4
6081 F20110115_AABRVO gallas_q_Page_255thm.jpg
f9bd7db37a25f817009b73fb50ae7c5b
8e4cb93bbcb369bea51c2dd73117844f439c4054
6928 F20110115_AABRIC gallas_q_Page_041thm.jpg
ef553c4018fab15ee41aec78c67afee2
b0eced097583411cb2751a0444d864e2fab70205
1617 F20110115_AABQYU gallas_q_Page_178.txt
ac8634d319f0ecf3f2f59d9fcd0ef88d
6d527c9cdff57aaaec5649533aa17140f2f27d79
4929 F20110115_AABOMW gallas_q_Page_320thm.jpg
5f3fc365998f08d1c090be78d7905c7d
0b6b05fee16e5b44b0097e2e91c8d5c5371a0809
39215 F20110115_AABQLJ gallas_q_Page_125.pro
354457143b10068dc293d8d21ff433ab
774223c3d83e88153ce3aa656b0bd24420e93f28
F20110115_AABPJP gallas_q_Page_017.jp2
23e858a789573cf57808f2bfb9f6b812
1f3a8c221f9058a7d0dd426eb103535beb1ed1e1
25089 F20110115_AABRID gallas_q_Page_042.QC.jpg
86fb65669549163363a98e4f8446f3e7
1bd9ee738ecfaf103ef98c8793efa5e1e46069b3
F20110115_AABQYV gallas_q_Page_179.txt
40c939c7ed015e9a051249f6df78e0c3
e85cd383b1e13aa9cda413614bce619c526d964c
2337 F20110115_AABOMX gallas_q_Page_286.txt
4318abdfb78767e2f3c8bee9ed56c441
7d889a5f4e7601345cedb0eda33bbc72f53d11fd
43764 F20110115_AABQLK gallas_q_Page_126.pro
536dfff88cc7965a668d423a4c406fc8
c5f5373292a0528a61ad8fea71a37e06dea7a09e
1051986 F20110115_AABPJQ gallas_q_Page_018.jp2
351f3726f90cce9c73b4dbad99a0b972
37c8bdd85ce8664b9246d95f1ae4e749be2aab57
22126 F20110115_AABRVP gallas_q_Page_256.QC.jpg
89bb1a2bd377b16ffa7842896681b650
f4eb23bfc66b54e030aac9783e8011ba7dd7bb7f
6897 F20110115_AABRIE gallas_q_Page_042thm.jpg
14749e4ba4870bc4371785361af65c60
61f243b03f5aad40b3ada50183e0ccc7e934634e
1099 F20110115_AABQYW gallas_q_Page_180.txt
8ecbf444ed2e4cadbc6ef2d49c8f5ee0
0729112e8be61cc78f7a76443568b9e9e2189514
648584 F20110115_AABOMY gallas_q_Page_181.jp2
2ecad691ea51a1bdb74501f7a85d8a7f
6e5ae37612c5bd1436f95db06c7e7411f489898b
45753 F20110115_AABQLL gallas_q_Page_127.pro
d22405ca6d0271263cf91e0ae0056ff1
67f94115102f3ac26d5f6cade81ffcb6d2258db4
52137 F20110115_AABPJR gallas_q_Page_020.jp2
bd33e6661dfd48e28b72670408fe8ed7
54a36ab55e16582edef9b96580d29ad4d538903a
6242 F20110115_AABRVQ gallas_q_Page_256thm.jpg
59bbb8bf8b67e73b6c9826a992ad20ab
ef9f8460db42cf2d464b2670ac1ff327f3fcdf99
24438 F20110115_AABRIF gallas_q_Page_043.QC.jpg
d010b1ad9ad1b39a6b514ae9846b974b
efd795bbbd1dab1e2f9c82f043dbf39ab9b019e5
1437 F20110115_AABQYX gallas_q_Page_181.txt
98b34daa5e2811a1be9b791b57f380e2
2e239b0c5e6b723065a52424e279ed5814d1c2f4
6136 F20110115_AABOMZ gallas_q_Page_083thm.jpg
d1cb99750b1625c6667e68ba74b15cc0
2005aaea0610b7cc019436888df52c4576fa73a2
19126 F20110115_AABQLM gallas_q_Page_128.pro
e8802250442704853b3008706be33bb9
c45427481ee77db2df25b9c70e893578a53f25a2
52688 F20110115_AABPJS gallas_q_Page_021.jp2
251abca966ed71bace0ce3626d373536
3f5bf7cbe1d0612c6540cd581e97b015e37021a5
17410 F20110115_AABRVR gallas_q_Page_257.QC.jpg
3c67c65d282e2a6771e912c769569c89
a4f440134add59c8a8506567cf1ba54b84826c5e
6715 F20110115_AABRIG gallas_q_Page_043thm.jpg
3752b84e69b09dd25aed411ba2bca044
251875551f3cdb8ff6e027ec52f449c674bd4d1d
1712 F20110115_AABQYY gallas_q_Page_182.txt
68b72486d635361ed52e9d4e624de306
6eb75a561103343a0c10d97f66fdb758dc4ba258
47271 F20110115_AABQLN gallas_q_Page_129.pro
26c8640c2e57721d58ead08990273e29
9e17fe3fc11c2f45e74194a295e6d756858441c9
64376 F20110115_AABPJT gallas_q_Page_022.jp2
116a14efc02b2675e9b621c451c26086
ec8d8f1ef80dbde095565990ba96f2e4addfec59
4970 F20110115_AABRVS gallas_q_Page_257thm.jpg
71c0f870bad94ee98cb52be41c965de4
8fb543baf6b23eace822e16dd4cb0548ee4665ac
25730 F20110115_AABRIH gallas_q_Page_044.QC.jpg
6b8e0ebb8987ceb334a61c56916a1a9a
15415cb4284567840b3927c057add7dafff210b3
2100 F20110115_AABQYZ gallas_q_Page_183.txt
b0499628ea69e9853a6872a3884a3018
9934cc26d13e8fbf7482b5b15d8663818346e1ed
40020 F20110115_AABQLO gallas_q_Page_130.pro
e2bde03d2e007cdc62db8a12b832b8b2
2f2ce11a83096672804f7ff8d6a6288c0b0d9128
58962 F20110115_AABPJU gallas_q_Page_023.jp2
344977efc3c195e07ba9051ce71d61fd
89da4d2b756c68f96ad631fd2a46a93534045b4a
16256 F20110115_AABRVT gallas_q_Page_258.QC.jpg
da1f6412a1c2d3e74cfae9adc3460552
f45117dc1e9e0391bdbe31666c49fa4bde855462
6791 F20110115_AABRII gallas_q_Page_044thm.jpg
de1a430ae07e17659db2bd612232a3eb
85280606f07ca561ae2b4e3d99158f80fe242949
54561 F20110115_AABQLP gallas_q_Page_132.pro
71a40cc1edd61dc22353ae8b3ccc65a8
c4ea5ff6e6d033508acefbf06d067bb4f8fb6eee
34904 F20110115_AABPJV gallas_q_Page_024.jp2
6baa0766fa13364cf7a7b4e8d25d9929
c2cd3edf1652a6d60d007c95fcbf34f10c33236d
5375 F20110115_AABRVU gallas_q_Page_258thm.jpg
0cc505d55e5673d2aae690342e5e9ff1
222168ae9910d2b0113e743f5219a252b968ef54
24585 F20110115_AABRIJ gallas_q_Page_045.QC.jpg
7400eee6b0f3a3b103a7de078cc26e39
7106174d47619b3e689a8fa0843254df0d6938b7
43092 F20110115_AABQLQ gallas_q_Page_133.pro
d91e8ea760672ba53e3de5a11e419796
3b9b58fc57d36902aeaee37d5ed6af319f3bb99d
57909 F20110115_AABPJW gallas_q_Page_025.jp2
d0ba87b14cab8535e7c0bb89cfd382c0
8a3140b0d4325acfb3e5f406405901d08cad2f06
5830 F20110115_AABRVV gallas_q_Page_259thm.jpg
e2691d8cb98d9fc1ba086132c66865ae
18c1eeca7d0875179f232ca923b74eb29d7e389c
6990 F20110115_AABRIK gallas_q_Page_045thm.jpg
7072c193e28eeb2587ff54865382bbc3
0337ed4bcc67032f35d5aa7ffd061425fa2cd3fe
36337 F20110115_AABQLR gallas_q_Page_134.pro
01e06ecd56d6a3a4aa920e843d490c89
b876a7241d3d0c66ee6b7882cbbf7056b009136f
87927 F20110115_AABPJX gallas_q_Page_026.jp2
91fc636868fe376209adcfa4652bd0f1
95d32189c918f2f84a09dbd9f5b2e93676eea14f
18129 F20110115_AABRVW gallas_q_Page_260.QC.jpg
14fba517409edb495e5990f6c180a6de
6b62297bda6dbeac507332a8e7b6400ab09c291c
24373 F20110115_AABRIL gallas_q_Page_046.QC.jpg
1ea2e6d8c0926664c73618c2fac08f6c
fff1899f107b4645bbd86f101d52c209506a7d52
41911 F20110115_AABQLS gallas_q_Page_135.pro
25ad69e74c8264aecd88299894f390e3
a08e7b1f89a71c132539e2fe82eeb6855ef7c5c5
70535 F20110115_AABPJY gallas_q_Page_027.jp2
20dd6562d0f70a3bb215f27415f6d634
086d9ff56019dd7891f5ace8a7c53bbbf728b456
5112 F20110115_AABRVX gallas_q_Page_260thm.jpg
ee4714d39537ddb463a20ed4eb543ae8
fba190081187def873173fd2c8a7717a87bbd924
6880 F20110115_AABRIM gallas_q_Page_046thm.jpg
ba4881c7caebe79647e6615610d76909
6a721f0bad129aa068853c997b626c188fed4c47
48539 F20110115_AABQLT gallas_q_Page_136.pro
3a6fd9b5df4766417e4c506574ba98c3
d6a92b630c552b102dcbd9f5f5470529e7bd3e47
90788 F20110115_AABPJZ gallas_q_Page_028.jp2
ead0dedbf5edeb638dbfbb2970d2b342
f2fa6c5afe71e1e168f908f918fd04132a2f1d97
12550 F20110115_AABRVY gallas_q_Page_261.QC.jpg
cc695ce011492e955b151a09f4bc5566
15d73df1e64c4469085fd1a9060333331f3a65b9
25355 F20110115_AABRIN gallas_q_Page_048.QC.jpg
489a2799a62449640521c8eff4ca0aa0
0bd80edde419bc24c080b6606e155a23969a9d60
42822 F20110115_AABQLU gallas_q_Page_137.pro
4d99a16427a842810e0b14eb24c42198
ec3f33496a0a625e7f971454eb2c479423b5a049
3699 F20110115_AABRVZ gallas_q_Page_261thm.jpg
26da16a6272a839c9799e875ed5f996e
6850cbb1cb7a8440dbc8eb94a79f9461064daeb3
6971 F20110115_AABRIO gallas_q_Page_048thm.jpg
f6f4080f6c671017390ebca305adfc30
322031c17bf9b60d052885de633762fd519092f5
1761 F20110115_AABOSA gallas_q_Page_249.txt
2c59a56bbd25ae1fc04162e658fd78dc
165bfbeabd3d568c6dd8a7a51840619c2a438d14
33966 F20110115_AABQLV gallas_q_Page_138.pro
173606939f00b66e2c78e0f5cc3fbd24
fb209cbd0e9f5acf67feea2e0d613aa5c623a8f6
7089 F20110115_AABRIP gallas_q_Page_049thm.jpg
286e1dd2282c4d55c20f376b49696ca6
3dfa9c5a03380434e0a559eb6cb13337d24c6f10
F20110115_AABOSB gallas_q_Page_099thm.jpg
56b127c4cc5a14619970bd32a4f4fa33
3e7e5ffb553da1ca40ccdf8e568243cc7bbae5c9
53528 F20110115_AABQLW gallas_q_Page_139.pro
6426c88cc08474598c10935bbee29ea3
11f4dbd8be7596c1b8309af0cbe053acf199af91
6698 F20110115_AABRIQ gallas_q_Page_050thm.jpg
b24e226a914066ad6017b1ef5a075929
390e0e2fe78ba745071a67922138fe299c182ce9
61722 F20110115_AABOSC gallas_q_Page_352.jp2
6bf4bcb9d276afe7993f0a2ebeb9c953
95e25c7164053b4ced7877b8dee3201bf4abe957
33343 F20110115_AABQLX gallas_q_Page_140.pro
05b23525d18f51c3137d722a0b5b1ae5
743cb83365d8cd342a6d4f1b97f0dc7ca398e804
24078 F20110115_AABRIR gallas_q_Page_051.QC.jpg
a34dd57384bd73a3effb9216840ac913
f76fa99e227fe033c29540ce2cff8322d91ca602
F20110115_AABOSD gallas_q_Page_229.tif
b82411e89a12b0c1a329bd3945a44bac
c6b35916a8b43b76112333891c585ec6168c7444
44218 F20110115_AABQLY gallas_q_Page_141.pro
b7d38e814c9073aff51be1e5dfde5db3
f39da24c727b69057c6412b849409835dc3dd839
F20110115_AABRIS gallas_q_Page_051thm.jpg
cc1618fbfa8e996f48a7f4cdd9d38551
bba87a29b3f24a792363bad940b251615005aa15
39442 F20110115_AABOSE gallas_q_Page_259.pro
2b553342ee1602ab33a2299112fff4a5
8953111f0f2324c4c39d18075cf41afe95cfa4c0
44958 F20110115_AABQLZ gallas_q_Page_142.pro
8314d6ca8ee3d886b9a94caa8f8583b2
a6ae87169e4eb7433d7b0eab9b212f5834a6e005
23837 F20110115_AABRIT gallas_q_Page_052.QC.jpg
7adad58441a4cd4f161c616b635f5438
dff3f7113e272ce1711584af2702472281c3d004
74638 F20110115_AABOSF gallas_q_Page_258.jp2
f53f41fa98867f6bb1801eb136b5a1ab
a2f30373f4d24aa236a938f93968a8fbc616bb2c
6874 F20110115_AABRIU gallas_q_Page_052thm.jpg
c7b702b5af8873af34847e04693ae01d
d6a2dd0c180abbd89e72d5f8c449cdeacdf13e4c
84500 F20110115_AABOSG gallas_q_Page_259.jp2
1824ce22492793a5477837275e741187
7b69eff3b5ce96817e4930f1e8efd74eb9fab5e1
6469 F20110115_AABRIV gallas_q_Page_053thm.jpg
59990fdb92986849ee37d1cfec3fe313
4af4adeece01f8e3162ef4f1ab97e61af917e74e
49807 F20110115_AABOSH gallas_q_Page_216.pro
c3e31a3b31b9466408be691f58f7223b
6815eb0800b58651b1e2b589706836f17e6d2ce3
819714 F20110115_AABPPA gallas_q_Page_192.jp2
48e685191c957d4eb557633c30ae0c26
c030682b357e64c6f4cddcf7e2734a6ff62a0c3a
23556 F20110115_AABRIW gallas_q_Page_054.QC.jpg
77236c7db605df4581beeaff7d4d1ef0
2f738af8375ae75cb9cc76d4f0294b20d4e87a36
1008 F20110115_AABOSI gallas_q_Page_276.txt
a39b708a140bfff58402094ea7f23ea9
8404a1d0d2e7682802114c857aeaa63e3b7ccc0f
698171 F20110115_AABPPB gallas_q_Page_193.jp2
1c254a4a943f4fc1e1715219a2347640
9283313b5781552e04f4b4e02e26537201c2db96
F20110115_AABRIX gallas_q_Page_054thm.jpg
d740524eb5da44dab721ce8e2a165bdd
f2c2d21051a8f48ddbc2b6d631c347e53bc64af2
56323 F20110115_AABOSJ gallas_q_Page_199.jpg
34bc7d426f83470f053d2ef9eec1dff5
90db9105074705834ba16275a0823895c9bc985c
104355 F20110115_AABPPC gallas_q_Page_194.jp2
23d1c2bdcc78749c3d2769277dcaddcf
0241ebf9bd6dee4ec9151787cf8617aac446f7ce
23761 F20110115_AABRIY gallas_q_Page_055.QC.jpg
63f5b9acb66042c03155aed6a4899a69
2aa2ecb6f92d5a0421ff0f3d9a3650e71d479078
6122 F20110115_AABOSK gallas_q_Page_189thm.jpg
3202f0926734c64c2f1060d0fd52a9b5
04db2319cb58eaf1273771889eb7b2243d67f732
892264 F20110115_AABPPD gallas_q_Page_196.jp2
78dbf0abda79e042bdab6cc0748078ea
9ed56ff35dda2379f6f3a44daeb50010559ad836
7403 F20110115_AABRIZ gallas_q_Page_056.QC.jpg
82b987f561520a0a472b8a789330b91c
0a08b2ba59bceb1cc748e70b9617e0ac536dd903
F20110115_AABOFA gallas_q_Page_265.tif
e16d4cb14acc1433f5d03b73c1b7e81c
61277f60e50abdbc9f6171e7b69ef907cd3e7ebd
6707 F20110115_AABOSL gallas_q_Page_066thm.jpg
9572e05110f06e7a17d1689c8df656f0
5d967c3d83f093d586f391e62d6cff5264db40b5
100196 F20110115_AABPPE gallas_q_Page_197.jp2
85a0b0224e3482f808683cb80e7fe4cb
7dfb3f5c94c7540bcb46951b5dba3e1e4f634792
961126 F20110115_AABOFB gallas_q_Page_121.jp2
50721fcb6394127ce960a8f6cf76f911
1e17264de7f53e32651dadbeb4b53388879a91ca
F20110115_AABOSM gallas_q_Page_189.tif
4c4effc5171db3e1a3aee1237ae8313d
f0c29f89c9d1e06664f778ef8c02430c0fcbaa0b
91615 F20110115_AABPPF gallas_q_Page_198.jp2
e5c44e15bcabb29b9ea3aaff4149e42b
3a6f4a50b9d810ea4336935224c13e1da58c41f7
1302 F20110115_AABOSN gallas_q_Page_150.txt
4dbb92b760ce28d0579898df829d8b66
2a2a291a707db37b78a3400eb163e3b72dd2780b
46862 F20110115_AABQRA gallas_q_Page_306.pro
aa564763aabf666ec0ffec632cb77f81
3330df0a9afbc5bbf9494521ef04c75a684fa7ea
740662 F20110115_AABPPG gallas_q_Page_199.jp2
509fc67bd8b995f33798d95ba9c15d62
d859b1d271c1d827b86c48461e3db9d9f9ea633f
44302 F20110115_AABOFC gallas_q_Page_146.pro
9fffc22b26ed2c3b436d7204661e81de
95368ccf65b610f352c7faea33d97540ca0f875e
F20110115_AABOSO gallas_q_Page_259.tif
0bd159b20e3f660208712dfb359f1700
34a5ea7b0096bf1c1ecdb5bba9f6ef856edd3273
39867 F20110115_AABQRB gallas_q_Page_307.pro
2da032054ade07a702baa11da4a4c12e
591b0016d4fa609d7874331d99b81bb4c386a8da
64750 F20110115_AABPPH gallas_q_Page_200.jp2
f3187fcc85cce11ee9d2fbe8c44da816
610cafe8cf7d3f0fb742d3630ceda756ba43cbd9
1935 F20110115_AABOFD gallas_q_Page_061.txt
d7c4c89619f1c9387d17da1801b42e45
c890a6ffcbeadbb631652d53dec523064a1a257e
24707 F20110115_AABQRC gallas_q_Page_308.pro
70ee936327943f0d59acf9c6353ced54
c8ac8d0f3b93b850debb71c3b3f4a605ec54885b
69792 F20110115_AABPPI gallas_q_Page_201.jp2
90c8071619974f82007dfd7c9675a5d9
3b2b8dd7eefaad3aaaae612d2eb00ca170f367f7
6387 F20110115_AABOFE gallas_q_Page_131thm.jpg
0864ee6c5a87dd36b5adc9277424f1d6
7b582144edb3535184375c00603fa6e6a315cc87
F20110115_AABOSP gallas_q_Page_227.tif
754e1b9b0aef2ad997a93803a6a65e2e
3578c97d2e78c275ed7634c189fff7ff6f613a6b
32515 F20110115_AABQRD gallas_q_Page_309.pro
b30a4236ce09aa97197d49765a0319c2
6c1483ab187d97708d1302d53784e3f0141963de
112959 F20110115_AABPPJ gallas_q_Page_202.jp2
affb2c67be93403c41243dc1af1d698d
6a64dd13c44c76f35bf7dd9d1f12865839475231
F20110115_AABOFF gallas_q_Page_301.txt
305a555d66dbd4ba35e1fc1523d014b7
6bf3ce8354e842481705bdff2da4dd1504c8b9d9
9791 F20110115_AABOSQ gallas_q_Page_163.pro
92b318acaebadddbb4fb66743b30e728
60de6104fb0d36b7e1bf2c77279c3488959ad713
34090 F20110115_AABQRE gallas_q_Page_310.pro
1e0889ecf878395676852642661ca144
fe5601f18fc324ab1c37203371e1321f6e685f6d
895829 F20110115_AABPPK gallas_q_Page_203.jp2
126e1653d3c0360cea0dac6a5e525029
dd5b83e3181d5ba302cdae036dc16bb09a148762
F20110115_AABOFG gallas_q_Page_141.tif
8500c492c73b0cec1e3cd12f50633dfb
73ac222c60db3e92c8874e29d7ee61dcf729580a
F20110115_AABOSR gallas_q_Page_284.txt
b1dc068f2d9588937a4c2bb0084dc7c0
e368cc32988ba4d3baf92195e96cb27be4d1e18e
33308 F20110115_AABQRF gallas_q_Page_312.pro
4dc7e2fb2fa2cd75de2223035d884f22
13993ba62f2ad44058622d547898699ae66b1c16
15368 F20110115_AABOFH gallas_q_Page_341.pro
59de34ed188bb240f9ea8640289d3b61
a43274656b37f0239a3ed4c3d14031af49877607
46359 F20110115_AABPCA gallas_q_Page_159.jpg
392a4b0d94347b527832c7e4191deba0
a0b188eb6e131901cf1fee979343687deacc474b
77794 F20110115_AABOSS gallas_q_Page_094.jpg
6e6fb8291e9e283074ff73f478cb436a
67b7c53e9eb40b7a48fa67c3ad8725b0650a7856
17868 F20110115_AABQRG gallas_q_Page_313.pro
e90514b7580899a76a6832eabd661d15
2123186bf6114188eb2e77016f86cc950e213f03
1003258 F20110115_AABPPL gallas_q_Page_205.jp2
55adf1493aaf3dbdf8cd435b3644498d
72e777adb744c0b65da76532028f530c5b5f2392
6988 F20110115_AABROA gallas_q_Page_134thm.jpg
deff689213506b56f834d2e9f91b32b6
a9ba9dd1c056df2928a54b5ab52a7a5f1262843a
107050 F20110115_AABOFI gallas_q_Page_375.jp2
9392bd7bed18f4bf5d59caebf72b72f1
18f8ab2281ba3bd062f563de2309f8dff1b71f00
70494 F20110115_AABPCB gallas_q_Page_160.jpg
46e89b0a172b72db973559e242a49519
b2a1337bc81fb88b083ce5ef60e34aaf431ca2cc
75059 F20110115_AABOST gallas_q_Page_240.jpg
3d0405826ef45a29d1f58db5930a261e
ef4d88b0db4b1b2d75c5b304e113d5e08a98850e
30297 F20110115_AABQRH gallas_q_Page_314.pro
ef454bbf5a1b653548384bd44e7f0511
98fd0fd827e5ddf548c86095a89e2c41bcb6cc23
F20110115_AABPPM gallas_q_Page_206.jp2
757408ebfe3077479a93b325bba8ed92
3db9510fe96df3ebcb934f48c4a3e59e002d59b4
19719 F20110115_AABROB gallas_q_Page_135.QC.jpg
c01b5dec30b48bd6fbf8bee5e9dd8078
425fb65e3dd9bc81f279e292aa1cf7ab9fd97848
F20110115_AABOFJ gallas_q_Page_253.txt
9e1896b6ed2266c3693be3b1e033ba77
1b98341e31832916fa211ba0130889c271904ad8
45827 F20110115_AABPCC gallas_q_Page_161.jpg
c140991992812768e0dd3b81d35d0d75
c3159636ed4847a20d3e693c110112841a256745
26180 F20110115_AABOSU gallas_q_Page_341.jp2
e3fb69aa37e4fae25f40be8bfd15e591
650669d6e029b06f0d2e72a30485bad8f8bb728e
8007 F20110115_AABQRI gallas_q_Page_315.pro
5de1136f7aae2956dfc6117efd93d28a
472dce104083888b83ac9fc24f4c142d76c4008a
84657 F20110115_AABPPN gallas_q_Page_207.jp2
2e9f003f1ecdfe57feb66e51c3633c18
0b24efc328fb47e61bb3d77cb949acc66c7b7291
5949 F20110115_AABROC gallas_q_Page_135thm.jpg
7e6aebb9e2a1abc1a186443c169dba4a
e8c1181990b13b1a044b35357c08923dd4645c2c
7078 F20110115_AABOFK gallas_q_Page_016thm.jpg
c9fddc3e36d2a00f5b9e4a0cb5420cdc
7938e1144c9f6775d8ecf3d91b8f2c98afdfceed
62521 F20110115_AABPCD gallas_q_Page_162.jpg
5ffec346ef6f39e124be9c1f679ccdb8
9a2950ec71c0d51dcd33be066bd9d9398a3b1d2e
F20110115_AABOSV gallas_q_Page_188.tif
d95aeedcdd4ebff19044996a67945e36
5b1a4ec20126dbed21a4ef94f9e9c85653e8556d
36287 F20110115_AABQRJ gallas_q_Page_317.pro
a63c9c1baf9baf9d152043c59bcaa0e8
5074c2f771ae0246de3607d4a18575d3f2eca951
751230 F20110115_AABPPO gallas_q_Page_208.jp2
25c92d649ce025abba457f48ea0df4d6
075aec3da79089675425fd5770ff3a2e87ac5e2d
23317 F20110115_AABROD gallas_q_Page_136.QC.jpg
16fc9344dc646861a9a2d04b8b9c6c7f
94cf3ee9e2a37a741ac9fa4e046de543e35e3acb
83468 F20110115_AABOFL gallas_q_Page_249.jp2
b4798718b2be47b6feeec0ba1c41000d
caa1d5612ecec9f217d507b0a62172cedb5e21af
20759 F20110115_AABPCE gallas_q_Page_163.jpg
fd3395d66f2e63fa885f6d632d3a798b
50ba4af425fa46b95ab1cd56f6df6c23828dd2dd
22866 F20110115_AABOSW gallas_q_Page_167.QC.jpg
f5404ba456c4dca38be6c0387c4c0f07
3b6688a8f1b1c761ce8491d58f69b31eb1686f1a
45848 F20110115_AABQRK gallas_q_Page_319.pro
81b376a1e212e2183bfd2506730c8cd0
268995fe29cc3c9a6a2b438e27d2412b13b8e8ef
85759 F20110115_AABPPP gallas_q_Page_209.jp2
8548d3b20280b6a2dd2716eae1003b85
9f3773f8c57cc653063bbbcd7a5016dd8f4530c0
6532 F20110115_AABROE gallas_q_Page_136thm.jpg
9313f547b522c356ace6e209a17f2058
c0761bef11e757946845ebdb154733299ec16a25
21456 F20110115_AABOFM gallas_q_Page_068.QC.jpg
467b59cadbbf44335d0f9887fd37afd4
5b2b14548da0a1907b27241ef1de92120628435d
66977 F20110115_AABPCF gallas_q_Page_164.jpg
b1ff1cb12d24d18cf3fc1ffc3d1fa5b4
f7983a3f4c83a0bf2717e469d7138b3660a92058
100580 F20110115_AABOSX gallas_q_Page_091.jp2
4b983dd7d0b42126174c59db6f4b7989
58cc0e44811f3fb4d4f2d49d835e0ccc86ebc759
8444 F20110115_AABQRL gallas_q_Page_321.pro
96b260ea4ef2a4457bb468665ee9734f
88ce802acce9ed6cd71c7355c096a8bee284bc4d
F20110115_AABPPQ gallas_q_Page_210.jp2
6e24a6e721a87fcfd4bc64789aeaddb4
5483834343c7197483dea58a29d2a8b1f664f98a
25806 F20110115_AABROF gallas_q_Page_137.QC.jpg
f46031547e90ab531fa98bd23d5f216b
98d5f6ae22567465628eca861f33538a40a88f86
103335 F20110115_AABOFN gallas_q_Page_057.jp2
af321f18ea1f758a7978e4519e4c4188
67f9ac3d0df29167c7ed8fdfe7ca799d4a02b572
F20110115_AABQEA gallas_q_Page_287.tif
9889c7a76fa26f208e0d5191c030c9c8
c47e6dc0ee8a34b2d10532ff7715d819aa7d8526
70389 F20110115_AABPCG gallas_q_Page_165.jpg
f1599c199559e7ec44437d6f3e437b41
eb9a37cd555b870dc80e08ceea08b91addc0ca69
23681 F20110115_AABOSY gallas_q_Page_019.pro
f8abe46a260a2dc3c4a2a7ec59efec78
22c74b850600998cf2f476ea1cf557f3efa43cd3
944923 F20110115_AABPPR gallas_q_Page_211.jp2
f91acc21cb011dc766f3495e1ea433c2
82d284a968777c8d06d7907718c850bb80c8effa
6978 F20110115_AABROG gallas_q_Page_137thm.jpg
4b1974e383ba2588cee53436f09249d5
55e83a4713007fb8c77cf7ad209b621503a69346
55811 F20110115_AABOFO gallas_q_Page_019.jp2
a744dd9be698eed9222fd9fc64069bdd
1b9c2de0da8add08df7154cb10f1f4c0bf7808f9
F20110115_AABQEB gallas_q_Page_288.tif
130240c0ce90d24da4b1af66d76611a0
7b0e3080dbbc4426a1e42ac84b50791c4be3b46e
69809 F20110115_AABPCH gallas_q_Page_167.jpg
25038e0839d22cfaeebc71b24a282d9e
b453bfcc30174b4c19616e2fbf04ad8d56198877
2014 F20110115_AABOSZ gallas_q_Page_213.txt
c60c8d99e54fb10b965c9a1b6dc16868
0a8ba4c5ddab6e360360d8a9103e28d42ca73526
18242 F20110115_AABQRM gallas_q_Page_322.pro
19393cfcc5592a914bf1c187e259372f
019d7393403d58b2651147988c893f9eb40b1e0a
92211 F20110115_AABPPS gallas_q_Page_212.jp2
fc8bffaa2cc81094092d83c044e756a1
749792da27ab85ed1fa7a44d581d96abf6bee028
6951 F20110115_AABROH gallas_q_Page_138thm.jpg
3f5b24e6e8c608b00d8ccbc5f70fa706
a3491b4469d00774d11783396f100fe9ef3f2dca
F20110115_AABQEC gallas_q_Page_289.tif
999ca6cb448ca60b356eef8f8651b7ba
2c1ca69e8707795fcb96f2aed78e850bffb3e971
63497 F20110115_AABPCI gallas_q_Page_168.jpg
9a7f9e3b4cd16458db9a30239aa5dbb0
42112330bd63c67d841f1c4551f5b160f4ebe9b6
F20110115_AABQRN gallas_q_Page_323.pro
c887e64a9070b01b5c04ae97ee9c9e49
2113eae47e281ec0dfcd95c186822653f9098c50
88743 F20110115_AABPPT gallas_q_Page_213.jp2
e94d56ae0d48848d97e29fd4318908a5
13d5b0d0d478f71d133e15fb4693f549caff70b4
6886 F20110115_AABOFP gallas_q_Page_377thm.jpg
d39b41f0453300edd287200d906dfeef
9a6ea630b18cdcb1477e9feabf3535c6fa638538
F20110115_AABQED gallas_q_Page_290.tif
f2d4bc3697f7ae2fb4947a431d6f1dc2
9bfbce473cc02ef499c4a96ddcc9f33150df38fc
75324 F20110115_AABPCJ gallas_q_Page_169.jpg
285c1dc6a6029d3e98a34ad9a55d96e5
0d292f0d77695c899a0e31c101f496052b6f19ff
20883 F20110115_AABQRO gallas_q_Page_324.pro
eb0882ed57279e43e324bf89332f0c46
461a7ebb7ff97966d455b771d20f54b5d254e412
F20110115_AABPPU gallas_q_Page_214.jp2
85c01e48e1f5a4089719c8c3ef32f83a
059d39e7ec65670cf5d067659578748189254799
10768 F20110115_AABOFQ gallas_q_Page_123.QC.jpg
1da29bf6b8416c4476ed047a8d29ff68
e963673943430ef06d3a42679b862073cf21614d
24739 F20110115_AABROI gallas_q_Page_139.QC.jpg
2c47aa8d7b61ba0d6c56a31632d62243
f17ddf25537e055118515d32e3c7cb63c789db59
F20110115_AABQEE gallas_q_Page_292.tif
d4d2ecbf3174e5b585b25ec062df05bb
9d6cb9d5ea5dea7de93da8ab4fcd55ae0652ddb6
50375 F20110115_AABPCK gallas_q_Page_170.jpg
4c408fe7f10dcacfd495f16ac8b6ce39
0c2d44bd62f9a1b74c07cf54b34963bc1f8f3023
26323 F20110115_AABQRP gallas_q_Page_325.pro
3780a1e20acde41d230c76371102f4e8
477a76ccebe7cd0415daf3d55ef6cfd7bed7de56
1051869 F20110115_AABPPV gallas_q_Page_215.jp2
76b1835c1c935273bd89ddfa66abd6a9
3c53999743b092a44d93848461ca5805e2386163
46894 F20110115_AABOFR gallas_q_Page_131.pro
bdfd28f216a22d223487d4858a78d4cb
9b71f54911e3b84ab3855050d98931d3e9730784
7044 F20110115_AABROJ gallas_q_Page_139thm.jpg
69e7b440c20ce82a60a561c3d416abd9
71005cd24528c0ec214ca48084a3d76fddab824f
F20110115_AABQEF gallas_q_Page_293.tif
6bc78e60b6207729edc49568e6ebe31e
d4a5d7834036d048efc1b888153475aa0a274592
61784 F20110115_AABPCL gallas_q_Page_171.jpg
fac03d5a5bd4618d4fd9606bd76906e5
14e48688658cef81df0b9f66826410c932fa6b34
22162 F20110115_AABQRQ gallas_q_Page_326.pro
c505ce9a73dc6df4202567c0337edcbc
9a922453251d306287d607d876c31d7ba3662e62
106962 F20110115_AABPPW gallas_q_Page_216.jp2
0bbd5a997cd37eda6842716c1dd92efd
c7b03080092366706f7f57a87dcb71086595eac9
1977 F20110115_AABOFS gallas_q_Page_117.txt
67752acf4ba4d74afeed91c1685eba8d
809a12f73dbc1818e12219ad7aef4970e4e09648
24453 F20110115_AABROK gallas_q_Page_140.QC.jpg
cb29f1c5a983f604d3b43bed72f9bb82
4eb967bbd1b56e83395c8ccf1ba8eab3b35391ce
25103 F20110115_AABQRR gallas_q_Page_327.pro
0de8e29620f1fe47e3711756830cae0c
35b2da3f3dce7f370644af0437a83832d96c8168
F20110115_AABQEG gallas_q_Page_294.tif
90e9ae3bf0e8931d5b930e67382254a5
61193f1635e0f885bf5abc677fb59bb99a323d9c
76258 F20110115_AABPCM gallas_q_Page_172.jpg
ac313ecfd2a34b3e3f0d7a15bb01bd87
5a6d8ecd2a6e87de614a7d538d9ff2bab5a5f4ac
94492 F20110115_AABPPX gallas_q_Page_217.jp2
84c949f062bbda151cc143bebf962757
22efaddf1726e32dcfff8d3a2b3cc7963319e742
579 F20110115_AABOFT gallas_q_Page_008.txt
7981b3d933876894da51a68da16ee2db
4d18b59a8201d8b2b07838982d80a475b18d7abd
26985 F20110115_AABROL gallas_q_Page_141.QC.jpg
4310361a9d91a11bb4829e181af8b2eb
6d718f38c7195f4767c5e645d8455e3079dee37b
1776 F20110115_AABRBA gallas_q_Page_246.txt
761ad339cd379b81031aee7dfd278551
f71ff976865b90c9ad1a428f696cc21b43302a14
28148 F20110115_AABQRS gallas_q_Page_328.pro
fbad4ad8c18ba224c89e336d54e3c786
a87e181b754bee1011cf9cd9d326c50b88421ee1
F20110115_AABQEH gallas_q_Page_295.tif
99b5ba62546c428f694124638b688917
ee2725aa60a0845d6955a806174fe41e99976139
51087 F20110115_AABPCN gallas_q_Page_173.jpg
c9a5c07446f9c4b6bb9cedc8a430816f
5d8dcd8fb4c3acf5206dada3268eff00d6433734
880772 F20110115_AABPPY gallas_q_Page_219.jp2
0594369d63f0e53dfd2a60ce9617144c
97a055ca97c1a36cd2dea56bdb1b48aac7b68ad8
F20110115_AABOFU gallas_q_Page_144.tif
b523d6de6dfb75129cc4fb247e021bff
0de6d34a1c95d59fae8e6ca90722970136f1c95a
21800 F20110115_AABROM gallas_q_Page_142.QC.jpg
070d1280aa737083c7a5275308990197
b3d82b918822a9cd6da5ff75713fbb637b553e48
1720 F20110115_AABRBB gallas_q_Page_247.txt
a3f8093891013246aa50a4b8824ac719
526b42ff9ee95ea56937e4ee45cb4dccef50cd9c
23162 F20110115_AABQRT gallas_q_Page_329.pro
3e17afecb26295bf8cc9018dcb17d158
17ec60a0dfaba3b34873c25ea81ab4dc97ac72a4
F20110115_AABQEI gallas_q_Page_296.tif
9939eba939fc70426a6ef0f8b14b1d43
09712c52d58a69198705b4b59544081d43026914
70682 F20110115_AABPCO gallas_q_Page_174.jpg
96d01787f4169f807934b32da6739903
cafdaf63711f50886c6aafa0f3e08174bbcb99d0
981839 F20110115_AABPPZ gallas_q_Page_220.jp2
076742346e1e0d0048f7f47c597ca043
ece1b125f55275edde434a8e09fec4a9069df647
86331 F20110115_AABOFV gallas_q_Page_247.jp2
5a6a88636fba89458657cf26e06d8223
4a3beb8e76c774aa807bbb47375d6106cd625af4
F20110115_AABRON gallas_q_Page_142thm.jpg
be318252516f8edb3837375cada5b939
fdd4d1a43e3d5360ee8944b6d0ee41220a72ccf6
1652 F20110115_AABRBC gallas_q_Page_248.txt
641db6682e8f5a3ee5d76035663ac2e4
10da8248ffdc536a5b77e187ed687cd966f203d0
22976 F20110115_AABQRU gallas_q_Page_330.pro
3deb2cf22d13478ff3257f374478c440
55dbb4b4fdde75b8aa3627a0f22bd565bdde4a3a
F20110115_AABQEJ gallas_q_Page_297.tif
386e18a65e2b7ad34731d3cc9272843d
c7ea0a1d705b470c6b6de420c6046e49fdc9aa4d
77764 F20110115_AABPCP gallas_q_Page_175.jpg
61d8207f753899a2481e40ddffe15f8e
ff4c851152357b640577756ae79e7f79d544cb9c
5278 F20110115_AABOFW gallas_q_Page_224thm.jpg
61c77c58da5ee9baa110155bd6d3fc11
bf0d1cdcc5a2216d3635781eb16d736f7c0611f2
22105 F20110115_AABROO gallas_q_Page_144.QC.jpg
e36ee962b749e99e19f0c23c6103caf9
60462ea23690e760d8544f9aa6775ea5398a46c5
1731 F20110115_AABRBD gallas_q_Page_250.txt
17efeb7b0a85f101a63c97c1f5a18648
87b3379acfac628d28f9c15e24cd76fd8843bd04
25780 F20110115_AABQRV gallas_q_Page_331.pro
c64274acbb167358a7aafec5888e3686
5473cf355cdb73741b6e746ebc8c129e82631c23
F20110115_AABQEK gallas_q_Page_299.tif
509998a9614d55e9f4d9376c4dbd3004
23bc94833ac1575433666cdab8b71295f5132d04
69484 F20110115_AABOYA gallas_q_Page_035.jpg
5b5f91c14b99617e2b65fda5af81613b
0d82849f1cab95f827ab648a5955ec10f72cd273
77374 F20110115_AABPCQ gallas_q_Page_176.jpg
a6ccd785c737b1a981ef616b0ed26066
857b4183aad2e59d3f4abbe1be6165a157041348
F20110115_AABOFX gallas_q_Page_225thm.jpg
b17c4645d33ff83f7dc0fb7b829a4ecd
9f67d9fc801f4331c89c41507a1297d7feaa8def
6526 F20110115_AABROP gallas_q_Page_144thm.jpg
0074ce2ae8dec5d52ca984a4dbdaf200
410f3c7799b6c2653143dff7275c3738b0073f8c
1647 F20110115_AABRBE gallas_q_Page_251.txt
3916a8e3b1846f97dd60a8c85a48249d
849f60684b21c29ad5637e4b0b8ca38dfbd3e3af
30060 F20110115_AABQRW gallas_q_Page_332.pro
203f1a9d27736f8af2d0563c35c77429
610af7442aea2ad3e3614ce24b2b485e84966172
F20110115_AABQEL gallas_q_Page_300.tif
f3d8e86c1c3ee6c2c5f5881077676c1e
85e3ba4d20f6ee1fc9f49bd2651692ca15eb1e70
70352 F20110115_AABOYB gallas_q_Page_036.jpg
f3e98c9809bceac566bd58c91a45df1a
0f34e2aff36ac1fb410bfe959e229718e8fc7634
73343 F20110115_AABPCR gallas_q_Page_177.jpg
a9f71b0a80be8a622da6addb84a6547c
7d3a9b271edc8a8e064c102da03f4d5afc757195
14256 F20110115_AABOFY gallas_q_Page_185.QC.jpg
2020eaca31356d7bddce649b262faf12
bc446703320a58d0d0081d2c5688ae7defe3f283
17921 F20110115_AABROQ gallas_q_Page_145.QC.jpg
22408c18a0056a55f2aa08a7efd60094
072a4871d3e464af5a70a0aa0f15eb2737979cc2
1760 F20110115_AABRBF gallas_q_Page_252.txt
68178d138b5f0c6817675fbde5e1f30d
08e9ad4c78d7d391259da711cf3a01c275bcfd47
44732 F20110115_AABQRX gallas_q_Page_334.pro
e57c3587616a06f8fec428baab763087
556ca09dc6b0692e70b14f698410c0bb75c5fa2b
F20110115_AABQEM gallas_q_Page_301.tif
436085c5df48a588e41c5eda80ef933b
59e11e2b43f2932afbb351fd975979e4ab410149
68965 F20110115_AABOYC gallas_q_Page_037.jpg
b81e678c8693796b5957a9d9e6f86ae6
a42a9bf65752888cde82bef133baa84ec2bb80ad
52514 F20110115_AABPCS gallas_q_Page_178.jpg
fbd2e4bacff1eae939ca902300f0836b
a79c58960a74938375644f12bb6057ee0cbb8cb5
45929 F20110115_AABOFZ gallas_q_Page_291.pro
4b23dd2ece3828db8ab3d38086e69f2e
db9278090c52b5d68647cf703901ef1653fe34af
5432 F20110115_AABROR gallas_q_Page_145thm.jpg
6ede21d8a294a9a4d5d4dfffa13221be
4863595015c7c113280f26c67be3ec6085850501
F20110115_AABRBG gallas_q_Page_254.txt
53f8f145e257c94c44cac3032c3c36dc
727ccbc0c030e4c1b08d4ec0cf968446d0803312
30533 F20110115_AABQRY gallas_q_Page_335.pro
914929252284b0451a88368b605ae22e
38b9eb20e43db2429b77ce287a360cc3d523dba0
F20110115_AABQEN gallas_q_Page_302.tif
e3983bf7c475ade145d0271a77d234fc
9cc7876967fcf859c2bbcfcd65c81d713d615680
74910 F20110115_AABOYD gallas_q_Page_038.jpg
73be73505242dd963ea57c25146d3e81
d95742dde1bea53aead2adfc13706310a2086de3
56149 F20110115_AABPCT gallas_q_Page_179.jpg
cc24360e9cbb5754fbae1968c8c7d2dd
925396baf01f6aec285d6224d8644e8ed4c3cb64
20867 F20110115_AABROS gallas_q_Page_146.QC.jpg
b110bb0eb9c01dac00c558788ca253e6
2c6e877bd2cc195feaf30d2cc5fc43f88db78126
1864 F20110115_AABRBH gallas_q_Page_255.txt
ac9529f9bd126e89541195630e2c5d77
969039404ddb56ea48b1293d04d1a593c2978461
36520 F20110115_AABQRZ gallas_q_Page_337.pro
2e65bdc64ac8a56fb259faa6272de3ca
a4eaa2012e622a3863bb66325e21ff76a493ee36
F20110115_AABQEO gallas_q_Page_303.tif
6d6ae6093a1a80dcf9ec56b80bb54413
ce97734d85fca0119f1f2ee5854e5b0dde1306d8
71065 F20110115_AABOYE gallas_q_Page_039.jpg
a09c5ad981036ddcbbf2a30b230e96d3
42b61586b0b67cdd521178079ca3301f6157be91
46213 F20110115_AABPCU gallas_q_Page_180.jpg
86226f10ed9a75b16221fd66a9e5fa8f
48055c46348aab204b9398e9e12569a8fccfd8e3
6235 F20110115_AABROT gallas_q_Page_146thm.jpg
db84f63f51268a4cbdfca786c1879b78
f0e12c9c87584370b4a19377f78f4e448a804a17
1902 F20110115_AABRBI gallas_q_Page_256.txt
cd1ecc68e7348f7bdd17268994bd0b5d
56a6086b774ef6033083ed7d33f90a4bc11fd9a4
F20110115_AABQEP gallas_q_Page_304.tif
7fd8dfa03bcdc54c824c90eb57d0ce52
d9534213a106307d05e0b2e56c48abcea1c111ea
74598 F20110115_AABOYF gallas_q_Page_041.jpg
98389d6671cbad680b78ef5b9f4fb049
89a4b87ff01b2ece38cb473885c08aaf5d635e90
46539 F20110115_AABPCV gallas_q_Page_181.jpg
73cddfe2f878296c03269a48f662c1e0
66fa16b6f33b5dc06b6e57267f63dca1e31e2f2e
19048 F20110115_AABROU gallas_q_Page_147.QC.jpg
1de528b002f02cc991cd936683c59552
909d287b61692d91d9e30be1fe3ca6aef56e1426
F20110115_AABRBJ gallas_q_Page_257.txt
07c84c19ddd063d2d191eb75a6967c44
5cbffb198606f2567840fb47c49ffe5c72e461c4
F20110115_AABQEQ gallas_q_Page_305.tif
7351021b71c415f34ceac4aa730bacea
6c7769d5331e9f16a6df802acb0b8eaa6925babc
75464 F20110115_AABOYG gallas_q_Page_042.jpg
8f81f501901395055ea49c844f515fae
2b29c8b2434dc3dea95ace60e724f8d7cfe1f6b0
67719 F20110115_AABPCW gallas_q_Page_183.jpg
20aa6f06e3022f1c772e46df70b8a0d9
aeb4dc682040217ea97dd693ca248cb970a042c3
5613 F20110115_AABROV gallas_q_Page_147thm.jpg
ca226e3a0e9a72e561f7a47bbd8b8877
4c26be71e4ff998e377d481f3eccc64404b701df
1807 F20110115_AABRBK gallas_q_Page_258.txt
5d0528fa5682a1e0f7c960e62e383ed0
3ce6cf6ad952606e1e380b1e014d38bf91badc6f
F20110115_AABQER gallas_q_Page_306.tif
8c7e35d3d432df4777c7b6d6c14d1bdd
9c392343ea14a694d91b657dd6fb2fcf6d2af313
72715 F20110115_AABOYH gallas_q_Page_043.jpg
dfac6c0ce852c7e92e09236f260ccd85
e692f23efb6cd61bd717b490e36bf3fa1ef8fc0b
61014 F20110115_AABPCX gallas_q_Page_184.jpg
aa802d4185ede6bc301809cf695d292b
c352a4eec263b6e429cccd2a507c1d44c6ec8e8c
125098 F20110115_AABPVA gallas_q_Page_382.jp2
6c520e81b70d4475043b31bd8d1b6d7f
b914dfc4303b81413a7954b7755c98a80a1b952a
6495 F20110115_AABROW gallas_q_Page_148thm.jpg
b6140102f49a0fefbb9602cef78107b0
56fa76bd23586cfe93dce9c2a7f556b672c913d4
F20110115_AABRBL gallas_q_Page_259.txt
f97cdfe19e7285077a08d5a6c4e4ba10
186e4522d388caa196a7e8a70fa1bec5ec48af69
F20110115_AABQES gallas_q_Page_307.tif
6f871bec1a01cad2e1209b69735e977e
c1daabf7930246bcc4d12ed83124b76160d60dd9
74537 F20110115_AABOYI gallas_q_Page_044.jpg
d09e87534b5ce5cbbcee5fd56e5ca54e
ad07152d7e100d92dbef71a4d4bb3815595d9500
49575 F20110115_AABPCY gallas_q_Page_185.jpg
20896241ac039c6aad604d9b759c642e
43ddfc0aabada83b2b900f9e2ca587c3a1326851
122848 F20110115_AABPVB gallas_q_Page_383.jp2
51e88e9977baa6335648a32256a12266
f25fc03b429cb669698c5fdd1afe5c037fee1eaf
15316 F20110115_AABROX gallas_q_Page_149.QC.jpg
0cb8c84156126f20441a59ec055ddddb
958a4e900e5aa106a763958d4d5a84d7b77d11c9
F20110115_AABRBM gallas_q_Page_260.txt
81ded906438d210ec48b6ce20f3bd06a
404aa08183c60b7f629b4d3dcb987b3146301cd1
F20110115_AABQET gallas_q_Page_308.tif
d38f9989ea426ee45d6ea3e6df5e1919
05d033305e83494b5825b86be8ba5b317cca01df
73454 F20110115_AABOYJ gallas_q_Page_045.jpg
12786e4c9ce1c21b4d7cad687fdf2af0
812d4d491450297d6feee9b0bdd103457f3c8c1a
67368 F20110115_AABPCZ gallas_q_Page_186.jpg
af30f5b6654ee0f6c8f85037cad7be1f
8aa1c754144f2cf6745f967a532c4c14698ecda6
120988 F20110115_AABPVC gallas_q_Page_384.jp2
9be40952ecb9a6a446aa297c682ce769
c56d40d1860d78903d0fb2ceb952dfcfed9a709f
F20110115_AABROY gallas_q_Page_149thm.jpg
3f88d1247e8c8ea26954fceed868a917
02c1959a621b4b2ce2a0e8b58e5a05e4bd9787bd
1318 F20110115_AABRBN gallas_q_Page_261.txt
8c16a6fad678a96f89aa69e4f4609a7a
2954ae8e71e5037f94956547f02288bbfbe69a70
F20110115_AABQEU gallas_q_Page_309.tif
68c610a2bdfac0347898c230001f5009
d26782cae5c47d4b6a7a7f0b9d23cfe1c7a86aba
73666 F20110115_AABOYK gallas_q_Page_046.jpg
c6801b1e63fb116f6e17095dcff859b4
8b638a797a489aea51a2e5e26d0ed1fd81b686c0
63122 F20110115_AABPVD gallas_q_Page_385.jp2
024e5f06944a95cb3edaa9e42c417fd9
794c2691e7e852ed1f8008674d1134ca226539ea
15894 F20110115_AABROZ gallas_q_Page_150.QC.jpg
1bcb5365c015958dfe1cf25761c03cd2
5ba7b27c6d6e96f90ce99cb977d5b34d17f5ad2f
2276 F20110115_AABRBO gallas_q_Page_262.txt
b7661dc9f563011184fd9846630e80a5
d6cb7c5fe4d75f75fe197cd69404cc88c7257779
F20110115_AABQEV gallas_q_Page_310.tif
e274067c69dae214fac6fca458a9ac95
6184d6773027d526140d9f989f73e08b5c0b13a2
69496 F20110115_AABOYL gallas_q_Page_047.jpg
81152ce20018d9e42208d54fc78afa90
3257cfec27fb3d401fdff7b03d9a91afd5f00c2c
61155 F20110115_AABPVE gallas_q_Page_386.jp2
0745c3b86c436530242df7797bdb75e2
654d171b072885614a3fcbb4e21583a4caede9a6
70812 F20110115_AABOLA gallas_q_Page_040.jpg
408bbbc077513ba4d0373337b571c08d
2825850f9c63886fcee9aab021100ab0b232be93
1616 F20110115_AABRBP gallas_q_Page_263.txt
26c9c7c228a10334df0767779c647cc6
174aae6ea335ec95b617561284b5dbf1a2766448
F20110115_AABQEW gallas_q_Page_311.tif
45bd21895dc6455acce099648a49a058
9a890868bbd128f99c41656ed399133e88146c60
76974 F20110115_AABOYM gallas_q_Page_048.jpg
0b03ac07655e8d6a5a11ea56d49f594f
789ab7e8f2ea5d474c6149e2a44af7669884656f
F20110115_AABPVF gallas_q_Page_001.tif
740cfd7ea1cdc860291c1c544587523f
896922500c6ff8d9219b83888db677520fe65c1a
F20110115_AABOLB gallas_q_Page_138.jp2
5d3953f359d15fe25b51f49660ebf8cd
70d3bfc1c0f7170b9f89bd2d97c77a2c623684d1
1940 F20110115_AABRBQ gallas_q_Page_265.txt
7e387f37190cba142d0591a42b48080d
879f6f6f73f59cd9bea799882f74ffc4eb0ea1ad
533 F20110115_AABQXA gallas_q_Page_123.txt
c83c9b34cbcf5155d454aa49cfc27bed
9d823cba338faadecadd0a7783ff3c481d0fdcf7
F20110115_AABQEX gallas_q_Page_312.tif
43c2a366108a8a9f33797986e68c123c
7e93b08211ecb96a6b2027e73ed542babad84b2b
72415 F20110115_AABOYN gallas_q_Page_050.jpg
59b727a2d856b0f7d4b3d167b74b36a0
a0415286fed5ea8a372dfe93fbaddd5d9b9566eb
F20110115_AABPVG gallas_q_Page_002.tif
a6cffa89d0472410d95f217578ba7dc9
7304159ab64fa9d786c7f727ef6380582ee7d5cc
26612 F20110115_AABOLC gallas_q_Page_352.pro
f15dcbc7994d432ae1f0675327326354
78fd2ac1c71d2e8d8a65df8cd3a4fcac07b813a2
2113 F20110115_AABRBR gallas_q_Page_266.txt
83ad6c8fdca55164c093ce3b59abc4cc
9c89f60cc1c463dc567be54329258f903b8bb667
1147 F20110115_AABQXB gallas_q_Page_124.txt
b4527d1a2707bb714a2ce0c386065539
e6db987931379959f1b61fc70878fb86c4857549
F20110115_AABQEY gallas_q_Page_313.tif
ae1ad07b88b0b51ca7fc7b8a9a57702a
c60c6dae51ddbb5a43a7a9cd5fa3c37f9141a8f6
73017 F20110115_AABOYO gallas_q_Page_051.jpg
9dc493a8e13fead38e322bdbb4fa49c5
aa9b19ee3dee87e9c6eebef2642532e6795233f0
F20110115_AABPVH gallas_q_Page_003.tif
aaa34c1b0506fe46bf5cbe9bd5ea3d7b
2bbf1f76d184ad7dc200b84fe64b80fa455d84ad
107936 F20110115_AABOLD gallas_q_Page_265.jp2
02cc731465e526682b62a011f7a5ed2e
e9af03ce9aa6876de8334f819ecf639de1945a35
1912 F20110115_AABRBS gallas_q_Page_267.txt
61e786908a56cc73075a3ec6c6d132ce
d819b2edf546923f7bd106e14eb9984bd0c5af85
1575 F20110115_AABQXC gallas_q_Page_125.txt
c87835a5ad419e94f7b50cb621a310bf
b68e959b37517e2a8b6e073ff09fddb9b05430d4
F20110115_AABQEZ gallas_q_Page_314.tif
8cc29e4afd20375eecc25b4ba6257061
70d6f0fc70f45269c4769279d3419c48dafefaa9
69712 F20110115_AABOYP gallas_q_Page_052.jpg
56429c2227c820f3ae7aa1c3ff9ecdff
ff8144ba1c6c28ee602637abff6c2a864c417aa9
F20110115_AABPVI gallas_q_Page_004.tif
112719f5c035adf31b5a0997162863cc
27440bc64fb7aae9f363a6252cb4e580f28b8778
F20110115_AABOLE gallas_q_Page_015.tif
edb07dc0a03a2d845bb6d70185859ea6
495c937ff6c7d08afbb962aaf1562ea8aa2d994e
2025 F20110115_AABRBT gallas_q_Page_268.txt
1918ed19feb146ceb29ffdb8dda319f3
26edba39ea7fcaeb69ff577afd12d3cf190f3a1d
1794 F20110115_AABQXD gallas_q_Page_126.txt
ea9849a7d9a0f0254536d555d49d3c22
bd06bdb66957c8c1dbda40c183a37dc45e2e9da0
70209 F20110115_AABOYQ gallas_q_Page_053.jpg
76957ffd75b1543904046077f1698a60
de011ab8e9cddb71651ff793d244ead6988b07af
F20110115_AABPVJ gallas_q_Page_005.tif
9006aa1a4e37cc0bab701785205f7d72
c670a4b7f087bbcde3e8d2b23350cfb078a08d95
F20110115_AABOLF gallas_q_Page_062.txt
3b6e3d11e0db6633da5a0c6f302e5731
fcb9dc9c088d7f89c1f67e829c71f57177251ed5
F20110115_AABRBU gallas_q_Page_269.txt
bb0207720015c068ed423031fc67b69c
03a21c0c5282893d1ec1de55b88b8f6e6fb13b02
1839 F20110115_AABQXE gallas_q_Page_127.txt
1db7fb539951edec0eaa9d09865f07fc
65daf90584ec23b1ad874aefa020312ec0dcc369
71680 F20110115_AABOYR gallas_q_Page_054.jpg
d9ebdc40af76176a6683bec62267d3c3
2f880e93c5797cea3f1eac3e2f3bbc46435ffa4f
F20110115_AABPVK gallas_q_Page_006.tif
7f6659ea8e00ee1e915951670ff563ba
39891f242d745d305bdcee509618b69be7b5df15
F20110115_AABOLG gallas_q_Page_328.tif
a0eb11f0f4af5cccf057d74c1f1b4a89
3f2908e1699ea2a433227e00baa388122b4c5902
F20110115_AABRBV gallas_q_Page_270.txt
a119c8fc7c89114f637a7f95bcc7acc2
e3931803e66740c4bbc883be12c4a84873340613
837 F20110115_AABQXF gallas_q_Page_128.txt
986fc622258f5c91fcebb4d2e9a446be
f96eb83fe9c8f79f94cfe2b68be332b94f5d036a
61543 F20110115_AABPIA gallas_q_Page_350.jpg
b40628c9f313f98940d45eceaa4a810b
b6febe2eae2a22ece37b4eea22411acfff908ceb
72515 F20110115_AABOYS gallas_q_Page_055.jpg
4f4da26ceba747f2ee91599557af0e6e
0d5d33da5686e829a17c921d25724286bf4c457c
F20110115_AABPVL gallas_q_Page_007.tif
99d6abda12e6772f17a3e44e7adbdff3
14e54aec378619df92ee13ba69bfccc67a23bf9b
F20110115_AABOLH gallas_q_Page_266.tif
5a676c78c9ebc1260a6f0f69e24a8c45
b23fc132aee340a17acec6df8b463c1bfa644830
1444 F20110115_AABRBW gallas_q_Page_271.txt
91f111e356ec06256f99b2ead2217383
b97e16cb331085b632d0ef054f252bcfa8de5a3d
F20110115_AABQXG gallas_q_Page_129.txt
a6d97891bae39414678a950959a84c58
035dc02faae356a1510cd3a2ba2393ff9e768584
33545 F20110115_AABPIB gallas_q_Page_351.jpg
63dd17f4ee4f0045cbd8588c7412c783
362ee68092b243715969df156a4e41336486af8b
69798 F20110115_AABOYT gallas_q_Page_057.jpg
c0663ef8038e7e360e49555267bb5b2b
7062ae4517235c2561a9fdfd479d6cd967c346c6
F20110115_AABPVM gallas_q_Page_008.tif
8693c56ac74013ddaa5d9648982c02b2
dbfd1b7e8004d30421c6ddab24ea963e4b9a3eaa
4602 F20110115_AABRUA gallas_q_Page_231thm.jpg
2d5de7a3edfcde8dbe09f61859e3ec73
ce37d8308d11bc280dce0e35ea83ffa5041f6084
1217 F20110115_AABRBX gallas_q_Page_274.txt
911f4f2710a99bb6d6d9ab2a8d064b80
b33911fa180056dac516150f1a69afbaf4acfc20
2529 F20110115_AABQXH gallas_q_Page_130.txt
3b5d20a1091c0efeb3f586e58ee31ea0
35b8726c95ad70b9c1c22df0a37449aeb9bb290b
46192 F20110115_AABPIC gallas_q_Page_352.jpg
3f40c801b8eb788eb672bab4dde4859d
b1e416449b4e9dcdb2bcfa1f8a08b598ad1be228
63555 F20110115_AABOYU gallas_q_Page_058.jpg
591e366aff3b58b59c4175e163ff69e8
e8a926aa179c8b3424bcd38fc9c7f5799a82ea40
F20110115_AABPVN gallas_q_Page_009.tif
a7affaf38d1e2f3017990f92a63a0a9a
5686bdf67cac97147417f416fd795d6bb72675bb
5877 F20110115_AABOLI gallas_q_Page_119thm.jpg
ed570741ca6b0af6b7b2778289f669f5
d2ed8631fb131e26037535c37651dc4e62db3726
17073 F20110115_AABRUB gallas_q_Page_232.QC.jpg
6145cd80b86c6a0eaddadc2a984ad849
3cd606b271ff5eac97a48c156d9cc8525a696832
F20110115_AABRBY gallas_q_Page_275.txt
624aa55c441418e5df731646ecba19ec
f74386cbdedf33a406b3ea7acb4e02e6e57ebdad
1860 F20110115_AABQXI gallas_q_Page_131.txt
1041092dfd9013bddbb9eda8182bcafa
6535387baf0b6b6e9cfcbc3d5f875b091a79d2ec
61276 F20110115_AABPID gallas_q_Page_353.jpg
53ba88a183cbfc04c1a6a1bbf630fc12
4c5b6e61bb55bcb9b6b7eb582938588661579744
F20110115_AABPVO gallas_q_Page_011.tif
d2fb5694aa75f1b0083b5abed0db54be
a8c8fc2c6be95f6625cc1264f5e58d0030c07673
F20110115_AABOLJ gallas_q_Page_096.tif
67f8cc52c1e5e959dbc3ebc29a79f550
99f09791c520a28f9fca186d4bc8e9c0e97cade2
4806 F20110115_AABRUC gallas_q_Page_232thm.jpg
b66575ac9b385c3310389b6feda5f136
4dfd947515c309177184f27032a337f9442d0825
983 F20110115_AABRBZ gallas_q_Page_277.txt
c39c69ebac5a53e6a48b14015326db92
4b8651b16102d13fa4e1193b4f9602d08a3bcf73
3337 F20110115_AABQXJ gallas_q_Page_132.txt
14677daa3f4583a23853b627bbf0398a
2b88af6d2ac83422ca044316e71d47f546c569f0
49229 F20110115_AABOYV gallas_q_Page_059.jpg
eccc1d918506a34cac9605d1e4323f41
e494e71ffa08ac32209686de67b212289f300024
F20110115_AABPVP gallas_q_Page_012.tif
c68287a1a11b7c3dd66925308e45cf4e
d880f8406a651776f1b8b9c2d791a63eb495c26b
55002 F20110115_AABOLK gallas_q_Page_377.pro
ab5fca1052afe7d914d85b7d0fcd4d7e
97f9a3f30b49f91ea459ae53cf50f0713da6c3ca
19557 F20110115_AABRUD gallas_q_Page_233.QC.jpg
0301233c54e092e7b9d734399fe1281a
10f263cbc9c8b62e6f89b66c26baee3ca72588aa
2033 F20110115_AABQXK gallas_q_Page_136.txt
bc0f4d27b124539ceed901a9e3d77dd1
e721e95d39844ce79eb90990a5d0a011ca70ccec
69412 F20110115_AABPIE gallas_q_Page_355.jpg
440ca42c31dfc6393020cda0b1a3b16b
4853e39b94e192da2f2f669ec35f7426fb8a908d
50910 F20110115_AABOYW gallas_q_Page_060.jpg
c6943bf205d4c613797689a831731551
dc964fda4702b10f0ffdc2e8709699f8a41d5a82
F20110115_AABPVQ gallas_q_Page_013.tif
b0c7495aadfd764308e415bbb860cc95
b6c372bc609d6c44ba821e62d7803de5b148ed17
665530 F20110115_AABOLL gallas_q_Page_161.jp2
e576bc2a0441937279b8f923ecaed266
992dde26b5880e48be5befe51bd4832a7d310e07
5706 F20110115_AABRUE gallas_q_Page_233thm.jpg
7aa54e6a978b6d675d1a8b90a93d418c
a3c2ee31a9eeac3b273a0ad2c336a27a25848669
2015 F20110115_AABQXL gallas_q_Page_137.txt
f529993ab31c1f637561be714d221b6d
11c202df5984a7aa013928f676320831c0f4c123
49630 F20110115_AABPIF gallas_q_Page_358.jpg
e4f57c558f0638e7a8c0cd3eac00d3e3
f4f96fb6556cf9b664fdbb25cd4650d2936808df
68423 F20110115_AABOYX gallas_q_Page_061.jpg
168348f5348315fe98eb97aa3fa17376
3d803b2a1f0b85ffc1d39ec6ae4716057830c050
5656 F20110115_AABOLM gallas_q_Page_009thm.jpg
669b731b1aa75f13ac84bbba3bef8379
c82db933aa6ef873deb0abbb688eb3090dfc4305
49534 F20110115_AABQKA gallas_q_Page_088.pro
a4f499a5ae2bd0b65d782df42f656e47
1ecab40773f7ea50b0cc0b617413b51f1183be66
23190 F20110115_AABRUF gallas_q_Page_234.QC.jpg
a41ea51a72872f2dc2dc31a03d8428f3
abffcf9a2e899c2286a5894f3b0d02b6ca48c852
1566 F20110115_AABQXM gallas_q_Page_138.txt
933b463d3af0dfb7ffecbb64459f5c89
85b959e42386baeb2673c104bb222640128cc99c
105057 F20110115_AABPIG gallas_q_Page_359.jpg
e33bf773d2f8baebc7cb9daab5613d25
fbb17487bc8ecd7eb49471580d881277359c152c
64514 F20110115_AABOYY gallas_q_Page_062.jpg
1e1bddbd0acc04f86289264bae7813f1
e0d0981da4f7302b3afa32f90a706372c86034e1
F20110115_AABPVR gallas_q_Page_014.tif
6e371f04a190375ac2d600296c528f17
6d8663ec496a484fa1bfa45c24e885be86327764
24760 F20110115_AABOLN gallas_q_Page_049.QC.jpg
10209173039fd85e0fdef2b9c8bcb859
a516b8614755e2219878ed575fca60a19050ff93
41419 F20110115_AABQKB gallas_q_Page_089.pro
6dcebcf5a60dbaee5a2e0705897b688b
bbddae6a40bb2bd116d3ef160ce7386045752e00
23525 F20110115_AABRUG gallas_q_Page_235.QC.jpg
09075990357cb529d3b9d886553534fb
f263bf7ddff86a63d15fc9c9439d3ad90d9c5d9f
2104 F20110115_AABQXN gallas_q_Page_139.txt
8108c5754092e09573698bb76dd54485
9820e7875cbf473e3207bbcf2bf968d504cdc5e6
101862 F20110115_AABPIH gallas_q_Page_360.jpg
9b217d9e1bf6e0bfcdeb65b343911169
ab0b5d3ef4c0593cf5697cb5fe04fb01d6ad65ba
59296 F20110115_AABOYZ gallas_q_Page_063.jpg
7c807c8d5c60e14b791ef580f3c33265
9f6566dc435410dbc9a65009ff86f7aa3fb16dc1
F20110115_AABPVS gallas_q_Page_016.tif
4d4f9f4ac9981b0cade45e848f5af78d
1a2774611223ef8d887f8e2b1493bc2aaeb5a3a6
F20110115_AABOLO gallas_q_Page_165.tif
ae7aece7adf5104c7c31cd154030beaa
4bb872236fae30ce6f173b2902110c508209aa4a
50541 F20110115_AABQKC gallas_q_Page_090.pro
18c27f69acf374a6e68190d753f1b5a3
5dbc8682513ec2a88a869a5a84f4b2ae85956291
6666 F20110115_AABRUH gallas_q_Page_235thm.jpg
ac62ab8adaeeebd432b731970c75e50e
a8549a047c6a0b85cba0a01c33684126960cc1ea
1557 F20110115_AABQXO gallas_q_Page_140.txt
5f29605bd49c8a07290948fa252d5b77
8499261678d353fe15e97b82608cc76ed67ed12d
98874 F20110115_AABPII gallas_q_Page_361.jpg
2eafc6f9b5b2c0e47199cf1667424290
1b054f90e68611d2e1ec630a3ca790d3d486f368
F20110115_AABPVT gallas_q_Page_018.tif
9ba2dd877353f4f68177d682ef261c5a
60bd24cbb22be105b289bc9bb5ee9dfa24a8d308
109219 F20110115_AABOLP gallas_q_Page_055.jp2
abf4b95c37f821153d06a4c2863fdab8
2fcaa4b806bcd2feb4c421f2f105c7f0d4c453e9
45999 F20110115_AABQKD gallas_q_Page_091.pro
9438f0101df613629f45f18aa4a6fda4
5b45c44e5cbfc3e12487587ac8963f7e110dd449
16410 F20110115_AABRUI gallas_q_Page_236.QC.jpg
14d203cc8f1f50d36c3263c87d1f3c90
f794b19191a3647cc45269cefeceabd4d3178ca3
2092 F20110115_AABQXP gallas_q_Page_141.txt
6ff4a3196c9a8724cff1240fc459e677
c0aaaf54b5dbb83291c9f773b8f1f04aa3a9f1ca
99473 F20110115_AABPIJ gallas_q_Page_362.jpg
b1cf46f3e48a17ed0d557f316cf83043
6be9a740f3a423406335987607a1f201b7774ce8
F20110115_AABPVU gallas_q_Page_019.tif
f349e79c905b986a36f1844689f1089d
1aab35bfdb6f924b871a9d3c7c2776d2ef4b55ee
F20110115_AABOLQ gallas_q_Page_380.tif
1624ec09e5c34c32b7ba3fc860cdcee7
7c6a24ef61ccd395b228cddb694fea5d9690406c
47869 F20110115_AABQKE gallas_q_Page_092.pro
ea2de1e316df755853c04a42a974cd49
3ce0395fce389cf8d84cdf7f266ec4ba5871c1d8
4821 F20110115_AABRUJ gallas_q_Page_236thm.jpg
194dede7d65b635a3c19a67a033fc9f0
dd0a3c359cfbbc497b70fd6cc932732ff64f8de6
1781 F20110115_AABQXQ gallas_q_Page_142.txt
d604ff8f3c8c6f5d78e86051849051b2
47439e51cb3bebd056e9764f10583b086f9abf75
102524 F20110115_AABPIK gallas_q_Page_363.jpg
bf59db8a17aca7b5abee068b020c3a9a
e2984b67e320024cd870915dd25d09b9f6fd1639
F20110115_AABPVV gallas_q_Page_020.tif
fc8e8be57df4e27e994f0759129d337b
f1b7e2c6465a3fa698052c690441e31e19f76f0c
42317 F20110115_AABOLR gallas_q_Page_118.pro
0432643b2b7a30c0be584743e8f4728e
5ab6a35b455885220dcb9a35a1b9fcfdc8467973
16787 F20110115_AABRUK gallas_q_Page_237.QC.jpg
488bcb55a82dd3b9a1df5c492937dcf2
6e9a6888a7f718f4fb380f6826997d9ea9104c12
F20110115_AABQXR gallas_q_Page_144.txt
a809b76554ab649dd19ee229f8bd41c7
87e4404be8d55b93ae174ea0647b1d5b3ba9d3e8
103376 F20110115_AABPIL gallas_q_Page_364.jpg
679626cc0c2cc4ad5ed424e812d963f6
bc8cdf132b9c19a3f16468e411120608ab47fe69
F20110115_AABPVW gallas_q_Page_021.tif
65aec0f7fc6022ad7cf02c702c4fa38c
533e51e4f1d586463b79700dbd7e056a10a4b0c6
31286 F20110115_AABOLS gallas_q_Page_145.pro
65128342f4082abafb197818308273a2
7ffe487b63c1558bedc13b0a4d74401968f1fb8c
46310 F20110115_AABQKF gallas_q_Page_093.pro
c5dfff1eb05139443dd6128c163a6c03
05e48878ee70cf985315ed737f9c93bb62df2b9c
4899 F20110115_AABRUL gallas_q_Page_237thm.jpg
20d59316625ba64fd90f2feb134921a4
5a6e75d540815eaa194c4c9ad3a644266ebe1ff2
4452 F20110115_AABRHA gallas_q_Page_023thm.jpg
2e68de628523b7c64ce7cb213c9b5250
da3ce14de387ae97f2f3b29fa34ec60d092c8756
104883 F20110115_AABPIM gallas_q_Page_365.jpg
e19e3ac75859e373723f94175ba8a277
6b4a41d87640d6203443628a4068a733ca2ad29d
F20110115_AABPVX gallas_q_Page_022.tif
50235bb8191d821aeaece13b4ec86ed1
636cf5fc264ace29c1f6e40074bd28ab43649f8d
19583 F20110115_AABOLT gallas_q_Page_300.QC.jpg
03825386db91950770bef9a1c36151c5
37eec37d0493ac7cbefc92c4b9c960a9cf50becc
47530 F20110115_AABQKG gallas_q_Page_094.pro
388a2f85abb7422edbc7162f8a2162b1
1aac4e2405d5097b1fcf0d25d20a6df16b89510e
6209 F20110115_AABRUM gallas_q_Page_238thm.jpg
42dac6e074e108ab28e0e53123b029ae
cd8db6f07fe2d37d0c7f150f70dc413abf0f275a
1618 F20110115_AABQXS gallas_q_Page_145.txt
b907dac9cbb5b5b9a432c8ae82e1e299
2b8ba2b2aab090514666836b565f5a8ce2a21512
102850 F20110115_AABPIN gallas_q_Page_367.jpg
3ea90386c355b9f2e681c5471b518c95
31c9e7b3a2724e15237d2b5fee78367c6fcc3348
F20110115_AABPVY gallas_q_Page_023.tif
50747744f9bffe75d04c10aea22837a7
3d27ba1cefeffb362e8b954cd4e6cf39b261bc0f
F20110115_AABOLU gallas_q_Page_350.tif
793fc6da9b413888a63f4c233fa07691
6b0bf0bab8c4f0d6d2f44ee83a0bacfa0deb6d51
31156 F20110115_AABQKH gallas_q_Page_095.pro
988f53fd64a2a4427d49a04acf999004
e628a1468f953e631674de855f77a0b3b650eb5c
7023 F20110115_AABRUN gallas_q_Page_239thm.jpg
630c8844c92dbbfd4c7b066892fcac2f
12bb7eafb64f241ce72847600b172bc3e76691fe
9658 F20110115_AABRHB gallas_q_Page_024.QC.jpg
cb58739cf70e71799698d24e320dc154
ad44c7df55a5bc76cb56292bfc7b8e604ae4a272
1969 F20110115_AABQXT gallas_q_Page_146.txt
5aa9f71f9f59bdb3b0335352158d3681
7f5d490a644f151a4f21e1aae5b17fa246437527
99534 F20110115_AABPIO gallas_q_Page_368.jpg
0ccbeeefafe757db855fc546b9ba9b70
8524c56da88cb8e1b177414bf195cff9264d93bb
F20110115_AABPVZ gallas_q_Page_024.tif
01a7dcb3cbc41592ae7896670c23d764
50187585d597975a8949c510f9337b2b297e3401
959240 F20110115_AABOLV gallas_q_Page_204.jp2
2bd7964ca9adba783bfca17b61fcfd7a
76ec8004660b9e9fa7498c2755324556cb7194e3
56540 F20110115_AABQKI gallas_q_Page_096.pro
dda1741bae8b9b497a387c797b9a0448
f1a6c490d3c9a9009e19934c1eb0e270e8925067
13390 F20110115_AABRHC gallas_q_Page_025.QC.jpg
5f59ab364d4c3a13237a1cdfea1210f4
a581f613a5e37d5d19f2053990cf20f068c3486e
1716 F20110115_AABQXU gallas_q_Page_147.txt
0bb2be84cc5c8dba25951889f6530556
8befab0f918fda01ab3ca164d711f0d1b919b293
100552 F20110115_AABPIP gallas_q_Page_371.jpg
f7a9c1c6d41d883e0b1b2c2f778356fd
f25eb8b5cc0b4a95faa1eb3bc3870d19c9cddbb6
21677 F20110115_AABOLW gallas_q_Page_198.QC.jpg
464af2aeb95563e2fc362a602675f88d
3fb472492c7138ff10838a2b808f5467eed5070d
84703 F20110115_AABQKJ gallas_q_Page_097.pro
2ad91c51c983928d000974e73daedc16
e7ba6724f8999df0f3ee3d1df0632aea9a5ea2d6
24262 F20110115_AABRUO gallas_q_Page_240.QC.jpg
71f857587b225130c92b43c66e8ee694
e8585c6d2aa4fc7cd13c905d74ce148177b37ec5
19286 F20110115_AABRHD gallas_q_Page_026.QC.jpg
ef99ccaa8cb50fb9d2b09bec7e115667
e478f61459a3abb9d6de0ef6687279ecff18ac5b
1984 F20110115_AABQXV gallas_q_Page_148.txt
b2443d13cf4c2345a6c3b4ef6832ab9c
e1b02feb362e0965f604b0c202f04b13db2411ee
101069 F20110115_AABPIQ gallas_q_Page_372.jpg
00eaacd2cc7a6b7b9f49254e9b5d9701
d5737232f441c2916173d068068003c8d9af2f71
19505 F20110115_AABOLX gallas_q_Page_070.QC.jpg
accf394134b55bbcb359885a2a736c65
d7938934648c5549f9bdcbe889b8c788c049bfb1
57589 F20110115_AABQKK gallas_q_Page_098.pro
b15a52e61c77e14b009e2729035bc20a
6c7b845664a1a8f3fd2fdd7820d6adf3aabcbfa1
21295 F20110115_AABRUP gallas_q_Page_241.QC.jpg
cec76b96bd5f26de59782052195e1753
35d975bae948f704b0074a545c682989e288a7b1
5645 F20110115_AABRHE gallas_q_Page_026thm.jpg
a71c5b04c2af2f1c886b07e6e7a81722
0ee63db538b989cbd58b3414d07b01613bc88c94
2263 F20110115_AABQXW gallas_q_Page_149.txt
2db401b2af8dc37a2bc8dbf9069ab2bd
35320d2084f8ad98e8cba62dce8d552b206d6d50
54268 F20110115_AABOLY gallas_q_Page_120.jpg
9311357a9db5050c2adbbd0598b46444
cc557f6d90efefc73319b297a473532482f40109
41070 F20110115_AABQKL gallas_q_Page_099.pro
5e0b8e6d3d128de57341638544b126c3
64465d96b2c8af2f7355399813ae51f8cb73d2a1
50493 F20110115_AABPIR gallas_q_Page_374.jpg
6f583f3f349d0a970e18e8014293e56b
39e584d2ca9ef2933244ee2b49cf82bd6daa710d
6409 F20110115_AABRUQ gallas_q_Page_241thm.jpg
79b685f210b06510bbed99f3f7a0f44d
554c80e99ece44345c44a80e5961fa9f3c11a815
F20110115_AABRHF gallas_q_Page_028.QC.jpg
ee866f5ef95065e51712f2307af969cc
cee1170967fe1012bf9bdc3ca728446dd425769e
1426 F20110115_AABQXX gallas_q_Page_151.txt
7fc3cd59a8cc646c1b2cdb4839bfa06c
fc0ad56346171c4ba12409b170f02fff96fa6de0
2887 F20110115_AABOLZ gallas_q_Page_085.txt
182b4fc868a1521bfd2534689971cb69
d47ac0a01964b4c0a5b3e6396bb2aa54328e71f8
11747 F20110115_AABQKM gallas_q_Page_100.pro
efd53a8174ba8e9ac10e2e435bcdc0d6
d34830605ff44bdb9c64f0cdb33160a2604f5a03
83997 F20110115_AABPIS gallas_q_Page_376.jpg
2474a06e522cd9df3113aa5d417cb097
cc21b0c09b6e8ba12830ac7e3dcdc3f34e31ec45
22989 F20110115_AABRUR gallas_q_Page_242.QC.jpg
7d48638adb3fb24ef938ec0f912be336
a2331432d99aa418617fe6dcc54fde73f2039813
6924 F20110115_AABRHG gallas_q_Page_029thm.jpg
4f92edbad8a3fc5b7a7e59e51333d95a
50ab3cbbad453855172ccb26a5e069f05fb0beed
1861 F20110115_AABQXY gallas_q_Page_152.txt
4c6a713579e8051adc86e24a5dca242c
4b3c156346c0def3928593b980fc70f7276c9a91
49957 F20110115_AABQKN gallas_q_Page_101.pro
0fcad43c817c81e2abfbc37db67ae45e
de0c0022aed451cea23cd642ed1c607808816742
83001 F20110115_AABPIT gallas_q_Page_378.jpg
2071781a43fb566b2eaa0188246d9d5c
9c13141d146568c9c524e08baa5019a05e6ea9f0
6845 F20110115_AABSEA gallas_q_Page_380thm.jpg
de45b7e6cd04ac57b57642b8dc1d21dc
5108954ff89361faa4f56a15bb32e147c4ecd8dc
6578 F20110115_AABRUS gallas_q_Page_242thm.jpg
7f951d3de04ae89990d96b48256b3870
f4e581dede11a030c5534e21b7e7f08dfe0cb3b4
23307 F20110115_AABRHH gallas_q_Page_030.QC.jpg
5aca99d173a216513277b391f6b09c4a
3140e030acb2cc8fbaf1a2b6985ecaaf16a1c05c
1410 F20110115_AABQXZ gallas_q_Page_153.txt
0a0467eb8a750a6c53cf1359da52b05f
593b2565e4e13b90d8f89cd0abd48540f9c56c75
37066 F20110115_AABQKO gallas_q_Page_103.pro
fa77b5726f786567bbc5bc84c852353d
4b1cb89c7d6d882c7d583279e5d6e1b7fc92692a
89139 F20110115_AABPIU gallas_q_Page_379.jpg
dc14ba6cf02170343f3a7525ce0bd4c9
99fed61daac4e53608ac54e3a3dcb287dada990a
25376 F20110115_AABSEB gallas_q_Page_381.QC.jpg
99a677e830ae3f61283ba7117475eb17
777e2751c0de97d4885878a0df28f8d7b75ffe31
21908 F20110115_AABRUT gallas_q_Page_243.QC.jpg
69fe1c250b6e4dc26148badcec4dbf36
fa741bf3797bae55be36ad4b01a0e2f116c57a2b
6516 F20110115_AABRHI gallas_q_Page_030thm.jpg
af9a733fc066e8e38e2eb02ba2e17683
6e3f32d1e7bffe207a4f06cb4510c47f207588e2
36341 F20110115_AABQKP gallas_q_Page_104.pro
46ec022780128ad5059c8eda5ebc5b52
ca1cc3637cd012448074a75200d7832ecd031c52
79678 F20110115_AABPIV gallas_q_Page_380.jpg
5ae396807037f811eeca584af0ded232
2f52073d05847b0974c7f12c4af6c1afdb91168e
7206 F20110115_AABSEC gallas_q_Page_381thm.jpg
5a767431af3a461157d1bbb78cedf4fb
d75c3e97cdd0cf3514c191edd8607d5e6d579996
23694 F20110115_AABRUU gallas_q_Page_244.QC.jpg
951ebfceb1d5e092eb7e2b0cd757a50e
439eea9d1c361cc7ad00c61281bcc729e55a418a
F20110115_AABRHJ gallas_q_Page_031.QC.jpg
19b61052995c1cc31a21bb750be8f3c5
a2d85b641f7085d8a1109571c33e1c40b9e3713b
47853 F20110115_AABQKQ gallas_q_Page_105.pro
5b338473161e78422acf5a4d245d04da
974a74a2b75720f1d35c223b388105c4da3d6e46
80470 F20110115_AABPIW gallas_q_Page_381.jpg
9c339b6ad4dd8a72a2b7d7c187c5d608
f3a099298bf8eb71d3d3cfb85d1f53a9e1f1b9e4
25885 F20110115_AABSED gallas_q_Page_382.QC.jpg
5b988561739e7b27debff967ad636f9f
5ca1313478c83c4a65b2c3874de1e8cb3bd19638
6852 F20110115_AABRUV gallas_q_Page_244thm.jpg
319a911ca46bc503b693fcfbfbf54271
eb7f9194a77b540cabf40334ca6a6644ed2d45d9
6100 F20110115_AABRHK gallas_q_Page_031thm.jpg
5001748b4c17ec91f334f600eac1da1d
96350d4b8f3d0f4eebfed716a4cc6831770a441d
41305 F20110115_AABQKR gallas_q_Page_106.pro
d9dfa47881ed80aefc6d23ea3e367bb2
1870364e582c9e52e8339c3e20cbbdc92a663cc3
89646 F20110115_AABPIX gallas_q_Page_382.jpg
5c1b15bfb4dbccddfd8c2f0d2fe85af4
f75a6cc7aa4f64c9c4444fb7897ea4001ec54528
7050 F20110115_AABSEE gallas_q_Page_382thm.jpg
44c9cd3a48ae6a56d588beccbc8581e0
247c6a3598cb49d0245e102d041a4d9845352972
20409 F20110115_AABRUW gallas_q_Page_245.QC.jpg
81c610983c7c430873472fd25549230a
1d8166ca5429578281364c52a37a0b806f91cdfd
20964 F20110115_AABRHL gallas_q_Page_032.QC.jpg
b1e17fd7ef078206674316e907066fba
9cfe060cb89307542f51f0926fda3c78688e58ab
37340 F20110115_AABQKS gallas_q_Page_107.pro
fbdf62e448ce77ef5f3e00d542951e71
c30f559fa785354c40b76cc9ff010b7dabd62123
84881 F20110115_AABPIY gallas_q_Page_383.jpg
049eb8be3ad2a718f6434d8f44503cd7
e3c98f6583ac8bc28da89f1884205da50fa75659
25133 F20110115_AABSEF gallas_q_Page_383.QC.jpg
2b9041bfeee94f70ae11c1ba0512e7a5
75a625a320296b4a651348d3e99a074824f1de8e
6104 F20110115_AABRUX gallas_q_Page_245thm.jpg
4db2605618544172f4961891b33f67e0
67a10993c289d57f03b59097de5af499615ac307
6065 F20110115_AABRHM gallas_q_Page_032thm.jpg
836fa80b176a88fb06cca8f6d85835ca
dd8cfc86d6ed28d802cd2b4872618b220dfe7f9a
49962 F20110115_AABQKT gallas_q_Page_108.pro
01a66672e351424a4a2be9f41c08ba47
cb472c3c848c0b09bfe8bb6ff1c129c9020d256c
86028 F20110115_AABPIZ gallas_q_Page_384.jpg
c3231f5440da8adbd28d61e9816e2b70
7cf31826bf4e70232d631586bcb4cea11c822d9c
6818 F20110115_AABSEG gallas_q_Page_383thm.jpg
cf925b9b8f221063b44703ef532006f7
3c003e7fbedca6e737faf8959104248b7a39f2bb
21054 F20110115_AABRUY gallas_q_Page_246.QC.jpg
0133c8253e63a9341243bf19b3ce1587
2b576f73a4687672712f931cef95e534a75fb092
7160 F20110115_AABRHN gallas_q_Page_033thm.jpg
9c27dce26ddba27a2f29dd914a213304
315a277c34814c002cebb3a6c63bb26fdf3b0572
46400 F20110115_AABQKU gallas_q_Page_109.pro
975d3ccb7032611d8ed52690e46da11a
e0073061f0eefdfc51773cddac17b1a641fd2dce
6916 F20110115_AABSEH gallas_q_Page_384thm.jpg
d51a8b7d851981ae76a0aec91496fbd8
54bcfe249106db14052173c94eb848eec9b025af
6035 F20110115_AABRUZ gallas_q_Page_246thm.jpg
a73762dfcd09670d04ab3a878a1badeb
ba144649c9e24a790a133d9e60c39abf7a7e42f5
23841 F20110115_AABRHO gallas_q_Page_034.QC.jpg
ac74a3bcd7e3e70df168aef0c9e96585
3aa48a4a2910849f56cda7b63e3299c7b32d82e3
109 F20110115_AABORA gallas_q_Page_002.txt
24c4d70e1be53896509d9039b1d38dd4
5b1536e0d549c03b26799c7769873c6b9e7eb1bf
36527 F20110115_AABQKV gallas_q_Page_110.pro
5823789ecd4e5eb2c5609b6161bf4605
d964b3ff8e4c0537026270e74a42e05106ff1a8d
13793 F20110115_AABSEI gallas_q_Page_385.QC.jpg
1fb7a79aa103c5407a113acd78bc474c
8bdc2cf76182ca82901f021358eca2d50dba7505
F20110115_AABRHP gallas_q_Page_034thm.jpg
f3435cb7be368694c941403f3449bde8
0e92f95f5414bb813c299db19e9fb495b11f657a
F20110115_AABORB gallas_q_Page_017.tif
6f5a791bfae403614c7d20c492293833
df0eb22a4d28a1ec6157b4a2a90d154d22a0cf03
25614 F20110115_AABQKW gallas_q_Page_111.pro
670ff9fb35c01caaceddb63d91caa5a4
4c63ea4a527d37a8cc954adc3ef637b9cf288c49
14529 F20110115_AABSEJ gallas_q_Page_386.QC.jpg
eb863ba4375e2eed8f340aba47d32c3e
a03066d891999887648594ecc5b15636fdef0015
22717 F20110115_AABRHQ gallas_q_Page_035.QC.jpg
4a90e3c91f8594df4be53c54621f3ab6
1736cbca00c59e878232624f8fe1ac6baae4df75
3974 F20110115_AABORC gallas_q_Page_097.txt
64a2c0e46fb6b4011b49dbbce814af4f
4b2dfd621738f938a3bb93ddc5eeabcf6ce52374
49764 F20110115_AABQKX gallas_q_Page_112.pro
15b669427a8371b7f582bd4e3d9e979a
4e0ea80482e2bab419ba9d84d3e9d83d0df40f84
4339 F20110115_AABSEK gallas_q_Page_386thm.jpg
2d68e24a1fe7da65749439a80e08add3
216a99a8d890a5d090c39dd62cd096b83015b1ee
6581 F20110115_AABRHR gallas_q_Page_035thm.jpg
270a901f6cfecec6e2e081d3992eaf6a
a69685289962122c92aa0a716231caa393fae97c
1440 F20110115_AABORD gallas_q_Page_273.txt
7852b8cbc77b69d27813df6e3df69879
f204b9223ebf74970d90300a75ac8a0c4b33920d
40862 F20110115_AABQKY gallas_q_Page_113.pro
3979693bf52afd063d1df3b84bef0f42
101e4b9841ca90ea2b4ab768cc8cdfe809c1c13a
440367 F20110115_AABSEL UFE0008338_00001.mets
160d369800ecaa57d2379d939a7e6340
9940f9ee68ca2c030d250255d473a1cca86464a0
23229 F20110115_AABRHS gallas_q_Page_036.QC.jpg
5addf16880eeed3362858672b114254e
81f7eb17926e1af85b5e42309c20161731b9b313
5462 F20110115_AABORE gallas_q_Page_006thm.jpg
74e0c750c676a7aef0722bd86f41d9d8
f4506900471b43d07f86b69c10f6e08d9f2d7199
37076 F20110115_AABQKZ gallas_q_Page_114.pro
599e74bf432be31cab2ada63c8a67b06
ab8d9a5eafc448cecac91fb2d734173fcf9464f1
6515 F20110115_AABRHT gallas_q_Page_036thm.jpg
a1364b2d6829dbf4a63633bd5d1114ee
730fcf85d582c17eee84d3d1c8ec438fc6a9919f
5807 F20110115_AABORF gallas_q_Page_182thm.jpg
565c0327515118a4411df06a53d5c982
4e5986a1877e9091acc38755abcacac85e61bbe3
22460 F20110115_AABRHU gallas_q_Page_037.QC.jpg
276f4a4486515e7bdf343df97ca5964e
941e1093317ad4c0dbb783912e166569fdcffcae
66735 F20110115_AABORG gallas_q_Page_127.jpg
1dc45dc0ed690c7fba28298e1bce0575
6b582c7fa2dd3429868647f226176766e560c116
24478 F20110115_AABRHV gallas_q_Page_038.QC.jpg
4732bda3fa98172e2ae8bd293d548c1e
2e87151860013f2419802c124444673571fce0d8
F20110115_AABORH gallas_q_Page_103.txt
6ced0727f13c9f1b04f44215ec109a14
9a8db46188ca61e827404e09f67ab6e3ad2c4efa
669906 F20110115_AABPOA gallas_q_Page_159.jp2
6a9c6da1b5389c12fb87c2cdc20abf7a
9425a63f4d21e9ada52b3c0af9366cacd2278d37
6835 F20110115_AABRHW gallas_q_Page_038thm.jpg
92342f487c7ad84af0bb654a237606f3
774c0a4c931c9d105a69b5447b32542353faf42e
61484 F20110115_AABORI gallas_q_Page_192.jpg
9af5b1ca959de72c9cf2d615f55d41fa
3f8f857cffe751b4fa2f3104734a34271b89bf5b
851576 F20110115_AABPOB gallas_q_Page_162.jp2
7accbc8a47c3631cb446fc85e01c539b
f0fa0dd65031b1fb9e8d53d327e3b6dc66ee7002
22888 F20110115_AABRHX gallas_q_Page_039.QC.jpg
41f94c0872ba3e0b04ea0e460c0f07c1
3ea014783242c71847cc4c3157c02338d32be289
74604 F20110115_AABORJ gallas_q_Page_012.pro
20db56210ccbe76d8d9034cd748a76ee
68d1e0b6c128fc707259488d6b7732401f911f98
24346 F20110115_AABPOC gallas_q_Page_163.jp2
32cba99ee7635112a61414b8fffc0361
ff75e43129fc1a40de983e0d4e7101818d82c464
6873 F20110115_AABRHY gallas_q_Page_039thm.jpg
a4303de99cd1ce2b2032398c4033b5b0
d618d6a5c301436c4b6c5ee678c9449c46d91d60
1798 F20110115_AABORK gallas_q_Page_197.txt
178068872c0ce8d50fe8af293751484c
16bea375cad3b8d08a67773d258f5a78e8e1be3d
99179 F20110115_AABPOD gallas_q_Page_164.jp2
20928449d67fbaf73f32db7784fd792a
c6817e057625975fd0ba03106f6b657d950ae880
23489 F20110115_AABRHZ gallas_q_Page_040.QC.jpg
d0fda92a3b6ae94497f0f8edd092dbab
c8418df4d57efc8bbe818f6703d163af0680f7fa
63579 F20110115_AABORL gallas_q_Page_227.jp2
6e5e5a78a4e73abb1d180212b759ef35
85c33838b22669742d6b3a426b64fad8070296a4
1051943 F20110115_AABPOE gallas_q_Page_165.jp2
42e9e8bfb782ccec81d7fb353ba8d293
5fa16944cc3dfcfe908cb99099dc7e8b152368e4
5858 F20110115_AABORM gallas_q_Page_114thm.jpg
4cdb7ac867ee43273d7a0d4b1ad567b2
8bd2c282a73bd5aba7d0976ee607d22a7f4c882b
1051954 F20110115_AABPOF gallas_q_Page_166.jp2
49a268058aac9ea6fee1deec5ca3a675
75d3336d1f22472b45c854025ad7c96e9af26974
68318 F20110115_AABORN gallas_q_Page_356.jpg
2205ed1fa17cc4f73567727fe585e097
85d5b900e2d059b82a507e19d65ac5d352152614
18587 F20110115_AABQQA gallas_q_Page_272.pro
743fc9baf10d586d7af8c23e0199ed03
cd0c8665e74f193a7b7584684ac38049253808a0
F20110115_AABPOG gallas_q_Page_167.jp2
a6c5f2300b9ad01709f5d20c02e4b7fa
2d04dbde4ef2ca3ba57dc12902ae7421165bce6a
F20110115_AABQQB gallas_q_Page_273.pro
28af058b7e1223640e7f8a16c9506c08
0214c11d8321af6f1159d9fa7e6a164333e37d3c
889636 F20110115_AABPOH gallas_q_Page_168.jp2
3d7c98412de2ff42b5025b6f08b3f39b
76709056fe8da8c6909ee64f9d57c9d1bbfb76bc
19988 F20110115_AABORO gallas_q_Page_207.QC.jpg
9770b366cf5b532daa372364ef8bb14e
e9f1601c4bd694dd6309c8ef99ccfc50b00fbed9
24382 F20110115_AABQQC gallas_q_Page_274.pro
4adf68e183a602ff55e6cae822b43d7c
ead89158e3540aea4a2f56ae3c741f3d92f760b6
110566 F20110115_AABPOI gallas_q_Page_169.jp2
54a3f60c416a572b55a1a574e4049d10
7cb1d12403ec4fb00107149040fdc6cfc0305c1a
5904 F20110115_AABORP gallas_q_Page_063thm.jpg
e8982c9d866151cc1975110ae2d75800
506368ea0b06b6804aea4c7f2d7e023bc488272c
20834 F20110115_AABQQD gallas_q_Page_275.pro
6adb467441a5277211def9c2ad734c9f
60d8e1812dea85de87206c341eec7a0d7f2530a2
900240 F20110115_AABPOJ gallas_q_Page_170.jp2
993a51defc05f27119930cb156de584d
1182ab8dddfbe2d90d16b88d3eb9368177ad48ee
6139 F20110115_AABORQ gallas_q_Page_077thm.jpg
efa5e268763b272b77923313c72b7223
7360afdff57249dcd7cfa0c18aebea1b7c310e83
20265 F20110115_AABQQE gallas_q_Page_277.pro
d2f9e49adc78ca18d8d663b149867b5b
f110bb04c34d9cf54a687a5a295048ef74661e2c
6800 F20110115_AABORR gallas_q_Page_094thm.jpg
7afab533afa38f0f8b53470eafad2062
34cb1b2524dbe1071748f0499c374154ad6ba61e
21823 F20110115_AABQQF gallas_q_Page_278.pro
0c35a857ce9fb1d4826292dc7ff66633
828b4a57ba6d038c72907ff6d9d517c6200cfd85
1051946 F20110115_AABPOK gallas_q_Page_171.jp2
356e75789231f2ae035ad54acaaaf968
7ca4ab0cd97a2dd9b9c3631068b2634b60ab4460
F20110115_AABPBA gallas_q_Page_130.jpg
48eda37b28c968dbd95d58deb1e2ba3f
7b9a382abf3d9361b91c56e0e7afafcf98f80d35
F20110115_AABORS gallas_q_Page_048.tif
ed45be1f7ce8d8ef241154362bc6d0af
b77ef309944a4dfa40659a302ae63011b9cf3a7e
19181 F20110115_AABQQG gallas_q_Page_279.pro
5efe743e414536b52b33931589347311
6f55971d5b04e27a61790805e6d01fa5dffbe988
1051927 F20110115_AABPOL gallas_q_Page_172.jp2
c5bb8e7101327f9271749570de2ab131
57b836d10764a13d2f9e4121118491dca3cb02a0
6125 F20110115_AABRNA gallas_q_Page_117thm.jpg
6bd1377c848927342727c5d36544945c
483173ce6839bb171299dc4a671288f1c9399f7c
69463 F20110115_AABPBB gallas_q_Page_131.jpg
bd86d12dd666e630da2bb1f254598e7f
90c0319ef6af0b4047d3c4bfa1ff2614599f0206
12906 F20110115_AABORT gallas_q_Page_336.QC.jpg
7ac742bddf37e50efd290a68c654da59
fc134120d800b5bc4de2ea157ec9ed3f407e9b99
30175 F20110115_AABQQH gallas_q_Page_280.pro
18c58ad668f68703fbc066391096cc0f
404826891f59857c93593328ef34ff31ab1c1ebb
1051967 F20110115_AABPOM gallas_q_Page_173.jp2
51bc459edb8a797d63671fc79b044a50
456a669cd8891a8f978cbf40348f07122608c0a9
22755 F20110115_AABRNB gallas_q_Page_118.QC.jpg
5b91d299101bb8ea8b5fa534fbb6297f
71b23d2ab2a43735974b8e5bcfcd3269d0105c65
F20110115_AABOEJ gallas_q_Page_111.jp2
c376882bef13f1cfff33cd18a6eeff28
3dfbb4dc2c21a1ce47702b7eeb20f4bca20782d7
68419 F20110115_AABPBC gallas_q_Page_132.jpg
36f085ebf589d1600cc4ef43765806f7
b456ba01b666d1b6d65b20bc7673b4e09e14dfa2
46077 F20110115_AABORU gallas_q_Page_314.jpg
71de14d50b880e6803a1c1bc2dd1aa77
dfd1e6d9b5ef8b91ec9034546b8b879dbb88f06b
54956 F20110115_AABQQI gallas_q_Page_281.pro
51eedcbee3d5c4f834445a202cca97e7
d4eb999699717f1b1f224dfdac4e25c7a121c298
F20110115_AABPON gallas_q_Page_174.jp2
353df13b0e38ed7f3e8d2f055a140a24
7de1cd2805bb789afebe000b67a8613016694eed
6361 F20110115_AABRNC gallas_q_Page_118thm.jpg
46436a56ffbb1cdffe363b95733cdafe
e33170fa327873cceb44317a5cb60d9a83ff8baa
26651 F20110115_AABOEK gallas_q_Page_138.QC.jpg
fb34f0e9dd8d6f44d55b39682e0b260a
476a8bd906fa3b7522ff8e78c3cee76ff704e748
65554 F20110115_AABPBD gallas_q_Page_133.jpg
6da7ff8a5ab033c7ce12f05f6f282cfe
2d06a5cf98a5b0b12eb91d07ea71b53623873f24
22325 F20110115_AABORV gallas_q_Page_183.QC.jpg
e42fd7df6e9e941bd1bed55ba0dfdba3
a9361e2f9ab091b9727e9a98f790bfc571aed1c5
35440 F20110115_AABQQJ gallas_q_Page_282.pro
ac4ac33a569f226b64736b1fa0fae6a4
f9e4eeb217a4c44e86c1929e8af0af44999a388f
F20110115_AABPOO gallas_q_Page_175.jp2
ebca6f1f1afc4487b13d7800ccbb9d19
172924dfc4e72fd4be7a46fbd7b7a6cf7cf826e3
21494 F20110115_AABRND gallas_q_Page_119.QC.jpg
8c4bef353cb1f4270e7b5572b859a82a
b06a83bdf0c842c89afbf43baf8fe006a4f6aa52
71826 F20110115_AABOEL gallas_q_Page_067.jpg
e517995ba8247e4fc391f4aa393ebd83
81faf1705850e12ac7e2bb3f22bda57df1411551
71177 F20110115_AABPBE gallas_q_Page_134.jpg
81236294208c17e2d5abda78d5e352ba
f2fd9c81223f26753a70cd5e36f71f3a6823cf10
21357 F20110115_AABORW gallas_q_Page_190.QC.jpg
80496a0574aa009ab232edcef5dd8619
47d2e42c45035102a4ee082dd8b315499d8625ef
12434 F20110115_AABQQK gallas_q_Page_283.pro
68037edea4ef25ded26d752011cb6e82
8020b2b8dab305f3c642a5b1875b65416efc10ef
F20110115_AABPOP gallas_q_Page_176.jp2
461cc3642ed82c004ce6ce791bad4474
de43a9bc0dd91294d1e6146c37c74dca858d2101
16471 F20110115_AABRNE gallas_q_Page_120.QC.jpg
b495f32926ec04b1ec8bbf6aef82fd90
e08d1d744e9e1086d440cf675d4ada4364714515
F20110115_AABOEM gallas_q_Page_323.tif
a8e4b7f823505626949c9fce07d6ebeb
7d3c5a1c8235b0306c80ba871aab3aa9e254a6c6
59271 F20110115_AABPBF gallas_q_Page_135.jpg
578fa5d824e73944ca4b1bdbbb591ef0
b5c9ea6f3b718f5b2b7f0c69a791af6ae8b04c20
48479 F20110115_AABORX gallas_q_Page_043.pro
