<%BANNER%>

Reducing Skin Friction and Heat Transfer over a Hypersonic Cruising Vehicle by Mass Injection

Permanent Link: http://ufdc.ufl.edu/UFE0020862/00001

Material Information

Title: Reducing Skin Friction and Heat Transfer over a Hypersonic Cruising Vehicle by Mass Injection
Physical Description: 1 online resource (143 p.)
Language: english
Creator: Nozaki, Yoshifumi
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: aerodynamics, aircraft, cruise, flight, friction, heat, hypersonic, reduction, skin, space, transfer, vehicle
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Aerospace Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Demonstrating technologies for hypersonic aircraft that cruise at speeds greater than Mach 5 is one of the long-term visions of many agencies, like NASA. Reducing skin friction and heat transfer on the surface of hypersonic cruising vehicles has been a focus of constant attention. General methods for estimating the aerodynamic forces and heat transfer around a hypersonic vehicle are used to evaluate the reduction in skin friction and heat transfer on the surface of a hypersonic vehicle by mass injection. Particular attention was paid to the X-24C configuration because of the existence of experimental data of X-24C performance against which the predictions can be compared. The local surface inclination method and the flat plate reference enthalpy methods for laminar and turbulent flow were used to find aerodynamic forces and heat transfer. High temperature effects were included by using a classical approximation of thermodynamic properties. Although this analysis is based on many approximations, these methods worked well and flow properties were reasonably predicted. Reducing skin friction and protecting surfaces from heating by injecting mass did result in a penalty in the form of decreased flight time of the vehicle, and therefore flight range. These penalties were often very light. Also, as more mass is injected, the effect of mass injection grows, but more slowly.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Yoshifumi Nozaki.
Thesis: Thesis (M.S.)--University of Florida, 2007.
Local: Adviser: Sforza, Pat M.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0020862:00001

Permanent Link: http://ufdc.ufl.edu/UFE0020862/00001

Material Information

Title: Reducing Skin Friction and Heat Transfer over a Hypersonic Cruising Vehicle by Mass Injection
Physical Description: 1 online resource (143 p.)
Language: english
Creator: Nozaki, Yoshifumi
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: aerodynamics, aircraft, cruise, flight, friction, heat, hypersonic, reduction, skin, space, transfer, vehicle
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Aerospace Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Demonstrating technologies for hypersonic aircraft that cruise at speeds greater than Mach 5 is one of the long-term visions of many agencies, like NASA. Reducing skin friction and heat transfer on the surface of hypersonic cruising vehicles has been a focus of constant attention. General methods for estimating the aerodynamic forces and heat transfer around a hypersonic vehicle are used to evaluate the reduction in skin friction and heat transfer on the surface of a hypersonic vehicle by mass injection. Particular attention was paid to the X-24C configuration because of the existence of experimental data of X-24C performance against which the predictions can be compared. The local surface inclination method and the flat plate reference enthalpy methods for laminar and turbulent flow were used to find aerodynamic forces and heat transfer. High temperature effects were included by using a classical approximation of thermodynamic properties. Although this analysis is based on many approximations, these methods worked well and flow properties were reasonably predicted. Reducing skin friction and protecting surfaces from heating by injecting mass did result in a penalty in the form of decreased flight time of the vehicle, and therefore flight range. These penalties were often very light. Also, as more mass is injected, the effect of mass injection grows, but more slowly.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Yoshifumi Nozaki.
Thesis: Thesis (M.S.)--University of Florida, 2007.
Local: Adviser: Sforza, Pat M.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0020862:00001


This item has the following downloads:


Full Text
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 E20101207_AAAAAN INGEST_TIME 2010-12-07T06:31:58Z PACKAGE UFE0020862_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES
FILE SIZE 25898 DFID F20101207_AAAILB ORIGIN DEPOSITOR PATH nozaki_y_Page_122.QC.jpg GLOBAL false PRESERVATION BIT MESSAGE_DIGEST ALGORITHM MD5
245a15eea62ec354aa11c36d469d4098
SHA-1
52c343b6cd6f90ad88144cc2de9389de711b5faf
28111 F20101207_AAAIKN nozaki_y_Page_106.QC.jpg
f70c5f750a0e90ad2b1c8b386066798d
1815c2981bd0ec1e30297bf79aea251993c3b3b1
18626 F20101207_AAAIJY nozaki_y_Page_090.QC.jpg
a1367b4738faf468e05c7dd1148424e5
9d280be41bc318ec35d264df6f8fe870ee474be8
778061 F20101207_AAAHHL nozaki_y_Page_059.jp2
bae82dc1aa158b8ed6683e32e8eaa50c
6ceceb37c3e346719d20e106f2123663ec0a0162
87268 F20101207_AAAHGW nozaki_y_Page_044.jp2
634b52f8dd5bb587884b62f3ce6fc07b
a980a86efb8ece8d85fb6b0cc286e13d4c1fd665
6978 F20101207_AAAILC nozaki_y_Page_123thm.jpg
1f87a43bed8467572f46c622af3f7cb8
21728d382acd25f61a7943bca497054b694b845c
5541 F20101207_AAAIJZ nozaki_y_Page_092thm.jpg
756b6513802fd404c597739fe0a77ec8
3a13e093159115f6cf30f369e5c06018bbb0d7c4
576007 F20101207_AAAHIA nozaki_y_Page_074.jp2
dfa31b9746c97c80a570ecf003b6d0d2
5848200720c3dad6e29973262d417142bdea644b
1044444 F20101207_AAAHGX nozaki_y_Page_045.jp2
9b17229043d312bc098548b5101d53d8
d14a119f0d93db977f076c3783a96c48b0833cb6
28962 F20101207_AAAILD nozaki_y_Page_125.QC.jpg
d7964e5cc35f3268855eeff89c2e0507
09b5af90e6b2593a848f0a62cc2ce159ea1dea9e
6936 F20101207_AAAIKO nozaki_y_Page_107thm.jpg
b21abac56299b1296b6a4dc61181d655
da7abc3943a31332f88cffe95abe9f133ce7d8c4
598031 F20101207_AAAHIB nozaki_y_Page_075.jp2
04a64230111973c6854bd33009b5c69e
8ee6009053b9e002dad468862ad2b3ab6f419c56
549100 F20101207_AAAHHM nozaki_y_Page_060.jp2
ce02eae856069e94a534c83d28df275b
05c5adc251f9f9d5fc8dae3ccba9dd91a64877e2
281092 F20101207_AAAHGY nozaki_y_Page_046.jp2
5d726633367e849c312b1144017ce219
a0a94e714b3233c80aff721717a33e75ca279823
6856 F20101207_AAAILE nozaki_y_Page_126thm.jpg
ea996850e9824f5a8b37acee891008ae
6e588dabed636f1c73d30c744cca74625fcaeafb
27739 F20101207_AAAIKP nozaki_y_Page_107.QC.jpg
818c6967ef34defd2679aeb75ef9437c
5a73e43fdc50ea8dc6a781ee5f82bcce02ec24ff
820068 F20101207_AAAHIC nozaki_y_Page_076.jp2
b28a377992258a81e854b84cc204f5a7
d817e7fe4ef34f2376601874b65c5f69237c44f5
536759 F20101207_AAAHHN nozaki_y_Page_061.jp2
3ace3105a81265ab74926181191bc48e
0f94a1352d4689c5c08ff4355e062d8249c57f9e
109520 F20101207_AAAHGZ nozaki_y_Page_047.jp2
ca1acccaaa0cc62e6d3b137bc39a1fb5
7d5aa5779cac4c1b624bcc39b4393bcb37b7fa06
28374 F20101207_AAAILF nozaki_y_Page_126.QC.jpg
efdc0735cb60bd80e6491077cc4e0840
a206062330f680f4bab32b27f68cbd6c0daa2a5e
5812 F20101207_AAAIKQ nozaki_y_Page_108thm.jpg
5a7ed6a0cad443a8c4bbfa2172b7d0d6
3982d2b33433496e6a9e9c5423948b5ff6de5016
796013 F20101207_AAAHID nozaki_y_Page_077.jp2
5aea2c7d6eed697f59246402c1202f70
f73c000ced464eec386b762889ccff96c4e6264e
540378 F20101207_AAAHHO nozaki_y_Page_062.jp2
0d683a871325025a9b7576bc8070991f
523e8fd15d4fd84c4834caa470462c66a5572f10
3932 F20101207_AAAILG nozaki_y_Page_128thm.jpg
478493f64808327223a71acb6991d4e9
e1d50d7cf3fae32322ab1d7ed6456d1e927211a4
5690 F20101207_AAAIKR nozaki_y_Page_109thm.jpg
ee4fc4c3da732dfd38f55ad7a7f62a67
4811d657494ee2c8770f41fb3e7f5e975875930b
703947 F20101207_AAAHIE nozaki_y_Page_078.jp2
7645f86c5f4bfffd9a7b0c823823212c
d32078d41338fa0a9f290d5985018028f9568f67
547772 F20101207_AAAHHP nozaki_y_Page_063.jp2
0380ffddcb60a105a33bafd730faa062
288a93118926673e4d98afafd559f6e0728b11d3
30531 F20101207_AAAILH nozaki_y_Page_129.QC.jpg
f1dfd87057c32229271811c88f818dfe
9b1132ce4ea017712a8ef45bab674c635a990e20
24151 F20101207_AAAIKS nozaki_y_Page_109.QC.jpg
b16d71a88eba39c9aa0aa51562762b48
bf44addae847fd35073bd5bebca08fd1fd15f1e8
560030 F20101207_AAAHIF nozaki_y_Page_079.jp2
f88370f4ff96b7146291530f605514c8
dd61a3f82faa85f84853d43acf09ff4b50f21ace
537351 F20101207_AAAHHQ nozaki_y_Page_064.jp2
f6b3d6f7070a6179f92cb75ab5a173f5
a8a957f400625e9dc6895398a2cf791facb8151b
7596 F20101207_AAAILI nozaki_y_Page_130thm.jpg
21bd6fcd41e45a290fe332fa3433596f
be39d208b877ef42eb447a7c13f4313f667dd697
29841 F20101207_AAAIKT nozaki_y_Page_110.QC.jpg
8feea31f87878fe7ed71be136a5b5ec3
9300dcc50de4eb2e6d5d5e0d14e3461e6ea40222
560319 F20101207_AAAHIG nozaki_y_Page_080.jp2
cece5d4f3e6ba4cf1b50ff3bc37cd7ea
e73ed31d57454f0a691d3eeed8e9110c49ffed7f
575137 F20101207_AAAHHR nozaki_y_Page_065.jp2
ff9ba25c1bfd43bb1dec94a349f0d3d5
9b865445e8edd8f5ca90e92c31f3b8c24ec49638
32963 F20101207_AAAILJ nozaki_y_Page_130.QC.jpg
3bb6f85a68db9732837f0d34aaebeea9
dabf5aace4ad3f4ebdb022d10c4851c9d83695c3
6243 F20101207_AAAIKU nozaki_y_Page_111thm.jpg
c1c44f5f13565bdb3e53b00dea38d3dd
8e32221348718d3beab936cf453ba1ae56340f81
584202 F20101207_AAAHIH nozaki_y_Page_081.jp2
96fbb2478f0a1e325694d0134468cfc3
dfb36f421016b5b30b5734fb5142006795370eb5
557185 F20101207_AAAHHS nozaki_y_Page_066.jp2
9495d3670c809411903cf5aa6ff14295
85caf8139f682af756201c0b7230ff7c6cde0c4d
6846 F20101207_AAAILK nozaki_y_Page_132thm.jpg
477e87f95126215920c4a17793dce270
243781cbc5bc7d8a45ce3cf53adb29b2e586aca6
21285 F20101207_AAAIKV nozaki_y_Page_114.QC.jpg
41bf843babb76e8a3df94dc0c42bde52
2d788b1eb502f4fb1f9502492882103494192228
528117 F20101207_AAAHII nozaki_y_Page_082.jp2
0c9cf56d0a441aa835b19553e646fbf5
ccd58b20c6745f9262fcbc4704cc63d39a0cb019
537479 F20101207_AAAHHT nozaki_y_Page_067.jp2
03532aa03125a12b088d1a1c448ef6c3
fe572eb09014558b8a50c34ca2edfff9e1de6177
1711 F20101207_AAAILL nozaki_y_Page_133thm.jpg
7bfb266dd3fc6c123140431939f9576d
4b03855c617098881b80dd42ba44e962bcd8f12d
6628 F20101207_AAAIKW nozaki_y_Page_116thm.jpg
19eb50a87031c20956895f9409cc3a2a
319e73fcbbcf6ac2fd61e3fb452e16146c183578
730049 F20101207_AAAHHU nozaki_y_Page_068.jp2
dc9574bfc32a53d9fd6ad1d12565cb5e
9c21c74c72239d770417e3e57f03e1663a70c068
580611 F20101207_AAAHIJ nozaki_y_Page_083.jp2
1cb952ab82a7c6ba2f1c6e46a627f65d
2c08a511cd509be13e997bbf105ee99e93d38f5d
7721 F20101207_AAAILM nozaki_y_Page_133.QC.jpg
fed11fd1cb08233bdb5313bfbe6575a4
2425aacbf676772c724da16b2b8ae491756576d1
27883 F20101207_AAAIKX nozaki_y_Page_116.QC.jpg
bea604abf4b1e592b1d74bc578f7c555
bc7c7a6c348a1bc9db73ee8aefa60357f29de9b1
690148 F20101207_AAAHHV nozaki_y_Page_069.jp2
34351084b5681df54958b5d3decac61c
7ca057b2bb9e47c78d45618a2cde7a823f4e0471
623652 F20101207_AAAHIK nozaki_y_Page_084.jp2
f6d35276de1e4fc8175beb326456bed9
551c408fd487a1822dd066f033e434700d68443b
5847 F20101207_AAAILN nozaki_y_Page_134thm.jpg
d871522c1a22cb24a94cf29d9da385c0
b38f54c07938e5cf8b08f333bab166a6f1f08502
3848 F20101207_AAAIKY nozaki_y_Page_117thm.jpg
4c02b004067bbcf23579e8e140b1b9f2
d756ad0e3e1c8e4c3f47746c41d16e96e337a712
542249 F20101207_AAAHHW nozaki_y_Page_070.jp2
6aab36a252a0df37bf3cede7ace0435e
eb77ba9ef8f80d007d59e2a6aaf7c8d1e070eb6d
739837 F20101207_AAAHIL nozaki_y_Page_085.jp2
57d745da05fb26a5cc2e56eedbed1c4a
bf6d120701a9166914c8504c9aa84255623592e6
26589 F20101207_AAAILO nozaki_y_Page_134.QC.jpg
a8a3b64477530edd296d24e5d3253018
45fb0114c0397682f00283ae830535aa351bb623
20928 F20101207_AAAIKZ nozaki_y_Page_118.QC.jpg
7cf8bca1cb43bfba77771bf050d3b645
cd70135306db0a88134e5be043ff652ed9db92f9
536333 F20101207_AAAHHX nozaki_y_Page_071.jp2
2548a1052c6e1477660006e5e3d89441
cebf26b1306d2fb3acecdab04949edd2663e5f2c
84267 F20101207_AAAHJA nozaki_y_Page_100.jp2
7a4e5b407bdff16cba797ea50dbb2e5e
be0387c3debb325138fcc9d99942a984431e9784
771126 F20101207_AAAHIM nozaki_y_Page_086.jp2
8c3a3fca690a319f0c9c5d5c380a4829
59eb321e3d81effaec5236b286f81c6031b93e4b
562436 F20101207_AAAHHY nozaki_y_Page_072.jp2
7f54293aa22f8bd95b2898e42d71f3ac
9860d08fdd9e6d57d125a33503ea6a9b87e871ac
37313 F20101207_AAAHJB nozaki_y_Page_101.jp2
10b3eb0acce868eca944da225c952b15
2f4969d28b893d98a4436db887a4cb84d982e931
5991 F20101207_AAAILP nozaki_y_Page_136thm.jpg
56ad41d0c4a7aebbd904ecc97e989a84
08956a7236802da7a85c07609525b5c3e59ba10d
511530 F20101207_AAAHHZ nozaki_y_Page_073.jp2
acd032da58071a6207c823f7e9cff8ed
b530dd7ad2f9c9ba38a5b75af57288ea07397e5e
40991 F20101207_AAAHJC nozaki_y_Page_102.jp2
29486d336390f2441bcc8fac8b2fb6f6
7b6a3fb2e7ab4173fab154f267cf56020c86a73b
679656 F20101207_AAAHIN nozaki_y_Page_087.jp2
80d1ba800b659ec5466a057d5796797b
f6e511ea8e4ab9d1cb4fea977148acc8cd3e7947
5075 F20101207_AAAILQ nozaki_y_Page_137thm.jpg
05c9b778479029507e1a2776f344bb56
2654fb13ee890e873699f069c98f509b63426d96
55457 F20101207_AAAHJD nozaki_y_Page_103.jp2
a2afc57d835fb85e13ccad6e8e631ca2
4ebe4c7d6bac0e3f3685ae08292ed22293419a99
536820 F20101207_AAAHIO nozaki_y_Page_088.jp2
7b5c0bb3629c96ada0c610b2520b2d27
28394a00daee8bcb602e2b5c57dd7a553a75785a
7504 F20101207_AAAILR nozaki_y_Page_139thm.jpg
c88fc55d552e6ea22414d60580570c5c
41989dffde1197448007227e9cd94d284ad9ce4d
75079 F20101207_AAAHJE nozaki_y_Page_104.jp2
2611d7cf07e81229912a0e4b26a1772e
f4ac4367b651880ff517f72ab2de6bffa6374d82
540004 F20101207_AAAHIP nozaki_y_Page_089.jp2
00c36f255342ae319f39b1168b9f8e21
f27a90f22b8b15aae407b99acc251641a1dab672
1655 F20101207_AAAILS nozaki_y_Page_140thm.jpg
cf2d88b08f3b9d40cd07be1c84ec3ecb
88798483fe0eea9a66380d7410f7345805055a3f
88262 F20101207_AAAHJF nozaki_y_Page_105.jp2
6633c1701d1818b1b3cc71c35ed9f258
dc8267af775b85b94780425800c8b75728e49ef9
568725 F20101207_AAAHIQ nozaki_y_Page_090.jp2
0cb09b44417e421d723e5de76e215f3d
2f861817a45816beba8974d0874b885a04c3239c
4801 F20101207_AAAILT nozaki_y_Page_141thm.jpg
943dae0076cc182738f6c5cf09276c96
9f0cfe9fa78a67d413e93cdb6533d495ba345f79
101044 F20101207_AAAHJG nozaki_y_Page_106.jp2
68ff5b10d5524afc901595f095b7a074
1e14aad93f9f1251aa2677de59efbc8e0d34d80d
506828 F20101207_AAAHIR nozaki_y_Page_091.jp2
65f17bf6c99d1bbce50023ab206b9a25
19fa9d6c17483c24eb0821b4a019f5a41db4bec0
18713 F20101207_AAAILU nozaki_y_Page_141.QC.jpg
fbc615b88a2173ea70055ab8aab8614c
b23cf827945cfd689f50cf9c08baa1405df14d1c
99343 F20101207_AAAHJH nozaki_y_Page_107.jp2
5c1efe85938a95e51eb3b8f5513684e3
34fd9750310b485db5feec9eb89c59dab5cee5dd
561751 F20101207_AAAHIS nozaki_y_Page_092.jp2
3cb33f3f7fb5294a2328cc2eac8de156
79447557c9be1366b907fd0fe70f2a4ce22c2692
30979 F20101207_AAAILV nozaki_y_Page_142.QC.jpg
78e150d50a9b840a87ec22668dc5658e
87c8c3d928416d4acf69f1cbed3aecd68fdb757a
83933 F20101207_AAAHJI nozaki_y_Page_108.jp2
dba8424869509ed489c16e411c4a2808
64f95c62caa884623f0e32d50ef4b0b87bae41ff
572333 F20101207_AAAHIT nozaki_y_Page_093.jp2
866d00680bc7aca355ebfb7dda0664a8
eb02c9ff6f6b5a25580deb6faa65dce1ab1ba8e2
2233 F20101207_AAAILW nozaki_y_Page_143thm.jpg
3ad9531a5c181b81867976ad9a704160
685ed1b4e3fe99ff2ed375ca198def187a564b98
91365 F20101207_AAAHJJ nozaki_y_Page_109.jp2
950c9808dec45f0fdc0ad1937c802762
a0ef63fafa98e1ace85b576515dd890f154d4b18
175992 F20101207_AAAHIU nozaki_y_Page_094.jp2
0dd29dc98306df0fb2204a4c04731214
6fcd07922e83d89c4305f56e6b358abaad002b3b
118627 F20101207_AAAHJK nozaki_y_Page_110.jp2
cfa2f61fa9123e56771b9c7e2a903ee9
e4d7d78285bd5d3d31194f35fe47b5a05b9018c4
114845 F20101207_AAAHIV nozaki_y_Page_095.jp2
c2a2be07a6abd2b123131bc164d23be0
098c953cdb2aa484486d0e8b37e6ca215498562b
104713 F20101207_AAAHJL nozaki_y_Page_111.jp2
4e76556eef32c19221ce45ebee5d6a2f
2f487cd77ab4ebbf2839e83b79a822b0844b525d
107356 F20101207_AAAHIW nozaki_y_Page_096.jp2
0029f851eb24146e43fdb423e742669f
e990b4315bdcada2addd15891af205a8df6ed069
110714 F20101207_AAAHKA nozaki_y_Page_126.jp2
7769fc2f4793330af309ba2d7a0f5f5c
b4c8c97e98be35d1f3b435755b547b874ee1c340
93771 F20101207_AAAHJM nozaki_y_Page_112.jp2
bc0e283fce621af410b4453bcabec8c5
c86471ed2760182d97a72c47c46da29123578894
12448 F20101207_AAAHIX nozaki_y_Page_097.jp2
f9dc0fdd28eeef7c850313ffab0e5c1b
6bd78dc71cf4418548c1bb87b7c0bdc727087ae3
67156 F20101207_AAAHKB nozaki_y_Page_127.jp2
2c2a476fce1b37ca5c388dca0302fae9
da4c8d9cdb4c97946fd89e7d42807180838fd433
110350 F20101207_AAAHJN nozaki_y_Page_113.jp2
cfca007b30541da61702390ef3c35c0a
9e061ca4b65ea5e513f635446e167fd569b0d195
111009 F20101207_AAAHIY nozaki_y_Page_098.jp2
41c942e7c7971ae58d14e303005bb86f
f3e9fdf00550f6451f19bd967e56626b499527f5
52157 F20101207_AAAHKC nozaki_y_Page_128.jp2
0435359458138da62b46c8f5f4936d0f
e283cd9034113962f4489ff617fa5635c46b9ade
117263 F20101207_AAAHIZ nozaki_y_Page_099.jp2
5f2b946f84f18bee46e9b104b61b364c
a1207e7efffaffc4776930abf8c9b58fe79f777c
118176 F20101207_AAAHKD nozaki_y_Page_129.jp2
3a3cfbe2e358f5bf18a775739a60ebd8
f5e070d60910cf5187229864b2dc71e9f9602a87
74755 F20101207_AAAHJO nozaki_y_Page_114.jp2
b0d6a0c31e15bbb38e5bed37bebf220e
677ab922700f8335bcdc74ededdb38d6e5ed57aa
130852 F20101207_AAAHKE nozaki_y_Page_130.jp2
a4b6465dca509a7bfc934df03e05fa10
b99f9a77ee7ededcaed133f4f350c2e75078c809
92539 F20101207_AAAHJP nozaki_y_Page_115.jp2
6d0f3cbf6ebb1ef2974566ada9534cf1
3933c1b82577f3afcddabeaaa0a3e616a147491e
94458 F20101207_AAAHKF nozaki_y_Page_131.jp2
a1252572e473b7393330d87c19807372
f3861b8b0a04caa8a36ab478390161c1e8d06e00
110682 F20101207_AAAHJQ nozaki_y_Page_116.jp2
17626873150b2b7a220b5de2720bb4c9
03dc26182f9c83130fe09b248b7aa577a1838337
132484 F20101207_AAAHKG nozaki_y_Page_132.jp2
25e8ff90b94af4510209d8910a61bd8f
e29d43552ae430793283c6f0a90e69fcf31cb6ad
39821 F20101207_AAAHJR nozaki_y_Page_117.jp2
78065fa6608753bd34ff750b59f9fae4
d030ad2a7fdae510bfd6bca40364bdd8e7f07603
30854 F20101207_AAAHKH nozaki_y_Page_133.jp2
4cad01c558f27e234439033f6b74a760
621591f951c9b9905bfd91a9718cd9b562d26a27
80023 F20101207_AAAHJS nozaki_y_Page_118.jp2
2d98f504d53dcb6370dad11a934aafe7
2f1d01707b00e73f08b2156e50cf8f6e74c9f185
105211 F20101207_AAAHKI nozaki_y_Page_134.jp2
d7526be4b51b99188b5fd4f2e930fb19
222eb87b1fe7dd8fc6aca04b5318f07a2ba50c4c
86992 F20101207_AAAHJT nozaki_y_Page_119.jp2
b27030796fc976e3a3d569d40be679bb
0b5be392b2f69f19dc9f08941c5c2f93affd2a28
89873 F20101207_AAAHKJ nozaki_y_Page_135.jp2
ef14f6ab7cac43d9d9d922b53867cbf5
1b638ebc363123425baf3e3cb769038c436b3dc5
91248 F20101207_AAAHJU nozaki_y_Page_120.jp2
af9dabf263bb6caa444b06e729e49394
7dcf629d5912bed48dfbc798c67563fa687633be
107964 F20101207_AAAHKK nozaki_y_Page_136.jp2
dca96401acb9278c1b714f38f15750e1
3aa7026478da97acc38a9e2644f2d0dfd84a71ba
95241 F20101207_AAAHJV nozaki_y_Page_121.jp2
5b1ad1e9b74e670ec447514f8ca90fb1
4be3e5471f0adfcd25065da5ef355b1f69c03a87
90507 F20101207_AAAHKL nozaki_y_Page_137.jp2
16b225d4fbaf81848a839c5589360991
97a79d1cf88c9d6213230c7a924006aaaec2541e
97792 F20101207_AAAHJW nozaki_y_Page_122.jp2
3187a12b0ddddcc1c6f154600ee90f5a
9249ca62647455326d786a05fd425082c2b9e286
145219 F20101207_AAAHKM nozaki_y_Page_139.jp2
fe0825ba1aed4196b5568ba15193e823
dadba0f18ee18040b22c1e04979ae3c893049e12
105001 F20101207_AAAHJX nozaki_y_Page_123.jp2
ca17d2ea9e8e5df8f05c303305f01f9d
ff5250ba9766fbe8f31c17f53a6ea6f73f8fa37b
25271604 F20101207_AAAHLA nozaki_y_Page_010.tif
a61436f530ab4ca789ebd9421a0b273b
bce1bff5046928955efbc2130f78adf2471be467
21499 F20101207_AAAHKN nozaki_y_Page_140.jp2
1fe968ed43484344b400b8d6bb83076f
4942e3d00065123dbbdf4e8040deaf30565a871b
113589 F20101207_AAAHJY nozaki_y_Page_124.jp2
3685e2a775855fd27bf09a5ba3e0831b
862afdae08e4e9bde605f5b9d1a1213239d68907
F20101207_AAAHLB nozaki_y_Page_011.tif
78a733a65f3447c4e3c10c252b899aff
bffd6acdd70616c22551507b46596251cca06f3d
69355 F20101207_AAAHKO nozaki_y_Page_141.jp2
7dcfe0a1b41a8931154ad7033dd5dbca
a3ce8a4950facdd217be848eab01936476491d02
112314 F20101207_AAAHJZ nozaki_y_Page_125.jp2
7104bd9e8210962bcdf81c452867fae3
8978121acf6a5115290f58abeac949c4cb9b6345
F20101207_AAAHLC nozaki_y_Page_012.tif
0a9ecc30159ba171057677cc147eb590
9d1949036e4e466c92d4311c570d2d9defcd05df
F20101207_AAAHLD nozaki_y_Page_013.tif
4bef00b779234e873a4ef46344d072a3
b9eba7367fd9e2b2e60e9214c352391176f3167a
109453 F20101207_AAAHKP nozaki_y_Page_142.jp2
129a8351eb14f0724376c4d0e48a87fe
066732fa08791e878ba96ed41fe36f76ca031650
F20101207_AAAHLE nozaki_y_Page_014.tif
a3a822b15234922aa4e5584916c174ca
02135eca7b0ac6a6797b6b09b6ef395877afcdca
28807 F20101207_AAAHKQ nozaki_y_Page_143.jp2
bf555c6807289f5882e3ce938ffc7329
60f6c8cc7fc74670c1a1ec32a71da5567539c29f
F20101207_AAAHLF nozaki_y_Page_015.tif
b362cedba65acd05ac314777852fc27e
82fed6ac25ac4deafbdefeb84e652dcb865861af
1053954 F20101207_AAAHKR nozaki_y_Page_001.tif
362bbc242d33cb62f2a359b3a52ae2d4
4527bda690fd3d6bceadeb46ea535a64fb323164
F20101207_AAAHLG nozaki_y_Page_016.tif