50bcbb1cda346453ad883e73920b084e
543897c91fa930b3d72987eb7bdcd4d2d926ae3e
108479 F20110115_AABPOQ gallas_q_Page_177.jp2
d22ab3896b6e3c5760ddffa2f306a302
9aea38d26d88feb9121e511df2678f67464f9930
4631 F20110115_AABRNF gallas_q_Page_120thm.jpg
5c584db1c518705f12a32c1ac35ff560
3fabf05b6cabedfe25a7b71bf98d554157f5d964
46066 F20110115_AABOEN gallas_q_Page_164.pro
4c93680a81be641527c1302973766e75
21248b16cbb039ee91ca85b0620ac557360dae6b
F20110115_AABQDA gallas_q_Page_253.tif
5503066684373b37b0b8ee9f6f6a0d00
e4e9123aa0ca7e23f37bf62551914fcbbdcac501
69504 F20110115_AABPBG gallas_q_Page_136.jpg
32f3f93efc0b353c479468c6860f2a2f
19c5ae36f49d81639830fb98e1e71cae73429336
F20110115_AABORY gallas_q_Page_369.tif
fef179e73508e57d1a3f16ea6436112f
c2e4a09ffeb155d152956a1bc4e499271b28ab46
25813 F20110115_AABQQL gallas_q_Page_284.pro
3886c3ffb9b5516a388ebe4f02d123b4
4a31f51b151cf7fad839ec1fe03171c25ab4f63c
77524 F20110115_AABPOR gallas_q_Page_178.jp2
c1e62ef159f48bbbc4c0cd29ed3362bb
80fd66db6728744f0e37b8ce287e3021738363f1
16838 F20110115_AABRNG gallas_q_Page_121.QC.jpg
94f46fe746f8e70152daacdc3bc4268c
86a55dc7b014d26200250631bc432730779d2c4e
21037 F20110115_AABOEO gallas_q_Page_153.QC.jpg
9e48eab2ef5f467f304ae9e68ae419e0
82153f62f5833cab78216278e5a7b65297f5561e
F20110115_AABQDB gallas_q_Page_254.tif
fefeddd84f12ab86147535265bf28a04
6dc99388a4a876b97d73213744f9641f25a0bac1
87971 F20110115_AABPBH gallas_q_Page_137.jpg
89701ae04ae7305946a90c1b7888f9fc
a63757fc221c526659b71c1d9ff3ab6c56b009e7
27591 F20110115_AABORZ gallas_q_Page_227.pro
464bb6cb75f1a800b04ec46f76face77
06365ac21286adf3b81ec864358b01cd12905edb
38985 F20110115_AABQQM gallas_q_Page_285.pro
d826abf6b75352b0fe895db381133506
6287fee21d74311b93ee6e8af3b9da8a8ab8bc9f
82753 F20110115_AABPOS gallas_q_Page_179.jp2
891b5623af0eda0860f1d791b132accd
70f45fbdf235b3ebd113bf736d6b7fe52d367c65
17772 F20110115_AABOEP gallas_q_Page_005.QC.jpg
195ecafe5ba7f75b441fe3cda39df5b4
14b81aa85296a3554dd80a43f85359c4b765789b
F20110115_AABQDC gallas_q_Page_255.tif
0e60da9a030b371d4256cdef9861e5cd
96db785b0556e256350048dcfef9a3830422177f
80894 F20110115_AABPBI gallas_q_Page_140.jpg
9b742f7afbfdda3056ce261d3161ab54
2d807dcc2cef5f821e5bc8ec20385ab5524527bb
52889 F20110115_AABQQN gallas_q_Page_286.pro
1f890815eec992bc06927df4253bc79e
d8ff0fa7c5b7edbce371037c5d99b5d0df90229d
87998 F20110115_AABPOT gallas_q_Page_182.jp2
5bdb92a53df4fb31a2807c135c6330fe
a0e81370b385f7da84909bcce2c553d80580adf9
4926 F20110115_AABRNH gallas_q_Page_121thm.jpg
0bd4ca69ea87031d5d9811f95b9af0f3
36d150bcd809ec45d837e27fc7a5fdeed3395fed
5782 F20110115_AABOEQ gallas_q_Page_125thm.jpg
053aeeefa6d3badd8644469d06ad3bd1
e20cbc5aa8788225d3b56e05005049cbb7ef70d7
F20110115_AABQDD gallas_q_Page_257.tif
4328c44062acfa0f43ff17131eef25c3
d95249feca1daebc16ae4ad965f90f2eaaf50d19
88721 F20110115_AABPBJ gallas_q_Page_141.jpg
e8519644b7aa5ac014bee985ac893acc
cfd72f74efd8a0e2aabd52246491e37dc7eb76e4
32484 F20110115_AABQQO gallas_q_Page_287.pro
dd6e0c9ec4857466d8253cb2dbda2820
665650be8daccd730d72b3c02cef5bf66b04e6fa
98658 F20110115_AABPOU gallas_q_Page_183.jp2
82ebc78de7520248d68bc021981519ba
94240abc6fe7e8bc71c9aba0ddc9433a05271d70
21219 F20110115_AABRNI gallas_q_Page_122.QC.jpg
2114d71b5f539220519a060f34097a58
55666191c6bf0800a5382b0f04bd6d97c7fd3cf0
21400 F20110115_AABOER gallas_q_Page_321.jp2
9c156d9f3c8f705a0e79c0ff453b2032
8f5a5e1c7544cd0aeedb2e2002deea103d795b04
F20110115_AABQDE gallas_q_Page_258.tif
0629da2439c166d0a4712df447969787
06141b742c57411bbde74a2056ecc49070abb2cf
64586 F20110115_AABPBK gallas_q_Page_142.jpg
357bd4bf785a40b13c1a5a8c3b07e860
df4b6b32a7166b99b591b8be33673c156316480d
39312 F20110115_AABQQP gallas_q_Page_288.pro
389e09f380a3cfc0038b6309cb89c58b
8313c76e810b248f1d38b08dc3def09e75b8166f
88598 F20110115_AABPOV gallas_q_Page_184.jp2
e2cc158afc69f66f6bbe0f2026b46ae7
67c1ba46110db5b237c89a54db89841962f60164
6176 F20110115_AABRNJ gallas_q_Page_122thm.jpg
0a53b091fc9141c1037acb601a6adade
301b96c2175b432e254c02f1210e51351010a998
42478 F20110115_AABOES gallas_q_Page_080.pro
c6496798dc7ff7159516fb62653265a9
00014337288c99051d86ccfcfe82385e4d717485
F20110115_AABQDF gallas_q_Page_260.tif
d75bb14a969dbc982aec6142a94fc684
4d663724e74653a0c91d0d0c171fdfdae8359713
52328 F20110115_AABPBL gallas_q_Page_143.jpg
a2198b41c3c4f74b4ef547b7eee92f31
77a4fc247d8787835d1c55a5789aad078ec2082c
59145 F20110115_AABQQQ gallas_q_Page_293.pro
ccec5897921136b8a442506613b349db
5e10cacea2b877c987c660d4ad7c683e6b3a6331
101472 F20110115_AABPOW gallas_q_Page_186.jp2
d987d01f4801f862261bd899e368de29
ed17a7e7ac3e2afc4ab692a7f5bd6a77ba6d491c
3505 F20110115_AABRNK gallas_q_Page_123thm.jpg
2af331bdc6e274e37092cf1fca3aceba
e63bf294017fb466cf2530ab4ded50a09f067fc4
F20110115_AABOET gallas_q_Page_078thm.jpg
1efd91e8474b20ec5453b59b899c4ffc
93f1c3015d57cb89f76291e621ab7b460e036669
F20110115_AABQDG gallas_q_Page_261.tif
f1c00206ad73fea8a98031f7ca83145a
648e18889634ca3f77327c9cd465ac85c9516440
65756 F20110115_AABPBM gallas_q_Page_144.jpg
9cd76c70fa3ff930ceeb09c20a638d50
71842f17ad24bcb5dc1a39d08ef1820e3f6e39a7
23251 F20110115_AABQQR gallas_q_Page_295.pro
ddadb17091f2c024a62f02b2b3f6006e
198c8eeec69bcee24555f46b2d5173ff33620cd3
93016 F20110115_AABPOX gallas_q_Page_189.jp2
598af89da4b47744eaae017ee7287acb
6c7a94e8d1fb47e572d377f79d5ef103b98f3c3a
14345 F20110115_AABRNL gallas_q_Page_124.QC.jpg
0adb39a7c5ed8a97f27e765f88012efd
15c888333d1eca57cbe6903e39037b3184ea6f1b
2111 F20110115_AABRAA gallas_q_Page_218.txt
08c2cef86ddbfc3bf7c4580fa03b6386
e16cc39fb18248dba7ac6cca90dda8a0b554d34b
4290 F20110115_AABOEU gallas_q_Page_025thm.jpg
54b8c5da67b1c29dd76bf2f4cde83257
0e280f10024088c03f321b57da9ab0b5afea32db
F20110115_AABQDH gallas_q_Page_262.tif
da24bece001871b16c784c97be0e0763
7dc0c81c30e0fb3472fcf05d9e177348fe6063e9
56530 F20110115_AABPBN gallas_q_Page_145.jpg
b1e2732a0a358f93c2530690e39e6b76
3baaea6267721539932241a96f2b7074af133c23
48941 F20110115_AABQQS gallas_q_Page_297.pro
a923226e424fac5083c8c5bccfea34c6
78115470e7b15edd9893f00517c2fc97ef453b97
94586 F20110115_AABPOY gallas_q_Page_190.jp2
b451fd1cd9c5e3b6558745dc3223a06c
d87b4404954541f91318a417eef8d663d108f19c
4628 F20110115_AABRNM gallas_q_Page_124thm.jpg
e44e43c5742331a776d9e692699bcf24
64d5e7a494cca36e69a25034633927046d6131f5
1657 F20110115_AABRAB gallas_q_Page_219.txt
980c26b0e4fd047b1535224f910e9c08
bf9f4bbc891a474fa07a8d2affdb803218cba025
107448 F20110115_AABOEV gallas_q_Page_108.jp2
70133b36c3a2a54fea311d58d4bd59c7
1a436f69b692d65312c96b71db9ef8d4abf402d7
F20110115_AABQDI gallas_q_Page_263.tif
4ed340cad64a0f352c5aa6f90d97a967
35239566a28e839172a523d9e065877d8dd0df44
62082 F20110115_AABPBO gallas_q_Page_146.jpg
788b8ec0f88fc803c11724ade2200bb2
4a78c0c368a86c56a2db7cbe760ec1ab0468b4bc
36941 F20110115_AABQQT gallas_q_Page_298.pro
cb06bae5eff4611c5340a32645fc565e
40544970f72efd86988decc802d780bbee2d6337
829938 F20110115_AABPOZ gallas_q_Page_191.jp2
dab01cb0b8e28d3bc0a04bc0d767d7de
a0ad1452c3645843787811de7d5a8a7cab9fd58b
19461 F20110115_AABRNN gallas_q_Page_125.QC.jpg
ccd5f2f28450611729eddbe9cd96786d
f320b68f1ad757923c0c4544854f542b911d4d35
F20110115_AABRAC gallas_q_Page_220.txt
4d2946052495c9148ae068ad277b275b
87a5996619f83153ad97e899e142908727117c19
62571 F20110115_AABOEW gallas_q_Page_153.jpg
7fd9d4d120d037d2d2fdd90b30a5cb0d
6a6475ea0d9279539e658c99cef0441246ccb924
F20110115_AABQDJ gallas_q_Page_264.tif
95e03d9f50da4ba7e447fdbc3c8ab851
ab1a15f0d314a453267ad0ad72bfc47214727826
58478 F20110115_AABPBP gallas_q_Page_147.jpg
d2f79947544dbd113b2ba613e788a04b
3fb77ee20ab6cc4a91ad92f91ef1118005275589
46854 F20110115_AABQQU gallas_q_Page_299.pro
c7d10e80e2d47946da3fc0555873db85
f0b92b7aa861ebfead1d0b3efff67db8005fcb5b
21115 F20110115_AABRNO gallas_q_Page_127.QC.jpg
c8322a4ccb2a6017494228076e42ee87
1c7f1c097345a8ad6fdd545007be3b23d058848f
1890 F20110115_AABRAD gallas_q_Page_221.txt
afd5fdf7028ff88158ca41e4cbb22243
7a98a83cde23dade9143b9ea079642e5b4c33417
F20110115_AABOEX gallas_q_Page_126thm.jpg
bcf611885afeb4d95ee2bcde56b04c3c
70ea2c7f58793f13fcd04a5957de3f038a5eb662
F20110115_AABQDK gallas_q_Page_268.tif
788e8c3e1d8b4dce12cb0c8604b414f0
be8340db49a0191e6970bb51e60996832b2250dc
69597 F20110115_AABOXA gallas_q_Page_005.jpg
2bbcb801376539522174c4af63aa4a67
f5ebe9c7209cb282d1badad62e19842c6448a598
68012 F20110115_AABPBQ gallas_q_Page_148.jpg
00ada754f89c6a5e304948814f2844ff
79809bf8193dc1904dae044ce72f343fdbccac3e
38265 F20110115_AABQQV gallas_q_Page_300.pro
5c8c8bc0cfc215786bc900fd49b4b685
1c40538dcef18b38af9c6b589b194169e17f90e3
24450 F20110115_AABRNP gallas_q_Page_128.QC.jpg
61a2555f304b2cd9cb8849ce906f5e2c
0f7ed8e103bd836296cec7e70fcd8193a9708cd9
1648 F20110115_AABRAE gallas_q_Page_222.txt
682fdd3d55a68d0a2430671b2aa247a1
49b2f3bd0b92f54b1abb1a9b6e955fe4bf9f0dce
43207 F20110115_AABOEY gallas_q_Page_276.jpg
eefee6fbd54646c319bf67a6ad411348
0d2ebf1095ff01c37278180ff9aba4efdbf1ffd8
F20110115_AABQDL gallas_q_Page_269.tif
029933fb88cfe7248cca70d5cecd0259
db03fdd8dcee572d02d2275db9be5f7d2736ff39
93890 F20110115_AABOXB gallas_q_Page_006.jpg
9baf53a3a34c946c10df54aeab52923d
47223f8d295b92c2c6095c24b385e224c4ebafe5
47810 F20110115_AABPBR gallas_q_Page_149.jpg
8725c6c0fa48bf18a3a296744a13c8ee
d76bbf35bd16ec2286ed693f49e2cf8e4ba45678
46340 F20110115_AABQQW gallas_q_Page_301.pro
afc0692d15d7999c3f824d95d3b9963e
fbdd85c3b88cd92cf1cae415d8636d6d6643466a
7143 F20110115_AABRNQ gallas_q_Page_128thm.jpg
4379b7fce267d99603396c071d25c4c8
0e9542172fd5480db4b2b8ca435edc5f3d93ba5e
F20110115_AABRAF gallas_q_Page_223.txt
46abe620ef8c8afc61a7bf5e49b1cbb5
9704e335c7d05f0487eed2be39eb17d96a5004e5
2027 F20110115_AABOEZ gallas_q_Page_049.txt
e40bdd391269c201efe7e9f1a831aed8
97d8108bec5024141a1199fcda3da7d5c0afc318
F20110115_AABQDM gallas_q_Page_270.tif
6315a2dd97a6d37429131f7e5a4bdf59
9c338663140f43bf87598b7ccbbe8d2337d204e0
102835 F20110115_AABOXC gallas_q_Page_007.jpg
dbdf9a9ddb90aba00c62589b238b09c6
fc8c339db5f04f9e3d2773f53971aa8c2688773c
51960 F20110115_AABPBS gallas_q_Page_150.jpg
2288949218ea7324efc6e931f0cf44cb
cfcb1bc51d7094e97b763a6078c2bdd4c4935d6f
47157 F20110115_AABQQX gallas_q_Page_302.pro
8ee0e99d6c8056db1328c9524c4fcf23
ccade4767b4f4c74b6079efc73551235d88b1aa1
6530 F20110115_AABRNR gallas_q_Page_129thm.jpg
bb92392a4b345848d0d1b40d41db3e86
8717453ff9cb71b54c438f18c507f7055a69002d
1892 F20110115_AABRAG gallas_q_Page_224.txt
79223fe318feac84ec28b6cde98d2169
a3b2ef3efb22b47ae58b593f70abd2322e0edbc0
F20110115_AABQDN gallas_q_Page_271.tif
c7d6c61531fbc62ab8b0ccb9df947b7b
a99c9b5380cab9a9989069757a96492a4772bd7d
18634 F20110115_AABOXD gallas_q_Page_008.jpg
69512c4bf0111de1b044f2f53b850cce
46ef843d8572f73fcbb90e1471cc849533ef39b5
61779 F20110115_AABPBT gallas_q_Page_151.jpg
a8e2f5ba7357e0808cb16201f62d7a47
bc83d551407810b9cb252f6ebb3322c77545b68f
47310 F20110115_AABQQY gallas_q_Page_303.pro
13f677d0cd83862f9a524eee1b631c04
db927b5e554b8786c15c74c85e84c3ed9c2f2ea9
19769 F20110115_AABRNS gallas_q_Page_130.QC.jpg
ffad32d150aa1f97e56ebf8be6897860
74cb87ca97a42da16510b1c4c808c86c398bc331
F20110115_AABRAH gallas_q_Page_227.txt
b74a32ce8eb31555084a1bae2da579ac
d8e9cbf01fc633dfac27dd25807d801dd33d045d
F20110115_AABQDO gallas_q_Page_272.tif
61356c8ab1b63d86fc82618683223e2b
7176d8f9f9fe76c56e49deb86cba5f4fb2707ae5
71141 F20110115_AABOXE gallas_q_Page_009.jpg
f9123ae610375066691a370322d63949
bf99a905f15fe434762e13aff951ece1a0abc660
64335 F20110115_AABPBU gallas_q_Page_152.jpg
5972b28af2ab81dfbbd2ba4a76e03823
2a481b439c6cb0a6aa42cb988b636f59d9a9fe7c
51472 F20110115_AABQQZ gallas_q_Page_304.pro
7444fe249ec6e89f8ffba0f544c377f3
d1767e436765c9fbb1c94486ffbd67cd4871d472
6042 F20110115_AABRNT gallas_q_Page_130thm.jpg
e593cf8ca18c66a465e724bcada496f7
8b7cfb9a8b904f7637c234b6f571344fdfdd728c
355 F20110115_AABRAI gallas_q_Page_228.txt
72696b723fb8a11e6f3503854d934a23
ee370547ee79fb3a931c10d1f2872c530608219b
F20110115_AABQDP gallas_q_Page_274.tif
7ff99ab47846c44259d1408b3b324303
ec47a5cbda38c6efe822a600ba61e5377cdeefb2
79992 F20110115_AABOXF gallas_q_Page_011.jpg
09b9508bf6b5ececa9962ea0e2b33693
1c6c26c667b8cee75abf77597938441197a90feb
80033 F20110115_AABPBV gallas_q_Page_154.jpg
bb54742b05b93a6a0f57ffa84b571143
159d2e0fa38fb9e9d710daa6dbec77cf54d605bb
23580 F20110115_AABRNU gallas_q_Page_131.QC.jpg
99c7be9a933a3e310ea9e237b79d67d2
0b24fe7f607b4d003a852b1abc20e6e5125d27c6
1842 F20110115_AABRAJ gallas_q_Page_229.txt
c05a559da826ef473d9d9d71d65601a3
1a1a1ef37365c298108c19fb538ff7e1fb5ed019
F20110115_AABQDQ gallas_q_Page_275.tif
631b55be4a489b6fa087fd5dda7ce1cb
1e5187651868ecf5206796ead55b73f5c62f151e
97716 F20110115_AABOXG gallas_q_Page_012.jpg
112803c80d1fc33760d0f2c35f534920
a1b31a7cfd70f8092aa10a89a0f277736089edff
76419 F20110115_AABPBW gallas_q_Page_155.jpg
83c7a097f31c1d716f8beb8fefbba0bb
1fd971e950c8304d7176e3bf7563e9e68f9062f4
20346 F20110115_AABRNV gallas_q_Page_132.QC.jpg
cfba28c4ce0d4098fdbbcb0fd0034460
6ac4706923acdae1125fb521ff5b65329b78a4b4
1802 F20110115_AABRAK gallas_q_Page_230.txt
a06c6061516813df1e84c454f75ab7f3
7aee1b2ec28a45454c67305ff15e790e6a33b2d6
F20110115_AABQDR gallas_q_Page_276.tif
54af33da82fab7f07b400f40ecd01688
7ca3e80c70c0b855c6289a884958427fb51974cf
95902 F20110115_AABOXH gallas_q_Page_014.jpg
a8341ababe079db43de7a5b0867006e1
b708071f8e1a4af5ed6143eb272c0f72e8d87be6
62831 F20110115_AABPBX gallas_q_Page_156.jpg
d7e05ff579f77744fd29f15ab0ab6e5d
dd0e205b5f4ef4a244ca02554aee53248b7bfdae
75121 F20110115_AABPUA gallas_q_Page_347.jp2
546dd75e1d597826c56aa457eaeb4da5
4494521f2e8656bbd5ce1fbfe478a3bc633d36ad
6013 F20110115_AABRNW gallas_q_Page_132thm.jpg
d145013afd8bc0cabf1fdef712b35c9e
1bba000f2a6274ab42f272ec5a3b0192b25931ed
1002 F20110115_AABRAL gallas_q_Page_231.txt
2f2d3e43a87925b8acf68a84461b50cb
95025652070e1e0e33ff6aacb57fa92210789d96
F20110115_AABQDS gallas_q_Page_277.tif
ec2943211bed3f4a55b0d6572c467eb7
7dd0d327f336d90b94c28324dcc9dec248fae2b9
99378 F20110115_AABOXI gallas_q_Page_015.jpg
2f393a669eb66a8d4bc50cd127dc2f87
adaaa4d5d2b8bad646f5f0679ed2328e8a2291e7
50676 F20110115_AABPBY gallas_q_Page_157.jpg
95257239841ffc78de958c2f53486224
397f09f570af34456156b74442cd627ce0b00040
73747 F20110115_AABPUB gallas_q_Page_348.jp2
e183e4703d29f05b208277bebd7bde34
0fff21282c8621a0ea3dc2c47cfa297a746faf81
19815 F20110115_AABRNX gallas_q_Page_133.QC.jpg
d40a20e2a0628e6597cf19b8de481351
5d42b140ecbffeb7af6670246a70976ef6b69083
1022 F20110115_AABRAM gallas_q_Page_232.txt
07a890a716e199ed7f6f0ec21ebfdcfe
a54c376df521e9e53bffe207edfd82dc7eb69c86
F20110115_AABQDT gallas_q_Page_278.tif
1afc2627830f1b6797f64ee41cca4545
816b7c75ef710143ff2f016943eda5725f741198
94923 F20110115_AABOXJ gallas_q_Page_017.jpg
eb531e7ccd7ef7e5ef0e28c8b14d3a69
638a2fddcb32da65d04467a556d1506a24905005
56369 F20110115_AABPBZ gallas_q_Page_158.jpg
b95e037a18ed9d88ce83da8da7c3cd66
17af92252573d47dbb6c1199c034a945dd5c2324
90922 F20110115_AABPUC gallas_q_Page_350.jp2
64088b0af1ca1ace565f7bcd3ab7b38a
d1e9bc8101dc970f6e60999ed96df77aaefdfbe0
6062 F20110115_AABRNY gallas_q_Page_133thm.jpg
ab3d473a0d5d796131eb026141c80399
719e87286177886eda52de11372de589e8070b04
1622 F20110115_AABRAN gallas_q_Page_233.txt
383c0e0fe436388f3095de354ef71de2
c8bbadd87f6454d11995d4857213f73489cd1c38
F20110115_AABQDU gallas_q_Page_279.tif
48e13496e919f246de721cdcd321387b
f660ed3123546321e03c91d05eb8eae1c8e09c6b
71159 F20110115_AABOXK gallas_q_Page_018.jpg
9bf068527d67f383948f6ffbb3c99ff4
f63474103a13b1a9dca84b1e104f6d915c386f73
87375 F20110115_AABPUD gallas_q_Page_353.jp2
ad48ce7b673fc8aabc3a3618c98a968a
c1a550fe8d267991f7150b5399b38c93edaaa129
23869 F20110115_AABRNZ gallas_q_Page_134.QC.jpg
0a7be8f5101ca2768a35c7be263f5620
2e98c76de6af1f84d87b067e5edc95be5773c358
2222 F20110115_AABRAO gallas_q_Page_234.txt
3aae33b0048fc7ede5e6ff0437e9e123
51bd708d4fca3e9f54355906a89f63921c8c8edc
F20110115_AABQDV gallas_q_Page_280.tif
812f81298ea7756ae1f63b99d4667f7c
2cef99d080208428ba1f8736c79ab5907fe96d9f
40581 F20110115_AABOXL gallas_q_Page_019.jpg
3c56b0e265878959079188da58954b19
350338fa6356cbe24cc8676548eda86efd48b1d9
112664 F20110115_AABPUE gallas_q_Page_354.jp2
9c58ad7798a8b2c63dd271c0e7aca319
926aca22d75ee9428a05361fdeaf960c192864bc
F20110115_AABOKA gallas_q_Page_146.tif
6852fda4e67b3f704e97392a1e802ede
b9409770dfb9ea99af0a96f40341a86502104a1e
2058 F20110115_AABRAP gallas_q_Page_235.txt
db9ec498b4e09a11c6623f3f87d9db25
14587cbfd71f5fece761b1e1b43860507085bb1a
F20110115_AABQDW gallas_q_Page_283.tif
74f7034a28bc0f0d52e6f41f1fba8f0c
4dee3b012b2ccbde91b4677485b5672c9e7543a1
38857 F20110115_AABOXM gallas_q_Page_020.jpg
855f001d5ec4e821d772f6aef43677f4
ab848265842f45953856e3260f8321a418f68c65
910897 F20110115_AABPUF gallas_q_Page_355.jp2
d8b4c2ef9dd6f45a80d6e062b08fcfbe
d0b37ced15a583f287c26607b45fbe7a59075b47
3153 F20110115_AABOKB gallas_q_Page_024thm.jpg
bda47a74b89b3dd5b6d55db16fe7b456
b08a1b393179497ae2491cdb1c00f4357c3c1aeb
1370 F20110115_AABRAQ gallas_q_Page_236.txt
b71c425aded15d0c863d528ca9586127
f3939792455c9f49893447101f648a23fda49770
1973 F20110115_AABQWA gallas_q_Page_092.txt
ae61a8d40a97e6f54c0d56df6a2db7d3
c5956f0bebeb62c6cca00ad26950b59ac02fd13e
F20110115_AABQDX gallas_q_Page_284.tif
b24f75b1a8a8072f83b80245345ae75f
c75a77dd08b1302653cac91d1b274a2193735816
37157 F20110115_AABOXN gallas_q_Page_021.jpg
c4e884a508212b094440deed249d2e48
5216df9dfb6c5720c38f793b04474a06f0ad56ab
F20110115_AABPUG gallas_q_Page_356.jp2
7d9c40bac3dd5f0d3c20e218830b0843
1574e60ae1ba59b607a257cfbb193802f90cceac
45077 F20110115_AABOKC gallas_q_Page_227.jpg
e4055584f3a81c1e607e5939ac78c8bc
f77475b8b99ac6d2eae30c8132cf320458bfde80
1288 F20110115_AABRAR gallas_q_Page_237.txt
f08e9ac47436bbda6e9dd5350a947304
cae337634da9f8282ed7a2fae08d0cc393241132
2297 F20110115_AABQWB gallas_q_Page_093.txt
02c75f8560f265eed33d4db05903b3c7
70bd6b43307179fc9682dabae549c620fcf60965
F20110115_AABQDY gallas_q_Page_285.tif
de9e09d9660d8e70f5c33d2c0d46ba20
051b685c6547d056478e15d7301d1e3202502468
44397 F20110115_AABOXO gallas_q_Page_022.jpg
764467d026a570f749d10d883c1ecedf
75bda2ca5ad022ae0ba8a9db187e92eb782eb235
70184 F20110115_AABPUH gallas_q_Page_358.jp2
d06440c910af229ab73ce24d8e79df93
37685acdbb0a430f11f25d3c0398dfe0b24a0c95
49445 F20110115_AABOKD gallas_q_Page_054.pro
919d7164bf02f79156f9cb605cfc2a9d
dc6d4a4327c0ee37d5f7df0a43c8b9110d462a65
1782 F20110115_AABRAS gallas_q_Page_238.txt
84460a5262dd4b73ff226580e2a952d8
bfb0e45ad4dd3f5b915e2424b93357cc311ef2bc
2090 F20110115_AABQWC gallas_q_Page_094.txt
1de62a93053184682876483fe9393f59
e1bd35451addb114917cb01f3a01f853ddb48d77
F20110115_AABQDZ gallas_q_Page_286.tif
ab9cb5639ef1f2f283b76d39a2f1f9a9
a2cb73d1dc3c5e355a5520b3736d020fdf0ade41
40681 F20110115_AABOXP gallas_q_Page_023.jpg
2578e929ec6c6e3c58d2f77dfa479983
c7f43f7b1be3d58fe62d31815e0582ab0b70d414
F20110115_AABPUI gallas_q_Page_359.jp2
454f6ee287d39f18daaa9ec55f4bf0b7
8d06c0ef70f76b6b608d9b8c0c322a39991e92c8
71401 F20110115_AABOKE gallas_q_Page_216.jpg
b1e3c08dabcdea4cba2862f3d12b48b4
e149e4f9304038271c4700551c62af9313e67b6d
F20110115_AABRAT gallas_q_Page_239.txt
7b1d8420bc79d1ab410444fa97713e42
1d862ec33e01988fd647586530e4243aa02ef673
1519 F20110115_AABQWD gallas_q_Page_095.txt
b69e09728870fc24beb441149c6e66a0
8a5c76217c03e3ffc184d7d3529b196d6e28044e
27034 F20110115_AABOXQ gallas_q_Page_024.jpg
a5f270ffb1160b1843c2d88c57cea8a4
fdca2e9f7cd984a7b34ff84831c53338b3b7d41d
1051972 F20110115_AABPUJ gallas_q_Page_360.jp2
a4c38da63e036902083eddd9a0ccb2a3
d9be5d018c415c894633ceeb1ef11f91a2b1570e
4917 F20110115_AABOKF gallas_q_Page_346thm.jpg
b0cb8dcb469a5386411b8b3306a48303
c536aade3fda7e6de5356034f18ef06fa0aa605e
F20110115_AABRAU gallas_q_Page_240.txt
259801240b2d93297dcd9fe827125096
e224e73740de92616d4643a7beb7aa6ab06626a0
2556 F20110115_AABQWE gallas_q_Page_096.txt
ad3b49e8e31fe1326035a11e40cd5976
d667f38554a7f7051a23f0d0a0454f6bce81e7f7
39661 F20110115_AABOXR gallas_q_Page_025.jpg
043896dbdecc8c53821399054af9a255
6f42e55a148f985f21fdce41f04b0c1d41d9cc20
1051938 F20110115_AABPUK gallas_q_Page_361.jp2
13cab4dd401414771d70add61dd43972
40e99c79eb29fb3b28967a6c605432871372a022
40891 F20110115_AABOKG gallas_q_Page_248.pro
5335790a1209c8f6920de70f64c1da6f
8f3af6f6877b52e9cced0710848bd1d6c2537c3b
2353 F20110115_AABRAV gallas_q_Page_241.txt
03f61f3ba74527f18f5eb8ab5bf8f8e1
5fda061dae2c09bdaed2568d2f64a7f17b343576
2628 F20110115_AABQWF gallas_q_Page_098.txt
de6212fd1001b415b268c5e72df3351e
79b97d987ae7e73713b75b9b9b1f6e2acdc497ef
19247 F20110115_AABPHA gallas_q_Page_321.jpg
ca6d9e717d7469eec272dd500a8f11b3
07413ce5ea199df6e781a2d363340cbe006215e4
60628 F20110115_AABOXS gallas_q_Page_026.jpg
bd36e3601f005d28b6572b2e27a8f34e
29db54c8cab362dd2558573644af635083be3efd
F20110115_AABPUL gallas_q_Page_362.jp2
db2b72e453928e33431f8155f9a2318c
65978697e4b3fc8e0586538e945e6caf51e64795
F20110115_AABRAW gallas_q_Page_242.txt
909a80c5d94c704cc4ee64f4304a9f8d
c28ef9da74c0a2ff4b714200acb06d4e7cfd20e8
1727 F20110115_AABQWG gallas_q_Page_099.txt
f0409ab0d3e6ecaa5a1182f1a355ad41
79e949700b324fcd964483392848b83752421a4f
38002 F20110115_AABPHB gallas_q_Page_322.jpg
9fd90b02875d6405f6ad5805a81ec5c7
ae8c19adb53afdd546de7a215cadcc41e7e40ec1
49001 F20110115_AABOXT gallas_q_Page_027.jpg
daf7ff93cf8aeee0deb7cdaf1194e090
7409f2dc62a09aa74bf1ad8f05b96ccbc5a24a68
F20110115_AABPUM gallas_q_Page_363.jp2
1f91d268f7879940ace498e4d98c1197
eb5a8d8b5a5db76894c3b07d22bc8079d2b1f47d
22008 F20110115_AABOKH gallas_q_Page_164.QC.jpg
23066d851b857e9d43d9160c1a80283f
906748a62e627372fa913fc14ef4014874fae309
6346 F20110115_AABRTA gallas_q_Page_215thm.jpg
da3e79ae9ca70a515c485c3e944c40ae
e26dbf0af83a9ad575bdfa7fefecbef6b8e960f7
2244 F20110115_AABRAX gallas_q_Page_243.txt
d757faeae0d7cf4d856983886075c279
109a08d1b37c25d33ed5d49e1e2c81be94cd94e7
555 F20110115_AABQWH gallas_q_Page_100.txt
c8575d55a61b8695bd6c1d920de71436
31768c89787bf25d347b14b519d170b37f9103fd
41315 F20110115_AABPHC gallas_q_Page_323.jpg
8cec149c613a6e6aec25c666026fe92c
b9723c74540c05f74bc623ed4a1cbe9a8cabea76
F20110115_AABPUN gallas_q_Page_365.jp2
fcb3b4c7dc6886604ec3f8a54ec2df8b
386288c93677d5f611eeae246595975ab5bc3bb4
F20110115_AABOKI gallas_q_Page_045.tif
6dd3909ce2b32396752b9931f5cef54d
1397b155382c47d255796caa42cb3780fe263341
24972 F20110115_AABRTB gallas_q_Page_216.QC.jpg
4f29beefcb7fc2a1a38060014e7903b3
f9d1311e87a0c698ec01cba73d6d9045f961de62
F20110115_AABRAY gallas_q_Page_244.txt
c30bc5dcd237a9b4f7fa2d5ab6228f50
dd2da5c745c07927970db29e7eb9cf9e09da1332
F20110115_AABQWI gallas_q_Page_101.txt
6927fd6e85dccef4bff492a20c5eeb37
0e0086f88de37b328464c38a6df8a3416ef2496b
60269 F20110115_AABOXU gallas_q_Page_028.jpg
f99a2fed35f15674d8d01835b248c3ab
066d3a99304c6e0a50d235e1651b9de431c4bf2c
F20110115_AABPUO gallas_q_Page_366.jp2
10d95410709efd20ea30765cdc42e48f
a8d57b03250c794a911805ee3d1ec2d952dce50c
3032 F20110115_AABOKJ gallas_q_Page_003.pro
14c71561e3eeadf22bef2de0c9647444
27e42f34012c0358d3defc032bb77814eaba9971
6883 F20110115_AABRTC gallas_q_Page_216thm.jpg
ddeb3cba1d293fd638fb012f635030a3
81c5a50b94eaaf99674fac899bfb1626c78d1467
F20110115_AABRAZ gallas_q_Page_245.txt
a957f25919507ded221c93f13430c501
22a7a0908575385fb64d47c2d08b29de616384ee
1995 F20110115_AABQWJ gallas_q_Page_102.txt
341040f3e796f40d9400c9ee6bfdd466
e81de0d7e31740061b6eb99a40c51ba407e3f4a5
38018 F20110115_AABPHD gallas_q_Page_324.jpg
5731d763ba743a328e6374c5e5911ebe
f79d93e31db754e394cf8709639a4eca3ab0daa0
70636 F20110115_AABOXV gallas_q_Page_030.jpg
700f8a8d537cbce53295a4e1850c2836
be8e906cc7d3a54d0386590ee313866a55111c78
F20110115_AABPUP gallas_q_Page_367.jp2
c6395a140766559b38e50b8a11c5f5ed
41def89fe8bd3ffdcc2bc159a3f8b93e520c378d
47495 F20110115_AABOKK gallas_q_Page_201.jpg
b8fefed24193b7223005101974dde9d2
1a02582bef79bc2a753c861b27c2e44cbd647c01
21299 F20110115_AABRTD gallas_q_Page_217.QC.jpg
e36f757aee2f40408f6eb1a15648d7f9
c1ce0cd6c357705d2c4450c028bdaed4e374ca5a
F20110115_AABQWK gallas_q_Page_104.txt
bc7c246223e08a5dd1ab95c6c9bf7fd8
c9c15b2e53ab46470a7bbab6b3279ec05928c695
38788 F20110115_AABPHE gallas_q_Page_325.jpg
413a3bf726e96f747f2797db532277b8
4eb6189a41c0d6fc8cb464b9859b3d8e27ee5151
66559 F20110115_AABOXW gallas_q_Page_031.jpg
ca9395d83cb6cedb8b8a208f3b65883c
afb1ef8f1cff0e26983521650e51de1872276f65
F20110115_AABOKL gallas_q_Page_181.tif
ebbc1f535a4cdf96280e81e8b1c85c8d
f1eff76921ec9233c769a9475a4ac53d084b3f2e
6216 F20110115_AABRTE gallas_q_Page_217thm.jpg
9c917caf8e65c60459ab72c5d793f5c2
501f6e7d15d30fa20b8631777d13fbe940b85571
1877 F20110115_AABQWL gallas_q_Page_105.txt
47b3354696948fcb6f542f3d9e83a3e1
10dee17ef4678c12bfe3b343cded8ec75860285d
49598 F20110115_AABQJA gallas_q_Page_055.pro
87c0d1050c4cd26a912ffe3b6cbb48a6
f7f8069cb74d0409f4ec9f9d608caebe2fa0ce17
34674 F20110115_AABPHF gallas_q_Page_326.jpg
1c7ff21511241bf23c1e7546f00a7830
b9128bb286285b345297cce59254651885e76d89
69112 F20110115_AABOXX gallas_q_Page_032.jpg
802d2a80d1e52fc9273686fbd0651d6e
cd12b10af404cb0ee1cad85d451c148d5a66aabc
F20110115_AABPUQ gallas_q_Page_368.jp2
ac40f81ce12c11223a0f63616e9f05c4
d50615396ad4b9bc98412127380cc85c1acfd692
59736 F20110115_AABOKM gallas_q_Page_009.pro
d8f3f5c1b04706906de1f136aa88e638
bdc45dc1480589a80f92878eb76829420bed4e63
19780 F20110115_AABRTF gallas_q_Page_218.QC.jpg
9f3f69138c7763ecee3ac042a25df7db
e4821d7737c7fc39233e84a8c6a6be80da7bad24
1993 F20110115_AABQWM gallas_q_Page_106.txt
6406ad76a0bc22c0431a525661727310
6d2a642d08a1d156195b12cf53cc5da020849473
11327 F20110115_AABQJB gallas_q_Page_056.pro
448d493e04414b906ea0042ceb50b11b
27605c23ff1333e08c0da2fed74abaff9ce3afe1
43132 F20110115_AABPHG gallas_q_Page_327.jpg
e20fbe77a5eb2493d9d7298baf4b684c
0b04d9b16a9a22aaef5d1a7eec33053d7874a7d9
85717 F20110115_AABOXY gallas_q_Page_033.jpg
13d34024d9d0e29e4b5b71969e077eb9
0168b67dda50b6852c3e129ff4807c58f1db78db
1051944 F20110115_AABPUR gallas_q_Page_369.jp2
a9925d05e822b5a11af05e78f0f68829
f74a294a1a77c47d2c363d28b22a6afe13ddd6bb
775680 F20110115_AABOKN gallas_q_Page_277.jp2
24a98507b55bce2053f305952ae1f5fa
2cf2e84d6817d933bc39a197698002a792024662
F20110115_AABRTG gallas_q_Page_218thm.jpg
c9f11e77e288b38331fd5402abf94552
9829171ec28739c3d7db2d2f7a8d2537ecab6f41
F20110115_AABQWN gallas_q_Page_107.txt
d88f5ac196f1d906d096ca604700ca83
28a6bfedc0861e7e4a4408915990e066c10a6dcf
47482 F20110115_AABQJC gallas_q_Page_057.pro
e6468d37ebf360597299b07181435ce4
6f5e975f79eb1d56ada3ae5d112c501efd722a35
49081 F20110115_AABPHH gallas_q_Page_328.jpg
91b2e3c756de26f7c3a58878c4ba0265
8122e3fd46e608d16f86e4963d249346b04cd743
70157 F20110115_AABOXZ gallas_q_Page_034.jpg
a350fc7bce6f9c88899cdf88ff55ab8b
ee76a0bdca60cde243f274df3e67535ee8af1688
F20110115_AABPUS gallas_q_Page_370.jp2
840fc397de8a1d0e8c6f05594eab8840
a01f7346172824bebe5287495f65137682db8eb7
F20110115_AABOKO gallas_q_Page_140.tif
2023798fbba5d0b7534bd2538550cca8
6b96eee948db70f090b4bceec38bccf52b224913
17253 F20110115_AABRTH gallas_q_Page_219.QC.jpg
328bd40eb741edccaa2d0b7c47676ced
a19003a95c7f167cd1fcd2e7dc6b6e098d663a96
2121 F20110115_AABQWO gallas_q_Page_109.txt
e291509daa4ecc4e333fae35bb833650
b892f3fe8de83b127512d1e4cc3a84bda3f080b0
43354 F20110115_AABQJD gallas_q_Page_058.pro
8cd24305e2146aea41badea3dcd3d5b5
1d79aac1f2127d454362e644c116088400e2c420
36829 F20110115_AABPHI gallas_q_Page_331.jpg
25596af4f8827963596cb2bb37439aa1
2f5dfda2aa9f59ae42685ee0dd8f04f3a637b518
F20110115_AABPUT gallas_q_Page_372.jp2
648f98f9021b1ad49161c814ddd2f653
c10d992c694ab1e2b9782e0291f235fde908aee9
65810 F20110115_AABOKP gallas_q_Page_314.jp2
6380a17430647f6291a0f903240bd5cc
c0d326584d1429e61c47b04a9b942e2722a43e05
5453 F20110115_AABRTI gallas_q_Page_219thm.jpg
7c1bb24adca35d7d70ce4baa55e5b3a3
59463f0833ad30869b4a7e4aebe34bdca8f8ff2a
1885 F20110115_AABQWP gallas_q_Page_110.txt
64a8b61f44ab645e4cc2435ce76e18d4
d2b51411ce3c7d08513f1d541e2019178aeb94f2
45485 F20110115_AABPHJ gallas_q_Page_332.jpg
a2d11b901b3db48aa512ca59d923016a
40f3eedfd8b42c158ba6fad3beeefff8313d86f3
F20110115_AABPUU gallas_q_Page_373.jp2
5995527a1c66272ce61fd09145f76213
4ffe70243f28e328e2ddc4147d1469d6de8e74aa
22562 F20110115_AABOKQ gallas_q_Page_129.QC.jpg
11c02c9aea76a7a4a4fe18e1fb96baa1
2a36fbdd9de658118612fb45fd89eef0f547daa8
6766 F20110115_AABRTJ gallas_q_Page_221thm.jpg
b3046111bd46d9a659f97e8eeb9ecf95
dae1d5d6ca64ac3cb0ae752176962b12621fd714
1359 F20110115_AABQWQ gallas_q_Page_111.txt
5e7b6a01ca60228123c86d58e07dd467
4eee396b4bc3e91e131715c51bdab8725d618336
33924 F20110115_AABQJE gallas_q_Page_059.pro
65cc63f8c4a1f14de25fa7b71a61f6a2
f06e3297158cea4a76ecd36ffefac0fe836c27a0
49889 F20110115_AABPHK gallas_q_Page_333.jpg
dfd033a98085e4e65874564c9ecceb9a
1150d7c63de59dbd3cae073589faed8247d1e194
730429 F20110115_AABPUV gallas_q_Page_374.jp2
3e3160e074c9fe7b1945ef13792352a1
57c618f81dd9273b430404d07314ce355784d4e9
1402 F20110115_AABOKR gallas_q_Page_206.txt
26bcabfe542708dfa63da5a50c7213fb
0a41d5140823c5b381087d66b408e817fa333105
20252 F20110115_AABRTK gallas_q_Page_222.QC.jpg
6393275ccc64c6691f135f9bed7c0fd5
ef36295ba772eca20f61817f0daa671d1622acc3
33894 F20110115_AABQJF gallas_q_Page_060.pro
164d41a6dbe14a68bf100a75101b4817
04c827cac288a847b634225a92516140df338410
67597 F20110115_AABPHL gallas_q_Page_334.jpg
5bcb4c6cab59f6a40cfedf56a0613201
d8858f51d7e30aa7914aa581a7826bfab80e5507
119269 F20110115_AABPUW gallas_q_Page_377.jp2
43909309d983c5677d98224cb8f970b9
54e37bffdcac1f92f8b4f76284937cafff44b9a5
F20110115_AABOKS gallas_q_Page_316.tif
8ec3a71a9167fc77d6d23e20b59793e4
94197b53906e9c98e28053a8bdaa41382b20ccde
6123 F20110115_AABRTL gallas_q_Page_222thm.jpg
ead37dafd86871659d6a2c7ee516c865
7b80bba27ce78a5d09367ded8c9ed8d75911154c
F20110115_AABQWR gallas_q_Page_112.txt
0c1fef3e1c10a5472d80c0e21dacaa1c
2a213bc726cedee28b0404e7eab717924b4bf32d
45658 F20110115_AABQJG gallas_q_Page_061.pro
a380ef4254d0332d77ff518954bab0cf
f95e9978eea92ff429958128e28c1ad17a305bac
41218 F20110115_AABPHM gallas_q_Page_335.jpg
98c503da92e81fe875efd3533f71cecd
06c95cd378ae8e94ee39ee1c0dab4d6840e31aeb
128101 F20110115_AABPUX gallas_q_Page_378.jp2
f140a6310d1920926ddc04196c2adb5a
375c2e61060f59ec91e932e68c6199ab134009bd
21251 F20110115_AABOKT gallas_q_Page_238.QC.jpg
e666a2cc7a3d8a442c1d4a389da0c761
665518ffa00a12afa5eb8a7acc0125267f1e15cf
15614 F20110115_AABRTM gallas_q_Page_223.QC.jpg
18933c9208a50ac797a7a5f0f9547aa1
613c11d37edde448295c064652078c16a31e7532
1878 F20110115_AABRGA gallas_q_Page_008thm.jpg
2192b5f67fad581170c2e1f5d7901200
afd7f7afd72ba937294cdc56ab31507e043dfc86
1795 F20110115_AABQWS gallas_q_Page_113.txt
10ff2a4d05ebe8acb4e8e0249de91d2a
b30eb866cea4bfd7e600d2dff7842c87d4ffb888
35075 F20110115_AABQJH gallas_q_Page_062.pro
af70e1f786cce8da8f3548f9ecfea89c
4d330585594332f2d345de3a356ebd2b355754f9
39771 F20110115_AABPHN gallas_q_Page_336.jpg
ece46f4ec732e4b6d2930c87722c1ff8
eac7dd4bf02e65b9762a7708894b1ad7ab45945c
127623 F20110115_AABPUY gallas_q_Page_379.jp2
8d03d0aa4baba026fec962f1d9d5ad2e
395fb32375cfa9f0bff48a73f4c1c5a6baacdf0a
105757 F20110115_AABOKU gallas_q_Page_016.jpg
7453523631116290f7dfac2318ac2112
f0d61e9eaa266192b571c6202b96842520a07ee9
20995 F20110115_AABRGB gallas_q_Page_009.QC.jpg
209a760416922e1e80e26f7d16a4da9f
c5ad6cba6dae3a35d7b8909ac8dac857bb9d15fc
1774 F20110115_AABQWT gallas_q_Page_114.txt
02c6e179e3a5dbb1874b7bdebc41a0ad
0dc552e1fbb410cff1e82949bac426d2a5a623d6
40703 F20110115_AABQJI gallas_q_Page_063.pro
3ae309bb1cd40ff6af554334e0d9450f
d9278797587b1ee6504a74eec2cb09151353eafa
52544 F20110115_AABPHO gallas_q_Page_337.jpg
69f1fe8df996a729a0633bf3de79832f
f63ccffef2ac0414c0f103a862410e148b4b4c70
119923 F20110115_AABPUZ gallas_q_Page_380.jp2
4eca066edfb0756ff3ca2b1a44b3558b
a83c39960f9987af2b7879ab07142387a30f1e25
51008 F20110115_AABOKV gallas_q_Page_224.jpg
83b0a8359d1d9a31953d5503b500a19e
819e669c0b140250486801d867904562fceeb3af
F20110115_AABRTN gallas_q_Page_223thm.jpg
22b2ee2859489b1bc798c11154c3866d
888163dd35096ba75f8aff156a9a1d51b62eed7e
12662 F20110115_AABRGC gallas_q_Page_010.QC.jpg
970a8deedf980b1f73649ebc46a1fdf9
fe118d2141fd03fbf2e5b47a3cbe65bc70c8e31b
1933 F20110115_AABQWU gallas_q_Page_115.txt
4b261d2099bfbccc67ec4412e2f9dd6d
0b952d632cb4b436d8bac04bd22b9d5b07be9002
50596 F20110115_AABQJJ gallas_q_Page_064.pro
b15136ac9739d57e78dc17e2b3848185
47003e0ac45a77eaa66c38715ccd88a139211fbe
39668 F20110115_AABPHP gallas_q_Page_338.jpg
0648569081673f76060db8a81a59f992
7eef8b8726be45e751731dcfe9300663216c0d0e
F20110115_AABOKW gallas_q_Page_376.tif
4082a17d2e0855520449ce4ee16db402
d92ff7a514b49fb74d838bfba785c199cfa54aea
17096 F20110115_AABRTO gallas_q_Page_224.QC.jpg
4aede976dc40075011e71694b6c0eb90
783ef8aac5b4ac8604cbcb8f15b52bb15c3f6bb2
3637 F20110115_AABRGD gallas_q_Page_010thm.jpg
27b3c1afec09147ff59b4748f9c80b91
41937b47f60bd554942e57851844102dcccb41a2
F20110115_AABQWV gallas_q_Page_118.txt
107ba4b532e10fb844bd5c43d82b6e07
3d953f70612705265847eb457d0393d66cd5f589
53760 F20110115_AABPHQ gallas_q_Page_339.jpg
7341b443e7407e20174d1299fa011160
26d3fb63f0d7e0943d7dd5681c3239cb59fb4af9
48289 F20110115_AABOKX gallas_q_Page_034.pro
a9e4e39b09deb5f2159ce1975e0c9c64
132104b942a800a4b93cb1c41e7e8b8857c305df
47655 F20110115_AABQJK gallas_q_Page_066.pro
92e76d86a1dec8b09aaa49948d1b97c2
1c4ef0c0d7a24c507419bc4aa885bb15520c1758
18051 F20110115_AABRTP gallas_q_Page_225.QC.jpg
618ba90261488971226426fa458879ca
ae4f276b61d208d6fe246036d3f1af518d47a648
22323 F20110115_AABRGE gallas_q_Page_011.QC.jpg
def9e5e6cbe5ada8c95489c32dda942a
3c1c9aaa7f416f6c780875fb217e5de7297502e0
2024 F20110115_AABQWW gallas_q_Page_119.txt
8ee526b1944a85e9c16459c986baba4c
d69b2d9b53887468db8d65c19dd40597064e7df0
59996 F20110115_AABPHR gallas_q_Page_340.jpg
d0ec0bb8a7282936b732e27a1bb82e7a
464867020b67bcc1bbb82a1628655eddd179ce87
67439 F20110115_AABOKY gallas_q_Page_122.jpg
4d0d2722cd3d41cd399814292150808b
b2519e066215502ae653b10d7458fb5eadf8148a
48658 F20110115_AABQJL gallas_q_Page_067.pro
13ebadd2ac005585d922fe17990e130f
b9cbca70e369814f0793963d1f06ea7eb53b0b76
17457 F20110115_AABRTQ gallas_q_Page_226.QC.jpg
2363912f24ba90806a26c32e2d17ae8a
e435e163e9150391157c7eca93796f047a141ee4
5795 F20110115_AABRGF gallas_q_Page_011thm.jpg
53028a79f021bc8b979fe28435053e3f
0b43c36c114a79de91bfeeb4c0856829662e2c73
F20110115_AABQWX gallas_q_Page_120.txt
dea3bac3ab2c5e00818171e537a8479f
86eb472e0bf820f3cccc04eca35ca09bba79c91a
24356 F20110115_AABPHS gallas_q_Page_341.jpg
7396a2f543d2369a64e1e4e713ddb28e
4c42d1943b5eae48ca44a7b44b9562cb0edd4638
35603 F20110115_AABOKZ gallas_q_Page_329.jpg
541880584ddaaca0b935581764e183be
730a079f915f33115863a8fb2059bc52a4a28dcf
44202 F20110115_AABQJM gallas_q_Page_068.pro
2f9b84eb4dbc7560fd72ce01abfb680a
3b45d6c7a08772dc57ec2674e2d366cc96451bc8
5217 F20110115_AABRTR gallas_q_Page_226thm.jpg
efeba9124f93440d053844bdb178eba3
d4649b5f3a9306e4088b51eb308e76d081dd65d3
26311 F20110115_AABRGG gallas_q_Page_012.QC.jpg
4b9a6efcdf912126ea3c80a5c55f8cd1
9cb6d12c392ac13b7ee50ce2d355fdc1e36ab660
1109 F20110115_AABQWY gallas_q_Page_121.txt
44d4be071c7823412ed9cf9a4847c22b
a426c58e2e44ed69810ff5139fc7b7db868298bf
49357 F20110115_AABPHT gallas_q_Page_342.jpg
e97e24539cd8ab6663620d18939b81fc
a6016687997d0991bc66fe9ccc3a3cc390bbd356
35647 F20110115_AABQJN gallas_q_Page_070.pro
5928029f0e338e243e4a0127430562bd
dd6e07676ebcdad86ffd0fbf056a0fe9942ff711
29578 F20110115_AABSDA gallas_q_Page_366.QC.jpg
eef75062f87757493cf7b9bb9a2b0248
88b2fb367be3694ae09593909513a067748a89b8
13336 F20110115_AABRTS gallas_q_Page_227.QC.jpg
889839773671da547feead5f2655f25d
8e8167f58e3d51678f450a184511373a25574014
7088 F20110115_AABRGH gallas_q_Page_012thm.jpg
ea6922ab5f0cffd981c068db55b35a72
1afc2674d62d9cd925c7d06e1418197af3af5e19
F20110115_AABQWZ gallas_q_Page_122.txt
cfb348bdd60b785b6b09ee89e0470748
96cb18482a77f8fce340477df51e205d353cbd10
47025 F20110115_AABPHU gallas_q_Page_343.jpg
4a40345eeeb32b510feda9217374f273
57441f1af4315ee89231802a5290c20a8f0dc565
43119 F20110115_AABQJO gallas_q_Page_071.pro
7701f12c5d5bb93ef2ece36df2c25ca8
62b4c9a3a7e8cf3e4a3dcea64da607226c583028
7271 F20110115_AABSDB gallas_q_Page_366thm.jpg
8c8acc969ff72f1a3494dfafdaff1661
960487ec4296ec7c29c8192c6e0c96db8c499108
4604 F20110115_AABRTT gallas_q_Page_227thm.jpg
603c1247190e115ffeb58a31f1abe535
a5c63ae82e62031c238ff2977a325b71dc2eb69b
27874 F20110115_AABRGI gallas_q_Page_013.QC.jpg
72e1ff6f4baf131abb162f34ada8cfa6
5d487d72ba5794d60fb405b2a9d14dca311174dd
43927 F20110115_AABPHV gallas_q_Page_344.jpg
57b5b3c8c7db4e64cf6d9c57d67b2d36
e2b545af14e94bbffb80f249f8448bbe38c179c1
40388 F20110115_AABQJP gallas_q_Page_072.pro
f7eada8a8d672ce695c61b54c8da23e8
5c18d9597ea6b9005d83a75b0f6e03db29778608
29138 F20110115_AABSDC gallas_q_Page_367.QC.jpg
3412a5aa6ead6765ce2257afb1deac84
9f0d9e67b9602c795f673b6295b8895f40dcf221
10725 F20110115_AABRTU gallas_q_Page_228.QC.jpg
8311e3cb393e7109b6071ed78b58aa5e
37f156ff9128e3f54350d1f6cdeb678bf7d4b4da
7179 F20110115_AABRGJ gallas_q_Page_013thm.jpg
c7ec65bfdedbba79f490b47359cf9570
8385eea93cada88475deaf0568c7ad086f823c9c
40958 F20110115_AABPHW gallas_q_Page_345.jpg
1184dc895d8f3e5ab33ae9072eb5ded3
b0452cc64a49d4937048f92450124ed43922d120
27588 F20110115_AABQJQ gallas_q_Page_076.pro
717876e6ad545658e3bb081045b704f2
f39815aa2b08a254d1881718ae01c8e9ba30a81a
7254 F20110115_AABSDD gallas_q_Page_367thm.jpg
594ce05063336a12eb9fa370bba154fa
1ad49eef88ddd7717c057ca5eb13869b80c51e09
22502 F20110115_AABRTV gallas_q_Page_229.QC.jpg
bcd42cbcfef805b90f9efebc86cacd5f
99a37098585ebe5efac7e425e3a1ae28c86fb862
26845 F20110115_AABRGK gallas_q_Page_014.QC.jpg
dfaf0726b81894e74a86c1803dd23fb6
56ae75ee38f628a55c4c2189c139529293ffb548
48235 F20110115_AABPHX gallas_q_Page_346.jpg
0e65ee7bb75e170b55a9a88e42d629ea
cb36214b033f639e05e217dc4b8309eec5bffb08
44845 F20110115_AABQJR gallas_q_Page_077.pro
e381b9307073590aa56473e8ea64a1c8
7b78fe327b735bbdfcf4d5ce5bd9a919a28e7d6f
29086 F20110115_AABSDE gallas_q_Page_368.QC.jpg
9f9ddbf8d3acc8a0c060cbd7359bb5c9
e8612f12558cbae8757b7d874f2ce62db59e503c
6658 F20110115_AABRTW gallas_q_Page_229thm.jpg
3ff435cc6781b28105304fde4a639e6a
fb6b0383c50dd6ae14c5171bcc9b588c9ef58374
F20110115_AABRGL gallas_q_Page_014thm.jpg
e1c2772156d5c910ac9000bf4cc3120c
15266b19bcce0659a00f1f3808c4217d9a7af5bf
51977 F20110115_AABPHY gallas_q_Page_347.jpg
16d12d2bf829496de700db2dbeb124c9
fb1986c0e52845889d04fe933f25c90d8aa96abf
47197 F20110115_AABQJS gallas_q_Page_078.pro
a44bf6d05d3970dac007efd4609b258b
6bc80ac2d9571505a98b3b85343e9a4af76e5bce
7422 F20110115_AABSDF gallas_q_Page_368thm.jpg
2b8276af80775306bc5649ce8bacad46
7d1ed46952d1bf933c67b9957510106b2e418e86
19554 F20110115_AABRTX gallas_q_Page_230.QC.jpg
c57e8ed27409017a1d8446b7042112d8
936c2c9e4a11ceee5162e57b6a399fc07b4c14bd
28144 F20110115_AABRGM gallas_q_Page_015.QC.jpg
647bad87ea062b33ee6aabaec6116b00
0580231b87cdb174ccf9a64a35a5f737248f3a9a
42843 F20110115_AABPHZ gallas_q_Page_349.jpg
e8cade92cb72e74e88f762574cb37c3b
88d219f2d48309dadfeeca072a09929726ce563e
41459 F20110115_AABQJT gallas_q_Page_079.pro
b32aa184e72ccebca568867030db7010
f6603293676328fa0a56330728fa6b0094370cfc
28737 F20110115_AABSDG gallas_q_Page_369.QC.jpg
b255543735e0861beae9925eaf03be10
6322b05e602e409d56914c003084f2cb9081ee2e
5958 F20110115_AABRTY gallas_q_Page_230thm.jpg
65d696a8388021a3e3261ddf4ce34a5c
12270edde911c253b4466c770f77caf61ef2dd42
6838 F20110115_AABRGN gallas_q_Page_015thm.jpg
de8c733dd613ea74a585bc76f26474ce
05a4f39a0062efae73e2f4ba2cdf6bf6f21a1908
34482 F20110115_AABQJU gallas_q_Page_081.pro
88e6c824f5eb27bc1e4ae8f6a3b9e606
bb005a30dc358179f2d946ccbbfa713bcaceb562
7117 F20110115_AABSDH gallas_q_Page_369thm.jpg
3928d93dc414a6cfb43006d949b36dee
2406ecabac8a92a2f6920422789e3a3b472f53f2
13815 F20110115_AABRTZ gallas_q_Page_231.QC.jpg
7e2954e34a23c4c3fd70f0542ddd05f0
b60e238b8cd2af22bd7c0c834a90111793be2e68
28236 F20110115_AABRGO gallas_q_Page_017.QC.jpg
28492fe11f9e72afc58d4835023c27a7
ab8e796c1f744871fa78ee8dce6c16b2bc160196
F20110115_AABOQA gallas_q_Page_092.tif
e8e0d20e2e9c8b55a933efb500d02acc
abb3029170a7201a04c8bea9dbc5b6c2679e7374
30911 F20110115_AABQJV gallas_q_Page_082.pro
b108eab1bddfd057be59d3161f14dfea
8f3050d4b9052a46cc0c6c2c558bf47e06f18702
29315 F20110115_AABSDI gallas_q_Page_370.QC.jpg
0f404d4e12c551014f25f49984b7b2e0
47ac520c0e37231ea3dbcc77258f8a5c32ffc692
7444 F20110115_AABRGP gallas_q_Page_017thm.jpg
bb8a11f88db925a637e636f5a775bfcd
8465e7292067dda1295800e68a8c7520647127c6
F20110115_AABOQB gallas_q_Page_137.tif
2bdd18e42819cda58d9e46c6fe38e7c5
4c5be66a1767446a6a9ac743e4bad5aea452d244
42263 F20110115_AABQJW gallas_q_Page_083.pro
1e5b4bf59066e97e488c36ef4b73e6ba
a4428c20e08f457ece4c5215969506800cd39889
28726 F20110115_AABSDJ gallas_q_Page_371.QC.jpg
82d12106f01d5511265270d1b2dc8f35
b031779a29a07bee35a8ed2aa86b1d123a347479
20686 F20110115_AABRGQ gallas_q_Page_018.QC.jpg
28eb90befc70d613cfcf96eb16a0fb9d
c895e1f6e39798fbf809d1858a5eb0afc57922c7
F20110115_AABOQC gallas_q_Page_221.tif
b459f0d703ca676bd80ebb2f5c19cba4
c519e98759d21c5239595d8871fc6130d578c8f7
46595 F20110115_AABQJX gallas_q_Page_084.pro
f933ba505cd1af8e0dafc61e94d5e759
af557b7f9b973500f82cb1b380bd743cba925888
7157 F20110115_AABSDK gallas_q_Page_371thm.jpg
68618df7bc9be1c631b337401a0c672a
4ed4e2f7c8dd4a59946c2f4af13aaf57caa3b83c
5373 F20110115_AABRGR gallas_q_Page_018thm.jpg
b53f2c95843e461571fd8b43262c094d
ed12fb8e122085068ccdec2aa193358111c98a2c
58668 F20110115_AABOQD gallas_q_Page_182.jpg
745e96f170bcb1261acbd43533654fac
c444e07a2856c3d4d2f10bae8e3288c449db513d
46658 F20110115_AABQJY gallas_q_Page_086.pro
00e340a7afa1e29c08be377b71601271
3fcd7c2cfbefe2246b3388f0a72b0b4a5919271b
29335 F20110115_AABSDL gallas_q_Page_372.QC.jpg
e75f31aa3cdc31f2bb93a0c66aa3ca0f
fe889ef0f227f5fcdc771412862231ab094061bc
13589 F20110115_AABRGS gallas_q_Page_019.QC.jpg
93a799c4364ce6cb28903bcac20347e9
6c52d0d881f3e749a42f6ad0adb18f21559ac38e
F20110115_AABOQE gallas_q_Page_264.txt
9e86974f124bb1611f43b13a5bded95e
3f264e340a20a9d7d5bd97b5c7025ae749bbb504
43713 F20110115_AABQJZ gallas_q_Page_087.pro
c781c07a23df156244b01ee3adc74f02
65b36885cec9f047ab447ee121ba7f749e0de80a
7338 F20110115_AABSDM gallas_q_Page_372thm.jpg
8c9c208a0dd71d790080fa4a7a2d5017
b768d13c6158807b5859eb0eb51ac2f1ac250dc1
4288 F20110115_AABRGT gallas_q_Page_019thm.jpg
c4fbf45b0d5696245ed428b32f46391b
6363ec40e5f3382405b86ac314a32b5b4a29f050
33101 F20110115_AABOQF gallas_q_Page_305.pro
44a650a28241ab67ecf8aed89f6df9b5
3c8f8a34f4155a0a37e94e96c7929c09a1a5c984
29008 F20110115_AABSDN gallas_q_Page_373.QC.jpg
1cd0936f3a05707779bb264c452d4df8
db5bb65f38c6f916e043fbf9d4b6b9f26f659a0f
12595 F20110115_AABRGU gallas_q_Page_020.QC.jpg
c6fb9c90c261de7257f723c2a986c809
702e538862ef59d2a1a9017918ab5f528287b173
11026 F20110115_AABOQG gallas_q_Page_357.QC.jpg
b1bb79f433c9140aa8ed9a38c629e1ba
653dcd11daeeb7c4060c4ccc9e42f9668cfaab41
7158 F20110115_AABSDO gallas_q_Page_373thm.jpg
1aabd62b0ab03a77d49ecf508763acc4
c57373c8d9dd939b73b1143a630ed9d103ca2e58
4196 F20110115_AABRGV gallas_q_Page_020thm.jpg
d73aee3c321bf360aece3d328e1dfe0d
6b4af7ac8956f5e1ad110709d6d3ee6d492b433a
1000965 F20110115_AABOQH gallas_q_Page_218.jp2
0f9da93fd512c2f25904a1344ef23d88
27e78d73ffeb5b09c08df63bf01d16c1767f4e25
99435 F20110115_AABPNA gallas_q_Page_127.jp2
ac11bd4e38f358fae92c90de914b6b0b
da26a0a648a0fd6d2cd92f58dd50155f4c029981
15114 F20110115_AABSDP gallas_q_Page_374.QC.jpg
48a492bcaba60003c259b6122793d3b6
99f9d9b09e2c85135b48ab85d39d932bded0ab49
12570 F20110115_AABRGW gallas_q_Page_021.QC.jpg
55e19dd2b0f92811eece7b6f202ed506
c3e86b9a4336363eb0ae1438d856fa0df0760d4a
F20110115_AABOQI gallas_q_Page_059.tif
6a6d112b3952170c381f7fe56711a00e
37993966b602e9c7f33809883d55065dc4d61958
F20110115_AABPNB gallas_q_Page_130.jp2
e9a9071739bb467814eae6fb8bd74dcf
7e3e258e929e387cf41b15313411575e005e87f3
4055 F20110115_AABSDQ gallas_q_Page_374thm.jpg
edc3a228a92b2f6f3d376358a93f2ece
4540bffdd4179dcb44591f88f468bd68935e3090
20297 F20110115_AABRZA gallas_q_Page_307.QC.jpg
54a76aa359696c5a99ad15e0bf0af1ad
e39815967ab5657e450b83f2eeea5e802d7f93cb
F20110115_AABRGX gallas_q_Page_021thm.jpg
373ccc0946c01f41dc7570d1d53795df
97b2ad8cb86f0d63ae3a0a2e627a05bea8f8799c
12174 F20110115_AABOQJ gallas_q_Page_326.QC.jpg
4eaec336be8c08f45c5d9b12e563d1e4
9ad79cc75bdb8dce356f6cf200461ad9e2323124
101011 F20110115_AABPNC gallas_q_Page_131.jp2
6c3f8bf2eca916ca9a135cea3b29e851
2c34e4b6b8f2a96a2c4b959ba9e609abc453b8aa
21366 F20110115_AABSDR gallas_q_Page_375.QC.jpg
e626d082cd049e0aa46ed118372a817d
95a6fe04aeea3acde6d53feff7e7021d2a33452e
6190 F20110115_AABRZB gallas_q_Page_307thm.jpg
88fa62c23b2c95e6f220d7645e51247d
bd5653c409487bbf20d17f848d353aec68179a27
13539 F20110115_AABRGY gallas_q_Page_022.QC.jpg
ab0c79726360e71dbd04ad9c06ca191e
c1c4a3bc973e5cb00b01950292bb9d2c5c8913f8
22654 F20110115_AABOQK gallas_q_Page_053.QC.jpg
7349c7a3fe81279a08374af6df464e4e
c0a4379aa6f866f169212eb0494c1a41a8b44e55
F20110115_AABPND gallas_q_Page_132.jp2
c6689b40255017a775aa30b71badbd78
ef44bb6e2cb3dd55947ad809d6e9e86d3e0941aa
F20110115_AABSDS gallas_q_Page_375thm.jpg
bac7b94cb23c72d48866fac4604a46f7
9cf66210d807a73a2fad2a6f2b95488f10499811
17087 F20110115_AABRZC gallas_q_Page_308.QC.jpg
96d1ce8f12db2d5834baaaaf64a1ec5b
c6ae42fd2a734c50d75b070b83c9454745724fb5
12751 F20110115_AABRGZ gallas_q_Page_023.QC.jpg
da25394afad4b96f71e55a70e1e988ed
0723f30b6f6cbe00a805a5d8f87c13228e37e7fd
974019 F20110115_AABOQL gallas_q_Page_095.jp2
6acd05af0ffdf6a02426d8af3dae9d1b
76697586ac80ebc3d530abdfc52795a2d12f6e9b
F20110115_AABPNE gallas_q_Page_133.jp2
b9d7005763669b1493c1ab3da48d83f8
87c37b0e4e57f3f487c9f7db83527bc1450109f7
25903 F20110115_AABSDT gallas_q_Page_376.QC.jpg
5b71f6c5dffa840b30bba2b0b8fdc2a7
4f824a1cc20ee4a33e4be0120803235725161f92
F20110115_AABRZD gallas_q_Page_309.QC.jpg
2588f64dc3ef380fba03650540ead41e
0c5cf69dd8a48849daf2375351f1de3539f65ea8
67570 F20110115_AABOQM gallas_q_Page_316.jpg
abfeec1a4653891cafdd1e1f40362695
7dcb22bb5becf8dd08da48768d1cdf5c8654910b
88156 F20110115_AABPNF gallas_q_Page_135.jp2
1bc15a8a08eb9cc5872f287150e9374e
01087ac7f29e368eeb92ddff6f6eba7290caca28
7048 F20110115_AABSDU gallas_q_Page_376thm.jpg
4e5ab32e9cf11a482d3d9b57a0a0617a
49d6836a089a678790b57022bf0212034c956e6d
4855 F20110115_AABRZE gallas_q_Page_309thm.jpg
586815796fe32673872def45701dda64
b1755b5aefdd1c85367b297c95473151f4fca3c5
49152 F20110115_AABQPA gallas_q_Page_241.pro
56407c1e004b2f145f3c60268c8f66e8
9963684259e58fa1e238831fc0275f93fe1c31dc
103919 F20110115_AABPNG gallas_q_Page_136.jp2
086669ad06031bdca3b61a1c9b4b88b5
60ede36920467f0fd3a08c74f1e24b2e4deaf4b8
24296 F20110115_AABSDV gallas_q_Page_377.QC.jpg
650679447c4913f0663cb08456372c1e
7a4781d9a9173bb6f0e0f940b300fdb412cbc628
17260 F20110115_AABRZF gallas_q_Page_310.QC.jpg
1b05e353e127b53c4cdc0dc777c8de41
1e4ac58eb690dc4bf4cf7f1ddd70fc56a587f2a5
1051950 F20110115_AABOQN gallas_q_Page_283.jp2
4f0b9e62541b03aa49a846abfbd088ef
5d68685d30556834ea6cb124f309838985f05496
48952 F20110115_AABQPB gallas_q_Page_242.pro
ab102f34991b3f162adbefd2c4207ca1
8702c5a34005be585fb9382354d350d01a670ca9
F20110115_AABPNH gallas_q_Page_137.jp2
98eb77091ec31c0ecb9a1d7ddcd20084
b7ec928aaae7975bc137303a89c5e2644985b5c5
25982 F20110115_AABSDW gallas_q_Page_378.QC.jpg
42e180226ea3f772465e638bc196dd5e
c46d3cba7ff121cbb49dc0a910ba9eb5410b7574
5192 F20110115_AABRZG gallas_q_Page_310thm.jpg
6cb874d9108fe5c547151ecfe7502944
4fff16d173c8eca3dbb1ecb7b9c746138dffa177
F20110115_AABOQO gallas_q_Page_051.tif
951d2727be58557ac819330429196051
9e7b95ab743990f72347c0dfb77d583d51e9479c
49525 F20110115_AABQPC gallas_q_Page_243.pro
0851e30ab64a8fb84deb204c29d81f0d
95c78159586ad78f2e0ad10133f2ff88ddb9e148
112325 F20110115_AABPNI gallas_q_Page_139.jp2
dcecb25fa38012ee6c0e2a65d39e080a
dd0e986020dc60c47bdcb112ee607bc79f4299bf
7069 F20110115_AABSDX gallas_q_Page_378thm.jpg
319a21f65e50039509904fc04cac2b8c
39e69ccaacefb0c8c07d502c642cd646ffb5b0f7
18047 F20110115_AABRZH gallas_q_Page_311.QC.jpg
94e65cf1bb6f7517c95fb0ba1c56dacf
5c845782b05d9f6f5bd91c2e112b72f863640d98
47907 F20110115_AABOQP gallas_q_Page_073.pro
6ac7b5ec7148b3bdb701b3bc85085c02
c4de4037dea568aee9213066288050a48b2ee4e9
50215 F20110115_AABQPD gallas_q_Page_244.pro
fc06f55e741f5dec8f18c2be6bd48d79
edd90f2e158772e2260cd0ab1c7049e10d02732d
25959 F20110115_AABSDY gallas_q_Page_379.QC.jpg
924acf5940607e4e748c920ae273648d
b00c31b451d90f5858356190faa5e85a4cb14d36
5446 F20110115_AABRZI gallas_q_Page_311thm.jpg
3a830ad5eb7333a6d22ba4bf3913a24f
031012bca70e39ca0f9299ae0b61ba10e1ae2b4a
F20110115_AABOQQ gallas_q_Page_291.tif
f48c4d63bb847cd5fd0e5bb042fc6281
93d33a301491a2dd83ee6b7ed8fcaf565ea1ed5d
34478 F20110115_AABQPE gallas_q_Page_245.pro
cee0c9d8c60a153f1e8ad7f114d04325
e5df43c1a27d6e3271ca68c9701e19c3ecb952ae
F20110115_AABPNJ gallas_q_Page_140.jp2
9c7df3d7f3eca8a45fa2b9e975f46b5e
978586b57a942c75d6100c7d92ce15805f5c5043
24146 F20110115_AABSDZ gallas_q_Page_380.QC.jpg
1bfb88a7376b5f959190906bb4f981ea
8f567d02bcdf4ac2c27be52b27f2c962bf7117e1
19205 F20110115_AABRZJ gallas_q_Page_312.QC.jpg
99748cbb202273fee549aada6e40343c
ebf3d458ca4fcfc3a18f48c3d72fed66ea79a978
F20110115_AABOQR gallas_q_Page_086.txt
86c7d8534d669c32a2801704830b52a3
f4a4dcb73d1dfee36171a5346f47f57e72ac8d9f
41162 F20110115_AABQPF gallas_q_Page_246.pro
6d833cd4da02029a2605e441a224202c
e0abfc35154b474dbb6e9ba5054786ac447f9809
F20110115_AABPNK gallas_q_Page_141.jp2
12bc1b59d3ee5ae74196fa74cf979137
00f42cb2905679ebcd14f3f4a707f7f6459c34db
6091 F20110115_AABRZK gallas_q_Page_312thm.jpg
7460b655a6d0415e962092edb009e60c
01333f58367e7be117b77c4472a8f1fef96351fd
112570 F20110115_AABPAA gallas_q_Page_097.jpg
36fd8c3fd639889c4d06bbc25fee01c3
412ee99a4166de831ab139981d047e9afaded8fa
13146 F20110115_AABOQS gallas_q_Page_331.QC.jpg
3752e05ea90ddf0b26276ec5bef75885
aa0748361278cfd3c154525549fada87c88f6a5f
39485 F20110115_AABQPG gallas_q_Page_247.pro
c17d319a2fd607fd0a670b7c50f94ed8
57ca9c837a9bf8603aa960967c5800236b82167a
96902 F20110115_AABPNL gallas_q_Page_142.jp2
f89ec60a0d292740345028ba28d1937c
2acacbe44010ede0df76964959737e7754e18994
16981 F20110115_AABRZL gallas_q_Page_313.QC.jpg
7978dbc5e35d418f784f5a3470c55358
8a419c70f96c7fd5cb0e3429ef29e472fefe55c8
20534 F20110115_AABRMA gallas_q_Page_104.QC.jpg
5bd82a3bbba8f6478ba4f249e6b3be77
e6a9fea33a990f704cd7af6cc5ebe439dcddeeca
85068 F20110115_AABPAB gallas_q_Page_098.jpg
ce67694b16e2878ffbec70b0341ac678
65d1afdb6177c85d30374d0892343e43ffbdaf49
1051964 F20110115_AABOQT gallas_q_Page_097.jp2
b8800122a47a09a9f1a2f26da9d87f23
e18684843c591a498b20b0b0ec8b36756c0267c1
39181 F20110115_AABQPH gallas_q_Page_249.pro
2e360dd402bdcafd30c90da0c580301d
9afdc8fbd430744c6053d9b5b52d42d9a27bb6ee
787544 F20110115_AABPNM gallas_q_Page_143.jp2
cf3a8ac4e665cbfb73698c82bf7aa7f8
63733413fdbd45715663de86e281fe8b2377f648
4959 F20110115_AABRZM gallas_q_Page_313thm.jpg
7203d66f4f8c897b86c03b0d383b823e
83f31c6cc3b09c54f422f7b6fc819fdaa6dde72f
5967 F20110115_AABRMB gallas_q_Page_104thm.jpg
18b251df44db418b05cedd5dd3cd80f9
5a310c7e7d1582e41d052290ef43a0d3d3fc58c2
60941 F20110115_AABPAC gallas_q_Page_099.jpg
ce042c547ea578e2cf0cfeb336ca3463
2358b481bc12055976fdfeee8d35c1a911eda6cb
16089 F20110115_AABOQU gallas_q_Page_204.QC.jpg
a943e82fee1298d4e4b988cc6b061d95
032081651647161a9168f68abd4c4839886f3a27
40418 F20110115_AABQPI gallas_q_Page_250.pro
fe93f90d6351a4e30c0ca9d7a0b60e99
a1afe6208258404696d740192734e8759ae2e232
95870 F20110115_AABPNN gallas_q_Page_144.jp2
ef5a3e643807cd2b8c6b89945b0d431c
c290cae179825e6331279a7987d2ae6c418f4a2f
15426 F20110115_AABRZN gallas_q_Page_314.QC.jpg
c364baabd623b9f29acfa1886dafe297
d81b0085fbcde2708db6133f1ed2c9d95844f5fd
F20110115_AABRMC gallas_q_Page_105.QC.jpg
8ebcc4e485fb886c83e431d783ee54cb
4c80c127f41fb2ca3c1af0b3f765c3e0201c7b9a
48306 F20110115_AABPAD gallas_q_Page_100.jpg
66ee631722fa1027c9597f0a01726ee2
384814b4865c763667de4f8d8c865f3415d9191b
100242 F20110115_AABOQV gallas_q_Page_369.jpg
90cb7d6466518e5bec2c108f59b1ae2f
5adfbff6ece4d08d7b167d26c33fdb4df9d6f17f
34756 F20110115_AABQPJ gallas_q_Page_251.pro
6162be21a481418b963f443d221bb2c2
465d3d09c77b5f2f5db5df568d018237ccdd5b04
774597 F20110115_AABPNO gallas_q_Page_145.jp2
221190567a833ec6125b7d43db64bd04
7481a326ca99fc7bec2114f1b2675ff0194fd7cf
4916 F20110115_AABRZO gallas_q_Page_314thm.jpg
3ba9d3d01a64710f911ed7db1687e941
614326d8a80c9a6307d5f3fff6c85aa5076c8653
6827 F20110115_AABRMD gallas_q_Page_105thm.jpg
bb43b6d67e9bea5e0534363b608a5a95
18a441714a3a830349df7712ea72e15bbb377a6d
58014 F20110115_AABPAE gallas_q_Page_102.jpg
49db2d4e03b18562d669271411833387
96272b5ff1965cf83936556fcde7605a96f9f519
1737 F20110115_AABOQW gallas_q_Page_347.txt
4654e0a122bb410312af2c231b7845df
780cd92717a72eed42aba671cfce79a2eb75285f
93483 F20110115_AABPNP gallas_q_Page_146.jp2
5e0df53ed8e0426b481cb2c1b5b8aee9
10a5139631aa0b118fdef09e3bce0354d93297cf
9823 F20110115_AABRZP gallas_q_Page_315.QC.jpg
836baa36e9862a5dd3c5c50b73ed39e0
422dba0ef6c037e82140a8e2c189aefd23c41130
21280 F20110115_AABRME gallas_q_Page_106.QC.jpg
ad698980cdfc8fbff8e3726e1b0e7c28
65769c4e18f550822284026c2acfd4d40a2cec3a
67178 F20110115_AABPAF gallas_q_Page_103.jpg
2c481614a5ec7a45f30900c94d1d0658
dc58b88ff8c3c36d76dfa7ff14d71d12ea01be48
127703 F20110115_AABOQX gallas_q_Page_381.jp2
657631a106d4891ef5e9ea8098c18923
816a4a17e1966c867c8b85ea5dfcb93f7703e7d2
31829 F20110115_AABQPK gallas_q_Page_252.pro
b32cde28d9eabcb493bbdc43d71325aa
4b8696a0a2538ca94331ad69b790cf88dce47081
841267 F20110115_AABPNQ gallas_q_Page_147.jp2
10fdca88ba90883bff1adadfa71dd4fd
f17838f317b12890f9afd31cc454afa6ef61750a
3308 F20110115_AABRZQ gallas_q_Page_315thm.jpg
e1ac926e73770d35ea233a6309d7f868
146daa5bb614e653081b1586e0afeacf8f2cbcf9
6022 F20110115_AABRMF gallas_q_Page_106thm.jpg
8a01bf621220b4fc3b821e3dd89213b1
542807835368eb38b1a3268946764e9b345e108b
F20110115_AABQCA gallas_q_Page_224.tif
53cdda0275e3f74c7ff3cd0db98a0b3b
709762972366cbd0039e471588fc33a11585e4d8
63442 F20110115_AABPAG gallas_q_Page_104.jpg
6e2ec83d8feeecab2f43532d6591230f
150f8e195376e19888309028a0c89348abc360bc
F20110115_AABOQY gallas_q_Page_046.tif
0d8a4e891b9fc00fba5a54cd3217b98e
3996da4c7eb94a8ceb0ddff28d61d210406000ed
43771 F20110115_AABQPL gallas_q_Page_253.pro
59a24d72ed41168d96220a015c48a930
3acb3a90fdd378746ed30f1a7ae6e5a46dcca7cd
101150 F20110115_AABPNR gallas_q_Page_148.jp2
59f40e1aee1457811061c27552612b40
ba0a34554dcb50e5298958ee2eeb83c7c425c6e6
23231 F20110115_AABRZR gallas_q_Page_316.QC.jpg
5d2c4c37d13e1789c1b9948448c8b0e3
af66f391ce4172a18b91745f5366fb63fa4c8aaa
F20110115_AABQCB gallas_q_Page_225.tif
49d1a69d15a22a5ba0b206de825053e7
a0ad9e260efe172e89142b07bfc8ee316f05717f
69527 F20110115_AABPAH gallas_q_Page_105.jpg
189cf405c1e51e306128243460a91ad8
7c52552f693162ec805b6dd773ea9efedf653159
F20110115_AABOQZ gallas_q_Page_039.txt
7925eee0faf84f123ba3186c7b41d4db
f4642ff920023b7a7fd4802f7e19c2082a36ff74
40511 F20110115_AABQPM gallas_q_Page_254.pro
cd72106e4def86d5677fbdc13ddc975d
852fc9e8f58bc69ff7e79fd3e5c1115042f6e894
722253 F20110115_AABPNS gallas_q_Page_149.jp2
0a4e5311b851cda42183637b20ea1eae
37a3fee11483eddca1968e7843650ecb86f847fe
6520 F20110115_AABRZS gallas_q_Page_316thm.jpg
cf88c4ff0a7c737db7b1b7a0d8b4778a
5b484ea29f50b910127256b2d8a75235484e75c3
20386 F20110115_AABRMG gallas_q_Page_107.QC.jpg
d3d454a00fb376ad874556e75f1d3fc5
7113725ea1be10b2d9cc35568c279a3313ae37c5
F20110115_AABQCC gallas_q_Page_226.tif
4ad0c71c7dc9598c0bd575fe326e5546
5ff1ae54fe5f15f9cdc83e3fcb22f8df1f49f504
66020 F20110115_AABPAI gallas_q_Page_106.jpg
2aa977642ce55db2714598b53a0f7a78
81a02bc48ed7ac3f48642d96ae6bce33fcdf68a0
42327 F20110115_AABQPN gallas_q_Page_255.pro
0834081e12f5f4a1f738698ece6ac2c5
228fcec4f12fe4c8e026b69814872b9adb7b05de
776495 F20110115_AABPNT gallas_q_Page_150.jp2
cf13bff16c4bd32c713e7b2ff7c4006f
17ca14886d8eee7b28c7f8ce7ea3577f01c298fd
6256 F20110115_AABRMH gallas_q_Page_107thm.jpg
2a962340b652442d68d0a1ec79b5ec4f
6f1eebe1814fa3150bfeb7f0796870682bbfd75e
F20110115_AABQCD gallas_q_Page_228.tif
d905ae50c13e87c0d7f8eaf12a6f568a
359b1578917adea3557e1b1af33e86d45abe4fa3
64965 F20110115_AABPAJ gallas_q_Page_107.jpg
b8bfe039d60aedc3061cb02261d58b62
fda5af1b44d59673755f5f7d76afa36a8b09d353
47251 F20110115_AABQPO gallas_q_Page_256.pro
deaf1b785899f8cbbbf45eb2a5249326
0436261e063b8b7642c4ac895b100efe83aa5c34
F20110115_AABPNU gallas_q_Page_151.jp2
d3e24bfe7d63b927a300fb89a2323003
d50158166babf27660226cd08559bd03e7afa077
17705 F20110115_AABRZT gallas_q_Page_317.QC.jpg
b1d6d695f4c56800838195fb5d96c3e5
43e429577d201c14309d948fcd4c09f3cd0fe1fe
23724 F20110115_AABRMI gallas_q_Page_108.QC.jpg
b7d723b16d8d9ae1d8287b3d3636d8d7
b16619f371838d648dc85dc09d3ec291392c3de1
F20110115_AABQCE gallas_q_Page_230.tif
8bb13f182dcff13230ca86a7b5aa1df1
75ebaf5de34bd27c9bbc6ce1f85fe60626f58e1b
71411 F20110115_AABPAK gallas_q_Page_108.jpg
5ab7fa7ef654e3778f1a865ee31d5ed1
5cfd26b03a8e3b4b8981bc82122f63bc4615e8de
34399 F20110115_AABQPP gallas_q_Page_257.pro
6c8f671f8fd8dc51882e9db22a45fcdd
442f0866751518afd7a6d3feb3d764c7423a4ddf
890640 F20110115_AABPNV gallas_q_Page_152.jp2
cc66c32733305075406df855529f5946
6e82f1fe3a6e92360d3f39b916258b51c058e018
F20110115_AABRZU gallas_q_Page_317thm.jpg
469c7c2fdae341b101efa96e70076874
ed342e8c92cb37ffa4262e7634b619e1310247a5
6796 F20110115_AABRMJ gallas_q_Page_108thm.jpg
858dbae3e82b2106bf0e56a89dc7bdf2
32956ae2197ad1d5df68344e4cd24baaa226e89f
F20110115_AABQCF gallas_q_Page_231.tif
1d0315c409a359e2207d36054651c68c
bad0fa932f02d570b2fcf60ab18ec2cc6ad4c735
67364 F20110115_AABPAL gallas_q_Page_109.jpg
9d693ee4d96e09afaefd433ff4aa60cf
5da1fa17b0f29ac5c158a09787b6433a4f007b60
35670 F20110115_AABQPQ gallas_q_Page_258.pro
119311d500daf2be9772bcdfe6fb23c9
540f36fed021b9fdfae494c0f7905566956f83c9
F20110115_AABPNW gallas_q_Page_153.jp2
f53c72434e2e6fed387aaa6d8a0c5c95
6c744ff28e82f32eefca93002a1ecb30df2cfd48
4046 F20110115_AABRZV gallas_q_Page_318thm.jpg
3afe9f0bfeb779e7a7133a590935d56e
f169b8030a081150d2afa413c03749903bce7635
21731 F20110115_AABRMK gallas_q_Page_109.QC.jpg
56a5f8805beca1c8a527e6f2f36b1a36
4e8ebd14cade8604870d595e353039305a35d0ae
F20110115_AABQCG gallas_q_Page_232.tif
c8dbf559e7eab6e49c20f04272415a97
7445208576e0e4f8cac82fb883651c5789885355
67823 F20110115_AABPAM gallas_q_Page_110.jpg
3a51072e4b68212d73eaf57a7e77651e
b7633f220754f451525064bb461003d5a8a8d71e
27406 F20110115_AABQPR gallas_q_Page_260.pro
1ee88d58b7ff92a1489009d0d9eb5ba1
b9aeb8e46c12a5d94969551ad71956bb684f172f
1051930 F20110115_AABPNX gallas_q_Page_154.jp2
dcd5ca05b2292483cb28ce944812ff1e
b12f47ae3c029a81cb97d9c8b54756e84f2eea8f
19810 F20110115_AABRZW gallas_q_Page_319.QC.jpg
4865efcadd620f656cd7e86fa6aeceea
f398f68036767de106733b4833f65c0e184258d6
F20110115_AABRML gallas_q_Page_109thm.jpg
49822d0df59d8194380140e2790f651c
6b352153badd7056a10babe87e1e579e57ee4e8e
F20110115_AABQCH gallas_q_Page_233.tif
421d48477c35a6505b69236887c57840
d46026972ae59a7d93206c26028a6b2f3fbf4242
60699 F20110115_AABPAN gallas_q_Page_111.jpg
52fe95bbf7fae901178c2f96f7fbba5d
a17ab27529f3fef74558f40abb98e8360795be4a
23243 F20110115_AABQPS gallas_q_Page_261.pro
02d35cd7dc98cb80f7434a72a055dd12
1670ce36d4e092f303241b790054e9536de7009b
91806 F20110115_AABPNY gallas_q_Page_156.jp2
41d6a48abbc187eb613df090affb6106
022a65d44c17083b7f5884cf1da28ea78331b321
5979 F20110115_AABRZX gallas_q_Page_319thm.jpg
9f6f33276c43dea50954b14eb96ac18f
f1c0fc2757a535f86a3bfc6e0cb750537fdc9945
21583 F20110115_AABRMM gallas_q_Page_110.QC.jpg
2e6c7bf48d7a713d38f0bfca82d497b4
e93838974ab633d65239205ef463658a8a86432f
F20110115_AABQCI gallas_q_Page_234.tif
8739da97fa516e57214c557f8fd3c9ef
7ba481e3014ec86a7655bc7967e4300a39b489c6
72946 F20110115_AABPAO gallas_q_Page_112.jpg
281494b1eec08a50080783d87a5d4888
5bc142615fa1ed8331a22f136dcbc5201e9cfe0a
44029 F20110115_AABQPT gallas_q_Page_262.pro
2dca169504f1c6f596d581daf4334594
365a6be63d5ed03e72dba13158b2ba8cd6e31301
761987 F20110115_AABPNZ gallas_q_Page_158.jp2
1e8257739c66e9a04d8ec1e26035c4bf
893e44544b5e150135a2be2fd6ace8409d6e0af9
15824 F20110115_AABRZY gallas_q_Page_320.QC.jpg
56615a07cc6d2404d16f92d9e139449d
2908bab14a7715fd24d55db8009577d5e674de75
6063 F20110115_AABRMN gallas_q_Page_110thm.jpg
a61c6c6f3554c996e140f84150c3dbe3
a9cd72b41e2cdc0d97a5be045e4af5436cfc2e59
F20110115_AABQCJ gallas_q_Page_235.tif
f061f9f89e24113de5c0ac7529797699
69e4fc2ade34a114bd81db61aa18dc09df2ecc30
60293 F20110115_AABPAP gallas_q_Page_113.jpg
68b91e109c09a4a68d3f44437ec60f96
c95066864536e3e1f9a4b7cdf22afd85b5067b5c
30126 F20110115_AABQPU gallas_q_Page_263.pro
ee1b773a21178e2b26fb3398ac3a1bef
b6d904f98547fdc1e458522e1265bc81de574ab7
5818 F20110115_AABRZZ gallas_q_Page_321.QC.jpg
54c657e5aa2ec48334852dde52341556
0f70137254bfb6022fdfb62a5f601b656514b337
18088 F20110115_AABRMO gallas_q_Page_111.QC.jpg
1e447c22fe86eb7aac45d6b4d4d6a5c8
4f2969f880fd4830e96d813d54bd9505f32e4923
F20110115_AABQCK gallas_q_Page_236.tif
3e761bcde95e0a104e45118f915c664e
3e5849c56012c3e4741e3165b291dbd1db8d94e9
49828 F20110115_AABOWA gallas_q_Page_348.jpg
3f0241316640f919542f4fd5cf9bf6f0
87f23075ea35416b731e349d0c54ced375f7372c
64278 F20110115_AABPAQ gallas_q_Page_114.jpg
d1dd3fd595644591888ccf8602b90696
2808850ed26ebb4049037d036d6c91da49ae57ef
37544 F20110115_AABQPV gallas_q_Page_264.pro
d4b34307da27ca029dfd6aa26ecc56a2
b53f9960e47220d48f6f22d3b3ed7bfd481cb99a
5486 F20110115_AABRMP gallas_q_Page_111thm.jpg
72a3132507e40adb24540e605f8a6dae
ac7e8d5b57eb56911b6b3f711fbdfd7b171b93ca
F20110115_AABQCL gallas_q_Page_237.tif
e3e165c99caa1b85912da493b7226340
8a4f62a0d6a1d211d2e531a210f41561e1a6200b
47356 F20110115_AABOWB gallas_q_Page_272.jp2
3c27cb05d18a5f3a185532b5985249ae
b8632f5b408d9ed3bf8405fa01b6aba5374020ec
66312 F20110115_AABPAR gallas_q_Page_115.jpg
6650f1fbed7c8a8768360fc252409c51
eeaddce2b1952fc116ecbdb0a173ed79fe1d61de
37715 F20110115_AABQPW gallas_q_Page_266.pro
b4734561fb20fb692149913f0f673374
29b17368b13840977c262a313c7e2387155a1af1
23756 F20110115_AABRMQ gallas_q_Page_112.QC.jpg
38b57c6d0b8409be6b6eb3262f247960
3059b47b78afac19ff181ae92a2b0f88daa5b2c6
F20110115_AABQCM gallas_q_Page_238.tif
15045787818b36eb9feee0ee437c050e
809797d0c16672777c8382e10fb4654fce63921e
59177 F20110115_AABOWC gallas_q_Page_300.jpg
4ae99bcd6f3fde85bbde133c7c8550d1
2889bdd3738db582d2e5ec828561981e5c80a425
63156 F20110115_AABPAS gallas_q_Page_116.jpg
13d5ee3cb114955da5198e6e5b960c0e
70b0352cf33968f1b5357d9a3f2b5662f22accc4
39483 F20110115_AABQPX gallas_q_Page_267.pro
7d118ca3a7e83375aa7dca38733a3546
3309e338f431633dedaf563ba47cdb6bf8b1628c
F20110115_AABRMR gallas_q_Page_112thm.jpg
f74e76788cea8606b3c57cecee586306
68a6410be952cdfe3691d46927f904b87e8088f9
F20110115_AABQCN gallas_q_Page_239.tif
e009af48bfc93246002159beff0bc2e9
0c9e5795b417dfd7a161615cd65e39afae38f21e
1000 F20110115_AABOWD gallas_q_Page_272.txt
101d8a7aa0dc923c12855174518cf697
4b00f9ce9bd3ad9bdc42d90124fc07671add84ca
59556 F20110115_AABPAT gallas_q_Page_117.jpg
4700783abd3d19b32500d51922ca9c8c
f0ecd6973cec49850cc1ed0acf64f7cb17b0927a
42235 F20110115_AABQPY gallas_q_Page_270.pro
05107e77c8b1d9aea7b888e7f34ca6bf
5cb4f122262d7d9bab2d54fca677c20192faf611
19423 F20110115_AABRMS gallas_q_Page_113.QC.jpg
b2d39c44ab16acd5c1f85ad1efc67061
e80584f86ef0c3fea715621107b6d2368a7596d1
F20110115_AABQCO gallas_q_Page_240.tif
aec9611991e84d929c5d7235de4f0824
cf892dd05f2a3085453cdf4f0c310f9485a13330
1051949 F20110115_AABOWE gallas_q_Page_089.jp2
14bf1335004ce2b9bf1d1247521639da
54fc5281c07b8e5ea951303b5af43b51dfe81b48
71786 F20110115_AABPAU gallas_q_Page_118.jpg
474313453200e5df1e85dd42799fd9f5
84a81e9912622cbe752f8ca85aa28cb606f1b741
31298 F20110115_AABQPZ gallas_q_Page_271.pro
0969f6b5f5a6719a4d764adaac217378
ba94d40a2643f1776d83ba6a82d56d949d7df980
F20110115_AABRMT gallas_q_Page_113thm.jpg
a37cb8ebff0d41156e1f8e997da94eca
2bd0eb70e564f3ee96781101e05df590c11a1806
F20110115_AABQCP gallas_q_Page_241.tif
1bf19c154aa7bc0c1ee1cbeb00a8abf1
68a4352d6c2100bd00f6bdfee3e48a080da638c2
878814 F20110115_AABOWF gallas_q_Page_110.jp2
f4b0219e52c55a892fe8c7de6bb669af
b654a11ff99b14221dc6acc354a4e6fb5bebf22f
67377 F20110115_AABPAV gallas_q_Page_119.jpg
b4729c5ccf67bbde25d94aa17009f030
d22700f1a6f593886a937415455c3ebd3fabcde8
20117 F20110115_AABRMU gallas_q_Page_114.QC.jpg
489ff1ad3f7156eea8ea6e26d8e4c3c2
a8dd8b573359eb2649dbc0634e136ba369f3c1d3
F20110115_AABQCQ gallas_q_Page_242.tif
6dae8a12cdae2718a5f57dd963956e56
0beb48ca8e1b1723b37b89a5f0b8e26d7544847a
6174 F20110115_AABOWG gallas_q_Page_212thm.jpg
b4d8dfd2c97c30790693257b47029444
b52d0e346a7114b1ec951a21966d918a26014e0e
33488 F20110115_AABPAW gallas_q_Page_123.jpg
b879f608bd10410ecce0c62aa8b7aa8a
f96cd50f02da7f28aca72d5bc77e191914d76fe8
F20110115_AABRMV gallas_q_Page_115.QC.jpg
a93d9b43f482b6f88b29d05029da2e18
e76b095ce700be6eaf904dbe63ae9ce567e1ee75
F20110115_AABQCR gallas_q_Page_243.tif
18df4360c6e799475cd38435d9b0c8c8
57f89712b4e358860c59958001f25e4a4afc7a67
79356 F20110115_AABOWH gallas_q_Page_377.jpg
0ebc86c8258a17bb547df54c95fed8a9
bfa7e2249c95734e6937c76b66a6b81d85db789d
42888 F20110115_AABPAX gallas_q_Page_124.jpg
da959a27fca66da4b6c5be1e98298690
b76fdb0edb9d8cbb3319e6cce1a80f3b61591302
52892 F20110115_AABPTA gallas_q_Page_318.jp2
062be46d35ec372739415dab0e5f4094
054ae542790b5394fe5359be391171ca56f13a3f
6476 F20110115_AABRMW gallas_q_Page_115thm.jpg
f8da92b42e99027d356eeb317b45f6a4
9615e52a85205b8688501cd005a7bb5e42960e6e
F20110115_AABQCS gallas_q_Page_244.tif
0c7508ef5bcad1efe042123ae41d03b6
de8a3956541c5572965eec025314d419f051b177
68553 F20110115_AABOWI gallas_q_Page_230.jpg
5f451f7c58aed1f07755a418104f1d10
5a361795a8674e0e9dc0c7a3fae28466c3870c2d
58533 F20110115_AABPAY gallas_q_Page_125.jpg
cd6297f4a7750c81927a1e6e471f01b3
2444effd8fc1363145892d2011d26994eace03c0
96200 F20110115_AABPTB gallas_q_Page_319.jp2
073d3e9986cfb82518775d2f19b88252
f0e69aef97009e5d243bc0b0d0bf1e420a0478f4
20008 F20110115_AABRMX gallas_q_Page_116.QC.jpg
e53f2830fc502e8c0d0d96958493a577
d8bffac8dd6ed8114e00f02e23cda7c7e895645e
F20110115_AABQCT gallas_q_Page_245.tif
53442d8cf3fd5291f82facabcdaa66f0
8dcdab0747fd3a71b6a9e1df27cad92c78bbcbfb
83077 F20110115_AABOWJ gallas_q_Page_359.pro
85df996eae13d0d99a639f30f51f236f
70de5ca35b2b17bcd59d861f413f0a19df7c66d1
65786 F20110115_AABPAZ gallas_q_Page_126.jpg
6328b2f5067f91b3c7007098f5a8d131
aa5576fb6d36f317d8c7e981fc376c0e5f85d61a
63101 F20110115_AABPTC gallas_q_Page_320.jp2
297bcf8a7b9b62066f220bf1c759d14d
2b56de0f1e72022578062d4e84bf975c86a6c1a0
5593 F20110115_AABRMY gallas_q_Page_116thm.jpg
bbcd5a51d210d6dd58f239f3be4f9ec7
e905b9b9362b9be5139bf914875f47fd5719f2c1
F20110115_AABQCU gallas_q_Page_246.tif
67bdd44fccc0cc66d6da5914a08ed9f0
4e250692484f01c9fe499f1f798bdfd46e4f97b4
105761 F20110115_AABOWK gallas_q_Page_092.jp2
1eedeeefb7e72aa9568d7530f15445c2
a8cca29c786e5c44c42abf6bda77ffecc7bc9e52
492987 F20110115_AABPTD gallas_q_Page_322.jp2
e26beda8d0a95685a5088a2bc06881f9
47502424dc07cfdd6448a21225304d32bfddf34c
20625 F20110115_AABRMZ gallas_q_Page_117.QC.jpg
77688b9acdab6136112a0a916aa5dc97
32e14ecfd333c277fc4053dc4782438e1a4444a6
F20110115_AABQCV gallas_q_Page_247.tif
4a2392eb752692a8fb29105faee5a604
5121a677c09c7610f87959cfc092734d6713b5ea
65626 F20110115_AABOWL gallas_q_Page_077.jpg
96d87cd59163901a45450d0793fea691
e737b55aaea75e12875cd63f8f5950dbbb648600
57723 F20110115_AABPTE gallas_q_Page_323.jp2
b614fbff8c4a8e1252a89c5be3e03257
631465a2f6ea7b1cb671e673bba16a0f4f208ad6
52113 F20110115_AABOJA gallas_q_Page_296.pro
5a91e538ee10ce7d0c888707448a9be1
797ffa221a23ebb0c51a7710c1d625f901a2f4d9
F20110115_AABQCW gallas_q_Page_248.tif
298ef50ec840656021295e3551b2b878
04836043202867339bd27aea3f5c2d4121ce9aa6
75381 F20110115_AABOWM gallas_q_Page_354.jpg
d2e66af126ba548ee94123b45f31bf7d
d7206a70c8d482f101ec910a3817922230a26790
51425 F20110115_AABPTF gallas_q_Page_324.jp2
8b8f5e8b9af270409253fbc72cfdadf6
2c6d4e030a7382694b7a79aae4f3d014d121bb57
67987 F20110115_AABOJB gallas_q_Page_166.jpg
e19ee7835642a47f5fcdaa5afc84b53d
a0c85ed028966a529917ea836fea8cb115f9d52a