d48784a47e686fc52d4212ee51bd94de
74949023d0e3dc42f25443955e7c1abf860e3217
F20101207_AAAHKS nozaki_y_Page_002.tif
4bff308d453c7cbafc25e02e4e20e231
cbe9b13c8acda87a69b5589c4c573c9b367d60b2
F20101207_AAAHLH nozaki_y_Page_017.tif
1c321c974bbf89152b5376e0596406ee
d0beb53fb168cf80e8bce57b8071d828c07c02c8
F20101207_AAAHKT nozaki_y_Page_003.tif
7e2ac5bdc22be0bf4f407a4a81990d27
5d3480694d334a6178be83cef51a3e8c98258235
F20101207_AAAHLI nozaki_y_Page_018.tif
0ce404589f665b4498303aa648bc2e61
f5026b46e909be9886874b184100bd743a4322c6
F20101207_AAAHKU nozaki_y_Page_004.tif
3cf74660cda5a6c8a112159978e7b0cb
da4e89f0d89b00dfa33450b0b8088d0e35b25587
F20101207_AAAHLJ nozaki_y_Page_019.tif
7a62ad3325dbcdae8758282ce31cf5bc
d06cabd57f3250401b6ebf521d74aff5b1e4edb5
F20101207_AAAHKV nozaki_y_Page_005.tif
c46bebd9f394e9253b7ad4615ade86f0
9a8a2ba852010efa1bea6d909b51146092e906b7
F20101207_AAAHLK nozaki_y_Page_020.tif
3469116d0611eccd613417a6a1308d75
e9f73d781e65da8149fd6cb58b2937c0f904e07e
F20101207_AAAHKW nozaki_y_Page_006.tif
f7eb48f914ac8ea306e892b929b6463b
eaac63f297af50dee6a74ee86985f9c81304bf24
F20101207_AAAHLL nozaki_y_Page_021.tif
633e38d7b95e0e9340b862b9269f3902
2a4ebc10e7eba4942163870433c6ea4f140e9275
F20101207_AAAHKX nozaki_y_Page_007.tif
9d2db5251aa2fcce87f6ddb1c9224fcd
7bf406ced169d06e7e0ce72c7263d6c760b2e31e
F20101207_AAAHMA nozaki_y_Page_036.tif
f07c7a9533ec9d99a88b9949e88f19c2
36d623902c2424f4bb2335abfcd24ba55fb3adc7
F20101207_AAAHLM nozaki_y_Page_022.tif
11e80a85f8ba026b282f086c15761fe5
9338c82a92e71275f199f5ac51b9bdd355e64afa
F20101207_AAAHKY nozaki_y_Page_008.tif
4ce3913ea30a2a45e6bf6081384aa7eb
ba20f56dc4a428fa9c059f1e85649f590e1a4ed7
F20101207_AAAHMB nozaki_y_Page_037.tif
1ff48bfba8ba1378499613fe220fe21c
94806ebddc5c5924047a8d4893a5a1063763ae3a
F20101207_AAAHLN nozaki_y_Page_023.tif
2153407a564eb864689ccaaafc504d08
dd075695fb1c19615467dc935422f001a73b779e
F20101207_AAAHKZ nozaki_y_Page_009.tif
3640a8c9976b66b9e4aefaebbac7f103
149d861d22fbea592e7e2bf24d9f83df18402daf
8423998 F20101207_AAAHMC nozaki_y_Page_039.tif
5e90447deb96065b499c5875bc85ef38
98becfc1b38eb25c5f41f6756de6a42954aaf83a
F20101207_AAAHLO nozaki_y_Page_024.tif
19cf10c76affe8f58cd94ffd6aeea3fe
ac923e866f1db99c05b9bbd840ab1161f84d6b4e
F20101207_AAAHMD nozaki_y_Page_040.tif
95637225ee5df0a0716800dc8cd028b1
9a124767c6802f2145e292b5a931b06ce8820920
F20101207_AAAHLP nozaki_y_Page_025.tif
cabe4761adf57370a0c61fee4097a373
fe7b6789aeaa6ba05abc51dc4f754011a403d1ec
F20101207_AAAHME nozaki_y_Page_041.tif
4620932e5abed8d73ecaaed3e48ef4c1
5af979f590a60abce0d6f395098edfef89924a2e
F20101207_AAAHMF nozaki_y_Page_042.tif
c3de5e46f1dc06e864f6d750064d174c
0a9c50e18a227e68bd380a26f58ea12d9a5b14b9
F20101207_AAAHLQ nozaki_y_Page_026.tif
73a7874842a822f89df5b256a13c96c1
d6debd0e2288e4d375d015d04d7a63e0215a8f48
F20101207_AAAHMG nozaki_y_Page_043.tif
12dccc28af67bae491ffb73721ce4712
8b66b52316cffb0106161f9dc4d13c06058977b6
F20101207_AAAHLR nozaki_y_Page_027.tif
55d86707b0180e2a2df393079ec29439
f4548ca44671e13c40f40be862df1b0237f7068a
F20101207_AAAHMH nozaki_y_Page_044.tif
7de1079cb6cb85ee0afb0e3c1ef49e84
3eb949d2e1358ba72084e7cc6980e27667e2b8e2
F20101207_AAAHLS nozaki_y_Page_028.tif
0564bcb2f90b2e25f4bc15b307413227
ebce6d856b973805cb114c83839324f68fe2f07c
F20101207_AAAHMI nozaki_y_Page_045.tif
bde2158613c9a8ec187ce6a3b6d96e54
8024fd4b1cacdeeb6c0a9a70bbce52147f2284ab
F20101207_AAAHLT nozaki_y_Page_029.tif
e056a79f0a4031852d22daef1c07e9e0
de6bdf1749f55832d4b3824f28ba5054af7df779
F20101207_AAAHMJ nozaki_y_Page_046.tif
61f34c258b3b84c190d7a7bc7d998164
bb9c205be5450ef3ce7818d5c1075574d84fc549
F20101207_AAAHLU nozaki_y_Page_030.tif
40d265beb0d4024dffed42526423c8f6
a66eb2b929e7631d1604f45882d9f74bae9ca5de
F20101207_AAAHMK nozaki_y_Page_047.tif
96da4a8c3703dbd4581c98f6aa920013
0d645831fc9154fdc9f28e14265042bb3e012ec1
F20101207_AAAHLV nozaki_y_Page_031.tif
2ddfd19364703fad9ee0bfc4865b7a19
501fa1eaa459a73b43218d255cf1dd44eeaacd57
F20101207_AAAHML nozaki_y_Page_048.tif
8a4e9629158f922c4613da9c490868a3
fa70790d5a27fb86319d7b494d711834e0651ee4
F20101207_AAAHLW nozaki_y_Page_032.tif
9311f52825bcfa9d1c5745c2c9f35040
fcbc6a3cef4e97dd364b36ad63802cb915a84580
F20101207_AAAHNA nozaki_y_Page_063.tif
2834887ec37315b75125020ba0f80f0d
0c12bdfc2b58a2c95d477a67e62efbd476ad8c84
F20101207_AAAHMM nozaki_y_Page_049.tif
be5fcc7cb97209557ce1c4b59edbd7b0
fac9a58d8d6a6eaf06c283b57d7104eaa01ff345
F20101207_AAAHLX nozaki_y_Page_033.tif
631b8e95a0250f9c4167eb6fb3e9c860
a1928d5a4b4cfec0eff7557c070f15fd87b3b2e9
F20101207_AAAHNB nozaki_y_Page_064.tif
378d0198bc24277714ffdfdb1a326fa9
c5486ad8bcd8f310c0e6cbb5b85b71fab333523a
F20101207_AAAHMN nozaki_y_Page_050.tif
116fbf7c6d2440348424807acdc60ca3
4f32e06ad82d821e8b5876d10348dd3670ccd38f
F20101207_AAAHLY nozaki_y_Page_034.tif
2700ee12c458f427d86d7244804a2baa
77c414c9caab05b0020a01f1c7cde713940f215a
F20101207_AAAHNC nozaki_y_Page_065.tif
ae30be94fc3ad2b147c129970cba0384
6f5775560b8b670b49d4e965bf62f0c4da5992e9
F20101207_AAAHMO nozaki_y_Page_051.tif
ca3fe5209a7777bcd7c6e732ddfd2a89
4dd5d853381dc5e05e812e5ed11fbbc9d7b38ec5
F20101207_AAAHLZ nozaki_y_Page_035.tif
9eda04ab73d182c8580ea7b72f33f7d4
3ba0722b11e198fa784aa3a312f0ce32bc679379
F20101207_AAAHND nozaki_y_Page_066.tif
ce7a60700102f7fd97b5ffb8a1bf640d
e5bfc55b48c3123fcb0c4cf2a04284d55996f86b
F20101207_AAAHMP nozaki_y_Page_052.tif
b7adad13dbdb94cda7c99b0de2a8feb0
74ff0b0b928a746e97ba949041aa154a3d5d60d2
F20101207_AAAHNE nozaki_y_Page_067.tif
76811b5acc990afe45277a0b6d81bd14
75fd56c4d5a5383f6410b45c6ce704a34661b87b
F20101207_AAAHMQ nozaki_y_Page_053.tif
b4eda5de2c88d145a6bfb1a9ca8a4ed1
0799a185d8d25d39a5773f1d92ded1c0cb08db1b
F20101207_AAAHNF nozaki_y_Page_068.tif
b9e855b9026381f04abbd03527d53998
aff6361eb4a24e97e41c9c50d87ae0fca742af2c
F20101207_AAAHMR nozaki_y_Page_054.tif
276cf9d1a37bc1c08f60fc29d013243f
0e59c1187e64e9bf704acc4bfb3304ce1f174cb2
F20101207_AAAHNG nozaki_y_Page_069.tif
831701e66a63ff2bd31ebe220fe7b9b1
00bad0183ff3fd46c09d0d775771c0e21ee575dd
F20101207_AAAHMS nozaki_y_Page_055.tif
977d5ddd72eee32382a72f9a6297105e
a9c6cfe63544fd9372523c4a5b71dbea69053af8
F20101207_AAAHNH nozaki_y_Page_070.tif
dc148a9c165d2fe80725be2d7fab7be7
978c51a8275cbbed46162ad4c9b16aecd78c5c91
F20101207_AAAHMT nozaki_y_Page_056.tif
e1f5bbb668ba5a3cf719c63d7b9ea836
22715ac110d37cf219dadedc253defb053fa733c
F20101207_AAAHNI nozaki_y_Page_071.tif
05a91009112d124890f3e6b9024c512c
9c73815c7565152587d271d1a20b273787c9262e
F20101207_AAAHMU nozaki_y_Page_057.tif
1b8f478d0d3ff044e151fe16eadc66cf
c76a4100142c1ae6b9cf2539ef17b5f66a3f2bcf
F20101207_AAAHNJ nozaki_y_Page_072.tif
a1339b61324637f59e41f1032a802d80
7f734997cb8f692ea0ba5d3a1a7c84a65bdea3e0
F20101207_AAAHMV nozaki_y_Page_058.tif
2eadab7e852113a491df53d2e2ecb36b
347ab49720a2d94fb6758bcbac45470ad65685b1
F20101207_AAAHNK nozaki_y_Page_073.tif
6d752fe748231ae196d90485e345019b
33a4648552d042d4a4236a263fd110d9291d0b12
F20101207_AAAHMW nozaki_y_Page_059.tif
bf738df8313aeb7ee0140cdbde074b53
9502804d649ac32e2e64e488715993b2c0ca939f
F20101207_AAAHNL nozaki_y_Page_074.tif
6a32a4f65a8446497faddff6f661e6c3
7882ea1502cd9b5dea373f6341cd19fb5d10f640
F20101207_AAAHMX nozaki_y_Page_060.tif
fb5ca1e17b4bc0fede58e768138e9627
5d3956f0fe69a5886c15310984b9dfd6442b45e6
F20101207_AAAHOA nozaki_y_Page_090.tif
5ec1b0f43a760c7103a735674951340d
c7e54be43c0c5abb9146cd1292e1ac07dff0a5e7
F20101207_AAAHNM nozaki_y_Page_076.tif
0135b72c151cf06d9b34d1922468ddcb
1cd99dd974808ddae659606adab90bf222f4777b
F20101207_AAAHMY nozaki_y_Page_061.tif
a1f2d9c91883fdcb1e1bb80f6ac4f3a1
120677faae44e9a4522b2f3ff12a28dbdfb37a69
F20101207_AAAHOB nozaki_y_Page_091.tif
e323a40ce5efe5ffe599e787831f407e
d7b6fae9c0787800b416e278e9ccc1a1d710e053
F20101207_AAAHNN nozaki_y_Page_077.tif
e50ab441981a0c931a3d35ee5309f33a
8ecebe2bca563e23db4b08a8a40d04f2b7dc70dc
F20101207_AAAHMZ nozaki_y_Page_062.tif
69e018fab578dda25f3b6dcdf7c75a00
9eceea4398dd0f234558f8034de0763c49c9695e
F20101207_AAAHOC nozaki_y_Page_092.tif
2db366e3fca65a556179af379297a71a
733571c61fc86787237d821061d76e0113000013
F20101207_AAAHNO nozaki_y_Page_078.tif
1882f9c4eb09c6f6deac7ef20d9d8867
86c4735297fa7d3b5a85bd786ece8fd3e8cfd912
F20101207_AAAHOD nozaki_y_Page_093.tif
ab8b2eb8cdc4e5b27dd074e680d956fa
1ab12cf8f7fc1a9a7b4cb264c55d2632d9b2e647
F20101207_AAAHNP nozaki_y_Page_079.tif
2f639c06f33607cacd490c303db6f10e
a1c71d95874f057df90f3ff088f69acd367b6140
F20101207_AAAHOE nozaki_y_Page_094.tif
8c06883f626440cf85df6b1af8f80b7a
beb70c70cd1d2d4a8c08fba964081d4e0936d942
F20101207_AAAHNQ nozaki_y_Page_080.tif
a1bf15c69987fff69b56290a5a5e9275
673767af16fe6833ad6f96d8bb10cf9ed06dffa8
F20101207_AAAHOF nozaki_y_Page_095.tif
257e6cf1fdefc07f695a656294e89235
dbf7741398eef948460457377f2954b933803955
F20101207_AAAHNR nozaki_y_Page_081.tif
5663e9f8fc4234bdf4ec94b352630c9a
ed13ba82de65f0303135bba9faa55bb7f8d52621
F20101207_AAAHOG nozaki_y_Page_096.tif
08b742747d0f0698593de94d8430dc1f
ad9ffec79c09aa5e4e7cba4a3be2bb1333660fd1
F20101207_AAAHOH nozaki_y_Page_097.tif
db37049171de7d0a55ccee45441ea699
c6ef4b5118bc3dcbdad95566a2898acd17f97678
F20101207_AAAHNS nozaki_y_Page_082.tif
4ec042b9b1cdd7293e0cff8afc508e96
098cee6c9459bb63f71a8ed068e011d2c4a8e9a1
F20101207_AAAHOI nozaki_y_Page_098.tif
bda586c864cccd4e197acb64c1db33f7
5323446b3365429185c47f8ad96f9b1f4b05e4f7
F20101207_AAAHNT nozaki_y_Page_083.tif
5aa2dddad12c3f119e6b5203b5b29685
d1c85bd303b34be06bcec7afa8983f633f49400a
F20101207_AAAHOJ nozaki_y_Page_099.tif
1a0d426270810b51e680754cacd021ec
a3cb27f60578f12b6636a521d8fca8e9517aeba2
F20101207_AAAHNU nozaki_y_Page_084.tif
232b6263d450f17f1a74770538caca43
6ea17df070ebb9c5d3f7e07bf85ad762f6df531d
F20101207_AAAHOK nozaki_y_Page_100.tif
1f38d24b5859a669ecf40890df97ab43
f72fa321ab70a546b35381ac21f66727a8bd0b8b
F20101207_AAAHNV nozaki_y_Page_085.tif
55d8a9dcbe2bf834228bbc594efac5f1
05e720223a58a2e1799e3b82aa2a32efd51fe4c2
F20101207_AAAHOL nozaki_y_Page_101.tif
e292b1b14c3575988e675f2c7f7f4497
dff8a817a1d10e53b5000d669fadbcf6df921068
F20101207_AAAHNW nozaki_y_Page_086.tif
5c47e70f103dd2c13b747281eadb5e53
f2609a95dca738c62bc6d505b0df5cd4d0eb1d71
F20101207_AAAHPA nozaki_y_Page_116.tif
60335095069d793669dba19c6fc0bcd7
bee891f23ae1d7bc3d2a7203c0492bdbda168a50
F20101207_AAAHOM nozaki_y_Page_102.tif
ffdb41c6a37f10f737ebe1f7775b0467
4a09d80678cffd1a96f004377c8637d9894e9d36
F20101207_AAAHNX nozaki_y_Page_087.tif
811269e0163c8b427ac1b11f4af7a87b