PAGE 1

ON THE MODELING AND DESIGN OF ZERO-NET MASS FLUX ACTUATORS By QUENTIN GALLAS A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2005

PAGE 2

Copyright 2005 by Quentin Gallas

PAGE 3

Pour ma famille et mes amis, dici et de l-bas (To my family and friends, from here and over there)

PAGE 4

iv ACKNOWLEDGMENTS Financial support for the research project was pr ovided by a NASA-Langley Research Center Grant and an AFOSR grant. Fi rst, I would like to thank my advisor, Dr. Louis N. Cattafesta. His continual guida nce and support gave me the motivation and encouragement that made this work possible. I would also like to express my gratitude especially to Dr. Mark Sheplak, and to the other members of my committee (Dr. Bruce Carroll, Dr. Bhavani Sankar, and Dr. Toshik azu Nishida) for advising and guiding me with various aspects of this project. I thank the members of the Interdisciplinary Microsystems group and of the Mechanical and Aerospace Engineering department (particularly fellow student Ryan Holman) fo r their help with my research and their friendship. I thank everyone who contributed in a small but sign ificant way to this work. I also thank Dr. Rajat Mittal (George Washington University) and his student Reni Raju, who greatly helped me with the comp utational part of this work. Finally, special thanks go to my family and friends, from the States and from France, for always encouraging me to pursu e my interests and for making that pursuit possible.

PAGE 5

v TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES.............................................................................................................ix LIST OF FIGURES...........................................................................................................xi LIST OF SYMBOLS AND ABBREVIATIONS............................................................xix ABSTRACT...................................................................................................................xxvi CHAPTER 1 INTRODUCTION........................................................................................................1 Motivation..................................................................................................................... 1 Overview of a Zero-Net Mass Flux Actuator...............................................................3 Literature Review.........................................................................................................7 Isolated Zero-Net Mass Flux Devices...................................................................7 Applications...................................................................................................8 Modeling approaches...................................................................................11 Zero-Net Mass Flux Devices with the Addition of Crossflow............................15 Fluid dynamic applications..........................................................................16 Aeroacoustics applications...........................................................................18 Modeling approaches...................................................................................19 Unresolved Technical Issues...............................................................................25 Objectives...................................................................................................................27 Approach and Outline of Thesis.................................................................................28 2 DYNAMICS OF ISOLATED ZERO-NET MASS FLUX ACTUATORS...............30 Characterization and Parameter Definitions...............................................................31 Lumped Element Modeling........................................................................................34 Summary of Previous Work................................................................................34 Limitations and Extensions of Existing Model...................................................38 Dimensional Analysis.................................................................................................44 Definition and Discussion...................................................................................44 Dimensionless Linear Transfer Function for a Generic Driver...........................46

PAGE 6

vi Modeling Issues..........................................................................................................51 Cavity Effect........................................................................................................51 Orifice Effect.......................................................................................................52 Lumped element modeling in the time domain............................................52 Loss mechanism...........................................................................................61 Driving-Transducer Effect...................................................................................63 Test Matrix..................................................................................................................69 3 EXPERIMENTAL SETUP........................................................................................72 Experimental Setup.....................................................................................................72 Cavity Pressure....................................................................................................75 Diaphragm Deflection.........................................................................................76 Velocity Measurement.........................................................................................79 Data-Acquisition System.....................................................................................82 Data Processing..........................................................................................................85 Fourier Series Decomposition....................................................................................92 Flow Visualization......................................................................................................97 4 RESULTS: ORIFICE FLOW PHYSICS....................................................................99 Local Flow Field.......................................................................................................100 Velocity Profile through the Orifice: Numerical Results..................................100 Exit Velocity Profile: Experimental Results.....................................................109 Jet Formation.....................................................................................................116 Influence of Governing Parameters..........................................................................118 Empirical Nonlinear Threshold.........................................................................119 Strouhal, Reynolds, and Stokes Nu mbers versus Pressure Loss.......................121 Nonlinear Mechanisms in a ZNMF Actuator...........................................................128 5 RESULTS: CAVITY INVESTIGATION................................................................137 Cavity Pressure Field................................................................................................137 Experimental Results.........................................................................................138 Numerical Simu lation Results...........................................................................141 Computational fluid dynamics...................................................................142 Femlab........................................................................................................147 Compressibility of the Cavity...................................................................................150 LEM-Based Analysis.........................................................................................151 Experimental Results.........................................................................................156 Driver, Cavity, and Orifice Volume Velocities........................................................162 6 REDUCED-ORDER MODEL OF ISOLATED ZNMF ACTUATOR....................171 Orifice Pressure Drop...............................................................................................171 Control Volume Analysis..................................................................................172 Validation through Numerical Results..............................................................175

PAGE 7

vii Discussion: Orifice Flow Physics......................................................................181 Development of Approximate Scaling Laws....................................................188 Experimental results...................................................................................188 Nonlinear pressure loss correlation............................................................194 Refined Lumped Element Model..............................................................................198 Implementation..................................................................................................198 Comparison with Experimental Data................................................................202 7 ZERO-NET MASS FLUX ACTUATOR INTERACTING WITH AN EXTERNAL BOUNDARY LAYER.......................................................................211 On the Influence of Grazing Flow............................................................................211 Dimensional Analysis...............................................................................................218 Reduced-Order Models.............................................................................................223 Lumped Element Modeling-Based Semi-Empirical Model of the External Boundary Layer.............................................................................................224 Definition...................................................................................................224 Boundary layer impedance implementation in Helmholtz resonators.......229 Boundary layer impedance implementation in ZNMF actuator.................238 Velocity Profile Scaling Laws...........................................................................241 Scaling law based on the je t exit velocity profile.......................................244 Scaling law based on the jet exit integral parameters................................261 Validation and Application........................................................................270 8 CONCLUSIONS AND FUTURE WORK...............................................................273 Conclusions...............................................................................................................273 Recommendations for Future Research....................................................................276 Need in Extracting Specific Quantities.............................................................276 Proper Orthogonal Decomposition....................................................................277 Boundary Layer Impedance Characterization...................................................279 MEMS Scale Implementation...........................................................................280 Design Synthesis Problem.................................................................................282 APPENDIX A EXAMPLES OF GRAZING FL OW MODELS PAST HELMHOLTZ RESONATORS........................................................................................................283 B ON THE NATURAL FREQUENCY OF A HELMHOLTZ RESONATOR..........291 C DERIVATION OF THE ORIFICE IMPEDANCE OF AN OSCILLATING PRESSURE DRIVEN CHANNEL FLOW..............................................................295 D NON-DIMENSIONALIZATION OF A ZNMF ACTUATOR...............................303 E NON-DIMENSIONALIZATION OF A PIEZOELECTRIC-DRIVEN ZNMF ACTUATOR WITH OUT CROSSFLOW................................................................312

PAGE 8

viii F NUMERICAL METHODOLOGY..........................................................................326 G EXPERIMENTAL RESULTS: POWER ANALYSIS............................................331 LIST OF REFERENCES.................................................................................................348 BIOGRAPHICAL SKETCH...........................................................................................359

PAGE 9

ix LIST OF TABLES Table page 2-1 Correspondence between synthetic jet parameter definitions...................................34 2-2 Dimensional parameters for ci rcular and rectangular orifices..................................49 2-3 Test matrix for ZNMF actuator in quiescent medium..............................................69 3-1 ZNMF device characteristic di mensions used in Test 1...........................................75 3-2 LDV measurement details.........................................................................................82 3-3 Repeatability in the experimental results..................................................................92 4-1 Ratio of the diffusive to convective time scales.....................................................109 5-1 Cavity volume effect on the device freque ncy response for Case 1 (Gallas et al.) from the LEM prediction........................................................................................153 5-2 Cavity volume effect on the device fr equency response for Case 1 (CFDVal) from the LEM prediction........................................................................................154 5-3 ZNMF device characteristic di mensions used in Test 2.........................................156 5-4 Effect of the cavity volume decreas e on the ZNMF actuator frequency response for Cases A, B, C, and D.........................................................................................157 7-1 List of configurations used for impeda nce tube simulations used in Choudhari et al............................................................................................................................. .216 7-2 Experimental operating cond itions from Hersh and Walker..................................230 7-3 Experimental operating c onditions from Jing et al.................................................236 7-4 Tests cases from numerical simulations used in the development of the velocity profiles scaling laws................................................................................................242 7-5 Coefficients of the nonlinear least squa re fits on the decomp osed jet velocity profile......................................................................................................................25 4

PAGE 10

x 7-6 Results from the nonlinear regression analysis for the velocity profile based scaling law..............................................................................................................259 7-7 Results for the parameters a b and c from the nonlinear system...........................265 7-8 Integral parameters results......................................................................................266 7-9 Results from the nonlinear regression an alysis for the integral parameters based velocity profile........................................................................................................267 A-1 Experimental database for grazing flow impedance models..................................290 B-1 Calculation of Helmholtz resonator frequency.......................................................293 D-1 Dimensional matrix of parameter vari ables for the isolated actuator case.............304 D-2 Dimensional matrix of paramete r variables for the general case............................308 E-1 Dimensional matrix of parameter variables............................................................314 G-1 Power in the experimental time data.......................................................................332

PAGE 11

xi LIST OF FIGURES Figure page 1-1 Schematic of typical zero-net mass flux devices interacting with a boundary layer, showing three different t ypes of excitation mechanisms..................................4 1-2 Orifice geometry.........................................................................................................5 1-3 Helmholtz resonators arrays........................................................................................6 2-1 Equivalent circuit model of a piezo electric-driven synthetic jet actuator.................35 2-2 Comparison between the lumped elem ent model and experimental frequency response measured using phase-locked LDV for two prototypical synthetic jets....37 2-3 Comparison between the lumped element model ( ) and experimental frequency response measured using phase-locked LDV () for four prototypical synthetic jets..............................................................................................................41 2-4 Variation in velocity profile vs. S = 1, 12, 20, and 50 for oscillatory pipe flow in a circular duct............................................................................................................42 2-5 Ratio of spatial average velocity to centerline velocity vs Stokes number for oscillatory pipe flow in a circular duct......................................................................43 2-6 Schematic representation of a generic-driver ZNMF actuator..................................47 2-7 Bode diagram of the second order system given by Eq. 2-20, for different damping ratio............................................................................................................48 2-8 Coordinate system and sign convent ion definition in a ZNMF actuator..................53 2-9 Geometry of the piezoelectric-driven ZNMF actuator from Case 1 (CFDVal). ......55 2-10 Geometry of the piston-driven ZN MF actuator from Case 2 (CFDVal). ................55 2-11 Time signals of the jet orifice velocit y, pressure across the orifice, and driver displacement during one cycle for Case 1................................................................57 2-12 Time signals of the jet orifice veloc ity, pressure across the orifice and driver displacement during one cycle for Case 2................................................................58

PAGE 12

xii 2-13 Numerical results of the time signals for A) pressure drop and B) velocity perturbation at selected locatio ns along the resonator orifice...................................59 2-14 Schematic of the different flow re gions inside a ZNMF actuator orifice.................62 2-15 Equivalent two-port circuit represen tation of piezoelectric transduction.................64 2-16 Speaker-driven ZNMF actuator................................................................................66 2-17 Schematic of a shaker-driven ZNMF actuator, showing the vent channel between the two sealed cavities................................................................................67 2-18 Circuit representation of a shaker-driven ZNMF actuator........................................68 3-1 Schematic of the experimental se tup for phase-locked cavity pressure, diaphragm deflection and off-axis, two-component LDV measurements................73 3-2 Exploded view of the m odular piezoelectric-driven ZNMF actuator used in the experimental test.......................................................................................................73 3-3 Schematic (to scale) of the locati on of the two 1/8 microphones inside the ZNMF actuator cavity...............................................................................................76 3-4 Laser displacement sensor apparatus to measure the diaphragm deflection with sign convention.........................................................................................................77 3-5 Diaphragm mode shape comparison be tween linear model and experimental data at three test conditions.......................................................................................79 3-6 LDV 3-beam optical configuration...........................................................................80 3-7 Flow chart of measurement setup.............................................................................83 3-8 Phase-locked signals acquired from the DSA card, showing the normalized trigger signal, displacement signal, pr essure signals and excitation signal..............84 3-9 Percentage error in Error! Objects ca nnot be created from editing field codes. from simulated LDV data at different signal to noise ratio, using 8192 samples.....87 3-10 Phase-locked velocity profiles and corresponding volume fl ow rate acquired with LDV for Case 14...............................................................................................89 3-11 Noise floor in the microphone meas urements compared with Case 52....................91 3-12 Normalized quantities vs. phase angle......................................................................93 3-13 Power spectrum of the two pressure r ecorded and the diaphragm displacement. ...95 3-14 Schematic of the flow visualization setup.................................................................97

PAGE 13

xiii 4-1 Numerical results of the orifice flow pattern showing axial and longitudinal velocities, azimuthal vorticity contours, and instantaneous streamlines at the time of maximum expulsion...................................................................................101 4-2 Velocity profile at different loca tions inside the orifice for Case 1........................103 4-3 Velocity profile at different loca tions inside the orifice for Case 2........................105 4-4 Velocity profile at different loca tions inside the orifice for Case 3........................106 4-5 Vertical velocity contours inside the orifice during the time of maximum expulsion.................................................................................................................107 4-6 Experimental vertical velocity profile s across the orifice fo r a ZNMF actuator in quiescent medium at different in stant in time for Case 71.....................................110 4-7 Experimental vertical velocity profile s across the orifice fo r a ZNMF actuator in quiescent medium at different in stant in time for Case 43.....................................111 4-8 Experimental vertical velocity profile s across the orifice fo r a ZNMF actuator in quiescent medium at different in stant in time for Case 69.....................................113 4-9 Experimental vertical velocity profile s across the orifice fo r a ZNMF actuator in quiescent medium at different in stant in time for Case 55.....................................114 4-10 Experimental results of the ratio between the timeand spatial-averaged velocity and time-averaged centerline velocity......................................................116 4-11 Experimental results on th e jet formation criterion................................................118 4-12 Averaged jet velocity vs. pressure fluctuation for different Stokes number...........120 4-13 Pressure fluctuation normalized by the dynamic pressure based on averaged velocity vs. Sthd ..................................................................................................122 4-14 Pressure fluctuation normalized by the dynamic pressure based on averaged velocity vs. Strouhal number..................................................................................123 4-15 Vorticity contours during the maximu m expulsion portion of the cycle from numerical simulations.............................................................................................124 4-16 Pressure fluctuation normalized by the dynamic pressure based on ingestion time averaged velocity vs. Sthd .........................................................................125 4-17 Vorticity contours during the maximu m ingestion portion of the cycle from numerical simulations.............................................................................................126 4-18 Comparison between Case 1 vertical ve locity profiles at the orifice ends.............127

PAGE 14

xiv 4-19 Comparison between Case 2 vertical ve locity profiles at the orifice ends.............128 4-20 Comparison between Case 3 vertical ve locity profiles at the orifice ends.............128 4-21 Determination of the validity of the sm all-signal assumption in a closed cavity...131 4-22 Log-log plot of the cavity pressure to tal harmonic distortion in the experimental time signals.............................................................................................................132 4-23 Log-log plot of the total harmonic dist ortion in the experimental time signals vs. Strouhal number as a function of Stokes number...................................................134 5-1 Coherent power spectrum of the pressure signal for Cases 9 to 20........................138 5-2 Phase plot of the normalized pr essures taken by microphone 1 versus microphone 2...........................................................................................................139 5-3 Pressure signals experimentally re corded by microphone 1 and microphone 2 as a function of phase in Case 59................................................................................140 5-4 Ratio of microphone amplitude (Pa) vs. the inverse of the Strouhal number, for different Stokes number..........................................................................................141 5-5 Pressure contours in the cavity and orif ice (Case 2) from nu merical simulations..143 5-6 Pressure contours in the cavity and orif ice (Case 3) from nu merical simulations..144 5-7 Cavity pressure probe locations in a ZNMF actuator from numerical simulations..............................................................................................................145 5-8 Normalized pressure inside the cavity during one cycle at 15 different probe locations from numerical simulation results...........................................................146 5-9 Cavity pressure normalized by 2 jV vs. phase from numerical simulations corresponding to the experi mental probing locations.............................................147 5-10 Contours of pressure phase inside the cavity by numerically solving the 3D wave equation using FEMLAB...............................................................................148 5-11 Cavity pressure vs. phase by solving the 3D wave equation using FEMLAB and corresponding to the experi mental probing locations.............................................149 5-12 Log-log frequency response plot of Case 1 (Gallas et al .) as the cavity volume is decreased from the LEM prediction........................................................................153 5-13 Log-log frequency response plot of Case 1 (CFDVal) as the cavity volume is decreased from the LEM prediction........................................................................154

PAGE 15

xv 5-14 Experimental log-log frequency respons e plot of a ZNMF act uator as the cavity volume is decreased for a constant input voltage...................................................158 5-15 Close-up view of the peak locations in the experimental actuator frequency response as the cavity volume is decr eased for a constant input voltage...............158 5-16 Normalized quantities vs. phase of th e jet volume rate, cavity pressure and centerline driver velocity........................................................................................160 5-17 Experimental results of the ratio of th e driver to the jet volume velocity function of dimensionless frequency as the cavity volume decreases..................................164 5-18 Experimental jet to driver volume fl ow rate versus actuation to Helmholtz frequency.................................................................................................................166 5-19 Current divider representation of a piezoelectric-driven ZNMF actuator..............168 5-20 Frequency response of the power cons ervation in a ZNMF actuator from the lumped element model circuit represen tation for Case 1 (Gallas et al.).................169 6-1 Control volume for an unsteady lamina r incompressible flow in a circular orifice, from y/h = -1 to y/h = 0...............................................................................172 6-2 Numerical results for the contribution of each term in the integral momentum equation as a function of pha se angle during a cycle..............................................176 6-3 Definition of the approximation of the or ifice entrance velocity from the orifice exit velocity.............................................................................................................178 6-4 Momentum integral of the exit and in let velocities normalized by Error! Objects cannot be created from editing field code s. and comparing with the actual and approximated entrance velocity..............................................................................179 6-5 Total momentum integral equation duri ng one cycle, showing the results using the actual and approximated entrance velocity.......................................................181 6-6 Numerical results of th e total shear stress term ve rsus corresponding lumped linear resistance during one cycle...........................................................................183 6-7 Numerical results of the unsteady term versus corresponding lumped linear reactance during one cycle......................................................................................184 6-8 Numerical results of the normalized te rms in the integral momentum equation as a function of phase angle during a cycle............................................................187 6-9 Comparison between lumped elemen ts from the orifice impedance and analytical terms from the control volume analysis.................................................188

PAGE 16

xvi 6-10 Experimental results of the orifi ce pressure drop normalized by the dynamic pressure based on averaged velocity versus Sthd for different Stokes numbers...................................................................................................................191 6-11 Experimental results of each term co ntributing in the orif ice pressure drop coefficient vs. Sthd.............................................................................................192 6-12 Experimental results of the relative magnitude of each term contributing in the orifice pressure drop coefficient vs. intermediate to low Sthd ..........................193 6-13 Experimental results for the nonlinear pressure loss coefficient for different Stokes number and orifice aspect ratio...................................................................196 6-14 Nonlinear term of the pressure lo ss across the orifice as a function of Sthd from experimental data...........................................................................................197 6-15 Implementation of the refined LEM tec hnique to compute the jet exit velocity frequency response of an isolated ZNMF actuator.................................................201 6-16 Comparison between the experimental da ta and the prediction of the refined and previous LEM of the impulse response of the jet exit centerline velocity. Actuator design corresponds to Case I from Gallas et al........................................203 6-17 Comparison between the experimental da ta and the prediction of the refined and previous LEM of the impulse response of the jet exit centerline velocity. Actuator design corresponds to Case II from Gallas et al.......................................205 6-18 Comparison between the experimental da ta and the prediction of the refined and previous LEM of the impulse response of the jet exit centerline velocity. Actuator design is from Gallas a nd is similar to Cases 41 to 50............................207 6-19 Comparison between the refined LEM pr ediction and experimental data of the time signals of the jet volume flow rate..................................................................209 7-1 Spanwise vorticity plots for three ca ses where the jet Reynolds number Re is increased..................................................................................................................212 7-2 Spanwise vorticity plots for thr ee cases where the boundary layer Reynolds number is increased. ...............................................................................................213 7-3 Comparison of the jet exit velo city profile w ith increasing....................................214 7-4 Pressure contours and streamlines for mean A) inflow, and B) outflow through a resonator in the presen ce of grazing flow...............................................................218 7-5 LEM equivalent circuit representation of a generi c ZNMF device interacting with a grazing boundary layer.................................................................................224

PAGE 17

xvii 7-6 Schematic of an effort divider diagram for a Helmholtz resonator........................230 7-7 Comparison between BL impedance m odel and experiments from Hersh and Walker as a function of Mach number for different SPL.......................................233 7-8 Experimental setup used in Jing et al......................................................................236 7-9 Comparison between model and experiments from Jing et al................................237 7-10 Effect of the freestream Mach numbe r on the frequency response of the ZNMF design from Case 1 (CFDVal) using the refined LEM...........................................239 7-11 Effect of the freestream Mach numbe r on the frequency response of the ZNMF design from Case 1 (Gallas et al.)...........................................................................240 7-12 Schematic of the two approaches used to develop the scaling laws from the jet exit velocity profile.................................................................................................244 7-13 Methodology for the development of th e velocity profile based scaling law.........245 7-14 Nonlinear least square curve fit on the decomposed jet velocity profile for Case I.............................................................................................................................. .247 7-15 Nonlinear least square curve fit on the decomposed jet velocity profile for Case III............................................................................................................................ .248 7-16 Nonlinear least square curve fit on the decomposed jet velocity profile for Case V.............................................................................................................................. 249 7-17 Nonlinear least square curve fit on the decomposed jet velocity profile for Case VII...........................................................................................................................2 50 7-18 Nonlinear least square curve fit on the decomposed jet velocity profile for Case IX............................................................................................................................2 51 7-19 Nonlinear least square curve fit on the decomposed jet velocity profile for Case XI............................................................................................................................2 52 7-20 Nonlinear least square curve fit on the decomposed jet velocity profile for Case XIII..........................................................................................................................2 53 7-21 Comparison between CFD velocity profile decomposed jet velocity profile, and modeled velocity profile, at the orific e exit, for four phase angles during a cycle........................................................................................................................25 5 7-22 Test case comparison between CFD da ta and the scaling law based on the velocity profile at four ph ase angles during a cycle................................................260 7-23 Methodology for the development of the integral parameters based scaling law...262

PAGE 18

xviii 7-24 Comparison between the results of the in tegral parameters from the scaling law and the CFD data for the test case...........................................................................268 7-25 Example of a practical application of the ZNMF act uator reduced-order model in a numerical simulation of flow past a flat plate..................................................271 8-1 POD analysis applied on numerical data for ZNMF actuator with a grazing BL...278 8-2 Use of quarter-wavelength open tube to provide an infinite impedance. ..............280 8-3 Representative MEMS ZNMF actuator..................................................................281 8-4 Predicted output of MEMS ZNMF actuator...........................................................281 A-1 Acoustic test duct and siren showin g a liner panel test configuration....................285 A-2 Schematic of test apparatu s used in Hersh and Walker..........................................286 A-3 Apparatus for the measurement of the acoustic impedance of a perforate used by Kirby and Cummings.........................................................................................288 A-4 Sketch of NASA Grazing Impedance Tube............................................................290 B-1 Helmholtz resonator................................................................................................291 C-1 Rectangular slot geometry a nd coordinate axis definition......................................295 D-1 Orifice details with coordinate system....................................................................303 F-1 Schematic of A) the sharp-interface method on a fixed Cartesian mesh, and B) the ZNMF actuator interacti ng with a grazing flow...............................................328 F-2 Typical mesh used for the computations A) 2D simulation. B) 3D simulation...329 F-3 Example of 2D and 3D numerical results of ZNMF interacting with a grazing boundary layer.........................................................................................................329

PAGE 19

xix LIST OF SYMBOLS AND ABBREVIATIONS 0c isentropic air speed of sound [m/s] aCC cavity acoustic compliance = 2 0c [s2.m4/kg] aDC diaphragm short-circuit acoustic compliance = 0acVP [s2.m4/kg] D C orifice discharge coefficient [1] fC skin friction coefficient = 20.5wjV [1] C momentum coefficient during the time of discharge [1] 12nC successive moments of je t velocity profile [1] d orifice diameter [m] H d hydraulic diameter = 4areawetted perimeter [m] D orifice entrance diameter (facing the cavity) [m] cD cavity diameter (for cylindrical cavities) [m] f actuation frequency [Hz] d f driver natural frequency [Hz] H f Helmholtz frequency = 012ncSh = 12aNaRadaCMMC [Hz] n f natural frequency of th e uncontrolled flow [Hz] 0 f fundamental frequency [Hz] 1 f ,2 f synthetic jet lowest and highest resonant frequenc ies, respectively [Hz]

PAGE 20

xx h orifice height [m] h effective length of the orifice = 0hh [m] 0h end correction of the orifice = 0.96nS [m] H cavity depth (m) / boundary layer shape factor = [1] 0 I impulse per unit length [1] k wave number = 0c [m-1] dK nondimensional orifice loss coefficient [1] 0L stroke length [m] aD M diaphragm acoustic mass = 22 2 02R Awrrdr [kg/m4] aN M orifice acoustic mass due to inertia effect [kg/m4] aO M orifice acoustic mass = aNaRadMM [kg/m4] aRadM orifice acoustic radiation mass [kg/m4] p acoustic pressure [Pa] P differential pressure on the diaphragm [Pa] iP incident pressure [Pa] Pw Power [W] q acoustic particle volume velocity [m3/s] cQ volume flow rate through the cavity = jdQQ [m3/s] dQ volume flow rate displaced by the driver = j [m3/s] jQ volume flow rate through the orifice [m3/s]

PAGE 21

xxi jQ time averaged orifice volume flow rate during the expulsion stroke [m3/s] r radial coordinate in cylindr ical coordinate system [m] R radius of curvature of the surface [m] aD R diaphragm acoustic resistance = 2aDaD M C [kg/m4.s] aN R viscous orifice acous tic resistance [kg/m4.s] aOlinR linear orifice acoustic resistance = aN R [kg/m4.s] aOnl R nonlinear orifice acous tic resistance [kg/m4.s] 0 R specific resistance [kg/m2.s] Re jet Reynolds number = jVd [1] s Laplace variable = j [rad/s] S Stokes number = 2d [1] St jet Strouhal number = jdV [1] cS cavity cross sectional area [m2] dS driver cross sectional area [m2] nS orifice neck area [m2] u acoustic particle velocity [m/s] bu bias flow velocity through the orifice [m/s] u wall friction velocity [m/s] U freestream mean velocity [m/s] CLv centerline orifice velocity [m/s]

PAGE 22

xxii jV spatial averaged jet exit velocity = jnQS = 2jV [m/s] jV spatial and time-averaged jet exit velo city during the expulsion stroke [m/s] acV input ac voltage [V] jV normalized jet velocity = jvU [m/s] w length of a rectangular orifice [m] ()wr transverse displacement of the diaphragm [m] W width of the cavity [m] 0W centerline amplitude of the driver [m] a X acoustic reactance = a M [kg/m4.s] 0 X specific reactance [kg/m2.s] 12 X skewness of jet velocity profile [1] dy vibrating driver displacement [m] jy fluid particle displacem ent at the orifice [m] a Z acoustic impedance = aa R jX = p q [kg/m4.s2] aC Z acoustic cavity impedance = 1 aCjC = cdjPQQ [kg/m4.s2] aO Z acoustic impedance of the orifice = aOlinaOnlaO R RjM = cjPQ [kg/m4.s2] aBL Z acoustic impedance of the grazing boundary layer = aBLaBL R jX [kg/m4.s2] aOt Z total acoustic impedance of the orifice = aOaBL Z Z [kg/m4.s2] 0 Z specific impedance = 00 R jX = p u [kg/m2.s2] 0, p Z perforate specific impedance = 0,0, pp R jX = 0Z [kg/m2.s2]

PAGE 23

xxiii thermal diffusivity [m2/s] nondimensional pressure gradient = wdPdx [1] normalized reactance [1] boundary layer thickness [m] boundary layer displacement thickness [m] Stokes Stokes layer thickness = [m] pc normalized pressure drop = 2 00.5yj p pV [1] cP cavity pressure [Pa] volume displaced by the driver [m3] a electroacoustic turns ratio of the piezoceramic diaphragm = aaDdC [Pa/ V] ic phase difference between the incident s ound field and the cavity sound field [deg] ratio of the specific heats [1] wavelength = 02 cfk [m] dynamic viscosity = [kg/m.s] cinematic viscosity [m2/s] density [kg/m3] A area density [kg/m2] boundary layer momentum thickness [m] / normalized resistance [1] porosity of the perforate plate = hole areatotal areaholesN [%] ratio of the orifice to cavity cross sectional area = ncSS [1] w wall shear stress [kg/m.s2]

PAGE 24

xxiv cavity volume [mm3] radian frequency =2 f [rad/s] v vorticity flux [m2/s] damping coefficient [1] / normalized impedance = j [1] p normalized impedance of a perforate = pp j [1] C compliance ratio = aDaCCC [1] M mass ratio = aDaO M M [1] R resistance ratio = aNaD R R [1] Commonly used subscripts: a acoustic domain c cavity CL centerline d driver D diaphragm ex expulsion phase of the cycle in injection phase of the cycle j jet lin linear nl nonlinear p perforate 0 specific freestream

PAGE 25

xxv Commonly used superscripts: spatial averaged spatial and time averaged fluctuating quantity Abbreviations: BL Boundary Layer CFD Computational Fluid Dynamics HWA Hot Wire Anemometry LDV Laser Doppler Velocimetry LEM Lumped Element Modeling MEMS Micro Electromechanical Systems MSV Mean Square Value PIV Particle Image Velocimetry POD Proper Orthogonal Decomposition RMS Root Mean Square ZNMF Zero-Net Mass Flux Throughout this dissertation, the term synthetic jet actuator has the same meaning as zero-net mass flux actuator, although the former is physically more restricting to specific applications (strictly speaking, a je t must be formed). Similarly, the terms grazing flow and bias flow in the acoustic community are used interchangeably with the respective fluid dynamics terminology crossflow and mean flow since they refer to the same phenomenon.

PAGE 26

xxvi Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ON THE MODELING AND DESIGN OF ZERO-NET MASS FLUX ACTUATORS By Quentin Gallas May 2005 Chair: Louis Cattafesta Major Department: Mechanic al and Aerospace Engineering This dissertation discu sses the fundamental dynamics of zero-net mass flux (ZNMF) actuators commonly used in active fl ow-control applications The present work addresses unresolved technical issues by providing a clear physical understanding of how these devices behave in a quiescent medium an d interact with an external boundary layer by developing and validating reduced-order models. The results are expected to ultimately aid in the analysis and development of design tools for ZNMF actuators in flow-control applications. The case of an isolated ZNMF actuator is first documented. A dimensional analysis identifies the key governing parameters of such a device, and a rigorous investigation of the device physics is conduc ted based on various th eoretical analyses, phase-locked measurements of orifice velo city, diaphragm disp lacement, and cavity pressure fluctuations, and available numerical simulations. The symmetric, sharp orifice exit velocity prof ile is shown to be primarily a f unction of the Strouhal and Reynolds numbers and orifice aspect ratio. The equivalence between Strouhal number and

PAGE 27

xxvii dimensionless stoke length is also demonstrat ed. A criterion is developed and validated, namely that the actuation-to-Helmholtz frequenc y ratio is less than 0.5, for the flow in the actuator cavity to be approximately inco mpressible. An improved lumped element modeling technique developed from the availabl e data is developed and is in reasonable agreement with experimental results. Next, the case in which a ZNMF actuato r interacts with an external grazing boundary layer is examined. Again, dimensional analysis is used to identify the dimensionless parameters, and the interacti on mechanisms are discussed in detail for different applications. An acoustic im pedance model (based on the NASA ZKTL model) of the grazing flow infl uence is then obtained from a critical survey of previous work and implemented in the lumped elem ent model. Two scaling laws are then developed to model the jet velocity profile re sulting from the interaction the profiles are predicted as a function of local actuator and flow condition and can serve as approximate boundary conditions for numerical simulations. Finally, extensive discussion is provided to guide future modeling efforts.

PAGE 28

1 CHAPTER 1 INTRODUCTION Motivation The past decade has seen numerous studies concerning an exciting type of active flow control actuator. Zero-net mass flux (Z NMF) devices, also know n as synthetic jets, have emerged as versatile actuato rs with potential applications such as thrust vectoring of jets (Smith and Glezer 1997), heat transfer augmentation (Campbell et al. 1998; Guarino and Manno 2001), active control of separatio n for low Mach and Reynolds numbers (Wygnanski 1997; Smith et al. 1998; Amitay et al. 1999; Crook et al. 1999; Holman et al. 2003) or transonic Mach numbers and modera te Reynolds numbers (Seifert and Pack 1999, 2000a), and drag reduction in turbul ent boundary layers (Rathnasingham and Breuer 1997; Lee and Goldstein 2001). This versatility is primarily due to several reasons. First, these devices provide unsteady forcing, wh ich has proven to be more effective than its steady counter part (Seifert et al. 1993). Second, since the jet is synt hesized from the working flui d, complex fluid circuits are not required. Finally the actuation frequency and waveform can usually be customized for a particular flow configurati on. Synthetic jets exhausting into a quiescent medium have been studied extensively both experimentally and numerically. Additionally, other studies have focused on the interaction with an external boundary layer for the diverse applica tions mentioned above. However, many questions remain unanswered regarding the fundamental physic s that govern such complex devices.

PAGE 29

2 Practically, because of the presence of rich flow physics and multiple flow mechanisms, proper implementation of these actua tors in realistic applications requires design tools. In turn simple design tools benefit si gnificantly from low-order dynamical models. However, no suitable models or design tools exist because of insufficient understanding as to how the performance of ZNMF actuator devices scales with the governing nondimensional parameters. Numer ous parametric studies provide a glimpse of how the performance characteristics of ZN MF actuators and their control effectiveness depend on a number of geometri cal, structural, and flow pa rameters (Rathnasingham and Breuer 1997; Crook and Wood 20 01; He et al. 2001; Gallas et al. 2003a). However, nondimensional scaling laws are required since they form an essential component in the design and deployment of ZNMF actuators in practical flow control applications. For instance, scaling laws are expected to play an important role in the aerodynamic design of wings that, in the futu re, may use ZNMF devices for separation control. The current design paradigm in the aerospace industry relies heavily on steady Reynolds Averaged Navier Stokes (R ANS) computations. A validated unsteady RANS (URANS) design tool is required for separation control applications at transonic Mach numbers and flight Reynolds number. Howe ver, these computations can be quite expensive and time-consuming. Direct modeling of ZNMF devices in these computations is expected to considerably increase this expense, since the simulations must resolve the flow details in the vicinity of th e actuator while also capturing the global flow characteristics. A viable alternative to minimize this cost is to simply model the effect of the ZNMF device as a timean d flow-dependant boundary condition in the URANS calculation. Such an approach requi res that the device be characterized by a

PAGE 30

3 small set of nondimensional parameters, and the behavior of the actuator must be well understood over a wide range of conditions. Furthermore, successful implementa tion of robust closed-loop control methodologies for this class of actuators call s for simple (yet effective) mathematical models, thereby emphasizing the need to deve lop a reduced-order model of the flow. Such low-order models will clearly aid in th e analysis and development of design tools for sizing, design and deployment of these act uators. Below, an overview of the basic operating principles of a ZNMF actuator is provided. Overview of a Zero-Net Mass Flux Actuator Typically, ZNMF devices are used to inj ect unsteady disturbances into a shear flow, which is known to be a useful tool fo r active flow control. Most flow control techniques require a fluid sour ce or sink, such as steady or pulsed suction (or blowing), vortex-generator jets (Sondergaard et al. 2002; Eldredge and Bons 2004), etc., which introduces additional constraints in the design of the actuator and sometimes results in complicated hardware. This motivates th e development of ZNMF actuators, which introduce flow perturbations with zero-net mass injection, the large coherent structures being synthesized from the surrounding working fluid (hence the name synthetic jet). A typical ZNMF device with different tran sducers is shown in Figure 1-1. In general, a ZNMF actuator contains three components: an oscillatory driver (examples of which are discussed below), a cavity, and an orifice or slot. Th e oscillating driver compresses and expands the fluid in the cavity by altering the cavity volume at the excitation frequency f to create pressure oscillations. As the cavity volume is decreased, the fluid is compre ssed in the cavity and expels so me fluid through the orifice.

PAGE 31

4 The time and spatial averaged ej ection velocity during this portion of the cycle is denoted jV Similarly, as the cavity volume is incr eased, the fluid expands in the cavity and ingests some fluid through th e orifice. Common orifice geometries include simple axisymmetric hole (height h, diameter d) and rectangular slot (height h, depth d and width w), as schematically shown in Figure 1-2. Downstream from the orifice, a jet (laminar or turbulent, depe nding on the jet Reynolds number RejVd ) is then synthesized from the entrained fluid and sh eds vortices when the driver oscillations exceed a critical amplitude (Utturkar et al. 2003). d h d h sin2 A ft p F acV AB UM UM d h C UM f jV f signal jV jV VolumeVolume Volume Figure 1-1: Schematic of t ypical zero-net mass flux devices interacting with a boundary layer, showing three different type s of excitation mechanisms. A) Piezoelectric diaphragm. B) Oscillat ing piston. C) Ac oustic excitation.

PAGE 32

5 Even though no net mass is injected into the embedded flow during a cycle, a non-zero transfer of momentum is establishe d with the surrounding flow. The exterior flow, if present, usually consists of a tu rbulent boundary layer (s ince most practical applications deal with such a turbulent fl ow) and is characterized by the freestream velocity U and acoustic speed c pressure gradient dPdx, radius of curvature R thermal diffusivity and displacement and momentum thicknesses. Finally, the ambient fluid is characterized by its density and dynamic viscosity h x y z d d h L z x y A B Figure 1-2: Orifice ge ometry. A) Axisymmetric. B) Rectangular. Figure 1-1 shows three kinds of drivers comm only used to generate a synthetic jet: An oscillating membrane (usually a piezo electric patch mounted on one side of a metallic shim and driven by an ac voltage). A piston mounted in the cavity (using an elec tromagnetic shaker, a camshaft, etc.). A loudspeaker enclosed in the cavity (an electrodynamic voice-coil transducer). For each of them, we are interested main ly in the volume displacement generated by the driver that will eject and ingest the fluid through the orifice. Although each driver will obviously have its own characteristics, common parameters of a generic driver are its frequency of excitation f the corresponding volume that it displaces, and the dynamic modal characteristics of the driver.

PAGE 33

6 Figure 1-3: Helmholtz resonators arrays. A) Schematic. B) Application in engine nacelle acoustic liners. Although noticeable differences exist, it is worthwhile to compare synthetic jets with the phenomenon of acoustic flow generation, the acoustic streaming extensively studied by aeroacousticians in the past (e.g., Lighthill 1978). Acoustic streaming is the result of a steady flow produced by an acoustic field and is the evidence of the generation of vorticity by the sound, wh ich occurs for example wh en sound impinges on solid boundaries. Quoting Howe (1998, p. 410), When a sound wave impinges on a solid surf ace in the absence of mean flow, the dissipated energy is usually converted direc tly into heat through viscous action. At very high acoustic amplitudes, however, free vorticity may still be formed at edges, and dissipation may take place, as in the presence of mean flow, by the generation of vortical kinetic energy which escapes from the interaction zone by selfinduction. This nonlinear mechanism can be important in small perforates or apertures. This type of flow generation could be rele vant in the application of ZNMF devices where similar nonlinear flow through the orif ice is expected. In particular, ZNMF devices are similar to flow-i nduced resonators, such as He lmholtz resonators used in acoustic liners as sound-absorber devices. As Figure 1-3 shows, a simple single degreeof-freedom (SDOF) liner consists of a pe rforate sheet backed with honeycomb cavities and interacting with a grazing flow. Similar liners wi th a second cavity (or more) are commonly used in engine nacelles to attenua te the sound noise level. More recently, Porous face sheet Honeycomb core Backing sheet A Acoustic Liners Inlet Fan Nacelle Exhaust B

PAGE 34

7 Flynn et al. (1990) and Urzyni cok and Fernholz (2002) used Helmholtz resonators for flow control applications. More details will be given in subsequent sections. Now that an overview of the problem ha s been presented along with a general description of a ZNMF device, an in-depth li terature survey is given to familiarize the reader with the existing developments on these subjects and to clearly set the scope of the current investigation. The objectives of th is research are then formulated and the technical approach described to reach these goals. Literature Review This section presents an overview of the relevant research found in the open literature. The goal is to highlight and extr act the principal featur es of the actuator and associated fluid dynamics, and to identify unresolved issues. First, the simpler yet practically significant case in which the synthe tic jet exhausts into a quiescent medium is carefully reviewed. The case in which the synthetic jet in teracts with a grazing boundary layer or crossflow is considered next. Th e survey reveals available experimental and numerical simulation data on the local inter action of a ZNMF device with an external boundary layer. In each subsection, the divers e applications that have employed a ZNMF actuator are first reviewed, as well as the diffe rent modeling approaches used. In the case of the presence of a grazing boundary layer, exampl es of applications in the field of fluid dynamics and aeroacoustics are presented where a parallel with sound absorber technology is drawn. Isolated Zero-Net Mass Flux Devices Numerous studies have addressed the funda mentals and applica tions of isolated ZNMF actuators. The list presented next is by no means exhaustive but reflects the major points and contributions to the unde rstanding of such devices.

PAGE 35

8 Applications Mixing enhancement, heat transfer, or thru st vectoring are the major applications of isolated ZNMF devices, as opposed to active fl ow control applications when the actuator is interacting with an external boundary layer that will be seen in the next section. Chen et al. (1999) demonstrated the use of ZNMF actuators to enhance mixing in a gas turbine combustor. They used two streams of hot and cold gas to simulate the mixing and they measured the temperature distri bution downstream of th e synthetic jet to determine the effectiveness of the mixing. Their experiments showed that ZNMF devices could improve mixing in a turbine jet engine without using additional cold dilution air. Similarly, modification and control of sm all-scale motions and mixing processes via ZNMF actuators were investigated by Davi s et al. (1999). Their experiments used an array of ZNMF devices placed around the pe rimeter of the primary jet. It was demonstrated that the use of these actuators made the shear layer of the primary jet spread faster with downstream distance, and the centerline velocity decreased faster in the streamwise direction, while the velocity fluctuations near the centerline were increased. In a heat transfer application, Campbell et al. (1998) explored the option of using ZNMF actuators to cool laptop computers. A small electromagnetic actuator was used to create the jet that was used to cool the pr ocessor of a laptop com puter. Using optimum combination of various design parameters, the synthesized jet was able to lower the processor operating temperature rise by 22% when compared to the uncontrolled case. Not surprisingly, it was envisi oned that optimization of the device design could lead to further improvement in the performance.

PAGE 36

9 Likewise, a thermal characterization study of laminar air jet impingement cooling of electronic components in a representativ e geometry of the CPU compartment was reported by Guarino and Manno (2001). They us ed a finite control-volume technique to solve for velocity and temperature fields (including convection, conduction and radiation effects). With jet Reynolds numbers ranging from 63 to 1500, their study confirmed the importance of the Reynolds number (rather than jet size) for effective heat transfer. Proof of the above concept was demonstrat ed with a numerical model of a laptop computer. In a thrust vectori ng application, Smith et al. (1999) performed an experiment to study the formation and interaction of two adjacent ZNMF actuators placed beside the rectangular conduit of the primary jet. Each actuator had tw o modes of operation depending on direction of the synthetic jet w ith respect to the primary jet. It was demonstrated that the primary jet could be vectored at different angles by operating only one or both actuators in different modes. La ter, Guo et al. (2000) numerically simulated these experimental results. Similarly, Sm ith and Glezer (2002) experimentally studied the vectoring effect between ZNMF devices ne ar a steady jet with va rying velocity, while Pack and Seifert (1999) did the same by employing periodic excitation. Others studies focused on characterizing isolated ZNMF actuators (Crook and Wood 2001; Smith and Glezer 1998). For instance, a careful experimental study by Smith and Glezer (1998) shows th e formation and evolution of two-dimensional synthetic jets evolving in a quiescent medium for a li mited range of jet performance parameters. The synthetic jets were viewed using schlieren images via th e use of a small tracer gas,

PAGE 37

10 and velocity fields were acqui red by hot wire anemometry at different locations in space, for phase-locked and long-time averaged signals. In these experiments, along with those fr om Carter and Soria (2002), Bra et al. (2001) or Smith and Swift (2003a), the simila rities and differences between a synthetic jet and a continuous jet have been noted and examined. Specifically, Amitay et al. (1998) and Smith et al. (1998) confirmed self-similar ve locity profiles in th e asymptotic regions via a direct comparison at the same jet Reynolds number. In terms of design characteristics, it is of practical importance to know if the ZNMF actuator synthesizes a jet via di screte vortex shedding. Utturk ar et al. (2003) derived and validated a criterion for whether a jet is formed at the orifice exit of the actuator. It is governed by the square of the orifice Stokes number 22Sd and the jet Reynolds number RejVd based on the orifice diameter d and the spatially-averaged exit velocity jV during the expulsion stro ke, which holds for both axisymmetric and two dimensional orifice geometry. Their derivati on is based on the crite rion that the induced velocity at the orifice neck mu st be greater than the suction velocity for the vortices to be shed; and was verified by numerical simulati ons and by experiments. Their data support the jet formation criterion 2Re SK, where K is 1O. In another attempt, Shuster and Smith (2004) based their criterion from PI V flow visualization fo r different circular orifice shape (straigh t, beveled or rounded) and found that it is governed by the nondimensional stroke length 0Ld and the orifice geometry, where 0L is the fluid stroke length assuming a slug flow mode l for the jet velocity profile.

PAGE 38

11 Modeling approaches Few analytical models have yet characte rized ZNMF actuator behavior, even for the simple case of a quiescent medium. Actually, most of the studies have been performed either via experimental e fforts or numerical simulations. Several attempts have been made to reduce computational costs. For instance, Kral et al. (1997) performed two-dimensional, incompressible simulations of an isolated ZNMF actuator. Interestingl y, their study was performed in the absence of the actuator per se. Instead, a sinusoidal velocity prof ile was prescribed as a boundary condition at the jet exit in lieu of simulating the actuator, including calculations in the cavity. Both laminar and turbulent jets were studied, and although the laminar jet simulation failed to capture the breakdown of the vor tex train that is commonly observed experimentally, the turbulent model showed the c ounter-rotating vortices quickly dissipating. This suggests that the modeled boundary condition could captu re some of the features of the jet, without the simulation of the flow inside the actuator cavity. In another numerical study, Rizzetta et al. (1999) used a direct numerical simulation (DNS) to solve the compressible Na vier-Stokes equations for both 2D and 3D domain. They calculated both the interior of the actuator cavity and the external flowfield, where the cavity flow was simu lated by prescribing an oscillating boundary condition at one of the cavity su rfaces. However, th e recorded profiles of the periodic jet exit velocity were used as the boundary condi tion for the exterior domain. Hence, by using this decoupling technique, they coul d calculate the exte rior flow without simultaneously simulating the flow inside the actuator cavity. To further reduce the computational cost, the planes of symmetry we re forced at the jet centerline and at the mid-span location, so only a quarter of the re al actuator was simulated. However, the 2D

PAGE 39

12 simulations were not able to capture the br eakdown of the vortices as a result of the spanwise instabilities. Cavity design earned the attention of seve ral researchers, such as Rizzeta et al. (1999) presented above; Lee and Goldstein ( 2002), who performed a 2D incompressible DNS study of isolated ZNMF actuators; and Utturkar et al. (2002) who did a thorough investigation of the sensitivity of the jet to cavity design using a 2D unsteady viscous incompressible solver using complex immersed moving boundaries on Cartesian grids. Utturkar et al. (2002) found that the plac ement of the driver inside the cavity (perpendicular or normal to the orifice exit ) does not significantly affect the output characteristics. The orifice is an important component of actuator modeling. While numerous parametric studies examined various orif ice geometry and flow conditions, a clear understanding of the loss mechanism is still lacking. Investiga tions based on orifice flows have been carried as far back as the 1950s. A comprehensive experimental study was carried out by Ingard and Is ing (1967) that examined the acoustic nonlinearity of the orifice. It was observed that the relation betw een the pressure and the velocity transitions from linear to quadratic nature as the transmitted velocity u crosses a threshold value criticu, i.e 0 p cu if criticuu and else 2 p u where is the density, 0c is the speed of sound and p is the sound pressure level. The phase relationship between the pressure fluctuations and the velocity were also investigat ed. Later, Seifert and Pack (1999), in an effort to investigate the effect of oscillatory blowi ng on flow separation, developed a simple scaling between the pres sure fluctuation inside the cavity and the velocity fluctuation. This scaling agrees with the work of Ingard and Ising (1967) and

PAGE 40

13 states that for low amplitude blowing 0upc whereas for high amplitude blowing up Recently, similar to the work by Smith and Swift (2003b) who experimentally studied the losses in an oscillatory flow through a rounded slot, Gallas et al (2004) performed a conjoint numerical and experime ntal investigation on the orifice flow for sharp edges to understand the unsteady flow be havior and associated losses in the orifice/slot of ZNMF devices exhausting in a quiescent medium It has been found that the flow field emanating from the orifice/ slot is characterized by both linear and nonlinear losses, governed by key nondimensional paramete rs such as Stokes number S Reynolds number Re, and stroke length L0. In terms of the orifice geom etry shapes, a large variet y has been used, although no one has determined the most efficient. Wh ile straight orifices are the most common, the orifice thickness to diameter ratio is widely varied. It ranges from perforate orifice plates (see discussion on Helmholtz resona tors) having very small thickness with the viscous effect confined at the edges where the vortices ar e shed, to long and thick orifices wherein the flow could be assumed fully-d eveloped (Lee and Goldstein 2002). In the case of a thick orifice, the flow can be modele d as a pressure driven oscillatory pipe or channel flow where the so-called Richardson effect may appear at high Stokes number of 10O (Gallas et al. 2003a). Furthermore, Ga llas (2002) experimentally determined a limit of the fully-developed flow assumption th rough a cylindrical orif ice in terms of the orifice aspect ratio 1hd Otherwise, the orifice could also have round edges or a beveled shape (NASA workshop CFDVal-Case 2, 2004). Another de sign, referred to as the springboard

PAGE 41

14 actuator, has been proposed by Jacobson and Reynolds (1995), in which both a small and a large gap are used for the slot. In the case of the presence of an external boundary layer, Bridges and Smith (2001) and Milanovic and Zaman (2005) experimentally studied different orifice shapes such as clustered, sh arp beveled, or with different angles with respect to the incoming flow. The principa l changes in the flow field between the different orifices studied were mostly found in the local vicinity of the orifice actuator, and less in the far (or global) field, for th e specific flow conditi ons used. Finally, the predominant difference between the different orif ices is that of a ci rcular orifice versus rectangular slot. Experimental studies often employ these two geometries, whereas numerical simulations preferably use the latter for computational cost considerations. In terms of analytical modeling of ZNMF actuators few efforts have been conducted, even for the simple case of a quies cent medium. Nonetheless, Rathnasingham and Breuer (1997) developed a simple anal ytical/empirical model that couples the structural and fluid characteris tics of the device to produce a set of coupled, first-order, non-linear differential equations. In their empirical model, the flow in the sl ot is assumed to be inviscid and incompressible and the uns teady Bernoulli equation is used to solve the oscillatory flow. Crook et al. (1999) experimentally compared Rathnasingham and Breuers simple analytical model and found th at the agreement betw een the predicted and measured dependence of the centerline velocity on the orifice diamet er and cavity height was poor, although the trends were similar. This discrepancy is mainly due to the lack of viscous effect in the orifice model, as we ll as the Stokes number dependence inside the orifice that is not considered by the flow model and which could lead to a non-parabolic velocity profile.

PAGE 42

15 Otherwise, with the aim of achieving real -time control of synthetic jet actuated flows, Rediniotis et al. (2002) derived a loworder model of two dimensional synthetic jet flows using proper orthogonal decomposition (P OD). A dynamical m odel of the flow was derived via Galerkin projection for sp ecific Stokes and Reynolds number values, and they accurately modeled the flow field in th e open loop response with only four modes. However, the suitability of this approach as a general analysis/design tool was not addressed. More recently in Gallas et al. (2003a), the author presented a lumped element model of a piezoelectric-driven synthetic jet actuator exhausting in a quiescent medium. Methods to estimate the parame ters of the lumped elemen t model were presented and experiments were performed to isolate diffe rent components of the model and evaluate their suitability. The model was applied to two prototypical ZNMF actuators and was found to provide good agreement with the meas ured performance over a wide frequency range. The results reveal that lumped elem ent modeling (LEM) can be used to provide a reasonable estimate of the frequency response of the device as a function of the signal input, device geometry, and mate rial and fluid properties. Additionally, based on this modeling appr oach, Gallas et al. (2003b) successfully optimized the performance of a baseline ZNMF actuator for specific applications. They also suggest a roadmap for the more general optimal design synthesi s problem, where the end user must translate desirable actuator ch aracteristics into quant itative design goals. Zero-Net Mass Flux Devices with the Addition of Crossflow By now letting a ZNMF act uator interact w ith an external boundary layer or grazing flow, a wide range of applications can be envisioned, from active control of separation in aerodynamics to sound abso rber technology in aeroacoustics.

PAGE 43

16 Fluid dynamic applications While the responsible physical mechanism is still unclear, it ha s been shown that the interaction of ZNMF actuato rs with a crossflow can disp lace the local streamlines and induce an apparent (or virtual) change in the shape of the surface in which the devices are embedded and when high frequency forci ng is used (Honohan et al. 2000; Honohan 2003; Mittal and Rampuggoon 2002). Changes in the flow are thereby generated on length scales that are one to two orders of magnitude larger than the characteristic scale of the jet. Furthermore, ZNMF devices have been de monstrated to help in the delay of boundary layer separation on cy linders and airfoils, hence generating lift and reducing drag or also increasing the stall margin for the latter. For cylinders, the case of laminar boundary layers has been investigated by Amita y et al. (1997), and the case of turbulent separation by Bra et al. (1998). For airfoils research has been conducted, for example, by Seifert et al. (1993) and Greenblatt and W ygnanski (2002). However, in ZNMF-based separation control, key issues such as op timal excitation frequencies and waveforms (Seifert et al. 1996; Yehoshua and Seifert 2003), as well as pressure gradient and curvature effects still remain to be rigorously investigated (Wygnanski 1997). For instance, it has been shown by some re searchers that control authority varies monotonically with jVU (Seifert et al. 1993, 1996, 1999; Glezer and Amitay 2002; Mittal and Rampuggoon 2002) up to a point where a further increase will likely completely disrupt the boundary layer, and where jV can be the peak, rms or spatialaveraged jet velocity during th e ejection portion of the cycle. On the other hand, control authority has a highly nonmonotonic variation with F (Seifert and Pack 2000b;

PAGE 44

17 Greenblatt and Wygnanski 2003; Glezer et al. 2003. Amitay and Glezer 2002), hence the existing current debate in c hoosing the optimum value for F, where nFff represents the jet actuation frequency f that is non-dimensiona lized by some natural frequency n f in the uncontrolled flow. In fact, it is still unclear about what definition of n f should be used, since it depends on the flow conditions. For example, n f could either be the characteristic frequency of the separa tion region, the vortex shedding frequency in the wake, or the natural vorte x rollup frequency of the shear layer, depending on whether separation delay control or separation alle viation control is sought (Cattafesta and Mittal, private communication, 2004). As noted earlier, another key issue in ZNMF devices is the form of the excitation signal. Researchers have used single si nusoids, but low-freque ncy amplitude-modulated (AM) signals (Park et al. 2001), burst mode signals (Yehoshua and Seifert 2003), and various envelopes have also been investig ated (Margalit et al 2002; Wiltse and Glezer 1993). From these studies, it seems clear th at the input signal waveform should be carefully chosen function of the natural frequency of uncontrolled flow n f as discussed above. In addition, it emphasizes the fact th at the dynamics of the actuator should not be ignored. Also of interest for flow control applica tions is the interaction of multiple ZNMF actuators (or actuator arrays) with an external boundary laye r, which has been experimentally investigated by several rese archers (Amitay et al. 1998; Watson et al. 2003; Amitay et al. 2000; Wood et al. 2000; R itchie and Seitzman 2000). However, the relative phasing effect between each actuator wa s usually not investigated. On the other hand, Holman et al. (2003) i nvestigated the effect of ad jacent synthetic jet actuators,

PAGE 45

18 including their relative phasing, in an airfoil separation cont rol application. They found that, for the single flow condition studied, separation control was independent of the relative phase, and also that for low actuation amplitudes, actuator placement on the airfoil surface could be critical in achieving desired flow cont rol. Similarly, Orkwis and Filz (2005) numerically investigated the e ffect of the proximity between two adjacent ZNMF actuators in crossflow and found that favorable interactions between the two actuators could be achie ved within a certain distance that separates them, but the optimal separation is different whether they are in phase or out of phase from each other. Finally, to the authors knowledge, besides a first scaling analysis performed by Rampunggoon (2001) which is based on a parame terization of the successive moments and skewness of the jet velocity profile, al ong with the study by McCormick (2000) that presents an electro-acoustic model to descri be the actuator characte ristics (in a similar manner to the lumped element modeling appr oach used by Gallas et al. 2003b), no other low-order models have been developed for a ZNMF actuator interactin g with an external boundary layer. Aeroacoustics applications For the past fifty years, people in the ac oustic community have tried to predict the flow past an open cavity (Elder 1978; Mei ssner 1987) or a Helmholtz resonator (Howe 1981b; Nelson et al. 1981). This is a generi c denomination for applications such as aircraft cavities, acoustic liner s, open sunroofs, mufflers for intake and exhaust systems, or simply perforates. This research lies in the domain of acoustic s of fluid-structure interactions which has generated significan t attention from numerous researchers. As noted earlier, a paralle l with ZNMF actuators can be draw with the study of acoustic liners, shown in Figure 1-3B. More specifically, the goal is usually to compute

PAGE 46

19 the acoustic impedance of the liner, since the notion of impedance simply relates a particle or flow velo city to the corresponding pressure. Such knowledge is required to design and implement liners in an engine nacelle. However, researchers are still facing gr eat challenges in extracting suitable impedance models of these perforate liners, usually composed of Helmholtz resonators. In fact, because of the presence of flow over the orifice, rigorous mathematical modeling of the interaction mechanisms are very di fficult to obtain, and the present state of analytical and numerical codes do not allow direct modeling of these interactions at relevant Reynolds numbers, as seen ea rlier in the case of ZNMF actuators. Consequently, most of the existing models of grazing flow past Helmholtz resonators are empirical or, at most, simplified mathematically models. Modeling approaches First of all, in terms of impedance mode ls of acoustic liners, Dquand et al. (2003) and Lee and Ih (2003) provide a good review of the existing models, along with their intrinsic limitations. The main distinctions between the proposed models lay first in the orifice model, then in the characterization of the grazing flow, and finally in the addition or not of a mean bias flow th rough the orifice (not to be confused with grazing flow over the orifice). The cavity is often modeled as a classical resonator ha ving a linear response (mass-spring system). When a bias flow is included, the prediction of its effect on the orifice impedance is usually carried out within the mechanism of sound-vortex interaction. And when grazing flow is present, most of th e orifice impedance models are either deduced from experimental data or rely on empiricism. With regards to orifice modeling, Ingard and Ising (1967) included effective end corrections in their impedance model that ta ke care of the acoustic nonlinearity of the

PAGE 47

20 orifice (mainly dependent on the ratio of th e acoustic orifice mome ntum to the boundary layer momentum when a grazing flow is incl uded). Depending on the flow conditions of the application, either low frequency or high frequency assumptions are used to model the flow through the orifice. Also, standard assumption is th at the orifice dimensions are much smaller than the acoustic wavelength of interest. Another important point to note is on the porosity factor of a perforate plate. Because of the direct applicati on of such a device to engine nacelle liners, the solution for a single orifice impedance is usually derive d and is then extended to multiple holes geometry. The simple relation between the sp ecific impedance of a perforate and a single orifice, 0,0pZZ holds when the orifices are not t oo close from each other in order to alleviate any jetting interaction effect between them. Here, the porosity factor is defined by holeshole areatotal area N, where holesN is the number of orifices in the perforate. Ingard (1953) states that the re sonators can be treated independently of each others if the distance between the orifices is greater than half of the acoustic wavelength. Otherwise, to account for the interaction effect between multiple holes, Foks function is usually employed (Melling 1973). The grazing flow is commonly characte rized as a fully-developed turbulent boundary layer (or fully-developed turbulent pipe flow), alth ough some investigations do not, which may lead to difficulties for comparison sake. The parameters extracted from the external boundary layer are usually the Mach number M friction velocity u or boundary layer thickness Although most of the models are empirical or semi-e mpirical, some are still analytical. The first models proposed were based on linear stability analysis where the

PAGE 48

21 shear layer (or grazing flow) is modeled using li near inviscid theory for infinite parallel flows. Later, more formal linearized mode ls have been emphasized. For instance, Ronneberger (1972) described th e orifice flow in terms of wave-like disturbances of a thin shear layer over th e orifice. Howe (1981a) modeled the grazing flow interaction as a Kelvin-Helmholtz instability of an infinite ly extended vortex sheet in incompressible flow, where the vortex strength is tuned to compensate the singularity of the potential acoustic flow at the downstream edge in orde r to meet the Kutta condition. Also, Elder (1978) describes the shear layer displacemen t as being shaped by a Kelvin-Helmholtz wave, while an acoustic response of the res onant system is modeled by an equivalent impedance circuit of a resonator adopted from organ pipe theory. He then treats the flow disturbances using linear shear layer instabil ity models and the oscillation amplitude is assumed to be limited by the nonlinear orifi ce resistance. Nelson et al. (1981, 1983) separated the total flow field into a purely vortical flow fiel d (associated with the shed vorticity of the grazing flow) where the vorticity of the shear layer is concentrated into point vortices traveling at a constant velocity on the straight line joining the upstream to the downstream edge, plus a po tential flow (unsteady part associated with the acoustic resonance). They also provide d a large experimental database in a companion paper that has been used by others (Meissner 2002; D quand et al. 2003). Innes and Creighton (1989) used matched asymptotic expansions for small disturbances to solve the nonlinear differential equations, the resonator wa veform containing a smooth outer part and the boundary layer a rapid change; then approximations were found in each region along with approximate values for th e Fourier coefficients. Also Jing et al. (2001) proposed a linearized potential flow model that uses the particle velocity continuity boundary

PAGE 49

22 condition rather than the more frequently used displacement in order to match the flowfields separated by the shea r layer over the orifice. Al l those models however still remain linear (or nearly so) and thus carry inherent assumption limitations. The simplified mathematical models descri bed above have been used as starting point to construct empirical models. Thes e are based upon parameters such as the thickness h and diameter d of the orifice/perforate, plate porosity grazing flow velocity (mean velocity U or friction velocity u ), Strouhal number StdU (U being some characteristic ve locity), or Stokes number 2Sd The major empirical models found in the open literature are pr oposed by Garrison (1969), Rice (1971), Bauer (1977), Sullivan (1979), Hersh and Walker (1979), Cu mmings (1986), or Rao and Munjal (1986), and Kirby and Cummings (1998). They differ from each other depending on whether they include orifice nonlin ear effects, orifice lo sses (viscous effect, compressibility), end corrections, single or clus tered orifices, radiati on impedance, etc. But most of all, and more interestingly, they use different functional forms for the chosen parameters that govern the physical behavior of the phenomenon, such as ,,,,,,... fhdkdStUu, as shown in Appendix A where some of these models are described in details. It should be noted th at each of them are applicable for a single application over a specific parameter ra nge (muffler, acoustic liner, etc.). Other less conventional approaches have also been attempted. For instance, Mast and Pierce (1995) used describing-functions an d the concept of a feedback mechanism. In this approach, the resonator-flow system is treated as an autonomous nonlinear system in which the limit cycles are found using desc ribing-function analysis Meissner (2002) gave a simplified, though still accurate, version of this m odel. Similarly, following

PAGE 50

23 Zwikker and Kostens (1949) theory for propagation of sound in channels, Sullivan (1979) and Parrott and Jones ( 1995) used transmission matrices to model parallel-element liner impedances. In another effort, Lee a nd Ih (2003) obtained an empirical model via nonlinear regression analysis of results co ming from various parametric tests. Furthermore, acoustic eduction techniques ha ve been used to determine the acoustic impedance of liners, such as a finite el ement method (employed by NASA, see Watson et al. 1998), that iterates on the numerical solutio n of the two dimensional convective wave equation to determine an impedance that reproduces the measured amplitudes and phases of the complex acoustic pressures; or a graz ing flow data analysis program (employed by Boeing, see Jones et al. (2003) and references therein for details) th at conducts separate computations in different regions to match the acoustic pressure and particle velocity across the interfaces that determines the moda l amplitudes in each of the regions; or also a two dimensional modal propagation met hod based on insertion loss measurements (employed by B. F. Goodrich, see Jones et al (2003) and references therein for details) that determines the frequency-dependent acoustic impedance of the test liner. Jones et al. (2003) reviewed and compared these impedance eduction techniques. Finally, as noted earlier, a few studies have been performed using numerical simulations. Indeed, as can be seen in Liu and Long (1998) and Ozyrk and Long (2000), it is computationally quite expens ive, difficult to implement, and strong limitations on the geometries are required. However, a promising numerical study by Choudhari et al. (1999) gives valu able insight into the flow p hysics of these devices, such as the effect of acoustic nonlineari ty on the surface impedance.

PAGE 51

24 Another important point concerns the meas urement techniques used to acquire the sample data which upon most of the model ar e derived, from simple to more elaborate curve fitting. The two microphone technique introduced by Dean (1974) is commonly employed for in situ measurements of the local wall acoustic im pedance of resonant cavity lined flow duct. This technique uses two microphones, one placed at the orifice exit of the resonator, the othe r flushed at the cavity bottom. Then a simple relationship for locally reactive liner betw een the cavity acoustic pressure and particle velocity is extracted, which is based on the continuity of particle velocities on either side of the cavity orifice (or surfac e resistive layer). However, the main drawbacks of this widely used method reside in the position of the micr ophone in front of the liner that must be in the hydrodynamic far field but at a distance less than the acoustic wavelength, and also in the grazing boundary layer thickness. Differ ent experimental apparatus are given in Appendix A for clarification and illustration. As an example, five models from the lit erature are presented in Appendix A that are thought to be interesting, either for the quality of the experiments which upon the model fits have been based on, or for the functional form they offer in terms of the dimensionless parameters which are believed to be of certain relevance. To some extent, they are all based on experimental data. From all the models currently available, it is not obvious wh ether one model will perform better than another, which is ma inly due to the wide range of possible applications, the limitations in the experimental data on which the semi-empirical models heavily rely, and because even the mathema tical models have their own limitations. However, the rich physical in formation carried within thes e semi-empirical models and

PAGE 52

25 the corresponding data on which they are based will undoubtfully aid the development of reduced-order models in ZNMF actuato r interacting with a grazing flow. Unresolved Technical Issues By surveying the literature, i.e. looking at the flow mechanism of isolated ZNMF actuators to more complex behavior when the actuator is interacting with an incoming boundary layer, along with examples of sound absorber technology, several key issues can be highlighted that still remain to be addressed. This subsection lists the principal ones. Fundamental flow physics. Clearly, there still exists a lack in the fundamental understanding of the flow mechanisms that govern the dynamics of ZNMF actuators. While the cavity design is well understood, the orifice modeling and especially the effect of the interaction with an external boundary la yer requires more in-depth consideration. Also, whether performing experimental studies or numerical simula tions, researchers are confronted with a huge parameter space that is time consuming and requires expensive experiments or simulations. Hence the development of simple physics-based reducedorder models is primordial. 2D vs. 3D. While most of the numerical simulations are performed for twodimensional problems, three-dimensionality e ffects clearly can be important, especially to model the flow coming out of a circular or ifice as shown in Rizzeta et al. (1998) or Ravi et al. (2004) that also found distinct a nd non negligible threedimensional effects of the flow. Compressibility effects. Usually, the entire flow field is numerically solved using an incompressible solver. However, such an assumption, although valid outside the actuator, may be violated inside the orifice at high jet velocity and, more generally, inside

PAGE 53

26 the cavity due to the acoustic compliance of the cavity. Indeed, th e cavity acts like a spring that stores the potential energy produced by the driver motion. Lack of high-resolution experimental data. Most of the experimental studies employed either Hot Wire Anemometry (HWA ), Particle Image Velocimetry (PIV) or Laser Doppler Velocimetry (LDV) to meas ure the flow. However, each of these techniques has shortcomings, as briefly enumerated below. In the case of HWA, since the flow is hi ghly unsteady and by definition oscillatory, its deployment must be carefully envisaged, especially considering the de-rectification procedure used to obtain the reversal flow. Since it is an intrusive technique that may perturb the flow, other issues are that it is a single point measurement (hence the need to traverse the whole flow fiel d), problems arise with measurements near zero velocity (transition from free to forced convection), and the accuracy may be affected by the calibration (sensitivity), the local temperat ure, or some conductive heat loss. With regards to PIV, although the main advantage resides in the fact that it is a non-intrusive flow visualization technique th at captures instantaneous snapshots of the flow field, the micro/meso scale of ZNMF devices requires very high resolution in the vicinity of the actuator orifice in order to obtain reasonable accuracy in the data. This is difficult to achieve using a sta ndard digital PIV system. Finally, a large number of samples are requi red in order to get proper accuracy in the data from LDV measurement, and excellent spatial resolution is difficult to achieve due to the finite length of the probe vol ume. Also, since LDV is a single point measurement, a traversing probe is required in order to map the entire flow field.

PAGE 54

27 Lack of accurate low-order models. Clearly, the few reduced-order models that are present so far are not sufficient to be able to capture the essential dynamics of the flow generated by a ZNMF actuator. Better models must be constructed to account for the slot geometry and the impact of the crossflow on the jet velocity profile. The five models of grazing flow past Helmholtz resonators summarized in Appendix A reveal the disparity in the impedance expressions as well as in the range of applications (see Table A-1). Clearly, the task of extracting a validated semi-empirical model is far from trivial. But leveraging past experience is critical to yielding accurate low-order models for implementation of a ZNMF actuator. Objectives The literature survey presented above has permitted the identification of key technical issues that remain to be resolved in order to fully implement ZNMF actuators into realistic applications. Currently, it is difficult for a prospective user to successfully choose and use the appropriate actuator that will satisfy specific requirements. Even though many designs have been used in the literature, no studies have systematically studied the optimal design of these devices. For instance, how large should the cavity be? What type of driver is most appropriate to a specific appli cation? Possibilities include a low cost, low power piezoelectric-d iaphragm, an electromagnetic or mechanical piston that will provide large flow rate but may require significant power, or a voice-coil speaker typically used in audio applications? What orifice geometry should be chosen? Options include sharp versus rounded edge s, large versus short thickness, an axisymmetric versus a rectangular slot? Clearly, no validated tools are currently available for end users to address these ques tions. Generally, a tr ial and error method

PAGE 55

28 using expensive experimental studies and/or time consuming numerical simulations have been employed. The present work seeks to address thes e issues by providing a clear physical understanding of how these devices behave an d interact with and without an external flow, and by developing and validating reduc ed-order dynamical models and scaling laws. Successful completion of these objectives will ultimately aid in the analysis and development of design tools for sizing, desi gn and deployment of ZNMF actuators in flow control applications. Approach and Outline of Thesis To reach the stated objectives, the following technical approach has been employed. First, the identification of outst anding key issues and th e formulation of the problem have been addressed in this chapter by surveying the literature concerning the modeling in diverse applicati ons of ZNMF actuators and ac oustic liner technology. The relevant information about the key device para meters and flow conditions (like the driver configuration, cavity, orifice shape, or the external boundary layer parameters) are thus extracted. Before investigating how a ZNMF device interacts with an external boundary layer, the case of an isolat ed ZNMF actuator must be fu lly understood and documented. This is the subject of Chapter 2. An isolated ZNMF device is first characterized and the relevant parameters are defined. Then, the previous work done by th e author in Gallas et al. (2003a) is summarized. Their work discusses a lumped element model of a piezoelectric-driven ZNMF actuator. One goal of the present work is to extend their model to more general devices and to remo ve, as far as possible, some restricting limitations, especially on the orifice loss coefficient. Consequently, a thorough nondimensional analysis is first carried out to extract the physics behind such a device.

PAGE 56

29 Also, some relevant modeling issues are discussed and review ed, for instance on the orifice geometry effects and the driving transducer dynamics. Th en, to study in great details the dynamics of isolated ZNMF actuato rs, an extensive experimental investigation is proposed where various test actuator configurations are ex amined over a wide range of operating conditions. The experimental se tup is described in Chapter 3.

PAGE 57

30 CHAPTER 2 DYNAMICS OF ISOLATED ZERO-NET MASS FLUX ACTUATORS Several key issues were highlighted in the introduction chap ter that will be addressed in this thesis. This Chapter is fi rst devoted to familiarize the reader with the dynamics of ZNMF actuators, their behavior an d inherent challenges in developing tools to accurately model them. One goal, before addressing the general case of the interaction with an external boundary laye r, is to understand the nonlinear dynamics of an isolated ZNMF actuator. This chapter is therefore enti rely dedicated to the analysis of isolated ZNMF actuators issuing into a quiescent medium, as outlined below. The device is first characterized and the relevant parameters defined in order to clearly define the scope of the present invest igation. The previous work performed by the author in Gallas et al. (2003a) is next summarized. Their work discusses a lumped element model of a piezoelectric-driven ZN MF actuator that rela tes the output volume flow rate to the input voltage in terms of a tr ansfer function. Their model is extended to more general devices and solutions to remove some restricting limitations are explored. Based on this knowledge, a thorough dimensional analysis is then carried out to extract the physics behind an is olated ZNMF actuator. A dimens ionless linear transfer function is also derived for a generic driver configur ation, which is thought to be relevant as a design tool. It is shown th at a compact expression can be obtained regardless of the orifice geometry and regardless of the driver configuration. Fina lly, relevant modeling issues pointed out in the first chapter are di scussed and reviewed. Some issues are then addressed, more particularly on the modeli ng of the orifice flow where a temporal

PAGE 58

31 analysis of the existing lumped element mode l is proposed along with a physically-based discussion on the orifice loss mechanism. Issues on the dynamics of the driving transducer are discussed as well. Finally, a test matrix construc ted to study the ZNMF actuator dynamics is presented. Characterization and Parameter Definitions Figure 1-1 shows a typical ZNMF actuator, where the geometric parameters are shown. First of all, it is worthwhile to define some precise quantities of interest that have been used in the published literature and try to unify them into a generalized form. For instance, people have used the im pulse stroke length, some spa tially or time averaged exit velocities, or Reynolds numbers based either on the circulation of vortex rings or on an averaged jet velocity to characterize the osci llating orifice jet flow. Here, an attempt to unify them is made. The inherent nature of the jet is both a f unction of time (oscillatory motion) and of space (velocity distribution across the orifice exit area). It is also valuable to distinguish the ejection from the ingestion portion of a cycle. Many researchers (Smith and Glezer 1998, Glezer and Amitay 2002) characterize a synthetic jet based on a simple slug velocity profile model that incl udes a dimensionless stroke length 0Ld and a Reynolds number ReCLVCLVd based on the velocity scale (avera ge orifice velocity) such that /2 0 0T CLCLVfLfvtdt (2-1) where CLvt is the centerline velocity, 1 Tf is the period, thereby 2 T representing half the period or the time of discharge for a sinusoidal signal, and 0L is the distance that

PAGE 59

32 a slug of fluid travels away from the orifice during the ej ection portion of the cycle or period. In addition, Smith and Glezer (1998) ha ve employed a Reynolds number based on the impulse per unit length (i.e., the moment um associated with the ejection per unit width), 00ReI I d where the impulse per unit width is defined as 2 2 0 0T CL I dvtdt. (2-2) Or similarly, following the physics of vortex ring formation (Glezer 1988), a Reynolds number, 0Re is used based on the initial ci rculation associated with the vortex generation process, with 0 defined by 2 22 0 011 222T CLCLT vtdtV (2-3) Alternatively (Utturkar et al. 2003), a spatial and time-av eraged exit velocity during the expulsion stroke is used to define the Reynolds number RejVd where the timeaveraged exit velocity jV is defined as 22 00212 ,nTT jn S nVvtxdtdSvtdt TST (2-4) where vt is the spatial averaged velocity, nS is the exit area of the orifice neck, and x is the cross-stream coordinate (see Figure 1-2 for coordinates definition). For general purposes, instead of limiting ourselves to a si mple uniform slug profile, the latter definition is considered thr oughout this dissertation.

PAGE 60

33 Notice that for a slug profile, it can be shown that the average orifice velocity scale defined above in Eq. 2-1 and Eq. 2-4 is related by 2CLjVV Similarly, 0/CLLdVfd is closely related to the i nverse of the Strouhal number St since 02 1 2jj CLVV LV dfdddSt (2-5) and since 221RejjVVd StddS (2-6) the following relationship always holds 0 21Re Ld StS (2-7) where is the time of discharge (= T/2 for a sinusoidal signal) and 2Sd is the Stokes number. The use of the Stokes number to characterize a synthetic jet and the relationship to the Strouhal number were prev iously mentioned in Utturkar et al. (2003) and Rathnasingham and Breuer (1997). Th e corresponding rela tions between the different definitions are su mmarized in Table 2-1. Correspondingly, the volume flow rate comi ng out of the orifi ce during the ejection part of the cycle can be defined as 01 ,njnjn SQvtxdtdSVS (2-8) And clearly, since we are dealing with a zero-net mass flux actuator, the following relationship always holds ,total,ex,in0jjjQQQ (2-9) where the suffices ex and in stand fo r expulsion and inges tion, respectively.

PAGE 61

34 Table 2-1: Correspondence between synthetic jet parameter definitions 0L d 1 21Re StS 0ReI, 0Re Re As seen from the above definitions, once a velocity or time scale has been chosen, a length scale must be similarly selected for the orifice or slot. Figur e 1-3 show two typical orifice geometries encountered in a ZNMF act uator, and give the geometric parameters and coordinates definition. Noti ce that the orifice is straight in both cases. No beveled, rounded or other shapes are taken into ac count, although other geometries have been investigated (Bridges and Smith 2001; Smith and Swift 2003b; Milanovic & Zaman 2005; Shuster and Smith 2004). Throughout this dissertation, the primary length scale used is the diameter or depth of the orifice d. The spanwise orifice width w is used as needed for discussions related to a rectangular slot and the height h is a third characteristic dimension. Clearly, if d is chosen as the characteristic length scale, then wd and hd are key nondimensional parameters. Lumped Element Modeling Summary of Previous Work A lumped element model of a piezoelectricdriven synthetic jet actuator exhausting in a quiescent medium has been recently de veloped and compared with experiments by Gallas et al. (2003a). In lumped element m odeling (LEM), the individual components of a synthetic jet are modeled as elements of an equivalent electrical circuit using conjugate power variables (i.e., power = generalized fl ow x generalized effort). The frequency response function of the circuit is de rived to obtain an expression for jacQV the volume flow rate per applied voltage LEM provides a compact analytical model and valuable

PAGE 62

35 physical insight into the dependence of the device behavior on geometric and material properties. Methods to estimate the parame ters of the lumped element model were presented and experiments were performed to isolate different components of the model and evaluate their suitability. The model was applied to two prototyp ical synthetic jets and found to provide very good agreement with the measured performance. The results reveal the advantages and shortcomings of th e model in its present form. With slight modifications, the model is applicable to any type of ZNMF device. Piezoceramic Composite Diaphragm Orifice Cavity Vac 1:aP I MaD Qd RaNMaNMaRadRaO QcQj Ceb CaD CaC i Ii Vac electrical domain acoustic/fluidic domain RaD electroacoustic coupling d h Figure 2-1: Equivalent circuit model of a piezoelectric-d riven synthetic jet actuator. The equivalent circuit mode l is shown in Figure 2-1. The structure of the equivalent circuit is explai ned as follows. An ac voltage acV is applied across the piezoceramic to create an effective acoustic pressure that drives the diaphragm into oscillatory motion. This re presents a conversion from th e electrical to the acoustic

PAGE 63

36 domain and is accounted for via a transformer with a turns ratio a An ideal transformer (i.e., power conserving) converts energy fr om the electrical to acoustic domain and converts an electrical impedan ce to an acoustic impedance. The motion of the diaphragm can either compress the fluid in the cavity (m odeled, at low frequencies, by an acoustic compliance aCC ) or can eject/ingest fluid through th e orifice. Physically, this is represented as a volume velocity divider, dcjQQQ The goal of the actuator design is to maximize the magnitude of the volume flow rate through the orifice per applied voltage jacQV given by (Gallas et al. 2003a) 432 43211j a acQs ds Vsasasasas (2-10) where ad is an effective piezoelectric constant obtained from composite plate theory (Prasad et al. 2002), sj and 124,,, aaa are functions of the material properties and dimensions of the piezoelectric di aphragm, the volume of the cavity orifice height h, orifice diameter d, fluid kinematic viscosity and sound speed 0c and are given by 1 2 3 4, , and .aDaOnlaNaDaCaOnlaN aDaRadaNaDaCaRadaNaCaDaDaOnlaN aCaDaDaOnlaNaRadaNaD aCaDaDaRadaNaCRRRCRR aCMMMCMMCCRRR aCCMRRMMR aCCMMM (2-11) In Eq. 2-11, aDC aD R and aD M are respectively the acoustic compliance, resistance and mass of the diaphragm. aCC is the acoustic compliance of the cavity. aN R aN M and aRadM are respectively the acoustic resistance, mass and radiation mass of the actuator

PAGE 64

37 orifice, while aOnl R represents the nonlinear resistance term associated with the orifice flow discharge and is a function of the volume flow rate jQ 0 500 1000 1500 2000 2500 3000 0 5 10 15 20 25 30 35 Frequency (Hz) Magnitude of maximum velocity (m/s) 0 500 1000 1500 0 10 20 30 40 50 60 70 Frequency (Hz) Magnitude of maximum velocity (m/s) Figure 2-2: Comparison between the lumped element model and experimental frequency response measured using phase-locked LDV for two protot ypical synthetic jets (Gallas et al. 2003a). The lumped parameters in the circuit in Figure 2-1 represent generalized energy storage elements (i.e., capacitors and inductors) and di ssipative elements (i.e., resistors). Model parameter estimation techniques, assu mptions, and limitations are discussed in Gallas et al. (2003a). The capability of the t echnique to describe the measured frequency response of two prototypical synthetic jets is shown in Figure 2-2. The case in the left half of the figure reveals the 4th-order nature of the frequency response. The two resonance peaks are related to the diaphragm natural frequency d f and the Helmholtz frequency H f thereby demonstrating the potential significance of compressibility effects. The case in the right half of the figure reveals how the model can be tuned to produce a device with a single resonance fre quency with large output velocities. The important point is that the model give s a reasonable estimate of the output of interest (typically within 20%) with minimal effort. The power of LEM is its simplicity

PAGE 65

38 and its usefulness as a design tool. LEM can be used to provide a reasonable estimate of the frequency response of the device as a f unction of the signal input, device geometry, and material and fluid properties. Limitations and Extensions of Existing Model The study performed in Gallas et al. (2003a) was restricted to ax isymmetric orifice geometry and the oscillating pressure driven flow inside the pipe was assumed to be laminar and fully-developed. Also, a piezoel ectric-diaphragm was chosen to drive the actuator. A straightforward extension of their model is that of a rectangular slot model. Appendix C provides a derivation of the solution of oscillating pressure driven flow in a 2D channel, assuming the flow is laminar, incompressible and fully-developed. The low frequency approximation then yields the lumped element parameters. Hence, for a 2D channel orifice the acoustic resistance and mass are found to be, respectively, 33 22aNh R wd and 3 52aNh M wd (2-12) Similarly, also of interest is the acoustic ra diation impedance for a rectangular slot. The acoustic radiation mass aRadM is modeled for 1kd as a rectangular piston in an infinite baffle by assuming that the rectangular slot is mounted in a plate that is much larger in extent than the slot size (Meissner 1987), 0 221 ln2 216aRadaRadc wd XMkd wddw kw (2-13) where aRadX corresponds to the acoustic radiation reactance.

PAGE 66

39 Another extension of their work can be made with regards to th e driver employed. As shown in the next section, a convenien t expression of the actuator response can be made in terms of the nondi mensional transfer function jdQQ the ratio of the jet to driver volume flow rate. Hence, by decoup ling the driver dynamics from the rest of the actuator one can easily implement any type of driver, under the condition that its dynamics are properly modeled. In the LEM representation, the dr iving transducer is represented in terms of a circ uit analogy; it thus requires th at the transducer components must be fully known, whether the driver tr ansducer is a piezoelectric-diaphragm, a moving piston (electromagnetic or mechanical), or an electromagnetic voice-coil speaker. A more detailed discussion on this issue is prov ided towards the end of this chapter. The most restricting limitations of the lumped element model in its current state, as presented above, are found in the orifice modelin g. First, the model cannot handle orifice geometries other than a straight pipe (or 2D channel, as seen above), i.e. no rounded edges or beveled shapes can be considered However, by analogy with minor losses in fluid piping systems, this should onl y affect the nonlinear resistance term aOnl R associated with the discharg e from the orifice, and not aOlinaN R R that represents the viscous losses due to the a ssumed fully-developed pipe flow. The nonlinear resistance term aOnl R is approximated by modeling the orifice as a generalized Bernoulli flow meter (White 1979; McCormick 2000), 20.5dj aOnl nKQ R S (2-14) where jQ is the amplitude of the jet volume flow rate, and dK is a dimensionless loss coefficient that is assumed, in this ex isting model, to be unity. In practice, dK is a

PAGE 67

40 function of orifice geometry, Reynolds numbe r, and frequency. Hence, a detailed analysis on the loss coeffici ent for various orifice shapes should yield a more accurate expression in terms of modeling the associated nonlinear resistance. This is actually one of the goals of this dissertation and this is systematically investigated in subsequent chapters. A second restricting assumption found in th e orifice model of Gallas et al. (2003a) comes from the required fully-developed hypothe sis of the flow inside the orifice. Clearly this limits the orifice design to a sufficiently large aspect ratio hd or low stroke length compare to the orifice height h The lumped parameters of the orifice impedance are based on the steady solution for a fully-d eveloped oscillating pi pe/channel flow (see Appendix C). In addition, th e author experimentally found (Gallas 2002) that reasonable agreement was achieved between the lumped element model and the measured dynamic response of an isolated ZNMF actua tor when the orif ice aspect ratio hd approximately exceeded unity. Figure 2-3 below reproduces this fact for four different aspect ratios, where the orifices considered were axis ymmetric, and the model prediction of the centerline velocity was compared to phase-loc ked LDV measurements versus frequency. Note that the diaphragm damping coefficient D was empirically adjusted to match the peak magnitude at the frequency governed by the diaphragm natural fr equency. Clearly, a careful study of the entrance effect in straight pipe/channe l flow should greatly enhance the completeness and validity of the orifice m odel in its current form, such a model being able to be applied to all sort s of straight orifices, from lo ng neck to short perforates. Again, additional insight into this issue is discussed at the end of the chapter.

PAGE 68

41 0 500 1000 1500 0 10 20 30 40 50 60 70 Frequency (Hz) Maximum Velocity (m/s) 0.015 0 500 1000 1500 0 10 20 30 40 50 60 70 Frequency (Hz) Maximum Velocity (m/s) 0.015 0 500 1000 1500 0 10 20 30 40 50 60 70 Frequency (Hz) Maximum Velocity (m/s) 0.013 0 500 1000 1500 0 10 20 30 40 50 60 70 Frequency (Hz) Maximum Velocity (m/s) 0.013 0 500 1000 1500 0 5 10 15 20 25 30 35 Frequency (Hz) y() 0.005 0 500 1000 1500 0 5 10 15 20 25 30 35 Frequency (Hz) y() 0.005 0 500 1000 1500 0 5 10 15 20 25 30 35 Frequency (Hz) y() 0.005 0 500 1000 1500 0 5 10 15 20 25 30 35 Frequency (Hz) y() 0.005 Figure 2-3: Comparison between the lumped element model () and experimental frequency response measured using phase-locked LDV () for four prototypical synthetic jets, having different orifice aspect ratio h/d (Gallas 2002). Finally, another constraint in the curr ent model is about the low frequency approximation. By definition LEM is fundament ally limited to low fr equencies since it is the main hypothesis employed. The characteris tic length scales of the governing physical phenomena must be much larger than the larg est geometric dimension. For example, for the lumped approximation to be valid in an acoustic system, th e acoustic wavelength ( = 1/k ) must be significantly larger than the device itself 1 kd This assumption permits decoupling of the temporal from the spa tial variations, and the governing partial 313 hd 515 hd 130.33 hd 531.66 hd

PAGE 69

42 differential equations for the distributed system can be lumped into a set of coupled ordinary differential equations. 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x/(d/2)v/vmax S=1 S=12 S=20 S=50 Figure 2-4: Variation in velocity profile vs. S = 1, 12, 20, and 50 for oscillatory pipe flow in a circular duct. However, it is well known that the flow inside a long pipe/channel is frequency dependent, as shown in Figure 2-4 and Figure 2-5. From Fi gure 2-4, it can be seen that, as the Stokes number S goes to zero, the velocity profile asymptotes to Poiseuille flow, while as S increases, the thickness of the Stokes layer decreases below 2d, leading to an inviscid core surrounded by a viscous annul ar region where a phase lag is also present between the pressure drop across the orifice and the velocity profile. Figure 2-5 shows that the ratio of the sp atial average velocity jvt to the centerline velocity CLvt, which is 0.5 for Poiseuille flow, is strongly de pendant on the Stokes number. Although it has been shown (Gallas et al. 2003a ) that the acoustic reactance is appr oximately constant with frequency, the acoustic resistance, whic h does asymptote at low frequencies to the steady value given by the lumped element mode l, gradually increases with frequency.

PAGE 70

43 Therefore, this frequency-dependence estimate should not be disregar ded, and care must be taken in the frequency range at which ZN MF actuators are running to apply LEM. For instance, the frequency depende nce given by Figure 2-5 can be easily implemented in the present model to provide estimates for the acoustic impedance of the orifice, as discussed in Gallas et al. (2003a). 1 10 100 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 S=( d2/ )1/2v / vCL Figure 2-5: Ratio of spatial average velocity to centerline velocity vs. Stokes number for oscillatory pipe flow in a circular duct. To summarize this section, the model given in Gallas et al. (2003a) has been presented and reviewed, and it has been shown that it could be extended to more general device configurations, particularly in terms of orifice geometry and dr iver configuration. Also, some of their restricting assumption lim its could be, if not completely removed, at least greatly attenuated, and this is further analyzed and di scussed in the last part of this chapter. But before, a general dimensional anal ysis of an isolated ac tuator is carried out in the next section that gives valuable insight on the parameter space and on the system response behavior.

PAGE 71

44 Dimensional Analysis Definition and Discussion In the first section of this chapter, the prim ary output variables of interest have been defined, and specifically the spatial and tim e-averaged ejection velocity of the jet jV defined in Eq. 2-4. It is then interes ting to rewrite them in terms of pertinent dimensionless parameters. Using the Buckingham-Pi theorem (Buckingham 1914), the dependence of the jet output velocity can be written in terms of nondimensional parameters. The derivation is presented in full in Appendix D and the results are summarized below: 3,,,,,, Rejd HdQQ hw StfnkdS ddd (2-15) The quantities in the left ha nd side of the functional ar e possible choices that the dependent variable jV can take. jdQQ represents the ratio of the volume flow rate of the driver ddQ to the jet volume flow ra te of the ejection part. St is the Strouhal number and Re is the jet Reynolds number defi ned earlier. Notice the close relationship between the jet Reynolds num ber, the Stokes number and the Strouhal number that were given by Eq. 2-7 and found again here by manipulation of the groups (see Appendix D for details). Therefor e, for a given geometric configuration, either the Strouhal or the Reynolds number s along with the Stoke s number could suffice to characterize the jet exit behavior. It is also interesting to view Eq. 2-7 as the basis for the jet formation criterion defi ned by Utturkar et al. (2003). Actually, it is intrusive to look at the different physical interpretations that the Strouhal number can take. In the

PAGE 72

45 fluid dynamics community, it is usually defined as the ratio of the unsteady to the steady inertia. However, it can also be interpreted as the ratio of 2 length scales or 2 time scales, such that 0 oscillation convection jj jjddd St L VV t d St t VVd (2-16) where 0dL is the ratio of a typical length scale d of the orifice to the particle excursion L0 through the orifice. The St rouhal number can also be the ratio of the oscillation time scale to the convective time scale. The physical significance of each term in th e RHS of Eq. 2-15 is described below: H is the ratio of the driving frequency to the Helmholtz frequency 0 HncSh (see Appendix B for a complete discussion on the definition and derivation of H ), a measure of the compressibility of the flow inside the cavity. hd is the orifice/slot height to diameter aspect ratio. wd is the orifice/slot width to diameter aspect ratio. d is the ratio of the operating frequency to the natural frequenc y of the driver. 3d is the ratio of the displaced volume by the driver to the orifice diameter cubed. kdd is the ratio of the orifice diam eter to the acoustic wavelength. 2Sd is the Stokes number, the ratio of the orifice diameter to the unsteady boundary layer thickness in the orifice It is evident that in the case of an isol ated ZNMF actuator, th e response is strongly dependant on the geometric parameters ,,,Hhdwdkd and the operating

PAGE 73

46 conditions 3,,ddS. In fact, from the functiona l form described by Eq. 2-15 and for a given device with fixed dimensions an d a given fluid, the actuator output is only dependent on the driver dynamics ,d and the actuation frequency Although compressibility effects in the orifice are neglected in this dissertation, it warrants a few lines. Compressibility will o ccur in the orifice for high Mach number flows and/or for high density flows. If the compressibility of the fluid has to be taken into account, it follows by definition that dens ity must be considered as a new variable. For instance, the pressure is now coupled to the temperature and density through the equation of state. Similarly, the continui ty equation is no longer trivial. Also, temperature is important, and one has to re minder that the variation of the thermal conductivity k and dynamic viscosity that are transport quantities with temperature may be important. Dimensionless Linear Transfer F unction for a Generic Driver Valuable physical insight into the depende nce of the device behavior on geometry and material properties is provided by th e frequency response of the ZNMF actuator device. In order to obtain an expression of the linear transfer func tion of the jet output to the input signal to the actuator, the compact nonlinear analytical model given by LEM is used in a similar manner as described and intr oduced in the previous section, since it was shown to be a valuable design tool. Notice however that the nonlinear part of the model in its present form -only confined in the or ificeis neglected fo r simplicity in this analysis. Figure 2-6 shows a schematic re presentation of a ZNMF actuator having a generic driver using LEM. This representati on enables us to bypa ss the need of an

PAGE 74

47 expression for the acoustic impedance aD Z of the driving transducer, although it lacks its dynamics modeling. Qd ZaD ZaC ZaO ( Qd-Qj) Qj Figure 2-6: Schematic re presentation of a genericdriver ZNMF actuator. In this case, a convenient representation of the transfer function is to normalize the jet volume flow rate by the driver volume flow rate, jdQQ, and obtain an expression via the current/flow divider shown in Figure 2-6, 21 1 1 1j aCaC daCaOaCaOaO aCaO aO aCaOaOQs ZsC QsZZsCRsM CM R ss CMM (2-17) assuming that the acoustic orifice impedance aOaOaO Z RM only contains the linear resistance aN R and the radiation mass aRadM is neglected or added to aO M Knowing that the Helmholtz resonator frequency of the actuator is defined by 1H aCaOCM, (2-18) and the damping ratio of the system by 1 2aC aN aOC R M (2-19) by substituting in Eqs. 2-18 and 2-19, Eq. 2-17 can then be rewritten as

PAGE 75

48 2 222j H dHHQs Qsss (2-20) This is a second-order system whose performance is set by the resonator Helmholtz frequency. Figure 2-7 below shows the effect of the damping coefficient on the frequency response of jdQQ, where for 1 the system is said to be underdamped, and for 1 the system is overdamped. The damping coefficient controls the amplitude of the resonance peak, allowing the system to yield more or less response at the Helmoholtz frequency. 10-1 100 101 -60 -40 -20 0 20 40 Magnitude (dB) 10-1 100 101 -200 -150 -100 -50 0 Phase (deg)/H =0.01=0.1=0.5=1 4 0 d B / d e c a d e Figure 2-7: Bode diagram of the second or der system given by Eq. 2-20, for different damping ratio. Since the expression of H differs from the orifice geometry, two different cases are examined and summarized in Table 2-2. The definitions can be found in Appendices B, C, and D. The damping coefficient is found from the following arrangement (shown for the case of a circular orifice, but one can similarly arrive at the same result for a rectangular slot)

PAGE 76

49 2 222 0 4 21864 2 2 432c hh d hd 2 8d 62 03c 2d 16h 4 22 22 2 2242242 0 1S 116 768144 3Hhh dcddcd (2-21) that is, 21 12HS (2-22) Table 2-2: Dimensional parameters for circular and rectangular orifices Circular orifice Rectangular slot dQ (m3/s) dj dj H (rad/s) 2 2 032 4dc h 2 052 3 wdc h aCC (s2.m4/kg) 2 0c 2 0c aN R (kg/m4.s) 48 2 h d 33 22 h wd aN M (kg/m4) 24 32 h d 3 52 h wd 1 2aC aN aNC R M 21 12HS 21 5HS Notice that the damping coefficient has the same fundamental expression whether the orifice is circular or rectangular, the difference being incorporated in a multiplicative constant. Substituting these results into Eq. 2-20 and replacing the Laplace variable sj yields the final form for a generic driver and a generic orifice 2 21 1 1jj d HHQQ Qj j S (2-23)

PAGE 77

50 Clearly, the advantage of non-dimensionali zing the jet volume flow rate by the driver flow rate allows us to isolate the driver dynamics fr om the main response, thereby decoupling the effect of the various device components from each other. Eq. 2-23 is an important result in predicting the linear system response in terms of the nondimensional parameters d H and S as a function of the driver performance. It yields such interesting results that actually a thorough anal ysis of Eq. 2-23 is pr ovided in details in Chapter 5 where the reader is referred to for completeness. To summarize, this section has provided a dimensional analysis of an isolated ZNMF actuator. A compact expression, in terms of the principal dimensionless parameters, has been found for the nondimensi onal transfer function that relates the output to the input of the actuator. Most importantly, such an expression was derived regardless of the orifice geometry and regardless of the driver configuration. Actually, as an example, a piezoelectric-driven ZNMF actua tor exhausting into a quiescent medium is also considered in Appendix E where the idea is to find the same ge neral expression as derived above in Eq. 2-15 for a generic ZNMF device, but starting from the specific and already known transfer function of a piezoelectric-driven synthetic jet actuator as given in Gallas et al. (2003a). Appendi x E presents the full assump tions and derivation of the non-dimensionalization and the de rivation of the linear transf er function for this case. Next, with this knowledge gained, the mo deling issues presen ted earlier in the introduction chapter and at the beginning of this chapter are further considered.

PAGE 78

51 Modeling Issues Cavity Effect The cavity plays an important role in the actuator performance. Intuitively, an actuator having a large cavity ma y not act in a similar fashio n to one having a very small cavity. As mentioned above, the cavity of a ZNMF actuator permits the compression and expansion of fluid. It is more obvious when looking at the equivalent circuit of a ZNMF device (see Figure 2-1 for instance), where the flow produced by the driver is split into two branches: one for the cavity where th e fluid undergoes succes sive compression and expansion cycles, the other one for the orifice neck where the fluid is alternatively ejected and ingested. The question arises as to wh en, if ever, an incompressible assumption is valid. The definition of the cavity incompress ibility limit is actually two-fold. First, from the equivalent circuit perspective, a high cavity impedance will prevent the flow from going into the cavity branch, thereby a llowing maximum flow into and out of the orifice neck, thus maximizing the jet output. Or from another point of view, the incompressible limit occurs for a stiff cavity hence for zero compliance in the cavity, which should yield to 1jdQQ On the other hand, from a computational point of view, it is rather essential to know whether th e flow inside the cavity can be considered as incompressible, the computation cost bei ng quite different between a compressible and an incompressible solver. Actually, because of its importance in numerical simulations and relevance in the physical understanding of a ZNMF actuator, Chapter 5 is entirely dedicated to the question of the cavity modeling. The reader is therefore referred to Chapter 5 for a thorough investigation on th e role of the cavity in a ZNMF actuator.

PAGE 79

52 Orifice Effect The orifice is one of the major component s of a ZNMF actuator device. Its shape will greatly contributes in the actuator response, and knowledge of the nature of the flow at the orifice exit is determinant in predic ting the system response. The LEM technique presented earlier was shown to be a satisfactory tool in this way, but has st ill fundamental limitations, especially in the expression of the orifice nonlinear loss coefficient Kd. Similarly, the existing lumped element mode l is employed in the frequency domain. Because of the oscillatory nature of the actuator response, it may also be instructive to study the response of ZNMF actua tor in the time domain. Lumped element modeling in the time domain The LEM technique presented above and used throughout this work identifies a transfer function in the Laplace domain, consequently in the frequency domain as well by assuming sjj Note that this variable substitution is only correct when an input function gt is absolutely integrable, that is if it satisfies gtdt (2-24) i.e., the signal must be causal and that the sy stem is stable -conditions that are always met in this work. For a given transfer functi on of the system (ZNMF actuator) relating the output (jet velocity) to the input (driver signal) in th e frequency domain, it could therefore be of interest to gain some in sight from the time domain response. Referring to Figure 2-6 and Eq. 2-17, the equation of motion for the ZNMF actuator is given by jaOaCdaCQZZQZ (2-25)

PAGE 80

53 where again 1aCaC Z jC is the acoustic impedance of the cavity, and aOaOlinaOnljaO Z RRQjM is the acoustic orifice impedance. The orifice mass aO M includes the contributions from the ra diation and inertia, while the orifice resistances are distinguishe d between the linear terms aOlinaN R R (viscous losses) and nonlinear aOnlj R fQ (dump loss) defined by Eq. 2-14. Also, jjnQyS is the jet volume flow rate, dddQyS is the volume velocity ge nerated by the driver, and jy and dy are, respectively, the fluid particle displa cement at the orifice and the vibrating driver displacement. Notice that jy can take positive or negative values, which corresponds respectively to the time of expulsion and ingest ion during a cycle, as seen in Figure 2-8. Therefore, since the nonlinea r resistance is associated to the time of discharge and considering the coefficient Kd as a constant independent of Qj, it takes the form 20.5 0.5dj d aOnljnlj nnKQ K R yAy SS (2-26) x y +yd-yd +yj-yjA time expulsion starts max expulsion ingestion starts max ingestionO O O O jy C ZaDZaCZaO PcQdQcQj + + B Figure 2-8: Coordinate syst em and sign convention definiti on in a ZNMF actuator. A) Schematic of coordinate system. B) Ci rcuit representation. C) Cycle for the jet velocity. The following expression for the equation of motion of a fluid part icle can then be easily derived

PAGE 81

54 1d njaOnlaOlinaOd aCaCS SyRRjMy jCjC (2-27) But since frequency and time domain are related through jddt and 1jdt and assuming a sinusoidal motion for the source term, i.e. 0sindyWt with 0W corresponding to the driver centerline amplit ude, then the equation of motion in the time domain is written as 0sinnd jnjnljnaOlinjnaOj aCaCSS ySyAySRySMyWt CC (2-28) or by rearranging the terms, 01 sind aOjnljjaOlinjj aCaCnS M yAyyRyyWt CCS (2-29) Similarly, the pressure cP across the orifice can be derived from continuity, cjaOdjaCPQZQQZ (2-30) Thus, substituting in Eq. 2-30 and rearranging yields 11cdaCjaCddnj aCaCPQZQZSySy jCjC (2-31) and finally the pressure drop takes the following expression 0 0sin sindnj dn cj aCaCaCSWtSy SS PWty CCC (2-32) To validate this temporal approach of th e lumped element model, three test cases are now considered having three different orifice shapes to also gain insight into the orifice geometric effects. Fi rst, the response of a ZNMF act uator having a simple straight rectangular orifice shape and a high aspect ratio hd is viewed, and that corresponds to

PAGE 82

55 Case 1 in the NASA LaRC workshop (CFDVal 2004), as shown in Figure 2-9. Then, Case 2 of the same workshop (CFDVal 2004) is considered since th e orifice of this ZNMF actuator has a rounded beveled shape ( 2Dd see Figure 2-10 for geometric definition) and an aspect ratio less than unity, where high values of the orifice discharge coefficient are expected. The actuator geom etry is shown in Figure 2-10. A third example is taken from the results provided by Choudhari et al. ( 1999), in which they perform a numerical simulation of flow past Helmholtz resonators for acoustic liners, with the orifice aspect ratio hd equal to unity. Figure 2-9: Geometry of the piezoelectricdriven ZNMF actuator from Case 1 (CFDVal 2004). 1.27 dmm, 0.59dD 10.6hd 28wd 445 f Hz (Reproduced with permission) Figure 2-10: Geometry of the piston-driv en ZNMF actuator from Case 2 (CFDVal 2004). 6.35 dmm, 0.5dD 0.68hd 150 f Hz (Reproduced with permission) slot

PAGE 83

56 Because of their special or ifice shape, pipe theory was used to model the dimensionless dump loss coefficient dK in the acoustic orifice impedance for Case 1 and Case 2 (CFDVal 2004). From pipe theo ry (White 1979), the dump loss coefficient for the orifice is 2 41dDKC (2-33) with dD is the ratio of the exit to the entrance orifice diameter, and with the discharge coefficient taking the form 0.50.99756.53ReDC (2-34) for a beveled shape, Re being the Reynolds number based on the orifice ex it diameter d. For each case, the Reynolds number given by the experimental data provided in the workshop (CFDVal 2004) is used in Eq 2-34, although it should be rigorously implemented in a converging l oop since this variable is us ually not known beforehand. For Case 1, it was found that 0.884dK while for Case 2, 0.989dK This is to be compared with the value 1dK that is used in Gallas et al. (2003a). Notice though that Eq. 2-34 is specifically define d for high Reynolds number, wh ich may not always be the case. Similarly, Eqs. 2-33 and 2-34 only acco unt for the expulsion part of the cycle. During the ingestion part the flow sees an i nversed orifice shape, hence the discharge coefficient should take a differe nt form. How to account for the oscillatory behavior on the orifice shape, i.e. to separate the e xpulsion to the ingestion phase for the flow discharge, is investigated in the next chapte rs of this dissertation. Yet, these results validate the approach used and provide valuab le insight into the nonlinear behavior.

PAGE 84

57 The nonlinear ODE that describes the motion of the fluid particle at the orifice, Eq. 2-29, is numerically integrated using a 4th order Runge-Kutta me thod with zero initial conditions for 000jjyy The integration is carried out until a steady-state is reached. The jet orifice velocity, pressure drop across the orifice via Eq. 2-32, and the driver displacement are shown in Figure 211 for Case 1. All quantities exhibit sinusoidal behavior, and it can be seen that the cavity pressure is in phase with the driver displacement, while the je t orifice velocity lags the driver displacement by 90. Once the pressure reaches its ma ximum (maximum compression, the fluid cavity starts to expand), the fluid is ingested from the orifi ce, then reaches its ma ximum ingestion when the cavity pressure is zero and finally, as th e fluid inside the cavity starts to be compressed, the fluid is ejec ted from the orifice. 0 45 90 135 180 225 270 315 360 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 phase driver displacement pressure drop jet orifice velocity Figure 2-11: Time signals of the jet orifi ce velocity, pressure across the orifice, and driver displacement during one cycle for Case 1. The quantities are normalized by their respective ma gnitudes for comparison. Normalized quantities

PAGE 85

58 The other test case response, namely Case 2, is plotted in Figure 2-12, where the jet orifice displacement and velocity, pressure drop across the orifice, and the driver displacement are shown for both the a) linear and the b) nonlinear solutions of the equation of motion Eqs. 2-29 and 2-32. The linear solution is obtained by setting 0aOnlR and is performed to verify the physics of the device behavior and thus confirm the modeling approach used. The linear solutio n in Figure 2-12A show s that the pressure inside the cavity (which equals the pressure drop across the orifice) and the driver motion are almost out of phase. All quantities e xhibit sinusoidal behavior. The jet orifice velocity jy lags the cavity pressure for both the lin ear and the nonlinear solution. Figure 2-12B shows the effect of the nonl inearity of the orifice resistan ce. Its main effect is to shift the pressure signal such that the fluid particle velocity and the cavity pressure are out of phase. Also, those two signals e xhibit obvious nonlinear behavior due to the nonlinear orifice resistance. Figure 2-12: Time signals of the jet orifice ve locity, pressure across the orifice and driver displacement during one cycle for Case 2. A) Linear solution. B) Nonlinear solution. The quantities are normali zed by their respective magnitudes for comparison. 0 45 90 135 180 225 270 315 360 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 phase Nonlinear Solution 0 45 90 135 180 225 270 315 36 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 phase Linear Solution driver displacement pressure drop jet orifice velocity B A Normalized quantities

PAGE 86

59 Then, Figure 2-13 shows the numerical resu lts from Choudhari et al. (1999), with their notation reproduced, where the reference signal shown corresponds to that measured at the computational boundary where the acoustic forcing is applied, and the x -axis in the plot is normalized by the period T of the incident wave. Notice that they used a perforate plate having a porosity equal to 5%. In a similar trend as for the previous case, the pressure drop and jet orifice velocity exhibit distinct nonlin earities in their time signals. From Figure 2-13A, it is seen that th e pressure perturbations at each end of the orifice are almost out of phase while in Figure 2-13B, the velo cities at different locations in the orifice are in phase with each other. Also, it appears that the pressure and velocity perturbations have about a 90 phase difference, similar to Case 1 above. Figure 2-13: Numerical results of the time sign als for A) pressure drop and B) velocity perturbation at selected locations along the resonator orifice. The subscripts i c, and e refer to the orifice opening toward s the impedance tube (exterior), the orifice center, and the orifice opening towards the backing cavity, respectively. 2.54 dmm 1hd 566 f Hz 0.05 (Reproduced with permission from C houdhari et al. 1999) Clearly, the orifice shape does have a si gnificant impact on the nonlinear signal distortion in the orifice regi on. It should be noted that the actuation frequency and amplitude are also important, as discussed in Choudhari et al. ( 1999), and mentioned in the introduction chapter where Ingard and Is ing (1967) and later Se ifert et al. (1999) A) Disturbance pressure 0 p c B) Streamwise velocity perturbation 0uc

PAGE 87

60 showed that for low actuation amplitude the pr essure fluctuations a nd the velocity scale as 0upc whereas for high amplitude up However, it still emphasizes the need to accurately model the orifice di scharge coefficient in terms of the flow conditions. As mentioned before, also of interest is the fully-developed assumption for the flow inside the orifice. Clearly, while Case 1 (CFDVal 2004) has an orifice geometry that justifies such an approximation, it seems quite doubtful for Case 2 (CFDVal 2004) and perhaps the Helmholtz resonator geometry from Choudhari et al. (1999) It is expected that a developing region exists at the orifice opening ends, where a different relationship relates the pressure drop and the fluid veloci ty, the velocity being now dependant on the longitudinal location inside the orifice. In this regard, the next subsection provides more details on this entrance region. Finally, another orifice issue that may not be negligible is the radius of curvature at the exit plane. In fact, the formation and subs equent shedding of the vo rtex ring (pair) at the orifice (slot) exit relies on the curvature of the exit plan e. Sharp edges facilitate the formation and roll-up of the vortices, due to a local higher pressure difference, while smooth edges having a large radi us of curvature lessen the formation of vortices at the exit plane, as shown in the recent work by Smith and Swift (2003b) who experimentally studied the losses in an oscillatory flow through a rounded slot. This parameter, R d, may enter in the present nondimensional analys is for completeness, although it is omitted in this dissertation.

PAGE 88

61 Loss mechanism In this subsection, an attempt is made to physically describe the flow mechanism inside the orifice. The flow inside the or ifice is by nature unsteady and is exhibiting complex behavior as demonstrat ed in the literature review. One approach to understand the nature of the flow physics is to consider known simpler cases. Firs t it is instructive to consider the simpler case of steady flow through a pipe where lo sses arise due to different mechanisms. In any undergraduate flui d mechanics textbook, these losses are characterized as major losse s in the fully developed fl ow region and minor losses associated with entrance and exit effects, etc. For laminar flow, the pressure drop p in the fully-developed region is linearly proportional to the volume flow rate jQ or average spatial velocity jV while the nonlinear minor pressure losses are proportional to the dynamic pressure 20.5jV. Similarly, for the case of unsteady laminar, fully-developed, flow driven by an oscillatory pressure gradient, the complex flow impedance, p Q can be determined analytically and decomposed into linear resistance and reactive components as already discusse d above. Unfortunately, no such solution is yet available for the nonlinear, and perhaps dominant, losses a ssociated with entrance and exit effects. It then appears that the orifice flow can be characterize by three dominant regions, as shown schematically in Figure 2-14, wh ere the first region is dominated by the entrance flow, then follows a linear or fully-d eveloped region away fr om the orifice ends, to finally include an exit region. Notice that this is for one half of the total period, but by assuming a symmetric orifice the flow will unde rgo a similar development as it reverses. Also shown schematically in Figure 2-14 are the pathlines or particle excursions for three

PAGE 89

62 different running conditions. The first one corresponds to the case where the stroke length is much smaller than the orifice height 0Lh -recall that the stroke length is simply related to the Strouhal number via Eq. 2-7. In this case it is expected that the flow inside the orifice may easily reach a fully-developed state, thus having losses dominated by the major linear viscous loss rather than the nonlinear minor ones associated with the entrance and exit regions. A second case o ccurs when the stroke length is this time much larger than the orifice height 0 L h. In this scenario, the losses are now expected to be largely domina ted by the minor nonlinear losses due to entrance and exit effects, the entrance region basically extend ing all the way through the orifice length. Finally, in the case where the stroke length a nd orifice height have the same order of magnitude 0Lh, the linear losses due to the fu lly-developed region should compete with the nonlinear losses from the entrance a nd exit effects. Notice that here, fullydeveloped means that there exists a region within the orifice away from either exit, where the velocity profile at a given phase during the cycle is not a function of axial position y X X X X X X X X h L0 >> h L0 << h L0 ~ h viscous loss (fully-developed flow) exit & entrance losses Figure 2-14: Schematic of the different flow regions inside a ZNMF actuator orifice.

PAGE 90

63 Thus to refine the existing lumped elem ent model presented a bove that uses the frequency-dependent analytical solution for the linear resist ance, the impedance of the nonlinear losses associat ed with the entrance and exit regions should be extracted. However, the relative importa nce and scaling of the linear and nonlinear components versus the governing dimensionless parame ters is unknown and remains a critical obstacle for designers of ZNMF actuators at th is stage. To achieve such a goal i.e., to improve the current understanding of the or ifice flow physics and consequently to improve the accuracy of low-order models, a careful experimental investigation is conducted and the extracted results are pres ented in the subsequent chapters. Driving-Transducer Effect Most of the numerical simulations impos e a moving boundary condition in order to model the kinematics of the ZNMF driver that generates the oscillating jet in the orifice neck. However, this approach does not capture the driver dynamics and in most instances, crude models of the mode shape are employed (Rizzetta et al. 1999; Orkwis and Filz 2005). Although this might not be cri tical if the actuator is driven far from any resonance frequency, the information provide d by the driver is relevant from a design perspective, with the freque ncy response (magnitude and phase) dictating the overall performance of the system and thus its desirabl e application. The approach used in this dissertation is to decouple th e dynamics of the driver from the rest of the device via the analysis of a dimensionless tr ansfer function. Hence, accu rate component models can be sought that will provide useful information on the overall behavior of the actuator. In this regard, LEM has been shown to be a suitable solution, as discussed below, for any type of drive configuration, i.e. piston-like diaphragm, piezoelectric diaphragm, etc.

PAGE 91

64 Figure 1-1 shows the three most common dr iving mechanisms that are employed in ZNMF actuators, namely an oscillating diaphr agm (usually a piezoelectric patch mounted on one side of a metallic shim and driven by an ac voltage), a piston mounted in the cavity (using an electromagnetic shaker, a camsh aft, etc.), or a louds peaker enclosed in the cavity (an electrodynamic voice-coil transdu cer). In addition to the driver dynamics, the characteristics of most interest are the volume displaced by the driver at the actuation frequency f Hence, the driver volumetric flow rate can simply be defined by 2dQjf (2-35) It has been shown that this compact e xpression is useful in the nondimensional analysis performed earlier. However, in or der to obtain the full dynamics of the actuator response, the LHS of Eq. 2-35 must also be known. Only then do the compact analytical expressions derived in the prev ious section reveal their usef ulness. Each of the three types of possible ZNMF actuator drivers are discussed below via LEM, since the analysis and design of coupled-domain transducer systems are commonly performed using lumped element models (Fishe r 1955; Merhault 1981; Rossi 1988). I.e., in addition to the driver acoustic impedance aD Z that is shown in Figure 2-6 and Figure 2-15, the transduction factor a and the blocked electrical impedance eBC must be explicitly given. + Vac+ P IQd aQdaVac+ CeB1:a CaD RaD MaD Figure 2-15: Equivalent two-port circuit representation of piezoelectric transduction. First, consider the case of a piezoelectric diaphragm driver. R ecently (Gallas et al. 2003a, 2003b), the author successfully im plemented a two-port model for the

PAGE 92

65 piezoceramic plate (Prasad et al. 2002) in th e analysis, modeling and optimization of an isolated ZNMF actuator. As shown in Figur e 2-15, the impedance of the composite plate was modeled in the acoustic domain as a seri es representation of an equivalent acoustic mass aD M a short-circuit acoustic compliance aDC (that relates an applied differential pressure to the volume displacement of th e diaphragm) and an acoustic resistance aD R (that represents the losses due to mechani cal damping effects in the diaphragm). Similarly, a radiation acoustic mass can be added if needed. The conversion from electrical to acoustic domain is performed via an ideal transformer possessing a turns ratio a that converts energy from the electrical domain to th e acoustic domain without losses. Figure 2-1 shows the two-port circ uit representation impl emented in a ZNMF actuator. a aD M and aDC are calculated via linear composite plate theory (see Prasad et al. 2002 for details). Noti ce that the acoustic resistance aD R given by 2aD aDD aDM R C (2-36) is the only empirically determined parameter in this model, since the damping coefficient D is experimentally determined. The probl em in finding a non-empirical expression for the diaphragm damping coefficient (for instance by using the known quality factor) comes mostly from the actual implementation of the driver in the device. A perfect clamped boundary condition is assumed, and deviation from this boundary condition and the problem of high tolerance/uncertainties between the manufactured piezoceramicdiaphragms can degrade the accuracy of the model. Nonetheless, the dynamics of the driver are well captured by this model and were successfully implemented in previous studies (Gallas et al. 2003a 2003b; CFDVal-Case 1 2004).

PAGE 93

66 ac CdVBL R SaSC 2 aECRBLR ()aS R CUcP N M N R cC N U Cavity/Neck DynamicsaD M (Coil resistance)a(Speaker + air mass)a(Speaker compliance)a(Speaker resistance)aConsider next an acoustic speaker that drives a ZNMF actuator. Similar to a piezoelectric diaphragm, a simp le circuit representation can be made. McCormick (2002) has already performed such an analysis, as show n in Figure 2-16. Th e speaker is actually a moving voice coil that creates acoustic pressu re fluctuations inside the cavity. Its principle is simple. It is usually compos ed of a permanent magnet, a voice coil and a diaphragm attached to it. When an ac current flowing through the voice coil changes direction, the coil's polar orientation reve rses, thereby changing the magnetic forces between the voice coil and the permanent magnet, and then the diaphragm attached to the coil moves and back and forth. This vibrat es the air in front of the speaker, creating sound waves. Figure 2-16: Speaker-driven ZNMF actuator. A) Physical arrangement. B) Equivalent circuit model representation obtained using lumped elements used in McCormick (2000). B L is the voice coil force constant (= magnetic flux x coil length) As represented in Figure 2-16B, the acoustic impedance aD Z of the driver is modeled via acoustic resistances (from the co il and the speaker) mount ed in series with acoustic masses (speaker plus air) and complia nces (from the speaker). The main issues concerning such an arrangement are, first, the practical deployment of the speaker to A B

PAGE 94

67 drive the ZNMF actuator in a desired frequency range. Also, a loudspeaker creates pressure fluctuations whose characteristics (amplitude and frequency) depend on the speaker dynamics. For example, if the speaker is mounted in a large cavity enclosure (whose size is greater than the acoustic wave length), it might excite the acoustic modes of the cavity, thereby resulting in three-dime nsionality of the flow in the slot. sealing membrane shaker bottom cavity cavity orifice vent channel Figure 2-17: Schematic of a shaker-driven ZNMF actuator, showing the vent channel between the two sealed cavities. Finally, consider a piston-like driver. It could be operated either mechanically, for instance by a camshaft or by other mechanical means, or by using an electromagnetic shaker. Here, we turn our attention to the latter application. An electromagnetic piston usually consists of a moving voice coil shaft that drives a rigid piston plate and, in essence, follows the same concept as pres ented above for the case of a voice coil loudspeaker. Although the previous discu ssion on the LEM representation remains the same here, the major difference comes from the nature of the piston itself. In fact, while the top face of the piston is facing the cavity of the ZNMF actuator, another cavity on the opposite side of the piston is present, as s hown in Figure 2-17. This cavity may or may not be vented to the other cavity. If s ealed, when the ZNMF device is running at a specific condition, an additional pressure load is created on the piston plate to account for the static pressure difference between the cavities that may deteriorate the nominal transducer performance. To alleviate this effect, the ZNMF cavity and the bottom cavity

PAGE 95

68 could be vented together, in a similar manne r to that employed for a microphone design. Also, this bottom cavity should be added in se ries with the ZNMF cavity (since they share the same common flow) in the circuit representation of the actuator that is shown in Figure 2-18. Qd :1 BL eU ZaCQd-Qv-QjQj ZaO Pc electromagnetic moving-coil transducer electrodynamic coupling electrical source ZaC bot ZaVentQv Figure 2-18: Circuit repr esentation of a shaker-dri ven ZNMF actuator, where aC Z is the acoustic impedance of the ZNMF cavity, botaCZ is the acoustic impedance of the bottom cavity, and aVentZ is the acoustic impedance of the vent channel. Even though tools are available using lumped element modeling, the ZNMF actuator driver must be modeled with care, especially when deployed in a physical apparatus. However, once the driver dynami cs have been successfully modeled, its implementation in the dimensionless analytical expressions derived in this chapter can yield powerful insight into the analysis and the design of a ZNMF actuator. This method can then be extended by including the effect of an external boundary layer, as shown in Chapter 7. Now that some insight has been gained on the dynamics of a ZNMF actuator in still air, a test matrix is constructed to car efully investigate bot h experimentally and numerically the unresolved features of these types of devices, especially on refining the nonlinear loss coefficient of the orifice.

PAGE 96

69 Test Matrix A significant database forms the basis of a te st matrix that includes direct numerical simulations and experimental results. The te st matrix is comprised of various test actuator configurations that are examined to ultimately assess the accuracy of the developed reduced-order models over a wide range of operating conditions. The goal is to test various act uator configurations in orde r to cover a wide range of operating conditions, in a quiescent medi um, by varying the key dimensionless parameters extracted in the above dimensiona l analysis. Available numerical simulations are used along with experimental data perf ormed in the Fluid Mechanics Laboratory at the University of Florida on a single piezoelect ric-driven ZNMF devi ce exhausting in still air. Table 2-3 describes the test matrix. The first six cases are direct numerical simulations (DNS) from the George Washi ngton University under the supervision of Prof. Mittal. They use a 2D DNS simulati on whose methodology is detailed in Appendix F. Case 8 comes from the first test cas e of the NASA LaRC workshop (CFDVal 2004). Then, Case 9 to Case 72 are experimental te st cases performed at the University of Florida for axisymmetric piezoelectric-driven ZNMF actuators. The experimental setup is described in details in Chapter 3, and the results are systematically analyzed and studied in Chapter 4, Chap ter 5, and Chapter 6. Table 2-3: Test matrix for ZNMF actuator in quiescent medium Case Type f (Hz) d (mm) h (mm) w/d (mm3) S Re St f/fH f/fd Jet 1 CFD 0.38 1 1 800 25.0 262 2.4 0.13 X 2 CFD 0.38 1 2 800 25.0 262 2.4 0.15 X 3 CFD 0.06 1 0.68 360 10.0 262 0.4 0.01 J 4 CFD 0.20 0.1 0.1 800 5.0 63.6 0.4 0.00 J 5 CFD 0.80 0.1 0.1 800 10.0 255 0.4 0.01 J 6 CFD 1.99 0.1 0.1 800 15.8 477 0.5 0.03 J 7 CFD 1.99 0.1 0.1 800 15.8 636 0.4 0.03 J 8 exp/cfd 446 1.27 13.5 28 7549 17.1 861 0.3 2.65 0.99 J 9 exp. 39 1.9 1.8 7109 7.6 8.79 6.6 0.06 0.06 X

PAGE 97

70 Case Type f (Hz) d (mm) h (mm) w/d (mm3) S Re St f/fH f/fd Jet 10 exp. 39 1.9 1.8 7109 7.6 12.0 4.8 0.06 0.06 J 11 exp. 39 1.9 1.8 7109 7.6 22.6 2.5 0.06 0.06 J 12 exp. 39 1.9 1.8 7109 7.6 33.2 1.7 0.06 0.06 J 13 exp. 39 1.9 1.8 7109 7.6 39.8 1.4 0.06 0.06 J 14 exp. 39 1.9 1.8 7109 7.6 46.5 1.2 0.06 0.06 J 15 exp. 39 1.9 1.8 7109 7.6 52.5 1.1 0.06 0.06 J 16 exp. 39 1.9 1.8 7109 7.6 59.7 1.0 0.06 0.06 J 17 exp. 39 1.9 1.8 7109 7.6 66.0 0.9 0.06 0.06 J 18 exp. 39 1.9 1.8 7109 7.6 73.7 0.8 0.06 0.06 J 19 exp. 39 1.9 1.8 7109 7.6 81.6 0.7 0.06 0.06 J 20 exp. 39 1.9 1.8 7109 7.6 88.2 0.6 0.06 0.06 J 21 exp. 780 1.9 1.8 7109 34.0 192 6.0 1.24 1.23 X 22 exp. 780 1.9 1.8 7109 34.0 242 4.8 1.24 1.23 J 23 exp. 780 1.9 1.8 7109 34.0 374 3.1 1.24 1.23 J 24 exp. 780 1.9 1.8 7109 34.0 513 2.2 1.24 1.23 J 25 exp. 780 1.9 1.8 7109 34.0 637 1.8 1.24 1.23 J 26 exp. 780 1.9 1.8 7109 34.0 750 1.5 1.24 1.23 J 27 exp. 780 1.9 1.8 7109 34.0 825 1.4 1.24 1.23 J 28 exp. 780 1.9 1.8 7109 34.0 930 1.2 1.24 1.23 J 29 exp. 780 1.9 1.8 7109 34.0 1131 1.1 1.24 1.23 J 30 exp. 780 1.9 1.8 7109 34.0 1120 1.0 1.24 1.23 J 31 exp. 780 1.9 1.8 7109 34.0 1200 1.0 1.24 1.23 J 32 exp. 780 1.9 1.8 7109 34.0 1264 0.9 1.24 1.23 J 33 exp. 780 1.9 1.8 7109 34.0 1510 0.8 1.24 1.23 J 34 exp. 780 1.9 1.8 7109 34.0 1589 0.7 1.24 1.23 J 35 exp. 780 1.9 1.8 7109 34.0 1683 0.7 1.24 1.23 J 36 exp. 780 1.9 1.8 7109 34.0 1774 0.6 1.24 1.23 J 37 exp. 780 1.9 1.8 7109 34.0 1842 0.6 1.24 1.23 J 38 exp. 780 1.9 1.8 7109 34.0 1876 0.6 1.24 1.23 J 39 exp. 780 1.9 1.8 7109 34.0 2755 0.4 1.24 1.23 J 40 exp. 1200 1.9 1.8 7109 42.1 90.8 19.5 1.91 1.90 X 41 exp. 39 2.98 1.05 7109 11.9 40.6 3.49 0.04 0.06 J 42 exp. 39 2.98 1.05 7109 11.9 47.3 2.99 0.04 0.06 J 43 exp. 39 2.98 1.05 7109 11.9 63.4 2.23 0.04 0.06 J 44 exp. 500 2.98 1.05 7109 42.6 1959 0.93 0.55 0.79 J 45 exp. 500 2.98 1.05 7109 42.6 2615 0.69 0.55 0.79 J 46 exp. 780 2.98 1.05 7109 53.2 109 26.0 0.86 1.23 X 47 exp. 780 2.98 1.05 7109 53.2 254 11.2 0.86 1.23 X 48 exp. 780 2.98 1.05 7109 53.2 571 4.96 0.86 1.23 J 49 exp. 780 2.98 1.05 7109 53.2 1439 1.97 0.86 1.23 J 50 exp. 780 2.98 1.05 7109 53.2 2022 1.40 0.86 1.23 J 51 exp. 39 2.96 4.99 7109 11.8 29.8 4.69 0.06 0.06 J 52 exp. 39 2.96 4.99 7109 11.8 43.0 3.25 0.06 0.06 J 53 exp. 39 2.96 4.99 7109 11.8 55.7 2.51 0.06 0.06 J 54 exp. 39 2.96 4.99 7109 11.8 71.9 1.94 0.06 0.06 J 55 exp. 780 2.96 4.99 7109 52.9 125 22.3 1.25 1.23 X 56 exp. 780 2.96 4.99 7109 52.9 318 8.79 1.25 1.23 X 57 exp. 780 2.96 4.99 7109 52.9 867 3.22 1.25 1.23 J 58 exp. 780 2.96 4.99 7109 52.9 2059 1.36 1.25 1.23 J 59 exp. 780 2.96 4.99 7109 52.9 3039 0.92 1.25 1.23 J

PAGE 98

71 Case Type f (Hz) d (mm) h (mm) w/d (mm3) S Re St f/fH f/fd Jet 60 exp. 39 1.0 5.0 7109 4.0 132 0.12 0.16 0.06 J 61 exp. 39 1.0 5.0 7109 4.0 157 0.10 0.16 0.06 J 62 exp. 39 1.0 5.0 7109 4.0 205 0.08 0.16 0.06 J 63 exp. 500 1.0 5.0 7109 14.3 286 0.72 2.10 0.79 J 64 exp. 500 1.0 5.0 7109 14.3 461 0.44 2.10 0.79 J 65 exp. 730 1.0 5.0 7109 17.3 269 1.11 3.07 1.16 J 66 exp. 730 1.0 5.0 7109 17.3 611 0.49 3.07 1.16 J 67 exp. 730 1.0 5.0 7109 17.3 893 0.33 3.07 1.16 J 68 exp. 730 1.0 5.0 7109 17.3 1081 0.28 3.07 1.16 J 69 exp. 730 1.0 5.0 7109 17.3 1361 0.22 3.07 1.16 J 70 exp. 39 0.98 0.92 7109 3.9 49.6 0.31 0.09 0.06 J 71 exp. 39 0.98 0.92 7109 3.9 112 0.14 0.09 0.06 J 72 exp. 39 0.98 0.92 7109 3.9 179 0.09 0.09 0.06 J To conclude this chapter, the existing lumped element model from Gallas et al. (2003a) has been presented and reviewed, and it has been shown that it could be extended to more general device configurations, par ticularly in terms of orifice geometry and driver configuration. Then, a dimensional analysis of an isolated ZNMF actuator was performed. A compact expression, in terms of the principal dimensionless parameters, was found for the nondimensional linear transfer function that relates the output to the input of the actuator, regardless of the orifice geometry and of the driver configuration. Next, some modeling issues have been inve stigated for the different components of a ZNMF actuator. Specifically, the LEM technique has been used in the time domain to yield some insight on the orifi ce shape effect, and a physical description on the associated orifice losses has been provided. Finally, sinc e one of the goals of this research is to develop a refined low-order mode l, which is presented in Chapter 6 and that builds on the results presented in the subsequent chapters a significant database forms the basis of a test matrix that is comprise d of direct numerical simulati ons and experime ntal results.

PAGE 99

72 CHAPTER 3 EXPERIMENTAL SETUP This chapter provides the details on the de sign and the specifica tions of the ZNMF devices used in the experimental study. De scriptions of the cavity pressure, driver deflection, and actuator exit ve locity measurements are prov ided, along with the dynamic data acquisition system employed. Then, th e data reduction process is presented with some general results. A desc ription of the Fourier series decomposition applied to the phase-locked, ensemble average time signals is presented next. Fina lly, a description of the flow visualization technique employed to determine if a synthetic jet is formed is then provided. Experimental Setup In this dissertation, two different experiments are pe rformed. The first one, referred to as Test 1, is used in the orifice flow analysis presented in Chapter 4 and the corresponding test cases are listed in Table 2-3. The second test, Test 2, is used in the cavity compressibility analysis (presented in Chapter 5). Test 1 consists of phase-locked measurements of the velocity profile at the orifice, cavity pressure, and diaphragm deflection, and the device uses a large dia phragm and has an axisymmetric straight orifice. On the other hand, in Test 2 only the frequency response of the centerline velocity and driver displacement are acquired, and the device uses a small diaphragm and the orifice is a rectangular slot. However, since the two tests share the same equipment and basic setup and Test 1 requires additional eq uipment, only Test 1 is detailed below.

PAGE 100

73 PMTs color separator bellows extender 200 mm micro lens to processor synthetic jet Z Y 3 component traverse X Y X Z probe from laser Side View Top Viewto processor mic 1 displacement sensor piezoelectric diaphragm mic 2 Figure 3-1: Schematic of the experimental setup for phase-locked cavity pressure, diaphragm deflection and off-axis, tw o-component LDV measurements. diaphragm mount body plate top plate clamp plate orifice plate d h cavity ( ) diaphragm ( = 37 mm) + Figure 3-2: Exploded view of the modular piezoe lectric-driven ZNMF actuator used in the experimental test.

PAGE 101

74 Figure 3-1 shows a schematic of the complete experimental setup, where a large enclosure 211mmm is constructed with a tarp to house the ZNMF actuator device, the LDV transmitting and receiving optics, and the displacement sensor. The ZNMF actuator consists of a piezoelectric diaphrag m driver mounted on the side of the cavity, and has an axisymmetric straight orifice. The commercially available diaphragm (APC International Ltd. Model APC 850) consists of a piezoelectri c patch (PZT 5A) which is bonded to a metallic shim (made of brass). The diaphragm is clamped between two plates and have an effective diameter equa ls to 37 mm. Figure 3-2 gives an exploded view of the device and Table 3-1 summa rizes the geometric dimensions. Only the orifice top plate is changed to allow five orifice aspect ratio configurations, and the input voltage and actuation frequency are also varied to yield a large parameter space investigation in terms of the following dimensional parameters: 3;;Re;;;;HdhdSkdd An emphasis is made in the orifice aspect ratio variation, hence the five different orifices used, and the input sinus oidal voltage applied to the driver varies from 4 Vpp to 60 Vpp, the frequencies being set to 39, 500, 730 and 780 Hz. This device is constructed specifically to operate in the low-to-moderate Stokes number range, 60S The signal source is provi ded by an Agilent model 33120A function generator. The signal from the functio n generator is applied to a Trek amplifier (model 50/750), and the amplified sinusoidal input voltage signal is th en applied to the driver via a small wire soldered to the piez oceramic patch, which converts the voltage into a mechanical deflection. Since the two variable input parameters are the freque ncy of oscillation, the amplitude of the forcing signal, and the diffe rent orifice plates, the change in these

PAGE 102

75 dimensional parameters can be converted into a change in dimensionless numbers like the Stokes number S the actuation-to-Helm holtz frequency ratio H f f the driving-todiaphragm natural frequency d f f the dimensionless wavenumber kd, and the dimensionless driver amplitude 3d Table 3-1: ZNMF device characteris tic dimensions used in Test 1 Cavity Volume (m3) 7.11 10-6 Orifice Diameter d (mm) 1.0 2.0 3.0 1.0 1.0 Height h (mm) 5.0 1.8 1.0 0.9 5.0 Piezoelectric diaphragm Shim (Brass) Elastic modulus (Pa) 8.963 1010 Poissons ratio 0.324 Density (kg/m3) 8700 Thickness (mm) 0.10 Diameter (mm) 37 Piezoceramic (PZT-5A) Elastic modulus (Pa) 6.3 1010 Poissons ratio 0.31 Density (kg/m3) 7700 Thickness (mm) 0.11 Diameter (mm) 25 Relative dielectric constant 1750 d31 (m/V) -1.75 10-10 Cef (nF) 76 Cavity Pressure The pressure fluctuations inside the cavity are measured simultaneously at two locations using flush-mount ed Brel and Kjr (B&K) 18 diameter condenser type microphones (Model 4138) powered by B&K 2670 pre-amplifiers and a B&K 2804 power supply. Before each test, th e microphones are calibrated using a B&K pistonphone type 4228. The operational freque ncies of the ZNMF device are usually from about 30 Hz to 1 kHz in this test, whic h is well within the frequency range of the

PAGE 103

76 microphone, from 6.5 Hz to 140 kHz ( 2 dB). The nominal sensitivity of the B&K 4138 type microphones is 601.5 dB (ref. 1V/Pa), or 1.0 mV/Pa. When assembling the device parts together, all leaks are carefully minimized by sealing the parts with RTV, and the pressure ports are properly sealed. Figure 3-3 shows a schematic of the two microphone measurement locations inside th e cavity. Notice that for the highest frequency of operation (780 Hz), the ratio of the wavelength 02cfk to the distance 28.7lmm separating the two microphones in the cavity is less than unity 0.41kl implying that the acoustic pressure waves inside the cavity change very little because the distance between microphones is small compared with the acoustic wavelength. 12.5 mm 28.7 mm 37.0 mm Mic 1 Mic 2 3.6 mm Orifice Diaphragm 18.5 mm 22.7 mm Figure 3-3: Schematic (to scal e) of the location of the two 18 microphones inside the ZNMF actuator cavity. Diaphragm Deflection The deflection of the diaphragm is meas ured using a laser displacement sensor Micro-Epsilon Model ILD2000-10. The sensitivity is 1 V/mm, with a full-scale range of 10 mm and a resolution of ~0.1 m. The sensor bandwidth is 10 kHz, and the spot size of the laser is 40 m. Figure 3-4 gives the displacem ent sensor sign convention between

PAGE 104

77 the measured deflection of the diaphragm an d the measured voltage. As the diaphragm moves inside the actuator cavity, the distance d increases and the measured voltage increases as well. Conversely, as the diaphragm deflects away from the cavity, the distance d measured by the laser sensor decreases and the corresponding voltage decreases. Therefore, a positive diaphragm displacement implies the driver deflects to decrease the cavity volume, leading to compression of the fluid in the cavity and hence an increase in cavity pressure. On the contrary, a negative diaphragm displacement implies the diaphragm deflects to increase the cavity volume, thus expanding the fluid inside the cavity and causing a decrease in th e pressure in the cavity. Amplifier + laser displacement sensor ZNMF actuator measured voltage ,as as acdisp acdispdV dV acdispV max in max out (58 mm) function generator + d Figure 3-4: Laser displacement sensor appa ratus to measure the diaphragm deflection with sign convention. Not to scale. This measurement is used to determine the volume velocity (m3/s) dQ of the diaphragm. We actually use two techniques, depending on the ratio d f f Recall that, assuming a sinusoidal steady state operating condition, dQ is given by 02dd SQjjwrWrdr (3-1)

PAGE 105

78 where 0wrwrW is the transverse displacemen t of the diaphragm normalized by the centerline amplitude 0W Therefore, if one knows the diaphragm mode shape, then only 0W is required via measurement to calculate dQ by virtue of Eq. 3-1. If the mode shape is not known, then it must also be measured. The form er technique is thus a singlepoint measurement, where only the centerlin e displacement of the oscillating diaphragm is acquired phased-locked to the drive signal. The mode shape is computed using the static linear composite plate theory described in Prasad et al. (2002) This model is only valid from frequencies ranging from DC up to the first natural frequency d f hence the importance of the frequency ratio d f f This piezoelectric diaphragm has its first natural frequency at about 632d f Hz. Then from Eq. 3-1, the diaphragm volume flow rate can be determined by simply integrating the mode shape of the circular piezoelectric diaphragm. In the case where the frequency ratio d f f is greater than one, the static mode shape is no longer valid, so a second measurement technique is employed to experimentally acquire the mode shape by systematically traversing the laser displacement sensor across the diaphragm ra dius. The root-mean-square value of the diaphragm deflection is computed for each pos ition, and assuming a sinusoidal signal the amplitude is obtained by multiplying the rms value by a factor 2. This sinusoidal assumption was visually check ed during the time of acquisition for all signals, and on some test cases a Fourier series decompos ition was performed that validated this assumption, as described at the end of this Chapter. Figure 3-5 shows the measured and computed mode shape of the piezoelectric diap hragm at several forci ng frequencies. In

PAGE 106

79 the case where 1dff the comparison between the expe rimentally determined mode shape and the linear model shows good agreem ent. Similarly, the figure shows the diaphragm deflection along vers us radius for the highest frequency used in this experimental test, 780 f Hz which clearly indicates the br eakdown of the static model. The slope discontinuity in the e xperimental data near the position 0.65 ra corresponds to the edge of the piezoelectric patch that is bonded via epoxy on the metallic shim and is a result of optical diffraction of the laser beam at this location. 0 0.2 0.4 0.6 0.8 1 0 0.01 0.02 0.03 0.04 0.05 0.06 normalized radiusmagnitude (mm) exp. data linear mode shape f/fd=0.79 f/fd=0.06 f/fd=1.23 Figure 3-5: Diaphragm mode shape comparis on between linear model and experimental data at three test conditions: 0.06dff and p p60 VacV 0.79dff and p p50 VacV and 1.23dff and p p20 VacV Velocity Measurement Velocity measurements of the flowfield emanating from the ZNMF orifice are obtained using Laser Doppler Velocimetry (LDV), the details of which are listed in Table 3-2. The synthetic jet actuator is mounted to a three-axis traverse with sub-micron spatial resolution to move the orifice with respect to the fixed laser probe volume location. The

PAGE 107

80 traverse is traversed in either 0.1 mm or 0. 05 mm steps across the orifice, yielding a total of 31 to 41 positions at which the phase-locke d velocities are measured, depending on the orifice diameter. The enclosure shown in Figure 3-1 is seed ed with LeMaitre haze fluid using a LeMaitre Neutron XS haze machine, where th e haze particles have a mean diameter small enough that it does not influence on the m easured flow field (this is verified by computing the time constant of the particle and then by showing that the particle response, which is like a 1st-order system, faithfully tracks velocity fluctuations at frequencies well below 1 The reader is referred to Ho lman (2005) for the details and analysis on the seed particle dynamics). Probe Combined 514.5 nm 488 nm beams Separate 514.5 nm and 488 nm beams in the horizontal plane LDV 1 LDV 2 Synthetic jet actuator v u (front view) (side view) Figure 3-6: LDV 3-beam op tical configuration. The 488 and 514.5 nm wavelengths of a Spectra-Physics 2020 argon-ion laser are used to obtain coincident, two-component velocity measurements using a Dantec FiberFlow system Typically, the beam st rength is approximately 30 ~ 50 mW for the green (514.5 nm) and 15 ~ 20 mW for the blue (488 nm). As shown in Figure 3-6, a three-beam optical combiner configuration is us ed to facilitate velocity measurements at

PAGE 108

81 the exit plane surface of the synthetic jet ac tuator. Due to mounting constraints, the actuator is mounted at a 45o angle with respect to the horiz ontal such that the scattered light from the probe volume may reach th e receiving optics. A direction cosine transformation is then applied to the acqui red velocity components LDV 1 and LDV 2 to extract the axial and radial velocity components. A 200 mm micro lens and bellows extender coll ects lights at 90 off-axis in order to improve the spatial resolution since only a s lice of the probe volume is seen by the optics. Scattered light from the probe volume is focused and passed through a 100 m diameter pinhole aperture. The resulting fiel d of view was imaged using a micro-ruler and found to be approximately 10 m, indicating that the effective length of the probe volume dz has been reduced by over an order of magn itude from that listed in Table 3-2. After the pinhole, a color se parator splits the 514.5 nm and 488 nm wavelengths and transmits the light to two separate photomultiplier tube s (PMTs), which convert the Doppler signal to a voltage, and it is then passed through a hi gh-pass filter to remove the Doppler pedestal. An additional band-pass filter is then applied to remove noise in the signal outside of the expected velocity range. Next, the FF T of the signals is computed, and the velocity is th en computed from the measured Doppler frequency and the fringe spacing. Finally, since two components of velo city are measured, a coincidence filter is applied to ensure that a Doppler signal is present on both channels at the same instant in time. At each radial measurement position, 8192 samples are acquired in both LDV1 and LDV2, which yields approximately 200 velocity values at each phase bin. Note that each data point has a time of arrival relative to the trigger signal that denotes the zero phase

PAGE 109

82 angle. The LDV data are then divided into phas e bins with 15o spacing, as explained in more details in the data processing section. Table 3-2: LDV measurement details Property LDV 1 LDV 2 Wavelength (nm) 514.5 488 Focal length (mm) 120 120 Beam diameter (mm) 1.35 1.35 Beam spacing (mm) 26.9 26.9 Number of fringes 25 25 Fringe spacing (m) 2.31 2.19 Beam half-angle (deg) 6.39 6.39 Probe volume dx(mm) 0.058 0.056 Probe volume dy (mm) 0.058 0.055 Probe volume dz(mm) 0.523 0.496 Data-Acquisition System Figure 3-7 shows a flow chart of the e xperimental setup. The piezoelectric diaphragm is actuated using an Agilent 33120A function generator wi th a Trek amplifier (Model 50/750). Using the sync signal of th e function generator, the measured quantities are acquired in a phase-locked mode. A National Instruments model NI-4552 dynamic signal analyzer (DSA) PCI card is used for da ta acquisition (DAQ). It is a 16-bit, sigmadelta DAQ card that can sample up to 4 channe ls of analog input simultaneously and has a bandwidth of approximately 200 kHz. In addition, a built-in an alog and digital antialiasing filter is used. The low-pass analog filter has a fixed cuto ff frequency of 4 MHz, which is well above the frequencies considered here and may be considered to have zero phase offset in the passband. The digital filter removes all fre quency components above the desired Nyquist frequency in the oversam pled signal and then decimates the resulting signal to achieve the de sired sampling rate. Similarly, since the signals are ac coupled to remove any dc offset and to increase the resolution in the signal measurements, an y slight amplitude attenuation and phase

PAGE 110

83 shift occurring at low frequenc ies due to the ac coupling high pass filter are accounted for. This ac coupling high pass filter has a dB cutoff frequency at approximately 3.4 Hz, and the .01 dB cutoff frequency is appr oximately 70.5 Hz. Finally, to guarantee statistical accuracy in the re sults, for each signal 100 samples per period are used and at least 500 blocks of data are acquired. For signals having very low amplitude, up to 5000 blocks were taken to minimize noise in the acquired phase-locked data. PC BSA flow software LDV processor LabVIEW Traverse LabVIEW Amplifier TTL pulse DSA card Mic 1 Displacement sensor Mic 2 1 2 3 4 Function generator excitation signal Figure 3-7: Flow chart of measurement setup. As showed in Figure 3-7, the DAQ card interfaces with a standard PC through National Instruments LabVIEW software. LabV IEW is also used to control the traverse for LDV velocity measurements and interface with the Dantec BSA Flow software that controls the LDV system. Of the 4 channe ls of the DSA card, the sync signal coming from the function generator is recorded in the first channel, the second channel acquires the input voltage to the piez oelectric diaphragm after amp lification, the third channel

PAGE 111

84 monitors the pressure fluctuat ions from microphone 1 situated at the bottom of the cavity, and the fourth channel acquires either the signa l from the displacement sensor or from the second microphone located in th e side of the cavity. 0 45 90 135 180 225 270 315 360 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 phaseNormalized quantities 0 45 90 135 180 225 270 315 360 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 phaseNormalized quantities Figure 3-8: Phase-locked signals acquired from the DSA card, showing the normalized trigger signal, displacement signal, pressu re signals and excitation signal. A) Case 70, f = 39 Hz. B) Case 65, f = 730 Hz. d f f A d f f B input signal trigger signal diaph disp Mic 1 Mic 2 input signal trigger signal diaph disp Mic 1 Mic 2

PAGE 112

85 Two sample graphs of the trigger signal, displacement signal, pressure signals and excitation waveform coming from the DSA card during one cycle are shown in Figure 3-8. Figure 3-8A is representative of a test case in which the driving signal frequency is below the resonance frequency of the diaphragm d f and it can be seen that the diaphragm displacement is out of phase with the input voltage. On the other hand, when the device is actuated beyond d f a 180o phase shift occurs in the diaphragm frequency response, hence the input signal and the displacement signal are nearly in phase, as shown in Figure 3-8B. Similarly, this mean s that a positive voltage from the function generator results in a diaphragm deflection ou t from the cavity. Note that this is a relevant observation when comparing the expe rimental results with the low-dimensional model discussed in later chapte rs. The dynamics of the diaphragm can also be seen from Figure 3-8 as it deflects in and out of the cav ity. An increase in the diaphragm deflection results in a rise in cavity pr essure (with a phase lag), and vi ce versa, which confirms the sign convention shown previ ously in Figure 3-4. Data Processing Once the data have been simultaneously acquired for the cavity pressures, diaphragm displacement, and the velocity prof ile from the setup described above, it then needs to be carefully processe d in order to have great conf idence in using the results. First, the pressure and diaphragm signals ar e averaged using a vector spectral averaging technique to eliminate noise from the synchrono us signals. This averaging technique, in contrast with the more common RMS av eraging technique th at reduces signal fluctuations but not the noise floor, computes the average of complex quantities directly, separating the real from the imaginary part which then reduces the noise floor since

PAGE 113

86 random signals are not phase-coherent from on e data block to the next. For instance, using the vector averaging technique, the power spectrum is computed such that (National Instruments 2000) GXX (3-2) where X is the complex FFT of a signal x X is the complex conjugate of X, and X is the average of X, real and imaginary part s being averaged separate ly. In contrast, the RMS averaging technique used the following equation for the power spectrum, GXX (3-3) Then, once the velocity data is acquired with the LDV sy stem, the velocity profiles must be integrated spatially and temporally to determine the average volume flow rate jQ and hence jV, via 01 ,njnjn SQvtxdtdSVS, (3-4) where 0t is the time of expulsion portion of the cycle. However, an important issue is statistical analysis of the LDV data Velocity measurements arrive at random points during a cycle, and like a ll experimental measurements, random noise also exists. Therefore, the velocity data points must be sorted into phase bins to generate a phase-locked velocity profile. Each bin is a representation of the mean and uncertainty for all of the velocity points th at fall within that bin. Th erefore, to know the optimum bin width to minimize the combined random and bias errors in the LDV measurements, Figure 3-9 illustrates the percent error in the computed quantity jV from simulated LDA data, for several simulated signal-to-noise ratios (SNR) and where 8192 samples are

PAGE 114

87 acquired. As expected, for very large bin widths on the order of 45o the error in jV is quite large. However, in the bin width range 5-20o, the error appears to be minimized. In this plot, the mean value of the error is indicative of the bias error due to the size of the bin width, while the error bars indicate the random error com ponent. Not surprisingly, as the SNR is increased, this random error decr eases. Most notably, however, the optimum phase bin width does not appear to be a func tion of the SNR. Based on this plot, an acceptable trade-off in the e xperimental test is found by choosing a bin width of 15o, which is equivalent to sampling 24 points per period. 0 10 20 30 40 50 -5 0 5 10 15 20 25 Bin width (deg)Vj error (%) SNR=0.5dB SNR=2dB SNR=8dB SNR=32dB SNR=128dB Figure 3-9: Percentage error in jV from simulated LDV data at different signal to noise ratio, using 8192 samples. Next, an outlier rejection t echnique is applied on the raw velocity data to ensure high quality experimental data. The modified Tau-Thomson outlier rejection criterion is extended for two joint probability distributio n function (pdf) distri butions, corresponding to the two set of data from LDV1 and LDV2, and a 99.9% confidence interval is retained. Basically, the value of the join t pdf is computed for each data pair and is compared to a

PAGE 115

88 look-up table that is generated depending on th e percentage confidence interval from a joint Gaussian pdf. This table gives the locus of points on the bounding ellipse and if a point falls outside the ellipse, it is considered as an outlier. The details of this outlier rejection criterion can be found in Holman (2005). Another source of uncertainty comes from the phase resolution in each of the signals. As seen above, the volume flow rate at the exit has a phase resolution of 15 where corresponds to half the bin width, i.e. 7.5. Similarly, the data acquired by the DSA card (trigger signal diaphragm displacement and pressure fluctuations) are acquired with 100 samples pe r period. That yields a phase uncertainty of .8 in these signals. Thus, the net uncer tainty in the phase between the pressure and the volume flow rate at the orif ice is then estimated to be ,jQP (3-5) where is the phase difference in Qj and P and 7.51.89.4 Next, the phase-locked profiles are spatiall y integrated to determine the periodic volume flow rate since ,njn SQtvtxdS (3-6) The spatial integration is numerically performed using a trapezoidal integration scheme. Figure 3-10 illustrate s a set of typical phase-loc ked axial velocity profiles during four different phases separated by 90 in the cycle, corresponding approximately to maximum expulsion, maximum ingestion, and the two phases half way between. Figure 3-10A plots the vertical velocity compon ent, while the radial component is plotted in Figure 3-10B, and Figure 3-10C gives the correspondi ng volume flow rate after integration across the orifice. The error bars represent an estimate of the 95% confidence

PAGE 116

89 interval for each velocity measurement and are obtained using a pe rturbation technique (Schultz et al. 2005) that yiel ds the same nominal values of uncertainty as a standard Monte Carlo technique but with signi ficantly less computational time. Figure 3-10: Phase-locked velocity prof iles and correspondi ng volume flow rate acquired with LDV for Case 14 (8 S p p28 VacV Re46.53% ), acquired at 0.05 yd A) Vertical velocity component. B) Horizontal velocity component. C) Volume flow rate. This method is employed to estimate the un certainty in the aver aged volume flow rate. The 95% confidence interval estimate of jQ, in turn, is used to estimate the -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 r/d horizontal velocity u (m/s) =0 =90 =180 =270 -0.4 -0.2 0 0.2 0.4 0.6 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 r/d vertical velocity v (m/s) =0 =90 =180 =270 B 0 45 90 135 180 225 270 315 360 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x 10-6 Phase (deg)Volume flow rate Qj (m3/s)C A

PAGE 117

90 uncertainty in the Reynolds number, which is in the range of 2-10%, via the following relationship jjnQVS (3-7) so the Reynolds number can be defined as, Rej nQd S (3-8) and similarly to compute the stroke length 0L based on the phase-locke d velocity profile, 0 01 ,nnj S nLvrtdSdtV S (3-9) The locus of the positive values of the volume flow rate are integrated to give the average volume flow rate during the expulsion part of the cycle, jQ, which is related to the average velocity by Eq. 3-7. In this e xperimental work, zero pha se angle corresponds to the volume flow rate Qj equal to zero with positive slope, meaning at the beginning of the expulsion phase of the cycle. Then, sin ce all signals are phase-locked to the trigger signal of the input voltage, a corresponding phase shif t is applied to each signal. Also, since the phase resolution is only 15o in the LDV data, the two points bracketing the data point where 0jQt are picked and a linear interpol ation is then performed between them with a phase resolution of 1o, as illustrated in Figure 3-10C. Furthermore, in order to gain more conf idence in the experimental data, some features of the device behavior are checked. Fi rst, the integration of the volume flow rate over a complete cycle, while never exactly equa l to zero, is found to be typically less than 1% of the amplitude of jQt, even though the acquired velo city profiles are always at about 0.1 mm above the surface of the orifice (so for 0.033;0.05;0.1 yd ), hence

PAGE 118

91 entraining some mass flow that could affect the volume flow rate. But this is not surprising since a previous study has shown that a synthetic jet appears to remain zero-net mass-flux even up to 0.4 yd (Smith and Glezer 1998); or actually as long as the distance above the orifice is small compared to the stroke length 0yL. Similarly for the cavity pressure measurements, the pressure signal sometimes is noisy at the low frequency and low amp litude (or Reynolds number) cases, which is principally due to 60 Hz line noise contamina tion. However, the signal is at least an order of magnitude higher th an the microphone noise floor, as shown in Figure 3-11 for Case 52, and the Fourier series decompositi on to the vector-averaged signal described next still provides a good f it to the time signal, while rejecting contaminated noise. 0 45 90 135 180 225 270 315 360 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 phasePressure (Pa) noise floor pressure from microphone 1 Figure 3-11: Noise floor in the microphone measurements compared with Case 52. Finally, repeatability in the extracted experi mental data is an important issue to be considered. Thus, to ensure fidelity in this experimental setup, seve ral cases were retaken at different periods in time. For instance, Case 20 and Case 29 have been experimentally tested twice four months apart, while Case 62 and Case 69 have al so been taken twice

PAGE 119

92 within a time frame of weeks. Table 3-3 compares the result s between these cases for the principal governing parameters. As can be seen, the results are within the estimated confidence interval. It shoul d be pointed out though that fo r Case 20 and Case 29, the velocity measurements were acquired at a slightly different di stance from the surface ( 0.07 yd and 0.05 yd respectively) that could explain the larger difference seen in jQ in these cases. Table 3-3: Repeatability in the experimental results cP (Pa) Case # S Re Mic 1 Mic 2 dQ (m3/s) 7.6 88.24% 3.5913% 3.214% 63.48107% 20 7.6 85.04% 3.2610% 63.79107% 33.9 113110% 414.916% 365.616% 56.411011% 29 33.9 968.86% 331.510% 56.271010% 3.9 204.94% 39.911% 43.012% 64.09106% 62 3.9 192.93% 45.13% 49.33% 64.18101%t 17.3 13615% 16104% 19573% 44.48102% 69 17.3 16854% 19743% 44.59102% Fourier Series Decomposition Typical results of the phase-locked meas urements are shown in Figure 3-12 for four test cases, where the jet volume flow rate and the pressure fluctuations from microphone 1 and microphone 2 are plotted as a function of phase during one full cycle of operation. Clearly, while the jet volume fl ow rate is nearly sinusoidal, the cavity pressure fluctuations deviate significantly from a sinusoid for Cases 44 and 72 in this example, indicating significant nonlinearities. Therefore, a Fourier series decomposition via least squares estimation is performed to determine the number of significant harmonic components for all the trace signals.