ca97affb904fc641f32a02fdb9b6631e2abf6473
F20101207_AAAHPB nozaki_y_Page_117.tif
5cc7d454df257eb6961d75643bdc7d43
b772712591329d195c0a0cbdb534653693177d06
F20101207_AAAHON nozaki_y_Page_103.tif
7d6d8c983f805cecf6c5080f1117021f
ffcd16b4b1de8ef410561abaaca72d11e15cbd4e
F20101207_AAAHNY nozaki_y_Page_088.tif
2f148eef38d86d2c038b8ffa74839428
9425563da3afc773428ac71e59b31841aaec84b2
F20101207_AAAHPC nozaki_y_Page_118.tif
4879cc4f3ba7cccfd4b8ba4025c190dd
e8e337b28290c742f3f95fd90997733d8efc33c2
F20101207_AAAHOO nozaki_y_Page_104.tif
fcee4a426eb21295ecc19141dddd499f
37da9210e6525b71800899942cf0a432c0fcccf4
F20101207_AAAHNZ nozaki_y_Page_089.tif
ac2cdda08fc975e52623743faa417439
4808d2e29b8769b7bb77f4372b5d64926d9b63ab
F20101207_AAAHPD nozaki_y_Page_119.tif
a405c25edebe84e366fbc3d2b3e3a223
84bac13d1738d8e5707dc24aa866e258d8a5e41f
F20101207_AAAHOP nozaki_y_Page_105.tif
c203bc20a9a2d5e801b882e3e00d83c1
47e66b78ab4f06e844dfb6d64402e5b37652bcf9
F20101207_AAAHPE nozaki_y_Page_120.tif
705893fe02139f07cf35097de07d35d8
7d11bdabea4a5cb117bdfa8f6f67430dff24b321
F20101207_AAAHOQ nozaki_y_Page_106.tif
4951083dd24209fc2a348ccd85689306
e543641e323294ff2c1b6f3f42d71461e2cb44da
F20101207_AAAHPF nozaki_y_Page_121.tif
70e0828f814fb5489c4c8064250f36dc
1e4455da101c237f7f9bca22f0a06e7ffad76a96
F20101207_AAAHOR nozaki_y_Page_107.tif
a4c6c908b58f7cf62b74e5cbee1d4713
7f4253a4f879b3c9b334221444c469dc00e59587
F20101207_AAAHPG nozaki_y_Page_122.tif
6199361dd162e3609de3e5680b785d59
c74f89fbe59dd5bd899b01a7fdd3f3a093b539de
F20101207_AAAHOS nozaki_y_Page_108.tif
9642e4cb74c8720b3089010fa725172c
43c9ded223a5ea8936c1a983c9c02c5e4f150afa
F20101207_AAAHPH nozaki_y_Page_123.tif
677ac859039b6a870c1aa4a49389bef7
bc1f4b8cb4bca549002ff45d3905db5a9cb3d756
F20101207_AAAHPI nozaki_y_Page_124.tif
4d6c33d9c4a55e2a0240a11d3c74b6a3
a23573dbaefce426fa5fd8fc014968ad6b9a541f
F20101207_AAAHOT nozaki_y_Page_109.tif
d84fcb45f615170aeb3f33c59c45aec5
604f334a5227040d4339861523a792f4e9d32a91
F20101207_AAAHPJ nozaki_y_Page_125.tif
5dd39af3d365fb4de0b7657275188da5
8f8fb9921985969b527cbf451d2926460264b3ae
F20101207_AAAHOU nozaki_y_Page_110.tif
d84fcec55b7e4f226e6127eca97c445d
36d60b9e2aa671fb934b233629e92139552c881e
F20101207_AAAHPK nozaki_y_Page_126.tif
2e23c8ca3c7f941eedd1b18b27d36133
08be2ae2bc8b222d353c59cfe64841d05a9e2738
F20101207_AAAHOV nozaki_y_Page_111.tif
80d366c17c166b80086579137f3177bb
ffff73db8f2162166b4af040d8281a384a8a10ef
F20101207_AAAHPL nozaki_y_Page_127.tif
083cdcc98bc1aadb6c270917b32d2d3b
740f69574e68698911068da756f2f4228e29a394
F20101207_AAAHOW nozaki_y_Page_112.tif
fbee3f7aa3a54c92b515203a5a6bdcbe
d3e301eebc3783e0e7788e98fdcf5a1fbcad06b6
F20101207_AAAHPM nozaki_y_Page_128.tif
d6bf000ece6e5a999e46909a01759299
cac773ae70f001bcf1f3233e1b79545770f0e20c
F20101207_AAAHOX nozaki_y_Page_113.tif
77c03a27ec9f681498ddd0441e96612a
7dd63fcccc6a91e2f7803468a8707429020c536d
F20101207_AAAHQA nozaki_y_Page_142.tif
171e4f5cae9497e07d9aebb3ed4287c1
9197e3e8bb96b6f4835eea46b42ff800de28efb7
F20101207_AAAHPN nozaki_y_Page_129.tif
0558887456fd147992dd037e174eab8f
116fb0a1088e72e45ecc1c7315e460b4d712a3bb
F20101207_AAAHOY nozaki_y_Page_114.tif
b153f1cc093933c8a6f2e9998bf53ee6
8d2d555d22bc7c9659d793069fc3fb08df3ed38f
F20101207_AAAHQB nozaki_y_Page_143.tif
68dbad65f5e6c923d1397e171b6a943f
b78d04c3005e8ae8afdd6715adc9563f33c1fbe1
F20101207_AAAHPO nozaki_y_Page_130.tif
206c6df1373c9a3b27eae95f5e386a61
e0b7125166151f4736778efc3fea47a87135f27e
F20101207_AAAHOZ nozaki_y_Page_115.tif
d58ac4c9e3114fa1858a853ca085f334
08079381e0f4183890dfb4cd02d44916ebf2dadb
8388 F20101207_AAAHQC nozaki_y_Page_001.pro
52f3b2cf49d237822bab21f9f3f09c10
c684a621050c8092acdf853a296cde983bdc5422
F20101207_AAAHPP nozaki_y_Page_131.tif
4f419e267f64088f519226eabbc64140
1f04ce3facb1f11b9412273cd1b4f142445b140b
861 F20101207_AAAHQD nozaki_y_Page_002.pro
5f78b19db545468bfaac3af7cb93b82f
65aa09d02a5b06488b0d52a993e3229edf57a943
F20101207_AAAHPQ nozaki_y_Page_132.tif
7755fff0ec5c0010ef97d809dac9d344
03640e898f6b1e5750fe6c12a70cb7f57ea3928c
5699 F20101207_AAAHQE nozaki_y_Page_003.pro
0a9464a7177d10916d4202fe35557aa5
98bd40d8c4f4344098542885e81fee56393c77bc
F20101207_AAAHPR nozaki_y_Page_133.tif
ec477fa41c422f247f4d9bf2f66ff7e5
189cde722db9c3de7f3b1c793398858e806cf394
4685 F20101207_AAAHQF nozaki_y_Page_004.pro
b8aebec09250792e3b548bf314055644
90f0cf69ccff8214f5d94be722f9fdf9a0631fb5
F20101207_AAAHPS nozaki_y_Page_134.tif
1238dce1711ef69c534acad4c5ccb75a
511889e49b0e0386245e13a8ac8362d51b084a81
80336 F20101207_AAAHQG nozaki_y_Page_005.pro
413f479230c87c77f87847e45623b888
e50f9ad39376a25ff90a1becb288cf71e1a72047
F20101207_AAAHPT nozaki_y_Page_135.tif
a2bd5b74aa5cb8b483ee1db034ebd63c
304d08cc6c2c6759db00d4edbe363a5bcbba60bf
24253 F20101207_AAAHQH nozaki_y_Page_006.pro
29701ee974b32381db89a94a655e517c
37fea24d07989e8de6bf4252c332377970d52b6a
21045 F20101207_AAAHQI nozaki_y_Page_007.pro
bc71082ff93585b84abbed3e0040419a
d7a532dde02415e81575581cbf104e7551e91d3d
F20101207_AAAHPU nozaki_y_Page_136.tif
b86785a6ef65ae3e54210a80a03985a2
7691b32406c4c7bef1ad2784dd49eeafaf11271f
70887 F20101207_AAAHQJ nozaki_y_Page_008.pro
9b5551b0c1bcb5fb0a3657527a2ac186
d6e34fbbefbf05963f98eb8abcf662638116fbd7
F20101207_AAAHPV nozaki_y_Page_137.tif
b523bfc4ace1d5256c3a07cd2df809d8
21d39752cdd9da418c8b31dfe7e8bce22f3081ca
76062 F20101207_AAAHQK nozaki_y_Page_009.pro
0b23166b9b9c8e8a4ddae57ed70df55b
49b613d34eb6dfad90f87156042a48f7be976aa0
F20101207_AAAHPW nozaki_y_Page_138.tif
83ea205de667debbb67d5d278dda42ed
70950870706f82575ad5aac31575b0612f02c421
70638 F20101207_AAAHQL nozaki_y_Page_010.pro
1dd0c63c059f05afef6bf17d8929f828
a070ba5d2367050cdedc8b65d5d275f9d8574076
F20101207_AAAHPX nozaki_y_Page_139.tif
9a88e4fb6051364016feb6a240e9cbe6
ab68aba046aeec7ab9fb12f67f8fc73f2664ed1a
46804 F20101207_AAAHRA nozaki_y_Page_025.pro
2eab1ed5ebb4f72ee33f4099795e5e3d
cca2a0a862c6d76902473bde96bc2f3a87349657
83528 F20101207_AAAHQM nozaki_y_Page_011.pro
0a781d189a5e8556580a64c48b084560
9f9ff0bf086bd7760319c946e14d4514edb74082
F20101207_AAAHPY nozaki_y_Page_140.tif
c960ef57af0bc8385cc67abb1783fadf
63c9140cb121253360780d4be99f6a49f6c31d45
54021 F20101207_AAAHRB nozaki_y_Page_026.pro
18d31bc2ceb467b9efe11c966ad584c9
36b0a9fda955ca54fdc878427d5d70bfaf6655a6
74769 F20101207_AAAHQN nozaki_y_Page_012.pro
10713180a02138aefbc8ed308d15ccfa
4d0b8104a9761519a3a7be30e80bc8ae4659997c
F20101207_AAAHPZ nozaki_y_Page_141.tif
024631314c98a01a70e915bd19b74847
5bd04077b8b295038a98585f558a9f085d65f7e8
39110 F20101207_AAAHRC nozaki_y_Page_027.pro
28263664c0f3cc36a035ef5cf9718b52
f8502d5bd12982004ac14de587e2bf0f126c7bab
69626 F20101207_AAAHQO nozaki_y_Page_013.pro
cadbf51f7579af818c28012acbfc2e5e
beefe0f63c018fd966bab75bef067b1f10c25732
38053 F20101207_AAAHRD nozaki_y_Page_028.pro
cb0a4a1d91c3ed11e4f009719d836549
8e1cb879dc4f7945286b9bdd028a36e14d1a0100
76476 F20101207_AAAHQP nozaki_y_Page_014.pro
001cd6f8d7bdab7de6d00189e6771fa2
276ca990cbb8a141fe58e99d50524ba6a5ff4174
43663 F20101207_AAAHRE nozaki_y_Page_029.pro
f86db05de35feb4f093b4c9cc9f6e601
25311d626ddfaafd81793a5ea61654957fec45c4
36786 F20101207_AAAHQQ nozaki_y_Page_015.pro
a97944a39d0a7dd9e8eb6022079aa823
8897db26e3e9fe6f46abca5b186afb65a498e67a
40893 F20101207_AAAHRF nozaki_y_Page_030.pro
d199044b2e8e65e88a34784733278a3a
c30352b861c39de895a77a294827d4389ed2bb27
46258 F20101207_AAAHQR nozaki_y_Page_016.pro
fc5552d03b0101bc1711bd5e750c9d06
b8ce47ae87c2ffe3a37ed1b030debef8484a059b
46714 F20101207_AAAHRG nozaki_y_Page_031.pro
2d3b628fa33a3ee88b23d0ea632ca58a
6d6defe917058ccb6f76582618bd5e1d53f15005
46642 F20101207_AAAHQS nozaki_y_Page_017.pro
b0c1da39c65bcf0c4bb82c51adcabb31
6738b5b8ec4ec614fd0d54c832dcd112e4111864
45692 F20101207_AAAHRH nozaki_y_Page_032.pro
c3965084de6a27e2a12f85b8d42e9c29
a3bb88a5d3c86eb40a9671887602e096c4299926
47772 F20101207_AAAHQT nozaki_y_Page_018.pro
72d50ab399e35fa66f5fa7e0a9f1aa8d
795538590758cd5eb2340f69a84511db85dfd800
46011 F20101207_AAAHRI nozaki_y_Page_033.pro
b9d4542d08d55eace42f1d67880f49dc
b65131934778327f067f885e866c61cdef79ad73
45023 F20101207_AAAHQU nozaki_y_Page_019.pro
36c38c4a4858dc154359a89f8a7e8f6b
011453e0c16ac5a6bd3ae3021928980b489c6967
54324 F20101207_AAAHRJ nozaki_y_Page_034.pro
cf087a12c10bf6b09012f37116611875
a7787b65774e05dfddc71b9c7d5bfd05934dd076
49976 F20101207_AAAHRK nozaki_y_Page_035.pro
4ccba27832386defa431089e3347900d
ae4e534d62fcc5e243419e16f181816fa4e10936
55142 F20101207_AAAHQV nozaki_y_Page_020.pro
f329f04dca0e6df4a9fae44aee33dcbc
8b12248a29efdb3404d14c6fd21f247b6b8df138
48167 F20101207_AAAHRL nozaki_y_Page_036.pro
a36fcfc9ce11dd2b902adcf7364ca17a
4e2dae39e2476de2c7fb2c72b476dae14a0fd3f9
3675 F20101207_AAAHQW nozaki_y_Page_021.pro
871d5461e09300075d59658c10dd26cb
17d5baa8c81669434c59cc3c454de0b61580b2b2
50497 F20101207_AAAHSA nozaki_y_Page_051.pro
232de9fb62e9ace5045845948497b3ab
4403a14242cab107126423d00038741ef558386e
7781 F20101207_AAAHRM nozaki_y_Page_037.pro
b93b74c7b35a9fc4d8b236a8be1ae944
cf82035a3f5c58181800ec6c5ebcfb9ada02cd81
47775 F20101207_AAAHQX nozaki_y_Page_022.pro
6196a13d24749031372125a211c3e88b
aff2c6a739ebf2a68f5f357c91e479d17956ebac
44658 F20101207_AAAHSB nozaki_y_Page_052.pro
8aeadeeca048e4e90b78f2fee5ec254f
bcb7890d2da245dbb3f3579d2bc181f7252912ef
7946 F20101207_AAAHRN nozaki_y_Page_038.pro
ca3b03e37a90237f43826dd340c790da
18749db54238a9d3310e3de0ead05e59324a0902
45039 F20101207_AAAHQY nozaki_y_Page_023.pro
f062a49680dadb7a4a8ced414a93128d
1701cd3ddcf4ef77a50f3f0ff8840cb1d93c6a3d
51312 F20101207_AAAHSC nozaki_y_Page_053.pro
28ca25af31d5e30e5de5028b543da655
c9b749a131759981055d0588ec6a27e8f40e3ead
11531 F20101207_AAAHRO nozaki_y_Page_039.pro
375cd07dad197716aa64d91b53eb14e1
e474e53f11cd3d9d4d5992cd85d4e0798eb44235
41280 F20101207_AAAHQZ nozaki_y_Page_024.pro
a7c844841e0c598d2e4da739ce6157c1
0aae79d7f94864cdd60486a69ccb3d10831a1cb8
19329 F20101207_AAAHRP nozaki_y_Page_040.pro
1f021f1d47998d0dc2273a2c26cfbac4
9fc25a91e1d2d53b2ba5a011af99348dc66959a3
53476 F20101207_AAAHSD nozaki_y_Page_054.pro
80c11f68e4e6522b1586d18baa428ccf
01df7ff49b741051b1c42995dbe3862692d92e6f
17831 F20101207_AAAHRQ nozaki_y_Page_041.pro
d35edc5fe6de1e433ac2291cb3739cb4
c957230fe7a9b5235b51aacdaf020372add9bef4
51483 F20101207_AAAHSE nozaki_y_Page_055.pro
a9fbaca7c3147338675a5a2ae7ef48c1
4fe1c57413bebdf3d6c2869ee023f99839a53ccc
49179 F20101207_AAAHRR nozaki_y_Page_042.pro