PAGE 120

93 0 45 90 135 180 225 270 315 360 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 phaseNormalized Quantities Re=1959 S=43 0 45 90 135 180 225 270 315 360 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 phaseNormalized Quantities Re=2059 S=53 Figure 3-12: Normalized quantitie s vs. phase angle. A) Case 44 0.35,0.93 hdSt B) Case 58 1.68,1.36 hdSt C) Case 63 5.0,0.72 hdSt D) Case 72 0.94,0.31 hdSt The symbols represents the experimental data, the lines are the Fourier series f it on the data using only 3 terms, and errorbars are omitted in the pressure signal for clarity. B A Qj Microphone 1 Microphone 2 Qj Microphone 1 Microphone 2

PAGE 121

94 0 45 90 135 180 225 270 315 360 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 phaseNormalized Quantities Re=286 S=14 0 45 90 135 180 225 270 315 360 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 phaseNormalized Quantities Re=179 S=4 Figure 3-12: Continued. To determine the number of relevant harmoni cs that capture the principal features of the signal, a vector averaged power spectr um analysis is performed for each individual case, as shown for four cases in Figure 3-13, and Table G-1 in Appendix G summarizes the percentage power contai ned in the fundamental and each harmonic along with the corresponding square of the residual norm. Cl early, although more than 90% of the total C D Qj Microphone 1 Microphone 2 Qj Microphone 1 Microphone 2

PAGE 122

95 power in the signal is present at the fundamental, th e contribution from subsequent harmonics may not be negligib le, especially from the 2nd harmonic (at 03 f ). There exist several criteria to determine the degree of conf idence in the relevant harmonics to keep in the Fourier series reconstruction. Here, we us e the residual of the least squares fit, where the signal is decomposed into k components until the least square estimation of the (k+1)th harmonic only fits noise, hence reaching a ne gligible residual value. This can be seen from Figure 3-13. Once the number of si gnificant harmonics retained in the signal has been validated for each case, the Fourier series fit to the waveforms for the volume flow rate and the two pressure signals are plot ted on top of the data points as a function of phase, as shown in Figure 3-12 for selected cases. In these cases, only the first 3 harmonics in the signals are kept. 0 1000 2000 3000 4000 5000 100 105 [Parms 2]Power spectrum Case 44 Microphone 1 Microphone 2 0 1000 2000 3000 4000 5000 10-15 10-10 [ mrms 2]Frequency (Hz) Diaphragm Figure 3-13: Power spectrum of the two pressure recorded and the diaphragm displacement. A) Case 44 0.35,0.93 hdSt B) Case 58 1.68,1.36 hdSt C) Case 63 5.0,0.72 hdSt D) Case 72 0.94,0.31 hdSt The symbols are exactly at the harmonics locations. 0500 f Hz A

PAGE 123

96 0 1000 2000 3000 4000 5000 6000 7000 100 105 [Parms 2]Power spectrum Case 58 Microphone 1 Microphone 2 0 1000 2000 3000 4000 5000 6000 7000 10-10 [ mrms 2]Frequency (Hz) Diaphragm 0 1000 2000 3000 4000 5000 100 [Parms 2]Power spectrum Case 63 Microphone 1 Microphone 2 0 1000 2000 3000 4000 5000 10-15 10-10 [ mrms 2]Frequency (Hz) Diaphragm Figure 3-13: Continued. 0780 f Hz 0500 f Hz B C

PAGE 124

97 0 50 100 150 200 250 300 350 100 [Parms 2]Power spectrum Case 72 Microphone 1 Microphone 2 0 50 100 150 200 250 300 350 10-15 [ mrms 2]Frequency (Hz) Diaphragm Figure 3-13: Continued. Flow Visualization In addition to the above experimental set up that provides quanti tative results on the ZNMF actuator device under a wide range of operating conditions, a qualitative visualization of the flow behavior emanati ng from the orifice is performed, mainly to ascertain whether a jet is formed or not, and if indeed a jet is formed, under which flow region it can fall within. Laser source Glass tank Light sheet optics ZNMF actuator Seeded flow field Light sheet Figure 3-14: Schematic of the flow visualization setup. 039 f Hz D

PAGE 125

98 Figure 3-14 shows a schematic of the flow visualization setup, where a continuouswatt argon-ion laser is used in conjunction with optical lenses to form a thin light sheet centered on the orifice axis, and atomized haze fluid is introduced into the tank to seed the flow. The topology of the orifice flow behavior is simply not ed and Table 2-3 in Chapter 2 lists the results for most of the cases. The nomenclature presented in this dissertation is crude and far from exhaustive. The reader is referred to the detailed work preformed by Holman (2005) for a complete qualitative and quantitative study on the different topological regimes of ZNMF actuato rs exhausting into a quiescent medium. The topological regimes identified through th is test matrix only include the no flow regime or a distinct flow pattern present at the orifice exit. In Table 2-3, it is referred to as follows: X: no jet formed J: jet formed To conclude this chapter, an extensiv e experimental inve stigation has been described, the results of which are used th roughout this dissertation. In particular, Chapter 4 focuses on orifice flow physics, hence presenting the results of the LDV measurements and the flow visualization. The cavity pressure and diaphragm deflection measurements are presented in Chapter 5 where the cavity behavior is thoroughly investigated. Finally, Chapter 6 leverages all the information gathered and uses all these results for the development of a refined reduced-order model.

PAGE 126

99 CHAPTER 4 RESULTS: ORIFICE FLOW PHYSICS This chapter presents the results of the experimental and numerical investigation described in Chapter 3 and Appendix F, respec tively. It focuses on the rich and complex flow physics of a ZNMF actuator exhausting in to a quiescent medium. The local flow field at the orifice exit is fi rst examined via the numerical si mulations that provide useful information on the flow pattern inside the actuator, followed by the results of the experimentally acquired velocity profiles. Some results on the jet formation are presented next. A detailed investigation is then performed on the influence of the governing parameters on the orifice flow field and more generally on the actuator performance. Finally, the diverse mechan isms that can gene rate non-negligible nonlinearities in the actuator behavior are reviewed and the related limitations addressed. Ultimately, this investigation on the orific e flow behavior will help in developing physics-based reduced-order models of ZNMF actuators exhausting in to quiescent air for both modeling and design purposes, as detailed in Chapter 6. The test matrix tabulated in Table 2-3 is designed to cover a significant parameter space, in terms of nondimensional parameters, where a total of 8 numerical simulations and 62 different experimental cases are consid ered. The dimensional parameters varied in this study are the orifice diameter d and height h, the actuation frequency and the input voltage amplitude (i.e., driver amplit ude). Hence, in terms of dimensionless parameters, this corresponds to varying the orifice aspect ratio hd, the jet Reynolds

PAGE 127

100 number RejVd the Stokes number 2Sd the dimensionless volume displaced by the driver 3d the actuation-to-Helmholtz frequency ratio H the actuation-to-diaphragm frequency ratio d and the dimensionless wavenumber kd. Recall that the Reynolds, Stokes, a nd Strouhal numbers are related via 2ReStS so that knowledge of any two di ctates the remaining quantity. The available numerical simulations are from the Geor ge Washington Univ ersity (lead by Prof. Mittal) in a collaborative joint effort be tween our two groups. The me thodology of the 2D numerical simulations is provided in Appendix F. Next the experimental setup is presented in detail in Chapter 3, and this investigation provides information on the velocity profile across the orifice hence jet volume flow rate, cavity pressure oscillations, and driver volume flow rate as a function of phase angl e and in terms of the above dimensionless parameters. Local Flow Field Velocity Profile through the Orifice: Numerical Results The major limitation in the experimental setup is that it is spatially limited, in the sense that data cannot be acquired inside the orifice. Therefore, the role of numerical simulations that can provide information anywhere inside the computed domain is relevant in this study. The direct numerical simulations described in detail in Appendix F are used to understand the flow behavior inside the orifice, particularly to examine the evolution of the velocity profile inside the slot. The test cases of interest correspond to Case 1, 2 & 3 in Table 2-3. They have the same Reynolds number Re = 262, but have different Stokes number (S = 25 or S = 10) and orifice aspect ratio h/d (1, 2, and 0.68, for

PAGE 128

101 Cases 1, 2, and 3, respectively). Note also th at they share a straight rectangular slot for the orifice and that the simulations are two-dimensional. d h y x y/h = -1 y/h = -0.5 y/h = -0.75 y/h = -0.25 y/h = 0 B) Case 2 D L 0 /h = 1.32 L 0 /h = 0.66 L 0 /h = 12 C) Case 3 Figure 4-1: Numerical results of the orifice flow pattern showing axial and longitudinal velocities, azimuthal vorticity contours and instantaneous streamlines at the time of maximum expulsion. A) Case 1 (h/d = 1, St = 2.38, S = 25). B) Case 2 (h/d = 2, St = 2.38, S = 25). C) Case 3 (h/d = 0.68, St = 0.38, S = 10). D) Actuator schematic with coordinate definition. A) Case 1

PAGE 129

102 Figure 4-1 shows the flow pattern inside the orifice for A) Case 1, B) Case 2 and C) Case 3. The azimuthal vort icity contours are plotted along with the axial and longitudinal velocities and some instantaneous streamlines during the time of maximum expulsion. Also, Figure 4-1D shows a schematic of th e actuator configura tion and provides the coordinate definition and labels used. Notice the recirculation zones inside the orifice for the cases of low stroke length L0 (Case 1 and Case 2). Clearly, the orifice flow undergoes significant changes as a function of the geom etry and actuation conditions. Therefore, the vertical velocity profile is probed at fi ve different locations along the orifice height from y/h = 0 to y/h = -1 and at different phases during one cycle, as schematized in Figure 4-1D. Figure 4-2, Figure 4-3, and Figure 4-4 show the comput ed vertical velocity profiles at various locations in the orifice and corresponding at f our different times during the cycle, for Case 1, Case 2, and Case 3, respec tively. Also for clarification, the azimuthal vorticity contours are shown in each figure. First of all, it can be seen that Case 1 and Case 2 are qualitatively similar, although the three cases show that the velocity profile undergoes significant development along the orifi ce length. In partic ular, Figur e 4-2 and Figure 4-3 show a strong phase dependence in the velocity pr ofile inside the orifice, which is not the case for Case 3. Similarl y, the Stokes number dependency in the shape of the velocity profile is clea rly denoted. In particular, th e velocity profiles at the exit (y/h = 0) during the time of maximum expulsion are nearly identical for Case 1 and Case 2 that have the same Stokes number, as shown in Figure 4-2B and Figure 4-3B, respectively.

PAGE 130

103 269 177 C D 95 Figure 4-2: Velocity profile at different locations inside the orifice for Case 1 (h/d = 1, St = 2.38, S = 25). A) Beginning of expulsion (2o). B) Maximum expulsion (95o). C) Beginning of ingestion (177o). D) Maximum ingestion (269o). The vertical velocity is normalized by jV. Also shown are the azimuthal vorticity contours for each phase. 2 A B

PAGE 131

104 For the low stroke length or high Strouhal number cases at the maximum expulsion time (Cases 1 and 2 in Figure 4-2B and Figure 4-3B, respectively), the variation in the boundary layer thickness at th e walls (from thin to thick as the fluid moves toward the orifice exit), along with the va riation of the core region is indicative of the flow acceleration inside the orifice. This tangential acceleration of fluid at the boundary wall generates vorticity (Morton 1984). Also, notice the smoother profiles near the walls along the orifice length for the time of beginning of the expulsion stroke (Figure 4-2A and Figure 4-3A) and beginning of the ingestion stroke (Fi gure 4-2C and Figure 4-3C), compared when the cycle reaches its maximum expulsion an d ingestion (Figure 4-2B and Figure 4-2D, and Fi gure 4-3B and Figure 4-3D). At the time of maximum expulsion velocity 90, for these two cases of high Strouhal number where no jet is formed, the velocity profiles are influenced by the vorticity that is not expelled at the exit (or inlet during maximum ingestion) and is trapped inside the orifice, leading to secondary vortices. In the case of a larger stroke length (L0/h = 12), as seen in Fi gure 4-4, the flow is always reversed near the walls. Interestingly, in Case 3 the flow is similar along the orifice height roughly independe nt of y, but is still dependa nt of the phase angle, hence of time. Notice that in this case where the st roke length is much larger than the orifice height, the flow is dominated by entrance and exit losses, where viscous effects are confined at the walls and the core region is moving in phase at each y location along the orifice. In this case, the flow never reaches a fully developed stage, as shown in Figure 4-4C.

PAGE 132

105 A B C D 2 92 182 270 Figure 4-3: Velocity profile at different locations inside the orifice for Case 2 (h/d = 2, St = 2.38, S = 25). A) Beginning of expulsion (2o). B) Maximum expulsion (92o). C) Beginning of ingestion (182o). D) Maximum ingestion (270o). The vertical velocity is normalized by jV. Also shown are the azimuthal vorticity contours for each phase.

PAGE 133

106 A 0 D 270 C 180 Figure 4-4: Velocity profile at different locations inside the orifice for Case 3 (h/d = 0.68, St = 0.38, S = 10). A) Beginning of expulsion (0o). B) Maximum expulsion (90o). C) Beginning of ingestion (180o). D) Maximum ingestion (270o). The vertical velocity is normalized by jV. Also shown are the azimuthal vorticity contours for each phase. 90 B

PAGE 134

107 S = 25 Re = 262 A B C Figure 4-5: Vertical velocity contours in side the orifice during the time of maximum expulsion. A) Case 1, (h/d = 1, St = 2.38). B) Case 2 (h/d = 2, St = 2.38). C) Case 3 (h/d = 1, St = 0.38). Figure 4-5 shows the vertical velocity c ontours inside the orifice for the three numerical cases, at the tim e of maximum expulsion in Figure 4-5A, Figure 4-5B, and Figure 4-5C, respectively. As noted above, Ca se 3 that has a large stroke length shows a flow inside the orifice that is never fully-dev eloped, still in its development stage while it is exhausting into the quiescent medium. The growing boundary layer at the orifice walls are clearly seen and never merge. This is not the case for lower stroke lengths (Cases 1 and 2). Indeed, Case 1 in Figure 4-5A is a case where the flow seems to be on the onset of reaching a fully-developed stage. And this is more clearly seen in Figure 4-5B where for Case 2 the boundary layers merge somewher e past the middle of the orifice height. However, as already seen in Figure 4-1B a nd Figure 4-3B, the fact that some of the nonejected vortices are trapped inside the orifi ce visibly perturb the flow pattern from the expected exact solution where the fully-dev eloped region should be represented by uniform velocity contours. S = 10 Re = 262 S = 25 Re = 262

PAGE 135

108 On the other hand, one can in terpret the flow pattern s hown in Figure 4-5 with a different point of view. For in stance, a vena contracta can be seen in Case 1 and Case 2 (Figure 4-5A and Figure 4-5B, respectively), bu t a core flow moving in phase in Case 3 (Figure 4-5C). None of these three cases are fully-developed in the strict sense (velocity profile invariant of position y). Clearly, Cases 1 and 2 are affected by the trapped z-vorticity that is generated at the wall and at the orifice leaps; and in the absence of this z-vorticity, the flow would a ppear to be fully-developed. Contrarily, for Case 3 (Figure 4-5C) the vena contract a extends the full height of the orifice and the flow never reaches a fully-developed stage. On the vorticity dynamics inside the orifice, the generation of the azimuthal or zvorticity comes from the pressure gradient pr esent at the sharp edges of the orifice exit (and inlet), and of the fluid tangential accelera tion at the wall boundary in side the orifice. This generation process is instantaneous and inviscid (Morton 1984). However, the decay or destruction of vorticity only re sults from the cross-diffusion of the two vorticity fluxes that are of opposite sense and that occurs at the center line. Here, the diffusion time scale for vorticity to diffuse across the slot is 2vistd (4-1) and the convective time scale for a fluid particle to travel the orifice height is given by convjthV. (4-2) Therefore, the ratio of the time scales, 2Rej vis convV t dd thh, (4-3)

PAGE 136

109 provides an indication of the establishment of fully-develope d flow as a function of Reynolds number. Table 4-1 summarizes this ra tio of the time scales for the 3 numerical test cases investigated above. As discussed above, the flow is more willing to appear as fully-developed for Case 2 than for Case 3 that has the largest stroke length. Table 4-1: Ratio of the diffusi ve to convective time scales Case 1 2 3 Revis convt d th 262 131 385 Exit Velocity Profile: Experimental Results The flow field at the vicinity of the or ifice exit surface is examined by extracting the velocity profiles. Four cases are considered that represent four t ypical flow regimes. They are shown in Figure 4-6, Figure 4-7, Figure 4-8, and Figure 4-9, corresponding in Table 2-3 to Case 71, Case 43, Case 69, an d Case 55, respectively. The first common parameter of interest is th e Stokes number, ranging from 4S to 53S, that clearly dictates the shape of the veloci ty profile, as a function of ph ase angle, as expected from the theoretical pressure-driven pipe flow solution. This is actually shown in the upper left plot in each test case figure, where the exact solution of the pressure-driven oscillatory pipe flow is plotted versus radius of the or ifice diameter during the time of maximum expulsion. Note that the amplitude of the exact solution is normalized by the corresponding experimental centerline velocity at maximum expulsion. At a low Stokes number (S = 4), Figure 4-6 shows a parabolic profile in the orifice velocity for each phase angle, representative of the steady state Poiseui lle pipe flow solution. Next, as the Stokes number increases (S = 12), as seen in Figure 4-7, an overshoot takes plac e near the edges known as the Richardson effect. For this ca se of low Reynolds number (Re = 63), the

PAGE 137

110 Figure 4-6: Experimental vertical veloc ity profiles across the orifice for a ZNMF actuator in quiescent medium at differe nt instant in time for Case 71: Re112, 0.94 hd, 0.1 yd The solid line in th e upper left plot is the exact solution of oscillatory pipe flow, normalized by the experimental centerline velocity, at maximum expulsi on. The zero phase corresponds to the start of the expulsion cycle. velocity profile seems to be slightly differe nt from expulsion to ingestion times in the cycle. As the Stokes number increases further, as in Figure 4-8 where S = 17, the overshoot is less pronounced, but the Reynolds number is much higher (Re = 1361) and now the ingestion and expulsion profiles exhibi t less variation in th eir profiles. Notice also that in this case, the orifice aspect ratio is 5 hd and 00.9Lh is less than unity so the flow is expected to reach a fully-deve loped state, compared with Case 43 in Figure -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 =15 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 =15 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 =15 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 exact solution=15 /2 /2 /4 /2 /2 /4 /2 /2 /4 /2 /2 /4 S=4 St=0.14 vertical velocity (m/s) vertical velocity (m/s) r/d r/d

PAGE 138

111 4-7 where for a similar Stokes number (S = 12), the orifice aspect ratio is less than unity and the stroke length is great er than the orifice height 01.3 Lh, meaning that the flow may not reach a fully-developed state and is dominated by entrance and exit region effects. Finally, the case of highest Stokes number (S = 53) shows a nearly slug velocity profile, as seen in Figure 4-9. Note that in th is case, no jet is formed at the orifice lip. Figure 4-7: Experimental vertical veloc ity profiles across the orifice for a ZNMF actuator in quiescent medium at different instant in time for Case 43: Re63 0.35 hd, 0.03 yd The solid line in the uppe r left plot is the exact solution of oscillatory pipe flow, normalized by the experimental centerline velocity, at maximum expulsion. The zero phase corresponds to the start of the expulsion cycle. -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 =15 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 =15 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 exact solution =15 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 =15 /2 /2 /4 /2 /2 /4 /2 /2 /4 /2 /2 /4 S=12 St=2.23 r/d r/d vertical velocity (m/s) vertical velocity (m/s)

PAGE 139

112 Another interesting result co mes from a comparison of these experimental velocity profiles with the theoretical ones, as shown in each figure in the uppe r left plot. Notice that the overall profile, part icularly the overshoot near th e wall if present, is well represented. However, because of the finite distance off the orifice surface at which the LDV data have been acquired (y/d = 0.1, 0.03, 0.1, and 0.03 for Case 71, 43, 69, and 55, respectively), the profiles cannot exactly match at the orifice edge. An additional reason for the difference noticed between the exact so lution and the experiment al results is that the flow may not be fully-developed by the time it reaches the orifice exit. Recall that the theoretical solution assumes a fully-develope d flow inside the orifice, meaning the boundary layer forming at the orif ice entrance has finally merged. If not, the flow is still evolving along the length of the orifice. Hence, it would be like having an effective diameter -less than the actual onefor which the exact solution should be valid (a change in the diameter d will change the Stokes number S and the shape of the velocity profile). This remark is important for modeling purposes. For the four cases represented here, and act ually for all the experimental test cases considered in this study, notice the large velo city gradients near the edge of the orifice that the LDV experimental setup is able to accurately capture. Especially for the large Reynolds number case (Case 69) in Figure 4-8, where the ve rtical velocity jumps from about zero to 40 m/s over a lengt h scale of 0.3 mm. Similarly, it can be seen from these plots that, although the edge s of the orifice are at 0.5 rd the velocity tends to a zero value beyond the orifice lip. This is due to th e fact that the LDV data have been acquired at a finite distance yd above the orifice surface, and that fluid entrainment is significant near the edge of the axisymmetric orifice. Indeed, although not shown here for these

PAGE 140

113 cases, but Figure 3-10 in the experimental se tup chapter is representative of a typical case, the radial veloc ity component assumes its maximum n ear the edge of the orifice. This is observed for the expul sion part of the cycle as we ll as for the ingestion part. Notice though that it is more the ratio 0yL rather than that the finite distance yd that does matter in this scenario (Smith and Swift 2003b). Figure 4-8: Experimental vertical veloc ity profiles across the orifice for a ZNMF actuator in quiescent medium at diffe rent instant in time for Case 69: Re1361 5 hd, 0.1 yd The solid line in the upper left plot is the exact solution of oscillatory pipe flow, normalized by the experimental centerline velocity, at maximum expulsi on. The zero phase corresponds to the start of the expulsion cycle. -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -14 -12 -10 -8 -6 -4 -2 0 2 4 =15 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -14 -12 -10 -8 -6 -4 -2 0 2 4 =15 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0 5 10 15 20 25 30 35 40 45 exact solution =15 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0 5 10 15 20 25 30 35 40 45 =15 S=17 St=0.22 r/d vertical velocity (m/s) /2 /2 /4 /2 /2 /4 /2 /2 /4 /2 /2 /4vertical velocity (m/s) r/d

PAGE 141

114 Figure 4-9: Experimental vertical veloc ity profiles across the orifice for a ZNMF actuator in quiescent medium at differe nt instant in time for Case 55: Re125 1.68 hd, 0.03 yd The solid line in the upper left plot is the exact solution of oscillatory pipe flow, normalized by the experimental centerline velocity, at maximum expulsi on. The zero phase corresponds to the start of the expulsion cycle. Next, in terms of phase angle during an entire cycle, as se en in all these plots, the velocity profiles are clearly phase dependent Notice also that the profiles are not symmetric from the expulsion to the ingest ion periods, especially in magnitude, the ingestion part having usually a broader velo city profile with decreased amplitude. Clearly, during the expulsion phase the flow is ejected into quiescent medium similar to a -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 =15 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 =15 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 exact solution =15 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 =15 S=53 St=22.3 vertical velocity (m/s) r/d r/d vertical velocity (m/s) /2 /2 /4 /2 /2 /4 /2 /2 /4 /2 /2 /4

PAGE 142

115 steady jet, whereas during the ingestion phase, th e flow is similar to that in the entrance region of a steady pipe flow. This observat ion corroborates our global approach outlined in Chapter 2 in making a clear distinction be tween the expulsion and the ingestion portion of the cycle. Also, it is worthwhile to note that all the test cases considered in this dissertation are close to zero-ne t mass flux. For instance, for the four experimental cases discussed above, the ratio between totQ, the total volume flow ra te during one cycle, and jQ, the volume flow rate during th e expulsion part of the cycl e, is equal to 0.17, 0.01, 0.39, and 0.09, for Cases 71, 43, 69, and 55, respectively. The total volume flow rate being at least an order of magnitude lower th an that during the expulsion part, the zeronet mass flux condition is indeed verified. Finally, another interesting observation is found in the relationship between the centerline velocity CLVt at the exit and the corresponding mean or spatially averaged velocity 2jjVtV. This is shown in Figure 4-10A and Figure 4-10B where the ratio of the two time-averaged velocities is plotted vers us Stokes number and Reynolds number, respectively. For instance, it is expected that 22CLjjVVV for the steady Poseuille flow, which is seen in Figure 4-10A, while for high Stokes number where the velocity profile is expected to be slug-li ke, it should asymptotes to unity. Recall the analytical solution for an oscillatory pipe fl ow shown in Figure 25 and plotted again in Figure 4-10A. However, there is no such we ll-defined behavior for all the cases studied here that will dictate a scaling law for this velocity ratio.

PAGE 143

116 1 10 100 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 SVj / Vj,CL 0
PAGE 144

117 flux is the key aspect that determines the f ormation of synthetic jets in quiescent flow (Utturkar et al. 2003, Holman et al. 2005). This flux of vorticity, v during the expulsion can be defined as 2 001 (,)(,) 22d vzx x tvxtddt dd (4-4) where (,)z x t is the azimuthal vorticity component of interest for an axisymmetric orifice, and is the time of expulsion. Simple sc aling arguments lead to the conclusion that the nondimensional vorticity flux is proportional to the Strouhal number via 1jK St Vd (4-5) where K was a constant determined to be 2.0 and 0.16 for two-dimensional and axisymmetric orifice, respectively, and that pr edicts whether or not a jet would be formed at the orifice. Only two topological regimes ar e identified in this di ssertation: jet formed or no jet formed, as summarized in Table 2-3 for all the test cases. Again, the reader is referred to Holman (2005) for a more comple te and thorough qualita tive and quantitative analysis on this topic. Fi gure 4-11 shows how this jet formation criterion defined in Utturkar et al. (2003) compares with the experimental data. Clearly, for the range of Stokes and Reynolds numbers investigated in the present experiments, the jet formation criterion defined in Eq. 4-5 fo r a circular orifice is in good agreement with the flow visualization results. The cases having a cl ear jet formed are we ll above the line 10.16 St, while the ones well below this line do not create a jet. And around this criterion line, the flow regions are more in a tr ansitional regime in terms of jet formation. Notice that although only the experimental re sults on the circular orifice are presented

PAGE 145

118 here, the numerical simulations featuring a re ctangular slot and shown in Table 2-3 do satisfy the jet formation criterion as well. Consequently, this investigation on the jet formation criterion, validated th rough the flow visualization re sults, gives confidence in using this criterion for the descriptio n of the orifice flow behavior. 101 102 103 104 100 101 102 103 104 S2Re jet no jet 1/St=0.16 Figure 4-11: Experimental results on the jet formation criterion. Influence of Governing Parameters In this section, the governi ng parameters extracted from the dimensional analysis and described in Chapter 2 are applied in th is experimental invest igation in order to confirm their validity and also investigat e their respective in fluence on the ZNMF actuator behavior. The functional form (E q. 2-15) is reproduced for illustration, 3,,,,,, Rejd HdQQ hw StfnkdS ddd (4-6) Note that the role of the Helmholtz frequency and of the cavity size and driver characteristics 3;;;Hddkd is not addressed in th is section, the next

PAGE 146

119 chapter being entirely dedicated to them. Since the experiment al test only uses axisymmetric orifices, the functional form for fixed driver/cavity parameters can be recast as ReSt h f nS d (4-7) So any two parameters between the Str ouhal number, Reynolds number and Stokes number, plus the orifice asp ect ratio should suffi ce in describing the ZNMF actuator flow characteristics. For completeness, as mentione d at the end of Chapter 2 in the description of the different regimes of the orifice flow, recall the dimensionless stroke length that is simply related to the above parameters by 0 2Re1L dd hhShSt (4-8) where the constant comes from the assumption of a sinusoidal jet velocity. Before presenting some results on the experimental data, a remark should be made concerning their interpretation. As explained previously, the cavity pressure fluctuations are used in lieu of the pressure drop across th e orifice since experimentally, it is rather difficult to acquire the dynamic pressure drop across the orifice for such small devices. However, the acquired cavity pressure may de viate from the actual pressure drop through the orifice. This will be disc ussed further in Chapter 5. Empirical Nonlinear Threshold First of all, the current approach to ch aracterize or calibra te an oscillatory fluidic actuator that was first indirectly a ddressed by Ingard and Labate (1950) and more recently by Seifert and Pack ( 1999) is applied here, which uses the simple empirical observation that the cav ity pressure fluctuation p is linearly proportional to the

PAGE 147

120 centerline exit velocity fluctuation CLv at low forcing levels, and to 2CLv (i.e., nonlinear) at sufficiently high forcing levels. Figure 4-12 shows the variation of the averaged jet velocity jV to the cavity fluctuating pressure cP for a specific Stokes number. Notice that two scaling regions can be extracted from this plot, i.e. as the pressure amplitude increases the jet velocity varies from a linear to a nonlinear s caling dependence. 10-1 100 101 102 103 104 10-2 10-1 100 101 102 Pc/Vj S=4 S=8 S=17 S=53 Vj 2 ~ Pc/c0 Vj ~ Pc/ Figure 4-12: Averaged jet velocity vs. pressu re fluctuation for different Stokes number. However, the threshold level from wh ich the linear proportionality can be distinguished from the nonlinea r one varies as a function of the Stokes number. Clearly, this calibration curve is Stokes number dependant and practical ly useless. This analysis is based only on the velocity and pr essure information and thus lacks crucial nondimensional parameters to be taken into account to capture more physics. This motivates the dimensional analysis performe d in Chapter 2, and the dependency of the actuator behavior on those paramete rs is investigated next.

PAGE 148

121 Strouhal, Reynolds, and Stokes Numbers versus Pressure Loss Consider the loss mechanisms inside the orifice, especially the minor nonlinear losses. Nonlinear losses are know n to be dependant on the fl ow parameters and, in the case of steady flow, empirical laws already exist (White 1991). However, for an oscillatory pipe or channel flow, this topic is still the focus of current research. Here, a physics-based qualitative descri ption on the nonlinear loss mechanism is attempted. The nonlinear loss coefficient can be written as 20.5c d jP K V (4-9) where cP represents the cavity pressure fluctuatio ns which is equivalent to the pressure drop across the orifice for a ZNMF actuato r (see Chapter 5 for more details on the pressure equivalence), and 20.5jV is the dynamic pressure based on the time and spatial-averaged expulsion velocity at the orifice exit jV. The experimentally determined loss coefficient dK is plotted versus Sthd which is equivalent to the ratio of the str oke length to the orifi ce height, is shown in Figure 4-13A and Figure 4-13B us ing linear and logarithmic scales, respectively. Notice that the 3 numerical simulation results discus sed above are also included for comparison. From the linear scale, Figure 4-13A, the pressu re loss data asymptote to a constant value of order of magnitude 1 O as 0SthdhL decreases beyond a cert ain value. This suggests that when the fluid particle excursion or stroke length is much larger than the orifice height h, minor nonlinear losses due to en trance and exit effects dominate the flow. However, the magnitude of these lo sses and the degree of nonlinear distortion is likely to be strongly dependent on Reynolds number, in a similar manner as for the steady

PAGE 149

122 state case where tabulated semi-empirical la ws, which are exclusiv ely a function of Re, are able to accurately predict such pressure loss (White 1991). The logarithmic plot in Figure 4-13B confirms that dK is not only a function of the Reynolds number but also of the Stokes number, hence Strouhal number, th e ratio of unsteady to steady inertia. 10-2 10-1 100 101 102 0 50 100 150 200 250 300 350 400 St.h/dKd= P/(0.5 v2) S=4 S=8 S=10 S=12 S=14 S=17 S=25 S=36 S=43 S=53 CFD results 10-2 10-1 100 101 102 101 102 103 St.h/dKd= P/(0.5 v2) S=4 S=8 S=10 S=12 S=14 S=17 S=25 S=36 S=43 S=53 CFD results Figure 4-13: Pressure fluctuation normali zed by the dynamic pressure based on averaged velocity jV vs. Sthd A) Linear scale. B) Logarithmic scale. A B

PAGE 150

123 10-2 10-1 100 101 102 0 50 100 150 200 250 300 350 400 StKd= P/(0.5 v2) S=4 S=8 S=10 S=12 S=14 S=17 S=25 S=36 S=43 S=53 CFD results 10-2 10-1 100 101 102 101 102 103 StKd= P/(0.5 v2) S=4 S=8 S=10 S=12 S=14 S=17 S=25 S=36 S=43 S=53 CFD results Figure 4-14: Pressure fluctuation normali zed by the dynamic pressure based on averaged velocity jV vs. Strouhal number. A) Linear sc ale. B) Logarithmic scale. Interestingly, the loss coefficient is ag ain shown in Figure 4-14 in a linear and logarithmic scale, but this time as a func tion of the Strouhal number only. Notice the linear plot shows better collapse in the data for high Strouhal number, i.e. for unsteady inertia greater than steady inertia, while fo r low Strouhal numbers, not much difference is noticed. This suggests that their exists 2 distinct regimes in which the loss coefficient B A

PAGE 151

124 dK is primarily a function of the Strouhal number for high St, while for low St, a dimensionless stroke length may be more a ppropriate in describi ng the variations in dK. S = 25 Re = 262 S = 25 Re = 262 A B Figure 4-15: Vorticity contours during the maximum expulsion portion of the cycle from numerical simulations. A) Case 1 ( h/d = 1, St = 2.38). B) Case 2 ( h/d = 2, St = 2.38). C) Case 3 ( h/d = 1, St = 0.38). As previously discussed in Ga llas et al. (2004), the resu lts of numerical simulations allow detailed investigation of these issues. Again, CFD simulations have the capability to provide information everywhere in th e computed domain. Figure 4-15 shows the variation of the spanwise vorticity for the thr ee computational cases (Case 1, 2 and 3) at the time of maximum expulsion. As already shown in Figure 4-11 on the jet formation criterion, for Cases 1 and 2 no jet is form ed (Figure 4-15A and Figure 4-15B), whereas for Case 3 a clear jet is formed (Figure 415C). The spanwise vor ticity contours show that the vortices formed during the expulsion cycle for Case 1 and 2 are ingested back S = 10 Re = 262 C

PAGE 152

125 during the suction cycle, leading to the trapping of vortices inside the orifice, which is in contrast when clear jet formation occurs as for Case 3. 10-2 10-1 100 101 102 101 102 103 St.h/dKd,in=P/(0.5vin 2) S=4 S=8 S=12 S=14 S=17 S=34 S=43 S=53 Figure 4-16: Pressure fluctuation normali zed by the dynamic pressure based on ingestion time averaged velocity vs. Sthd Finally, it is interesting to compare the re sults from the expulsion to the ingestion phases during a cycle. Usually, only the expulsi on part is considered since it is the most important and relevant in terms of practic al applications. However, momentum flux occurs for both expulsion and ingestion, a nd for modeling purposes the ingestion part should not be disregarded. Especially from the experime ntal and numerical results shown in the first section of this chapter on th e velocity profiles inside and at the exit of the orifice, which noticeably identify a cl ear distinction between the ingestion and expulsion profiles in time. Hence, similarl y to Figure 4-13, the nondimensional pressure loss coefficient dinK based on the spatial and time averaged exit velocity during the ingestion phase is shown in Figure 4-16 as a function of Sthd for several Stokes numbers. Interestingly, a similar trend is observed between the i ngestion and expulsion

PAGE 153

126 time of the cycle. This observation is furthe r validated via the analysis of the numerical data, where similarly to the data presented in Figure 4-15, the spanwise vorticity contours occurring during the maximum ingestion are show n for Cases 1, 2 and 3 in Figure 4-17. S = 25 Re = 262 S = 25 Re = 262 S = 10 Re = 262 A B C Figure 4-17: Vorticity contour s during the maximum ingesti on portion of the cycle from numerical simulations. A) Case 1 ( h/d = 1, St = 2.38). B) Case 2 ( h/d = 2, St = 2.38). C) Case 3 ( h/d = 1, St = 0.38). This is an important result that will be used later on when developing the reducedorder models of ZNMF actuators in Chapter 6. Indeed, the analysis of the oscillatory flow through a symmetric orifice (i.e., same geometry on both ends) can be simplified as follows: whatever is true during the expulsi on stroke will be valid for the ingestion stroke as well. The experimental setup onl y permits measurement of the exhaust flow during expulsion and inlet flow during ingestio n. During the expulsion phase, the flow at the orifice exit sees a baffled open medium where the flow exhausts, while during the

PAGE 154

127 ingestion phase, the flows s ees the orifice exit as an en trance region. Again, this simplification is possible for symmetric orifices only, so no as ymmetric orifice can be considered in this analysis. To confirm this, the CFD results are again used. Indeed, to be true the velocity profile at the orifice exit ( y/h = 0) during maximum ingesti on should match the velocity profile at the orifice inlet ( y/h = -1) during maximum expulsion. This is shown in Figure 4-18, Figure 4-19, and Figure 4-20 for Case 1, Ca se 2, and Case 3, respectively. The left hand plot compares the vertic al velocity (normalized by jV ) at the start of expulsion versus the start of ingestion, at both orifice ends (inlet: y/h = -1, and exit: y/h = 0). The right hand plot is similar but for the times of maximum e xpulsion and ingestion during a cycle. Notice how the velocity profiles are close to each other, especially for Case 2 (Figure 4-19), which confirms the argument st ated above: whatever is true during the expulsion stroke at the orifice ex it will be valid for the ingest ion stroke at the orifice inlet as well, and vice-versa. Figure 4-18: Comparison between Case 1 verti cal velocity profiles at the orifice ends. A) At start of expulsion a nd start of ingestion. B) At maximum expulsion and maximum ingestion. B A

PAGE 155

128 Figure 4-19: Comparison between Case 2 verti cal velocity profiles at the orifice ends. A) At start of expulsion a nd start of ingestion. B) At maximum expulsion and maximum ingestion. Figure 4-20: Comparison between Case 3 verti cal velocity profiles at the orifice ends. A) At start of expulsion a nd start of ingestion. B) At maximum expulsion and maximum ingestion. Nonlinear Mechanisms in a ZNMF Actuator In view of the experimental results, the effect of the different nonlinear mechanisms present in the system may be a crit ical issue that needs to be addressed if one B A B A

PAGE 156

129 wants to gain confidence in the interpretation and the use of the experimental data. If one takes a ZNMF actuator apart, it is basically comprised of the driv er (a piezoelectric diaphragm in the case of the current experime ntal tests), the cavity, and the orifice. Hence, by considering the pressure fluctua tion signal as the output signal of interest, nonlinearities in this signal can arise due to: 1. orifice nonlinearities 2. cavity nonlinearities 3. driver nonlinearities First, the oscillatory nature of the flow through the orifice can generate nonlinearities in the pressure signal due to the entrance and exit regions. These nonlinearities are the focus of this dissertation, the goal being to isolate them in order to develop a suitable reduced-order model that accounts for these types of nonlinearities in the pressure signal. Before proceeding down this path, we first need to understand how nonlinearities due to the cavity pressure fluctu ations and the driver scale with operating conditions. Starting with the cavity pressure fluctuati ons, nonlinearities in the signal can arise due to deviations of the sound speed from the isentropic small-signal sound speed (Blackstock 2000, pp. 34-35). The ge neral isentropic equation of state 0 p ppp can be expressed in terms of a Ta ylor series expansion, such that 2 02 0 000112 1 2!3!cp p (4-10) where is the ratio of specific heats, and the superscript / denotes fluctuating quantities and the subscript 0 denotes nominal values Here, the small-signal isentropic sound

PAGE 157

130 speed is defined as 000cp that is strictly speaking only valid in the limit as 0 It is therefore of interest to appl y Eq. 4-10 in the case of the ZNMF actuator having a closed cavity to isolat e its effect. For a closed cavity, the conservation of mass can be directly written as 0 t (4-11) or, 0 dd dtdt (4-12) which is simply equivalent to dd (4-13) By then substituting Eq. 4-13 in Eq. 4-10, and for an adiabatic gas, Figure 4-21 can be generated that shows the variation between the linear small-signal approximation and the exact nonlinear solution, as a function of the change of volume inside the cavity. Hence, significant nonlinearities due to the departure of the cavity small-signal approximation will not arise for pressures below ~160 dB, and/or for change in the cavity volume 0.02 d. Notice that the change in volum e is dictated by the driver volume flow rate dQj where here d The maximum change in cavity volume and pressure seen in our experiments is for Case 69, where 0.014 d and the pressure is equal to 64 dB, which is we ll below the departure of the small-signal approximation. This effect is therefor e not an issue in our experiments.

PAGE 158

131 0.01 0.1 1 10 150 160 170 180 190 200 210 220 230 240 250 -d / Pressure (dB) small-signal approximation (linear) exact solution (nonlinear) Figure 4-21: Determination of the validity of the small-signal assumption in a closed cavity. Next, the driver nonlinearities are considered. Obviously, by driving the piezoelectric diaphragm at frequencies much higher than the firs t natural frequency d f some nonlinearity can result in the driver si gnal. Hence, most of the test cases are operating at frequencies below fd = 632 Hz, and only two frequencies above d f (at f = 730 Hz and f = 780 Hz) are considered in the experi mental investigation, for which the distortion of the driver signal is closely monitored. Sim ilarly, nonlinear behavior can occur at dc, coming from the distortion in the measured displacement signal for a pure tone input. Note that nonlinearities can also arise from the power amplifier. As detailed in Chapter 3, the input signal is amplified before arriving to the piezoelectric driver, and the amplifier has intrinsic dynamics.

PAGE 159

132 10-5 10-4 10-3 10-2 10-1 10-6 10-4 10-2 100 102 104 d / THD in Pc (%) S=4 S=12 S=14 S=17 S=43 S=53 0 0.5 1 1.5 2 2.5 3 3.5 10-6 10-4 10-2 100 102 104 / HTHD in Pc (%) S=4 S=12 S=14 S=17 S=43 S=53 Figure 4-22: Log-log plot of the cavity pressure total harmonic distortion in the experimental time signals. A) Versus d B) Versus H After being identified, these nonlinearities mu st also be extracted and quantified to determine their effect on the actuator behavior A useful tool in the investigation of nonlinear effects is found in th e study of the total harmonic distortion (THD). The THD is defined as the ratio of the sum of the powers of all harmonic frequencies above the fundamental frequency to the power of the fundamental one (National Instruments 2000): A B

PAGE 160

133 1 0THD %100N k kG G (4-14) where k = 1N is the number of harmonics and k = 0 represents the fundamental frequency. The results of the spectral anal ysis of the time signal presented in Chapter 3 are used in this investigation. Note that in this analysis the THD contains the measured total harmonic distortion up to and including the highest harmonic at 10 (N = 10), hence is not limited to the first few harmonics. First, Figure 4-22 shows the THD present in the cavity pressure (taken with microphone 1, s ee Chapter 3 for definition) as a function of the change in the cavity volume d and function of the ratio of the Helmholtz to actuation frequency H. Clearly, the distortions in th e cavity pressure signal are not affected by the change in cavity volume, as shown in Figure 4-22A and described above. Similarly, compressibility effects appear to not play a role in th e cavity pressure signal distortion, as seen from Figure 4-22B. The next chapter (Cha pter 5) discusses the cavity compressibility effect in more details. Next, Figure 4-23 shows the T HD variation in the time signa ls as a function of the Strouhal number for different Stokes numbers. From the pressure signal (acquired by microphone 1, see Figure 3-3 in Chapter 3 for definition) plotted in Figure 4-23A, significant nonlinearities are pres ent especially at the low Strouhal number cases. This is in accordance with the time trac es already seen in Figure 3-1. Figure 4-23B shows the THD in the jet volume velo city which, besides a few cases at low Strouhal numbers, is less than 1%. This means that the ma jority of the cases can have jQ accurately represented by a pure sinusoidal si gnal. Finally, the THD present in the diaphragm signal is shown in Figure 4-23C Clearly, the motion of the diaphragm

PAGE 161

134 displacement in time can be correctly assumed to be sinusoidal for all the cases considered, a negligible percen t of nonlinearities in the signal being present. Therefore, practically the nonlinearities present in the experimental signal mostly come from the orifice, no cases are found to be strongly affect ed by nonlinearities that are not due just to the orifice. 10-2 10-1 100 101 102 10-6 10-4 10-2 100 102 10 4 StTHD in Pc (%) S=4 S=12 S=14 S=17 S=43 S=53 10-2 10-1 100 101 102 10-2 10-1 100 101 StTHD in Qj (%) S=4 S=12 S=14 S=17 S=43 S=53 Figure 4-23: Log-log plot of the total harm onic distortion in the experimental time signals vs. Strouhal number as a func tion of Stokes number. A) Cavity pressure. B) Jet volume flow rate. C) Driver volume flow rate. A B

PAGE 162

135 10-2 10-1 100 101 102 10-3 10-2 10-1 100 101 StTHD in Qd (%) S=4 S=12 S=14 S=17 S=43 S=53 Figure 4-23: Continued. To summarize this chapter, a joint experi mental and numerical investigation of the velocity profiles, at the orifice exit as well as inside the orifice, has been performed. Numerical simulations are a useful tool to elucidate the orifice flow physics in ZNMF actuators and complement the experimental resu lts. Clearly, the orifice flow is far from trivial, especially for such small orifices and flow conditions, and it exhibits a rich and complex behavior that is a function of the location inside the orifice and a function of phase angle during the cycle. Next, the influence of the governing parameters, such as the orifice aspect ratio h/d Stokes number S Reynolds number Re, Strouhal number St or stroke length L0, has been experimentally and numerically investigated. It has been found that a dimensionless stroke length equivalent to the Strouhal number times h/d is the main parameter in describing the losses associated with th e pressure drop across the orifice. Finally, a survey of the possible sources of nonlinearities present in the time signals of interest (pressure, jet volume flow rate ) has been performed. Potential nonlinear C

PAGE 163

136 sources were identified and evaluated; their overall influence on the actuator performance has been quantified through a total harmonic distortion an alysis. The information gathered through this study on th e orifice flow results will ai d in the understanding and the development of a physics-based reduced-ord er model of such actu ators in subsequent chapters.

PAGE 164

137 CHAPTER 5 RESULTS: CAVITY INVESTIGATION This chapter discusses the cavity behavior of a ZNMF actuator device, based on the experimental results presente d in the previous chapter and using available numerical simulation results. A discussion is first pr ovided on the measured and computed cavity pressure field, based on e xperimental and numerical results. Then follows a careful analysis of the compressibility effects occurr ing inside the cavity where it is shown that the Helmholtz frequency is the critical parame ter to be considered. Finally, the driver, cavity and jet volume velocities are consider ed, specifically their respective roles and how they interact and couple with each other. Ultimately, this investigation on the cavity will give valuable insight and help in th e understanding of the physical behavior of ZNMF actuators in quiescent air for both modeling and design purposes. Cavity Pressure Field The knowledge of the pressure inside the cavit y is of great intere st since it dictates the orifice flow behavior, whic h is naturally a pressure-drive n oscillatory flow. In fact, the cavity pressure fluctuations are approximate ly equivalent to the pressure drop across the orifice; hence it plays a cen tral role in the overall actuat or response. Specifically, the magnitude and the phase of the pressure signa l are of interest, and comparing the data from two separate microphones placed at diffe rent locations inside the cavity, as shown in Figure 3-3, provide some answers. More over, since a characteri stic feature of the reduced-lumped element model pres ented in Chapter 2 is to assume that the pressure drop across the orifice is equivalent to the cavity pr essure, it is of great importance to know

PAGE 165

138 whether or not this assertion is valid. This is detailed below, base d on both experimental and numerical results. Experimental Results First of all, a spectrum analysis has b een performed on the pressure traces to characterize the dominant features of the ti me signals. Figure 5-1 shows the coherent power spectrum of Cases 9 to 20 (all with th e same Stokes number of 8) recorded via Microphone 1, that clearly indicates non negl igible harmonic components present in almost all cases, with th e fundamental component f0 always capturing most of the total power and the 2nd harmonic at 3f0 having the next most contribution. Notice however the presence of the 60 Hz and 120 Hz line noise from the noise floor measurement shown on the front face. Also, it is found that only s uper-harmonics are present, no sub-harmonics, which shows that using a Fourier series decomposition of the phase-locked pressure signal is a valid approach. Figure 5-1: Coherent powe r spectrum of the pressure signal for Cases 9 to 20, 8S and Re988

PAGE 166

139 Figure 5-2: Phase plot of the normali zed pressures taken by microphone 1 versus microphone 2. A) Case 46. B) Case 49. C) Case 59. D) Case 62. Next, the phase difference between the two microphones is analyzed. Four different cases are examined, one when the tw o pressure signals appear quite sinusoidal and similar in shape as in Case 46 Re109,26 St and Case 49 Re1439,2 St another one (Case 59, Re3039,0.9 St ) when one microphone exhibits some distortion while the other is ra ther sinusoidal, and finally the scenario when both signals are clearly nonlinear, as in Case 62 Re157,0.1 St Figure 5-2 shows the phase plots of these four cases, where the pressure data is normalized by subtracting the mean and dividing by the standard deviation Cleary, in each scenario the phase between the two microphones is surprisingly invarian t, with the exception of Case 59. And Re157,0.1 St Re3039,0.9 St Re109,26 St Re1439,2 St A B C D

PAGE 167

140 although only four cases are report ed here, this behavior is t ypical for all cases. As for Case 59, Figure 5-3 plots the phase locked pressure signals during one cycle, and the phase difference observed from the phase plot is clearly seen here when crossing the zero axis, but the peak amplitudes occur at the same phase for each signal, i.e. at the maximum expulsion and maximum ingesti on time of the cycle. 0 45 90 135 180 225 270 315 360 -800 -600 -400 -200 0 200 400 600 800 phase (degree)Pressure (Pa) Microphone 1 Microphone 2 Figure 5-3: Pressure sign als experimentally recorded by microphone 1 and microphone 2 as a function of phase in Case 59 53,Re3039,0.9 SSt The amplitude of the pressure inside the cavity is investigated next. While the phase seems spatially invariant inside the cavity a change in amplitude is noted. This is already seen in Figure 5-3 for Case 59, but is also represented for all cases in Figure 5-4 that plots the ratio of the total amplitude between microphone 2 and 1, as a function of the inverse of the Strouhal number. Noti ceably, referring to Figure 3-3 for the microphone locations, whether the pressure amp litude is recorded on the side or on the bottom of the cavity does matte r. Notice that by plotting ,2,1 ccPP against 1 St, one can also infer the influence of the jet formati on criterion on the pressu re data. Certainly,

PAGE 168

141 whether a jet is formed or not may affect the pressure amplitude variation inside the cavity. Moreover, when looking at the value of kH the wavenumber times the largest cavity dimension for these cases, and indicate d in the legend of Fi gure 5-4, it is clear that for the high Stokes number cases, th e compact acoustic source approximation may not be valid anymore, meaning that the cav ity does not act like a pure compliance and some mass, or inertia, term s may come into play. 10-2 10-1 100 101 102 0.2 0.4 0.6 0.8 1 1.2 1.4 1/St Pc, 2 / Pc, 1 S=4, kH=0.029 S=12, kH=0.029 S=14, kH=0.37 S=17, kH=0.55 S=43, kH=0.37 S=53, kH=0.58 No jetJet Figure 5-4: Ratio of microphone amplitude (P a) vs. the inverse of the Strouhal number, for different Stokes number. The vert ical line indicates the jet formation criterion. Numerical Simulation Results Numerical simulations are a useful tool, es pecially when experiments fail. Indeed, in the present context it is really difficult, if not impossible, to measure the actual pressure drop across the orifice hence the two microphones placed inside the cavity. Therefore, the importance of the CFD results takes its entire place for cavity flows.

PAGE 169

142 Computational fluid dynamics To confirm the experimental observations, available num erical simulation data is thus analyzed. These data have been prev iously reported in Gallas et al. (2004), the methodology for the numerical simulations is given in Appendix F, and Case 2 Re262,2.4 St and Case 3 Re262,0.4 St in the test matrix (Table 2-3) are considered here. Notice however that this simulation uses an incompressible solver for the cavity where the pressure field is comput ed by solving the Poisson equation, and that it assumes a 2D sinusoidal vibrating membra ne at the bottom of the cavity, thereby neglecting any three-dimensional effects. Ye t the solution can be considered valid since the actuation frequency is far below the Helmho ltz frequency (the next section describes this compressibility effect in great detail), and since the cavity size is much smaller than the wavelength. Also, previous work (Uttu rkar et al. 2002) showed that the ZNMF actuator performance was rather insensitive to the driver placement inside the cavity. The pressure distribution at one instant in time is first given for Case 2, where Figure 5-5A corresponds to 45o during the expulsion portion of the cycle (0o corresponding to the onse t of jet expulsion), and Figure 5-5B is at the beginning of the ingestion cycle. In this case where no jet is formed, the pressure is fairly uniform inside the cavity away from the orific e entrance. On the other hand in the case where a clear jet is formed, as for Case 3, the pressure inside the cavity has a more disturbed pattern, as it can be seen in Figure 5-6 where contours of the pressure field is shown at different phases during the ingestion porti on of the cycle. Nodes are present inside the cavity as a function of phase, which is main ly due to the high stroke lengt h that is characteristic of this case. During the ingestion process, flui d particle reach and impinge on the bottom of

PAGE 170

143 the cavity, hence generating some circulation at the corners that quickly dissipates as the driver starts a new cycle. Figure 5-5: Pressure contours in the cavity and orifice for Re262 and 2.4 St (Case 2) from numerical simulations. A) 45o during expulsion. B) Beginning of the suction cycle, referenced to Qj. phase Qj180o0o360o expulsioningestionA phase Qj180o0o360o expulsioningestionB

PAGE 171

144 Figure 5-6: Pressure contours in the cavity and orifice for Re262 and 0.4 St (Case 3) from numerical simulations at four different phases during the ingestion part of the cycle. To complete this picture of the pressure field, the cavity is probed at fifteen locations, as schematized in Figure 5-7, and th e instantaneous pressure is recorded as a function of time during one cycle. The result s for Case 2 (no jet) are plotted in Figure 5-8A and for Case 3 (strong jet) in Figure 58B. The vertical axis shows the magnitude 180 225 270 315

PAGE 172

145 of the pressure normalized by 2 jV, on one of the horizontal axes is the phase angle and on the other one the five slices corresponding to the five cuts made parallel to the driver up to the orifice inlet, as schematized in Figur e 5-7. For each slice, the side, middle and center probes are plotted on top of each other. In these two examples, the effect of a jet being formed at the orifice exit, and hence at the orifice inlet as well, does appear to influence the pressure field inside the cavity. center probes middle probes side probes orifice driverXX X XX X XX X XX X XX X X pressure probe Figure 5-7: Cavity pressure probe locat ions in a ZNMF actuator from numerical simulations. Actually, to try comparing the CFD data with the experimental results, although the driver is not on the same side of the cavity and is modeled as a 2D vibrating membrane, the three locations corresponding to the positions of the two microphones in the experimental setup plus just at the orifice entran ce are extracted from the above figures and are shown in Figure 5-9. Clearly, as one move towards the orifice, the pressure decreases and increasing distor tion in the time signals are noted for the large stroke length case. Also, the pressure is much la rger in amplitude for the higher Stokes number case, although the two cases have the same jet Reynolds number. Note that the phase between the different pressure probes is again spatially invariant.

PAGE 173

146 Figure 5-8: Normalized pressure inside the cavity during one cycle at 15 different probe locations from numerical simulation results. A) Case 2 (no jet formed). B) Case 3 (jet formed). A B

PAGE 174

147 Figure 5-9: Cavity pressure normalized by 2 jV vs. phase from numerical simulations corresponding to the experi mental probing locations. A) Case 2 (no jet formed). B) Case 3 (jet formed). Femlab Finally, a simple calculation was also performed in FEMLAB to check the pressure field inside the cavity. The geometry of the device utilized in the experiments is used to construct a 3D simulation. A time-harmoni c analysis is then applied on the meshed domain that solve the Helmholtz equation 2 2 01 0 p pq c (5-1) where q is a dipole source. Sound hard boundari es are applied on the walls (normal derivative of the pressure is zero on the boundary), an impedance boundary condition is prescribed at the orifice exit that is based on the experimental resu lts, and the diaphragm is simply modeled as an accelerating bound ary in an harmonic manner, the threedimensional mode shape being modeled via a Bessel function (representative of the solution of the wave equation for a clamped membrane). The steady state wave equation is then solved for a specified driving frequency, i.e. the pressure p is equal to it p e Note (a) (b) 0 45 90 135 180 225 270 315 360 15 10 -5 0 5 10 15 phase Microphone 1 Microphone 2 Orifice entrance 0 45 90 135 180 225 270 315 360 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 phase Microphone 1 Microphone 2 Orifice entrance Re262,0.4 St Re262,2.4 St A B Normalized pressure Normalized pressure

PAGE 175

148 that even though the orifice is present in th e geometry, viscous effects are completely ignored and only the acoustic fiel d is considered. Two experi mental cases are simulated, namely Case 55 39 f Hz and Case 58 780 f Hz Figure 5-10: Contours of pressure phase insi de the cavity by numerically solving the 3D wave equation using FEMLAB. A) Case 55. B) Case 58. The results are shown in Figure 5-10 and Figure 5-11, where Fi gure 5-10 shows the contour plot of the pressure phase inside th e cavity which can be seen to be invariant throughout the entire domain. Similarly, Figure 5-11 shows the pressure amplitude versus phase for the probe points that corres pond to the locations of the microphones, as well as the point right at the orifice inlet, in the same manner as described above in Figure 5-9. Clearly, the pressure is fairly uniform at these two driving frequencies, f = 39 Hz and f = 780 Hz It should be pointed out that th e pressure recorded here does not match the experimental results since this simu lation is kept at a simple level, bypassing the complex structural and fluidic interactions that occur in the real device, only the wave equation being solved here. The all point of th is exercise is to infer the uniformity of the max = 2.534 min = 2.541 max = 2.637 min = 2.275 39 f Hz 780 f Hz A B

PAGE 176

149 pressure time signal within the cavity at two forcing frequencies, as well as the spatial invariance of the phase. Finally, Femlab is also used to solve the modal analysis of the sealed cavity. The first eigenvalue mode is found to occur at a frequency equals to 8740 Hz, far below the excitation frequencies utilized in the experiments. Figure 5-11: Cavity pressure vs. phase by solving the 3D wave equation using FEMLAB and corresponding to the experimental pr obing locations. A) Case 54. B) Case 58. To summarize this discussi on on the cavity pressure, the pressure experimentally acquired inside the cavity shows some nonuniformity, especially for small Strouhal numbers. This could be due to uncertaint ies in the calibrati on of the microphone, and most likely also because for such low Strouhal numbers the particle excursion can reach the cavity sides and generates additional viscous scrubbing losses. This effect may be significant for a small cavity in terms of accu rate modeling. On the other hand, the pressure field is fairly uniform for large Str ouhal number flows. These results have been confronted and compared with two sets of numerical simula tions. An important result though is that the phase is shown to be indepe ndent of the location in side the cavity. On 0 45 90 135 180 225 270 315 360 -600 -400 -200 0 200 400 600 phasePressure (Pa) Microphone 1 Microphone 2 Orifice entrance 0 45 90 135 180 225 270 315 360 -500 -400 -300 -200 -100 0 100 200 300 400 500 phase Microphone 1 Microphone 2 Orifice entrance 39 f Hz 780 f Hz Pressure ( Pa ) Pressure ( Pa ) A B

PAGE 177

150 the contrary, the amplitude of the pressu re fluctuations does depend on the probe location, and the pressure amplitude just at the orifice entrance seems to be always slightly different than anywhere else insi de the cavity. In fact, the microphones are measuring not only the dynamic pressure fluctu ation due to the oscillating flow within the orifice, but also any hydrodynamics and acoustic s effects, such as radiation. This fact has to be taken into account for impedance estimation of the orifice since LEM assumes an equal pressure inside the cavity to that acr oss the orifice. In practice, one should place the microphones in a similar way to what is commonly employed in tabulated orifice flow meters that use corner pressure ta p (White 1979). Therefore, the quantitative experimental results based on the cavity pressu re should be considered with cautious. Compressibility of the Cavity The question of the validit y of an incompressible assumption for modeling the cavity is of great interest and practical importa nce. First, from a computational point of view, it is rather essential to know whether th e flow inside the cavity can be considered as incompressible, the computational appro ach being quite differe nt for a compressible and an incompressible solver. Second, from the equivalent circuit perspective of the lumped element model presented in Chapter 2, a high cavity impedance (which occurs for a stiff or incompressible cavity) will prevent the flow from going into the cavity branch. On the other hand, a compliant or compressible cavity wi ll draw fluid flow hence reducing the output response. The co mpressibility behavior is explored via illustrative cases, both analytically and expe rimentally. The LEM prediction serves in providing the general trend and behavior in the frequency domain, while experimental data are used here to validate these findings.

PAGE 178

151 LEM-Based Analysis First, consider some analytical examples. They are Case 1 described in Gallas et al. (2003a) and Case 1 of the NASA Langley workshop CFDVal200 4 (2004). Both examples have a piezoelectric-diaphragm driv er and are thus expected to exhibit two resonant frequencies. The acoustic impedance of the cavity aC Z is systematically varied through the cavity vo lume variable since, assuming an isentropic ideal gas, they are directly related via 2 01aC aCc Z j Cj (5-2) and the frequencies that govern the system response are recorded and compared. From Eq. 5-2, it is expected that as the cavity vol ume decreases and tends to zero, the acoustic compliance aCC also tends to zero, and the cavity becomes stiff. These frequencies are defined as follows. In particular, 1 f and 2 f are the first and second resonance frequencies, respectively, in the syntheti c jet frequency response and are defined in Gallas et al. (2003a) 2222210dHdHffff C, (5-3) where aDaCCC C is the compliance ratio, and 2 i f The two roots of the quadratic equation Eq. 5-3 are the square of the natural frequencies of the synthetic jet, i.e. 2 1 f and 2 2 f Here, 2HHf is the Helmholtz frequency of the synthetic jet resonator and since 1H aOaC M C, (5-4)

PAGE 179

152 is directly proportional to the cavity and or ifice geometrical dimensions via both the acoustic mass of the orifice aO M and the acoustic compliance of the cavity aCC (see Eq. 5-2). Similarly, 2ddf is the natural frequency of th e actuator diaphragm. In general 1 or H d f ff and 2or dH f ff and only for the limiting cases when 1 f and 2 f are widely separated in frequency do the tw o peaks approach the driver and Helmholtz frequencies. Nevertheless, these two frequencies are alwa ys constrained via 12 dH f fff With this information as background, consid er Case 1 from Gallas et al. (2003a), in which all parameters are fixed to their resp ective nominal values and the cavity volume is progressively decreased. The baseline case is such that H d f f and the natural frequency of the diaphragm along with the or ifice dimensions are held constant. Table 5-1 shows the impact of the decrea se of the cavity volume on the frequency response of the system, and is illustrated in th e log-log plot in Figure 5-12. The first frequency 1 f is clearly governed by the diaphragm natural frequency and tends to a fixed value equal to d f as the volume decreases, while the second frequency 2 f is influenced by the Helmholtz frequency H f that tends to infinity as th e volume is decreased. Notice however that LEM breaks down for high frequencies since the assumption of 1kd is no longer valid.

PAGE 180

153 Table 5-1: Cavity volume effect on the devi ce frequency response for Case 1 (Gallas et al. 2003a) from the LEM prediction. 2114d f Hz H f Hz 1 f Hz 2 f Hz Baseline: 63 02.510 m 941 918 2,167 02 1,331 1,254 2,243 05 2,104 1,685 2,640 010 2,976 1,832 3,434 020 4,208 1,885 4,719 050 6,654 1,911 7,363 0100 9,410 1,918 10,372 0500 21,042 1,924 23,123 01000 29,757 1,924 32,690 100 101 102 103 104 105 10-2 10-1 100 101 102 Frequency (Hz)Centerline velocity (m/s) 0=2.6e-6 m3 = /5 = /100 = /100 fd + 2 0 d B / d e c a d e 2 0 d B / d e c a d e 6 0 d B / d e c a d e Figure 5-12: Log-log frequency response plot of Case 1 (Gallas et al. 2003a) as the cavity volume is decreased from the LEM prediction.

PAGE 181

154 Table 5-2: Cavity volume effect on the de vice frequency response for Case 1 (CFDVal 2004) from the LEM prediction. 460d f Hz H f Hz 1 f Hz 2 f Hz Baseline: 63 07.410 m 1,985 446.2 2,048 02 2,808 446.5 2,894 05 4,440 446.7 4,574 010 6,279 446.8 6,468 020 8,880 446.8 9,146 050 14,044 446.9 14,461 0100 19,856 446.8 20,451 0500 44,400 446.8 45,729 01000 62,791 446.8 64,671 100 101 102 103 104 105 10-4 10-3 10-2 10-1 100 101 102 Frequency (Hz)Centerline velocity (m/s) 0=2.6e-6 m3 = /5 = /100 = /1000 fd + 2 0 d B / d e c a d e 6 0 d B / d e c a d e 2 0 d B / d e c a d e Figure 5-13: Log-log frequency response plot of Case 1 (C FDVal 2004) as the cavity volume is decreased from the LEM prediction.

PAGE 182

155 Similarly, as a second example, all parameters are based on Case 1 of the NASA workshop CFDVal2004 (2004), and the cavity vo lume is again prog ressively decreased from its nominal value. This time, the baseline case is such that H d f f and Table 5-2 and Figure 5-13 are generated to illustrate the behavior of the actuator frequency response. In this case, the first resonant frequency is governed by the cavity resonant frequency H f that tends to infinity as the cavit y volume is decreased, while the second frequency is limited by the natural frequency of the diaphragm d f This case is actually the continuation of the previous exampl e but starting with H f already greater than d f hence starting with a smaller cavity. Interestingly, in both cases the system exhibits a 20 dB/decade rise at low frequencies, and has a -60 dB/decade roll o ff at high frequencies representative of a system with a pole-zero ex cess of 3. In between th e two resonant frequencies 1 f and 2 f the response decreases at a rate of 20 dB/decade, similar to a 1st-order system. The influence of the cavity volume is clearly conf ined to one of the peaks in the actuator response. For both cases, as the cavity volum e shrinks to zero, a single low frequency peak near the diaphragm natural frequency is obtained. The second peak progressively moves to higher frequencies as the cav ity volume is decreased, and since 1Hf the following limit behavior is observed 1 0 2 0lim limd Hff ff (5-5)

PAGE 183

156 Experimental Results This interesting behavior is now experimentally verifi ed. In the experimental investigation described in Chapter 3, this is re ferred to as Test 2 in the setup. A nominal synthetic jet device is taken and the cavity volume is systematically decreased to yield four different actuators, with all other components held fixe d. The dimensions and test conditions of the devices are li sted in Table 3-1. The phase -locked centerline velocity is then acquired at different frequencies using LDV measurements, in the same manner as discussed in Chapter 3. Table 5-3: ZNMF device characteris tic dimensions used in Test 2 Property: Case A Case B Case C Case D Cavity volume (m3) 4.49 10-6 2.42 10-6 1.09 10-6 0.71 10-6 Orifice diameter d (mm) 1.5 Orifice thickness h (mm) 2.7 Orifice width w (mm) 11.5 Diaphragm diameter (mm) 23 Input sine voltage acV (Vpp) 30 Diaphragm natural frequency d f (Hz) 2114 Helmholtz frequency H f (Hz) 1275 1738 2586 3221 (*) computed from Eq. 5-6 The results are plotted in a log-log scal e in Figure 5-14 an d Figure 5-15 gives a close-up view of the peak locations in a linear plot. Also, Table 5-4 lists the different frequencies of interest. Two sets of frequencies are compared: ones that are experimentally measured, the others that are analytically computed. The frequency response plot in Figure 5-15 provides 1,exp f and 2,exp f the two natural frequencies of the system. For the two test cases that have a ca vity wide enough to al low the insertion of a microphone inside (Case A and Case B), the Helmholtz frequency is experimentally determined by a simple blowing test (effect of blowing over an open bottle) where the

PAGE 184

157 spectra of the microphone is recorded while the actuator is passive ly excited by blowing air at the orifice lip. Then, analytically 1 f and 2 f are computed solving Eq. 5-3 that only requires the knowledge of the diaphrag m and cavity acoustic compliances and d f and H f Here, H f is calculated from its acoustical definition, i.e., 0 01 2n HS fc hh (5-6) where 00.96nhS is the orifice effective length for an arbitrary aperture (see Appendix B). Note also that in this experimental se tup, the largest dimension of the device is the cavity height H equals to 26.8mm. The frequency limit under which Eqs. 5-4 and 5-6 are still valid corre sponds to about 1 kH or 1/6 H In terms of frequency, this means that the LEM assumption in these test cases is only valid for frequencies 2200 f Hz, i.e. about up to the natural frequency of the di aphragm. And clearly, as seen in Table 5-4, this assumption is violated for the 2 smalle st cavities, hence the di screpancy between the experimental and analytical 1 f and 2 f Table 5-4: Effect of the cavity volume decrease on the ZNMF actuator frequency response for Cases A, B, C, and D. from experiments from analytical equations 2114d f Hz H f Hz 1 f Hz 2 f Hz H f Hz 1 f Hz 2 f Hz Case A 1272 1200 2100 1275 1253 2152 Case B 1732 1600 2000 1738 1651 2226* Case C N/A 1700 2400 2586* 1972 2774* Case D N/A 1700 2600 3221* 2014 3383* LEM assumption no longer valid: lim,2200LEM f Hz

PAGE 185

158 101 102 103 10-3 10-2 10-1 100 101 Frequency (Hz) fd = 4.49 x 10-6 m3 = 2.42 = 1.09 = 0.71 Centerline velocity amplitude (m/s) Figure 5-14: Experimental log-log frequenc y response plot of a ZNMF actuator as the cavity volume is decreased for a constant input voltage. 1000 1500 2000 2500 3000 2 6 10 13 Frequency (Hz)Centerline velocity amplitude (m/s) fdfH, DfH, AfH, BfH, C Figure 5-15: Close-up view of the peak locatio ns in the experimental actuator frequency response as the cavity volume is decreas ed for a constant input voltage. The arrows point to the analytically determined Helmholtz frequency H f for each case. () Case A: 634.4910 m () Case B: 632.4210 m () Case C: 631.0910m, () Case D: 630.7110m.

PAGE 186

159 An identical behavior seen in the lumped element model applied above for the two examples is seen in the results. First the overall dynamic response is still characterized by a +20 dB/decade rise at the low frequenc ies and -60 dB/decade roll off for the high frequencies. Also, the system response exhi bits two frequency peak s. Figure 5-15 shows a close-up view of the peak locations, where the arrows indicate the Helmholtz frequency location given by Eq. 5-6. As the cavity volume decreases, H f increases while d f remains constant. Also, if 1Hdff H f is easily distinguished from d f (as in Case A or Case B), and the actual peak frequencies 1 f and 2 f are close to H f and d f However, when 1Hdff the experimentally determined peaks 1 f and 2 f tend to move away from d f (Case C and Case D). As H d f f 1 f and 2 f approach each other. Then as H f exceeds d f they separate agai n, and eventually 1 f tends to d f Then, as the cavity volume is further decreased, 2 f and the Helmholtz frequency move toward higher frequencies, while 1 f tends to d f as in Case D. Notice al so how the frequency response is unaffected by the cavity size -hence compre ssibility effectsfor frequencies smaller than H f of Case A, as seen in Figure 5-14. This suggests that thei r exists a threshold limit below which the actuator response is i ndependent of the Helmholtz frequency, or for 0.5Hff To further confirm this trend experimentally, a smaller cavity size would have been ideal, but physical constraints in the actuator configuration prevented it; Case D already has the smallest feasible cavity. Nonetheless, the experimental results validate the lumped element model analysis presented above, where a similar change in the frequency

PAGE 187

160 response of a ZNMF actuator occurs due to th e cavity volume varia tion, hence affecting the Helmholtz frequency peak location, as described by Eq. 5-5. Figure 5-16: Normalized quantities vs. phase of the jet volume rate, cavity pressure and centerline driver velocity. A) Case 20: Re102,7 S B) Case 70: Re50,4 S C) Case 46: Re109,53 S D) Case 65: Re269,17 S Actually, the results from Test 1 described in Chapter 3 where the pressure fluctuations are recorded inside the cavity can also give additional proof in the above analysis. This is shown in Figure 5-16 wher e the normalized jet volume flow rate, cavity 0 50 100 150 200 250 300 350 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 phase 0 50 100 150 200 250 300 350 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 phase 0 50 100 150 200 250 300 350 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 phase 0 50 100 150 200 250 300 350 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 phase Vd Pcav Qj A C 0.86Hff 3.28Hff 0.09Hff 0.06Hff D B

PAGE 188

161 pressure and driver centerline velocity ar e plotted phase-locked for four different H f f ratios. Notice that in these plots the small e rrobars are omitted for better illustration. For cases actuated at a frequency away from the Helmholtz frequency, as seen in Figure 5-16A and Figure 5-16B, the volume flow rate a nd centerline driver velo city are nearly in phase, indicating that the flow is incompressi ble. In contrast, for cases of driver frequencies close to or greater than H f as in Figure 5-16C and Figure 5-16D, the orifice volume flow rate is not in phase with the driver velocity, ostensibly due to compressibility effects in the cav ity. If the flow in the cavity is incompressible, it has the effect of not delaying the time signals. The driver-to-Helmholtz frequency ratio H f f is thus the key parameter in this analysis. Recall from Eq. 5-2 and Eq. 54 that a small cavity volume with a large Helmholtz frequency is equivalent to having an incompressible cavity. Therefore, if the actuation frequency of the ZNMF actuator is well below its Helmholtz frequency, the flow within the cavity of the device can be treated as incompressible, whereas if the actuator is excited near its Helmholtz freq uency or above some critical frequency 0.5Hff certainly the flow inside the cavity is compressible, which then has to be consistently considered for modeling purposes. This is an important result that can be summarized by stating that 0.5 incompressible cavity otherwise compressible cavityHf f (5-7) This criterion should be taken into account for numerical simu lations and design considerations.

PAGE 189

162 Driver, Cavity, and Orifice Volume Velocities The previous analysis shows the impact of the actuation to Helmholtz frequency ratio H f f on the frequency response of a ZNMF actuator in quies cent air that results in a criterion for the cavity incompressibility limit. However, more results can be extracted from this experimental investigation in te rms of the actuator response magnitude. As suggested from Figure 5-14, the variation in amplitude of the jet velocity is a direct function of the Helmholtz frequency. To ha ve a first estimate of these variations, the dimensionless linear transfer function derive d in Chapter 2 for a generic driver and orifice (see Eq. 2-23) that gives a scaling argument for jdQQ is considered and reproduced below: 2 21 1 1jj d HHQQ Qj j S (5-8) Recall that this expression used Eq. (5-4) to define the Helmholtz frequency, hence neglecting the radiation mass that results in an effective length. Also, Eq. 5-8 was derived assuming a linear model, neglecting a ny nonlinear resistance terms. Yet this expression is still valid for scaling arguments. Eq. 5-8 shows that the system is expected to be governed by the driver response, and when d f f (the actuation frequency matches the natural frequency of the driver) jdQQ is a 2nd order system that is a function of H f f and S In the incompressible limit, as seen from the previous section, this is equivalent to 0 or Hf And while 1Hff the actuator output jdQQ tends to 1; i.e. the jet flow rate is dir ectly proportional to the driver performance.

PAGE 190

163 On the other hand, in the compressible case, aCC is finite (i.e. the gas in the cavity has an acoustic compliance and can be compressed). Hence, H f is finite and, near the cavity resonance ( H f f ), the actuator output amplitude jQ is expected to be larger than that of the driver volume flow rate dQ (jdQQ) and to be out of phase; the system produces a larger amplitude with higher Stokes number. Once again, experimental results are used to validate this analytical analysis. First, Test 2 in the experimental setup (Cases A, B, C, and D) is considered. In addition to the centerline velocitie s acquired in a frequency sweep at a single input voltage, jet velocity profiles have been acquired at se lected frequencies to compute jQ and jQ and the diaphragm flow rate dQ has also been recorded at each frequency. Notice that in this analysis the time averaged jQ is employed, which is related to the jet volume flow rate amplitude jQ by 2jjQQ (5-9) for a sinusoidal signal.. But since only an or der of magnitude -or sc alinganalysis is performed here, the overhead ba r is dropped for convenience. The reader is referred to the data processing section in Chapter 3 fo r a clear definition on how these different quantities are defined and computed. Figure 5-17 plots the ratio be tween the input flow rate dQ and the output flow rate jQ of the ZNMF actuator as a function of the driver to Helmholtz frequency H f f for these four experimental cases where the cavity volume is systemati cally decreased. The response predicted by the linear tr ansfer function in Eq. 5-8 is clearly seen here, where at

PAGE 191

164 low frequency jdQQ, then around H f f jdQQ and finally at H f f, jdQQ However, in these cases it has been show n that the two dominant frequency peaks 1 f and 2 f tend to overlap (see discussion a bove), and that the Helmholtz frequency H f overpredicts the peak location (see Table 54, the LEM assumption being no longer valid for the high frequency cases). Therefore, Figur e 5-17B plots again the ratio of the driver to jet volume flow rate but as a function of 1 f f for Case A and Case B (where H d f f ), and as a function of 2 f f for Cases C and D where H d f f This shows the similar observed trend but with the data more collapsed. Note that there is still some scatter since the experimentally determined peaks 1 f and 2 f have a resolution of 100 Hz only. 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 2 4 6 8 10 12 Qj/Qdf/fH = 4.49, fH<fd = 0.71, fH>>fd Qj/Qd = 1 Figure 5-17: Experimental results of the ratio of the driver to the jet volume velocity function of dimensionless frequency as the cavity volume decreases. A) Function of H f f B) Function of 1 f f for 634.4910 m and 632.4210 m and function of 2 f f for 631.0910 m and 630.7110m. A

PAGE 192

165 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 2 4 6 8 10 12 Qj/Qd(f/f1) or (f/f2) = 4.49, f/f1 = 2.42, f/f1 = 1.09, f/f2 = 0.71, f/f2 Qj/Qd = 1 Figure 5-17: Continued. To confirm these results, the test cases coming from Test 1, ranging from Case 41 to Case 72, are also used where the driver vo lume velocity is compared to the jet volume flow rate. Figure 5-18A shows the variati on in the ratio of the two quantities as a function of H f f where the symbols are grouped by Stokes number Figure 5-18B is identical except that jdQQ is plotted for different Reynol ds numbers. First, note that jdQQ is close to unity when H f f then is greater than unity near 1Hff, and is much less than unity for H f f. This is exactly what is seen in Figure 5-17 which was for a fixed input voltage. With reference to Eq. 5-8, the Stokes number dependence can be seen in Figure 5-18A where jdQQ is at a maximum for high Stokes number near 1Hff. Also, Figure 5-18B shows that an in crease in Reynolds number results in a decrease in the ratio jdQQ near 1Hff. This is due to the nonlinear damping terms present in the orifice that are proportional (in part, see Chapter 5 for more details) to the B

PAGE 193

166 Reynolds number and decrease the overall respon se near resonance. Again, since Eq. 5-8 is a linear transfer function, this Rey nolds number dependence cannot be seen. 0 0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 1.5 2 2.5 3 3.5 f/fHQj/Qd S=4, f/fd=0.06 S=12, f/fd=0.06 S=14, f/fd=0.79 S=17, f/fd=1.15 S=43, f/fd=0.79 S=53, f/fd=1.23 Re 0 0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 1.5 2 2.5 3 3.5 f/fHQj/Qd 0
PAGE 194

167 dcjQQQ (5-10) the driver volume velocity being split into the cavity and the orifice br anches. Recall that the Q s are represented via phasors as complex va riables. In view of the above results, the role of the cavity in this flow divider depends on the va lue of the cavity impedance that, as shown above, is related to the Helmho ltz frequency. In th e limit when the cavity acoustic impedance aCC tends to zero or for 1Hff, the impedance 1aCaC Z jC takes high values and then discourages the flow from going into its branch, which therefore minimizes the cavity volume velocity cQ since aCcc Z PQ This is the case when the cavity can be assumed to be incompressible and yields jdQQ, as seen in the previous figures. However when the cavity acoustic impedance aC Z takes finite values, some non-negligible flow enters the cavity br anch in Figure 5-19, and in this case where the cavity is clearly compressible two differe nt scenarios can take place, whether the actuator is driven near cavity resonance or not. At re sonance, the reactance of the complex impedance in the loop formed with the cavity and the or ifice branches is identically zero and the flow is purely resistive. This case then allows jQ to be greater than dQ via an acoustic lever arm. At frequencies away from resonance and/or for really large cavitiesthe acous tic impedance of the cavity goes to zero, thus letting the cavity volume velocity cQ be non-negligible when compared to the other Q s, thus yielding a small output flow rate jQ compared to the input dQ Further consideration on this matter will be to experimentally compute the cavity volume flow rate. But this is a non-trivial problem because of the inherent complex nature of the quantity to measure, and is the subject of future work.

PAGE 195

168 ZaDZaCQc Qj Pc ZaOQd 1: aP Vac + + + + Figure 5-19: Current divider representation of a piezoelectric-driven ZNMF actuator. Similarly, another important aspect of this flow divider representation is in the conservation of power through the different branch es of the circuit in Figure 5-19. Power is defined as the multiplication of an effort variable and a flow variable. Practically, it is rather difficult to experimentally estim ate the power delivered to the driver, and especially in the cavity. Nonetheless, the lumped element model should provide reasonable estimates of the power, and it is shown in Figure 5-20, where again Case 1 from Gallas et al. (2003a) has been used for illustration purposes. In LEM, the governing equations are written in conjugate power va riable form by assuming sinusoidal steady state operating conditions. Ideally, the piez oelectric diaphragm actuator driver is modeled as a lossless transformer, which has an input power defined by ddPwQP (5-11) where P is related to the piezoelectric dia phragm via the two-port element model by aacPV (5-12) The power in the cavity branch is given by cccPwQP (5-13) and at the orifice exit the power takes the form jjcPwQP (5-14)

PAGE 196

169 For the power to be conserved in the circuit, the following identity should hold at any frequency, jcdPwPwPw (5-15) and this is plotted in Figure 5-20 where the real and imaginar y part of the power is shown as a function of frequency, taking the parame ters from Case 1 (Gallas et al. 2003a). 0 500 1000 1500 2000 2500 -0.4 -0.2 0 0.2 0.4 Real[Pwj + Pwc] Pwd 0 500 1000 1500 2000 2500 -0.4 -0.2 0 0.2 0.4 ImaginaryFrequency (Hz) fHfd Figure 5-20: Frequency response of the power conservation in a ZNMF actuator from the lumped element model circuit representati on for Case 1 (Gallas et al. 2003a). Note that the power is in fact conserved at all frequencies, especially at cavity resonance when H f f However, at the mechanical resonance, d f f a jump is observed which is primarily due to the fact that the piezoelectric diaphragm is modeled as a lossless transformer that is valid only up to its natura l frequency, and beyond this frequency, the main assumption of LEM fails. To summarize this chapter, it has been found that the cavity play s an import ant role in the actuator response, in terms of geom etric parameters and operating frequency. More particularly, it was found th at the pressure inside the cav ity may not be equal to the LEM validity limit

PAGE 197

170 pressure across the orifice, as the LEM assu mes it, at least quantitatively in terms of amplitude. Therefore, care must be taken when using the experimental cavity pressure. Next, the linear dimensionless transfer function developed from LEM has been experimentally validated and can be used as a starting guess in a design tool. It is shown that the cavity can either have a passive role by not aff ecting the device output, or can greatly enhance the actuator performance. Th is is a function of the driver-to-Helmholtz frequency as well as the Stokes and Reynolds numbers, a nd for piezoelectric-driven devices the diaphragm frequency may ha ve a non-negligible impact when d f is close to H f More interestingly, large output can be expected jdQQ at the cavity resonance but only at low forcing level, the nonlinear or ifice resistance tending then to decrease the output as the input amplitude increases. This says that the optimal response is not simply given by just maximizing the actuator input. A tradeoff between the cavity design and actuation amplitude must be made, depending on the desire d output to be achieved. Notice also that this analysis has been ma de for a piezoelectric-diaphragm driver. Obviously, using an electromagnetic driver will remove the dimensionless frequency d f f but the above results still hold and Eq. 5-8 can still be applied since the driver dynamics are confined in the LHS. Nevertheless the major impact of this analysis is that by operating near H f the device produces greater output fl ow rates than the driver due to the acoustic resonance. An adde d benefit is that the driver is not operated at mechanical resonance where the device may have less tolerance to failure.

PAGE 198

171 CHAPTER 6 REDUCED-ORDER MODEL OF ISOLATED ZNMF ACTUATOR In this chapter, the lumped element mode l of an isolated ZNMF actuator presented in Chapter 2 is refined based on an investig ation of the orifice flow physics. More precisely, the orifice impedance model is improved to account for geometric and flow parameter dependence. This refined model st ems from a control volume analysis of the unsteady orifice flow. The results from the experimental setup presented in Chapter 3, along with the discussion on the orifice and cavity flow physics given in Chapter 4 and Chapter 5, are used to construct a scaling law of the pressure lo ss across the orifice, which is found to be essentially a function of the product of the Strouhal number and the orifice aspect ratio h/d This improved lumped element model is then compared along with the existing previous versi on (Gallas et al. 2003a ) to some experimental test cases. Orifice Pressure Drop In the existing lumped element model of an isolated ZNMF actuator presented in Chapter 2, the major limitation is found in th e expression of the nonlinear acoustic orifice resistance that is directly related to the loss coefficient dK such that, 20.5dj aOnl nKQ R S (6-1) A primary goal of this effort is to provide a physical understanding of the orifice flow behavior, along with a more accurate expression for the coefficient dK in terms of dimensionless geometric and flow parameters, i.e., in terms of the orifice aspect ratio h/d Reynolds number Re, and Strouhal number St Note that in the existing version of the

PAGE 199

172 lumped element model, the coefficient dK is set to unity (McCormick 2000; Gallas et al. 2003a). In this section, a control volume anal ysis of the unsteady pressure-driven oscillatory pipe flow is pres ented. Figure 6-1 shows a schematic of the control volume with the coordinate definitions. The governin g equations are first derived to obtain an expression of the pressure drop coefficient across the orifice. Then, the analytical results are validated via available numerical simula tions, which are also used to examine the relative importance of each term in the governing equation fo r the orifice pressure drop. h boundary layer potential core fully developed flow y/h = 0 y/h = -1 y x ambient region cavity Figure 6-1: Control volume for an unsteady laminar incompressible flow in a circular orifice, from y/h = -1 to y/h = 0. Control Volume Analysis Assuming an unsteady, incompressible, la minar flow and a nondeformable control volume, as shown in Figure 6-1, the continuity equation becomes 0CVCSCSdVdAVdA t (6-2)

PAGE 200

173 or simply inletexitQQ Since the y location of the outflow boundary is arbitrary, it directly follows that ()QQy or QQt Similarly, the y -momentum equation becomes y CVCSFvdvVdA t (6-3) or, for an axisymmetric orifice, 0 02 2y ynFDFD CVCSd p pSydyvdvVdA t (6-4) where the subscript FD signifies fully developed, is the wall shear stress, and 22nSd is the circular orifice area. Since density is assumed to be constant, the volume integral can be expressed as follows 22 22 0 0 00002222 22dd yy ynFDFDy Qconstdd ppSydyyvxdxdyvvxdx t (6-5) Since the volume flow rate is independent of the location y inside the orifice, ()QQy 2 22 0 0 00222 22d y ynFDFDyddQ p pSydyyyuuxdx t (6-6) Then, assuming that the jet volume flow rate is sinusoidal, sinjQQt and using again the timeand spatialaveraged exit velocity during the expulsion stroke jV as the characteristic velocity, i.e.,

PAGE 201

174 2 00011 2sin 222 .d jyj nn Q jj j nnVvxdxdtQtdt SS QQ V SS (6-7) Next, the integral momentum equation can be written in nondimensional form as 22 2 1 0 0 222 2 0 04 2cos4 1 2222 0.5 2yd y y FD FD j jjj jpp vv yyxx dytd dddd V VVV V .(6-8) By using the definition of the Strouhal number jStdV and the skin friction coefficient 20.5 f jCV, and defining the normalized pr essure drop across the orifice by 0 20.5y p j p p c V (6-9) Eq. 6-8 can then be rewritten as 22 1 0 ,, 2 0 04 4cos4 22yd y pffFDfFD j IIIII I IVvv yyyxx cCCdCSttd ddddd V .(6-10) Eq. 6-10 shows that the pressure drop across the orifice is comprised of four terms: I = excess shear contributi on to the pressure drop II = fully-developed shear contribution III = unsteady inertia term (= 0 if flow is steady) IV = nonlinear unsteady pressure drop to accelerate the flow (convective term) Notice that the first two terms ( I and II ) can be recombined to yield the total skin friction coefficient integral, 04yd fCdyd, in the pressure drop expression.