96e45b0182610318876151ca7a210e75
a785ec1cb20a93c79071a4e24c3255fa41b40a00
46803 F20101207_AAAHSF nozaki_y_Page_056.pro
d37dd2d24e7a1c5dae9d8fa364b9617e
3937be76825fa9848551aaf8a7a4f6f95e37b4a5
37164 F20101207_AAAHRS nozaki_y_Page_043.pro
545c54ac71fccee86db46181558c8039
36e75eb828919ec8e263669fb34d6681182a840b
39638 F20101207_AAAHSG nozaki_y_Page_057.pro
32d0afc186d8ea59aba76a14fe414c85
f76c13674751875ebe582da078daffd52c5bd497
41655 F20101207_AAAHRT nozaki_y_Page_044.pro
02358ca740480ac5e2830c5b66f3ce81
0951a898b8846020eed7adc17933ad8ece9659b7
17563 F20101207_AAAHSH nozaki_y_Page_058.pro
1b79c9f98f937acfd5b9141e1dba7fa9
7f46ca282bb93f82c994cb94fe63fc96bafbf266
42452 F20101207_AAAHRU nozaki_y_Page_045.pro
da1c214e181ee4d485bf70031f6a9288
2301424ffddff010402b8fceb57086c561819a1b
22469 F20101207_AAAHSI nozaki_y_Page_059.pro
adfdc1878c64c1dc2595c8d31a68ae08
70ea439baef94cae1c437b89c9b4cb8fbd0420c4
6580 F20101207_AAAHRV nozaki_y_Page_046.pro
10cbc268367b60d9410e1f0b46eb67cc
fdbc2352952c54343e6f1f5f86986dcf94258fda
22934 F20101207_AAAHSJ nozaki_y_Page_060.pro
c9e58ed6d82e8a7945d764601003c3b0
9d2aa4d4c6cc9d01db57d54c4268e60fb377628c
18986 F20101207_AAAHSK nozaki_y_Page_061.pro
277d6e445cdc0a3a04e0d510fe78e669
ae463626078e2d1e86f1994a379d07672a4e2fba
52090 F20101207_AAAHRW nozaki_y_Page_047.pro
4ef0cba939f8b361891609d6b1f7341e
5b4add23323f7d64a07e32259210759261240e1e
21659 F20101207_AAAHSL nozaki_y_Page_062.pro
f3c039667636ecb1112fb7e79706add6
36d541108fa51eaa557243912e03b93e636c7499
36042 F20101207_AAAHRX nozaki_y_Page_048.pro
a49476014cc17393d1c717d120c85780
b59665483995a6ba342944e7e99d6e00d0b89bc3
24295 F20101207_AAAHTA nozaki_y_Page_077.pro
b7352f080532f272566777ec05063f5e
bea8c0e6d9be03bacb7b78e575f11446f731f06f
20522 F20101207_AAAHSM nozaki_y_Page_063.pro
79deccb60cb872f9a3264058b744b155
841fdd89435035b740fa66ddfbc72436503fffa5
44139 F20101207_AAAHRY nozaki_y_Page_049.pro
8948605a4c14958d886ffd42576ee9c4
86ba919c159bcb4cfb0fd1063d7eaffdaf2e2692
22952 F20101207_AAAHTB nozaki_y_Page_078.pro
a18e77e93da4bac5e3eaf27ddd930f2d
d796e1e5b2c01bfb03bad43f59af4f1ef15eb199
22946 F20101207_AAAHSN nozaki_y_Page_064.pro
e416011aa45667cccda4f88f80d6c06c
55d570b94295d021d107ae57c9d1697200e1a5a0
54500 F20101207_AAAHRZ nozaki_y_Page_050.pro
d7d4f2e0d3af45c71035200f43e0c05f
dc3001cef4fd6ff243fb33254f694cb1ab7dcb78
24208 F20101207_AAAHTC nozaki_y_Page_079.pro
1ac87d75e50ecd67f592d6d8e4548bf0
f243637a19cdaa3217e52d3ae1998fd851f58e82
28059 F20101207_AAAHSO nozaki_y_Page_065.pro
0212763896b56a6ca103e2a62194bca9
5369c63950743d4fde082f3d127fced0f810d74a
19033 F20101207_AAAHTD nozaki_y_Page_080.pro
0d749a899e71c653647e230eeb2c5be6
d241593dc917d872edae8f721121741429203cb2
7236 F20101207_AAAHSP nozaki_y_Page_066.pro
6f70261f92a4f2e68ed90c4c3c096785
1eddcddbf73ff5616fa392cc63a2df2fbf9a1f5e
25429 F20101207_AAAHTE nozaki_y_Page_081.pro
e45be47d99ff032d1f9dbf8efbbe4c49
111b922523df5e2f5a350c4aa1310f13b3bdc34a
10475 F20101207_AAAHSQ nozaki_y_Page_067.pro
f080f7edd54d994c5f271e1edeaf6b36
83a78051e127c3efca8c41a15e08aaadbc318521
19028 F20101207_AAAHTF nozaki_y_Page_082.pro
369389babaa77d189272fee8beda7f9b
383e6c26a31389d7bc7c6d0e5d97e387757a5c31
22160 F20101207_AAAHSR nozaki_y_Page_068.pro
82959311eead811fd637aabeb35fee66
db709b7b7c0bf488697b664d8e10af9c2712a9f9
20001 F20101207_AAAHTG nozaki_y_Page_083.pro
b87d892e08b3df1b90edd417837513de
f4c527f3e91ea2c661bfce1436c32721ea7729b4
21989 F20101207_AAAHSS nozaki_y_Page_069.pro
eddfee8362f3a8ba77317cedd241c9fd
ffcc48c78f9c0e6322f4db8d103ce22ebbacd427
13950 F20101207_AAAHTH nozaki_y_Page_084.pro
7227595419c6bdc7f18343e4d7f64566
ef0ad015234681b7faa41e9726e615be7f461fd3
22182 F20101207_AAAHST nozaki_y_Page_070.pro
51e07861f8ceb93e54b5d6e1eccdaf93
968787f6999b30e00b860a6e114f71e139395d27
13285 F20101207_AAAHTI nozaki_y_Page_085.pro
a62e31f977e8568aaf083a23f03fb9c3
fb87afb58e7b4643f33459500c8ecfd33f9ea55a
20247 F20101207_AAAHSU nozaki_y_Page_071.pro
ea7b95a4a98f90479935e5cd51de3847
be71471d829035604973830761154202dccc7a9c
22512 F20101207_AAAHTJ nozaki_y_Page_086.pro
9d0e0d6af2d6f062bc09f0673e1c0365
ec9efa70e3ea47fdd67fb1a4e1f548b9073c9513
21952 F20101207_AAAHSV nozaki_y_Page_072.pro
c8aaba2389687ee1dbc28e38736fd332
ebfc2553175a19310b937b6c8fb0ad38b1cceb9e
22581 F20101207_AAAHTK nozaki_y_Page_087.pro
1a6ecb4d03bbcb30a15c4f8e8f828018
7147f628a0696f9b215adefd412a060cf0950b24
21881 F20101207_AAAHSW nozaki_y_Page_073.pro
44f17ce1a8beeefafb8e240f1ac52d2a
6b8f68de441ff77eb1d46a2c63d6def1efab2824
22174 F20101207_AAAHTL nozaki_y_Page_088.pro
05e3665f2eedecabe5fb9dd30f02ef1f
4835fa377c1f8112c5a61a8c0f9b99be7d8b3839
24503 F20101207_AAAHUA nozaki_y_Page_103.pro
3df87d4b8cef04b2245799bb500568a0
07c3f337ae644a233a61a88e12f3d1a5c26cc124
18169 F20101207_AAAHTM nozaki_y_Page_089.pro
26c5e8915c42be44f6757cece7b2d706
94c95654c8c67c547157904bca53da3736bbcf02
17926 F20101207_AAAHSX nozaki_y_Page_074.pro
5ef0a71dd16fe54e4157a400622fb9e4
bf87fa3d9f2096312a31ed3ec6bd7bce57f304ab
31781 F20101207_AAAHUB nozaki_y_Page_104.pro
5841340525a74401385691b971e18236
45e6154bae7cf899f2db9061bbb57a4262f96c0b
18165 F20101207_AAAHTN nozaki_y_Page_090.pro
c7752b69d895709a7b32a71c2e77a588
2e18710e1c6917b11bb2a9e6c4a646c65a1ae9e6
16562 F20101207_AAAHSY nozaki_y_Page_075.pro
ab81a83cffbc06a40d290e4889819621
d623380faecda283342bc5354486e86a09ffbe21
40085 F20101207_AAAHUC nozaki_y_Page_105.pro
d8181ec7942b8ddb28f953a8e5cf20b3
2a06bb55dd8963e7baddc841aca6f7b32c98a60b
18640 F20101207_AAAHTO nozaki_y_Page_091.pro
56f4fe123f4d24ec403b0ed0ef56b554
7f5af43662872636759ec0d558f49de45d872ae1
14634 F20101207_AAAHSZ nozaki_y_Page_076.pro
3904418aa09f78ad914c672ac2e274e7
2510079fda9f50456e9e620820826c2797591760
45038 F20101207_AAAHUD nozaki_y_Page_106.pro
de231e06fbf2d9116f7b07950618f154
a3dc0280d3fbe751aaef9eb92ff001109fd73bee
17884 F20101207_AAAHTP nozaki_y_Page_092.pro
e24a506c7e75606e350188e8d8464eec
97a538749c6962ab0152a52e2d494591814e3be9
42661 F20101207_AAAHUE nozaki_y_Page_107.pro
3490bb717eb6af48fb3c8514e3a3d277
45e56a122b068babdc8e85fbd37309f4f033f667
15965 F20101207_AAAHTQ nozaki_y_Page_093.pro
94a1d67e05e227ea32939f7cc4b9f87e
b3f21916e848ac542d35af84509d3c1ae05b4468
36348 F20101207_AAAHUF nozaki_y_Page_108.pro
d8ec73178e89ce0b451ef3fcbc0e6aa9
cf0bfe35d1d932b03471fbdf2c888505a6b196dc
2426 F20101207_AAAHTR nozaki_y_Page_094.pro
5e232f80be31ac7130feefd873822406
71a80bacb9696d0f817158451927e5723fca8baf
1519 F20101207_AAAIAA nozaki_y_Page_118.txt
90ff9b1084e257577e69dfec8f1279d3
47f6843d7aad7cf2a6b6bfb933e550feb8f472bf
44498 F20101207_AAAHUG nozaki_y_Page_109.pro
97d6c17938398fdb62f012459a86ff07
86357fc96c4bf138048e6d69c70a95dda290926b
53644 F20101207_AAAHTS nozaki_y_Page_095.pro
373b0faa7b9921bbd616db095bfef499
519037c2395dc8b3d565e7924772693b11f6d51f
1717 F20101207_AAAIAB nozaki_y_Page_119.txt
a199b8439efb1b3c1fa411024f993833
6367d716044358985e35f90cf3634cc050ed12af
55120 F20101207_AAAHUH nozaki_y_Page_110.pro
5a1f90c2aebd017b217caeb5910999ac
9aec1f78d7761c4fd155c28d13c611c62c922fde
50798 F20101207_AAAHTT nozaki_y_Page_096.pro
906347ed68a95c45d162469d60d57ac4
5fda5cba44885d3c0b13b5b06d7d543a3fb38abd
1853 F20101207_AAAIAC nozaki_y_Page_120.txt
620972902e432870fc3f56e0b5f74bfe
8a9c5f596c091d2aa2aa7a141e757d28af64d4db
47293 F20101207_AAAHUI nozaki_y_Page_111.pro
e5f75ee9d3791cd04f12f52bc50902ea
27e11c3fc9ac906098cfdabc57be733dd806b9e4
4202 F20101207_AAAHTU nozaki_y_Page_097.pro
d57a9ad77fd7368d0dff5ab214f72f96
3010e378ed5150d58caed818ca8c9cb35eb36c13
1719 F20101207_AAAIAD nozaki_y_Page_121.txt
2270919afea0d58eee941549fbeb55c7
6044bc2d8fc1a09507174038fcded8f724236bc8
41845 F20101207_AAAHUJ nozaki_y_Page_112.pro
65d4ab61fbfb05f35319e22488c47c41
edc6dc9e722aec9eb38b12aee5e1c053d66686fc
43729 F20101207_AAAHTV nozaki_y_Page_098.pro
6ae0fa377860cd8bf955a8bf02c4d0f8
f8ecc41dcc20b88db0fa114f13fad2eddcc7afb9
51966 F20101207_AAAHUK nozaki_y_Page_113.pro
e23dac650e8f2b326f8f1da2f45db9ad
282d096d834631ad0d75c29c004e9ab34288b5d0
55373 F20101207_AAAHTW nozaki_y_Page_099.pro
08d33f2b32fb0a818f1b984332d8e30c
6805fe966787ff45ad4a6e4f3c782b494279b742
1862 F20101207_AAAIAE nozaki_y_Page_122.txt
435d1bbdadc622cf5e12aee5b3bcccb7
13d3c8099d923b0a6746af2724ce1b6525abc317
34947 F20101207_AAAHUL nozaki_y_Page_114.pro
b50468f1f89707770b1b5c39b1d62e12
e9fcff6ed9a4ef59a9e4a6a84dd2d0169884a1b0
39841 F20101207_AAAHTX nozaki_y_Page_100.pro
a6e7d50626587a233da6c7d87812e863
1fdafa4600f848381639b07c19446b0c0bffffd6
2036 F20101207_AAAIAF nozaki_y_Page_123.txt
a31d3b17c6780a4dc232beb870a6417a
f24e887a9b761481bd135ea5ce9e0e1f8cb9abb2
45500 F20101207_AAAHUM nozaki_y_Page_115.pro
1c86eb73cfe7d2f918d479c083aeccff
40ec7f237709ab0fa31abb880f562b267f8f24a3
2064 F20101207_AAAIAG nozaki_y_Page_124.txt
7b756911e9f1f5f9d87fef1e4a82070b
bc01050e8f1a69dc4f3a11410682f8a97bc102fc
60740 F20101207_AAAHVA nozaki_y_Page_130.pro
af26220ff04007edbd54283bcba29534
45f5800cd2cb34de039237d2342afe7e5bedbf14
46843 F20101207_AAAHUN nozaki_y_Page_116.pro
d72446b5e668cb9b986d7b0960a9cacf
67c5d65171cc85ce8f0ba798f5860c928293d165
18371 F20101207_AAAHTY nozaki_y_Page_101.pro
7bbc1b4ebabb1f6a9d483226e43d33f7
4919f86506ef9ca9892ba3d022668b062aa74120
2001 F20101207_AAAIAH nozaki_y_Page_125.txt
5b08a23f231eda4575188556292fa057
41b4ac2ac523ad7bf2960dcc8a1a67398b7e196a
43445 F20101207_AAAHVB nozaki_y_Page_131.pro
4d55de0ea8b06b0ffbeed1fb4c43cb46
3bcc6bbbddd3591063b9065d8f6f2d3622490fcd
19558 F20101207_AAAHUO nozaki_y_Page_117.pro
163dcf394dd739883af2fa8d68145113
e81024466eadaf7dee204416fdef13ef6d3ab989
19737 F20101207_AAAHTZ nozaki_y_Page_102.pro
0c239ecfd459edb157aa838afda38dcc
d853da64fb86519677d52a304c250e42711a4043
1959 F20101207_AAAIAI nozaki_y_Page_126.txt
d28f8da592b05602838d3cb9abc68507
5bfeaa2d665fc41b34f0a116973ac7364fb077dc
70084 F20101207_AAAHVC nozaki_y_Page_132.pro
b25b0e565b998e301be31de84b2397f8
07cd2969cd68c01082091347f60b4a2376c257c6
36764 F20101207_AAAHUP nozaki_y_Page_118.pro
0a14650ecfde948c7256982f68b701bb
d5f6b9cac6263e4647df75f11337016f6e590a52
1228 F20101207_AAAIAJ nozaki_y_Page_127.txt
ca0e879e994bd878618c486c6c19afd7
070a349de78c48138f9428838b3b286184982563
11952 F20101207_AAAHVD nozaki_y_Page_133.pro
ad7336343097c482ade002b4e96eb077
94817b012e6f85b087461642ae6d5f231b10a834
42469 F20101207_AAAHUQ nozaki_y_Page_119.pro
be1f2ecb0fdf82c84a6979a3234f9bd2
1fae80b93fdd4fe61a0879c418d5596ead82d9e0
950 F20101207_AAAIAK nozaki_y_Page_128.txt
c6f9da56d9de67b855c51a9da31b15fb
a3017deb742879fa02923577c3e131e7f6cf03e3
51480 F20101207_AAAHVE nozaki_y_Page_134.pro
4fe3af6ff29b47ad5f905a5ca28f52bd
17fb076104aa413cc7491f4bd0652d47382fa8b7
46498 F20101207_AAAHUR nozaki_y_Page_120.pro
97cf12ec6364e2771640849d32ac848e
68ba311219cd9d4cc39c0e276698f4fdabed2e15
1359007 F20101207_AAAIBA nozaki_y.pdf
b594e4a0d6fd2fc993c68d8b3d2e14b9
2c854b317db3b47c7f7640224a2a04809f94d17a
1916 F20101207_AAAIAL nozaki_y_Page_129.txt
add37669312af86db54733ee1154c330
6b85caa56ceac1b2c2e0e30e310e5af768d74c83
48179 F20101207_AAAHVF nozaki_y_Page_135.pro
f8ac5e31aab21b171bd40a88736b365b
86af6ec687d345700975ff229127760052940a2e
42986 F20101207_AAAHUS nozaki_y_Page_121.pro
52104c2baf30ca9fb22975e3f5c6b6ac
610c0dd233897bd5bd13b1cdcc193ca08608f3c2
5224 F20101207_AAAIBB nozaki_y_Page_039thm.jpg
cb96e47d26949a985e9e52b21e1be38d
6249245ac02000b09a10f4fc743038e6b6fd44c8
2401 F20101207_AAAIAM nozaki_y_Page_130.txt
0fd8816c9de72b6af1ed20f2012767e5
cd3d37bc4db9d4a04710fa0fd8cb2b0d2e1173ab
52583 F20101207_AAAHVG nozaki_y_Page_136.pro
4859906092df17ad4cebef42e9f75cfe
721150c03e66bb198ab06250437b36ada28a3b37
45498 F20101207_AAAHUT nozaki_y_Page_122.pro
f623f8fae15a7b613c6308ee7d31c198
2d85ec36342ecba3b5a89cfc419919b04ce095be
5038 F20101207_AAAIBC nozaki_y_Page_062thm.jpg
4ed460f64de6a20a046f1d3222c70fde
94d697329903e52ce88670a812b65b7732a59e46
1752 F20101207_AAAIAN nozaki_y_Page_131.txt
84da271be4112fff4add6b6b15d2e11e
0f044e8fdaa9c766b7d1b7c69605e2057095db66
44722 F20101207_AAAHVH nozaki_y_Page_137.pro
7a316fd4fd7a422f972991c55ae56326
285a81772cd9a30b418a6db9e16ee48749ae79d1
50418 F20101207_AAAHUU nozaki_y_Page_123.pro
059422757b1abd6cf20e67c847daba9e
952838704582021241b607b8d4ae90843d47f07d
35123 F20101207_AAAIBD nozaki_y_Page_047.QC.jpg
e404ed6460f791c7e9af4503fce5ae26
4f5aeef07fdd2dcc4e9f6ae7efd5267f401ac029
2783 F20101207_AAAIAO nozaki_y_Page_132.txt
237788181e39014b4bf44ec219ecebd2
865d079f4522b505896db9504c58adca59befe92
68801 F20101207_AAAHVI nozaki_y_Page_138.pro
be44be5f32286eb6097060103342e879
638d8fa334019e3f60c2708962a3d242ee2d8dbf
51894 F20101207_AAAHUV nozaki_y_Page_124.pro
12064fd90a5b301afd2460f132150ce1
57c96511236ad9c528ed420a4451164107e6fffe
19108 F20101207_AAAIBE nozaki_y_Page_093.QC.jpg
2c02d30ae423e9719d0d2bbc968c4cbf
7fa330a477ad619a17a6a8ff956571b3d33a0b4c
474 F20101207_AAAIAP nozaki_y_Page_133.txt
8625df40744469d942d50e3ed97ce4e0
09f36f225cd96677dc3cb0614da060c5ec2a4fbc
77348 F20101207_AAAHVJ nozaki_y_Page_139.pro
15bba7a6dc72f1381c6fa0aa229aa6fe
6c0bf46c08c125dc43526cf25abbf0886a5bdec9
51336 F20101207_AAAHUW nozaki_y_Page_125.pro
fc475b7954cec96032feea6af7f1715d
479412ba1f878e44da1952907815d493a0f7ca9e
2087 F20101207_AAAIAQ nozaki_y_Page_134.txt
f934a79e96374498c640426de718bb39
1d7aa94a6b43caf94990654719cdfda6df5ce3b4
9754 F20101207_AAAHVK nozaki_y_Page_140.pro
c5fba4b37dee5998f44b566b2d654f88
a93506036121e5509262a4c7edb00ac3105326ce
50193 F20101207_AAAHUX nozaki_y_Page_126.pro
729a505fdd7a2a8c057feb2bfcdbc027
81473b60d3ac9d0b1d193300422e9aee5e773f61
37677 F20101207_AAAIBF nozaki_y_Page_013.QC.jpg
19d1dc373f4c976d13a8ae74abdbcc6d
c9e8cc8b5701ad2d64654d91d36f4a1e2af74cc7
1920 F20101207_AAAIAR nozaki_y_Page_135.txt
2f068d49c0b797a973b9ef6de6e15a5f
75782a60f0c5f147e15872b2cbccad81a3479b66
31517 F20101207_AAAHVL nozaki_y_Page_141.pro
97f40ec7867fffc35d4a3fb581be5b40
a7208fb2848276f755d5b6c3037cb65bfbc2c011
30505 F20101207_AAAHUY nozaki_y_Page_127.pro
890ee62e9ff77770e3e8c72b3186ffe1
b646a05f6ac35367721d21ae31fe6847f7d14b65
5313 F20101207_AAAIBG nozaki_y_Page_060thm.jpg
f6343b03dfd35ac0095260c869622f93
80c0635861209c0f94ff81094e3fb06015dd04a7
2800 F20101207_AAAHWA nozaki_y_Page_013.txt
3113bfdc6144a25aaa026f3c311a0413
341918a00b1a9552ec5e9fc9f45d159b890cca0c
2123 F20101207_AAAIAS nozaki_y_Page_136.txt
1bb92be818533860e286c2f17c7fe270
d89606f8328c3858a70bcb929bbc1ed1c3eed025
49431 F20101207_AAAHVM nozaki_y_Page_142.pro
2e487a8b36a18f060c72e3e88f3947dc
6adfa0520c1bbf32cb4867625fabb7412d01b67b
24442 F20101207_AAAIBH nozaki_y_Page_115.QC.jpg
55e3a93fe691e259f3dc115de305c422
a78730e30810b3599c2c93215858f16808c788d3
3076 F20101207_AAAHWB nozaki_y_Page_014.txt
4d6e5c7aab69d2f0429a6233b38080f2
2fc343b965a8785ef34ab9cc20948eddd23682a8
1792 F20101207_AAAIAT nozaki_y_Page_137.txt
24743605812d3228625dd8419ea9574e
1710d00fa75fb630c091947ffa64d5b65980f69e
11256 F20101207_AAAHVN nozaki_y_Page_143.pro
08f446b8ca4118719460a23109734b56
de5dc7313570e73df403b5535f4bef6bedcee164
47761 F20101207_AAAHUZ nozaki_y_Page_129.pro
e637554635f9ef5ebd55d1626fd1ecc4
0e5d05900cf8a36bbf38dbc89af0ae4f27ce25f2
5131 F20101207_AAAIBI nozaki_y_Page_118thm.jpg
91478bc54cd7c289867072458191b5e3
6cfd22cd40a604dc6016a2aaf0dd36e9e1917871
1484 F20101207_AAAHWC nozaki_y_Page_015.txt
b22f068282377c048abb723b68270d98
55f04c821e22ce697b331f2f03ad2b2d6328d97b
2727 F20101207_AAAIAU nozaki_y_Page_138.txt
99cbd2b8149fbeca5fab7baa1d3c33e4
fb9086c23a0f2998c902f84d5bb020e74861507d
501 F20101207_AAAHVO nozaki_y_Page_001.txt
47f9d9df725fb5638ad5475b7ce130b1
dbefcb529778efef7a4962ad777deab1ff570de3
6837 F20101207_AAAIBJ nozaki_y_Page_028thm.jpg
51cd3c2ae722d116ac66079118350c6d
35196f85f856756784041a8866fd5cc799e085f4
2024 F20101207_AAAHWD nozaki_y_Page_016.txt
cca7993acd445e950a7defa54b66a8f0
90c9ffbca68e869bdfe38b0243ff2018a10fbe73
405 F20101207_AAAIAV nozaki_y_Page_140.txt
167244919683edff5c27f8ff3d774619
af3667e775db2e3a2cccf76c64deff2269559d92
93 F20101207_AAAHVP nozaki_y_Page_002.txt
e38456c3841defa0e93813f55d892645
c71498219eeb7c578ca5928030c6eb3d83d98693
27952 F20101207_AAAIBK nozaki_y_Page_032.QC.jpg
2a874941b3694927df2f50fac432a024
54137f6a5a4d350cb3bcc7dbf5a073d779d7e623
2027 F20101207_AAAHWE nozaki_y_Page_017.txt
95d839f93dc7c6f40d4787db386c2ef7
5a3ee35c412956628f283107be7522b5f42d5a75
1543 F20101207_AAAIAW nozaki_y_Page_141.txt
a1e3e900a878bfc2a625f0f257f96435
dd34b07783ba3e5c05363d04fc2a7d62d1c7e0d1
290 F20101207_AAAHVQ nozaki_y_Page_003.txt
977af399025e37c7bc921c5310472ff2
042ffed094d0e3bb0b266375b763bf06fb121bef
25136 F20101207_AAAIBL nozaki_y_Page_027.QC.jpg
ee6805544fc2873da8b26ae39f3de30a
21a89e8d9e7450038f6e3fdf4a6140ed1dfa091f
2053 F20101207_AAAHWF nozaki_y_Page_018.txt
578fa5f92cbba1dc2996a9f65915ee8b
0d5faf70fb638bc722de7a6cf67b04ba363b94af
2021 F20101207_AAAIAX nozaki_y_Page_142.txt
cca17c5dbfb2f0f5f2ceaaa437d6bca3
033f0ae972b50d984eebac01d31806cc218e5e4f
226 F20101207_AAAHVR nozaki_y_Page_004.txt
8ad81e9461132c3069a8ae434c2c46a9
d8ef5d5d2ff56589447e50c3e5e45b453d01392c
7780 F20101207_AAAICA nozaki_y_Page_016thm.jpg
66c167f2395f53062b0861f0fd943c92
83f325d7c989f186fc2a0345f4b6277991184463
18439 F20101207_AAAIBM nozaki_y_Page_079.QC.jpg
75f03595cafa67d0f5e404e64f17fe35
a2c8d6623c71b23114feaa2853748f7242acc77e
2291 F20101207_AAAHWG nozaki_y_Page_019.txt
20d3e7c4deb6e2947d641e45d5c6c543
4efbe7fad865a0ef726755d40ef8c73162ec5212
486 F20101207_AAAIAY nozaki_y_Page_143.txt
757f68eac8f3823a97ba8c9eec4e19f2
ad4b13b842af62b53f1f5a11b2c735b0d5185d38
3290 F20101207_AAAHVS nozaki_y_Page_005.txt
30f4b3633f9ab508c1ff0f3d281b561a
4c0713cc475cb0a36c42fc51065783aec148adc0
22919 F20101207_AAAICB nozaki_y_Page_108.QC.jpg
a18cecb0ff39813546de81a9e4c10376
1e221d595d7d984a6dbce424e476c53f24e5dab8
5301 F20101207_AAAIBN nozaki_y_Page_088thm.jpg
ea5f57a6d739602bd6dd49a64260f725
4368dfb4ad19b8e1cd31bbd8384ce0f6614bf2d5
2381 F20101207_AAAHWH nozaki_y_Page_020.txt
4bfe4a80d6c098cddf61dd42ede668bd
8db9de2171e97990402fddb56f13d6dc88c1afb5
2105 F20101207_AAAIAZ nozaki_y_Page_001thm.jpg
6d186aa63f0811cee16314a8085a568a
3ab6c9f5aa5aac4553e8d9a95715e0d0d1d293de
944 F20101207_AAAHVT nozaki_y_Page_006.txt
3d55d9b79eaf3f588a48eb9a42af06c1
962da00fee1f82f98dbbc58038d4880f5fe4a6ca
10562 F20101207_AAAICC nozaki_y_Page_007.QC.jpg
d6e9b01698e37b3e0779b9202ea4ec8c
f28302e1349eb32adb186a060a51a472ba47126b
8076 F20101207_AAAIBO nozaki_y_Page_035thm.jpg
0f1865a67f5c1517cb080be2e3466dcf
088f2f9b80dbb329787a4de9af1ffe25d6367bf7
174 F20101207_AAAHWI nozaki_y_Page_021.txt
13067deeb4a9365e25d743a2a8ea75c5
6bab1e6a8bbc5f3a73a8a869b230d492ac2a938d
884 F20101207_AAAHVU nozaki_y_Page_007.txt
f80c4d69fd92b6f70fc79199e5ee3678
4fbf9c0f56ebdf6a39551d650c1718adf25385ae
27602 F20101207_AAAICD nozaki_y_Page_099.QC.jpg
6e20020b9e0e0fe585fb93834b790814
0dd8ad474ea692c18622493d9526f322f4f02b09
2583 F20101207_AAAIBP nozaki_y_Page_094thm.jpg
a3b39318d86c588ac5e1b91d1eb05c51
002e5161787e4c06debc24c9f6870d70354cd570
2080 F20101207_AAAHWJ nozaki_y_Page_022.txt
01ad0a7de9ad16b7da90a66212c7ef11
e43efa43955abac406b7cd78d206013484365caf
2857 F20101207_AAAHVV nozaki_y_Page_008.txt
43dbe6206b39e22f846dfa5794500605
635864e328cb3bd00543bdf82eed0b8a3bf10d8f
29750 F20101207_AAAICE nozaki_y_Page_023.QC.jpg
d503974d527808f3a54c80f8e2439744
e18053914a4496151e38d75aff21e451b8322e70
7708 F20101207_AAAIBQ nozaki_y_Page_023thm.jpg
2820526992ba4b06cf7e8f6e25d2a929
c79b0195c97379d17e98dc689fe897eb80aabde3
1945 F20101207_AAAHWK nozaki_y_Page_023.txt
7332389b8573447fc49e7cf4c6ad0313
541453da7886185d85996b5bec3b45b0a5b9eb2d
3064 F20101207_AAAHVW nozaki_y_Page_009.txt
052ef9485bec412fa32da0940e975550
27f4cde1ef8d7f6ed4118db545cf9e22ac694b76
18563 F20101207_AAAICF nozaki_y_Page_074.QC.jpg
7e508394b66c971be40fd4a8adb898c6
32751a811c0d20be7619674bca1ccd3af4595753
6321 F20101207_AAAIBR nozaki_y_Page_121thm.jpg
799624e882c97b4c909be202cf734d1d
f790b2faef7ca75d7c659a40b992ca52f30d839e
1863 F20101207_AAAHWL nozaki_y_Page_024.txt
d7ca0e55bc4a409d544e0c0bc80c44a0
1fb2343460f55650362833391979e3fe909c0b13
2827 F20101207_AAAHVX nozaki_y_Page_010.txt
3f65fc88388309ba223f83118d0882ca
e0f64d82af44b5c652c5ce6450b136b886e9d64f
4958 F20101207_AAAIBS nozaki_y_Page_127thm.jpg
89a95ce77cd1ffb158f236ad84a3d98d
8db17cd03cec2d8693f0c1a8d78ab8edbf431264
1957 F20101207_AAAHWM nozaki_y_Page_025.txt
b8d3cdc6de6f5b42955ab1458813967d
7fa0038728e24e9be0f6970b04b2c2ff4b3e5c9f
3356 F20101207_AAAHVY nozaki_y_Page_011.txt
48a35366c59dc3356af6e030cffd1b80
98ad9eb235cfba1b32344ef831407e00d1519a09
25058 F20101207_AAAICG nozaki_y_Page_135.QC.jpg
5f96a172c61d808e4a83a5a615ffa0ea
bc311038f79e426f9891cde1ac1da4f6884ce072
812 F20101207_AAAHXA nozaki_y_Page_039.txt
84e611c905b836e143f1ec6c0a91da78
4abf494bdc04b44ac633cf72f23dce62a3ea7f6e
8083 F20101207_AAAIBT nozaki_y_Page_142thm.jpg
8d90c0ad32956d3af4e4f66538b84340
6dc6dd1ecd8d59c88cbc6f1a4f340245729af619