PAGE 202

175 It should be pointed out that this analysis in derived for an isentropic flow, and that since only the continuity and momentum equations are used, no assumptions are taken for the heat transfer. From the energy equation, a simple scaling analysis for the pipe flow (see end of Appendix C for details) shows that the viscous and thermal boundary layer are of the same order of magnitude assumi ng a Prandtl number (ra tio of viscous to thermal diffusivity) of unity for air. However, since no significant he at source is present, the thermal effect are neglected in this an alysis. Notice that Choudhari et al. (1999) performed a theoretical analys is (confirmed with numerical simulations) on the influence of the viscothermal effect on flow through th e orifice of Helmholtz resonators. They showed that the thermal effect can be neglected for such flows. Next, before examining the physics behind the expression for the orifice pressure drop, one can examine each term in Eq. 6-10 from a numerical simulation to validate this theoretical analysis and evaluate their relative importance. Validation through Numerical Results Once again, the 2D numerical simulations fr om the George Washington University described in Appendix F are used to evaluate the analytical expression for the orifice pressure drop derived above. Three test cases are employed and are referred to as Case 1 ( S = 25, St = 2.38, h/d = 1, no jet is formed), Case 2 ( S = 25, St = 2.38, h/d = 2, no jet is formed), and Case 3 ( S = 10, St = 0.38, h/d = 0.68, a jet is formed) in the test matrix shown in Table 2-3. Figure 6-2 shows the va riations during one cycle of each of the terms in Eq. 6-10, for Case 1, Case 2, and Case 3 (Figure 6-2A, Figure 6-2B, and Figure 6-2C, respectively). Actually, the terms I and II in Eq. 6-10 have been recombined together to remove the explicit fully-developed part and to yield only the total wall shear stress contribution, since the fully-developed re gion may not be well defined in these test

PAGE 203

176 cases (see discussion in Chapter 4). Note th at the pressure has been averaged across the orifice cross section, and ag ain zero-phase corresponds to the onset of the jet volume velocity expulsion stroke. Also, Eq. 6-10 is de rived for a circular orifice, and because the numerical simulations are carried out for a 2D slot, it has been ad justed accordingly. Recall also the relationship between the Strouhal number St orifice aspect ratio h/d and the stroke length (or pa rticle displacement) 0L via, 0hh St dL (6-11) The three numerical cases examined, while no t exhaustive, include low and high stroke length cases and should ther efore be representative of the general case. 0 45 90 135 180 225 270 315 360 -8 -6 -4 -2 0 2 4 6 8 phase (degree) Cp Unsteady term Momentum int. Shear term Figure 6-2: Numerical results for the contribut ion of each term in the integral momentum equation as a function of phase angl e during a cycle. A) Case 1: h/d = 1, St = 2.38, Re = 262, S = 25. B) Case 2: h/d = 2, St = 2.38, Re = 262, S = 25. C) Case 3: h/d = 0.68, St = 0.38, Re = 262, S = 10. A

PAGE 204

177 0 45 90 135 180 225 270 315 360 -15 -10 -5 0 5 10 15 phase (degree) Cp Unsteady term Momentum int. Shear term 0 45 90 135 180 225 270 315 360 -1 -0.5 0 0.5 1 1.5 phase (degree) Cp Unsteady term Momentum int. Shear term Figure 6-2: Continued. Clearly, it can be seen that the unsteady in ertia term that is directly proportional to the Strouhal number is by far the most im portant contribution in the pressure drop in the orifice, which is not surprising since the two first cases have a large Strouhal number. The momentum integral (or convective) and fri ction coefficient integral terms seem quite small but actually should not be completely ne glected since they contribute in the balance B C

PAGE 205

178 of the pressure drop, especially for the lo w Strouhal number Case 3. Notice also how the pressure drop is shifted by almost 90o (referenced to the volume velocity) which is primarily due to the unsteady term, but al so by the shear stress contribution, the momentum integral term being in phase with the jet volume flow rate. However, it should be noted that the re sults for Case 3 (Re = 262, S = 10, St = 0.38, h/d = 0.68), even though shown here in Figure 6-2C, should be regarded with caution as some nonnegligible residuals may be present in the computed pressure drop that may be due to grid/time resolution for extracting the shear stress component and velocity momentum integral (private communication with Dr. Mi ttal, 2005). Nonetheless, the results for the orifice pressure drop magnitude are still used, as seen later. 0 90 180 270 360 0 90 180 270 360 Vexit Ventrance Figure 6-3: Definition of th e approximation of the orifice entrance velocity from the orifice exit velocity. Next, the goal is to extend this analysis to practical experimental results. However, there are no such results available for the velo city profiles at the orifice inlet adjacent to the cavity or for the friction coefficient al ong the orifice wall. What are known are the ,, ,, exinletinexit ininletexexitVV VV

PAGE 206

179 time-dependant velocity profiles at the orifice exit (to ambient) and pressure oscillations inside the cavity. However, it was shown in Chapter 4 that, for a symmetric orifice, the velocity at the exit can be used to estim ate the velocity at the inlet, with a 180o phase shift: the flow sees th e entrance of the orifice as its exit during the ot her half of the cycle, and vice versa, as shown in Figure 6-3. 0 45 90 135 180 225 270 315 360 0 0.5 1 1.5 2 2.5 3 3.5 phase (degree) momentum integral Vexit momentum integral Vinlet approx momentum int. Vinlet Figure 6-4: Momentum integral of th e exit and inlet velocities normalized by 2 jV and comparing with the actual and approximate d entrance velocity. A) Case 1: h/d = 1, St = 2.38, Re = 262, S = 25. B) Case 2: h/d = 2, St = 2.38, Re = 262, S = 25. C) Case 3: h/d = 0.68, St = 0.38, Re = 262, S = 10. 0 90 180 270 360 0 0.5 1 1.5 2 2.5 3 phase (degree) momentum integral Vexit momentum integral Vinlet approx momentum int. Vinlet 0 90 180 270 360 0 0.5 1 1.5 2 2.5 3 phase (degree) momentum integral Vexit momentum integral Vinlet approx momentum int. Vinlet A B C

PAGE 207

180 This approximation for the entrance velocity is further verified via Case 1, Case 2, and Case 3. The normalized momentum integral of the exit and inlet velocities, defined by 2 1 0 2 12jv x d d V and 2 1 2 12yh jv x d d V are plotted in Figure 64A and Figure 6-4B, and Figure 6-4C, respectively for Case 1, Case 2, and Case 3, during one cycle along with the approximated momentum integral of the inlet velocity. As can be seen, the result for the approximated inlet velocity is in fair ag reement with the actu al entrance velocity, although for the large stroke length case (C ase 3) the inlet velo city is slightly overpredicted by the approximated one but only during the ingestion stroke. It should be emphasized that this is only valid for a symmetric orifice. Finally, the sum of the source terms in Eq. 6-10 that balance the pressure drop pc are plotted as a functio n of time for the first two numeri cal test cases (as noted above, Case 3 is not shown here). Results from us ing both the actual and approximate entrance velocity are also shown in Figure 6-5. Clear ly, the CFD results confirm the validity of Eq. 6-10. Therefore, Eq. 6-10 can be used w ith confidence to compute the pressure drop across the orifice, and the orifice entrance velo city can also be com puted from the orifice exit velocity in the experimental result s, and the corresponding timeand spatialaveraged velocity can be defined as ,, ,, exinletinexit ininletexexitVV VV (6-12)

PAGE 208

181 0 90 180 270 360 -10 -8 -6 -4 -2 0 2 4 6 8 10 phase (degree) cp Tunsteady + actual(Tmomentum) + Tshear Tunsteady + approx(Tmomentum) + Tshear 0 90 180 270 360 -20 -15 -10 -5 0 5 10 15 20 phase (degree) cp Tunsteady + actual(Tmomentum) + Tshear Tunsteady + approx(Tmomentum) + Tshear Figure 6-5: Total momentum integral equa tion during one cycle, showing the results using the actual and approximated en trance velocity. A) Case 1: h/d = 1, St = 2.38, Re = 262, S = 25. B) Case 2: h/d = 2, St = 2.38, Re = 262, S = 25. Discussion: Orifice Flow Physics Now that Eq. 6-10 has been validated via num erical simulations, it is worthwhile to examine the physics behind each term that co mpose Eq. 6-10, as discussed below. A B

PAGE 209

182 I = excess shear contribution to the pressure drop This is a linear contribution to the pressure drop. It corresponds to the excess shear needed to reach a fully developed state (in which the time-dependent velocity profile is invariant along the length of the orifice). In particular, it corresponds to the viscous effect in a starting orifice flow and is exp ected to have both dissi pative (resistance) and inertial (mass) components since it will affect the magnitude and phase of the pressure drop. This is in accordance with the discu ssion provided on the velocity profiles shown in Chapter 4 in Figure 42, Figure 4-3, and Figure 4-4 for Case 1, Case 2, and Case 3 respectively. However, as seen from the numerical results (F igure 6-2), this term appears to be negligible for the low and large Strouhal number cases examined. It is therefore neglected in the rest of this analysis. II = fully developed shear contri bution to the pressure drop This is again a linear contribution to the pressure drop. In fact, the friction coefficient term comes from viscous effects at the orifice walls that are linear by nature. In the case of a fully developed, steady orif ice flow, the corresponding pressure loss can be written as 2 ,1 4 2fFDjh PCV d (6-13) or, since ,16Re16jfFDj VCVd and jjVV for a steady pipe flow (White 1991), it directly follows that 2 232 4161 2j j jhV h PV dd Vd (6-14) which can be recast in term s of an acoustic impedance

PAGE 210

183 4 41288 2aOaOlin jPhh ZR Qd d (6-15) This is exactly the linear acoustic resistance aOlinR of the orifice due to viscous effect derived previously in Chapter 2. Hence, the shear term II in Eq. 6-10 corresponds to the viscous linear resistance in the existing lumped element model. As a validation, the numerical data from Case 1 and Case 2 are again used. In Figure 6-6A and Figure 6-6B the total shear stress contribution (terms I and II ) from the numerical data for Case 1 and Case 2, respectively, are compared w ith the corresponding ac oustic linear resistance aOlinR that actually only models term II Clearly, the magnitude of the fully developed contribution (term II ) is dominant, while the main effect of the excess shear is believed to add a small phase lag in the signal. This result provides confidence in the assumption of neglecting the excess shear contribution, i.e. term I Figure 6-6: Numerical results of the total shear stress te rm versus corresponding lumped linear resistance during one cycle. A) Case 1: h/d = 1, St = 2.38, Re = 262, S = 25. B) Case 2: h/d = 2, St = 2.38, Re = 262, S = 25. 0 45 90 135 180 225 270 315 36 0 -1.5 -1 -0.5 0 0.5 1 1.5 phase (degree) Total shear term (I + II) RaO,linear <=> Shearfully developed (II) 0 45 90 135 180 225 270 315 36 0 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 phase (degree) Total shear term (I + II) RaO,linear <=> Shearfully developed (II) B A

PAGE 211

184 III = unsteady inertia term This is again a linear contribution to the orifice pressure drop, with a 90o phase shift referenced to the volume flow rate (or ve locity). In a similar manner as above, the unsteady term contribution can be rewritten such that 21 2jh PStV d (6-16) or in terms of an acoustic impedance, 21 2 343 434 2j j aO aN jnn jnhd V d V Phh Z M QSS VS (6-17) where aN M is the linear acoustic mass of the orif ice associated with the fully developed pipe flow. Therefore, the unsteady inertia term is equivalent to a mass (or inertia) in the orifice. Notice that Eq. 6-17 is derived for a circular orifice and that in the case of a 2D slot the multiplicative constant is equal to 5/6 instead of 3/4. Figure 6-7: Numerical result s of the unsteady term versus corresponding lumped linear reactance during one cycl e. A) Case 1: h/d = 1, St = 2.38, Re = 262, S = 25. B) Case 2: h/d = 2, St = 2.38, Re = 262, S = 25. 0 45 90 135 180 225 270 315 360 -15 -10 -5 0 5 10 15 phase (degree) ( cp)Unsteady term .5/6.MaN 0 45 90 135 180 225 270 315 360 -8 -6 -4 -2 0 2 4 6 8 phase (degree) ( cp)Unsteady term .5/6.MaN B A

PAGE 212

185 Again, the CFD data are compared with the corresponding linear lumped parameter aN M as shown in Figure 6-7A and Figure 6-7B for Case 1 and Case 2, respectively. This term along with the skin friction integral (term I which is also frequency dependant when the flow is not steady) are the sources of the reactance term in the linear acoustic total orifice impedance model aOaOaO Z RjM IV = momentum integral term The momentum integral that comes from the convective term is the nonlinear term that is the source of the distortion in the orifice pressure loss signal. As a simple example, if the flow is steady and if the location y is chosen such that the flow is fully developed, then the velocity is given by 22 22211 22yjjxx vxVV dd (6-18) and, by assuming a uniform velocity profile at the orifice inlet, the last integral (term IV in Eq. 6-10) would be simply 2/3, exactly that found for the case of steady flow in the inlet of ducts derived in White (1991, p. 291). However, in the general case, this term is both resistive and reactive i.e., it has a magn itude and a phase component, as shown from the numerical results of Case 1 and Case 2 in Figure 6-8A and Figure 6-8B, respectively. The magnitude of this nonlinear term is clearl y non-negligible at low Sthd (or high dimensionless stroke length 0Lh ) as seen in Figure 6-2. Also, as shown in Figure 6-8, the momentum integral clearly exhibits a 3 component. This suggests that the nonlinear term IV cannot be only modeled by a nonlinea r resistor, but should also have a reactance component.

PAGE 213

186 In this regard, one can use a zero-memory square-law with sign model in the momentum integral expression (Bendat 1998), which is defined by YXX (6-19) where the output Y would correspond to the output pressure drop and the input X is the spatial averaged velocity at any location y inside the orifice. It can be easily shown (see Bendat (1998) who performed a similar deriva tion but for an input white noise ) that by assuming the input X as a sine wave given by sin XtAt (6-20) where A is the magnitude and the phase ( ) is uniformly distributed, and by minimizing the mean square estimate, then this square-law with sign model can be successfully approximated by a cubic polynomial Y of the form 31632 1515 A YXXXX A (6-21) Notice that the ratio between the two polynomial coefficients is equal to 22 A which is over the inverse of the power in the input sine wave. Substituting Eq. 6-20 in Eq. 6-21, the output of the zero-memor y square-law with sign nonlinear model takes the form 281 sinsin33 35 A Yttt (6-22) The square law with sign produces a cubi c nonlinearity. The nonlinear system redistributes energy to the fundamental () and to the 2nd harmonic (3). Notice also the relative magnitude between the two contributions in Eq. 6-22 such that it looks like the nonlinear contribution is small while the linear contribution is large. This principal feature of the model can clearly be seen in the numerical results shown in Figure 6-8.

PAGE 214

187 How to correlate this square-law with si gn model with the momentum integral (term IV in Eq. 6-10) is investigated in the next section. Figure 6-8: Numerical results of the nor malized terms in the integral momentum equation as a function of phase angle during a cycle. A) Case 1: h/d = 1, St = 2.38, Re = 262, S = 25. B) Case 2: h/d = 2, St = 2.38, Re = 262, S = 25. Each term has been normalized by its respective magnitude. In summary, a physical explanation has b een given of each of the term that composes the equation of the orifice pressu re drop given by Eq. 6-10. Each term was related to its lumped element counterpart. It was found that the ex cess shear contribution from the starting flow (term I ) can be neglected in compar ison to the magnitude of the other terms, the fully developed shear stress component (term II ) is equivalent to the linear acoustic resistance from LEM, and the unsteady inertia term (term III ) corresponds to the acoustic linear orifice reactance. Finally, the momentum integral (term IV ) is the only nonlinear contribution to th e pressure drop and can be represented by a nonlinear system having both a resistive aOnlR and a reactive aOnlM part. Therefore, if one is able to find a correlation for this nonlinear term (term IV ) as a function of the governing dimensionless parameters, then it can be implemented into the existing low-order lumped 0 45 90 135 180 225 270 315 36 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 phase (degree) Cp Unsteady term (III) Momentum int. (IV) Shear term (I+II) 0 45 90 135 180 225 270 315 36 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 phase (degree) Cp Unsteady term (III) Momentum int. (IV) Shear term (I+II) B A

PAGE 215

188 model. These findings are s hown schematically in Figure 69, where a physical parallel is provided between each of the terms in the acoustic orifice impedance of a ZNMF actuator and the control volume analysis described above. Figure 6-9: Comparison between lumped elements from the orifice impedance and analytical terms from the control volume analysis. Development of Approximate Scaling Laws Experimental results Now that an analytical expression of the pressure drop across the orifice has been derived and validated, the experimental data presented in Chapter 3 and used throughout this dissertation are used to develop scaling la ws of the orifice pressure drop coefficient, LEM ,,,, aOaOlinearaOnonlinearaOlinearaOnonlinear j P ZRRjMM Q Control volume analysis 22 2 0 1 0 0c 4 o 4 2 4 s 2yd ffF F p y j D fDy vv x x d C d dd y CCd y S c t d V t d aN R faCR 0, aOnlRfaCM 0 aN M linear resistance due to starting developing viscous flow (neglected) linear resistance due to fully-developed viscous flow nonlinear resistance due to velocity momentum reactfaC aN aOnl aNR R R M ,ance due to flow unsteadiness reactance due to starting developing viscous flow (neglected) nonlinear reactance due to velocity momentumfaC aOnlM M aOnlM

PAGE 216

189 to improve the existing lumped element model. In Chapter 4, the experimentally determined orifice pressure loss coefficient has already been plotte d versus the Strouhal number as well and the nondimensional stroke length 0SthdhL However, large scatter in the pressure data were noted, since it was assumed that the pressure inside the cavity is equivalent to the pressure drop acro ss the orifice. This is not always a valid assumption, as discussed in the first part of Chapter 5. Therefore, the RHS of Eq. 6-10 is now used explicitly to compute the orifice pressure drop pc Notice however that the shear stress contribution is neglected in this experimentally-based investigation, simply because no such information is available an d also since, as discussed above, the CFD results suggest that this term is indeed neglig ible. Likewise, as validated in the previous section, the entrance velocity is approximated by the exit velocity via Eq. 6-12 to compute the velocity momentum integral (term IV in Eq. 6-10). Figure 6-10 shows the experimental results of the total orifice pressure drop coefficient for different Stokes number and as a function of Sthd The pc is computed from the control volume analysis (using the RHS of Eq. 6-10 less the shear term). However, the pc measured from the cavity pres sure data using Microphone 1 or Microphone 2 is also shown only for illustration purposes. In addition to the experimental results, the results for the numer ical simulations used above are included. The experimental results using the theore tical control volume analysis show good collapse of the data over the whole range of inte rest. This is especially true even at high Sthd (or low dimensional stroke length by recalling that 0SthdhL ) where the orifice pressure drop linearly increases with Sthd This is in accordance with the fact

PAGE 217

190 that the unsteady term in Eq. 6-10 is a function of Sthd and was shown to be the dominant term. However, at lower values 1 Sthd the collapse in the data is less pronounced since for such low Strouhal numbe rs the nonlinear term becomes significant due to jet formation, as confirmed from the CFD data and shown previously in Gallas et al. (2004). In this scenario at low Sthd the orifice flow may be seen as quasi-steady and/or as a starting flow due to the large stroke length; hence the pressure drop should asymptote to the solution of steady pipe flow, which is mainly a function of geometry and Reynolds number. Notice also that the case of low Sthd may also be due to a very thin orifice design, similar to a perforate, for which the orifice flow is always in a developing state. On the other hand, the scatter in the data using the experimental cavity pressure is made evident when joining the corresponding da ta from Mic 1 to Mic 2 to estimate the uncertainty in the pressure data. Although th e orifice pressure drop is overestimated for certain experimental data cases when using the cavity pressure in formation, given the large uncertainty in the pressure drop data, the overall trend is well-defined over the intermediate-to-high range of Sthd while the lower range shows an asymptotic behavior to a constant value. In any case, the two distinct regions are well defined. At low dimensionless stroke length, the flow is clearly unstea dy, while for high dimensionless stroke length the flow is quasi -steady, as delimited by the dotted line in Figure 6-10, which corresponds to 0.62 Sthd or 05 Lh.

PAGE 218

191 10-2 10-1 100 101 102 10-1 100 101 102 103 St.h/d = .h/L0 cp= P/(0.5 Vj 2) S=4 S=10 S=12 S=14 S=17 S=25 S=43 S=53 p using Control Volumep using Mic 1p using Mic 2 CFD 0.62 Figure 6-10: Experimental results of the or ifice pressure drop normalized by the dynamic pressure based on averaged velocity jV versus Sthd for different Stokes numbers. The pressure dr op is computed using e ither the control volume analysis (terms III and IV ) or the experimental cavity pressure (Mic 1 and Mic 2). Next, each term in Eq. 6-10 less term I that is neglected is also plotted versus the dimensionless stroke length Sthd using the experimental data. Practically, the nonlinear momentum integral (term IV ) is computed from the exit velocity profile and using the approximation discussed above to co mpute the orifice entr ance velocity (recall the equivalence with the nonlinear acoustic resistance RaO,nl and mass MaO,nl). The unsteady inertia component (term III ) is directly computed vi a its definition (equivalent to the acoustic mass MaN). Then, the fully developed friction coefficient contribution (term II ) is also computed from its definition (recall the equivalence with the linear acoustic resistance RaN). The experimental results for these three terms are shown in Figure 6-11.

PAGE 219

192 10-1 100 101 102 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 St.h/d S=4 S=10 S=12 S=14 S=17 S=25 S=43 S=53 Figure 6-11: Experimental results of each te rm contributing in the orifice pressure drop coefficient vs. Sthd A) Term II : friction coefficient integral due to fully developed flow. B) Term III : unsteady inertia. C) Term IV : nonlinear momentum integral from convective term. First of all, the contribution of the friction coefficient integral from the fully developed pipe flow that corresponds to the linear acoustic resistance in the LEM is shown in Figure 6-11A. Not surprisingly, it ha s a rather small effect overall and linearly increases with Sthd Note that the data will collapse if one plots it as a function of Re hd (recall that 2Re StS ). Then, shown in Figure 6-11B, is the contribution of 10-2 10-1 100 101 102 10-1 100 101 102 10 3 St.h/d S=4 S=10 S=12 S=14 S=17 S=25 10-2 10-1 100 101 102 10-3 10-2 10-1 100 101 St.h/d S=4 S=12 S=14 S=17 S=43 S=53 A B Unsteady inertia Fully developed flow friction coefficient integral C Nonlinear momentum integral

PAGE 220

193 the unsteady inertia effects that varies linearly with Sthd and which is clearly the dominant feature in the total orifice pressure loss, especially for 0.62 Sthd Figure 6-11C shows next the variations of the nonlin ear momentum integral as a function of the dimensionless stroke length. It can first be noted that the data seem scattered and that no obvious trend can be discerned. Notice also that the data oscillate around a value of unity, which is the assumed value for the nonlinear loss coefficient Kd in the existing lumped model. Finally, Figure 6-12 shows the relative magnitudes of each term in the pressure loss equation for the intermediate to low Sthd cases. It confirms that the nonlinear term is only really significant for low values of 3 Sthd where above this value the unsteady inertia term (term III ) dominates and takes on a value greater than 10 (see Figure 6-11C), while term IV never exceeds 2 (and is usually less than that). 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 10 20 30 40 50 60 70 80 90 100 St.h/dpercentage (%) Fully developed shear (term II) Unsteady inertia (term III) Mometum integral (term IV) Figure 6-12: Experimental results of the rela tive magnitude of each term contributing in the orifice pressure drop coefficient vs. intermediate to low Sthd Therefore, based on these experimental results from the control volume analysis, the next step to be undertaken is to obtai n a correlation of the nonlinear term in the

PAGE 221

194 pressure drop expression, which is ultimatel y to be related to the nonlinear coefficient Kd from the LEM defined in previous chapters. The other terms in Eq. 6-10 are already defined, as shown in Figure 6-9. Then the scaling law will be implemented in the existing lumped model from Gallas et al. (2003a) to yield a refined model. Nonlinear pressure loss correlation In the previous section, it was shown that the nonlinear part of the pressure loss coefficient can be successfully approximated by a square-law with sign model, which has both magnitude and phase information. The ex perimental results are then used to find a correlation for the magnitude. However, it is difficult to obtain accurate phase information at the present time. Since we are primarily interested in the magnitude of the actuator output, we will con centrate on the nonlinear resist ance component. Applications that require accurate phase information (e.g., feedback flow control models) will ultimately require this aspect to be addressed. As shown in Figure 6-11C, there is no su ch obvious correlati on for the magnitude from the data over the entire range of Sthd However, as noted earlier, two regions of operation can be distinguished from each other. A quasi-steady flow for high dimensionless stroke length 05 Lh and unsteady flow for intermediate to lower 0Lh In the former case where the nonlinear term IV is important, a different functional form should be envisaged from known steady pipe flow solutions that usually rely on the orifice geometry and flow Re ynolds number. For instance, when studying flows in the inlet of ducts, White (1991, p. 291) describe s a correlation of the pressure drop in the entrance of a duct for a laminar steady flow as a function of Re yd. Also, another

PAGE 222

195 common approach employed is from orifice fl ow meters. There, from pipe theory (Melling 1973; White 1979), the steady pipe flow dump loss coefficient for a generalized nozzle is given by 2 41dDKC (6-23) with dD is the ratio of the exit to the entrance orifice diameter, and where D C is the discharge coefficient that takes the form 0.50.99756.53ReDC (6-24) for high Reynolds number Re. The problem however resides in the facts that Eq. 6-23 is based on a beveled-type of orifice, and th at it is valid only fo r high Reynolds number 4Re10 Here, a similar approach is used to correlate the quasi-steady cases. This is shown in Figure 6-13 where the experimentally determined nonlinear loss ( cp)nonlinear is plotted against the Reynolds number Re in Figure 6-13A and against Re hd in Figure 6-13B. In these plots, the circled data are the one s of interest since they occur at a low Sthd i.e., 0.62 Sthd or 05 Lh Note that a distinction has been made on the orifice aspect ratio h/d (small h/d are in red symbols, intermediate h/d are in green, and large h/d are in blue). Once again, the 3 numerical te st cases have been a dded to the figures for completeness. An estimate can then be found for the low Sthd range in terms of Re hd, as shown by the regression line in Figure 6-13B. The two outliers in Figure 6-13B are Case 60 ( S = 4, h/d = 5, Re = 132, St = 0.12) and Case 61 ( S = 4, h/d = 5, Re = 157, St = 0.10).

PAGE 223

196 101 102 103 104 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 ReKd = (cp)Nonlinear S=4, h/d=0.94 S=4, h/d=5 S=10, h/d=0.68 S=12, h/d=1.68 S=12, h/d=0.35 S=14, h/d=5 S=17, h/d=5 S=25, h/d=1 S=25, h/d=2 S=43, h/d=0.35 S=53, h/d=0.35 S=53, h/d=1.68 small h/d intermediate h/d large h/d 0 0.01 0.02 0.03 0.04 0.05 0.06 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 (h/d)/ReKd = (cp)Nonlinear S=4, h/d=0.94 S=4, h/d=5 S=10, h/d=0.68 S=12, h/d=1.68 S=12, h/d=0.35 S=14, h/d=5 S=17, h/d=5 S=25, h/d=1 S=25, h/d=2 S=43, h/d=0.35 S=53, h/d=0.35 S=53, h/d=1.68 small h/d intermediate h/d large h/d Kd=(1-20(h/d)/Re)/(0.4+300(h/d)/Re) Figure 6-13: Experimental results for the non linear pressure loss coefficient for different Stokes number and orifice aspect ratio. A) Versus Reynolds number Re. B) Versus Re hd. The circled data correspond to 05 Lh On the other hand, for the cas e of intermediate to high Sthd one can find a crude correlation as a function of Sthd as shown in Figure 6-14, that should be able to represent the principal variations in the nonlinear part of the orifice pressure loss. Once A B ( cp)nonlinear ( cp)nonlinear

PAGE 224

197 again, the 3 numerical test cases have been added to the figure for completeness. The two outliers in Figure 6-14 are Case 48 ( S = 53, h/d = 0.35, Re = 571, St = 4.96) and Case 56 ( S = 53, h/d = 1.68, Re = 318, St = 8.79). 10-1 100 101 102 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 St.h/dKd = ( cp)Nonlinear S=4 S=10 S=12 S=14 S=17 S=25 S=43 S=53 Kd=0.43+(St.h/d)-1 0.62 Figure 6-14: Nonlinear term of the pressure loss acros s the orifice as a function of Sthd from experimental data. The straight line shows a curve fit to the data in the intermediate to high Sthd range. Therefore, based on these simple regr essions performed on the data, a rough correlation on the amplitude of the nonlinear pressure loss co efficient can be obtained as a function of Sthd At low values of Sthd the nonlinear coefficient varies with Re hd, while for intermediate to high values, the nonlinear pressure drop coefficient is a function of Sthd Thus, the following scaling law of the amplitude of the dimensionless orifice pressure loss is proposed ( cp)nonlinear

PAGE 225

198 0 -1 0 ,120 Re for 0.62 or 5 0.4300 Re 0.43 for 0.62 or 5pnl pnlhd L h cSt hd dh L hh cStSt ddh (6-25) Notice that these scaling laws are not optimal since they do not overlap at 0.62 Sthd Although for high Sthd it seems accurate, the functional form for the scaling law for low Sthd can be greatly refined from an extended available database. Then, based on this development of a scaling law for the nondimensional pressure loss inside the orifice of an is olated ZNMF actuator, the next logical step is to implement it into the existing reduced-order lumped el ement model. This is described in the following section. Refined Lumped Element Model Implementation The lumped element model presented in Chapter 2 has been derived from the hypothesis of fully developed pipe or cha nnel flow. The acoustic impedance of the orifice, which is the component to be improved, is defined as a complex quantity that has both a resistance and a reactance term (Gallas et al. 2003a), ,, aOaOlinaOnlaO Z RRjM (6-26) where aOlinR and aO M are, respectively, the linear acoustic resistance and mass (i.e., reactance) terms from the exact solution fo r steady fully-developed pipe flow. The nonlinear acoustic resistance, aOnlR is defined as 20.5dj aOnl nKQ R S (6-27)

PAGE 226

199 where Kd is the dimensionless orifice loss coefficient that is assumed to be unity (McCormick 2000) in the existing version of the lumped element model. From the previous analysis using a cont rol volume, the correspondence between the lumped elements and the pressure drop terms was shown in Figure 6-9. All terms were appropriately modeled via lumped elements exce pt for the nonlinear term that is the focus of this effort and that has both a resistance and a reacta nce. From the scaling law developed next, only the magnitude was successfully correlated with the main nondimensional geometric and flow parameters not the phase. The magnitude and phase of the nonlinear term are related to the resistance and mass in the LEM impedance analogy via the following relationships. Si nce the acoustic impedance is defined as aOaOaO jP ZRjM Q (6-28) and that the orifice pressure drop is 20.5p jP c V (6-29) then, the correspondence between LEM and th e control volume analysis is given by j aOp jnV P Z c QS (6-30) However, the nonlinear pressure drop from the momentum integral was shown to be accurately modeled via a squa re-law with sign model (see Eq. 6-22). So accounting only for the nonlinear part, Eq. 6-30 becomes

PAGE 227

200 ,,,, 31 5nlnlj aOnlaOnlaOnlpnl n jtAjtA nlV Z RjMc S Aee (6-31) where nljnpnlAVSc Notice also that the relationship between the dimensionless orifice loss coefficient Kd defined in Eq. 6-27 and the nonlinear part of pc defined in Eq. 6-29 is such as 2 ,2dpnlKc (6-32) Hence, the parameters introduced in Eq 6-31 are related to each other via, 22 2 ,, ,cotnlaOnlaOnl aOnl nl aOnlARM M A R (6-33) The problem resides in the fact that, ev en though a scaling law was developed for the nonlinear magnitude nl A insufficient information is available to model the nonlinear phase component nlA Hence the system of equation Eq. 6-33 cannot be solved for both ,aOnlR and ,aOnlM Nonetheless, as a first pass, the phase lag from the nonlinear term is neglected, so that the scaling law developed above in Eq. 6-25 for pnlc is directly implemented into the total orifice acoustic impedance ZaO through the refined nonlinear acoustic resistance ,aOnlR via Eqs. 6-31 and 6-32.

PAGE 228

201 start input actuator design frequency loop f > flim compute lumped parameters:,,,,aDaCaOaOlinZZMR compute nonlinear lumped parameters:, daOnlaOKRZ initial guess compute jet volume flow rate aca j aCaDaCaOaOaDV Q Z ZZZZZ end new guess Newton-Raphson algorithm compute jet velocity jjnVQS convergence criterion F T T F Figure 6-15: Implementation of the refine d LEM technique to compute the jet exit velocity frequency response of an isolated ZNMF actuator.

PAGE 229

202 Comparison with Experimental Data The problem being now closed, the refi ned lumped element model can now be implemented and compared to ex perimental data. Notice that Kd is now a function of the output flow, so it should be implemented in an iterative converging loop. Also, LEM provides a frequency response of the actuator output (strictl y speaking, it is an impulse response since the system is nonlinear). Th e actual sequence to compute the jet exit velocity using the refined LEM technique is depicted in the flow chart shown in Figure 6-15. The nonlinear terms in the orifice acoustic impedance are computed via a NewtonRaphson algorithm. Next, the refined low-order model is im plemented and compared with available frequency response experimental data. The two test cases that were used to validate the first version of the lumped model in Gallas et al. (2 003) are again utilized for comparison. These two cases are already show n in Chapter 2 (see Figure 2-2), and the reader is referred to Gallas et al. (2003a) for the details of the experimental setup and actuator configuration. In Figure 6-16 and Figure 6-17, the impulse response of the jet exit velocity acquired at the centerline of th e orifice is compared with the two lumped element models: the previous LEM corresponds to the model developed in Gallas et al. (2003a), and the refined LEM corresponds to the refined model developed in this chapter. Each model prediction is applied to Case I and Case II, as shown in Figure 6-16A and Figure 6-17A, respectively. Notice that here the only empirical factor the diaphragm damping coefficient D has been adjusted so that the refined model matches the peak magnitude at the frequency governed by the diaphragm natural frequency.

PAGE 230

203 Before discussing the results, it should be pointed out that the experimental data are for the centerline velocity CLVt of the ZNMF device. The lumped element model gives a prediction of the jet volume flow rate am plitude (or spatial-averaged exit velocity jVt ) which is like a bulk velocity. And as seen in Chapter 4, there is no simple relationship between jVt and CLVt (see Figure 4-10) for the test cases considered in this study. Therefore, in order to represen t this uncertainty, the two minima from the theoretical ratio jCLVV for a fully developed pipe flow, that is already shown in Figure 2-5, are bounding the refined LEM prediction, as seen in Figure 6-16A and Figure 6-17A. 0 500 1000 1500 2000 2500 3000 0 5 10 15 20 25 30 35 frequency (Hz)centerline velocity (m/s) exp. data previous LEM refined LEM bounds in the expected value of VCL for LEM Figure 6-16: Comparison between the experiment al data and the prediction of the refined and previous LEM of the impulse response of the jet exit ce nterline velocity. A) Centerline velocity versus fre quency, where the LEM prediction is bounded by the minima of the theoretical ratio jCLVV B) Jet Reynolds number versus S2. C) Nonlinear pressure loss coefficient versus S2. Actuator design corresponds to Case I from Gallas et al. (2003a). A

PAGE 231

204 0 500 1000 1500 2000 2500 3000 3500 4000 4500 0 500 1000 1500 2000 2500 3000 3500 4000 S2Reynolds number exp. data refined LEM Re based on VCLRe based on Vj /\ 0 500 1000 1500 2000 2500 3000 3500 4000 4500 0 0.2 0.4 0.6 0.8 1 1.2 S2Kd Figure 6-16: Continued. Similarly, the Reynolds number based either on CLV for the experimental data or jV for the LEM prediction is plotted versus the Stokes number squared, as shown in Figure 6-16B and Figure 6-17B. And finally, Figure 6-16C and Figure 6-17C show the C B

PAGE 232

205 corresponding nonlinear orifice pres sure loss is plotted versus S2 for Case I and Case II, respectively. 0 500 1000 1500 0 10 20 30 40 50 60 70 80 frequency (Hz)centerline velolcity (m/s) exp. data previous LEM refined LEM bonds in the expected value of VCL for LEM 0 100 200 300 400 500 600 0 500 1000 1500 2000 2500 3000 3500 4000 S2Reynolds number exp. data refined LEM Re based on VCLRe based on Vj /\ Figure 6-17: Comparison between the experiment al data and the prediction of the refined and previous LEM of the impulse response of the jet exit ce nterline velocity. A) Centerline velocity versus fre quency, where the LEM prediction is bounded by the minima of the theoretical ratio jCLVV B) Jet Reynolds number versus S2. C) Nonlinear pressure loss coefficient versus S2. Actuator design corresponds to Case II from Gallas et al. (2003a). A B

PAGE 233

206 0 100 200 300 400 500 600 -0.5 0 0.5 1 1.5 2 2.5 S2Kd Figure 6-17: Continued. Clearly, the main effect of the refined nonlinear orifice loss is to provide a slightly better prediction on the overall frequency re sponse. For instance in Case I (Figure 6-16A), the peak near the Helmholtz frequenc y (first peak in the frequency response) is still overdamped by this new resistance, a lthough the trough between the two resonance peaks and the response in the high freque ncies are in better agreement with the experimental data. It is believed that the nonlinear mass information that is still missing in the model is a possible explanation for th e residual discrepancy seen. In Case II (Figure 6-17A), the refined model tends to ma tch closely the experi mental data, and over the entire frequency range the peak in the experimental results near 1200 Hz corresponds to a harmonic of the piezoelectric diaphragm resonance frequency, which the lumped model does not account fo r. In this case the dampi ng of the Helmholtz resonance peak, occurring around 450 Hz, is well pred icted. Notice also the jump in Kd seen in Figure 6-17B around 1050 Hz that is due to the discontinuity betw een the two scaling laws (Eq. 6-25) at 0.62 Sthd C

PAGE 234

207 However, this refined lumped element model fails in predicting some ZNMF actuator configurations, as shown in Figur e 6-18. Although the uncertainty in the centerline velocity may explain some of the di screpancy, there are yet some deficiencies in the current lumped model. Some possible explanations would be first on the lack in the nonlinear mass that is non negligible for low Sthd which corresponds to the frequencies above 300 Hz in Figure 6-18B. Similarly, it was shown that, in the timedomain, the nonlinear term includes the generation of 3 terms given a forcing at While this is true in a time-domain, it may not be exactly similar in the frequency domain method employed above. The amplitude does match for the frequency domain, but the phase information is incorrect, which affects the impedance prediction via Eq. 6-33. This is further investigated next. Figure 6-18: Comparison between the experiment al data and the prediction of the refined and previous LEM of the impulse response of the jet exit ce nterline velocity. A) Centerline velocity, where the refined LEM prediction is bounded by the minima of the theoretical ratio jCLVV B) Nonlinear pressure loss coefficient Kd. Actuator design is from Gallas (2002) and is similar to Cases 41 to 50 ( h/d = 0.35). 0 500 1000 150 0 0 0.5 1 1.5 2 2.5 frequency(Hz)B A Centerline velocit y ( m/s ) K d 0 500 1000 1500 0 5 10 15 20 25 30 35 frequency (Hz) exp data previous LEM refined LEM bounds in the expected value of VCL for LEM

PAGE 235

208 The above analysis is performed on the fr equency response of the actuator output. However, as outlined in Chapter 2, the LEM technique can be easily implemented in the time domain to then provide the time signals of the jet exit volume flow rate at a single frequency of operation. Subsequently it can be easily compared with some of the experimental test cases listed in Table 2-3. The equation of motion in the time domain of an isolated ZNMF actuator has been previously derived in Chapter 2 in Eq. 229 that is reproduced here for convenience 00.5 1 sindd aOjjjaOlinjj naCaCnKS M yyyRyyWt SCCS (6-34) In the previous lumped model Kd was set to unity, so the se cond term in the LHS of Eq. 6-34 is a constant. However, Kd is now a function of either Sthd or Re hd via Eq. 6-25, so that the equation of motion should be rearranged accordingly. Then, the nonlinear ODE (Eq. 6-34) that de scribes the motion of the fluid particle at the orifice is numerically integrated using a 4th order Runge-Kutta algorithm with zero initial conditions for the part icle displacement and velocity, as outlined in Chapter 2, until a steady state is reached. The results of the jet volume velocity at the orifice exit are compared with two experimental test cases namely Case 29 and Case 41, which are shown in Figure 6-19A and Figure 6-19B, resp ectively. Again, note that zero phase corresponds to the onset of th e expulsion stroke. While th e magnitude of the jet volume flow rate is clearly well predicted by the refined model, especially for Case 41 (Figure 6-19B), the distortion seen in Case 29 (Fi gure 6-19A) is not captured by the low-order model that remains nearly sinusoidal. The di stortions in the signal are presumably due to the phase distortions that are not completely account ed for in this refined model. Note

PAGE 236

209 that at this particular fr equency the frequency domain method described above gives a similar value for the jet volume flow rate amplitude. 0 45 90 135 180 225 270 315 360 -4 -3 -2 -1 0 1 2 3 4 5 x 10-5 phase (degree) exp. data refined LEM 0 45 90 135 180 225 270 315 360 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 x 10-6 phase (degree) Figure 6-19: Comparison between the refine d LEM prediction and experimental data of the time signals of the jet volume flow rate. A) Case 29: S = 34, Re = 1131, St = 1.1, h/d = 0.95. B) Case 41: S = 12, Re = 40.6, St = 3.49, h/d = 0.35. In conclusion, a refined lumped element model as been presented to predict the response of an isolated ZNMF actuator. The model builds on a control volume analysis A Jet volume flow rate ( m3/s ) Jet volume flow rate ( m3/s ) B

PAGE 237

210 of the unsteady orifice flow to yield an e xpression of the dimensi onless pressure drop across the orifice as a function of th e Reynolds number Re, Strouhal number St and orifice aspect ratio h/d The model was validated via num erical simulations, and then a scaling law of the orifice pre ssure loss was devel oped based on experime ntal data. Next, the refined pressure loss coefficient was implemented into the existing low-dimensional lumped element model that predicts the actuator output. The new model was then compared with some experimental test ca ses in both the frequenc y and time domain. This refined model is able to reasonably pred ict the magnitude of the jet velocity. Notice however that this model can be applicable to any type of ZNMF devices, meaning the driver and cavity of the actuator are well m odeled, the only refinement made being for the orifice flow. And as seen in Chapter 4, it exhibits a rich and complex dynamics behavior that the refined model developed abov e is in essence able to capture, while still lacking in the details. Clearly, the reduced-o rder model as presented in this chapter will greatly beneficiate from a larger available high quality database, both numerically and experimentally.

PAGE 238

211 CHAPTER 7 ZERO-NET MASS FLUX ACTUATOR IN TERACTING WITH AN EXTERNAL BOUNDARY LAYER This chapter is dedicated to the interac tion of a ZNMF actuator with an external boundary layer, in particular with a laminar, flat-plate, zero pressure gradient (ZPG) boundary layer. First, a qualitative discus sion is provided c oncerning grazing flow interaction effects. This discussion is ba sed on the numerical simulations performed by Rampuggoon (2001) for the case of a ZNMF de vice interacting with a Blasius laminar boundary layer and also on studies of other appli cations such as acoustic liners. Next, the nondimensional analysis performed in Chapter 2 for the case of an actuator issuing into ambient air is extended to include the grazing flow interaction effects. Based on these results, two approaches to develop reduced-order models are proposed and discussed. One model builds on the lumped element modeli ng technique that was previously applied to an isolated device and leverages the semi-empirical models developed in the acoustic liner community for grazing flow past Helmho ltz resonators. Next, two scaling laws for the exit velocity profile beha vior are developed that are ba sed on available computational data. Each model is develope d and discussed, and the effect s of several key parameters are investigated. On the Influence of Grazing Flow As mentioned in Chapter 1, most applicati ons of ZNMF devices involve an external boundary layer. Intuitively, the performa nce of a ZNMF actuator will be strongly affected by some key grazing flow parameters that need to be identified. Rampuggoon

PAGE 239

212 (2001) performed an interesting parametric study on the influence of the Reynolds number based on the bou ndary layer thickness Re the orifice aspect ratio hd, and the jet orifice Reynolds number RejVd for a ZNMF device interacting with a Blasius boundary layer. As shown in Figure 7-1, if the jet Reynolds number Re is small compared with that of the boundar y layer, for a constant ratio 2 d the vortex formation process at the orif ice neck is completely dist urbed by the grazing boundary layer. In particular, the counterclockwise (CCW) rotation vortex that usually develops on the upstream lip of the slot in quiescent flow cases is quickly cancelled out by the clockwise (CW) vorticity in the grazing boun dary layer, while a distinct clockwise rotating vortex is observe d to form, although it rapidl y diffuses as it convects downstream. However, as the jet Reynolds number Re increases, both vortices of opposite sign vorticity generated at the slot are immediately conv ected downstream due to the grazing boundary layer and are confined inside the boundary layer. Furthermore, due to vorticity cross-anihilation (Morton 1984), the CCW vortex rapidly diminishes in strength such that further dow nstream only the CW vortex is visible. Notice that these simulations are two-dimensional, and that ac tually there are not really two distinct vortices but a closed vortex loop. Figure 7-1: Spanwise vorticity plots for thr ee cases where the jet Reynolds number Re is increased. A) Re = 63. B) Re = 125. C) Re = 250. With Re254 1 hd and 10 S (Reproduced with permission from Rampuggoon 2001).

PAGE 240

213 By increasing the jet Reynolds number, the vortices now completely penetrate through the boundary layer and em erge into the freestream fl ow, which is primarily due to the relatively high jet momentum. In each cycle, one vortex pairs with a counterrotating vortex of the previous cycle and this vortex pair pr opels itself in the vertical direction through self-i nduction while being continuously swept downstream due to the external flow. However, in an actual separa tion control application, it is unlikely that such a scenario of complete disruption of the boundary layer will be possible (due to actuator strength limitations) or even desira ble. Similarly in another case study, Rampuggoon (2001) looked at the effect of the orifice aspect ratio hd and found no significant difference in the initial developm ent of the vortex st ructures, although it yielded slightly different vortex dynamics further downstream. Figure 7-2: Spanwise vorticity plots for three cases where the boundary layer Reynolds number Re is increased. A) Re = 0. B) Re = 400. C) Re = 1200. With Re = 250, 1 hd and 10 S (Reproduced with permission from Rampuggoon 2001). Similarly, the Reynolds number based on the BL thickness Re was systematically varied while holding all other pa rameters fixed. In this case, it was found that as Re increases, the vortex structures generated at the orifice lip are quickly swept away and convected downstream, but can still penetr ate through the BL thickness. When such vortex structures are large e nough to directly entrain freestr eam fluid into the boundary A B C

PAGE 241

214 layer, this entrainment becomes an importa nt feature since in an adverse pressure gradient situation, the resulti ng boundary layer is more resist ant to separation. Figure 7-2 shows spanwise vorticity plots for three cases in which the boundary layer Reynolds number Re is gradually increased from 0 to 1200. x/d v/Vinv max -0.5 -0.25 0 0.25 0.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 Re=0 Re=254 Re=400 Re=800 Re=1200 Re=2600 x/d v/Vinv max -0.5 -0.25 0 0.25 0.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 Re=0 Re=254 Re=400 Re=800 Re=1200 Re=2600 Figure 7-3: Comparison of the jet exit velocity profile with increasing Re from 0 to 2600, with Re = 250, 1 hd and 10 S A) Expulsion profiles. B) Ingestion profiles. (Reproduced with permission from Rampuggoon 2001). Next, Figure 7-3 shows the impact of Re on the exit velocity profile of the jet. It is clear that the jet profile in the case of quiescent flow, Re = 0, is significantly different from the case where there is an external boundary layer, Re 0. In the case of an external boundary layer, the jet velocity profile may not be characterized by just one parameter, such as the conve ntional momentum coefficient C (defined below in Eq. 7-1 ), that is commonly employed in active fl ow control studies using ZNMF devices (Greenblatt and Wygnanski 2000; Yehoshua and Seifert 2003). In particular, the jet velocity profile is increasingly skewed in the flow direction as the Reynolds number of the boundary layer Re increases; this has a direct effect on the flux of momentum, B A

PAGE 242

215 vorticity, and energy from the slot. Therefore, from the point of view of parameterization of the jet velocity profile, th e skewness appears to be an im portant parameter that should be considered, and is introduced in the next section. Similarly, it was shown (Utturkar et al. 2002) that the momentum coefficient differs during the ingestion versus the expulsion portion of the stroke a nd both are different from the ambient case. The above discussion permits one to gain significant insight on the influence of several key dimensionless parameters on th e overall behavior of a ZNMF actuator interacting with an external boundary layer. Howe ver, Rampuggoons study was limited to the special case of a Blasiu s boundary layer, which is an incompressible, laminar, zero pressure gradient boundary layer over a flat plat e. Hence, a further discussion is provided below based on the work performed on flow past Helmholtz resonators over a wider range of flow conditions. As previously discussed in Chapter 1, research involving flow -induced resonators has been mainly triggered by the desire to s uppress oscillations, such as those occurring for example on automobile sunroofs (Elder 1978; Meissner 1987), or in sound absorbing devices, such as mufflers (Sullivan 1979) or acoustic liners in engine nacelles (Malmary et al. 2001). Others have also suggested that an array of Helmholtz resonators driven by a grazing flow can modify a turbulent boundary layer (Flynn et al 1990). Even though these flow-induced resonators are passive as compared to active ZNMF actuators, their major findings are of interest and warrant a di scussion. It should al so be noted that the key parameter that has been widely used by researchers to quantify the interaction between the acoustic field and the grazing flow at the orifice exit is the specific acoustic

PAGE 243

216 impedance of the treated surface. Conveniently, this is similar to that of our previous research for isolated ZNMF actuators in using LEM. Choudhari et al. (1999) performed an interesting study by comparing their numerical simulation results of flow pa st a Helmholtz resonator to published experimental data. Three different configuratio ns for the resonator were studied, as listed in Table 7-1. The two-dimensional or axis ymmetric laminar compressible Navier-Stokes equations were solved using an-house, node-bas ed finite volume Cartesian grid solver. When applicable, a turbulent model was used based on the one-equation Spalart-Allmaras model (Spalart and Allmaras 1992). The reader is referred to their paper for a discussion of the numerical scheme that was employe d. Although not reproduced here, the numerical simulations compared well, both qua litatively and quantitatively, with the experimental data from Hersh and Wa lker (1995) and Melling (1973). Table 7-1: List of configur ations used for impedance tube simulations used in Choudhari et al. (1999). Reference Orifice diameter (or width) dmm Thickness to diameter ratio hd Open area ratio % Acoustic amplitude SPL dB Cavity height Hmm Freq. f Hz Hersh & Walker (1995) Single circular orifice 9.52 1.33 3.5 95 126 22.23** 250-600 Melling (1973) Perforate 153 A/00 1.27 0.5 7.5 114 162* 25.44 3400 LaRC (1998-1999) Slot Perforate 2.54 2.54 1 2.5 5 5 linear 114 148* 76.2 76.24 566 1139 *Free space SPL **Tuned for 500 f Hz As previously discussed in Chapter 4, although incomplete in terms of essential dimensionless parameters, two different regimes were identified in terms of the sound

PAGE 244

217 pressure level (SPL): one for low-amplitude that is termed linear and one for high acoustic amplitude it is nonlinear. The com putation from Choudhari et al. (1999) showed that in the linear regime, the fully-develope d unsteady pipe flow theory applied to perforates with an 1 O aspect ratio hd gave reasonable estima tes, although the flow near the orifice edges is dominated by the rapid acceleration around the corners. Also, they were able to show that the dissipation occurring in the orifice is mainly due to viscous effects rather than thermal dissipati on. In the nonlinear re gime, clear distortion in the probe signals (pressure fl uctuation, orifice velocity) ar e present as already shown in the first part of Chapter 5 in Figure 5-9. When a laminar boundary layer interacts with the liner surface, as shown in Figure 7-4, the in flow part of the cycl e exhibits a narrower vena contracta than for the outflow phase. This supports the hypethesis reported in earlier experimental studies (e.g., Budoff a nd Zorumski 1971) that, in the presence of grazing flow, the resistance to blowing into the flow is significantly less than the resistance to suction from the stream. Physically, this is equivalent in comparing the expulsion phase from a quiescent medium in side the resonator to the ingestion phase that directly interacts with a grazing flow. Such a resu lt is relevant and should be taken into account when modeling a ZNMF actuator. Therefore, from the study of previous wo rk performed in aerodynamics as well as in aeroacoustics, some main features of the interaction of a grazing flow with a Helmholtz resonator and/or a ZNMF actuator can be extracted that yield more insight into the flow physics of such complex in teraction behavior. In this regard, a nondimensional analysis is first described below, followed by the development of physics-based reduced-order models.

PAGE 245

218 Figure 7-4: Pressure contour s and streamlines for mean A) inflow, and B) outflow through a resonator in the presence of grazing flow (laminar boundary layer at Re3120 1 d 0.5 hd and average inflow/outflow velocity 10% of grazing velocity). (Reproduced w ith permission from Choudhari et al. 1999) Dimensional Analysis In Chapter 2, the actuator output parameters of interest we re identified and defined from the timeand spatial-averaged jet velocity jV during the expulsion portion of a cycle defined in Eq. 2-4. Examples of such quantities are the jet Reynolds number Re, or amplitude of the jet output volume flow rate jQ Another quantity of interest in the case of a grazing boundary layer is the oscillatory mo mentum coefficient. In the presence of a grazing boundary layer, to quantify the addition of momentum by the actuator and following the definition suggested by Greenbl att and Wygnanski (2000), the total (mean plus oscillatory) momentum coefficient of the periodic excitation is de fined as the ratio of the momentum flux of the jet to the freestream dynamic pressure times a reference area. For a 2-D slot, 2 rms 212jn refuS C US (7-1)

PAGE 246

219 where the subscript j refers to the jet, nSdw is the slot area, refSLw is a reference area with L being any relevant length scale of either the airfoil model or the grazing BL (chord length c boundary layer momentum thickness displacement thickness etc.). Notice that since no net mass is injected from the jet to the exterior medium (indeed, the jet is synthesized fr om the working ambien t fluid), and if the turbulent boundary layer is assumed incomp ressible along with the flow through the orifice, then no significant density variations are expect ed, neither in the incoming boundary layer nor in the jet orifice. Ther efore the fluid density of the jet can be considered as the same as the ambient fluid, i.e. j Similarly, ev en though the jet velocity contains both mean and oscillatory components, here only the oscillatory part of C is retained since the mean component is identically zero for a zero-net mass flux device. Thus, for incompressible flow and after time-averaging, the momentum coefficient is defined as 2 rms 22 ud C U (7-2) where 2 rmsu is the mean square value of the osci llatory jet velocity normal component, and the boundary layer momentum thickness is chosen as the relevant local boundary layer length scale. Based on the e xperimental results on the orific e flow described in Chapter 4, a clear distinction between the ejection and th e ingestion part of the cycle exists. Thus, the momentum coefficient defined in Eq. 7-2 can be rewritten such as ,, exinCCC (7-3)

PAGE 247

220 where the subscripts ex and in refer to, respectively, the expulsion and ingestion portions of the cycle. Yet other parameters, such as energy or vorticity flux, etc. might also play an important role in determining the effect of the jet on the boundary layer, not limiting ourselves to the momentum coefficient as in previous studies (Amitay et al. 1999; Seifert and Pack 1999; Yehoshua and Seifert 2003). In this current work, a more general approach to characterizing the jet behavior via successive moments of the jet velocity profile is thus advocated, fo llowing Rampuggoon (2001). The nth moment of the jet is defined as 12 12nn jC V, where jV is the jet velocity normalized by a suitable velocity scale (e.g., freestream velocity) and 12 represents an integral over the jet exit plane and a phase average of n jV over a phase interval from 1 to2 This leads to the following expression 2 12 12111 ,nn n jn S nCtxddS S V. (7-4) Note the similarity with the definition of the jet velocity jV given by Eq. 2-4 previously defined, where one period of the cycle and the phase interval are related by 21T and the normalized jet velocity is related by ,j jvtx tx U V, (7-5) if one takes, for instance, the freestream velocity U as a suitable velocity scale. As observed from the discussion above preliminary simulations (Rampunggoon 2001; Mittal et al. 2001) indica te that the jet velocity prof ile is significantly different

PAGE 248

221 during the ingestion and expulsion phases in th e presence of an external boundary layer. Defining the moments separately for the ingestion and expuls ion phases, they are denoted by n inC and n exC respectively. Furthermore, it sh ould be noted that this type of characterization is not simply for mathema tical convenience, sinc e these moments have direct physical significance. For example, 11 inexCC corresponds to the jet mass flux (which is identically equal to zero for a ZNMF device). The mean normalized jet velocity during the expulsion phase is 1 exC Furthermore, 22 inexCC corresponds to the normalized momentum flux of the jet, while 33inexCC represents the jet kinetic energy flux. Finally, for n 1/n n exC corresponds to the norma lized maximum jet exit velocity. In addition to the moments, the skewness or asymmetry of the velocity profile about the center of the orif ice is found to be useful (see Rampuggoon 2001) and can be estimated as 2 12 12 0 2111 ,, 2d jj X xxddx d VV. (7-6) Assuming the external boundary layer to be flowing in the positive x direction, if 120 X the jet velocity profile is skewed towards the positive x i.e. the jet has higher velocity in the downstream portion of the orifice than in its upstream part, while for 120 X the trend is inversed. If 120 X the jet velocity profile is symmetric about the orifice center in an averag e sense, which would, for example, correspond to the nograzing flow or ambient case. Similarly, th e flux of vorticity can be defined as (Didden 1979),

PAGE 249

222 2 12 01 2d vzjvxddx d (7-7) where zj zV is the vorticity com ponent of interest. Building on the dimensional analysis carri ed out in Chapter 2, the dependence of the moments and skewness can be written in terms of nondimensional parameters using the Buckingham-Pi theorem. The derivation is presented in full in Appendix D, and the results are summarized below: 12 123 grazing BL device,,,,,,Re,,,,,,n f HdC hw fnSHMC ddddR X (7-8) By comparison with Eq. (2.19), the new te rms are all due to the grazing BL. The physical significance of these new terms in th e RHS of Eq. 7-8 is now described; refer back to Eq. 2-15 and accompanying text for an explanation of the isolated device parameters. Re is the Reynolds number ba sed on the local BL momentum thickness, the ratio of the inertial to viscous forces in the BL. d is the ratio of local momentum thickness to slot width. H is the local BL shape factor. 0 M Uc is the freestream Mach number, th e measure of the compressibility of the incoming crossflow. *wdPdx is the Clauser equilibrium di mensionless pressure gradient parameter, relating the pressure force to the inertial force in the BL, where w is the local wall shear stress. 20.5fwCU is the skin friction coefficient, the ratio of the friction velocity squared to the freestream velocity squared.

PAGE 250

223 R is the ratio of the local momentum th ickness to the surface of curvature. Notice that the parameters based on th e BL momentum thickness have been selected versus the BL thickness or disp lacement thickness, by analogy with the LEMbased low dimensional models developed in this dissertation. Also, it is fairly obvious that the parameter space for this configuration is extremely large and some judicious choices have to be made to simplify the para metric space. For instance, in the case of a ZNMF actuator interacting with an incompressible, zero pressure gradient laminar boundary layer (i.e., a Blasius bou ndary layer), the functional form of Eq. 7-8 takes the form 12 123 Blasius,,,,,,Re,n HdC hw fnS dddd X (7-9) which is the situation for which the low-order models described next are restricted to. Reduced-Order Models From the discussion provided in the prev ious sections, two approaches can be sought to characterize the interaction of a ZNMF actuator with an external boundary layer. One approach is an extension of the lumped el ement model to account for the grazing flow on the orifice impedance. Ho wever, this method does not provide any details regarding the velocity profile. A sec ond approach is thus to develop a scaling law of the velocity profile at the orifice exit and its integral parameters that will represent the local interaction of the ZNMF actuator with the incoming grazing bou ndary layer. Both of these are discussed below.

PAGE 251

224 Lumped Element Modeling-Based Semi-Empir ical Model of the External Boundary Layer Definition As a first model, the LEM technique pr eviously introduced, described, and validated for a ZNMF actuator exhausting into st ill air is extended to include the effect of a grazing boundary layer. Figure 7-5 sh ows a typical LEM equivalent circuit representation of a generic ZNMF device interacting wi th a grazing boundary layer, where the parameters are specified in the ac oustic domain (as denoted by the first letter a in the subscript). The boundary layer impedan ce is introduced in seri es with the orifice impedance, since they share the same volume flow rate jQ the ZNMF actuator exhausting into the grazing boundary layer. ZaDZaCQd-QjQd Qjexisting model crossflow addition Pc ZaO ZaBL Figure 7-5: LEM equivalent ci rcuit representation of a ge neric ZNMF device interacting with a grazing boundary layer. For clarification, each com ponent of the equivalent circ uit shown in Figure 7-5 is briefly summarized below. First, the acoustic driver impedance aD Z is inherently dependant on the dynamics of the utilized driver, although the volumetric flow rate dQ that it generates can be ge neralized to be equal to 0sinddQjjSWt (7-10)

PAGE 252

225 The acoustic impedance of the cavity is modeled as an acoustic compliance 1c aC djaCP Z QQjC (7-11) where the cavity acoustic compliance is given by 2 0 aCC c (7-12) Then, the acoustic impedance of the orifice is defined by (see previous Chapter for details) ,, aOaOlinaOnlaO Z RRjM (7-13) where the linear acoustic resistance aOlinR corresponds to the viscou s losses in the orifice and is set to be aOlinaN R R (7-14) which takes a different functional form dependi ng on the orifice geometry as described in Chapter 2 and Appendix E. As discussed in Chapter 2 and in great detail in Chapter 6, the nonlinear acoustic resistance aOnlR represents the nonlinear losses due to the momentum integral and is given by 20.5dj aOnl nKQ R S (7-15) where dK is the nonlinear pressure drop coefficient that is a function of the orifice shape, Stokes number and jet Reynolds number (see Chap ter 6 for details). Finally, the acoustic orifice mass aO M groups the effect of the ma ss loading (or inertia effect) aN M and that of the acoustic radiation mass aRadM such that aOaNaRadMMM (7-16)

PAGE 253

226 where again each quantity is a function of the orifice ge ometry (see Appendix E). The new term is the acoustic boundary la yer impedance, which takes the form aBLaBLaBL Z RjX (7-17) where the acoustic resistance aBL R and reactance aBL X will be defined further below. The total acoustic impedance of the orifice, including the gr azing boundary layer effect is then defined by c aOtaOaBL jP ZZZ Q (7-18) where the boundary layer impedance is in series with the isolated orifice impedance since they share a common flow. Note that in the ZNMF actuator lumped element model, the pressure inside the cavity cP is equal to the pressure drop across the orifice (see discussion on the pressure field in Chapter 5). Also, the radiation impedance of the orifice is modeled as a circ ular (rectangular) piston in an infinite baffle for an axisymmetric (rectangular) orifice, and only the mass contribution is taken into account, since at low wavenumbers, kd, the radiation resistance term is almost negligible (Blackstock 2000, p. 459). The goal here is to find an analytical expression fo r the acoustic grazing boundary layer impedance aBL Z that will capture the main c ontributions of the grazing boundary layer, i.e. increase the resistance of the orif ice and reduce the effective mass oscillating in the orifice. From the dimensionless analysis carried out in Chapter 2 and in the previous section, a large parameter space has been revealed that should be sampled. Based on the acoustic liner literature revi ewed in Chapter 1 and Appendix A, the so-called NASA Langley ZKTL (Betts 2000) is first implemented in the application of a

PAGE 254

227 ZNMF device to extract a simple analytical expression. Specifically, the impedance model is derived from the boundary conditions used in the ZKTL impedance model (see Eqs. A-12 and A-13), which finds its origin s in the work done by Hersh and Walker (1979), Heidelberg et al. (1980) for the resist ance part, and by Rice (1971) and Motsinger and Kraft (1991) for the reactance part of the impedance. With sli ght modifications and rearrangements discussed below, the model is extended to the present problem to yield the following impedance model in the acoustic domain 021.256aBL nc M R S d (7-19) for the acoustic resistance part and 0 310.85 1305aBL nDc kd X SCM (7-20) to characterize the acoustic reactance of the grazing impedance. The quantity 0 ncS corresponds to the characteristic acoustic im pedance of the medium and is used for normalization to express the results in the acoustic domain, D C is the orifice discharge coefficient that has been previously introduced, and 00.96nhS is an orifice end correction (see Appendix B for de tails). Notice that the original expressions, Eqs. A-12 and A-13, are functions of th e porosity factor. However, the resistance part was originally derived from fi rst principles for a single orifice (Hersh and Walker 1979) and then extended to an array of independent orifices (hence perforated plate) via the simple relation 0, single orifice 0, perforateZ Z (7-21) where the porosity is defined by

PAGE 255

228 holeshole area total area N (7-22) and holesN is the number of holes in the perforate. Eq. 7-21 is applicable when assuming that the orifices are not too close to each ot her in order to allevi ate any interactions between them. Ingard (1953) st ates that the resonators can be treated independently of each other if the distance betw een the orifices is greater than half of the acoustic wavelength. This statement can be related to the discussion in Chapter 4 on the influence of the dimensionless stroke length. The poros ity factor in the resi stance expression of Eq. A-12 can then be disregarded to yield Eq 7-19. Similarly, the end correction 0.8510.7 d in the reactance expression fr om Eq. A-13 is found from Ingard (1953) when perforate plates are used and s hould be compared with the single orifice end correction 0.85 d for a circular orifice (see Appendi ces A and B). Thus, the acoustic reactance due to the grazing flow eff ect takes the form of Eq. 7-20. It is worthwhile to note that the boundary layer mode l in its present form is primarily a function of the grazing flow Mach number M the ratio between the orifice diameter and the acoustic wavelength 2 kdd and the ratio of the boundary layer thickness to the orifice diameter d the latter mainly limiting the resistance contribution. Also, the orifice effect is represented by the discharge coefficient D C in the reactance expression. Furthermore, it is sometimes useful to denote the specific reactance in terms of the effective length 0h such that 00 X h (7-23)

PAGE 256

229 From Eq. 7-20 and Eq. 7-23, it can be seen that when the specific reactance is normalized by the orifice area, it yields the reactance expression in the acoustic domain. The effect of the grazing boundary layer tends to decrease the no crossflow orifice effective length 00.96nhS (see Appendix B for a complete definition of 0h ) by the quantity 31305DCM which is a function of the orif ice shape, flow parameters, and freestream Mach number. Before directly implementing this grazi ng boundary layer impedance into the full lumped element model of a ZNMF actuato r and observing its effect on the device behavior, the model is compared to previous data for flow past Helmholtz resonators in order to validate it. Boundary layer impedance implemen tation in Helmholtz resonators In Appendix A, five different models of grazing flow past Helmholtz resonators are presented in detail, and Table A-1 summar izes the operating conditions. A large variation in operating conditions for a range of applications is considered. However, in the process of gathering suitable data to compare the impedance model presented above, two main difficulties appeared: First, proper documentation of the experimental setup and operating conditions (especially the grazing BL) is often de ficient. Therefore, some available experimental databases were not used because one or more variable definitions were lacking. Second, since practical applications of ac oustic liners often deal with a thin face sheet perforate, the orifice ratio hd is usually much less than unity. As seen from the results of modeling of a ZNMF actuato r in a quiescent medium, this can yield complex orifice flow patterns and thus represents a limiting case of 0 hd in the impedance model.

PAGE 257

230 Nonetheless, two datasets from two diffe rent publications were found to suit our purpose. The first database comes from th e extensive experimental study performed by Hersh and Walker (1979). Only the thick orif ice investigation is used here in order to fulfill the model assumption of 1 hd The two-microphone impedance test data is summarized herein for the five orifice resonato r configurations described in Table 7-2. The complete dataset can be found in He rsh and Walker (1979), and Figure A-2 in Appendix A gives the schematic of the test apparatus that was used. It is basically an effort divider, as shown in Figure 7-6. Table 7-2: Experimental operating c onditions from Hersh and Walker (1979). Resonator model cDmm Hmm dmm hmm hd 1 31.75 12.7 1.78 0.51 0.28 2 1.01 0.57 3 1.03 1.14 4 4.06 2.28 5 8.13 4.56 22 cdD f Hz TK PkPa d 1 0.003 552 292.04 101.93 4.8 2 530 295.93 101.83 3 414 292.04 100.07 4 333 297.04 101.93 5 255 296.48 101.93 ZaOPiQj ZaC ZaBLPceffort divider Figure 7-6: Schematic of an effort di vider diagram for a Helmholtz resonator.

PAGE 258

231 The data is presented for different values of incident pressure iP and grazing flow velocity U in terms of the total resonator area-averaged specific resistance and reactance normalized by the specifi c medium impedance, respectively 00 R c and 00 X c The resistance and reactance were computed by measuring the amplitude of the incident iP and cavity cP sound waves, and also by m easuring the phase difference between the incident sound field and the cavity sound field ic These values are substituted into Eqs. 7-24 and 7-26 given below, respectively, for the resistance and reactance SPLSPL 0 20 00sin 10 sinic icR cHc (7-24) following the effort divider depicted in Figure 7-6, 11 0 0ReRecaC nCnC iaOaBLaCRPZ ZZ cPZZZ (7-25) and SPLSPL 0 20 00cos 10 sinic icX cHc (7-26) where SPLSPL ic represents the sound pre ssure level difference (in dB) between the incident sound field and the cavity sound field, H is the cavity depth of the resonator, ncSS is an averaged area (ratio of the orif ice-to-cavity cross se ctional area), and nC Z is the area-averaged normalized acoustic cavity impedance such that 0 n nCaCS ZZ c (7-27)

PAGE 259

232 0 nSc being the characteristic impedance of the medium in the acoustic domain. For each resonator tested, the frequency was adjusted to ach ieve resonance at 70iPdB and 0 U by seeking the frequency for which the phase difference between the incident and cavity s ound pressure fields were 90o. The results presented hereafter are from the five orifice models as listed in Table 7-2. The normalized area-averaged impedance, defined by j for a single orifice, as a function of the grazing flow Mach number are plotted in Figure 7-7A to Fi gure 7-7E. Specifically, the total specific resistance 0 R of the resonator is normalized by th e characteristic impedance of the medium 0c and the cavity reactance is subtracted from the total re sonator reactance such that 0,0, 00 00000cotOtOt CXX XX H ccccc (7-28) where 0 O X is the specific orifice reactance that includes the inertia effect and the BL contribution, 0 0cotCX kH c (7-29) is the normalized specific reactance of the cavity, and 0kc is the wavenumber. Notice that Eq. 7-29 is similar to the defi nition of the acoustic cavity impedance aC Z given by Eqs. 7-11 and 7-12, since for 1 kH the Maclaurin series expansion of the cotangent function can be truncated to its first term, such that 1 33 0 0 0cot... 3C X c kH kHkH cH (7-30) and the normalized acoustic cavity impedance is given by

PAGE 260

233 0 aCnZS c 2 0c nS j 0c 000 0 C n cccX Sj jHSjHc (7-31) where cSH is the cross sectional area of the cavity. 0 0.05 0.1 0.15 0.2 0.25 0 0.02 0.04 0.06 0.08 0.1 =R0/c0model 1, h/d= 0.28 0 0.05 0.1 0.15 0.2 0.25 -20 -15 -10 -5 0 5 x 10-3 M=X0/c0 Pi=120 dB (Exp) Pi=125 dB (Exp) Pi=130 dB (Exp) Pi=135 dB (Exp) Pi=140 dB (Exp) Pi=120 dB (model) Pi=125 dB (model) Pi=130 dB (model) Pi=135 dB (model) Pi=140 dB (model) 0 0.05 0.1 0.15 0.2 0.25 0 0.02 0.04 0.06 0.08 0.1 =R0/c0model 2, h/d= 0.57 0 0.05 0.1 0.15 0.2 0.25 -0.015 -0.01 -0.005 0 0.005 0.01 M=X0/c0 Pi=120 dB (Exp) Pi=125 dB (Exp) Pi=130 dB (Exp) Pi=135 dB (Exp) Pi=140 dB (Exp) Pi=120 dB (model) Pi=125 dB (model) Pi=130 dB (model) Pi=135 dB (model) Pi=140 dB (model) Figure 7-7: Comparison between BL impeda nce model and experiments from Hersh and Walker (1979) as a function of Mach number for different SPL. The Helmholtz resonators refer to Table 7-2: A) Resonator model 1. B) Resonator model 2. C) Resonator model 3. D) Resonator model 4. E) Resonator model 5. B A

PAGE 261

234 0 0.05 0.1 0.15 0.2 0.25 0 0.02 0.04 0.06 0.08 0.1 =R0/c0model 3, h/d= 1.14 0 0.05 0.1 0.15 0.2 0.25 -20 -15 -10 -5 0 5 x 10-3 M=X0/c0 Pi=120 dB (Exp) Pi=125 dB (Exp) Pi=130 dB (Exp) Pi=135 dB (Exp) Pi=120 dB (model) Pi=125 dB (model) Pi=130 dB (model) Pi=135 dB (model) 0 0.05 0.1 0.15 0.2 0.25 0 0.02 0.04 0.06 0.08 0.1 =R0/c0model 4, h/d= 2.28 0 0.05 0.1 0.15 0.2 0.25 -10 -5 0 5 x 10-3 M=X0/c0 Pi=115 dB (Exp) Pi=120 dB (Exp) Pi=125 dB (Exp) Pi=130 dB (Exp) Pi=115 dB (model) Pi=120 dB (model) Pi=125 dB (model) Pi=130 dB (model) Figure 7-7: Continued. C D

PAGE 262

235 0 0.05 0.1 0.15 0.2 0.25 0 0.02 0.04 0.06 0.08 0.1 =R0/c0model 5, h/d= 4.56 0 0.05 0.1 0.15 0.2 0.25 -0.015 -0.01 -0.005 0 0.005 0.01 M=X0/c0 Pi=115 dB (Exp) Pi=120 dB (Exp) Pi=125 dB (Exp) Pi=130 dB (Exp) Pi=135 dB (Exp) Pi=115 dB (model) Pi=120 dB (model) Pi=125 dB (model) Pi=130 dB (model) Pi=135 dB (model) Figure 7-7: Continued. Clearly, the resistance is well captured, a lthough the experimental data suggest a nonlinear increase with the grazi ng flow Mach number. The resistance tends to not vary for very low Mach numbers but increases after a threshold in the Mach number is reached, and this is true for all models with different orifice aspect ratio hd. It also appears that the effect of the incident pressure is primarily felt for low Mach numbers and tends to saturate for higher values. With regards to the reactance, the data are consistently overp redicted by the model and start in the positive axis for the no flow condition, but th e trend of a nearly constant value with a slight decrease for higher Mach numbers is well captured. Also, the reactance model is insensitive to the incident pressure amplitude. Note that although no information was provided in Hersh and Walk er (1979) about the grazing flow boundary layer for the different Mach number tested it was assumed that the boundary layer thickness was held constant from the nominal case such that 7.62mm for all tests. E

PAGE 263

236 Another suitable experimental dataset is th at of Jing et al. ( 2001). Their set up is shown in Figure 7-8, and Table 7-3 summarizes the test conditions and device geometry. A grazing flow of Mach number varying from 0 to 0.15 was introduced through a squaresection wind tunnel of internal width 120.0 mm A boundary layer su rvey was performed using a Pitot-static tube and they show that the profile agrees with the well-known oneseventh order power law for a turbulent bound ary layer. The amplitudes of the sound pressures measured by the two microphone met hod and their phase difference were then utilized to compute the acoustic impedance of the tested sample in a similar manner as presented above. Table 7-3: Experimental operating conditions from Jing et al. (2001). dmm hmm cDmm Hmm % f Hz mm 3 2 32 150 2.94 200 30 Flow perforated plate cylindrical cavity microphones A/D computer noise source Pitot-static tube 35 mm 30 mm 150 mm Figure 7-8: Experimental se tup used in Jing et al. (2001) (Arranged from Jing et al. 2001)

PAGE 264

237 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 MZ0/c0h/d= 0.66 Re(Z0/c0) Experiment Re(Z0/c0) model Im(Z0/c0) Experiment Im(Z0/c0) model Figure 7-9: Comparison betw een model and experiments fr om Jing et al. (2001). The resonator design refers to Table 7-3. Figure 7-9 compares the present model with the experimental data from Jing et al. (2001), where the normalized impedance is pl otted as a function of the grazing flow Mach number. As in the previous exampl e, the resistance model agrees with the experimental data for low Mach numbers, whil e the overall reactance trend is captured as well (nearly constant value as the Mach numbe r increases). However, the resistance data do not follow the same trend as in the pr evious example, since no plateau in the resistance curve is observed in the low Mach number region for the data from Jing et al. (2001). It should be pointed out, however, that all these experiment al data should be regarded with some skepticism. They re ly on the two microphone impedance technique (Dean 1974) and no uncertainty estimates are provided. Also, good reactance data are more difficult to obtain than resistance data since the method principally relies on the phase difference knowledge which, for instance, can be systematically altered by

PAGE 265

238 instrumentation equipment data acquisiti on hardware and hydrodynamic effects in the cavity. Also, the data were usually acq uired when the device was operating near resonance, when the radiated sound pattern can clea rly extend to several orifice diameters away from the resonator (typically, at res onance a Helmholtz resonator scattering cross sectional area scales with the wavelength s quared), hence resulting in a different acoustic mass near the orifice exit. Proper placemen t of the microphone near the orifice is therefore of great importance in order to retrieve the correct mass due to the end correction. As generally concluded by th e acoustic liner community, more accurate calculations of the variation of the resonator resistance and reactance could only be made if more flow details in the vici nity of the orif ice are known. Nevertheless, it should be emphasized that the goal of this exercise was not to validate the grazing flow impedance model via available experimental data, since at the present time no one has been able to accomplis h this goal. The validation of low-order models for flow past Helmholtz resonators is not the focus of this research. However, the above discussion improves our understanding of the BL impedance model in its present form and gives us some confidence in its use, while keeping in mind its limitations and shortcomings. Boundary layer impedance implementation in ZNMF actuator In order to fully appreciate the effect of the key parameters present in the BL impedance model, such as the Mach number M the boundary layer th ickness to orifice length ratio d or kd, on the frequency response of a ZNMF actuator, the synthetic jet design used in the NASA Langley workshop (C FDVal 2004) and denoted as Case 1 is modeled and employed. In a similar way, the actuator designed by Gallas et al. (2003a)

PAGE 266

239 and referred therein as Case 1 is also used, since the two resonant peaks that characterize their dynamic behavior are reversed. In pa rticular, in Case 1 (CFDVal 2004) the first peak is due to the natural fr equency of the diaphragm while the second one is governed by the Helmholtz frequency of th e resonator, while the opposite is true in Case 1 from Gallas et al. (2003a). The first peak is di ctated by the Helmholtz frequency while the second peak corresponds to the piezoelectric-dia phragm natural frequency. The reader is referred to the discussion in Chapter 5 on the cavity compressibility effect, where a similar comparison between these two cases has already been performe d; this discussion gives a clear definition of the different gove rning frequencies of the system and their respective effects. 0 500 1000 1500 2000 2500 3000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Frequency [Hz]VCL(LEM) / VCL(exp) M = 0 M = 0.05 M = 0.1 M = 0.2 M = 0.3 d = 1.27 mmBL = 10 mmM Figure 7-10: Effect of the freestream M ach number on the frequency response of the ZNMF design from Case 1 (CFDVal 2004) using the refined LEM. The centerline velocity is normalized by th e experimental data at the actuation frequency.

PAGE 267

240 0 500 1000 1500 2000 2500 3000 0 5 10 15 20 25 30 35 40 45 50 Frequency [Hz]Centerline Velocity [m/s] M = 0 M = 0.05 M = 0.1 M = 0.2 M = 0.3 d = 1.65 mmBL = 10 mmM Figure 7-11: Effect of the freestream M ach number on the frequency response of the ZNMF design from Case 1 (Gallas et al. 2003a). Figure 7-10 shows the effect of va rying the freestream Mach number M on the centerline velocity of the act uator versus frequency for the Case 1 (CFDVal 2004) design, while Figure 7-11 is for the Case 1 (Gallas et al. 2003a) design. The incoming grazing flow is assumed to be characterized by a boundary layer 10 mm and a freestream Mach number ranging from 0 to 0.3. Clearly, the effect of the freestream Mach number is principally experienced at the Helmholtz frequency peak, while a global decrea se in magnitude is still seen over the entire frequency range due to the increase in the total orifice resistance. Recalling the definition of the Helmholtz frequency, Eqs. B-1 and B-2, the shift in frequency of the peak is explained by the modification of th e acoustic mass by the boundary layer or, more specifically, by the decrease of the effective orifice length 0h Since aBLM and aO M are weak functions of the grazi ng flow parameters (only M ), the Helmholtz frequency that strongly depends of the acoustic masses in th e system will therefore be only slightly

PAGE 268

241 affected by the external BL. Hence, the cav ity compressibility criterion described in Chapter 5 should not be greatly affected and can be generalized to a ZNMF actuator with an external boundary layer. Also, letting the ratio d vary will affect the overall magnitude of the device response since it is present in the acoustic BL resistance expression, although it will not affect the location of the frequency peaks since the acoustic BL mass expression does not contain the ratio d Velocity Profile Scaling Laws Despite the power of LEM that resides in its simplicity and reasonable estimate (typically within 20% ) achieved with minimal effort, it unfortunately does not provide any information on the profile or shape of th e jet exit velocity which is also strongly phase dependant as seen in Chapter 4. In this regard, a low-dimensional model or description of the jet velocity shape is need ed, i.e. a parameterization of the profile in terms of the key parameters that capture th e important dynamic and ki nematic features of the orifice flow, as well as scaling laws that relate these parameters to the other flow variables. In the first secti on of this chapter, it is proposed that the successive moments and skewness of the jet velocity profile can be useful in characterizing ZNMF actuators. However, dimensional analysis revealed a large parameter space (see Eq. 7-8). To be applicable, some restrictions need to be em ployed since a candidate jet profile should be low dimensional and also capable of reasona bly matching the observed and measured jet profile characteristics. Therefore, as a firs t step, a Blasius boundary layer is assumed to characterize the incoming grazing flow that reduces the parameter space to 12 123,,,,,,Re,n HdC hw fnS dddd X (7-32)

PAGE 269

242 Two approaches are described next that yi eld two different scaling laws of a ZNMF actuator issuing into a grazing boundary layer. One focuses on fitting the velocity profile vxt at the actuator exit, while the othe r one employs a model based on the local integral parameters of the actuator, such as the successive moments 12nC and skewness 12 X as shown in Figure 7-12. Table 7-4: Tests cases from numerical si mulations used in the development of the velocity profiles scaling laws Case hd d S Rej Re jVU Wd Hd 0Wd I 1 0.266 20 188 133 0.375 3 1.5 0.393 II 1 0.266 20 281 133 0.563 3 1.5 0.393 III 1 0.266 20 375 133 0.75 3 1.5 0.393 IV 1 0.133 20 188 133 0.188 3 1.5 0.393 V 1 0.399 20 62 133 0.188 3 1.5 0.393 VI 1 0.532 20 47 133 0.188 3 1.5 0.393 VII 1 0.266 20 24 33 0.188 3 1.5 0.393 VIII 1 0.266 20 47 66 0.188 3 1.5 0.393 IX 1 0.266 20 188 266 0.188 3 1.5 0.393 X 1 0.266 5 94 133 0.188 3 1.5 0.393 XI 1 0.266 10 94 133 0.188 3 1.5 0.393 XII* 1 0.266 20 94 133 0.188 4 1.5 0.393 XIII 1 0.266 50 94 133 0.188 3 1.5 0.393 Nominal / Test case To develop these scaling laws, numerical simulations from the George Washington University, courtesy of Prof. Mittal, are again used in a joint effort. The 2D numerical simulations described in Appendix F are employe d to construct the test matrix given in Table 7-4. It consists of 13 cases, all based on a nominal flow condition (Case XII), 4 flow parameters being systematically varied around the nominal case. In Cases I to III, the ratio jVU is varied from about 0.2 to 0. 75. Case IV to Case VI vary d whereas

PAGE 270

243 in Cases VII to IX the jet Reynolds number is varied. Finally the St okes number is varied in Cases X to XIII. The velocity profile scaling laws are next detailed. For both approaches, the idea is to first assume a candidate jet velocity profile and, based on the test matrix comprised of CFD simulation results (summarized in Table 74), the candidate jet velocity profile is refined, and a regression analysis is then pe rformed to yield a scaling law that predicts either the velocity profile or the integr al parameters as a function of the main dimensionless numbers. The candidate prof ile is adapted from Rampuggoon (2001) who performed a similar study on modeling the velo city profile of ZNMF actuator exhausting in an external crossflow (his motivation was to try to match the integral parameters of his test cases). He assumed a candida te velocity profile of the form ,sinj x tTxt V, (7-33) where 2 x xd is the normalized spatial coordinate across the orifice. However, his chosen profile Tx was just a parabolic-t ype profile of steady cha nnel flow. Here, this work is extended to a more gene ral approach, where the choice of Tx is motivated by the results of the investigation outlined in Chapter 4 on the 2D slot flow physics of a ZNMF actuator in a quiescent medium. It takes the form cosh2 1 cosh2 x Sj Tx Sj (7-34) which satisfies the no-slip condition at the orifice walls and is already Stokes-number dependant in accordance with pressure-driven oscillatory flow in a channel (White 1991). Each scaling law is now detailed.

PAGE 271

244 ,sin xtTxtTx V Figure 7-12: Schematic of the two approaches used to develop the scaling laws from the jet exit velocity profile. Scaling law based on the jet exit velocity profile This approach focuses on the shape of the velocity profile at the actuator orifice exit, as a function of the phase angle. The methodology to develop a scaling law is summarized in Figure 7-13 and is comprised of 5 steps. In the first step, a candidate velocity prof ile is chosen, as detailed above. Next, since the velocity profile is sinusoidal in nature, it can be simply decomposed by a dc component equivalent to an average pl us a magnitude and phase angle components, such that arg,sindecompdcmag x txxtx VVVV. (7-35) Then, based on the candidate jet velocity profile Txt, the local average (dc), magnitude, and phase angle are extracted fr om the CFD results, and a nonlinear leastsquares curve fit is performed to yield a corrected candidate velocity profile, mod, Txt for each component. Jet exit scaling laws based on Match the velocity profile x t V Match the integral parameters 3,,,,vCXC

PAGE 272

245 cosh2 1 cosh2 x Sj Tx Sj arg,sindecompdcmagxtt VVVV argfind ,, such that find such that find ,, such that sincx mag hx dcabcTabe deTdxe ghiigxe V V V modmod,mod,mod,argsindcmagTTtT V mod, cx magTTabe mod,argTTdxe mod,sinhx dcTigxe 4 1230 000 0,, Re ,, Re ,,b bbb j jabc VU hdd dea hdd VU ghi Figure 7-13: Methodology for the development of the velocity profile based scaling law. Candidate velocity profile Decompose CFD velocity profile Fit low-order models for each components via nonlinear least square curve fits Nonlinear regression analysis to obtain an empirical scaling law of the form:

PAGE 273

246 The results are shown in Figure 7-14, Fi gure 7-15, Figure 7-16, Figure 7-17, Figure 7-18, Figure 7-19, and Figure 7-20 for Case I, Ca se III, Case V, Case VII, Case IX, Case XI, and Case XIII, respectively; Table 7-5 su mmarizes the value that all 8 coefficients take for each test case. For each figure, th e comparison between the candidate velocity profile Txt, decomposed into its magnitude T and argument T, is compared with the equivalent model (mod, magT and mod,argT respectively) and the CFD data. The choice of the three models, namely mod, mod,arg mod,sincx mag hx dcTTabe TTdxe Tigxe (7-36) is motivated so that it yields the best fit for all cases studied. For instance, the ratio of the amplitudes, magT V, has usually large gradients near the edge of the orifice but remains quite flat in the center. Similarly, it is found that the phase difference argT V varies linearly over the slot depth. Finally, notice that the dc value of the decomposed velocity profile, which can be thou ght of as the velocity average across the orifice, is usually an order of magnitude less than the amplitude value and has a sinusoidal-type shape. Although not perfect, the modeled profiles ar e in agreement with the CFD data.