2359 F20101207_AAAHWN nozaki_y_Page_026.txt
7d09bd4d14ef3fd426558d1a2c9c4e8f
acaadaff8a41be584ea9fd7b0a720912c2bc29fe
2981 F20101207_AAAHVZ nozaki_y_Page_012.txt
8fd03a745c69e33aaf57cc9672c01935
d2c26953d1c457d3057c0a60d8f40059d92a2e9e
20648 F20101207_AAAICH nozaki_y_Page_048.QC.jpg
51c30a8b23c78ec44a9d6e74c50ad52f
1636a57cafb80e6d3b45287eaf4b19dd3c851926
1267 F20101207_AAAHXB nozaki_y_Page_040.txt
b7c0c9fb085fa5eca9e45e5205c962fc
6c1716647f04e26cc5e35e5d60e6c83e12a889f1
33695 F20101207_AAAIBU nozaki_y_Page_139.QC.jpg
f8ca9daaeb1d9e5e8d27d341cda50a0e
453af3b0e7a319683d9401c95af6e159da641adf
1824 F20101207_AAAHWO nozaki_y_Page_027.txt
70625d73e474655d1684bcec8b049f8c
1b415799f4cd90a6deb51b85ebae73144d822008
27218 F20101207_AAAICI nozaki_y_Page_036.QC.jpg
2107bd3eb2dc59579095b6556d9846d0
463debec5c0f8c8457562a10404dd2a8d112c4a1
1300 F20101207_AAAHXC nozaki_y_Page_041.txt
f30e3fd46004ff2c005a8f51f3567c6d
7a70b677627ee3319eb40de273fea204fb4d2727
1325 F20101207_AAAIBV nozaki_y_Page_004thm.jpg
b382aac830668fe4d3d95864830281c3
2f8707de3d84b55a6ef98d9a9635cd442a3ee734
1743 F20101207_AAAHWP nozaki_y_Page_028.txt
6cc9d41a26f53d01ac30948d01d7ec04
418807942722021d26985d41aaf5bf575d801ca3
15670 F20101207_AAAICJ nozaki_y_Page_128.QC.jpg
62f126fa754ce8823263d2837528457c
38dcc7d67aa73d2ce2c19476f5f4336745027fa0
2056 F20101207_AAAHXD nozaki_y_Page_042.txt
9f7ee70d6e589533d7c05e1c98ba49a9
87d77a7380e5e4937fabc399c37971f643273f11
7713 F20101207_AAAIBW nozaki_y_Page_018thm.jpg
c3ec592401bab91f5484c7abc92a237e
360a2b06a76fed23f0bd2c647ba6b08cac2325ea
1930 F20101207_AAAHWQ nozaki_y_Page_029.txt
0d981b6a8cc974c3281e611d4863d5c0
deccd9241a9ff9d4807546f9aae2dd8f703514ae
6781 F20101207_AAAICK nozaki_y_Page_138thm.jpg
354eeb06a232911ffcdd97de0e7c66bd
c246822e6c2ab95d842e6a638f44975dc8e92a33
F20101207_AAAHXE nozaki_y_Page_043.txt
a5e53736e40339620d655fb1803a0496
9731eeadc7003f89c12ee235843ceabecfc41f08
37995 F20101207_AAAIBX nozaki_y_Page_009.QC.jpg
2fd067b51378d814866ae55a546171d8
21195487d9ee834df471e3a66c101ec3ffa23482
1826 F20101207_AAAHWR nozaki_y_Page_030.txt
5d9b44dc1f9469c4b0e0dcf165c7185f
9c901711934e62cfc0011dd51ed6159ae563c3cb
22517 F20101207_AAAIDA nozaki_y_Page_069.QC.jpg
0bb3bae418da8f0b6e8650b22569ec80
7e7da52bb5888ed819714edead6779a9901b8eb7
6534 F20101207_AAAICL nozaki_y_Page_005thm.jpg
a24fb11c68ac227ee932a1640b552db8
731c2073453851ff88ce7e715a6aba405a167c0c
1804 F20101207_AAAHXF nozaki_y_Page_044.txt
81a88bba147d1778fbf44aa0d1a123c9
c765caa281a8123644e5590619031800b17bf29a
2330 F20101207_AAAIBY nozaki_y_Page_101thm.jpg
b6538cdf9809aabf22509e33ab845cb8
86c3eddca0c784945c0e3e4e9c0b2ba18467fdd8
2146 F20101207_AAAHWS nozaki_y_Page_031.txt
7720265820bb66e11e7d643d787568b9
1232fd6a055d6043efbe3f5863c58e46ee25c8d3
8084 F20101207_AAAIDB nozaki_y_Page_022thm.jpg
39103aafa2c5329767e55fc1c0889893
bfea3094232952beda91e2c41cbdd55ba56ba6ca
8193 F20101207_AAAICM nozaki_y_Page_096thm.jpg
a0e3f73843b5a30fa4b7e29a2154913c
839a2f8e613742c02a8ca291bb7e812fe3c272ec
1844 F20101207_AAAHXG nozaki_y_Page_045.txt
ef6abb943c0cff5b4098cdc0509cfde4
d9e450554fc55c0f2ff6326ed1f5c4638c63bdd0
2134 F20101207_AAAHWT nozaki_y_Page_032.txt
0edf18383f5d91d4fc5e62d5afe3c151
61d2dcc77d45c9da00d573b8999bacfeb07b5144
52224 F20101207_AAAHAA nozaki_y_Page_006.jpg
d05b0e33f6ae8be4a1c1f2b1bdbe8167
d9d87f468ad6a37f6908aa457347b73d2277c73a
19574 F20101207_AAAIDC nozaki_y_Page_104.QC.jpg
6237876f0c13658e8c4fb2a736c073e5
61ecff1240696b4c380f37e87129a94748dfc3d0
27495 F20101207_AAAICN nozaki_y_Page_111.QC.jpg
f2275c5e74ee6c00953ebb7103dff2f9
1976a9c624b2dc3eda378247320755aec94d8d61
316 F20101207_AAAHXH nozaki_y_Page_046.txt
e7261b7d05039425f52047fd5233ef53
62fb8929507efbdcaa4e45a6e219d8506c2c9098
5183 F20101207_AAAIBZ nozaki_y_Page_091thm.jpg
101b98ece4664a9cded1c3cda8fa5e5c
b8a196e264632dedbac125432166b918e8cd6ea9
1922 F20101207_AAAHWU nozaki_y_Page_033.txt
8a037ec1a1df58309240f2cf059817b5
3542b90ea096639cfc92f92dc05989836f0dd096
37410 F20101207_AAAHAB nozaki_y_Page_007.jpg
cc0083b2590b378862d68e99018b8e96
cbf6d5d996768628fd6fd3bff58a515557c5a942
6347 F20101207_AAAIDD nozaki_y_Page_087thm.jpg
b32b1bf748c9139105b78fa3eff596e4
53235da26e220682aa21f82a23ecd292f2fcee85
30612 F20101207_AAAICO nozaki_y_Page_056.QC.jpg
b90dbcd497063fff2a923f9386be34c4
c17909be9e30fe74c53a4ebcf4436c6a1333b869
2210 F20101207_AAAHXI nozaki_y_Page_047.txt
2bcfb21b9080ec6f6325ab89a464b6ad
779594b869ddc364277feeda4955b11e8ee247cf
2128 F20101207_AAAHWV nozaki_y_Page_034.txt
443e41508d2953dcfa7bdd6deaf01e0d
e0bef231de0be7fa16841984916d4504315522f0
121543 F20101207_AAAHAC nozaki_y_Page_008.jpg
5a544ccaba2d26ca5922feb5af270ca5
de2d95adcfdcf903911db6b64d9260ced43430ec
6850 F20101207_AAAIDE nozaki_y_Page_036thm.jpg
827fdf9a53954728ec73540fcd00c9b6
9469efa6fbe298086d8ae53bc5aab6fbe456d500
33573 F20101207_AAAICP nozaki_y_Page_035.QC.jpg
1a8ca9d768215831a72d6699315ce74d
41aeef01293b8a52d864a89fb17f3637752474fd
1758 F20101207_AAAHXJ nozaki_y_Page_048.txt
2b05b18ea84fbd955e9fe1d59e93061d
48fb58939ced858533a0e7646c02ad02be2aa1ff
2028 F20101207_AAAHWW nozaki_y_Page_035.txt
5179aa4a501e9c0cf04727fc57fb17e8
2e9df7cbb44bef69a9c83dda5b24ada7e701718c
139291 F20101207_AAAHAD nozaki_y_Page_009.jpg
538ca01b5b9789eea81072b59ba7c999
2f6889fc430a542ddc70184d96a0ddeddba5d8f4
7027 F20101207_AAAIDF nozaki_y_Page_032thm.jpg
196f6d9fd277758e22a5ae2b436753cd
8a19b2122eff00e03c8815293a10563ec116f4f2
32104 F20101207_AAAICQ nozaki_y_Page_138.QC.jpg
dd5135d6f2e76c213a894d188f5bdeb6
145aba85a08fc6808a4349ac89d1f7e930cf874f
2133 F20101207_AAAHXK nozaki_y_Page_050.txt
70d333cc7f0947ec23416d9d28d72a3d
251fe9c8b89ce50264f266575eeb651e74c2faa4
2397 F20101207_AAAHWX nozaki_y_Page_036.txt
74f27102de12f384aadc44737582bd4a
646afdefaa56c2fd9c1a297ad04e36992dc23db3
128505 F20101207_AAAHAE nozaki_y_Page_010.jpg
0586325cfe716b937b2b80869b6cb24c
1368e86387455950aad987e352e08a17c3e2fe01
7838 F20101207_AAAIDG nozaki_y_Page_042thm.jpg
fe9037d5ece1d8388137f97b2aca5bcb
81753c05bd59a844553e611425219f01f411a9ed
28391 F20101207_AAAICR nozaki_y_Page_113.QC.jpg
88524c3293c6aabbafbb9861aa63e2b8
9c050dbaf903050c9349edfd605e8abb50dbd1d1
1985 F20101207_AAAHXL nozaki_y_Page_051.txt
0bf8759f5af6ec18e14836380e5d9077
9dbca2a74c283914c36e79e81010dcecf0abf7f8
438 F20101207_AAAHWY nozaki_y_Page_037.txt
ca194f3ba58cf696970ff47c982bcad8
74814dc85dc75cd59e4b7f3cc38a645084512db7
307 F20101207_AAAHYA nozaki_y_Page_066.txt
d88b5813a08cb52c960dff2c907661d9
e987d6a28a6f0ab10bb18eca88e1fc5e274e2e6b
5523 F20101207_AAAICS nozaki_y_Page_071thm.jpg
e7b973ec21ec46d9f93cfa2cb194c626
76b70b5ca71472ce44aa64a40731f91399ec505b
1877 F20101207_AAAHXM nozaki_y_Page_052.txt
fc0f88c8a0bfdb108fc547721a921bef
921982261ccbc3b566a7cb52e7ff2d0af6e5719c
492 F20101207_AAAHWZ nozaki_y_Page_038.txt
c238abc8dabfb1782cbff2e6fb712f59
237d71b0d0652e9588b0938b4e67db8f903e5033
141625 F20101207_AAAHAF nozaki_y_Page_011.jpg
e6a4f0a1c937103bc79ea398d8dd9735
873ff16191c3ad98e19476acf0d2c56b2d15fbf4
1298 F20101207_AAAIDH nozaki_y_Page_002.QC.jpg
b1f0d00bbbffc819503eda19a54fde62
f73ea9bb392fb618ab448494b0b78d36cffa14f1
636 F20101207_AAAHYB nozaki_y_Page_067.txt
4f9a0475ab8b4c16b79d59ac27abbdcb
4d7737af7ff3fcc839474e234b84ea21d1d10317
22586 F20101207_AAAICT nozaki_y_Page_087.QC.jpg
3c56827b943f89a57182e5789b6382b0
1df2feeb026583848d42c0bdfb275e05612731a3
2010 F20101207_AAAHXN nozaki_y_Page_053.txt
a8567ae45aa1777b2d1eddd5c422d7e6
2a1b02e4d3f8dd981600728c9324d607858211f3
138515 F20101207_AAAHAG nozaki_y_Page_012.jpg
3fadc4b385022234c19335fbf61b0a7e
97d44f15531ec2c99624c9b48417696d4c845e08
17829 F20101207_AAAIDI nozaki_y_Page_071.QC.jpg
cf5c383794840c5e20f29908615583ec
cc18b70e748417deb78cb9b7b82cd1646a238247
1140 F20101207_AAAHYC nozaki_y_Page_068.txt
a6a9df287998426a37b1a17cb4d4e5b5
e76d306d37e487fc9cf91a4e09ad1589637a51d9
8949 F20101207_AAAICU nozaki_y_Page_053thm.jpg
7feed4329b7a359db20d763e99b5b75a
e15a910c90f16e0f684668260e29921653b49697
2099 F20101207_AAAHXO nozaki_y_Page_054.txt
dc414e32419c778343302b63b1e83a92
b4a57559796e26843bb1ac0ba76fb970ffaf6649
129368 F20101207_AAAHAH nozaki_y_Page_013.jpg
172d0612af8f793266c641fdc6d1c238
6faea1df8f251aecffc4c81b1953ce3830f48cbf
8619 F20101207_AAAIDJ nozaki_y_Page_095thm.jpg
06910c3613b6140f0ffad6a7d6dcd8ce
ad5d3bc61975dd2579486c4789fe6508b99bc0ed
1128 F20101207_AAAHYD nozaki_y_Page_069.txt
b89e327808141a5e6c61b208170a02dc
34daf15d1475c80be4ac8f2445e64b4ca5133727
7702 F20101207_AAAICV nozaki_y_Page_052thm.jpg
c6692cd0080d4b7f8dba3f2ac4278c51
694184662351f494c58520fc413d9812f8dbfbda
2025 F20101207_AAAHXP nozaki_y_Page_055.txt
7ce7e5c5d6851b6fb2883049351676c4
6829343112dc557ba9f4b1bde5f5750589d9ac0f
137872 F20101207_AAAHAI nozaki_y_Page_014.jpg
87ea603a1057ee8e41ece432e64ea7f4
b6d6a6a84ad52a80105ed91d75a58eebab4622ff
12539 F20101207_AAAIDK nozaki_y_Page_117.QC.jpg
1700aad652a899261553050a89ff1762
25ed6252cb398a39aad8d894ac98f54cb87dcfda
1270 F20101207_AAAHYE nozaki_y_Page_070.txt
bf1c07615a8c63b04408f6a1d1aa329c
d3402508f300297917631fa037eb6647acd1d27c
24665 F20101207_AAAICW nozaki_y_Page_112.QC.jpg
ddc059288c558cfb0434db3e466da359
e2ffddac6a530a952573b7e010275ee3876d58fb
F20101207_AAAHXQ nozaki_y_Page_056.txt
2e1019543d45a30fd34f55ceb7c4e6ea
0594ae552dc809eac620ead5c26d8632e1e4bf86
12819 F20101207_AAAIEA nozaki_y_Page_103.QC.jpg
b5397879b8bc67fc602ca69b18c995b5
458d8b48159bcedfa8246c68c4128f8ab48912fd
5054 F20101207_AAAIDL nozaki_y_Page_015thm.jpg
8225e09c2951be5b787e639f990037b5
903ab873366cca6a4fea0e65fdcac8c2e717df3e
75154 F20101207_AAAHAJ nozaki_y_Page_015.jpg
bb60c23eb681633b271a83cb779c482c
cdeeae1487dc43b8e769aa9619297ab1b1baa489
1226 F20101207_AAAHYF nozaki_y_Page_071.txt
99ebbabff904f69fddc06cdbdd0b3359
dc8268cee9f2b94000e71ad0431fe8983d55154c
9468 F20101207_AAAICX nozaki_y_Page_009thm.jpg
a108cba7bbf36cd009f8394c2dc83868
d31f3f1f346a5c108c29de53a8d1c83149c287ad
1887 F20101207_AAAHXR nozaki_y_Page_057.txt
d98e0f3fd5b37a98daac6142bd649a0e
33c7d15ff9f99e34afd6032f1f414fab4bb309cb
8290 F20101207_AAAIEB nozaki_y_Page_026thm.jpg
088c2c41d99a8e18b24950ca65f3a23f
a078a3c742160090e7315ed28a04eb511ec50606
18712 F20101207_AAAIDM nozaki_y_Page_083.QC.jpg
782106432057af4cb248dace32647e45
e52e02c67dac47e042798961a4026105fcf3e30c
97330 F20101207_AAAHAK nozaki_y_Page_016.jpg
7f84a186f16a9d677138b02c03f34c95
6f3d4843653c44144ead08449683d0a8a0b9084d