PAGE 274

247 -1 -0.5 0 0.5 1 -0.1 -0.05 0 0.05 0.1 0.15 x/(d/2)averagemodel = i.sin(gx).ehx CFD Tmod Figure 7-14: Nonlinear least s quare curve fit on the decompos ed jet velocity profile for Case I. A) Amplitude. B) Phase angle. C) dc components. The blue curves are for the components of the candidate profile Txt; the green curves are for the components of the modeled profile mod, Txt; the red curves are the CFD results. -1 -0.5 0 0.5 1 0.5 1 1.5 2 x/(d/2)amplitude ratiomodel = a + becx -1 -0.5 0 0.5 1 0 0.5 1 1.5 amplitude T Tmod CFD -1 -0.5 0 0.5 1 -50 0 50 x/(d/2)phase diff (deg)model = dx+e -1 -0.5 0 0.5 1 -50 0 50 100 p h ase (d eg ) T Tmod CFD Re188 Re133 20 S C A B

PAGE 275

248 -1 -0.5 0 0.5 1 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 x/(d/2)averagemodel = i.sin(gx).ehx CFD Tmod Figure 7-15: Nonlinear least s quare curve fit on the decompos ed jet velocity profile for Case III. A) Amplitude. B) Phas e angle. C) dc components. The blue curves are for the components of the candidate profile Txt; the green curves are for the components of the modeled profile mod, Txt; the red curves are the CFD results. -1 -0.5 0 0.5 1 0.5 1 1.5 2 x/(d/2)amplitude ratiomodel = a + becx -1 -0.5 0 0.5 1 0 0.5 1 1.5 amplitude T Tmod CFD -1 -0.5 0 0.5 1 -50 0 50 x/(d/2)phase diff (deg)model = dx+e -1 -0.5 0 0.5 1 -50 0 50 100 p h ase (d eg ) T Tmod CFD Re375 Re133 20 S C A B

PAGE 276

249 -1 -0.5 0 0.5 1 -0.1 -0.05 0 0.05 0.1 0.15 x/(d/2)averagemodel = i.sin(gx).ehx CFD Tmod Figure 7-16: Nonlinear least s quare curve fit on the decompos ed jet velocity profile for Case V. A) Amplitude. B) Phase angle. C) dc components. The blue curves are for the components of the candidate profile Txt; the green curves are for the components of the modeled profile mod, Txt; the red curves are the CFD results. -1 -0.5 0 0.5 1 0.5 1 1.5 2 x/(d/2)amplitude ratiomodel = a + becx -1 -0.5 0 0.5 1 0 0.5 1 1.5 amplitude T Tmod CFD -1 -0.5 0 0.5 1 -40 -20 0 20 x/(d/2)phase diff (deg)model = dx+e -1 -0.5 0 0.5 1 -50 0 50 phase (deg) T Tmod CFD Re62 Re133 20 S C A B

PAGE 277

250 -1 -0.5 0 0.5 1 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 x/(d/2)averagemodel = i.sin(gx).ehx CFD Tmod Figure 7-17: Nonlinear least s quare curve fit on the decompos ed jet velocity profile for Case VII. A) Amplitude. B) Phase angle. C) dc components. The blue curves are for the component s of the candidate profile Txt; the green curves are for the component s of the modeled profile mod, Txt; the red curves are the CFD results. -1 -0.5 0 0.5 1 0.5 1 1.5 2 x/(d/2)amplitude ratiomodel = a + becx -1 -0.5 0 0.5 1 0 0.5 1 1.5 amplitude T Tmod CFD -1 -0.5 0 0.5 1 -20 -10 0 10 x/(d/2)phase diff (deg)model = dx+e -1 -0.5 0 0.5 1 -50 0 50 phase (deg) T Tmod CFD C Re24 Re33 20 S A B

PAGE 278

251 -1 -0.5 0 0.5 1 -0.1 -0.05 0 0.05 0.1 0.15 x/(d/2)averagemodel = i.sin(gx).ehx CFD Tmod Figure 7-18: Nonlinear least s quare curve fit on the decompos ed jet velocity profile for Case IX. A) Amplitude. B) Phase angle. C) dc components. The blue curves are for the components of the candidate profile Txt; the green curves are for the components of the modeled profile mod, Txt; the red curves are the CFD results. -1 -0.5 0 0.5 1 0 1 2 3 x/(d/2)amplitude ratiomodel = a + becx -1 -0.5 0 0.5 1 0 1 2 amplitude T Tmod CFD -1 -0.5 0 0.5 1 -100 -50 0 50 x/(d/2)phase diff (deg)model = dx+e -1 -0.5 0 0.5 1 -50 0 50 100 phase (deg) T Tmod CFD Re188 Re266 20 S C B A

PAGE 279

252 -1 -0.5 0 0.5 1 -0.1 -0.05 0 0.05 0.1 x/(d/2)averagemodel = i.sin(gx).ehx CFD Tmod Figure 7-19: Nonlinear least s quare curve fit on the decompos ed jet velocity profile for Case XI. A) Amplitude. B) Phase angle. C) dc components. The blue curves are for the components of the candidate profile Txt; the green curves are for the components of the modeled profile mod, Txt; the red curves are the CFD results. -1 -0.5 0 0.5 1 0 2 4 6 x/(d/2)amplitude ratiomodel = a + becx -1 -0.5 0 0.5 1 0 1 2 amplitude T Tmod CFD -1 -0.5 0 0.5 1 -100 -50 0 50 x/(d/2)phase diff (deg)model = dx+e -1 -0.5 0 0.5 1 -50 0 50 100 phase (deg) T Tmod CFD C Re94 Re133 10 S A B

PAGE 280

253 -1 -0.5 0 0.5 1 -0.6 -0.4 -0.2 0 0.2 0.4 x/(d/2)averagemodel = i.sin(gx).ehx CFD Tmod Figure 7-20: Nonlinear least s quare curve fit on the decompos ed jet velocity profile for Case XIII. A) Amplitude. B) Phase angle. C) dc components. The blue curves are for the component s of the candidate profile Txt; the green curves are for the component s of the modeled profile mod, Txt; the red curves are the CFD results. -1 -0.5 0 0.5 1 0.5 1 1.5 2 x/(d/2)amplitude ratiomodel = a + becx -1 -0.5 0 0.5 1 0 0.5 1 1.5 amplitude T Tmod CFD -1 -0.5 0 0.5 1 -20 -10 0 10 x/(d/2)phase diff (deg)model = dx+e -1 -0.5 0 0.5 1 -20 0 20 40 phase (deg) T Tmod CFD C Re94 Re133 50 S A B

PAGE 281

254 Table 7-5: Coefficients of the nonlinear least square fits on the decomposed jet velocity profile Case a b c d e g h i I 2.46 -1.45 0.11 -27.57 -5.18 -3.15 7.29 -5.10-5 II 2.71 -1.66 0.13 -25.97 -11.82 -1.29 -1.28 -0.05 III 0.56 0.34 1.09 -28.13 -10.44 -2.82 -0.37 -0.08 IV 0.38 1.33 0.52 -59.83 6.71 -3.12 0.22 0.11 V 0.91 0.002 6.48 -12.91 -6.49 -0.43 0.49 -0.15 VI 0.90 0.003 5.67 -6.70 -6.42 4.89 1.39 -0.02 VII 0.89 0.003 5.69 -6.82 -7.08 -12.56 5.18 5.10-5 VIII 0.90 0.002 6.01 -13.02 -5.63 -3.12 10.78 -2.10-5 IX 0.81 0.01 5.40 -43.95 -5.03 -3.49 -0.40 0.084 X 0.68 0.01 6.80 -13.06 -23.61 -1.61 -0.16 -0.05 XI 0.70 0.02 5.81 -41.91 -3.32 -0.61 -0.311 -0.09 XII 0.93 0.002 6.09 -33.17 -5.69 -0.32 1.34 -0.18 XIII 0.85 0.006 4.82 -0.07 -8.69 -2.65 0.89 0.24 Next, the 4th step shown in Figure 7-13 consists of recombining each component of the modeled profile developed above, such th at the final modeled ve locity profile takes the form modmod,mod,mod,arg,sindcmag x tTxTxtTx V (7-37) and is a function of the 8 parameters ,,,,,,, abcdeghi. Notice that Eq. 7-37 is time and spatial dependant and that it n eeds at least these 8 parameters to represent it. Figure 7-21 compares the velocity profiles at the orifice exit from the CFD results, the decomposition of the velocity decompV defined in Eq. 7-35, and the modeled velocity profile modV defined by Eq. 7-37. First of all, it can be seen that the velocity profile decomposition in terms of a dc term plus a sinusoidal time variation is a good approximation of the velocity profile at the orifice exit from the CFD results for all cases studied. Similarly, following the discussion above, the overall modeled profiles tend to be in agre ement with the CFD data, and again at each instant in time dur ing a cycle (although only four phase angles have been shown in Figure 7-21 for clarity). Clearly, the ch oice of the candidate velocity

PAGE 282

255 profile that is Stokes number dependent is able to capt ure the Richardson effect (overshoot near the orifice edge) that is present in all cases. Notice also how different can the velocity profiles be among the test cas es considered, and still this 8-parameters candidate velocity profile model is capable of representing a large variety of velocity profiles, some being completely skewed, othe rs nearly symmetric. Thus, based on this finding, the nest step in deve loping a scaling law can be take n and is described next. Figure 7-21: Comparison between CFD velocity profile, decomposed jet velocity profile, and modeled velocity profile, at the orif ice exit, for four phase angles during a cycle. A) Case I. B) Case II. C) Case III. D) Case IV. E) Case V. F) Case VI. G) Case VII. H) Case VIII. I) Case IX. J) Case X. K) Case XI. L) Case XIII. The velocity in the ve rtical abscise is normalized by U. -1 -0.5 0 0.5 1 -1.5 -1 -0.5 0 0.5 1 1.5 2x/d CFD Vdecomp Vmod = 0 = 92 = 229 = 266 -1 -0.5 0 0.5 1 -1.5 -1 -0.5 0 0.5 1 1.5 2x/d CFD Vdecomp Vmod = 0 = 92 = 229 = 266A B

PAGE 283

256 Figure 7-21: Continued. -1 -0.5 0 0.5 1 -1.5 -1 -0.5 0 0.5 1 1.5 2x/d CFD Vdecomp Vmod = 0 = 92 = 229 = 266 -1 -0.5 0 0.5 1 -1.5 -1 -0.5 0 0.5 1 1.5 2x/d CFD Vdecomp Vmod = 0 = 92 = 229 = 266G H -1 -0.5 0 0.5 1 -1.5 -1 -0.5 0 0.5 1 1.5 2x/d CFD Vdecomp Vmod = 0 = 92 = 229 = 266 -1 -0.5 0 0.5 1 -1.5 -1 -0.5 0 0.5 1 1.5 2x/d CFD Vdecomp Vmod = 0 = 92 = 229 = 266E F -1 -0.5 0 0.5 1 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2x/d CFD Vdecomp Vmod = 0 = 92 = 229 = 266 -1 -0.5 0 0.5 1 -1.5 -1 -0.5 0 0.5 1 1.5 2x/d CFD Vdecomp Vmod = 0 = 92 = 229 = 266C D

PAGE 284

257 Figure 7-21: Continued. As shown in Figure 7-13, the next logical step is to extract a scaling law relating the computed values of the parameters ,,,,,,, abcdeghi to the dimensionless flow parameters. Because the relationship among the involved parameters and the target values, i.e. the family set ,,,,,,, abcdeghi, is nonlinear as can be seen by inspection, a nonlinear regression technique is sought for deriving an empiri cal scaling law, which can be implemented in any available commercial st atistical calculation software such as SPSS -1 -0.5 0 0.5 1 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2x/d CFD Vdecomp Vmod = 0 = 92 = 229 = 266 -1 -0.5 0 0.5 1 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2x/d CFD Vdecomp Vmod = 0 = 92 = 229 = 266K L -1 -0.5 0 0.5 1 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2x/d CFD Vdecomp Vmod = 0 = 92 = 229 = 266 -1 -0.5 0 0.5 1 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2x/d CFD Vdecomp Vmod = 0 = 92 = 229 = 266I J

PAGE 285

258 (Statistical Analysis System). Taking into account the effect of the most important parameters, such as the orifice aspect ratio hd, the Stokes number S (already present in the functional form of the velocity profile), the BL momentum thickness to orifice diameter d the BL Reynolds number Re and the nominal jet-to-freestream velocity ratio jVU, an empirical scaling law for the 8 co efficients of the modeled velocity profile in Eq. 7-37 can be obtained by the regr ession analysis. The chosen target function takes the general form 4 1230 000 0,, Re ,, Re ,,b bbb j jabc VU hdd dea hdd VU ghi (7-38) where 0a and ib are the regression coefficients (with 1,2,3,4 i ). Here, 0a is the respective nominal value of a b c d e g h or i while the b s are the exponent of each nondimensional term. These regression coefficients are determined by the nonlinear regression analysis with the data provided in Table 7-5, i.e. for 12 cases since the test case (Case XII) is left out of this regression analysis for verification purposes. Th e results are gi ven in Table 7-6 where R2 is the correlation coefficient. Before commenting on these results, it should be pointed out that this problem is clearly ove r-parameterized, i.e., the family set contains 8 parameters for only 12 numerical cases to do the regression analysis. Therefore, the next steps are explained only for illustration purposes.

PAGE 286

259 Table 7-6: Results from the nonlinear regression analysis for the velocity profile based scaling law R2 a0b1b2b3 b4 a 0.225 0.9031.00.276-0.0182 0.490 b 0.102 -0.1231.01.0280.300 1.161 c 0.786 4.9831.00.533-0.0969 -4.402 d 0.730 -20.701.0-1.5261.046 0.238 e 0.122 -6.1821.00.668-0.085 0.405 g 0.163 0.0101.0-3.5023.078 -11.02 h 0.303 8 x10-101.032.43-0.0375 -0.576 i 0.267 1.7721.00.087-1.008 -0.329 First of all, notice the sm all correlation coefficients R2 for all parameters but c and d far from unity, indicative of the poor conf idence level in the co rresponding regression coefficients. Clearly, such low correlation co efficients indicate a sub-optimal regression form. One way to increase the R2 values is to increase the test matrix, by more covering the parametric space used here. Keeping in mind the poor level of confidence in these parameters, it is still worthwhile to examine the relative values of the coefficients a0 and bi, a0 being representative of th e importance of the parameter a to i It can be seen from the parameter a that the dc part of the profile (parameters g h and i ) does not have a significant influence on the ove rall profile, compared with d and e from the phase angle or a b and c from the magnitude. Next, the constant value for the coefficient b1 is due to the fact that the ratio hd has not been varied in the test cases used in this analysis, as shown in Table 7-4. Finally, at this stage it is quite difficult to draw firm conclusions concerning the other coefficients b2, b3, and b4, with such low associated R2 values. Nonetheless, for verification purposes the test case (Case XII) is used to evaluate the velocity profile based scaling law. Th e results are shown in Figure 7-22 where the numerical data are plotted along with the s caling law of the veloc ity profile obtained by

PAGE 287

260 applying the results in Table 7-6 into the mode led profile defined in Eq. 7-37. Only four phase angles 0;;54;32 are plotted for clarity. Cl early, the proposed scaling law fails to accurately predict th e actual velocity profile. Although the velocity is in agreement near the upstream edge of the orif ice, it is clearly ove r-predicted near the downstream orifice edge. This should mainly come from the functional form chosen for the magnitude term mod, cx magTTabe which has really poor associated regression coefficients R2. Recall however that this all an alysis has been performed on only 12 cases, which is a modest but valu able start in view of the results presented in this section. It is clearly not enough if one considers the wide parameter space to span and the strongly coupled interactions between each dimensionless parameter. -1 -0.5 0 0.5 1 -8 -6 -4 -2 0 2 4 6 8 2x/dvelocity (vj/U) CFD scaling law = 0 = 92 = 229 = 266 Figure 7-22: Test case comparison between CFD data and the scaling law based on the velocity profile at four phase angles during a cycle. Case XII: S = 20, Re = 94, 0.26 d Re133

PAGE 288

261 Scaling law based on the jet exit integral parameters The first scaling law previously presented is using the spatial velocity profile at the orifice exit, but disregards the integral parameters (momentum coefficient, skewness, vorticity flux,). Another approach presente d next is to base the scaling law on these integral parameters, regardless of the actua l velocity profile. The methodology of this approach is outlined in Figure 7-23. First, a candidate velocity profile is chosen, in a similar fashion as already explained above. Because of the zero-net mass flux nature of the device, the dc or average component of the velocity should be identically zero in a time average sense. Hence, the candidate profile is refined such that the new low-order model for the velocity profile takes the form modarg,sinmag x txtx VVV, (7-39) where the magnitude and argument of the velocity are defined by 2 arg mag x axbxcTx xbxcTx V V (7-40) Notice that mod, x t V is a low-parameterized model since it is only function of 3 parameters: a b and c Again, this functional form is motivated by the results of the investigation outlined in Chapter 4 on the 2D slot flow physics of a ZNMF actuator in a quiescent medium. But since only the integral parameters are of interest in here, the shape of the velocity profile is not consider ed as crucial and thus does not have a more complex functional form as seen in the previous scaling law.

PAGE 289

262 cosh2 1 cosh2 x Sj Tx Sj 2 arg magaxbxcTx bxcTx V V modargsinmagt VVV 23 ,/ ,////,,,,jexin exinexinexinexinCXC V 1,,mod,,mod,, 22 2,/,mod,/ 3/,mod/ 4/,mod/ 33 5/,mod/0 0 0 0 0jexjinjexjin exinexin exinexin exinexin exinexinf fCC fXX f fCC VVVV 4 1230 000 0Re ,, Reb bbb j jVU hdd abca hdd VU Figure 7-23: Methodology for the development of the integral parameters based scaling law. Nonlinear regression analysis to obtain an empirical scaling law of the form: Candidate velocity profile Compute integral parameters from CFD simulations find { a b c } such that

PAGE 290

263 The requirements of this model profile are: 1. zero-net mass flux (identically satisf ied by the assumed functional form) 2. match momentum coefficient 21 2 0111 22 x Cxdd dd V (7-41) 3. match skewness coefficient 21 001 ,, 22 x X xxdd d VV (7-42) 4. match vorticity flux 212 2 0101 ,,0, 22vdx vxvxddvd dxd (7-43) 5. match jet kinetic energy flux 21 3 3 0111 22 x Cxdd dd V (7-44) Recall that ,, x vxU V is the normalized velocity and that Eqs. 7-41, 7-42, 7-43, and 7-44 are derived for a 2D slot orifice geometry. Also, the vorticity flux should be nondimensionalized wi th, for instance, the quantity jVd As outlined in Figure 7-23, the procedure is thus to compute these integral parameters from the CFD data of the test cases tabulated in Table 7-4, and then to solve for the coefficients a b and c from the modeled velocity profile (Eq. 7-39) to match them. This yields a system of 5 equations a nd 3 unknowns to solve, that can be written as

PAGE 291

264 1,,mod,,mod,, 22 2,/,mod,/ 3/,mod/ 4,/,mod,/ 33 5/,mod/0 0 find ,, such that0 0 0jexjinjexjin exinexin exinexin vexinvexin exinexinf fCC abcfXX f fCC VVVV (7-45) Eq. 7-45 is clearly an over-determined system, with more equations than unknowns. Recall also that the suffix ex and in stand for expulsi on and ingestion. So one can actually compute the equations f2, f3, f4, or f5 for either the expulsion part or the ingestion part of the cycle, which can add the number of equations up to 9. Therefore, some choices have to be made to reduce the number of equations in Eq. 7-45 First of all, f1 can be removed since it insures the zero-net mass flux criterion, which is automatically satisfied by the assumed func tional form (Eqs. 7-39 and 7-40). Then, the momentum flux can be recast to account for both the expulsion and ingestion parts, and only the expulsion parts of the skewness coefficient and normalized vorticity flux are retained. The new nonlinear system to be solved can then be written as 2222 1,,mod,,mod,, 2,mod 3,,mod,0 find ,, such that0 0exinexin exex vexjvexjfCCCC abcfXX fVdVd (7-46) These 3 coefficients are numerically obt ained via the Matlab function FSOLVE. The results are summarized in Table 7-7 showing the results for the 3 parameters a b and c along with the corresponding equations f1, f2, and f3 from Eq. 7-46. Also, Table 7-8 shows the resulting integral parameters computed from the CFD data and the loworder model. Clearly, the candidate velocity profile is able to accurately predict the integral parameters when compared with the CFD data for the expulsion and ingestion

PAGE 292

265 parts of the cycle. It should be noted that even by choosing different functions in the nonlinear system of equations in Eq 7-46 for instance by choosing the jet kinetic energy flux, or skewness coefficient a nd vorticity flux during the inges tion part of the cycle the results presented in Table 7-7 and Table 7-8 do not notably vary. Then, based on these computed parameters a b and c the next step in constr ucting a scaling law for the velocity profiles can be pursued. Table 7-7: Results for the parameters a b and c from the nonlinear system Case a b c f1 f2 f3 I -1.111 0.0650.5083.06 x10-121.84 x10-15 -5.13 x10-12 II -1.748 0.1790.7773.17 x10-11-7.81 x10-15 1.72 x10-11III -2.701 0.3671.0521.06 x10-81.01 x10-10 -2.75 x10-9IV -0.758 0.0640.2427.71 x10-145.93 x10-16 6.59 x10-12V -0.649 0.0340.2241.57 x10-103.95 x10-13 1.80 x10-10VI -0.647 0.0240.2211.01 x10-102.04 x10-13 2.12 x10-9VII -0.646 0.0190.2227.05 x10-111.34 x10-13 1.45 x10-9VIII -0.645 0.0300.2238.31 x10-82.28 x10-10 -6.09 x10-10IX -0.709 0.0390.2409.04 x10-123.26 x10-14 1.56 x10-10X -1.002 0.2120.2431.29 x10-71.39 x10-9 -2.41 x10-8XI -0.849 0.1330.2337.91 x10-96.49 x10-11 1.15 x10-8XII* -0.673 0.0370.2363.74 x10-101.01 x10-12 3.76 x10-10XIII -0.614 -0.0690.2094.58 x10-113.25 x10-14 7.97 x10-10 Test case Noting that a b and c are themselves functions of the dimensionless flow parameters defined in Eq. 7-32, the next logi cal step is to extract a scaling law relating the computed values of the parameters ,, abc to the flow parameters. As already mentioned in the previous section, since th e relationship among the involved parameters and the target values, i.e. the family set ,, abc, is nonlinear, a nonlinear regression technique is sought for derivi ng an empirical scaling law, which can be implemented in

PAGE 293

266 any available commercial statistical calcula tion software such as SPSS (Statistical Analysis System). Table 7-8: Integral parameters results C ,modC X mod X Case ex in ex in ex in ex in I 0.114 0.106 0.110 0.110 0.017 -0.008 0.017 -0.017 II 0.281 0.258 0.257 0.282 0.069 -0.031 0.069 -0.076 III 0.662 0.441 0.538 0.565 0.171 -0.069 0.171 -0.179 IV 0.037 0.034 0.037 0.035 0.027 -0.061 0.027 -0.026 V 0.027 0.027 0.0267 0.027 0.010 0.004 0.010 -0.010 VI 0.025 0.026 0.025 0.026 0.004 -0.003 0.004 -0.004 VII 0.025 0.026 0.026 0.026 0.001 -0.006 0.001 -0.001 VIII 0.025 0.026 0.025 0.027 0.007 0.001 0.007 -0.008 IX 0.031 0.031 0.029 0.032 0.011 -0.038 0.011 -0.012 X 0.035 0.031 0.033 0.033 0.072 -0.056 0.072 -0.072 XI 0.035 0.030 0.033 0.033 0.055 -0.047 0.055 -0.055 XII* 0.029 0.028 0.028 0.028 0.011 0.008 0.011 -0.011 XIII 0.028 0.034 0.029 0.033 -0.051 -0.049 -0.051 0.056 vjVd ,mod vjVd 3C 3 modC Case ex in ex in ex in ex in I 0.856 1.252 0.856 0.856 0.049 -0.042 0.033 -0.033 II 1.384 1.053 1.384 1.375 0.173 -0.156 0.109 -0.122 III 2.328 1.183 2.328 2.325 0.705 -0.352 0.201 -0.212 IV 1.514 1.221 1.514 1.516 0.009 -0.009 -0.0001 0.0001 V 0.846 0.864 0.846 0.846 0.005 -0.005 0.001 -0.001 VI 0.908 0.922 0.908 0.907 0.005 -0.005 0.001 -0.001 VII 0.890 0.934 0.890 0.890 0.005 -0.005 0.001 -0.001 VIII 0.858 0.895 0.858 0.857 0.005 -0.005 0.001 -0.001 IX 1.057 1.238 1.057 1.053 0.007 -0.008 0.001 -0.001 X 1.429 1.201 1.429 1.429 0.010 -0.008 0.002 -0.002 XI 1.612 1.244 1.612 1.612 0.0010 -0.007 0.001 -0.001 XII* 0.834 1.267 0.834 0.834 0.006 -0.006 0.001 -0.001 XIII 1.771 0.337 1.770 1.764 0.006 -0.009 -0.002 0.002 Test case Taking into account the effect of the most important parame ters, such as the orifice aspect ratio hd, the Stokes number S (already present in the functional form of the velocity profile), the BL momentum thickness to orifice diameter d the BL Reynolds number Re and the jet to freestream velocity ratio jVU an empirical scaling law for

PAGE 294

267 the coefficients ,, abc of the modeled velocity profil e in Eq. 7-39 can be obtained by the nonlinear regression analysis. The chosen target function takes the general form 4 1230 000 0Re ,, Reb bbb j jVU hdd abca hdd VU (7-47) where 0a and ib are the regression coefficients (with 1,2,3,4i ). Again, 0a is the respective nominal value of a b or c while the b s are the expone nt of each nondimensional term. These regression coe fficients are determined by the nonlinear regression analysis with the data provided in Table 7-7, i.e. for 12 cases since the test case (Case XII) is left out of this regres sion analysis for verification purposes. The results are given in Table 7-9 where R2 is the correlation coefficient. Table 7-9: Results from the nonlinear regression analysis for the integral parameters based velocity profile R2 a0 b1 b2 b3 b4 a 0.945 -0.698 1.0 -0.124 0.059 0.928 b 0.625 0.042 1.0 -0.620 0.291 1.494 c 0.999 0.232 1.0 -0.068 0.041 1.093 Recall that the parameters a b and c are the coefficient of the quadratic term in front of the amplitude of the mode led velocity, and that the same b and c parameters are the coefficients for the linear term in front of the argument of the modeled velocity profile. First of all, notice the large correlation coefficients R2 for the a and c parameters, close to unity, indicative of the good conf idence level in the corresponding regression coefficients. On the other hand, although accepta ble, the correlation coefficients for the b parameters indicate that the assumed regression form is sub-optimal.

PAGE 295

268 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 CFD data scaling law CXvC3ex inex inexinex in -0.02 -0.01 0 0.01 0.02 0.03 0.04 CFD data scaling law CXvC3ex inex inexinex in Figure 7-24: Comparison between the results of the integral parameters from the scaling law and the CFD data for the test case. Case XII: S = 20, Re = 94, 0.26 d Re133 A) Full view. B) Close-up view. Consider next the relative values of the coefficients a0 and bi, a0 being representative of the im portance of the parameter a b or c It can be seen that the parameter a does have the most significant influence on the overall profile, especially compared with b Next, the constant value for the coefficient b1 is due to the fact that the ratio hd has not been varied in the test cases used in this analysis, as shown in Table A B zoom in

PAGE 296

269 7-4. The coefficient b2 weights the momentum thickness influence, which clearly has a dominant influence on the parameter b although one has to be cautious with respect to the associated correlation coefficient, and a minor influence on the parameter c Similarly, the Reynolds number associated w ith the boundary layer mainly influences the parameter b of the profile, which shows that the skewness of the velocity profile is strongly dependant on the momentum of the incoming boundary layer. Finally, it can be seen that the ratio of the jet-to-freestream velocity equally weights all velocity profile parameters. Next, the test case (Case XII) is used to evaluate the scaling law. The results are shown in Figure 7-24 where the integral parame ters from the numerical data are plotted along with those from the scaling law of th e velocity profile obtained by applying the results shown in Table 7-9. Clearly, the scali ng law in its present form is globally able to provide reasonable estimates of the principal integral parameters, for both the expulsion and the ingestion part of the cycle. Mo re particularly, the momentum coefficient C predicted by the scaling law closely matches the numerical data. However, the ingestion part is poorly represented in terms of the skewness X This can be e xplained by the low correlation coefficient associated with the parameter b As for the vorticity flux v the scaling law predicts an equal value for both the expulsion and the expulsion part, which is not quite true as seen from the CFD da ta. Finally, the jet kinetic energy flux 3C although only shown here for verification purpose s since it does not enter in the system of equations to be solved, is under-estimated by the scaling la w. Recall however that this all analysis has been performed on only 12 cases which is a modest but valuable start in view of the results presented in this section. It is clearly not enough if one considers the

PAGE 297

270 wide parameter space to span and the st rongly coupled interactions between each dimensionless parameter. Validation and Application The next step in developing these scaling la ws of a ZNMF actuator interacting with a grazing boundary layer is to first validate them, and then apply them in practical applications. Here, a road map is pr esented to achieve such a goal. First of all, in orde r to be valid the two scaling la ws developed above need to be refined based on a larger databa se, especially the scaling law that is based on the velocity profile and for whom the nonlin ear regression analysis gi ves unsatisfactory regression coefficients R2. Next, the scaling laws must be im plemented in practical cases. Recall that one goal in deve loping such reduced-order models is to use them in a numerical simulation as a boundary condition in lieu of re solving the local flow details near the actuator. This is illustrated in Figure 7-25, where the concept is to use the results of the scaling law presented above and set it as th e boundary condition for a simple application (e.g. flow over a flat plate). Then, the numerical results for the full computational domain (flow over the airfoil plus the whole ZNMF act uator) are compared with the numerical results where the actuator is only modeled as a time-dependant boundary condition at the orifice exit. Computed flow parameters at specific locations are probed i.e., right at the orifice edge to see the local flow region, and farther downstream for the global flow region to check the corres pondence between the two simulations. Once this validation of the current scaling law presented above in the previous sections has been accomplished, the m odel can be extended to include more dimensionless parameters, such as pressure gr adient, surface curvature, etc., hence to be

PAGE 298

271 extended to more general flow conditions (e.g., flow past an airfoi l). This requires a more important test matrix of available numerical simulations. ZNMF actuator computational domain M Re integral parameters to probe ZNMF actuator ZNMF actuator computational domain M Re integral parameters to probe ZNMF actuator boundary condition (scaling law) Figure 7-25: Example of a practical applic ation of the ZNMF actuator reduced-order model in a numerical simulation of flow past a flat plate. A) Computational domain is flow over the plate + actuator. B) Computational domain is flow over the plate only. Finally, the next logical step to be undert aken would be to compute the impedance aBL Z (see Eq. 7-17) from the scal ing law based jet exit velocity profiles. This impedance is then to be compared with the results from the extension of the low-dimensional lumped elements that include a boundary layer impeda nce from the Helmholtz resonator analogy. Such a comparison will help in validating both approaches, as well as refining the LEMbased reduced-order model. However, the sca ling law must first be sufficiently accurate before taking this next step. To conclude this chapter, the interacti on of a ZNMF actuator with an external boundary layer has been investigated in great detail, starting from a physical description A B

PAGE 299

272 of the different interactions and the effects on the local velocity profile, and then followed by a dimensional analysis used to extract the governing pa rameters. Since the parameter space is extremely large, as a first step a variation in some of the dimensionless numbers have been neglected, such as th e surface curvature and shape factor. Next, two reduced-order models have been presented. Th e first one is an extension of the LEM detailed in the previous chapters for a ZNMF actuator in quiescent flow, where the effects of an external boundary la yer have been added to the model. This model is based on the work done in the acous tic liner community and looks promising, although it is only a function of few flow parameters ( kd Cd, d and M ). A logical extension to this model would be to include the jet-to-freestream velocity ratio jVU a boundary layer Reynolds number, such as Re and the BL integral parameter d instead of d The second low-dimensional model is based on a regression anal ysis on available numerical data that provides the jet veloci ty profile as a function of 5 dimensionless parameters (S, hd, d Re and jVU ). Two scaling laws are developed, one based on the jet velocity profile at the or ifice exit, the other one on the integral parameters of the local flow at the orifice exit. The results are encouraging, but more test cases are needed to ensure a better valid ation of the results due to the nonlinear relationship between the correlation coefficients and also due to the large parameter space. Finally, a discussion is provided on the ne xt steps that have to be taken in order to fully appreciate the usefulne ss of such reduced-order m odels of a ZNMF actuator interacting with a graz ing boundary layer.

PAGE 300

273 CHAPTER 8 CONCLUSIONS AND FUTURE WORK This chapter summarizes the work presented in this dissertation. Concluding remarks are provided along with sugg estions for future research. Conclusions The dynamics governing the behavior of zero net mass flux (ZNMF) actuators interacting with and without an external fl ow have been presented and discussed, and physics-based low-order models have been de veloped and compared with an extensive database from numerical simulations and ex perimental results. The objective was to facilitate the physical understa nding and to provide tools to aid in the analysis and development of tools for sizing, design a nd deployment of ZNMF actuators in flow control applications. From the standpoint of an isolated ZNMF actuator issuing into a quiescent medium, a dimensional analysis highlighted identifi ed the key dimensionless parameters. An extensive experimental setup, along with some available numerical simulations, has permitted us to gain a physical understanding on the rich and complex behavior of ZNMF actuators. The results of the numerical simu lations and experiments both revealed that care must be exercised concerning modeling the flow physics of the device. Based on these findings, a refined reduced-order, lu mped model was successfully developed to predict the performance of candidate devi ces and was shown to be in reasonable agreement with experimental frequency response data.

PAGE 301

274 In terms of interacting with an external flow, a dimensional analysis revealed additional relevant flow para meters, and the interaction mechanism was qualitatively discussed. An acoustic impedance model of the grazing boundary layer influence based on the NASA ZKTL model (Betts 2000) was th en evaluated and implemented in the original lumped element model described in Gallas et al. (2003a). Its validation must await a future investigation. Next, two scaling laws were de veloped for the timedependent jet velocity profile of a ZNMF actuator interacti ng with an external Blasius boundary layer. Although the preliminary results seem promising, further work is still required. The main achievements of this work are summarized below. Orifice flow physics (Chapters 4 and 5) The rich and complex orifice flow field of an isolated ZNMF actuator has been thoroughly investigated using numerical and ex perimental results, both in terms of the velocity and pressure fields. The straight orifice exit ve locity profile is primarily a function of Strouhal number St (or, alternatively, the dimensionless particle stroke length), Reynolds number Re, and orifice aspect ratio h/d Actuator design (Chapters 2, 4, and 5) An analytical criterion has been devel oped on the incompressibility assumption of the cavity, based on the actuati on-to-Helmholtz frequency ratio H f f This is especially relevant for computational studies that seek to model the flow inside the cavity. A simple linear dimensionless transfer function relating the jet-to-driver volume flow rate is developed, regard less of the driver dynamics. It can be used as a starting point as a design tool. It is found that by operating near acoustic resonance, the device

PAGE 302

275 can produce greater output flow rates than th e driver, hence revealing an acoustic lever arm that can be leveraged in practical applic ations where actuation au thority is critical An added benefit is that the driver is not operated at mechanical resonance where the device may have less tolerance to failure. The sources of nonlinearities present in a ZNMF actuator have been systematically investigated. Nonlinearities from the driver arise due to the driving-transducer dynamics and depend on the type of driver used (piezoelectric, electro magnetic ). Nonlinearities from large cavity pressure fluctuations can arise due to a departure from the isentropic speed of sound assumption, but this effect was found to be negligible for the test conditions considered in this study. Fina lly, appropriately mode ling the nonlinearities from the orifice is the main focus of the current reduced-order models. Reduced-order model of an isolat ed ZNMF actuator (Chapter 6) Based on a control volume analysis for an unsteady orifice flow, a refined physicsbased, low-order model of the actuator or ifice has been successfully developed that accounts for the nonlinear losses in the orifice that are a function of geometric (orifice aspect ratio h/d ) and flow parameters (Strouhal St and Reynolds Re numbers). Two distinct flow regimes are identified. The firs t one is for high dimensionless stroke length where the flow can be considered as quasi-steady and where nonlinear effects may dominate the orifice pressure drop. Another re gime occurs at intermediate to low stroke length where the pressure losse s are clearly dominated by th e flow unsteadiness. The refined lumped element model builds on two a pproximate scaling laws that have been developed for these two flow regimes.

PAGE 303

276 Reduced-order models of a ZNMF actua tor interacting with a grazing boundary layer (Chapter 7) Reduced-order models of a ZNMF actuato r interacting with a grazing Blasius boundary layer have been developed. On e model is based on the orifice acoustic impedance and leverages the work done in th e acoustic liner commun ity. Two others are based on scaling laws for the exit velocity profile: one using th e velocity profile information, the other one using the integral parameters of the jet exit velocity. While promising, these models need further validati on. These models can be used to provide approximate, time-dependent boundary c onditions for ZNMF actuators based on computed upstream dimensionless parameters of the flow. This approach frees up computational resources otherwise required to resolve the local details of the actuator flow to instead resolve the global effects of the actuators on the flow. Recommendations for Future Research The physics-based low-order models presented and developed in this dissertation can always be refined and will certainly bene fit from a larger high quality database, both numerically and experimentally This database should c over a wide range of flow parameters such as Strouhal and Reynol ds number (hence Stokes number) and geometric parameters such as the orifice aspect rati o. The following discussion indicates some directions for future work that are envi sioned to enhance and complete the present physical understanding of ZNMF actuator behavi or and to improve th e low-order models developed in this dissertation. Need in Extracting Specific Quantities The reduced-order model of the isolated act uator case mainly suffers from the lack of an appropriate model of the nonlinear reactance associated with the momentum

PAGE 304

277 integral given in Eq. 6-10. In order to have a valuable indication of how this component scales with the flow parameters, careful numerical simulations are required. An oscillatory orifice flow can be simulated for various Strouhal and Reynolds numbers and orifice aspect ratios wher e flows having large and smal l stroke lengths must be explored. Then the quantities of interest to be extracted are th e time-dependent (1) velocity profiles at the orifice entrance and ex it, (2) pressure drop across the orifice, and (3) wall shear stress along the orifice. Note that some of these quantities are small and converged stationary statistics are required to extract the magnitude and phase of these terms. Proper Orthogonal Decomposition Besides the reduced-order models presen ted in chapter 5, another low-order modeling technique can be developed usi ng proper orthogonal decomposition (POD) to characterize the interaction of a ZNMF actuator with an external flow. POD is a modelreduction method based on singular value decomposition. It identifies the modes that, on average, contain the most kinetic energy. POD, also known as the Karhunen-Love decomposition, is a classical tool in probabi lity theory and was introduced into the study of turbulent flows by Lumley (1967). The heart of this method is that, given an ensemble of data from either numerical or experi mental database, a modal decomposition is performed to extract a set of eigenfunctions (or modes) representing a spatial basis. These eigenfunctions physically represent the flow characteristics, and also have the property of being the optimal orthogonal basis in terms of a minimal energy representation. Sirovich ( 1987) introduced the snapshot application of the POD to model the coherent structures in turbulent flows. When l ooking at a series of snapshots (either from experimental or co mputational data), each taken at a different instant in time,

PAGE 305

278 the solution is essentially an eigenvalue problem that needs to be solved to determine the corresponding set of optimal ba sis functions that represen t the flow (i.e. yields a parametric collection of the component modes of the variable of interest). Finally, to obtain the corresponding low-or der model, the Galerkin projection method is usually used to obtain a reduced system of ordi nary differential equations from the POD expansion. Figure 8-1: POD analysis a pplied on numerical data for ZN MF actuator with a grazing BL. A) Energy present in each mode fo r Case X. B) Energy present in each mode for Case XII. C) Profiles of the fi rst 4 modes for Case X. D) Profiles of the first 4 modes for Case XII. 0 5 10 15 20 25 30 35 40 0.85 0.9 0.95 1 Number of modesEnergy 0 5 10 15 20 25 30 35 40 0.985 0.99 0.995 1 Number of modes gy A B Ener gy Ener gy -1 -0.5 0 0.5 1 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 x/(d/2) POD modes mode 1 mode 2 mode 3 mode 4 -1 -0.5 0 0.5 1 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 x/(d/2) POD modes mode 1 mode 2 mode 3 mode 4 D C

PAGE 306

279 Some preliminary results are presented in Figure 8-1 for two numerical test cases (as listed in Table 7-4), namely Case X ( S = 5, Rej = 94, Re = 1) and Case XII (33, S = 20, Rej = 94, Re = 133). Notice that from Figure 81A and Figure 8-1B, it appears that only the first 3 modes are needed to capture 99.5% of the flow energy. However, the profiles of these first few mode s show disparity in their form, as seen in Figure 8-1C and Figure 8-1D. So the next step would be to find a suitable correlation for each mode, which is expected to provide a suitable scaling law (similar to what has been developed in Chapter 7) of the ZNMF actuator profiles at the orifice exit. Then, and as outlined at the end of Chap ter 7, these low-order models of ZNMF actuators interacting with a grazing boundary layer should be implemented into practical numerical simulations. The actuator is now represented as a simple boundary condition in an unsteady simulation, and the results are probed and compared with those from a full simulation (that takes into account and the w hole actuator device and the grazing flow) to validate the behavior of these models for the local and the global field, as depicted in Figure 7-25. Boundary Layer Impedance Characterization Consider a tube of length l. The impedance seen by a source placed at one of the end of the tube is found to be 0tan Z ljZkl (8-1) where 0 Z is the specific impedance of the medium, and k is the wavenumber. Clearly, if the tube length is an integral number of half wavelengths, the impedance seen by the source becomes zero. However, if 4 l 34 54 , the impedance seen by the source is infinite. Such a specific design is called quarter-wavelength design. The high

PAGE 307

280 impedance of a quarter-wavelength open tube is sometimes used for applications, such as the study of sound propagation in a duct in whic h the air is moving, as shown in Figure 8-2. Source Air in Air out Air flow /4 /4 Figure 8-2: Use of quarter-w avelength open tube to provide an infinite impedance. (Adapted from Blackstock 2000) Here, consider the case in which the cavity depth of a ZNMF devi ce is a quarter of the wavelength of interest. The cavity impe dance becomes infinite, thereby leaving only the boundary layer impedance of the crossflow superimposed on the orifice impedance. If the orifice dimensions are j udiciously chosen such that th e flow inside the orifice is well behaved and has a validated model, it will then be possible to isolate the BL impedance for analysis, thereby extracting a low-order model to be implemented as a design tool. MEMS Scale Implementation Several previous works on ZNMF actuators have proposed the use of MEMS devices (Mallison et al. 2003, 2004) as opp osed to the meso-scale devices usually employed, as in this dissertation. MEMS-bas ed actuators consist of devices that have been fabricated using silicon micromachin ing technology (see for example Madou (1997)). A candidate MEMS ZNMF actua tor can be designed using fundamental structural models and lumped element m odels previously developed, such as thermoelastic (Chandrasekaran et al. 2003) and piezoelectric (Wang et al. 2002) actuators.

PAGE 308

281 d h H t 2a50 500 50 500 500 500 4 mdm mhm Hm am tm Figure 8-3: Representati ve MEMS ZNMF actuator. 0 2 4 6 8 10 x 104 0 1 2 3 4 5 6 7 8 9 10 Frequency [Hz]Centerline velocity [m/s] h=50 m h=100 m h=500 m d=50 m H=0.5mm d=0.1 h increasing Figure 8-4: Predicted output of MEMS ZNMF actuator assuming a diaphragm mode shape 2 2 01 wrWra 00.2 Wm and 65 d f kHz A preliminary design using LEM is perf ormed for an isolated ZNMF actuator composed of a general circular driver having a peak deflection 00.2 Wm and a natural frequency of 65 kHz. Figure 8-3 shows a sc hematic of a representative MEMS ZNMF actuator, while Figure 8-4 s hows peak velocities of 110 Oms for various orifice heights. Notice the similar trend as previously observed in the optimization study

PAGE 309

282 performed in Gallas et al. (2003b). These pr omising results suggest that a MEMS ZNMF actuator is capable of producing a reasonable velocity jet. An interesting analysis will be to investig ate the effect of scaling the results found in this dissertation for the meso-scale down to the MEMS scale, and to examine the corresponding effects with the intrinsic limitati ons. Also, an appropriate review on the relevance of such micro-devices in flow-cont rol applications must be discussed. Design Synthesis Problem In Gallas et al. (2003b), th e author performed an optimi zation of an isolated ZNMF actuator, decoupling the driver optimization to the actuator cavity and orifice optimization. However, it was limited to improving an existing baseline design. A more interesting, though more challe nging, case is the optimal desi gn synthesis problem. In this problem, the designer seeks to achieve a desired frequency response function. Due to the nonlinear nature of the system, the desi gn objective can be approximated by a linear transfer function that is valid at a particular driving voltage. A key challenge here is that the end user must be able to translate desi rable actuator characteris tics into quantitative design goals.

PAGE 310

283 Equation Chapter 1 Section 1 APPENDIX A EXAMPLES OF GRAZING FLOW M ODELS PAST HELMHOLTZ RESONATORS It should be noted that this discussion is far from exhaus tive. Even several versions may exist for each model presented. The firs t model presented is from Rice (1971) and is based on the continuity and momentum equati ons through the orifice while the cavity is lumped as a simple spring model. The results yield the following model of the normalized specific impedance of the orifice subjected to grazing flow pp j j (A-1) where the normalized specific resistance p of an array of resonators is given by 0, 00 grazing flow viscous losses0.3 8 1p pR M h cdc (A-2) and the normalized specific reactance p for an array of resonators is 0, 3 00.8510.7 1305p pX k h cM (A-3) Here 0, p R and 0, p X represent, respectively, the spec ific resistance an d reactance of the perforate, 0c is the characteristic impedance of the medium, is the kinematic viscosity, is the porosity of the perforate, d is the orifice diameter, h is the thickness of the orifice, is the radian frequency, and k is the wavenumber, and M is the grazing flow Mach number. The model is va lidated with data using the two-pressure

PAGE 311

284 measurement method obtained by Pratt & Whitn ey (see Garrison 1969) and the Boeing Company. Rice (1971) made the following re mark regarding the data provided: The data at 0 U are questionable since the electro-pne umatic driver provided substantial air flow which had to be bl ed off before reaching the sa mple and recirculating flows resulted (conversation with Garrison). Therefore, this model may not work well at 0 M Next, Bauer (1977) proposed the follo wing empirical normalized specific impedance model containing the in fluence of crossflow velocity: 0 001.150.25 8 0.3 1 1buckhd M ph j cucd (A-4) where p and u are respectively the acoustic pressure and particle velocity, and bu is the bias flow velocity through th e perforate (steady flow). No tice that in this model, the grazing flow affects only the resistance part of the impedance and not the reactance. Figure A-1 shows the test apparatus used. The liners were tested using the two microphone technique, a microphone being mounted at the botto m of the liner cavity and another one on the liner surface. The incomi ng grazing flow has become fully turbulent by the time it has reached the test panel and a boundary la yer survey show ed a velocity profile close to the 1/7 power shape.

PAGE 312

285 absorptive liners test panel acoustic wave fronts microphone siren horn air inlet duct flow Figure A-1: Acoustic test duct and siren sh owing a liner panel test configuration. (Adapted from Bauer 1977). Another model is presented by Hersh and Walker (1979). They derive a semiempirical impedance model for a single orif ice, where it is assumed that the sound particle enters the resonator cavity in a sphe rical, radically manner during the inflow halfcycle, following a vena contracta path. For non-zero grazing flow, they predict the following orifice area-averaged norm alized resistance and reactance 0 01.870.17 R M cd (A-5) and 13 00 00.142.070.43ln3.72.63 1.190.11 d EE Xc c d (A-6) where the quantity 8 D iECdP, with iP being the incident pressure, and 28HDeCdd with the orifice inertial length being defined by 0.8511.25ecdhddD Here 00c R AApu and 00c X AApu are respectively the area-avera ged (ratio of orifice to cavity cross sectional area) specific resistance and reactance of the orifice. Notice that in this model representation, the

PAGE 313

286 grazing flow effects is only se en in the resistance part of the impedance, and that no viscous losses in the orifice are represente d. A schematic of the apparatus setup and instrumentation hardware used is given in Fi gure A-2. Extensive experimental data have been reported, from single to clustered orifices thin perforate plate to thick orifices and within a large range of SPL and grazing fl ow velocity. For the purpose of this dissertation, only the thick orifices database is taken, as documented in Table A-1 at the end of this Appendix. 0.125 m Mic. 0.125 m Mic. 0.10 m 0.125 m d 0.25 m L D PcPiOrifice Horn coupler Driver power amplifier oscillator digital phase Synch. Filter Mtr. DVM 1/10 Oct. analyser Figure A-2: Schematic of test apparatus us ed in Hersh and Walk er (1979). (Adapted from Hersh and Walker 1979)

PAGE 314

287 Following the previous work done by Cu mmings (1986), Kir by and Cummings (1998) measured the acoustic impedance of perforates with and without a porous backing. An empirical model of perforat es without porous backing is given by 0.169 026.16204.055fc u h fddfd (A-7) for the normalized flow induced resistance of the orifice, and the mass end correction by 0 010.18 10.6exp0.181.80.60.18 u hd hfhh u hhhd u dh fhhd hddfhh .(A-8) The acoustic impedance is normalized such that 0 0 0fZ i c (A-9) where 00, pc Z AApu is the specific area-averaged impedance of the perforate, 0,pA being here the total area of all orifices in the perforate test sample and cA the cavity cross-sectional area. Here the orifice re sistance due to viscous loss is given by 0 08 h cd (A-10) and the normalized orifice reactance can be obtained from the end correction ratio 0hh given by Eq. A-8 and by the following relation, 00.85 h khd h (A-11)

PAGE 315

288 Power amplifier Thandar TG503 signal generator Ono Sokki CF-35OZ FFT analyser test cavity JBL 2445J compressor driver air in duct 2.5 m 0.4 m 33 mm 33 mm 72 mm 72 mm duct cavity perforate Bruel & Kjoer 1/2" condenser microphones Type 4134 section through duct and test cavity Figure A-3: Apparatus for the measurement of the acoustic impedance of a perforate used by Kirby and Cummings (1998). (Adapted from Kirby and Cummings 1998)

PAGE 316

289 under the assumption that the end correction le ngth without flow is approximately equal to 0.85 d for an isolated orifice if d being the wavelength. This last assumption is discussed in more rigorous details by Ingard (1953) and is used to eliminate the jetting interaction effect due to closely spaced orifices in a flat plat e. In this model the friction velocity is a function of the rectangular duct area based Reynolds number, as discussed by Cummings (1986). Noti ce that this model is a function of the inverse of Strouhal number based on the grazing flow friction velo city and on either the diameter or the thickness of the orifice, and shows two different regimes fo r the reactance model function of the orifice aspect ratio. The experiments were pe rformed for different Helmholtz resonator configurations as listed in Table A1, the grazing flow being fully turbulent by the time it reaches the test section. The e xperimental setup is s hown in Figure A-3. Finally, the last model presented in this dissertation is the so-called NASA Langley Zwikker-
Permanent Link: http://ufdc.ufl.edu/UFE0008338/00001

Material Information

Title: On the Modeling and Design of Zero-Net Mass Flux Actuators
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0008338:00001

Permanent Link: http://ufdc.ufl.edu/UFE0008338/00001

Material Information

Title: On the Modeling and Design of Zero-Net Mass Flux Actuators
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0008338:00001


This item has the following downloads:


Full Text












ON THE MODELING AND DESIGN OF ZERO-NET MASS FLUX ACTUATORS


By

QUENTIN GALLAS


















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2005

































Copyright 2005

by

Quentin Gallas

































Pour mafamille et mes amis, d'ici et de la-bas...
(To my family and friends, from here and over there...)















ACKNOWLEDGMENTS

Financial support for the research project was provided by a NASA-Langley

Research Center Grant and an AFOSR grant. First, I would like to thank my advisor, Dr.

Louis N. Cattafesta. His continual guidance and support gave me the motivation and

encouragement that made this work possible. I would also like to express my gratitude

especially to Dr. Mark Sheplak, and to the other members of my committee (Dr. Bruce

Carroll, Dr. Bhavani Sankar, and Dr. Toshikazu Nishida) for advising and guiding me

with various aspects of this project. I thank the members of the Interdisciplinary

Microsystems group and of the Mechanical and Aerospace Engineering department

(particularly fellow student Ryan Holman) for their help with my research and their

friendship. I thank everyone who contributed in a small but significant way to this work.

I also thank Dr. Rajat Mittal (George Washington University) and his student Reni Raju,

who greatly helped me with the computational part of this work.

Finally, special thanks go to my family and friends, from the States and from

France, for always encouraging me to pursue my interests and for making that pursuit

possible.
















TABLE OF CONTENTS

page


A C K N O W L E D G M E N T S ................................................................................................. iv

LIST OF TABLES ........... ............................... ............... ............. ix

LIST O F FIG U RE S .... ........................... ............ xi

LIST OF SYMBOLS AND ABBREVIATIONS .................................................... xix

A B S T R A C T .......................................................... ............... xxv i

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

M o tiv atio n ..................... ... .... .. ............................................... .
Overview of a Zero-Net Mass Flux Actuator............................................................3
L literature R eview ................... .. .............. .................. .......... ..............
Isolated Zero-N et M ass Flux Devices ....................................... ............... 7
A application s .............................................. ....................... 8
M modeling approaches ............................................. .... ..... .......... ........ 11
Zero-Net Mass Flux Devices with the Addition of Crossflow............................15
Fluid dynam ic applications ........................................ ....... ............... 16
A eroacoustics applications ................................... ...................................... 18
M odeling approaches ............................................................................19
U resolved Technical Issues ........................................ .......................... 25
O bj ectives .................................. .......................... ....... ........... 27
Approach and Outline of Thesis ................................ .......................... 28

2 DYNAMICS OF ISOLATED ZERO-NET MASS FLUX ACTUATORS ..............30

Characterization and Param eter D efinitions .................................... ........................31
Lum ped Elem ent M odeling ......................................................... ............... 34
Sum m ary of Previous W ork ...................................... ........................ .......... 34
Limitations and Extensions of Existing M odel ................................................38
D im ensional A naly sis............ ... ............................................................ .. .... ... ... 44
D definition and D discussion ...................... ... ........... ............... ...44
Dimensionless Linear Transfer Function for a Generic Driver...........................46


v











M modeling Issues ........................................................................................... ........51
C a v ity E ffe ct.................................................................................................. 5 1
Orifice Effect ............. .... .. ...... ..... ......... .... .. ....... ......... ............ 52
Lumped element modeling in the time domain.........................................52
L oss m echanism ..................... .. .. ..................... .... .. ........... 6 1
D riving-Transducer Effect........................................................ ............... 63
T est M atrix ........................................................................................ 69

3 E X PE R IM E N TA L SE TU P ............................................................. .....................72

E xperim mental Setup ............. .......................................................................... .... 72
C av ity P re ssu re ............................................................................... 7 5
D iaphragm D election .............................................................. .....................76
V elocity M easurem ent.............................................................. .....................79
D ata-A acquisition System ......................................................... ............. 82
D ata P processing .............................................................85
Fourier Series D ecom position ............................................................................. 92
F low V isu alization ........ ....................................................................... ....... .. ..... .. 97

4 RESULTS: ORIFICE FLOW PHYSICS......................................... ............... 99

L ocal F low F ield ................................. ....... ........... ........................ 100
Velocity Profile through the Orifice: Numerical Results...............................100
Exit Velocity Profile: Experimental Results ............................................. 109
Jet Formation ............... ....... .......... ......... 116
Influence of Governing Param eters ................................................. ............... 118
Empirical N onlinear Threshold ............. ................................................... 119
Strouhal, Reynolds, and Stokes Numbers versus Pressure Loss.......................121
Nonlinear Mechanisms in a ZNMF Actuator ........... .................................128

5 RESULTS: CAVITY INVESTIGATION..... ...........................................137

C av ity P ressu re F ield .................................................................. .. .................... 137
E x p erim ental R esu lts............................................ ....................................... 13 8
N um erical Sim ulation Results................................ ................................... 141
Com putational fluid dynamics ....................................... ............... 142
Fem lab ................................... ............................... ........ 147
Com pressibility of the Cavity ........................................................ ............. 150
L E M -B ased A n aly sis............................................ ....................................... 15 1
E xperim ental R esults................................................... .................. 156
Driver, Cavity, and Orifice Volum e Velocities....................................................... 162

6 REDUCED-ORDER MODEL OF ISOLATED ZNMF ACTUATOR..................171

O rifice P ressu re D rop .................................................................... .................... 17 1
C control V olum e A analysis .......................................................................... 172
Validation through Numerical Results ............................... ..................175









Discussion: Orifice Flow Physics ........... ............................. ............... 181
Development of Approximate Scaling Laws ................................. ................188
E xperim ental results .............................................................. ............... 188
Nonlinear pressure loss correlation ............. ............................................ 194
R efined Lum ped Elem ent M odel..................................... ........................ ........... 198
Im plem entation ................... .. ..... ........................... ...... ............. 198
Com prison with Experim ental Data ..................................... .................202

7 ZERO-NET MASS FLUX ACTUATOR INTERACTING WITH AN
EXTERNAL BOUNDARY LAYER ....................................................................211

On the Influence of Grazing Flow ................................ ......................... ........ 211
D im ensional A naly sis........... ........................................................... .... .... ... ....2 18
R educed-O rder M odels....................................................................................... 223
Lumped Element Modeling-Based Semi-Empirical Model of the External
B ou n d ary L ay er ................................................................... ................ .. 2 2 4
D definition ................................................. 224
Boundary layer impedance implementation in Helmholtz resonators .......229
Boundary layer impedance implementation in ZNMF actuator...............238
Velocity Profile Scaling Laws ..................................... 241
Scaling law based on the jet exit velocity profile................ ...............244
Scaling law based on the jet exit integral parameters .............................261
V alidation and A application ............................................. ............... 270

8 CONCLUSIONS AND FUTURE W ORK.................................................... ......... 273

C o n c lu sio n s ............... ....... ... ................................................................... 2 7 3
Recommendations for Future Research...................... ......................... 276
Need in Extracting Specific Quantities .................................. ............... 276
Proper Orthogonal Decomposition.............................................. 277
Boundary Layer Impedance Characterization...........................279
M EM S Scale Im plem entation ........................................ ........ ............... 280
Design Synthesis Problem .................................................................... 282

APPENDIX

A EXAMPLES OF GRAZING FLOW MODELS PAST HELMHOLTZ
RESONATORS .................................. .. .. ........ .. ............283

B ON THE NATURAL FREQUENCY OF A HELMHOLTZ RESONATOR ..........291

C DERIVATION OF THE ORIFICE IMPEDANCE OF AN OSCILLATING
PRESSURE DRIVEN CHANNEL FLOW .............................................................295

D NON-DIMENSIONALIZATION OF A ZNMF ACTUATOR ..............................303

E NON-DIMENSIONALIZATION OF A PIEZOELECTRIC-DRIVEN ZNMF
ACTUATOR W ITHOUT CROSSFLOW ........................................... ............... 312









F NUMERICAL METHODOLOGY ............................ ... .................... 326

G EXPERIMENTAL RESULTS: POWER ANALYSIS .........................................331

L IST O F R E F E R E N C E S ........................................................................ ....................348

B IO G R A PH IC A L SK E T C H ........................................... ...........................................359
















































viii
















LIST OF TABLES


Table page

2-1 Correspondence between synthetic jet parameter definitions.............................. 34

2-2 Dimensional parameters for circular and rectangular orifices............... ..............49

2-3 Test matrix for ZNMF actuator in quiescent medium ...........................................69

3-1 ZNMF device characteristic dimensions used in Test 1 .......................................75

3-2 LD V m easurem ent details............................................... .............................. 82

3-3 Repeatability in the experimental results..... ...................... ............92

4-1 Ratio of the diffusive to convective time scales ............. ..... .................109

5-1 Cavity volume effect on the device frequency response for Case 1 (Gallas et al.)
from the LEM prediction. .............................................. ............................. 153

5-2 Cavity volume effect on the device frequency response for Case 1 (CFDVal)
from the LEM prediction. .............................................. ............................. 154

5-3 ZNMF device characteristic dimensions used in Test 2.............. ...............156

5-4 Effect of the cavity volume decrease on the ZNMF actuator frequency response
for C ases A B C and D .............................................. ............................... 157

7-1 List of configurations used for impedance tube simulations used in Choudhari et
al.............. ..................... ............................................. ...... 2 16

7-2 Experimental operating conditions from Hersh and Walker ...............................230

7-3 Experimental operating conditions from Jing et al..........................................236

7-4 Tests cases from numerical simulations used in the development of the velocity
profit les scaling law s............ ............................................................. .... .... .... .. 242

7-5 Coefficients of the nonlinear least square fits on the decomposed jet velocity
p ro fi le ................................. ........................................................... ............... 2 5 4









7-6 Results from the nonlinear regression analysis for the velocity profile based
sc a lin g law ..............................................................................................................2 5 9

7-7 Results for the parameters a, b and c from the nonlinear system .........................265

7-8 Integral param eters results ............................................. ............................. 266

7-9 Results from the nonlinear regression analysis for the integral parameters based
v elo city p profile ................................................................................... 2 6 7

A-1 Experimental database for grazing flow impedance models ...............................290

B-l Calculation of Helmholtz resonator frequency..................................................293

D-1 Dimensional matrix of parameter variables for the isolated actuator case ...........304

D-2 Dimensional matrix of parameter variables for the general case............................308

E-l Dim ensional m atrix of param eter variables..........................................................314

G-l Power in the experimental time data............. ....... ...............................332















LIST OF FIGURES


Figure pge

1-1 Schematic of typical zero-net mass flux devices interacting with a boundary
layer, showing three different types of excitation mechanisms................................4

1-2 Orifice geom etry. ......................... ................. ............. .. .. ..5

1-3 H elm holtz resonators arrays....................................... ................................ 6

2-1 Equivalent circuit model of a piezoelectric-driven synthetic jet actuator ................35

2-2 Comparison between the lumped element model and experimental frequency
response measured using phase-locked LDV for two prototypical synthetic jets. ...37

2-3 Comparison between the lumped element model (-) and experimental
frequency response measured using phase-locked LDV (*) for four prototypical
sy nth etic jets......... ............................................................................. 4 1

2-4 Variation in velocity profile vs. S = 1, 12, 20, and 50 for oscillatory pipe flow in
a circular duct.................... ...... .... .. ... ....................... ........... 42

2-5 Ratio of spatial average velocity to centerline velocity vs. Stokes number for
oscillatory pipe flow in a circular duct................................... ...............43

2-6 Schematic representation of a generic-driver ZNMF actuator ..............................47

2-7 Bode diagram of the second order system given by Eq. 2-20, for different
dam ping ratio ...................................................... ................. 4 8

2-8 Coordinate system and sign convention definition in a ZNMF actuator ................53

2-9 Geometry of the piezoelectric-driven ZNMF actuator from Case 1 (CFDVal). ......55

2-10 Geometry of the piston-driven ZNMF actuator from Case 2 (CFDVal). ................55

2-11 Time signals of the jet orifice velocity, pressure across the orifice, and driver
displacement during one cycle for Case 1. .................................... ............... 57

2-12 Time signals of the jet orifice velocity, pressure across the orifice and driver
displacement during one cycle for Case 2. .................................... .................58









2-13 Numerical results of the time signals for A) pressure drop and B) velocity
perturbation at selected locations along the resonator orifice..............................59

2-14 Schematic of the different flow regions inside a ZNMF actuator orifice ...............62

2-15 Equivalent two-port circuit representation of piezoelectric transduction. ................64

2-16 Speaker-driven ZNM F actuator. ........................................ ......................... 66

2-17 Schematic of a shaker-driven ZNMF actuator, showing the vent channel
betw een the tw o sealed cavities. ........................................ ......................... 67

2-18 Circuit representation of a shaker-driven ZNMF actuator .............. ...............68

3-1 Schematic of the experimental setup for phase-locked cavity pressure,
diaphragm deflection and off-axis, two-component LDV measurements ...............73

3-2 Exploded view of the modular piezoelectric-driven ZNMF actuator used in the
experim mental test. ......................................................................73

3-3 Schematic (to scale) of the location of the two 1/8" microphones inside the
Z N M F actuator cavity ....................................................................... ..................76

3-4 Laser displacement sensor apparatus to measure the diaphragm deflection with
sign convention. .......................................................................77

3-5 Diaphragm mode shape comparison between linear model and experimental
data at three test conditions ............................................... ............. ............... 79

3-6 LDV 3-beam optical configuration. ........................................ ....................... 80

3-7 Flow chart of m easurem ent setup. ........................................... ........................83

3-8 Phase-locked signals acquired from the DSA card, showing the normalized
trigger signal, displacement signal, pressure signals and excitation signal .............84

3-9 Percentage error in Error! Objects cannot be created from editing field codes.
from simulated LDV data at different signal to noise ratio, using 8192 samples.....87

3-10 Phase-locked velocity profiles and corresponding volume flow rate acquired
w ith L D V for C ase 14 ....................................................................... ..................89

3-11 Noise floor in the microphone measurements compared with Case 52 ..................91

3-12 N orm alized quantities vs. phase angle ........................................... ............... 93

3-13 Power spectrum of the two pressure recorded and the diaphragm displacement. ...95

3-14 Schem atic of the flow visualization setup...................................... .....................97









4-1 Numerical results of the orifice flow pattern showing axial and longitudinal
velocities, azimuthal vorticity contours, and instantaneous streamlines at the
tim e of m axim um expulsion. ............... .......... ......... ................................. 101

4-2 Velocity profile at different locations inside the orifice for Case 1......................103

4-3 Velocity profile at different locations inside the orifice for Case 2........................105

4-4 Velocity profile at different locations inside the orifice for Case 3.......................106

4-5 Vertical velocity contours inside the orifice during the time of maximum
ex pu lsion ........................................................................ 10 7

4-6 Experimental vertical velocity profiles across the orifice for a ZNMF actuator in
quiescent medium at different instant in time for Case 71 ............................... 110

4-7 Experimental vertical velocity profiles across the orifice for a ZNMF actuator in
quiescent medium at different instant in time for Case 43 ..................................11

4-8 Experimental vertical velocity profiles across the orifice for a ZNMF actuator in
quiescent medium at different instant in time for Case 69. ................................113

4-9 Experimental vertical velocity profiles across the orifice for a ZNMF actuator in
quiescent medium at different instant in time for Case 55 ............................... 114

4-10 Experimental results of the ratio between the time- and spatial-averaged
velocity and time-averaged centerline velocity. .......................... ....................116

4-11 Experimental results on the jet formation criterion. ............................................... 118

4-12 Averaged jet velocity vs. pressure fluctuation for different Stokes number...........120

4-13 Pressure fluctuation normalized by the dynamic pressure based on averaged
velocity vs. St h/d ................................................................. .... ........... 122

4-14 Pressure fluctuation normalized by the dynamic pressure based on averaged
velocity vs. Strouhal num ber. ............................................................................ 123

4-15 Vorticity contours during the maximum expulsion portion of the cycle from
num erical sim ulations. ................................................ ................................ 124

4-16 Pressure fluctuation normalized by the dynamic pressure based on ingestion
tim e averaged velocity vs. St h d ............................. ..... ............................ 125

4-17 Vorticity contours during the maximum ingestion portion of the cycle from
num erical sim ulations. ................................................ ................................ 126

4-18 Comparison between Case 1 vertical velocity profiles at the orifice ends ...........127









4-19 Comparison between Case 2 vertical velocity profiles at the orifice ends. ............128

4-20 Comparison between Case 3 vertical velocity profiles at the orifice ends. ............128

4-21 Determination of the validity of the small-signal assumption in a closed cavity. ..131

4-22 Log-log plot of the cavity pressure total harmonic distortion in the experimental
tim e sign als. ...................................................... ................. 132

4-23 Log-log plot of the total harmonic distortion in the experimental time signals vs.
Strouhal number as a function of Stokes number. ............................................... 134

5-1 Coherent power spectrum of the pressure signal for Cases 9 to 20........................138

5-2 Phase plot of the normalized pressures taken by microphone 1 versus
m microphone 2 ............................................ ........ ................. 139

5-3 Pressure signals experimentally recorded by microphone 1 and microphone 2 as
a function of phase in Case 59. .............................. ....... .. ............... ...... 140

5-4 Ratio of microphone amplitude (Pa) vs. the inverse of the Strouhal number, for
different Stokes num ber. ............................................... ............................... 141

5-5 Pressure contours in the cavity and orifice (Case 2) from numerical simulations.. 143

5-6 Pressure contours in the cavity and orifice (Case 3) from numerical simulations.. 144

5-7 Cavity pressure probe locations in a ZNMF actuator from numerical
sim ulations. .......................................... ........................... 145

5-8 Normalized pressure inside the cavity during one cycle at 15 different probe
locations from numerical simulation results. .................................. ............... 146

-2
5-9 Cavity pressure normalized by pVj vs. phase from numerical simulations
corresponding to the experimental probing locations...................................147

5-10 Contours of pressure phase inside the cavity by numerically solving the 3D
w ave equation using FEM LAB .......................................................... ....... ........ 148

5-11 Cavity pressure vs. phase by solving the 3D wave equation using FEMLAB and
corresponding to the experimental probing locations...................................149

5-12 Log-log frequency response plot of Case 1 (Gallas et al.) as the cavity volume is
decreased from the LEM prediction.................................. 153

5-13 Log-log frequency response plot of Case 1 (CFDVal) as the cavity volume is
decreased from the LEM prediction.................................. 154









5-14 Experimental log-log frequency response plot of a ZNMF actuator as the cavity
volume is decreased for a constant input voltage. ............................................. 158

5-15 Close-up view of the peak locations in the experimental actuator frequency
response as the cavity volume is decreased for a constant input voltage. ............158

5-16 Normalized quantities vs. phase of the jet volume rate, cavity pressure and
centerline driver velocity.. ............................. .... ...................................... 160

5-17 Experimental results of the ratio of the driver to the jet volume velocity function
of dimensionless frequency as the cavity volume decreases. ............................... 164

5-18 Experimental jet to driver volume flow rate versus actuation to Helmholtz
frequency..................................... .......................... .... ..... ......... 166

5-19 Current divider representation of a piezoelectric-driven ZNMF actuator. .............168

5-20 Frequency response of the power conservation in a ZNMF actuator from the
lumped element model circuit representation for Case 1 (Gallas et al.)...............69

6-1 Control volume for an unsteady laminar incompressible flow in a circular
orifice, from y = -1 to = 0 ............... ..................................... ............... 172

6-2 Numerical results for the contribution of each term in the integral momentum
equation as a function of phase angle during a cycle ................ ......... ..........176

6-3 Definition of the approximation of the orifice entrance velocity from the orifice
exit velocity ............ ... ......................................... ......................... 178

6-4 Momentum integral of the exit and inlet velocities normalized by Error! Objects
cannot be created from editing field codes. and comparing with the actual and
approxim ated entrance velocity. ........................................ ......................... 179

6-5 Total momentum integral equation during one cycle, showing the results using
the actual and approximated entrance velocity. .................. .............................. 181

6-6 Numerical results of the total shear stress term versus corresponding lumped
linear resistance during one cycle. ............................................... ............... 183

6-7 Numerical results of the unsteady term versus corresponding lumped linear
reactance during one cycle. .............................................. ............................ 184

6-8 Numerical results of the normalized terms in the integral momentum equation
as a function of phase angle during a cycle. ............................. .................187

6-9 Comparison between lumped elements from the orifice impedance and
analytical terms from the control volume analysis. .............................................. 188









6-10 Experimental results of the orifice pressure drop normalized by the dynamic
pressure based on averaged velocity versus St h/d for different Stokes
num bers................................... ................................. ........... 191

6-11 Experimental results of each term contributing in the orifice pressure drop
coefficient vs. St h/d ....................... .............. ................. ........ 192

6-12 Experimental results of the relative magnitude of each term contributing in the
orifice pressure drop coefficient vs. intermediate to low St h/d ........................193

6-13 Experimental results for the nonlinear pressure loss coefficient for different
Stokes number and orifice aspect ratio. ...................................... ............... 196

6-14 Nonlinear term of the pressure loss across the orifice as a function of St h/d
from experim mental data. ............................................... ............................... 197

6-15 Implementation of the refined LEM technique to compute the jet exit velocity
frequency response of an isolated ZNMF actuator. .........................................201

6-16 Comparison between the experimental data and the prediction of the refined and
previous LEM of the impulse response of the jet exit centerline velocity.
Actuator design corresponds to Case I from Gallas et al.......................................203

6-17 Comparison between the experimental data and the prediction of the refined and
previous LEM of the impulse response of the jet exit centerline velocity.
Actuator design corresponds to Case II from Gallas et al....................................205

6-18 Comparison between the experimental data and the prediction of the refined and
previous LEM of the impulse response of the jet exit centerline velocity.
Actuator design is from Gallas and is similar to Cases 41 to 50. .........................207

6-19 Comparison between the refined LEM prediction and experimental data of the
time signals of the jet volume flow rate .......................................................209

7-1 Spanwise vorticity plots for three cases where the jet Reynolds number Re is
in crea se d ............................. .......................................................... ............... 2 12

7-2 Spanwise vorticity plots for three cases where the boundary layer Reynolds
num ber is increased. ....................................... ................. ..........213

7-3 Comparison of the jet exit velocity profile with increasing..................................214

7-4 Pressure contours and streamlines for mean A) inflow, and B) outflow through a
resonator in the presence of grazing flow. ............ ...................... ....................218

7-5 LEM equivalent circuit representation of a generic ZNMF device interacting
w ith a grazing boundary layer.................................................................... ...... 224









7-6 Schematic of an effort divider diagram for a Helmholtz resonator ......................230

7-7 Comparison between BL impedance model and experiments from Hersh and
Walker as a function of Mach number for different SPL. ............................... 233

7-8 Experim mental setup used in Jing et al........................................... ............... 236

7-9 Comparison between model and experiments from Jing et al .............................237

7-10 Effect of the freestream Mach number on the frequency response of the ZNMF
design from Case 1 (CFDVal) using the refined LEM. ........................................239

7-11 Effect of the freestream Mach number on the frequency response of the ZNMF
design from Case 1 (G allas et al.) ................................................. .. ... .......... 240

7-12 Schematic of the two approaches used to develop the scaling laws from the jet
exit velocity profile. ......................................... ..................... .......244

7-13 Methodology for the development of the velocity profile based scaling law.........245

7-14 Nonlinear least square curve fit on the decomposed jet velocity profile for Case
I ...........................................................................................2 4 7

7-15 Nonlinear least square curve fit on the decomposed jet velocity profile for Case
III ................... ......................................................................... 2 4 8

7-16 Nonlinear least square curve fit on the decomposed jet velocity profile for Case
V ...................................................................................... . 2 4 9

7-17 Nonlinear least square curve fit on the decomposed jet velocity profile for Case
V II ........................................................................................2 50

7-18 Nonlinear least square curve fit on the decomposed jet velocity profile for Case
IX .................. ......................................................... ................ 2 5 1

7-19 Nonlinear least square curve fit on the decomposed jet velocity profile for Case
X I. ........................................................................................2 52

7-20 Nonlinear least square curve fit on the decomposed jet velocity profile for Case
X III ...................................... .................................................... 2 5 3

7-21 Comparison between CFD velocity profile, decomposed jet velocity profile, and
modeled velocity profile, at the orifice exit, for four phase angles during a
cy cle. ..............................................................................2 55

7-22 Test case comparison between CFD data and the scaling law based on the
velocity profile at four phase angles during a cycle.................................... 260

7-23 Methodology for the development of the integral parameters based scaling law...262









7-24 Comparison between the results of the integral parameters from the scaling law
and the CFD data for the test case.................................... ......................... 268

7-25 Example of a practical application of the ZNMF actuator reduced-order model
in a numerical simulation of flow past a flat plate ............................................271

8-1 POD analysis applied on numerical data for ZNMF actuator with a grazing BL...278

8-2 Use of quarter-wavelength open tube to provide an infinite impedance. ..............280

8-3 Representative MEMS ZNMF actuator. ....................................... ............... 281

8-4 Predicted output of MEMS ZNMF actuator .........................................................281

A-1 Acoustic test duct and siren showing a liner panel test configuration..................285

A-2 Schematic of test apparatus used in Hersh and Walker. ..........................286

A-3 Apparatus for the measurement of the acoustic impedance of a perforate used
by K irby and C um m ings. ........................................ .........................................288

A-4 Sketch of NASA Grazing Impedance Tube..........................................................290

B -l H elm holtz resonator ........................................................................ ..................29 1

C-1 Rectangular slot geometry and coordinate axis definition............... .......... 295

D-l Orifice details with coordinate system .... ........... ........ .......................... 303

F-l Schematic of A) the sharp-interface method on a fixed Cartesian mesh, and B)
the ZNMF actuator interacting with a grazing flow. ............................................328

F-2 Typical mesh used for the computations. A) 2D simulation. B) 3D simulation...329

F-3 Example of 2D and 3D numerical results of ZNMF interacting with a grazing
b o u n d ary lay er ................................................................................... 3 2 9


xviii














LIST OF SYMBOLS AND ABBREVIATIONS

c, isentropic air speed of sound [m/s]

Ca cavity acoustic compliance = V/pco2 [s2.m4/kg]

CD diaphragm short-circuit acoustic compliance =AV/Pl 0 [s2m4/kg]

CD orifice discharge coefficient [1]

C. skin friction coefficient = r,/O.5pV2 [1]

C momentum coefficient during the time of discharge [1]

C"2 successive moments of jet velocity profile [1]

d orifice diameter [m]

dH hydraulic diameter = 4(area)/(wetted perimeter) [m]

D orifice entrance diameter (facing the cavity) [m]

Dc cavity diameter (for cylindrical cavities) [m]

f actuation frequency [Hz]

f, driver natural frequency [Hz]

fH Helmholtz frequency= (1/2;) co~ n/V = 1/ (2z (M^, +Mad )C)c [Hz]

fn natural frequency of the uncontrolled flow [Hz]

f, fundamental frequency [Hz]

f, f2 synthetic jet lowest and highest resonant frequencies, respectively [Hz]









h orifice height [m]

h' effective length of the orifice = h+h0 [m]

ha "end correction" of the orifice = 0.964S- [m]

H cavity depth (m) / boundary layer shape factor = 0/3* [1]

I0 impulse per unit length [1]

k wave number = c/co [m-1]

Kd nondimensional orifice loss coefficient [1]

L0 stroke length [m]


MaD diaphragm acoustic mass = A 2 [w r2 rdr [kg/4]

M, orifice acoustic mass due to inertia effect [kg/m4]

M o orifice acoustic mass = M + + Mad [kg/m4]

MaRad orifice acoustic radiation mass [kg/m4]

p' acoustic pressure [Pa]

P differential pressure on the diaphragm [Pa]

P, incident pressure [Pa]

Pw Power [W]

q' acoustic particle volume velocity [m3/s]

Qc volume flow rate through the cavity = Q Qd [m3/s]

Qd volume flow rate displaced by the driver = jiAV [m3/s]

Q, volume flow rate through the orifice [m3/s]









Q, time averaged orifice volume flow rate during the expulsion stroke [m3/s]

r radial coordinate in cylindrical coordinate system [m]

R radius of curvature of the surface [m]

R, diaphragm acoustic resistance = 24JMaD /C [kg/m4s]

R, viscous orifice acoustic resistance [kg/m4s]

Roohn linear orifice acoustic resistance = R, [kg/m4s]

Ron, nonlinear orifice acoustic resistance [kg/m4s]

R? specific resistance [kg/m2s]

Re jet Reynolds number = Vd/v [1]

s Laplace variable =jco [rad/s]

S Stokes number = od/v [1]

St jet Strouhal number = cd/V [1]

So cavity cross sectional area [m2]

Sd driver cross sectional area [m2]

S, orifice neck area [m2]

u' acoustic particle velocity [m/s]

Ub bias flow velocity through the orifice [m/s]

u, wall friction velocity [m/s]

U, freestream mean velocity [m/s]

VCL centerline orifice velocity [m/s]









V( spatial averaged jet exit velocity = Q /S, = (;r/2) V [m/s]

V spatial and time-averaged jet exit velocity during the expulsion stroke [m/s]

Vac input ac voltage [V]

V normalized jet velocity = vJ /U [m/s]

w length of a rectangular orifice [m]

w(r) transverse displacement of the diaphragm [m]

W width of the cavity [m]

W, centerline amplitude of the driver [m]

X0 acoustic reactance = o)M [kg/m4s]

X, specific reactance [kg/m2s]

XI2 skewness of jet velocity profile [1]

Yd vibrating driver displacement [m]

yJ fluid particle displacement at the orifice [m]

Z, acoustic impedance = R + jX = p'/q' [kg/m4.2]

Z c acoustic cavity impedance = (jcoCac) 1= APj(Q Qj ) [kg/m4.s2]

Z o acoustic impedance of the orifice = Ror,, + ko,,,i + joMo = A/Qj [kg/m4s2]

ZBL acoustic impedance of the grazing boundary layer = RL + jXL [kg/m4.2]

Zo, total acoustic impedance of the orifice = Zo + ZBL [kg/m4s2]

Z, specific impedance = R + jXo = p'/u' [kg/m2.2]

Z,p perforate specific impedance = R, + jX, = Zo/cr [kg/m2s2]









a thermal diffusivity [m2/s]

p nondimensional pressure gradient = (3*/rz)(dP/dx) [1]

x normalized reactance [1]

3 boundary layer thickness [m]

3* boundary layer displacement thickness [m]

stokes Stokes layer thickness = -v/O [m]

Acp normalized pressure drop = (pO -Py 0.5pV) [1]

AN cavity pressure [Pa]

AV volume displaced by the driver [m3]

0, electroacoustic turns ratio of the piezoceramic diaphragm = Id/C, [Pa/ V]

&Of phase difference between the incident sound field and the cavity sound field [deg]

7 ratio of the specific heats [1]

A wavelength = co/f = 27/k [m]

p dynamic viscosity = pv [kg/m's]

v cinematic viscosity [m2/s]

p density [kg/m3]

PA area density [kg/m2]

0 boundary layer momentum thickness [m] / normalized resistance [1]

a porosity of the perforate plate = Nhole x (hole area)/total area [%]

a ratio of the orifice to cavity cross sectional area = S,/SC [1]

z, wall shear stress [kg/m s2]


xxiii









V cavity volume [mm3]

co radian frequency = 2;if [rad/s]

Q, vorticity flux [m2/s]

" damping coefficient [1] / normalized impedance = 0 + j [1]

Cp normalized impedance of a perforate = O + jp [1]

S compliance ratio = CD/CaC [1]

9NR mass ratio = MaD/MA [1]

91 resistance ratio = R, /RD [1]


Commonly used subscripts:

a acoustic domain

c cavity

CL centerline

d driver

D diaphragm

ex expulsion phase of the cycle

in injection phase of the cycle

j jet

lin linear

nl nonlinear

p perforate

0 specific

o0 freestream


xxiv









Commonly used superscripts:


spatial averaged

spatial and time averaged

fluctuating quantity

Abbreviations:

BL Boundary Layer

CFD Computational Fluid Dynamics

HWA Hot Wire Anemometry

LDV Laser Doppler Velocimetry

LEM Lumped Element Modeling

MEMS Micro Electromechanical Systems

MSV Mean Square Value

PIV Particle Image Velocimetry

POD Proper Orthogonal Decomposition

RMS Root Mean Square

ZNMF Zero-Net Mass Flux


Throughout this dissertation, the term syntheticc jet actuator has the same meaning

as zero-net mass flux actuator, although the former is physically more restricting to

specific applications (strictly speaking, a jet must be formed). Similarly, the terms

grazingflow and bias flow in the acoustic community are used interchangeably with the

respective fluid dynamics terminology crossflow and mean flow, since they refer to the

same phenomenon.















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

ON THE MODELING AND DESIGN OF ZERO-NET MASS FLUX ACTUATORS

By

Quentin Gallas

May 2005

Chair: Louis Cattafesta
Major Department: Mechanical and Aerospace Engineering

This dissertation discusses the fundamental dynamics of zero-net mass flux

(ZNMF) actuators commonly used in active flow-control applications. The present work

addresses unresolved technical issues by providing a clear physical understanding of how

these devices behave in a quiescent medium and interact with an external boundary layer

by developing and validating reduced-order models. The results are expected to

ultimately aid in the analysis and development of design tools for ZNMF actuators in

flow-control applications.

The case of an isolated ZNMF actuator is first documented. A dimensional

analysis identifies the key governing parameters of such a device, and a rigorous

investigation of the device physics is conducted based on various theoretical analyses,

phase-locked measurements of orifice velocity, diaphragm displacement, and cavity

pressure fluctuations, and available numerical simulations. The symmetric, sharp orifice

exit velocity profile is shown to be primarily a function of the Strouhal and Reynolds

numbers and orifice aspect ratio. The equivalence between Strouhal number and


xxvi









dimensionless stoke length is also demonstrated. A criterion is developed and validated,

namely that the actuation-to-Helmholtz frequency ratio is less than 0.5, for the flow in the

actuator cavity to be approximately incompressible. An improved lumped element

modeling technique developed from the available data is developed and is in reasonable

agreement with experimental results.

Next, the case in which a ZNMF actuator interacts with an external grazing

boundary layer is examined. Again, dimensional analysis is used to identify the

dimensionless parameters, and the interaction mechanisms are discussed in detail for

different applications. An acoustic impedance model (based on the NASA "ZKTL

model") of the grazing flow influence is then obtained from a critical survey of previous

work and implemented in the lumped element model. Two scaling laws are then

developed to model the jet velocity profile resulting from the interaction the profiles are

predicted as a function of local actuator and flow condition and can serve as approximate

boundary conditions for numerical simulations. Finally, extensive discussion is provided

to guide future modeling efforts.


xxvii














CHAPTER 1
INTRODUCTION

Motivation

The past decade has seen numerous studies concerning an exciting type of active

flow control actuator. Zero-net mass flux (ZNMF) devices, also known as synthetic jets,

have emerged as versatile actuators with potential applications such as thrust vectoring of

jets (Smith and Glezer 1997), heat transfer augmentation (Campbell et al. 1998; Guarino

and Manno 2001), active control of separation for low Mach and Reynolds numbers

(Wygnanski 1997; Smith et al. 1998; Amitay et al. 1999; Crook et al. 1999; Holman et al.

2003) or transonic Mach numbers and moderate Reynolds numbers (Seifert and Pack

1999, 2000a), and drag reduction in turbulent boundary layers (Rathnasingham and

Breuer 1997; Lee and Goldstein 2001). This versatility is primarily due to several

reasons. First, these devices provide unsteady forcing, which has proven to be more

effective than its steady counterpart (Seifert et al. 1993).

Second, since the jet is synthesized from the working fluid, complex fluid circuits

are not required. Finally the actuation frequency and waveform can usually be

customized for a particular flow configuration. Synthetic jets exhausting into a quiescent

medium have been studied extensively both experimentally and numerically.

Additionally, other studies have focused on the interaction with an external boundary

layer for the diverse applications mentioned above. However, many questions remain

unanswered regarding the fundamental physics that govern such complex devices.









Practically, because of the presence of rich flow physics and multiple flow

mechanisms, proper implementation of these actuators in realistic applications requires

design tools. In turn, simple design tools benefit significantly from low-order dynamical

models. However, no suitable models or design tools exist because of insufficient

understanding as to how the performance of ZNMF actuator devices scales with the

governing nondimensional parameters. Numerous parametric studies provide a glimpse

of how the performance characteristics of ZNMF actuators and their control effectiveness

depend on a number of geometrical, structural, and flow parameters (Rathnasingham and

Breuer 1997; Crook and Wood 2001; He et al. 2001; Gallas et al. 2003a). However,

nondimensional scaling laws are required since they form an essential component in the

design and deployment of ZNMF actuators in practical flow control applications.

For instance, scaling laws are expected to play an important role in the

aerodynamic design of wings that, in the future, may use ZNMF devices for separation

control. The current design paradigm in the aerospace industry relies heavily on steady

Reynolds Averaged Navier Stokes (RANS) computations. A validated unsteady RANS

(URANS) design tool is required for separation control applications at transonic Mach

numbers and flight Reynolds number. However, these computations can be quite

expensive and time-consuming. Direct modeling of ZNMF devices in these

computations is expected to considerably increase this expense, since the simulations

must resolve the flow details in the vicinity of the actuator while also capturing the global

flow characteristics. A viable alternative to minimize this cost is to simply model the

effect of the ZNMF device as a time- and flow-dependant boundary condition in the

URANS calculation. Such an approach requires that the device be characterized by a









small set of nondimensional parameters, and the behavior of the actuator must be well

understood over a wide range of conditions.

Furthermore, successful implementation of robust closed-loop control

methodologies for this class of actuators calls for simple (yet effective) mathematical

models, thereby emphasizing the need to develop a reduced-order model of the flow.

Such low-order models will clearly aid in the analysis and development of design tools

for sizing, design and deployment of these actuators. Below, an overview of the basic

operating principles of a ZNMF actuator is provided.

Overview of a Zero-Net Mass Flux Actuator

Typically, ZNMF devices are used to inject unsteady disturbances into a shear

flow, which is known to be a useful tool for active flow control. Most flow control

techniques require a fluid source or sink, such as steady or pulsed suction (or blowing),

vortex-generator jets (Sondergaard et al. 2002; Eldredge and Bons 2004), etc., which

introduces additional constraints in the design of the actuator and sometimes results in

complicated hardware. This motivates the development of ZNMF actuators, which

introduce flow perturbations with zero-net mass injection, the large coherent structures

being synthesized from the surrounding working fluid (hence the name "synthetic jet").

A typical ZNMF device with different transducers is shown in Figure 1-1. In

general, a ZNMF actuator contains three components: an oscillatory driver (examples of

which are discussed below), a cavity, and an orifice or slot. The oscillating driver

compresses and expands the fluid in the cavity by altering the cavity volume V at the

excitation frequency f to create pressure oscillations. As the cavity volume is

decreased, the fluid is compressed in the cavity and expels some fluid through the orifice.









The time and spatial averaged ejection velocity during this portion of the cycle is denoted

V Similarly, as the cavity volume is increased, the fluid expands in the cavity and

ingests some fluid through the orifice. Common orifice geometries include simple

axisymmetric hole (height h, diameter d) and rectangular slot (height h, depth d and

width w), as schematically shown in Figure 1-2. Downstream from the orifice, a jet

laminarr or turbulent, depending on the jet Reynolds number Re= Fd/v) is then

synthesized from the entrained fluid and sheds vortices when the driver oscillations

exceed a critical amplitude (Utturkar et al. 2003).


pU,,M


J
dIHI


Volume V





U',M
P. --


A '0




Volume V


I sin (27ift)
Ft


I 1--r signal (f)

Figure 1-1: Schematic of typical zero-net mass flux devices interacting with a boundary
layer, showing three different types of excitation mechanisms. A)
Piezoelectric diaphragm. B) Oscillating piston. C) Acoustic excitation.









Even though no net mass is injected into the embedded flow during a cycle, a

non-zero transfer of momentum is established with the surrounding flow. The exterior

flow, if present, usually consists of a turbulent boundary layer (since most practical

applications deal with such a turbulent flow) and is characterized by the freestream

velocity U. and acoustic speed c., pressure gradient dP/dx, radius of curvature R,

thermal diffusivity a~, and displacement 53 and momentum 0 thicknesses. Finally, the

ambient fluid is characterized by its density pm and dynamic viscosity /u,.




L y
A B L


I- -t h zx V

d vi h
I \/'
Figure 1-2: Orifice geometry. A) Axisymmetric. B) Rectangular.

Figure 1-1 shows three kinds of drivers commonly used to generate a synthetic jet:

* An oscillating membrane (usually a piezoelectric patch mounted on one side of a
metallic shim and driven by an ac voltage).

* A piston mounted in the cavity (using an electromagnetic shaker, a camshaft, etc.).

* A loudspeaker enclosed in the cavity (an electrodynamic voice-coil transducer).

For each of them, we are interested mainly in the volume displacement generated

by the driver that will eject and ingest the fluid through the orifice. Although each driver

will obviously have its own characteristics, common parameters of a generic driver are its

frequency of excitation f, the corresponding volume AV that it displaces, and the

dynamic modal characteristics of the driver.










A Porous B Acoustic Liners
A /"^ Porous B __
Sface sheet


V ^d Inlet



Honeycomb core sheet Nacelle Fan


Figure 1-3: Helmholtz resonators arrays. A) Schematic. B) Application in engine
nacelle acoustic liners.

Although noticeable differences exist, it is worthwhile to compare synthetic jets

with the phenomenon of acoustic flow generation, the acoustic streaming, extensively

studied by aeroacousticians in the past (e.g., Lighthill 1978). Acoustic streaming is the

result of a steady flow produced by an acoustic field and is the evidence of the generation

of vorticity by the sound, which occurs for example when sound impinges on solid

boundaries. Quoting Howe (1998, p. 410),

When a sound wave impinges on a solid surface in the absence of mean flow, the
dissipated energy is usually converted directly into heat through viscous action. At
very high acoustic amplitudes, however, free vorticity may still be formed at edges,
and dissipation may take place, as in the presence of mean flow, by the generation
of vortical kinetic energy which escapes from the interaction zone by self-
induction. This nonlinear mechanism can be important in small perforates or
apertures.

This type of flow generation could be relevant in the application of ZNMF devices

where similar nonlinear flow through the orifice is expected. In particular, ZNMF

devices are similar to flow-induced resonators, such as Helmholtz resonators used in

acoustic liners as sound-absorber devices. As Figure 1-3 shows, a simple single degree-

of-freedom (SDOF) liner consists of a perforate sheet backed with honeycomb cavities

and interacting with a grazing flow. Similar liners with a second cavity (or more) are

commonly used in engine nacelles to attenuate the sound noise level. More recently,









Flynn et al. (1990) and Urzynicok and Fernholz (2002) used Helmholtz resonators for

flow control applications. More details will be given in subsequent sections.

Now that an overview of the problem has been presented along with a general

description of a ZNMF device, an in-depth literature survey is given to familiarize the

reader with the existing developments on these subjects and to clearly set the scope of the

current investigation. The objectives of this research are then formulated and the

technical approach described to reach these goals.

Literature Review

This section presents an overview of the relevant research found in the open

literature. The goal is to highlight and extract the principal features of the actuator and

associated fluid dynamics, and to identify unresolved issues. First, the simpler yet

practically significant case in which the synthetic jet exhausts into a quiescent medium is

carefully reviewed. The case in which the synthetic jet interacts with a grazing boundary

layer or crossflow is considered next. The survey reveals available experimental and

numerical simulation data on the local interaction of a ZNMF device with an external

boundary layer. In each subsection, the diverse applications that have employed a ZNMF

actuator are first reviewed, as well as the different modeling approaches used. In the case

of the presence of a grazing boundary layer, examples of applications in the field of fluid

dynamics and aeroacoustics are presented where a parallel with sound absorber

technology is drawn.

Isolated Zero-Net Mass Flux Devices

Numerous studies have addressed the fundamentals and applications of isolated

ZNMF actuators. The list presented next is by no means exhaustive but reflects the major

points and contributions to the understanding of such devices.









Applications

Mixing enhancement, heat transfer, or thrust vectoring are the major applications of

isolated ZNMF devices, as opposed to active flow control applications when the actuator

is interacting with an external boundary layer that will be seen in the next section.

Chen et al. (1999) demonstrated the use of ZNMF actuators to enhance mixing in a

gas turbine combustor. They used two streams of hot and cold gas to simulate the mixing

and they measured the temperature distribution downstream of the synthetic jet to

determine the effectiveness of the mixing. Their experiments showed that ZNMF devices

could improve mixing in a turbine jet engine without using additional cold dilution air.

Similarly, modification and control of small-scale motions and mixing processes

via ZNMF actuators were investigated by Davis et al. (1999). Their experiments used an

array of ZNMF devices placed around the perimeter of the primary jet. It was

demonstrated that the use of these actuators made the shear layer of the primary jet

spread faster with downstream distance, and the centerline velocity decreased faster in

the streamwise direction, while the velocity fluctuations near the centerline were

increased.

In a heat transfer application, Campbell et al. (1998) explored the option of using

ZNMF actuators to cool laptop computers. A small electromagnetic actuator was used to

create the jet that was used to cool the processor of a laptop computer. Using optimum

combination of various design parameters, the synthesized jet was able to lower the

processor operating temperature rise by 22% when compared to the uncontrolled case.

Not surprisingly, it was envisioned that optimization of the device design could lead to

further improvement in the performance.









Likewise, a thermal characterization study of laminar air jet impingement cooling

of electronic components in a representative geometry of the CPU compartment was

reported by Guarino and Manno (2001). They used a finite control-volume technique to

solve for velocity and temperature fields (including convection, conduction and radiation

effects). With jet Reynolds numbers ranging from 63 to 1500, their study confirmed the

importance of the Reynolds number (rather than jet size) for effective heat transfer.

Proof of the above concept was demonstrated with a numerical model of a laptop

computer.

In a thrust vectoring application, Smith et al. (1999) performed an experiment to

study the formation and interaction of two adjacent ZNMF actuators placed beside the

rectangular conduit of the primary jet. Each actuator had two modes of operation

depending on direction of the synthetic jet with respect to the primary jet. It was

demonstrated that the primary jet could be vectored at different angles by operating only

one or both actuators in different modes. Later, Guo et al. (2000) numerically simulated

these experimental results. Similarly, Smith and Glezer (2002) experimentally studied

the vectoring effect between ZNMF devices near a steady jet with varying velocity, while

Pack and Seifert (1999) did the same by employing periodic excitation.

Others studies focused on characterizing isolated ZNMF actuators (Crook and

Wood 2001; Smith and Glezer 1998). For instance, a careful experimental study by

Smith and Glezer (1998) shows the formation and evolution of two-dimensional synthetic

jets evolving in a quiescent medium for a limited range of jet performance parameters.

The synthetic jets were viewed using schlieren images via the use of a small tracer gas,









and velocity fields were acquired by hot wire anemometry at different locations in space,

for phase-locked and long-time averaged signals.

In these experiments, along with those from Carter and Soria (2002), Bera et al.

(2001) or Smith and Swift (2003a), the similarities and differences between a synthetic

jet and a continuous jet have been noted and examined. Specifically, Amitay et al. (1998)

and Smith et al. (1998) confirmed self-similar velocity profiles in the asymptotic regions

via a direct comparison at the same jet Reynolds number.

In terms of design characteristics, it is of practical importance to know if the ZNMF

actuator synthesizes a jet via discrete vortex shedding. Utturkar et al. (2003) derived and

validated a criterion for whether a jet is formed at the orifice exit of the actuator. It is

governed by the square of the orifice Stokes number S2 = cod2/v and the jet Reynolds

number Re= Vd/v based on the orifice diameter d and the spatially-averaged exit

velocity V during the expulsion stroke, which holds for both axisymmetric and two

dimensional orifice geometry. Their derivation is based on the criterion that the induced

velocity at the orifice neck must be greater than the suction velocity for the vortices to be

shed; and was verified by numerical simulations and by experiments. Their data support

the jet formation criterion Re/S2 >K, where K is 0(1). In another attempt, Shuster

and Smith (2004) based their criterion from PIV flow visualization for different circular

orifice shape (straight, beveled or rounded) and found that it is governed by the

nondimensional stroke length Lo/d and the orifice geometry, where LO is the fluid

stroke length assuming a slug flow model for the jet velocity profile.









Modeling approaches

Few analytical models have yet characterized ZNMF actuator behavior, even for

the simple case of a quiescent medium. Actually, most of the studies have been

performed either via experimental efforts or numerical simulations.

Several attempts have been made to reduce computational costs. For instance, Kral

et al. (1997) performed two-dimensional, incompressible simulations of an isolated

ZNMF actuator. Interestingly, their study was performed in the absence of the actuator

per se. Instead, a sinusoidal velocity profile was prescribed as a boundary condition at

the jet exit in lieu of simulating the actuator, including calculations in the cavity. Both

laminar and turbulent jets were studied, and although the laminar jet simulation failed to

capture the breakdown of the vortex train that is commonly observed experimentally, the

turbulent model showed the counter-rotating vortices quickly dissipating. This suggests

that the modeled boundary condition could capture some of the features of the jet,

without the simulation of the flow inside the actuator cavity.

In another numerical study, Rizzetta et al. (1999) used a direct numerical

simulation (DNS) to solve the compressible Navier-Stokes equations for both 2D and 3D

domain. They calculated both the interior of the actuator cavity and the external

flowfield, where the cavity flow was simulated by prescribing an oscillating boundary

condition at one of the cavity surfaces. However, the recorded profiles of the periodic jet

exit velocity were used as the boundary condition for the exterior domain. Hence, by

using this decoupling technique, they could calculate the exterior flow without

simultaneously simulating the flow inside the actuator cavity. To further reduce the

computational cost, the planes of symmetry were forced at the jet centerline and at the

mid-span location, so only a quarter of the real actuator was simulated. However, the 2D









simulations were not able to capture the breakdown of the vortices as a result of the

spanwise instabilities.

Cavity design earned the attention of several researchers, such as Rizzeta et al.

(1999) presented above; Lee and Goldstein (2002), who performed a 2D incompressible

DNS study of isolated ZNMF actuators; and Utturkar et al. (2002), who did a thorough

investigation of the sensitivity of the jet to cavity design using a 2D unsteady viscous

incompressible solver using complex immersed moving boundaries on Cartesian grids.

Utturkar et al. (2002) found that the placement of the driver inside the cavity

(perpendicular or normal to the orifice exit) does not significantly affect the output

characteristics.

The orifice is an important component of actuator modeling. While numerous

parametric studies examined various orifice geometry and flow conditions, a clear

understanding of the loss mechanism is still lacking. Investigations based on orifice

flows have been carried as far back as the 1950s. A comprehensive experimental study

was carried out by Ingard and Ising (1967) that examined the acoustic nonlinearity of the

orifice. It was observed that the relation between the pressure and the velocity transitions

from linear to quadratic nature as the transmitted velocity u' crosses a threshold value

nrtlc, i.e p' pcou' if u' < u rtC and else p' pu'2, where p is the density, co is the

speed of sound and p' is the sound pressure level. The phase relationship between the

pressure fluctuations and the velocity were also investigated. Later, Seifert and Pack

(1999), in an effort to investigate the effect of oscillatory blowing on flow separation,

developed a simple scaling between the pressure fluctuation inside the cavity and the

velocity fluctuation. This scaling agrees with the work of Ingard and Ising (1967) and









states that for low amplitude blowing u' ~ p'/pco whereas for high amplitude blowing

u'~7p/p.

Recently, similar to the work by Smith and Swift (2003b) who experimentally

studied the losses in an oscillatory flow through a rounded slot, Gallas et al (2004)

performed a conjoint numerical and experimental investigation on the orifice flow for

sharp edges to understand the unsteady flow behavior and associated losses in the

orifice/slot of ZNMF devices exhausting in a quiescent medium. It has been found that

the flow field emanating from the orifice/slot is characterized by both linear and

nonlinear losses, governed by key nondimensional parameters such as Stokes number S,

Reynolds number Re, and stroke length Lo.

In terms of the orifice geometry shapes, a large variety has been used, although no

one has determined the most "efficient." While straight orifices are the most common,

the orifice thickness to diameter ratio is widely varied. It ranges from perforate orifice

plates (see discussion on Helmholtz resonators) having very small thickness with the

viscous effect confined at the edges where the vortices are shed, to long and thick orifices

wherein the flow could be assumed fully-developed (Lee and Goldstein 2002). In the

case of a thick orifice, the flow can be modeled as a pressure driven oscillatory pipe or

channel flow where the so-called "Richardson effect" may appear at high Stokes number

of 0(10) (Gallas et al. 2003a). Furthermore, Gallas (2002) experimentally determined a

limit of the fully-developed flow assumption through a cylindrical orifice in terms of the

orifice aspect ratio h/d > 1.

Otherwise, the orifice could also have round edges or a beveled shape (NASA

workshop CFDVal-Case 2, 2004). Another design, referred to as the springboard









actuator, has been proposed by Jacobson and Reynolds (1995), in which both a small and

a large gap are used for the slot. In the case of the presence of an external boundary

layer, Bridges and Smith (2001) and Milanovic and Zaman (2005) experimentally studied

different orifice shapes such as clustered, sharp beveled, or with different angles with

respect to the incoming flow. The principal changes in the flow field between the

different orifices studied were mostly found in the local vicinity of the orifice actuator,

and less in the far (or global) field, for the specific flow conditions used. Finally, the

predominant difference between the different orifices is that of a circular orifice versus

rectangular slot. Experimental studies often employ these two geometries, whereas

numerical simulations preferably use the latter for computational cost considerations.

In terms of analytical modeling of ZNMF actuators, few efforts have been

conducted, even for the simple case of a quiescent medium. Nonetheless, Rathnasingham

and Breuer (1997) developed a simple analytical/empirical model that couples the

structural and fluid characteristics of the device to produce a set of coupled, first-order,

non-linear differential equations. In their empirical model, the flow in the slot is assumed

to be inviscid and incompressible and the unsteady Bernoulli equation is used to solve the

oscillatory flow. Crook et al. (1999) experimentally compared Rathnasingham and

Breuer's simple analytical model and found that the agreement between the predicted and

measured dependence of the centerline velocity on the orifice diameter and cavity height

was poor, although the trends were similar. This discrepancy is mainly due to the lack of

viscous effect in the orifice model, as well as the Stokes number dependence inside the

orifice that is not considered by the flow model and which could lead to a non-parabolic

velocity profile.









Otherwise, with the aim of achieving real-time control of synthetic jet actuated

flows, Rediniotis et al. (2002) derived a low-order model of two dimensional synthetic jet

flows using proper orthogonal decomposition (POD). A dynamical model of the flow

was derived via Galerkin projection for specific Stokes and Reynolds number values, and

they accurately modeled the flow field in the open loop response with only four modes.

However, the suitability of this approach as a general analysis/design tool was not

addressed.

More recently in Gallas et al. (2003a), the author presented a lumped element

model of a piezoelectric-driven synthetic jet actuator exhausting in a quiescent medium.

Methods to estimate the parameters of the lumped element model were presented and

experiments were performed to isolate different components of the model and evaluate

their suitability. The model was applied to two prototypical ZNMF actuators and was

found to provide good agreement with the measured performance over a wide frequency

range. The results reveal that lumped element modeling (LEM) can be used to provide a

reasonable estimate of the frequency response of the device as a function of the signal

input, device geometry, and material and fluid properties.

Additionally, based on this modeling approach, Gallas et al. (2003b) successfully

optimized the performance of a baseline ZNMF actuator for specific applications. They

also suggest a roadmap for the more general optimal design synthesis problem, where the

end user must translate desirable actuator characteristics into quantitative design goals.

Zero-Net Mass Flux Devices with the Addition of Crossflow

By now letting a ZNMF actuator interact with an external boundary layer or

grazing flow, a wide range of applications can be envisioned, from active control of

separation in aerodynamics to sound absorber technology in aeroacoustics.









Fluid dynamic applications

While the responsible physical mechanism is still unclear, it has been shown that

the interaction of ZNMF actuators with a crossflow can displace the local streamlines and

induce an apparent (or virtual) change in the shape of the surface in which the devices are

embedded and when high frequency forcing is used (Honohan et al. 2000; Honohan

2003; Mittal and Rampuggoon 2002). Changes in the flow are thereby generated on

length scales that are one to two orders of magnitude larger than the characteristic scale

of the jet.

Furthermore, ZNMF devices have been demonstrated to help in the delay of

boundary layer separation on cylinders and airfoils, hence generating lift and reducing

drag or also increasing the stall margin for the latter. For cylinders, the case of laminar

boundary layers has been investigated by Amitay et al. (1997), and the case of turbulent

separation by Bera et al. (1998). For airfoils, research has been conducted, for example,

by Seifert et al. (1993) and Greenblatt and Wygnanski (2002). However, in ZNMF-based

separation control, key issues such as optimal excitation frequencies and waveforms

(Seifert et al. 1996; Yehoshua and Seifert 2003), as well as pressure gradient and

curvature effects still remain to be rigorously investigated (Wygnanski 1997).

For instance, it has been shown by some researchers that control authority varies

monotonically with V,/U, (Seifert et al. 1993, 1996, 1999; Glezer and Amitay 2002;

Mittal and Rampuggoon 2002) up to a point where a further increase will likely

completely disrupt the boundary layer, and where Vi can be the peak, rms or spatial-

averaged jet velocity during the ejection portion of the cycle. On the other hand, control

authority has a highly non-monotonic variation with F+ (Seifert and Pack 2000b;









Greenblatt and Wygnanski 2003; Glezer et al. 2003. Amitay and Glezer 2002), hence the

existing current debate in choosing the optimum value for F where F = f/f

represents the jet actuation frequency f that is non-dimensionalized by some natural

frequency f, in the uncontrolled flow. In fact, it is still unclear about what definition of

f, should be used, since it depends on the flow conditions. For example, f, could either

be the characteristic frequency of the separation region, the vortex shedding frequency in

the wake, or the natural vortex rollup frequency of the shear layer, depending on whether

separation "delay" control or separation "alleviation" control is sought (Cattafesta and

Mittal, private communication, 2004).

As noted earlier, another key issue in ZNMF devices is the form of the excitation

signal. Researchers have used single sinusoids, but low-frequency amplitude-modulated

(AM) signals (Park et al. 2001), burst mode signals (Yehoshua and Seifert 2003), and

various envelopes have also been investigated (Margalit et al. 2002; Wiltse and Glezer

1993). From these studies, it seems clear that the input signal waveform should be

carefully chosen function of the natural frequency of uncontrolled flow f, as discussed

above. In addition, it emphasizes the fact that the dynamics of the actuator should not be

ignored.

Also of interest for flow control applications is the interaction of multiple ZNMF

actuators (or actuator arrays) with an external boundary layer, which has been

experimentally investigated by several researchers (Amitay et al. 1998; Watson et al.

2003; Amitay et al. 2000; Wood et al. 2000; Ritchie and Seitzman 2000). However, the

relative phasing effect between each actuator was usually not investigated. On the other

hand, Holman et al. (2003) investigated the effect of adjacent synthetic jet actuators,









including their relative phasing, in an airfoil separation control application. They found

that, for the single flow condition studied, separation control was independent of the

relative phase, and also that for low actuation amplitudes, actuator placement on the

airfoil surface could be critical in achieving desired flow control. Similarly, Orkwis and

Filz (2005) numerically investigated the effect of the proximity between two adjacent

ZNMF actuators in crossflow and found that favorable interactions between the two

actuators could be achieved within a certain distance that separates them, but the optimal

separation is different whether they are in phase or out of phase from each other.

Finally, to the author's knowledge, besides a first scaling analysis performed by

Rampunggoon (2001) which is based on a parameterization of the successive moments

and skewness of the jet velocity profile, along with the study by McCormick (2000) that

presents an electro-acoustic model to describe the actuator characteristics (in a similar

manner to the lumped element modeling approach used by Gallas et al. 2003b), no other

low-order models have been developed for a ZNMF actuator interacting with an external

boundary layer.

Aeroacoustics applications

For the past fifty years, people in the acoustic community have tried to predict the

flow past an open cavity (Elder 1978; Meissner 1987) or a Helmholtz resonator (Howe

1981b; Nelson et al. 1981). This is a generic denomination for applications such as

aircraft cavities, acoustic liners, open sunroofs, mufflers for intake and exhaust systems,

or simply perforates. This research lies in the domain of acoustics of fluid-structure

interactions which has generated significant attention from numerous researchers.

As noted earlier, a parallel with ZNMF actuators can be draw with the study of

acoustic liners, shown in Figure 1-3B. More specifically, the goal is usually to compute









the acoustic impedance of the liner, since the notion of impedance simply relates a

particle or flow velocity to the corresponding pressure. Such knowledge is required to

design and implement liners in an engine nacelle.

However, researchers are still facing great challenges in extracting suitable

impedance models of these perforate liners, usually composed of Helmholtz resonators.

In fact, because of the presence of flow over the orifice, rigorous mathematical modeling

of the interaction mechanisms are very difficult to obtain, and the present state of

analytical and numerical codes do not allow direct modeling of these interactions at

relevant Reynolds numbers, as seen earlier in the case of ZNMF actuators.

Consequently, most of the existing models of grazing flow past Helmholtz resonators are

empirical or, at most, simplified mathematically models.

Modeling approaches

First of all, in terms of impedance models of acoustic liners, Dequand et al. (2003)

and Lee and Ih (2003) provide a good review of the existing models, along with their

intrinsic limitations. The main distinctions between the proposed models lay first in the

orifice model, then in the characterization of the grazing flow, and finally in the addition

or not of a mean bias flow through the orifice (not to be confused with grazing flow over

the orifice). The cavity is often modeled as a classical resonator having a linear response

(mass-spring system). When a bias flow is included, the prediction of its effect on the

orifice impedance is usually carried out within the mechanism of sound-vortex

interaction. And when grazing flow is present, most of the orifice impedance models are

either deduced from experimental data or rely on empiricism.

With regards to orifice modeling, Ingard and Ising (1967) included effective end

corrections in their impedance model that take care of the acoustic nonlinearity of the









orifice (mainly dependent on the ratio of the acoustic orifice momentum to the boundary

layer momentum when a grazing flow is included). Depending on the flow conditions of

the application, either low frequency or high frequency assumptions are used to model

the flow through the orifice. Also, standard assumption is that the orifice dimensions are

much smaller than the acoustic wavelength of interest.

Another important point to note is on the porosity factor of a perforate plate.

Because of the direct application of such a device to engine nacelle liners, the solution for

a single orifice impedance is usually derived and is then extended to multiple holes

geometry. The simple relation between the specific impedance of a perforate and a single

orifice, Z0p = Zo/c, holds when the orifices are not too close from each other in order to

alleviate any jetting interaction effect between them. Here, the porosity factor is defined

by =Nholes x (hole area)/total area, where Nhol, is the number of orifices in the

perforate. Ingard (1953) states that the resonators can be treated independently of each

others if the distance between the orifices is greater than half of the acoustic wavelength.

Otherwise, to account for the interaction effect between multiple holes, Fok's function is

usually employed (Melling 1973).

The grazing flow is commonly characterized as a fully-developed turbulent

boundary layer (or fully-developed turbulent pipe flow), although some investigations do

not, which may lead to difficulties for comparison sake. The parameters extracted from

the external boundary layer are usually the Mach number M., friction velocity u., or

boundary layer thickness 3.

Although most of the models are empirical or semi-empirical, some are still

analytical. The first models proposed were based on linear stability analysis where the









shear layer (or grazing flow) is modeled using linear inviscid theory for infinite parallel

flows. Later, more formal linearized models have been emphasized. For instance,

Ronneberger (1972) described the orifice flow in terms of wave-like disturbances of a

thin shear layer over the orifice. Howe (1981a) modeled the grazing flow interaction as a

Kelvin-Helmholtz instability of an infinitely extended vortex sheet in incompressible

flow, where the vortex strength is tuned to compensate the singularity of the potential

acoustic flow at the downstream edge in order to meet the Kutta condition. Also, Elder

(1978) describes the shear layer displacement as being shaped by a Kelvin-Helmholtz

wave, while an acoustic response of the resonant system is modeled by an equivalent

impedance circuit of a resonator adopted from organ pipe theory. He then treats the flow

disturbances using linear shear layer instability models and the oscillation amplitude is

assumed to be limited by the nonlinear orifice resistance. Nelson et al. (1981, 1983)

separated the total flow field into a purely vortical flow field (associated with the shed

vorticity of the grazing flow) where the vorticity of the shear layer is concentrated into

point vortices traveling at a constant velocity on the straight line joining the upstream to

the downstream edge, plus a potential flow (unsteady part associated with the acoustic

resonance). They also provided a large experimental database in a companion paper that

has been used by others (Meissner 2002; Dequand et al. 2003). Innes and Creighton

(1989) used matched asymptotic expansions for small disturbances to solve the non-

linear differential equations, the resonator waveform containing a smooth outer part and

the boundary layer a rapid change; then approximations were found in each region along

with approximate values for the Fourier coefficients. Also, Jing et al. (2001) proposed a

linearized potential flow model that uses the particle velocity continuity boundary









condition rather than the more frequently used displacement in order to match the

flowfields separated by the shear layer over the orifice. All those models however still

remain linear (or nearly so) and thus carry inherent assumption limitations.

The simplified mathematical models described above have been used as starting

point to construct empirical models. These are based upon parameters such as the

thickness h and diameter d of the orifice/perforate, plate porosity U, grazing flow

velocity (mean velocity U. or friction velocity u.), Strouhal number St = cod/U (U


being some characteristic velocity), or Stokes number S= od/v. The major

empirical models found in the open literature are proposed by Garrison (1969), Rice

(1971), Bauer (1977), Sullivan (1979), Hersh and Walker (1979), Cummings (1986), or

Rao and Munjal (1986), and Kirby and Cummings (1998). They differ from each other

depending on whether they include orifice nonlinear effects, orifice losses (viscous effect,

compressibility), end corrections, single or clustered orifices, radiation impedance, etc.

But most of all, and more interestingly, they use different functional forms for the chosen

parameters that govern the physical behavior of the phenomenon, such as

f(h/d,kd,St, ,U ,u,,...), as shown in Appendix A where some of these models are

described in details. It should be noted that each of them are applicable for a single

application over a specific parameter range (muffler, acoustic liner, etc.).

Other less conventional approaches have also been attempted. For instance, Mast

and Pierce (1995) used describing-functions and the concept of a feedback mechanism.

In this approach, the resonator-flow system is treated as an autonomous nonlinear system

in which the limit cycles are found using describing-function analysis. Meissner (2002)

gave a simplified, though still accurate, version of this model. Similarly, following









Zwikker and Kosten's (1949) theory for propagation of sound in channels, Sullivan

(1979) and Parrott and Jones (1995) used transmission matrices to model parallel-element

liner impedances. In another effort, Lee and Ih (2003) obtained an empirical model via

nonlinear regression analysis of results coming from various parametric tests.

Furthermore, acoustic education techniques have been used to determine the acoustic

impedance of liners, such as a finite element method (employed by NASA, see Watson et

al. 1998), that iterates on the numerical solution of the two dimensional convective wave

equation to determine an impedance that reproduces the measured amplitudes and phases

of the complex acoustic pressures; or a grazing flow data analysis program (employed by

Boeing, see Jones et al. (2003) and references therein for details) that conducts separate

computations in different regions to match the acoustic pressure and particle velocity

across the interfaces that determines the modal amplitudes in each of the regions; or also

a two dimensional modal propagation method based on insertion loss measurements

(employed by B. F. Goodrich, see Jones et al. (2003) and references therein for details)

that determines the frequency-dependent acoustic impedance of the test liner. Jones et al.

(2003) reviewed and compared these impedance education techniques.

Finally, as noted earlier, a few studies have been performed using numerical

simulations. Indeed, as can be seen in Liu and Long (1998) and Ozyoruk and Long

(2000), it is computationally quite expensive, difficult to implement, and strong

limitations on the geometries are required. However, a promising numerical study by

Choudhari et al. (1999) gives valuable insight into the flow physics of these devices, such

as the effect of acoustic nonlinearity on the surface impedance.









Another important point concerns the measurement techniques used to acquire the

sample data which upon most of the model are derived, from simple to more elaborate

curve fitting. The two microphone technique introduced by Dean (1974) is commonly

employed for in situ measurements of the local wall acoustic impedance of resonant

cavity lined flow duct. This technique uses two microphones, one placed at the orifice

exit of the resonator, the other flushed at the cavity bottom. Then a simple relationship

for locally reactive liner between the cavity acoustic pressure and particle velocity is

extracted, which is based on the continuity of particle velocities on either side of the

cavity orifice (or surface resistive layer). However, the main drawbacks of this widely

used method reside in the position of the microphone in front of the liner that must be in

the hydrodynamicc far field" but at a distance less than the acoustic wavelength, and also

in the grazing boundary layer thickness. Different experimental apparatus are given in

Appendix A for clarification and illustration.

As an example, five models from the literature are presented in Appendix A that

are thought to be interesting, either for the quality of the experiments which upon the

model fits have been based on, or for the functional form they offer in terms of the

dimensionless parameters which are believed to be of certain relevance. To some extent,

they are all based on experimental data.

From all the models currently available, it is not obvious whether one model will

perform better than another, which is mainly due to the wide range of possible

applications, the limitations in the experimental data on which the semi-empirical models

heavily rely, and because even the mathematical models have their own limitations.

However, the rich physical information carried within these semi-empirical models and









the corresponding data on which they are based will undoubtfully aid the development of

reduced-order models in ZNMF actuator interacting with a grazing flow.

Unresolved Technical Issues

By surveying the literature, i.e. looking at the flow mechanism of isolated ZNMF

actuators to more complex behavior when the actuator is interacting with an incoming

boundary layer, along with examples of sound absorber technology, several key issues

can be highlighted that still remain to be addressed. This subsection lists the principal

ones.

Fundamental flow physics. Clearly, there still exists a lack in the fundamental

understanding of the flow mechanisms that govern the dynamics of ZNMF actuators.

While the cavity design is well understood, the orifice modeling and especially the effect

of the interaction with an external boundary layer requires more in-depth consideration.

Also, whether performing experimental studies or numerical simulations, researchers are

confronted with a huge parameter space that is time consuming and requires expensive

experiments or simulations. Hence the development of simple physics-based reduced-

order models is primordial.

2D vs. 3D. While most of the numerical simulations are performed for two-

dimensional problems, three-dimensionality effects clearly can be important, especially

to model the flow coming out of a circular orifice as shown in Rizzeta et al. (1998) or

Ravi et al. (2004) that also found distinct and non negligible three-dimensional effects of

the flow.

Compressibility effects. Usually, the entire flow field is numerically solved using

an incompressible solver. However, such an assumption, although valid outside the

actuator, may be violated inside the orifice at high jet velocity and, more generally, inside









the cavity due to the acoustic compliance of the cavity. Indeed, the cavity acts like a

spring that stores the potential energy produced by the driver motion.

Lack of high-resolution experimental data. Most of the experimental studies

employed either Hot Wire Anemometry (HWA), Particle Image Velocimetry (PIV) or

Laser Doppler Velocimetry (LDV) to measure the flow. However, each of these

techniques has shortcomings, as briefly enumerated below.

In the case of HWA, since the flow is highly unsteady and by definition oscillatory,

its deployment must be carefully envisaged, especially considering the de-rectification

procedure used to obtain the reversal flow. Since it is an intrusive technique that may

perturb the flow, other issues are that it is a single point measurement (hence the need to

traverse the whole flow field), problems arise with measurements near zero velocity

(transition from free to forced convection), and the accuracy may be affected by the

calibration (sensitivity), the local temperature, or some conductive heat loss.

With regards to PIV, although the main advantage resides in the fact that it is a

non-intrusive flow visualization technique that captures instantaneous snapshots of the

flow field, the micro/meso scale of ZNMF devices requires very high resolution in the

vicinity of the actuator orifice in order to obtain reasonable accuracy in the data. This is

difficult to achieve using a standard digital PIV system.

Finally, a large number of samples are required in order to get proper accuracy in

the data from LDV measurement, and excellent spatial resolution is difficult to achieve

due to the finite length of the probe volume. Also, since LDV is a single point

measurement, a traversing probe is required in order to map the entire flow field.









Lack of accurate low-order models. Clearly, the few reduced-order models that

are present so far are not sufficient to be able to capture the essential dynamics of the

flow generated by a ZNMF actuator. Better models must be constructed to account for

the slot geometry and the impact of the crossflow on the jet velocity profile. The five

models of grazing flow past Helmholtz resonators summarized in Appendix A reveal the

disparity in the impedance expressions as well as in the range of applications (see Table

A-i). Clearly, the task of extracting a validated semi-empirical model is far from trivial.

But leveraging past experience is critical to yielding accurate low-order models for

implementation of a ZNMF actuator.

Objectives

The literature survey presented above has permitted the identification of key

technical issues that remain to be resolved in order to fully implement ZNMF actuators

into realistic applications. Currently, it is difficult for a prospective user to successfully

choose and use the appropriate actuator that will satisfy specific requirements. Even

though many designs have been used in the literature, no studies have systematically

studied the optimal design of these devices. For instance, how large should the cavity

be? What type of driver is most appropriate to a specific application? Possibilities

include a low cost, low power piezoelectric-diaphragm, an electromagnetic or mechanical

piston that will provide large flow rate but may require significant power, or a voice-coil

speaker typically used in audio applications? What orifice geometry should be chosen?

Options include sharp versus rounded edges, large versus short thickness, an

axisymmetric versus a rectangular slot? Clearly, no validated tools are currently

available for end users to address these questions. Generally, a trial and error method









using expensive experimental studies and/or time consuming numerical simulations have

been employed.

The present work seeks to address these issues by providing a clear physical

understanding of how these devices behave and interact with and without an external

flow, and by developing and validating reduced-order dynamical models and scaling

laws. Successful completion of these objectives will ultimately aid in the analysis and

development of design tools for sizing, design and deployment of ZNMF actuators in

flow control applications.

Approach and Outline of Thesis

To reach the stated objectives, the following technical approach has been

employed. First, the identification of outstanding key issues and the formulation of the

problem have been addressed in this chapter by surveying the literature concerning the

modeling in diverse applications of ZNMF actuators and acoustic liner technology. The

relevant information about the key device parameters and flow conditions (like the driver

configuration, cavity, orifice shape, or the external boundary layer parameters) are thus

extracted. Before investigating how a ZNMF device interacts with an external boundary

layer, the case of an isolated ZNMF actuator must be fully understood and documented.

This is the subject of Chapter 2. An isolated ZNMF device is first characterized and the

relevant parameters are defined. Then, the previous work done by the author in Gallas et

al. (2003a) is summarized. Their work discusses a lumped element model of a

piezoelectric-driven ZNMF actuator. One goal of the present work is to extend their

model to more general devices and to remove, as far as possible, some restricting

limitations, especially on the orifice loss coefficient. Consequently, a thorough

nondimensional analysis is first carried out to extract the physics behind such a device.






29


Also, some relevant modeling issues are discussed and reviewed, for instance on

the orifice geometry effects and the driving transducer dynamics. Then, to study in great

details the dynamics of isolated ZNMF actuators, an extensive experimental investigation

is proposed where various test actuator configurations are examined over a wide range of

operating conditions. The experimental setup is described in Chapter 3.














CHAPTER 2
DYNAMICS OF ISOLATED ZERO-NET MASS FLUX ACTUATORS

Several key issues were highlighted in the introduction chapter that will be

addressed in this thesis. This Chapter is first devoted to familiarize the reader with the

dynamics of ZNMF actuators, their behavior and inherent challenges in developing tools

to accurately model them. One goal, before addressing the general case of the interaction

with an external boundary layer, is to understand the nonlinear dynamics of an isolated

ZNMF actuator. This chapter is therefore entirely dedicated to the analysis of isolated

ZNMF actuators issuing into a quiescent medium, as outlined below.

The device is first characterized and the relevant parameters defined in order to

clearly define the scope of the present investigation. The previous work performed by

the author in Gallas et al. (2003a) is next summarized. Their work discusses a lumped

element model of a piezoelectric-driven ZNMF actuator that relates the output volume

flow rate to the input voltage in terms of a transfer function. Their model is extended to

more general devices and solutions to remove some restricting limitations are explored.

Based on this knowledge, a thorough dimensional analysis is then carried out to extract

the physics behind an isolated ZNMF actuator. A dimensionless linear transfer function

is also derived for a generic driver configuration, which is thought to be relevant as a

design tool. It is shown that a compact expression can be obtained regardless of the

orifice geometry and regardless of the driver configuration. Finally, relevant modeling

issues pointed out in the first chapter are discussed and reviewed. Some issues are then

addressed, more particularly on the modeling of the orifice flow where a temporal









analysis of the existing lumped element model is proposed along with a physically-based

discussion on the orifice loss mechanism. Issues on the dynamics of the driving

transducer are discussed as well. Finally, a test matrix constructed to study the ZNMF

actuator dynamics is presented.

Characterization and Parameter Definitions

Figure 1-1 shows a typical ZNMF actuator, where the geometric parameters are

shown. First of all, it is worthwhile to define some precise quantities of interest that have

been used in the published literature and try to unify them into a generalized form. For

instance, people have used the impulse stroke length, some spatially or time averaged exit

velocities, or Reynolds numbers based either on the circulation of vortex rings or on an

averaged jet velocity to characterize the oscillating orifice jet flow. Here, an attempt to

unify them is made.

The inherent nature of the jet is both a function of time oscillatoryy motion) and of

space (velocity distribution across the orifice exit area). It is also valuable to distinguish

the ejection from the ingestion portion of a cycle. Many researchers (Smith and Glezer

1998, Glezer and Amitay 2002) characterize a synthetic jet based on a simple "slug

velocity profile" model that includes a dimensionless stroke length Lo/d and a Reynolds

number Re, = VCLd/v based on the velocity scale (average orifice velocity) such that


VCL =L= f vcL (t)dt, (2-1)

where vL (t) is the centerline velocity, T = 1/f is the period, thereby T/2 representing

half the period or the time of discharge for a sinusoidal signal, and L0 is the distance that









a "slug" of fluid travels away from the orifice during the ejection portion of the cycle or

period.

In addition, Smith and Glezer (1998) have employed a Reynolds number based on

the impulse per unit length (i.e., the momentum associated with the ejection per unit

width), Reo = Io/ /d, where the impulse per unit width is defined as


Io = pdL T2 (t)dt. (2-2)

Or similarly, following the physics of vortex ring formation (Glezer 1988), a

Reynolds number, Rer = Fo/v, is used based on the initial circulation associated with the

vortex generation process, with F0 defined by

1 IT/2 1T
0 C (t)dt= 2 CL. (2-3)

Alternatively (Utturkar et al. 2003), a spatial and time-averaged exit velocity during

the expulsion stroke is used to define the Reynolds number Re = Vd/v, where the time-

averaged exit velocity V, is defined as

2 1 T/2 2 T/2
V T fo v(t, x)dtdS = o T (t)dt, (2-4)
T f S, TJo

where v(t) is the spatial averaged velocity, S, is the exit area of the orifice neck, and x

is the cross-stream coordinate (see Figure 1-2 for coordinates definition). For general

purposes, instead of limiting ourselves to a simple uniform "slug" profile, the latter

definition is considered throughout this dissertation.









Notice that for a "slug" profile, it can be shown that the average orifice velocity

scale defined above in Eq. 2-1 and Eq. 2-4 is related by VL =2V. Similarly,

L, id = VL/(fd) is closely related to the inverse of the Strouhal number St since


L0 VCL 2V V 1
L0 -CL (2-5)
d fd cod/2i cod St

and since

1 J Vd v Re
(2-6)
St cod v d o2 S2

the following relationship always holds

1 Re Lod
(2-7)
St S2 co r

where r is the time of discharge (= T 2 for a sinusoidal signal) and S = od 2/v is the

Stokes number. The use of the Stokes number to characterize a synthetic jet and the

relationship to the Strouhal number were previously mentioned in Utturkar et al. (2003)

and Rathnasingham and Breuer (1997). The corresponding relations between the

different definitions are summarized in Table 2-1.

Correspondingly, the volume flow rate coming out of the orifice during the ejection

part of the cycle can be defined as

QJ = J v(t,x)dtdS, = VjS,,. (2-8)


And clearly, since we are dealing with a zero-net mass flux actuator, the following

relationship always holds

j,total = j,ex + Q, = 0, (2-9)

where the suffices 'ex' and 'in' stand for 'expulsion' and 'ingestion', respectively.









Table 2-1: Correspondence between synthetic jet parameter definitions
L, 1 1 Re
d O) St S2
Re, Rero Re

As seen from the above definitions, once a velocity or time scale has been chosen, a

length scale must be similarly selected for the orifice or slot. Figure 1-3 show two typical

orifice geometries encountered in a ZNMF actuator, and give the geometric parameters

and coordinates definition. Notice that the orifice is straight in both cases. No beveled,

rounded or other shapes are taken into account, although other geometries have been

investigated (Bridges and Smith 2001; Smith and Swift 2003b; Milanovic & Zaman

2005; Shuster and Smith 2004). Throughout this dissertation, the primary length scale

used is the diameter or depth of the orifice d. The spanwise orifice width w is used as

needed for discussions related to a rectangular slot, and the height h is a third

characteristic dimension. Clearly, if d is chosen as the characteristic length scale, then

w/d and h/d are key nondimensional parameters.

Lumped Element Modeling

Summary of Previous Work

A lumped element model of a piezoelectric-driven synthetic jet actuator exhausting

in a quiescent medium has been recently developed and compared with experiments by

Gallas et al. (2003a). In lumped element modeling (LEM), the individual components of

a synthetic jet are modeled as elements of an equivalent electrical circuit using conjugate

power variables (i.e., power = generalized flow x generalized effort). The frequency

response function of the circuit is derived to obtain an expression for Q /IVC the volume

flow rate per applied voltage. LEM provides a compact analytical model and valuable









physical insight into the dependence of the device behavior on geometric and material

properties. Methods to estimate the parameters of the lumped element model were

presented and experiments were performed to isolate different components of the model

and evaluate their suitability. The model was applied to two prototypical synthetic jets

and found to provide very good agreement with the measured performance. The results

reveal the advantages and shortcomings of the model in its present form. With slight

modifications, the model is applicable to any type of ZNMF device.

Orifice



Cavity(v)



Vac Piezoceramic
Composite Diaphragm

electroacoustic
coupling ... .- ------.
.-j a.D RaD R a 'RM M
-.aD RaD MaD "RaN MaN

-i d c' ,--------' aO
> / '* / l MaRad *
a\c ,b

electrical- acoustic/fluidic--
domain domain

Figure 2-1: Equivalent circuit model of a piezoelectric-driven synthetic jet actuator.

The equivalent circuit model is shown in Figure 2-1. The structure of the

equivalent circuit is explained as follows. An ac voltage V, is applied across the

piezoceramic to create an effective acoustic pressure that drives the diaphragm into

oscillatory motion. This represents a conversion from the electrical to the acoustic








domain and is accounted for via a transformer with a turns ratio An ideal transformer

(i.e., power conserving) converts energy from the electrical to acoustic domain and

converts an electrical impedance to an acoustic impedance. The motion of the diaphragm

can either compress the fluid in the cavity (modeled, at low frequencies, by an acoustic

compliance Ca) or can eject/ingest fluid through the orifice. Physically, this is

represented as a volume velocity divider, Qd = Q + Q The goal of the actuator design

is to maximize the magnitude of the volume flow rate through the orifice per applied

voltage Q, /Va, given by (Gallas et al. 2003a)


Q, (s) dos
Q (s) d (2-10)
Vac(S) a4S4 + +a2s +1as+1'

where d0 is an effective piezoelectric constant obtained from composite plate theory

(Prasad et al. 2002), s = jco, and al,a2,...,a are functions of the material properties and

dimensions of the piezoelectric diaphragm, the volume of the cavity V, orifice height h,

orifice diameter d, fluid kinematic viscosity v, and sound speed co, and are given by

-ai = CD (RkOn + RaR +R CaC (kROn + Rao),
a2 = CD (MRad +MA, +M D) +CC (MORad +MN) +CacCaDRaD (Ron +RaN),
(2-11)
a3 = C D MaD ( RDon + R, )+(MaORad +MN ) RD ], and
a4 = CaCCDMa (MoRad +M-A).

In Eq. 2-11, CD, Ra and MaD are respectively the acoustic compliance, resistance and

mass of the diaphragm. Cc is the acoustic compliance of the cavity. R., MA, and

MaRad are respectively the acoustic resistance, mass and radiation mass of the actuator










orifice, while R represents the nonlinear resistance term associated with the orifice


flow discharge and is a function of the volume flow rate Q,.


35 70

30----- ----- 60---------

> 25- - 50- -

E E
20----- -- ---- 40---------------- -


0 00 1000 100 2000 200 3000 0 00 1000 100


Frequency (Hz) Frequency (Hz)
Figure 2-2: Comparison between the lumped element model and experimental frequency
response measured using phase-locked LDV for two prototypical synthetic
O0 500 1000 1500 2000 2500 3000 500
Frequency (Hz) Frequency (Hz)
Figure 2-2: Comparison between the lumped element model and experimental frequency
response measured using phase-locked LDV for two prototypical synthetic
jets (Gallas et al. 2003a).

The lumped parameters in the circuit in Figure 2-1 represent generalized energy

storage elements (i.e., capacitors and inductors) and dissipative elements (i.e., resistors).

Model parameter estimation techniques, assumptions, and limitations are discussed in

Gallas et al. (2003a). The capability of the technique to describe the measured frequency

response of two prototypical synthetic jets is shown in Figure 2-2. The case in the left

half of the figure reveals the 4th-order nature of the frequency response. The two

resonance peaks are related to the diaphragm natural frequency f, and the Helmholtz


frequency f,, thereby demonstrating the potential significance of compressibility


effects. The case in the right half of the figure reveals how the model can be "tuned" to

produce a device with a single resonance frequency with large output velocities.

The important point is that the model gives a reasonable estimate of the output of

interest (typically within +20%) with minimal effort. The power of LEM is its simplicity









and its usefulness as a design tool. LEM can be used to provide a reasonable estimate of

the frequency response of the device as a function of the signal input, device geometry,

and material and fluid properties.

Limitations and Extensions of Existing Model

The study performed in Gallas et al. (2003a) was restricted to axisymmetric orifice

geometry and the oscillating pressure driven flow inside the pipe was assumed to be

laminar and fully-developed. Also, a piezoelectric-diaphragm was chosen to drive the

actuator.

A straightforward extension of their model is that of a rectangular slot model.

Appendix C provides a derivation of the solution of oscillating pressure driven flow in a

2D channel, assuming the flow is laminar, incompressible and fully-developed. The low

frequency approximation then yields the lumped element parameters. Hence, for a 2D

channel orifice the acoustic resistance and mass are found to be, respectively,

3 auh 3ph
Rv = u and MaN = (2-12)
2w(d 2) 5w(d 2)

Similarly, also of interest is the acoustic radiation impedance for a rectangular slot. The

acoustic radiation mass MOaad is modeled for kd <1 as a rectangular piston in an infinite

baffle by assuming that the rectangular slot is mounted in a plate that is much larger in

extent than the slot size (Meissner 1987),


XaRad = coMaRad kd k (2-13)
wd ; In (2d w) 2; (1 kV /6)


where Xlad corresponds to the acoustic radiation reactance.









Another extension of their work can be made with regards to the driver employed.

As shown in the next section, a convenient expression of the actuator response can be

made in terms of the nondimensional transfer function Q /Qd the ratio of the jet to

driver volume flow rate. Hence, by decoupling the driver dynamics from the rest of the

actuator one can easily implement any type of driver, under the condition that its

dynamics are properly modeled. In the LEM representation, the driving transducer is

represented in terms of a circuit analogy; it thus requires that the transducer components

must be fully known, whether the driver transducer is a piezoelectric-diaphragm, a

moving piston (electromagnetic or mechanical), or an electromagnetic voice-coil speaker.

A more detailed discussion on this issue is provided towards the end of this chapter.

The most restricting limitations of the lumped element model in its current state, as

presented above, are found in the orifice modeling. First, the model cannot handle orifice

geometries other than a straight pipe (or 2D channel, as seen above), i.e. no rounded

edges or beveled shapes can be considered. However, by analogy with minor losses in

fluid piping systems, this should only affect the nonlinear resistance term Raon

associated with the discharge from the orifice, and not RooR, = Ra that represents the

viscous losses due to the assumed fully-developed pipe flow. The nonlinear resistance

term Ron, is approximated by modeling the orifice as a generalized Bernoulli flow meter

(White 1979; McCormick 2000),

0.5KdpQ
oR n= (2-14)
n

where Q, is the amplitude of the jet volume flow rate, and Kd is a dimensionless loss

coefficient that is assumed, in this existing model, to be unity. In practice, Kd is a









function of orifice geometry, Reynolds number, and frequency. Hence, a detailed

analysis on the loss coefficient for various orifice shapes should yield a more accurate

expression in terms of modeling the associated nonlinear resistance. This is actually one

of the goals of this dissertation and this is systematically investigated in subsequent

chapters.

A second restricting assumption found in the orifice model of Gallas et al. (2003a)

comes from the required fully-developed hypothesis of the flow inside the orifice.

Clearly this limits the orifice design to a sufficiently large aspect ratio h/d or low stroke

length compare to the orifice height h. The lumped parameters of the orifice impedance

are based on the steady solution for a fully-developed oscillating pipe/channel flow (see

Appendix C). In addition, the author experimentally found (Gallas 2002) that reasonable

agreement was achieved between the lumped element model and the measured dynamic

response of an isolated ZNMF actuator when the orifice aspect ratio h/d approximately

exceeded unity. Figure 2-3 below reproduces this fact for four different aspect ratios,

where the orifices considered were axisymmetric, and the model prediction of the

centerline velocity was compared to phase-locked LDV measurements versus frequency.

Note that the diaphragm damping coefficient CD was empirically adjusted to match the

peak magnitude at the frequency governed by the diaphragm natural frequency. Clearly,

a careful study of the entrance effect in straight pipe/channel flow should greatly enhance

the completeness and validity of the orifice model in its current form, such a model being

able to be applied to all sorts of straight orifices, from long neck to short perforates.

Again, additional insight into this issue is discussed at the end of the chapter.










70 70
= 0.015 h/d 3/1 =3 = 0.013 h/d =5/1= 5
60 - 60

50--------- L- 50 --

40-------- -- ---- 40--- -

20-------- ---f-- -- ---- 20---------- 30


0 1 0 L
10- -------- 10- -

S500 1000 1500 0 500 1000 1500
Frequency (Hz) Frequency (Hz)

= 0.005 hd =1/3 =0.33 0.005 hd5/31.66
30 -- 30 -- --
**

205- -- -- -- ----< -- -- -- -- -- -- -- -- -- 205-- -- - L- - -

15 --- -- \ -- -- - 15 --- -- -- -- -- -- -- -- -




5 5 -' -

0 500 Frequency (Hz) 1000 1500 0 500 Frequency (Hz) 1000
Frequency (Hz)
Figure 2-3: Comparison between the lumped element model (-) and experimental
frequency response measured using phase-locked LDV (*) for four
prototypical synthetic jets, having different orifice aspect ratio h d (Gallas
2002).

Finally, another constraint in the current model is about the low frequency


approximation. By definition LEM is fundamentally limited to low frequencies since it is


the main hypothesis employed. The characteristic length scales of the governing physical


phenomena must be much larger than the largest geometric dimension. For example, for


the lumped approximation to be valid in an acoustic system, the acoustic wavelength (A =


1 k) must be significantly larger than the device itself (kd < 1). This assumption permits


decoupling of the temporal from the spatial variations, and the governing partial









differential equations for the distributed system can be "lumped" into a set of coupled

ordinary differential equations.






0.8 S---:- \-

0.6 S=1 -
S------ S=12\
S0.5- -- S=20 ------- ---------- \\\
0.4 ---s =50 -
0.3 1
0.2 -
0.1

0 0.2 0.4 0.6 0.8 1
x/(d/2)
Figure 2-4: Variation in velocity profile vs. S = 1, 12, 20, and 50 for oscillatory pipe
flow in a circular duct.

However, it is well known that the flow inside a long pipe/channel is frequency

dependent, as shown in Figure 2-4 and Figure 2-5. From Figure 2-4, it can be seen that,

as the Stokes number S goes to zero, the velocity profile asymptotes to Poiseuille flow,

while as S increases, the thickness of the Stokes layer decreases below d/2, leading to

an inviscid core surrounded by a viscous annular region where a phase lag is also present

between the pressure drop across the orifice and the velocity profile. Figure 2-5 shows

that the ratio of the spatial average velocity i, (t) to the centerline velocity vC (t), which

is 0.5 for Poiseuille flow, is strongly dependant on the Stokes number. Although it has

been shown (Gallas et al. 2003a) that the acoustic reactance is approximately constant

with frequency, the acoustic resistance, which does asymptote at low frequencies to the

steady value given by the lumped element model, gradually increases with frequency.










Therefore, this frequency-dependence estimate should not be disregarded, and care must

be taken in the frequency range at which ZNMF actuators are running to apply LEM. For

instance, the frequency dependence given by Figure 2-5 can be easily implemented in the

present model to provide estimates for the acoustic impedance of the orifice, as discussed

in Gallas et al. (2003a).



0.95----- --

0.9

0.85 ---

0.8 /
I
> 0.75 -

0.7 -

0.65 -

0.6 -

0.55---- f- '-------

0.5
1 10 100
S=(I d2 1/2
SI cod I)1
Figure 2-5: Ratio of spatial average velocity to centerline velocity vs. Stokes number for
oscillatory pipe flow in a circular duct.

To summarize this section, the model given in Gallas et al. (2003a) has been

presented and reviewed, and it has been shown that it could be extended to more general

device configurations, particularly in terms of orifice geometry and driver configuration.

Also, some of their restricting assumption limits could be, if not completely removed, at

least greatly attenuated, and this is further analyzed and discussed in the last part of this

chapter. But before, a general dimensional analysis of an isolated actuator is carried out

in the next section that gives valuable insight on the parameter space and on the system

response behavior.









Dimensional Analysis

Definition and Discussion

In the first section of this chapter, the primary output variables of interest have been

defined, and specifically the spatial and time-averaged ejection velocity of the jet V,

defined in Eq. 2-4. It is then interesting to rewrite them in terms of pertinent

dimensionless parameters. Using the Buckingham-Pi theorem (Buckingham 1914), the

dependence of the jet output velocity can be written in terms of nondimensional

parameters. The derivation is presented in full in Appendix D and the results are

summarized below:


Sf os h (w A15)
St f= d,,ddkdS (2-15)
Re H d


The quantities in the left hand side of the functional are possible choices that the

dependent variable V can take. Q /Qd represents the ratio of the volume flow rate of

the driver (Qd = WdAV) to the jet volume flow rate of the ejection part. St is the

Strouhal number and Re is the jet Reynolds number defined earlier. Notice the close

relationship between the jet Reynolds number, the Stokes number and the Strouhal

number that were given by Eq. 2-7 and found again here by manipulation of the nI-

groups (see Appendix D for details). Therefore, for a given geometric configuration,

either the Strouhal or the Reynolds numbers along with the Stokes number could suffice

to characterize the jet exit behavior. It is also interesting to view Eq. 2-7 as the basis for

the jet formation criterion defined by Utturkar et al. (2003). Actually, it is intrusive to

look at the different physical interpretations that the Strouhal number can take. In the









fluid dynamics community, it is usually defined as the ratio of the unsteady to the steady

inertia. However, it can also be interpreted as the ratio of 2 length scales or 2 time scales,

such that

St cod d d
St = -
V o) L,
i V (2-16)
Sft = od o) tOscillation
VJ d convection

where d/L, is the ratio of a typical length scale d of the orifice to the particle excursion

Lo through the orifice. The Strouhal number can also be the ratio of the oscillation time

scale to the convective time scale.

The physical significance of each term in the RHS of Eq. 2-15 is described below:

* 3o/oH is the ratio of the driving frequency to the Helmholtz frequency
OH = co /h'V (see Appendix B for a complete discussion on the definition and
derivation of oH ), a measure of the compressibility of the flow inside the cavity.

* h/d is the orifice/slot height to diameter aspect ratio.

* w/d is the orifice/slot width to diameter aspect ratio.

* c0/cod is the ratio of the operating frequency to the natural frequency of the driver.

* AV/d3 is the ratio of the displaced volume by the driver to the orifice diameter
cubed.

* kd = d/A is the ratio of the orifice diameter to the acoustic wavelength.

* S = odjv is the Stokes number, the ratio of the orifice diameter to the unsteady
boundary layer thickness in the orifice v/co.

It is evident that in the case of an isolated ZNMF actuator, the response is strongly

dependant on the geometric parameters {co/cH ,h/d,w/d,kd} and the operating









conditions ({c/od ,AV/d3 ,S}. In fact, from the functional form described by Eq. 2-15

and for a given device with fixed dimensions and a given fluid, the actuator output is only

dependent on the driver dynamics (od, AV) and the actuation frequency c .

Although compressibility effects in the orifice are neglected in this dissertation, it

warrants a few lines. Compressibility will occur in the orifice for high Mach number

flows and/or for high density flows. If the compressibility of the fluid has to be taken

into account, it follows by definition that density must be considered as a new variable.

For instance, the pressure is now coupled to the temperature and density through the

equation of state. Similarly, the continuity equation is no longer trivial. Also,

temperature is important, and one has to reminder that the variation of the thermal

conductivity k and dynamic viscosity /u that are transport quantities with temperature

may be important.

Dimensionless Linear Transfer Function for a Generic Driver

Valuable physical insight into the dependence of the device behavior on geometry

and material properties is provided by the frequency response of the ZNMF actuator

device. In order to obtain an expression of the linear transfer function of the jet output to

the input signal to the actuator, the compact nonlinear analytical model given by LEM is

used in a similar manner as described and introduced in the previous section, since it was

shown to be a valuable design tool. Notice however that the nonlinear part of the model

in its present form -only confined in the orifice- is neglected for simplicity in this

analysis. Figure 2-6 shows a schematic representation of a ZNMF actuator having a

generic driver using LEM. This representation enables us to bypass the need of an









expression for the acoustic impedance ZD> of the driving transducer, although it lacks its

dynamics modeling.


IQd- Q



\ Z-C Z ia


Figure 2-6: Schematic representation of a generic-driver ZNMF actuator.

In this case, a convenient representation of the transfer function is to normalize the

jet volume flow rate by the driver volume flow rate, Q, /Q,, and obtain an expression via

the current/flow divider shown in Figure 2-6,

QJ (s) Z1c /sC,
Qd (s) Zac + Zo 1/sCc + Ro + sMo
1 (2-17)
CaMaM
1 + Ro s+s2
CacM o Mao

assuming that the acoustic orifice impedance Zo = Ro +Mo, only contains the linear

resistance R, and the radiation mass Mo1d is neglected or added to MIO.

Knowing that the Helmholtz resonator frequency of the actuator is defined by

S-, (2-18)
H = acMo

and the damping ratio of the system by


r= R (2-19)
2 r)Cva ( )


by substituting in Eqs. 2-18 and 2-19, Eq. 2-17 can then be rewritten as







48



Q (s)
Q Ws) 02 (2-20)
Qd (S) S2 + 2C(HS + H2

This is a second-order system whose performance is set by the resonator Helmholtz

frequency. Figure 2-7 below shows the effect of the damping coefficient ; on the


frequency response of Q /Qd, where for ; <1 the system is said to be underdamped,


and for ; > 1 the system is overdamped. The damping coefficient controls the amplitude

of the resonance peak, allowing the system to yield more or less response at the

Helmoholtz frequency.


40

-0 -20--




-60
1I I I 1 1 1 1 1





10- 100 10

0 .......... ... .. ..... .. "

-50 =01
I I I I I I I---- =0.5
S-100 I II I I I I I 1
-60 -----------------------------------L^





101 100 10
0 .............................................
..... ........... I ..... =0.01. .






-200



Figure 2-7: Bode diagram of the second order system given by Eq. 2-20, for different
damping ratio.

Since the expression of aH differs from the orifice geometry, two different cases


are examined and summarized in Table 2-2. The definitions can be found in Appendices
o -100 - - - f".. - = 1
















B, C, and D. The damping coefficient is found from the following arrangement (shown

for the case of a circular orifice, but one can similarly arrive at the same result for a

rectangular slot)
D:'- -150o - - .- ^ "- "i- ..\- -

-200 -------------------------------------L^

















rectangular slot)









1 8,h
2 z(d 2)4 (4ph)

j76Vh vh v
l L; X


642/2zh V 3V/
d/o6) pc 16p


(2-21)


-' V 0) 2
3rd2C2 Id4w)2
I/4


01
"=12--
0)H S2


(2-22)


Table 2-2: Dimensional parameters for circular and rectangular orifices
Circular orifice Rectangular slot
Qd (m3/s) JOdAV JOdAV

(, (rad/s) 3r(d 2)2 c 5w(d2)
4hV 3hV
V V
C, (s2.m4/kg) 2
pCo pc,
8/ph 3/ h
R, (kg/m4.s) 8h4 3
z (d 2) 2w (d 2)3
4ph 3ph
MAN (kg/m4) 3(d )2
S3r (d 2)2 5w(d 2)
1 C (o 1 o 1
= R2v r 12 2 5-
2 (A M mH S H S

Notice that the damping coefficient has the same fundamental expression whether

the orifice is circular or rectangular, the difference being incorporated in a multiplicative

constant. Substituting these results into Eq. 2-20 and replacing the Laplace variable

s = jo) yields the final form for a generic driver and a generic orifice

Q- Q(). (2-23)
a e i,


that is,









Clearly, the advantage of non-dimensionalizing the jet volume flow rate by the

driver flow rate allows us to isolate the driver dynamics from the main response, thereby

decoupling the effect of the various device components from each other. Eq. 2-23 is an

important result in predicting the linear system response in terms of the nondimensional

parameters co/cod, Ho/WoH and S as a function of the driver performance. It yields such

interesting results that actually a thorough analysis of Eq. 2-23 is provided in details in

Chapter 5 where the reader is referred to for completeness.

To summarize, this section has provided a dimensional analysis of an isolated

ZNMF actuator. A compact expression, in terms of the principal dimensionless

parameters, has been found for the nondimensional transfer function that relates the

output to the input of the actuator. Most importantly, such an expression was derived

regardless of the orifice geometry and regardless of the driver configuration. Actually, as

an example, a piezoelectric-driven ZNMF actuator exhausting into a quiescent medium is

also considered in Appendix E where the idea is to find the same general expression as

derived above in Eq. 2-15 for a generic ZNMF device, but starting from the specific and

already known transfer function of a piezoelectric-driven synthetic jet actuator as given in

Gallas et al. (2003a). Appendix E presents the full assumptions and derivation of the

non-dimensionalization and the derivation of the linear transfer function for this case.

Next, with this knowledge gained, the modeling issues presented earlier in the

introduction chapter and at the beginning of this chapter are further considered.









Modeling Issues

Cavity Effect

The cavity plays an important role in the actuator performance. Intuitively, an

actuator having a large cavity may not act in a similar fashion to one having a very small

cavity. As mentioned above, the cavity of a ZNMF actuator permits the compression and

expansion of fluid. It is more obvious when looking at the equivalent circuit of a ZNMF

device (see Figure 2-1 for instance), where the flow produced by the driver is split into

two branches: one for the cavity where the fluid undergoes successive compression and

expansion cycles, the other one for the orifice neck where the fluid is alternatively ejected

and ingested. The question arises as to when, if ever, an incompressible assumption is

valid. The definition of the cavity incompressibility limit is actually two-fold. First,

from the equivalent circuit perspective, a high cavity impedance will prevent the flow

from going into the cavity branch, thereby allowing maximum flow into and out of the

orifice neck, thus maximizing the jet output. Or from another point of view, the

incompressible limit occurs for a stiff cavity, hence for zero compliance in the cavity,

which should yield to Q /Qd 1. On the other hand, from a computational point of

view, it is rather essential to know whether the flow inside the cavity can be considered

as incompressible, the computation cost being quite different between a compressible and

an incompressible solver.

Actually, because of its importance in numerical simulations and relevance in the

physical understanding of a ZNMF actuator, Chapter 5 is entirely dedicated to the

question of the cavity modeling. The reader is therefore referred to Chapter 5 for a

thorough investigation on the role of the cavity in a ZNMF actuator.









Orifice Effect

The orifice is one of the major components of a ZNMF actuator device. Its shape

will greatly contributes in the actuator response, and knowledge of the nature of the flow

at the orifice exit is determinant in predicting the system response. The LEM technique

presented earlier was shown to be a satisfactory tool in this way, but has still fundamental

limitations, especially in the expression of the orifice nonlinear loss coefficient Kd.

Similarly, the existing lumped element model is employed in the frequency domain.

Because of the oscillatory nature of the actuator response, it may also be instructive to

study the response of ZNMF actuator in the time domain.

Lumped element modeling in the time domain

The LEM technique presented above and used throughout this work identifies a

transfer function in the Laplace domain, consequently in the frequency domain as well by

assuming s = c + jo) -> j) Note that this variable substitution is only correct when an

input function g(t) is absolutely integrable, that is if it satisfies


g (t)t < 00, (2-24)

i.e., the signal must be causal and that the system is stable -conditions that are always met

in this work. For a given transfer function of the system (ZNMF actuator) relating the

output (jet velocity) to the input (driver signal) in the frequency domain, it could

therefore be of interest to gain some insight from the time domain response.

Referring to Figure 2-6 and Eq. 2-17, the equation of motion for the ZNMF

actuator is given by


Qj (Z + ZC) = QdZ, c,


(2-25)









where again Za= /jcoCc is the acoustic impedance of the cavity, and

Zao =RaOhn +Raonl(QJ)+jiwMoo is the acoustic orifice impedance. The orifice mass

Moo includes the contributions from the radiation and inertia, while the orifice

resistances are distinguished between the linear terms Rohn = Ra (viscous losses) and

nonlinear R on = f(Q ("dump loss") defined by Eq. 2-14. Also, Qj = y,S, is the jet

volume flow rate, Qd = ydSd is the volume velocity generated by the driver, and y, and


Yd are, respectively, the fluid particle displacement at the orifice and the vibrating driver

displacement. Notice that yJ can take positive or negative values, which corresponds

respectively to the time of expulsion and ingestion during a cycle, as seen in Figure 2-8.

Therefore, since the nonlinear resistance is associated to the time of discharge and

considering the coefficient Kd as a constant independent of Q,, it takes the form

0.5KdpQj 0.5Kdp
RaOn s2 y = A yn .j (2-26)
n Sn

A Y B C
+yJ Y, max ingestion
xQ + expulsion starts
Q C
APc 0
time
|d exptl sion
------ ------ ---------
stitrts
---.-- ---------- .max
Yd ingestion

Figure 2-8: Coordinate system and sign convention definition in a ZNMF actuator. A)
Schematic of coordinate system. B) Circuit representation. C) Cycle for the
jet velocity.

The following expression for the equation of motion of a fluid particle can then be

easily derived









1 S
Sj- +Ron +Rohn + joMo = d Yd,. (2-27)


But since frequency and time domain are related through jo -> d/dt and 1/jo -> dt,

and assuming a sinusoidal motion for the source term, i.e. Yd = W sin(o(), with WO

corresponding to the driver centerline amplitude, then the equation of motion in the time

domain is written as

S S
S + S ,4A1, A + S, Roon jV + SMooy = d Wo sin(cot), (2-28)


or by rearranging the terms,

MAoyj,+ +An Y +Ro~jn~, + y, =- Wo sin (0t). (2-29)
aC aCSn

Similarly, the pressure API across the orifice can be derived from continuity,

AP = QjZZ = (Qd -Q ) Z. (2-30)

Thus, substituting in Eq. 2-30 and rearranging yields


A = QdZac QZac = SYd Sn, (2-31)


and finally the pressure drop takes the following expression

S S SdW0 sin(ct)- S,y
A = Wosin(mot) y,= d ) nyj (2-32)
C C"C Cac

To validate this temporal approach of the lumped element model, three test cases

are now considered having three different orifice shapes to also gain insight into the

orifice geometric effects. First, the response of a ZNMF actuator having a simple straight

rectangular orifice shape and a high aspect ratio hid is viewed, and that corresponds to










Case 1 in the NASA LaRC workshop (CFDVal 2004), as shown in Figure 2-9. Then,

Case 2 of the same workshop (CFDVal 2004) is considered since the orifice of this

ZNMF actuator has a rounded beveled shape (D/d = 2, see Figure 2-10 for geometric

definition) and an aspect ratio less than unity, where high values of the orifice discharge

coefficient are expected. The actuator geometry is shown in Figure 2-10. A third

example is taken from the results provided by Choudhari et al. (1999), in which they

perform a numerical simulation of flow past Helmholtz resonators for acoustic liners,

with the orifice aspect ratio h/d equal to unity.






h





diaphragm




ozone 2
moving diaphragm located
at slade ofvity
1 ZOnrl 3
Zone 1not visible



Figure 2-9: Geometry of the piezoelectric-driven ZNMF actuator from Case 1 (CFDVal
2004). d =1.27mm, d/D=0.59, h/d =10.6, w/d=28, f = 445Hz.
(Reproduced with permission)


d_ K- Plate Surface (Flow side)
h -) D
_'I'I Caviy_ -


Actuator

Figure 2-10: Geometry of the piston-driven ZNMF actuator from Case 2 (CFDVal
2004). d = 6.35mm, d/D = 0.5, h/d = 0.68, f = 150Hz. (Reproduced with
permission)









Because of their special orifice shape, pipe theory was used to model the

dimensionless "dump loss" coefficient Kd in the acoustic orifice impedance for Case 1

and Case 2 (CFDVal 2004). From pipe theory (White 1979), the dump loss coefficient

for the orifice is


Kd D(1-,ICD) (2-33)


with / = d/D is the ratio of the exit to the entrance orifice diameter, and with the

discharge coefficient taking the form

CD = 0.9975 -6.53(//Re)o5, (2-34)

for a beveled shape, Re being the Reynolds number based on the orifice exit diameter d.

For each case, the Reynolds number given by the experimental data provided in the

workshop (CFDVal 2004) is used in Eq. 2-34, although it should be rigorously

implemented in a converging loop since this variable is usually not known beforehand.

For Case 1, it was found that Kd = 0.884, while for Case 2, Kd = 0.989. This is to be

compared with the value Kd = 1 that is used in Gallas et al. (2003a). Notice though that

Eq. 2-34 is specifically defined for high Reynolds number, which may not always be the

case. Similarly, Eqs. 2-33 and 2-34 only account for the expulsion part of the cycle.

During the ingestion part the flow sees an inversedd" orifice shape, hence the discharge

coefficient should take a different form. How to account for the oscillatory behavior on

the orifice shape, i.e. to separate the expulsion to the ingestion phase for the flow

discharge, is investigated in the next chapters of this dissertation. Yet, these results

validate the approach used and provide valuable insight into the nonlinear behavior.









The nonlinear ODE that describes the motion of the fluid particle at the orifice, Eq.

2-29, is numerically integrated using a 4th order Runge-Kutta method with zero initial

conditions for y, (0) = y (0) = 0. The integration is carried out until a steady-state is

reached. The jet orifice velocity, pressure drop across the orifice via Eq. 2-32, and the

driver displacement are shown in Figure 2-11 for Case 1. All quantities exhibit

sinusoidal behavior, and it can be seen that the cavity pressure is in phase with the driver

displacement, while the jet orifice velocity lags the driver displacement by 900. Once

the pressure reaches its maximum (maximum compression, the fluid cavity starts to

expand), the fluid is ingested from the orifice, then reaches its maximum ingestion when

the cavity pressure is zero and finally, as the fluid inside the cavity starts to be

compressed, the fluid is ejected from the orifice.


-1 .-...-.-- driver displacement
S---- pressure drop
0.8 /--- ---- jet orifice velocity
0. ------- --







-0.4 -
7)
S0.6 .
-* 0.84 \










-1
phase
Figure 2-11: Time signals of the jet orifice velocity, pressure across the orifice, and
c= 0.2 i I I







driver displacement during one cycle for Case 1. The quantities are






normalized by their respective magnitudes for comparison.
-0.2 \ 1 ''
0 -0.4 q \ T \\ 1 / n
,\ '//

-0.8 \ -

0 45 90 135 180 225 270 315 360
phase
Figure 2-11: Time signals of the jet orifice velocity, pressure across the orifice, and
driver displacement during one cycle for Case 1. The quantities are
normalized by their respective magnitudes for comparison.









The other test case response, namely Case 2, is plotted in Figure 2-12, where the jet

orifice displacement and velocity, pressure drop across the orifice, and the driver

displacement are shown for both the a) linear and the b) nonlinear solutions of the

equation of motion Eqs. 2-29 and 2-32. The linear solution is obtained by setting

Ron = 0 and is performed to verify the physics of the device behavior and thus confirm

the modeling approach used. The linear solution in Figure 2-12A shows that the pressure

inside the cavity (which equals the pressure drop across the orifice) and the driver motion

are almost out of phase. All quantities exhibit sinusoidal behavior. The jet orifice

velocity y, lags the cavity pressure for both the linear and the nonlinear solution. Figure

2-12B shows the effect of the nonlinearity of the orifice resistance. Its main effect is to

shift the pressure signal such that the fluid particle velocity and the cavity pressure are

out of phase. Also, those two signals exhibit obvious nonlinear behavior due to the

nonlinear orifice resistance.

Linear Solution --- driver displacement Non linear Solution
1 \ .""-. ---- pressure drop 1 /-
-- ,/ \ ,\-- jet orifice velocity / \ /
0.8-- 08 -0.8 -
S I / I \ I I I I
S0.6---/ / \ -0.4 --

02 ,0.2 0 L -- I
0.2 \ \ ------- 0.2 ------ -
S \ \
S\displacement during one cycle for Case 2. A) Linear solution. B) Nonlinear
\ / - 0.2
S-04 \ / '04 -
\'A // \
-0.6 -- __.0.6 -
i \ / /\

0 45 90 135 180 225 270 315 360 0 45 90 135 180 225 270 315 360
phase phase
Figure 2-12: Time signals of the jet orifice velocity, pressure across the orifice and driver
displacement during one cycle for Case 2. A) Linear solution. B) Nonlinear
solution. The quantities are normalized by their respective magnitudes for
comparison.









Then, Figure 2-13 shows the numerical results from Choudhari et al. (1999), with

their notation reproduced, where the reference signal shown corresponds to that measured

at the computational boundary where the acoustic forcing is applied, and the x-axis in the

plot is normalized by the period T of the incident wave. Notice that they used a

perforate plate having a porosity a equal to 5%. In a similar trend as for the previous

case, the pressure drop and jet orifice velocity exhibit distinct nonlinearities in their time

signals. From Figure 2-13A, it is seen that the pressure perturbations at each end of the

orifice are almost out of phase, while in Figure 2-13B, the velocities at different locations

in the orifice are in phase with each other. Also, it appears that the pressure and velocity

perturbations have about a 900 phase difference, similar to Case 1 above.

.... .






T UT




A) Disturbance pressure p/pco B) Streamwise velocity perturbation u/co

Figure 2-13: Numerical results of the time signals for A) pressure drop and B) velocity
perturbation at selected locations along the resonator orifice. The subscripts
i, c, and e refer to the orifice opening towards the impedance tube (exterior),
the orifice center, and the orifice opening towards the backing cavity,
respectively. d= 2.54mm, h/d= 1, f = 566Hz, = 0.05. (Reproduced
with permission from Choudhari et al. 1999)

Clearly, the orifice shape does have a significant impact on the nonlinear signal

distortion in the orifice region. It should be noted that the actuation frequency and

amplitude are also important, as discussed in Choudhari et al. (1999), and mentioned in

the introduction chapter where Ingard and Ising (1967) and later Seifert et al. (1999)









showed that for low actuation amplitude the pressure fluctuations and the velocity scale

as u' p'/pco whereas for high amplitude u' ~ -p/p. However, it still emphasizes

the need to accurately model the orifice discharge coefficient in terms of the flow

conditions.

As mentioned before, also of interest is the fully-developed assumption for the flow

inside the orifice. Clearly, while Case 1 (CFDVal 2004) has an orifice geometry that

justifies such an approximation, it seems quite doubtful for Case 2 (CFDVal 2004) and

perhaps the Helmholtz resonator geometry from Choudhari et al. (1999). It is expected

that a developing region exists at the orifice opening ends, where a different relationship

relates the pressure drop and the fluid velocity, the velocity being now dependant on the

longitudinal location inside the orifice. In this regard, the next subsection provides more

details on this entrance region.

Finally, another orifice issue that may not be negligible is the radius of curvature at

the exit plane. In fact, the formation and subsequent shedding of the vortex ring (pair) at

the orifice (slot) exit relies on the curvature of the exit plane. Sharp edges facilitate the

formation and roll-up of the vortices, due to a local higher pressure difference, while

smooth edges having a large radius of curvature lessen the formation of vortices at the

exit plane, as shown in the recent work by Smith and Swift (2003b) who experimentally

studied the losses in an oscillatory flow through a rounded slot. This parameter, R/d,

may enter in the present nondimensional analysis for completeness, although it is omitted

in this dissertation.









Loss mechanism

In this subsection, an attempt is made to physically describe the flow mechanism

inside the orifice. The flow inside the orifice is by nature unsteady and is exhibiting

complex behavior as demonstrated in the literature review. One approach to understand

the nature of the flow physics is to consider known simpler cases. First it is instructive to

consider the simpler case of steady flow through a pipe where losses arise due to different

mechanisms. In any undergraduate fluid mechanics textbook, these losses are

characterized as "major" losses in the fully developed flow region and "minor" losses

associated with entrance and exit effects, etc. For laminar flow, the pressure drop Ap in

the fully-developed region is linearly proportional to the volume flow rate Q or average


spatial velocity VJ, while the nonlinear minor pressure losses are proportional to the

-2
dynamic pressure 0.5pVj Similarly, for the case of unsteady, laminar, fully-developed,

flow driven by an oscillatory pressure gradient, the complex flow impedance, Ap/Q, can

be determined analytically and decomposed into linear resistance and reactive

components as already discussed above. Unfortunately, no such solution is yet available

for the nonlinear, and perhaps dominant, losses associated with entrance and exit effects.

It then appears that the orifice flow can be characterize by three dominant regions,

as shown schematically in Figure 2-14, where the first region is dominated by the

entrance flow, then follows a linear or fully-developed region away from the orifice ends,

to finally include an exit region. Notice that this is for one half of the total period, but by

assuming a symmetric orifice the flow will undergo a similar development as it reverses.

Also shown schematically in Figure 2-14 are the pathlines or particle excursions for three









different running conditions. The first one corresponds to the case where the stroke

length is much smaller than the orifice height (L0 << h) -recall that the stroke length is

simply related to the Strouhal number via Eq. 2-7. In this case it is expected that the flow

inside the orifice may easily reach a fully-developed state, thus having losses dominated

by the "major" linear viscous loss rather than the nonlinear "minor" ones associated with

the entrance and exit regions. A second case occurs when the stroke length is this time

much larger than the orifice height (L0 > h). In this scenario, the losses are now

expected to be largely dominated by the minor nonlinear losses due to entrance and exit

effects, the entrance region basically extending all the way through the orifice length.

Finally, in the case where the stroke length and orifice height have the same order of

magnitude (L0 h), the linear losses due to the fully-developed region should compete

with the nonlinear losses from the entrance and exit effects. Notice that here, "fully-

developed" means that there exists a region within the orifice away from either exit,

where the velocity profile at a given phase during the cycle is not a function of axial

position y.

exit & entrance losses
viscous loss
(fully-developed flow)

Lo> h "/" "" h""
L << h---- ....--. --...-~--4--




<-------
Figure 2-14 Schematic of the different flow regions inside a ZNMF actuator orifice.
Figure 2-14: Schematic of the different flow regions inside a ZNMF actuator orifice.









Thus to refine the existing lumped element model presented above that uses the

frequency-dependent analytical solution for the linear resistance, the impedance of the

nonlinear losses associated with the entrance and exit regions should be extracted.

However, the relative importance and scaling of the linear and nonlinear components

versus the governing dimensionless parameters is unknown and remains a critical

obstacle for designers of ZNMF actuators at this stage. To achieve such a goal i.e., to

improve the current understanding of the orifice flow physics and consequently to

improve the accuracy of low-order models, a careful experimental investigation is

conducted and the extracted results are presented in the subsequent chapters.

Driving-Transducer Effect

Most of the numerical simulations impose a moving boundary condition in order to

model the kinematics of the ZNMF driver that generates the oscillating jet in the orifice

neck. However, this approach does not capture the driver dynamics and in most

instances, crude models of the mode shape are employed (Rizzetta et al. 1999; Orkwis

and Filz 2005). Although this might not be critical if the actuator is driven far from any

resonance frequency, the information provided by the driver is relevant from a design

perspective, with the frequency response (magnitude and phase) dictating the overall

performance of the system and thus its desirable application. The approach used in this

dissertation is to decouple the dynamics of the driver from the rest of the device via the

analysis of a dimensionless transfer function. Hence, accurate component models can be

sought that will provide useful information on the overall behavior of the actuator. In this

regard, LEM has been shown to be a suitable solution, as discussed below, for any type

of drive configuration, i.e. piston-like diaphragm, piezoelectric diaphragm, etc.









Figure 1-1 shows the three most common driving mechanisms that are employed in

ZNMF actuators, namely an oscillating diaphragm (usually a piezoelectric patch mounted

on one side of a metallic shim and driven by an ac voltage), a piston mounted in the

cavity (using an electromagnetic shaker, a camshaft, etc.), or a loudspeaker enclosed in

the cavity (an electrodynamic voice-coil transducer). In addition to the driver dynamics,

the characteristics of most interest are the volume displaced by the driver AV at the

actuation frequency f Hence, the driver volumetric flow rate can simply be defined by

Qd= j(27rf)AV. (2-35)

It has been shown that this compact expression is useful in the nondimensional

analysis performed earlier. However, in order to obtain the full dynamics of the actuator

response, the LHS of Eq. 2-35 must also be known. Only then do the compact analytical

expressions derived in the previous section reveal their usefulness. Each of the three

types of possible ZNMF actuator drivers are discussed below via LEM, since the analysis

and design of coupled-domain transducer systems are commonly performed using

lumped element models (Fisher 1955; Merhault 1981; Rossi 1988). I.e., in addition to the

driver acoustic impedance Z, that is shown in Figure 2-6 and Figure 2-15, the

transduction factor and the blocked electrical impedance CeB must be explicitly given.


I aQd 1: CaD MaD RaDd
+ r a+

Vac eB oaV P


Figure 2-15: Equivalent two-port circuit representation of piezoelectric transduction.

First, consider the case of a piezoelectric diaphragm driver. Recently (Gallas et al.

2003a, 2003b), the author successfully implemented a two-port model for the









piezoceramic plate (Prasad et al. 2002) in the analysis, modeling and optimization of an

isolated ZNMF actuator. As shown in Figure 2-15, the impedance of the composite plate

was modeled in the acoustic domain as a series representation of an equivalent acoustic

mass M ,D, a short-circuit acoustic compliance CaD (that relates an applied differential

pressure to the volume displacement of the diaphragm) and an acoustic resistance RD

(that represents the losses due to mechanical damping effects in the diaphragm).

Similarly, a radiation acoustic mass can be added if needed. The conversion from

electrical to acoustic domain is performed via an ideal transformer possessing a turns

ratio a that converts energy from the electrical domain to the acoustic domain without

losses. Figure 2-1 shows the two-port circuit representation implemented in a ZNMF

actuator. 0, MaD and CaD are calculated via linear composite plate theory (see Prasad

et al. 2002 for details). Notice that the acoustic resistance RD given by


ROD =2D (2-36)
SCaD

is the only empirically determined parameter in this model, since the damping coefficient

4D is experimentally determined. The problem in finding a non-empirical expression for

the diaphragm damping coefficient (for instance by using the known quality factor)

comes mostly from the actual implementation of the driver in the device. A perfect

clamped boundary condition is assumed, and deviation from this boundary condition and

the problem of high tolerance/uncertainties between the manufactured piezoceramic-

diaphragms can degrade the accuracy of the model. Nonetheless, the dynamics of the

driver are well captured by this model and were successfully implemented in previous

studies (Gallas et al. 2003a, 2003b; CFDVal-Case 1 2004).









Consider next an acoustic speaker that drives a ZNMF actuator. Similar to a

piezoelectric diaphragm, a simple circuit representation can be made. McCormick (2002)

has already performed such an analysis, as shown in Figure 2-16. The speaker is actually

a moving voice coil that creates acoustic pressure fluctuations inside the cavity. Its

principle is simple. It is usually composed of a permanent magnet, a voice coil and a

diaphragm attached to it. When an ac current flowing through the voice coil changes

direction, the coil's polar orientation reverses, thereby changing the magnetic forces

between the voice coil and the permanent magnet, and then the diaphragm attached to the

coil moves and back and forth. This vibrates the air in front of the speaker, creating

sound waves.
(Speaker corpliance)a
(Speaker resistance)
Moving voice coil M R U R =(BL)2/R aD Ca R4 U
actuator c
| (Coil resistance)a T

Cs (Speaker + air rass),a M

cBL c
U RcSd N
M C A

A B Cavity/NeckDynamics

Figure 2-16: Speaker-driven ZNMF actuator. A) Physical arrangement. B) Equivalent
circuit model representation obtained using lumped elements used in
McCormick (2000). BL is the voice coil force constant (= magnetic flux x
coil length)

As represented in Figure 2-16B, the acoustic impedance ZaD of the driver is

modeled via acoustic resistances (from the coil and the speaker) mounted in series with

acoustic masses (speaker plus air) and compliances (from the speaker). The main issues

concerning such an arrangement are, first, the practical deployment of the speaker to









drive the ZNMF actuator in a desired frequency range. Also, a loudspeaker creates

pressure fluctuations whose characteristics (amplitude and frequency) depend on the

speaker dynamics. For example, if the speaker is mounted in a large cavity enclosure

(whose size is greater than the acoustic wavelength), it might excite the acoustic modes

of the cavity, thereby resulting in three-dimensionality of the flow in the slot.

Sorifice .vent
sealing
membrane channe
cavity r
bottom T
cavityv---

shaker


Figure 2-17: Schematic of a shaker-driven ZNMF actuator, showing the vent channel
between the two sealed cavities.

Finally, consider a piston-like driver. It could be operated either mechanically, for

instance by a camshaft or by other mechanical means, or by using an electromagnetic

shaker. Here, we turn our attention to the latter application. An electromagnetic piston

usually consists of a moving voice coil shaft that drives a rigid piston plate and, in

essence, follows the same concept as presented above for the case of a voice coil

loudspeaker. Although the previous discussion on the LEM representation remains the

same here, the major difference comes from the nature of the piston itself. In fact, while

the top face of the piston is facing the cavity of the ZNMF actuator, another cavity on the

opposite side of the piston is present, as shown in Figure 2-17. This cavity may or may

not be vented to the other cavity. If sealed, when the ZNMF device is running at a

specific condition, an additional pressure load is created on the piston plate to account for

the static pressure difference between the cavities that may deteriorate the nominal

transducer performance. To alleviate this effect, the ZNMF cavity and the bottom cavity









could be vented together, in a similar manner to that employed for a microphone design.

Also, this bottom cavity should be added in series with the ZNMF cavity (since they

share the same common flow) in the circuit representation of the actuator that is shown in

Figure 2-18.

el ectFedTnamic" dcorpng
(BL):1 Qd Qj
i IId j-^ V\-- --------i
electrical \ v d Qj
source










acoustic impedance of the ZNMF cavity, Zac bot is the acoustic impedance of
the bottom cavity, and ZaVet is the acoustic impedance of the vent channel.

Even though tools are available using lumped element modeling, the ZNMF

actuator driver must be modeled with care, especially when deployed in a physical

apparatus. However, once the driver dynamics have been successfully modeled, its








Chapter 7.

Now that some insight has been gained on the dynamics of a ZNMF actuator in still
-



























air, a test matrix is constructed to carefully investigate both experimentally and

numerically the unresolved features of these types of devices, especially on refining the

nonlinear loss coefficient of the orifice.
nonlinear loss coefficient of the orifice.









Test Matrix

A significant database forms the basis of a test matrix that includes direct numerical

simulations and experimental results. The test matrix is comprised of various test

actuator configurations that are examined to ultimately assess the accuracy of the

developed reduced-order models over a wide range of operating conditions.

The goal is to test various actuator configurations in order to cover a wide range of

operating conditions, in a quiescent medium, by varying the key dimensionless

parameters extracted in the above dimensional analysis. Available numerical simulations

are used along with experimental data performed in the Fluid Mechanics Laboratory at

the University of Florida on a single piezoelectric-driven ZNMF device exhausting in still

air. Table 2-3 describes the test matrix. The first six cases are direct numerical

simulations (DNS) from the George Washington University under the supervision of

Prof Mittal. They use a 2D DNS simulation whose methodology is detailed in Appendix

F. Case 8 comes from the first test case of the NASA LaRC workshop (CFDVal 2004).

Then, Case 9 to Case 72 are experimental test cases performed at the University of

Florida for axisymmetric piezoelectric-driven ZNMF actuators. The experimental setup

is described in details in Chapter 3, and the results are systematically analyzed and

studied in Chapter 4, Chapter 5, and Chapter 6.

Table 2-3: Test matrix for ZNMF actuator in quiescent medium
d h w V
Case Type f(Hz) w/d S Re St f f/fd Jet
(mm) (mm) (mm3
1 CFD 0.38 1 1 oo 800 25.0 262 2.4 0.13 X
2 CFD 0.38 1 2 oo 800 25.0 262 2.4 0.15 X
3 CFD 0.06 1 0.68 oo 360 10.0 262 0.4 0.01 J
4 CFD 0.20 0.1 0.1 oo 800 5.0 63.6 0.4 0.00 J
5 CFD 0.80 0.1 0.1 oo 800 10.0 255 0.4 0.01 J
6 CFD 1.99 0.1 0.1 oo 800 15.8 477 0.5 0.03 J
7 CFD 1.99 0.1 0.1 oo 800 15.8 636 0.4 0.03 J
8 exp/cfd 446 1.27 13.5 28 7549 17.1 861 0.3 2.65 0.99 J
9 exp. 39 1.9 1.8 7109 7.6 8.79 6.6 0.06 0.06 X












Case

10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59


Type

exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exp.
exo.


f(Hz) d
(mm)
39 1.9
39 1.9
39 1.9
39 1.9
39 1.9
39 1.9
39 1.9
39 1.9
39 1.9
39 1.9
39 1.9
780 1.9
780 1.9
780 1.9
780 1.9
780 1.9
780 1.9
780 1.9
780 1.9
780 1.9
780 1.9
780 1.9
780 1.9
780 1.9
780 1.9
780 1.9
780 1.9
780 1.9
780 1.9
780 1.9
1200 1.9
39 2.98
39 2.98
39 2.98
500 2.98
500 2.98
780 2.98
780 2.98
780 2.98
780 2.98
780 2.98
39 2.96
39 2.96
39 2.96
39 2.96
780 2.96
780 2.96
780 2.96
780 2.96
780 2.96


h
(mm)
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
4.99
4.99
4.99
4.99
4.99
4.99
4.99
4.99
4.99


V
w/d
wd (mm3)
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
-- 7109
- 7109
- 7109


S

7.6
7.6
7.6
7.6
7.6
7.6
7.6
7.6
7.6
7.6
7.6
34.0
34.0
34.0
34.0
34.0
34.0
34.0
34.0
34.0
34.0
34.0
34.0
34.0
34.0
34.0
34.0
34.0
34.0
34.0
42.1
11.9
11.9
11.9
42.6
42.6
53.2
53.2
53.2
53.2
53.2
11.8
11.8
11.8
11.8
52.9
52.9
52.9
52.9
52.9


Re

12.0
22.6
33.2
39.8
46.5
52.5
59.7
66.0
73.7
81.6
88.2
192
242
374
513
637
750
825
930
1131
1120
1200
1264
1510
1589
1683
1774
1842
1876
2755
90.8
40.6
47.3
63.4
1959
2615
109
254
571
1439
2022
29.8
43.0
55.7
71.9
125
318
867
2059
3039


St f/fH f/fd Jet

4.8 0.06 0.06 J
2.5 0.06 0.06 J
1.7 0.06 0.06 J
1.4 0.06 0.06 J
1.2 0.06 0.06 J
1.1 0.06 0.06 J
1.0 0.06 0.06 J
0.9 0.06 0.06 J
0.8 0.06 0.06 J
0.7 0.06 0.06 J
0.6 0.06 0.06 J
6.0 1.24 1.23 X
4.8 1.24 1.23 J
3.1 1.24 1.23 J
2.2 1.24 1.23 J
1.8 1.24 1.23 J
1.5 1.24 1.23 J
1.4 1.24 1.23 J
1.2 1.24 1.23 J
1.1 1.24 1.23 J
1.0 1.24 1.23 J
1.0 1.24 1.23 J
0.9 1.24 1.23 J
0.8 1.24 1.23 J
0.7 1.24 1.23 J
0.7 1.24 1.23 J
0.6 1.24 1.23 J
0.6 1.24 1.23 J
0.6 1.24 1.23 J
0.4 1.24 1.23 J
19.5 1.91 1.90 X
3.49 0.04 0.06 J
2.99 0.04 0.06 J
2.23 0.04 0.06 J
0.93 0.55 0.79 J
0.69 0.55 0.79 J
26.0 0.86 1.23 X
11.2 0.86 1.23 X
4.96 0.86 1.23 J
1.97 0.86 1.23 J
1.40 0.86 1.23 J
4.69 0.06 0.06 J
3.25 0.06 0.06 J
2.51 0.06 0.06 J
1.94 0.06 0.06 J
22.3 1.25 1.23 X
8.79 1.25 1.23 X
3.22 1.25 1.23 J
1.36 1.25 1.23 J
0.92 1.25 1.23 J










d h V
Case Type f(Hz) () ( w/d S(m3 Re St f/f, f/fd Jet
(mm) (mm) (mm3)
60 exp. 39 1.0 5.0 7109 4.0 132 0.12 0.16 0.06 J
61 exp. 39 1.0 5.0 7109 4.0 157 0.10 0.16 0.06 J
62 exp. 39 1.0 5.0 7109 4.0 205 0.08 0.16 0.06 J
63 exp. 500 1.0 5.0 7109 14.3 286 0.72 2.10 0.79 J
64 exp. 500 1.0 5.0 7109 14.3 461 0.44 2.10 0.79 J
65 exp. 730 1.0 5.0 7109 17.3 269 1.11 3.07 1.16 J
66 exp. 730 1.0 5.0 7109 17.3 611 0.49 3.07 1.16 J
67 exp. 730 1.0 5.0 7109 17.3 893 0.33 3.07 1.16 J
68 exp. 730 1.0 5.0 7109 17.3 1081 0.28 3.07 1.16 J
69 exp. 730 1.0 5.0 7109 17.3 1361 0.22 3.07 1.16 J
70 exp. 39 0.98 0.92 7109 3.9 49.6 0.31 0.09 0.06 J
71 exp. 39 0.98 0.92 7109 3.9 112 0.14 0.09 0.06 J
72 exp. 39 0.98 0.92 7109 3.9 179 0.09 0.09 0.06 J


To conclude this chapter, the existing lumped element model from Gallas et al.

(2003a) has been presented and reviewed, and it has been shown that it could be extended

to more general device configurations, particularly in terms of orifice geometry and

driver configuration. Then, a dimensional analysis of an isolated ZNMF actuator was

performed. A compact expression, in terms of the principal dimensionless parameters,

was found for the nondimensional linear transfer function that relates the output to the

input of the actuator, regardless of the orifice geometry and of the driver configuration.

Next, some modeling issues have been investigated for the different components of a

ZNMF actuator. Specifically, the LEM technique has been used in the time domain to

yield some insight on the orifice shape effect, and a physical description on the associated

orifice losses has been provided. Finally, since one of the goals of this research is to

develop a refined low-order model, which is presented in Chapter 6 and that builds on the

results presented in the subsequent chapters, a significant database forms the basis of a

test matrix that is comprised of direct numerical simulations and experimental results.














CHAPTER 3
EXPERIMENTAL SETUP

This chapter provides the details on the design and the specifications of the ZNMF

devices used in the experimental study. Descriptions of the cavity pressure, driver

deflection, and actuator exit velocity measurements are provided, along with the dynamic

data acquisition system employed. Then, the data reduction process is presented with

some general results. A description of the Fourier series decomposition applied to the

phase-locked, ensemble average time signals is presented next. Finally, a description of

the flow visualization technique employed to determine if a synthetic jet is formed is then

provided.

Experimental Setup

In this dissertation, two different experiments are performed. The first one,

referred to as Test 1, is used in the orifice flow analysis presented in Chapter 4 and the

corresponding test cases are listed in Table 2-3. The second test, Test 2, is used in the

cavity compressibility analysis (presented in Chapter 5). Test 1 consists of phase-locked

measurements of the velocity profile at the orifice, cavity pressure, and diaphragm

deflection, and the device uses a large diaphragm and has an axisymmetric straight

orifice. On the other hand, in Test 2 only the frequency response of the centerline

velocity and driver displacement are acquired, and the device uses a small diaphragm and

the orifice is a rectangular slot. However, since the two tests share the same equipment

and basic setup and Test 1 requires additional equipment, only Test 1 is detailed below.











Top View


displacement sensor


3 component
traverse
I //


Figure 3-1: Schematic of the experimental setup for phase-locked cavity pressure,
diaphragm deflection and off-axis, two-component LDV measurements.


diaphragm


LV WL cavity (V) U/
top plate body plate diaphragm clamp plate
mount
Figure 3-2: Exploded view of the modular piezoelectric-driven ZNMF actuator used in
the experimental test.