1227 F20101207_AAAHYG nozaki_y_Page_072.txt
a99822c0e3df3e23e0bcca1ae3eb5f7e
464c4ae9abb88a402c2f217adec7a4fd6e387ed6
3545 F20101207_AAAICY nozaki_y_Page_006thm.jpg
6a1ca8e77e124723da70108682281853
5170433e210bf8fbc0caeba089ca0c1af4e883ba
883 F20101207_AAAHXS nozaki_y_Page_058.txt
15fdf5f09f8194cff86777654bcff573
e9920c4d289c0ede18ef3b640bba48c20b5cc758
30568 F20101207_AAAIEC nozaki_y_Page_025.QC.jpg
83bf9bcf2917d328e8433b8b0783b4e2
829cb10933d5980a8db0f7a0c6b6b6f2ac4b1e07
4297 F20101207_AAAIDN nozaki_y_Page_038thm.jpg
27d348088cf762f0f6b205ea8fa282f2
64369f7c1a14e1ba54ef2018c317348e52fb06ec
91794 F20101207_AAAHAL nozaki_y_Page_017.jpg
ee3a148a84242bac600e16da8e7b824d
46ad7d8d75df9b3f06167d6701723f73c45d1773
1155 F20101207_AAAHYH nozaki_y_Page_073.txt
8f535546bc21c42d8e6d7d7891ecd40e
13778ae29616d12917a4a91ed968edda6684a4ed
7341 F20101207_AAAICZ nozaki_y_Page_124thm.jpg
37d9da21c127824c65914832d9a5d1b8
0caf0e0076d10555da86d8d6f5bf482b0eccca09
1075 F20101207_AAAHXT nozaki_y_Page_059.txt
686b4f276e8355bc1a48d41f8a5642e2
f7ca1364172a2a044a8daa6d183bab4c181b5b70
91574 F20101207_AAAHBA nozaki_y_Page_033.jpg
6e29d9b542150d8e66da4d4ab3484966
107e97f4d225191f81ea66762a99740eb80351e1
6886 F20101207_AAAIED nozaki_y_Page_030thm.jpg
fadd0438a2d051bd8529e83442943584
1d536fb7670c69503fbae1655b34ce734a4cec05
7307 F20101207_AAAIDO nozaki_y_Page_029thm.jpg
d0bb367ac35ca32dbd99ac156a812b73
6f0d5246d184c6cfafa7b51c82f2dfc8d82d58ff
92353 F20101207_AAAHAM nozaki_y_Page_018.jpg
534ae3b731d4fdb5242ba41779061953
58506dc914b91537fe48d973d220c3168c4f3185
996 F20101207_AAAHYI nozaki_y_Page_074.txt
5331152e4de96a09109a3ff755750dec
aa91be2dd0883722983b8176c0c77c50d01cfe2b
1141 F20101207_AAAHXU nozaki_y_Page_060.txt
542c97141f994b5a9fc353249100f297
0f6424c525946efd687d7e515b10fb67e393602a
107991 F20101207_AAAHBB nozaki_y_Page_034.jpg
cdb76649c12ccab7bc03e00babecc2fd
bff44ea9f6e0c17509f8d9838ab3769756d67122
26423 F20101207_AAAIEE nozaki_y_Page_121.QC.jpg
5f5af62b69e5261c743efd49091e2da9
74ad8bb9d4d71f7034827edd6bf8c4d2e5a5dc47
30715 F20101207_AAAIDP nozaki_y_Page_057.QC.jpg
95bdeaa9c94da71172682fb587d7f9ea
bd7e1980c01c5c7d7e0b52f35e4fab2f260ff9e5
74082 F20101207_AAAHAN nozaki_y_Page_019.jpg
a0ad673aacc27c5d7050e94660b1e4e0
598205efb7ad50546ccce073d02f7d4b5602be73
830 F20101207_AAAHYJ nozaki_y_Page_075.txt
5b24b3bcfb5c14b6c20fbb196d0694b3
463c471043f96e72fea8a4bc1c5a9b216f72db56
1086 F20101207_AAAHXV nozaki_y_Page_061.txt
182ec3c1e275bdfe7845521c2d1bbfbf
d5635441a750774b2f90e7106dc11a60073b9059
99612 F20101207_AAAHBC nozaki_y_Page_035.jpg
fcfb6685015b747f780722bfec73b909
84f8a2f675966d84abae6d83a59a16e402de003b
29512 F20101207_AAAIEF nozaki_y_Page_033.QC.jpg
c1017a73dd4f14a56d94c925d1a03838
26bf0d7450bde4205142f6316e5f02038b89c0a9
5407 F20101207_AAAIDQ nozaki_y_Page_135thm.jpg
d2693bde6d25954d1c58bb3982c604f6
fa94e093ee6879606f556cbcd821d7744187c213
103631 F20101207_AAAHAO nozaki_y_Page_020.jpg
b36449be7dd55e32a2ffc3ca01c1896c
e80433578e1536624b6960edad544f9bbd5bd321
777 F20101207_AAAHYK nozaki_y_Page_076.txt
ea65c176305166d27cfb6f7e6b0bb751
66aaa81c1e87ab3b2861a157826e5dd712d18834
1292 F20101207_AAAHXW nozaki_y_Page_062.txt
5e395f38f75791db0efd6bf6824ba254
04c1f6881665b6091fecbb79fbfae6f9b88c52ea
82621 F20101207_AAAHBD nozaki_y_Page_036.jpg
93d41b83e12f160f40000b77edef0350
c8d25aa31d27816fd159f1546985750a1686649c
32347 F20101207_AAAIEG nozaki_y_Page_132.QC.jpg
51624e2e812470fb8a256b97a83bca68
23698aef4aa325e4b6877998c3b5a724fc89a489
6232 F20101207_AAAIDR nozaki_y_Page_099thm.jpg
1bc3e59b14e8996c1e50bb2e3de2aba8
846917aaedefb2a02bfa6c508f5d4e170182037d
15616 F20101207_AAAHAP nozaki_y_Page_021.jpg
09e68657bbcee653b4b6d54cd8791f30
8138dbf8f36bae927ea9c3f4fc4621986c81b4de
1218 F20101207_AAAHYL nozaki_y_Page_077.txt
ec585671a18162bc10fe0a97a82aa31d
02191cc6ab4649eff36af03f18b4a8bf2f8242fe
1170 F20101207_AAAHXX nozaki_y_Page_063.txt
fd56758fa2ddae7bc9da3acdb8b70659
cbc6085fa851d0fa62015fb701f8b1b442e2ee67
29086 F20101207_AAAHBE nozaki_y_Page_037.jpg
28413fef047e9180f1749619a1750a9f
f91380fc6c00e866ffee4eeb0eff29c0217c4e5c
5857 F20101207_AAAIEH nozaki_y_Page_119thm.jpg
5b659353590825cca213fe4ecdc6f050
08369a9de5de671d44a883e19d0b0ee1ca850321
2300 F20101207_AAAIDS nozaki_y_Page_102thm.jpg
4f0c01c187fcad9659cf33fdebc662f6
e40c1dfb0c9999912431642cbcade9dec4f20ab2
97133 F20101207_AAAHAQ nozaki_y_Page_022.jpg
7750b8960b7a43176b5ff62e301b0563
abc206c035876d9e7897b58f4636cc9f73744623
1014 F20101207_AAAHZA nozaki_y_Page_092.txt
71e60b6eb9bcb59acc8a20410dee3f44
1d9c10ff49ab77ce804281836056832415984aed
1202 F20101207_AAAHYM nozaki_y_Page_078.txt
722bb91246699b12f0b3c72e103c08b6
847cbd5d837c2b9c70b47e58853394cfa59aefb5
1188 F20101207_AAAHXY nozaki_y_Page_064.txt
83d6f418cd980fc9c28df53b8591140b
09e61429fea2e8efa513e14316cc39f42ecd0dae
41992 F20101207_AAAHBF nozaki_y_Page_038.jpg
222e96934d8077e97cc2b06f36c58370
23254cfadb03d89e48d061ff8258632909fd976c
7610 F20101207_AAAIDT nozaki_y_Page_031thm.jpg
d38061780dd170eec7315b038822ace7
3c14c7300f8516eb989189a76ba8176a2790d497
88469 F20101207_AAAHAR nozaki_y_Page_023.jpg
548318ca269d571a84a07a8ed0e56760
105e5b617977362ed9e5566501c8eb8c46b3903b
788 F20101207_AAAHZB nozaki_y_Page_093.txt
6df362bfa0c1c13d82e29461d5742796
76daf3ea71b425b956e8ac0a1809de8222ef47ad
1408 F20101207_AAAHYN nozaki_y_Page_079.txt
88889ed08db1665840d9a88b048b8f6c
88c701f04a6ff3a632a9f20e737ec9e3759510d6
1448 F20101207_AAAHXZ nozaki_y_Page_065.txt
fa8cbd9ac6f3aeac813efc90748c05dd
10739cf0d920a49856c50ad8db6c25fb09e93c22
9190 F20101207_AAAIEI nozaki_y_Page_050thm.jpg
7d7c88482011038b050ef292551cd7bd
55957159d1c36682fc27d2c1bee7536829f60575
6332 F20101207_AAAIDU nozaki_y_Page_078thm.jpg
38dd2dcd2537370d49a32eff12ac68cd
b63c5b7d48294916ac0921cd986ba372db64f2a7
80708 F20101207_AAAHAS nozaki_y_Page_024.jpg
4758eb8645875ba8c9a73aadd390d1dc
dccf4ae4131ec42b2b66c9c65f2886baf87c6657
119 F20101207_AAAHZC nozaki_y_Page_094.txt
3dabd23a5065a49689ae284b7c928e58
58d7eb324f6fd29fa4e47d7c036e98b814df35a9
1052 F20101207_AAAHYO nozaki_y_Page_080.txt
1ee30effc8b692e93345dcea2db65466
b17ca1c36d68730f0fb54030c4696820f0dc2448
44884 F20101207_AAAHBG nozaki_y_Page_039.jpg
4ec5a52b7b671fe1bde2402837095a6c
8ae3e2bd791129219581f0073542d645ba3f672a
6491 F20101207_AAAIEJ nozaki_y_Page_122thm.jpg
cef0a72906e701812d37830f71b7179c
3a23364a632901b003795ab2a66fd341bb0bfd0c
19463 F20101207_AAAIDV nozaki_y_Page_065.QC.jpg
ae30addd5cfa8ef55e17f4f5d3619a4c
323cb22ad94be418fd2fb1e3e45b77ba1d30261d
91930 F20101207_AAAHAT nozaki_y_Page_025.jpg
135828aee7de1985c526dbcd5f730c3c
e6441165aae051270f4d44e2129022216041bd8e
2214 F20101207_AAAHZD nozaki_y_Page_095.txt
bbc9d249e343aae1571d56da8dcdcee9
f591d1cf1f2e03f61eb71d9976251dc153804994
1450 F20101207_AAAHYP nozaki_y_Page_081.txt
dde2f0dfe1a053a771ee0940be405af3
ae26316efc74745e1bd981cd649a134e713d86c6
49111 F20101207_AAAHBH nozaki_y_Page_040.jpg
334bb0a2a0d1bc6961de76de73220ebe
6a41bfa61ebe516ad9116856f1db0a0c6885e21c
5722 F20101207_AAAIEK nozaki_y_Page_120thm.jpg
ba5499d77dc3617f803aa4306eae1e05
604b4bd2e0a04c2881dbcc858db1086245d814cd
F20101207_AAAIDW nozaki_y_Page_019thm.jpg
6e8c8d09fb59de7d74fe10063b4eb628
b8ac0491f9aae0a5d70a137f8642cdf57a9c3fca
100018 F20101207_AAAHAU nozaki_y_Page_026.jpg
5c1eb5c72a4587b88b41e25b7888ed75
5ac9372fca50b35b614cf2e66804ba72727360a4
2046 F20101207_AAAHZE nozaki_y_Page_096.txt
6a37f6fc9c36028ec4445fadce9dc6fc
c853889cb22546b92fc80b9309bcc1150700bf3e
1036 F20101207_AAAHYQ nozaki_y_Page_082.txt
9ce0c3944a63e2e4664d1102bc859c0d
416815b84055b6b37dbc6eaaf72ccf925dfa3455
48693 F20101207_AAAHBI nozaki_y_Page_041.jpg
a3622803fa577fe649a021d9e44ddbc0
0c9c868e5213d288a95510e6cff93457f04086ac
6503 F20101207_AAAIFA nozaki_y_Page_066thm.jpg
d089f6ca242dab2d4f41e2187aba1bae
8bf3c9eeeb2ea144797121eda78449d8398443c3
17100 F20101207_AAAIEL nozaki_y_Page_088.QC.jpg
16bb078d71ec82a358d0e66850f8176e
210d0b869f4862d8f43522b85e4d5e47095630fb
7278 F20101207_AAAIDX nozaki_y_Page_125thm.jpg
837315e3cf0058f579eaa8e2a6381910
d1cfd7cbe9b52a099b300841ce212a8bb4f45738
75082 F20101207_AAAHAV nozaki_y_Page_027.jpg
ed8ecb236f1a295fb8513220b5b1328b
a7573957b20919638e2b2e7741196321d405018d
170 F20101207_AAAHZF nozaki_y_Page_097.txt
1bbe7d7cba0406d1ddb9f00d56de3ac6
5c4a8f0339aca0aa6473a4b9a85bbf2069fd3a4e
1135 F20101207_AAAHYR nozaki_y_Page_083.txt
361614c19dfe6fe9b88a08dcde01e815
acbf48e1bd363cfc1eefb3d1f5f35ed9f7549d64
99173 F20101207_AAAHBJ nozaki_y_Page_042.jpg
e2d4e48a1df6cf78bedfbdbf938d795c
5d15339a9558a36a55b3bf134050bfc9352b3386
23037 F20101207_AAAIFB nozaki_y_Page_137.QC.jpg
9d79ee5fc00f399670e89121e7d996c5
07ce9dbfc6db5ebb9bc0cbcc792d602e31fe730f
507 F20101207_AAAIEM nozaki_y_Page_002thm.jpg
4adf3d48e8ca55118ef1544fd71db60c
fd7e6a9755bbf00690bd3ba7d8f56dea9cf0ecb3
5201 F20101207_AAAIDY nozaki_y_Page_089thm.jpg
75192b58b54a56a85323857090b6a74c
441120336c2f8e28ae17c642df5840e61178c0bb
76043 F20101207_AAAHAW nozaki_y_Page_028.jpg
29f2bf8ed270b7774cef3e18407ced75
a8f8493816b2db1db52da7827360a954b052a72b
1780 F20101207_AAAHZG nozaki_y_Page_098.txt
934181102187c3329964b043df2f12d4
13f6992b4b2cdf3122d4266fed26d1512eab3b70
766 F20101207_AAAHYS nozaki_y_Page_084.txt
13e85ef7d2873bc45bfb5dd4774c78e4
2e14ccfc4cb6b1e5aa68a075e75dec54bb463534
64821 F20101207_AAAHBK nozaki_y_Page_043.jpg
aa2ca81fd75e598bbc368e97b73d8439
d86a802942bf5470ae7e759fcd784787040d9607
28017 F20101207_AAAIFC nozaki_y_Page_031.QC.jpg
5fd6b6eca111bbe332e027c6c7ee67a2
1c00577e6b6747cfca6d44d7b285252e9d544065
6948 F20101207_AAAIEN nozaki_y_Page_129thm.jpg
ca3aae131e6aefd39c1ba1aa87ee50ef
d76e7389693a9caa3719230908658cdd78dd848e
5238 F20101207_AAAIDZ nozaki_y_Page_072thm.jpg
7d194a4baf9d9b3730dc8c838bb3a6a3
544882450a485e8b628e55a335036621ea1397e1
84925 F20101207_AAAHAX nozaki_y_Page_029.jpg
7729eeebcee0f0b40960375fb5adfd93
2706f76e44acb651c112069c697830ef01434e1c
2164 F20101207_AAAHZH nozaki_y_Page_099.txt
c947bbbe66cd6b37d19c2df22332cdea
a702ccebdc6f5423fb1d1efb54b4a9c3f13f352d
773 F20101207_AAAHYT nozaki_y_Page_085.txt
1f7d6f1e5680400344daf2b410f74098
9fa80fa736e2540e9fc2086fd3a2e2e106d71d9b
54957 F20101207_AAAHCA nozaki_y_Page_060.jpg
ef6e14870787335a9fcb9cb8694418a6
98170d8f68c70e4dcb4b6a2aa19e6341c7c392ff
80177 F20101207_AAAHBL nozaki_y_Page_044.jpg
47a84c670a0baacf7b87d79901427012
f7e59aff3520b78fd7543a6b9c59d1cc18529742
6055 F20101207_AAAIFD nozaki_y_Page_140.QC.jpg
03266ef690d0f0ec7d6d51f85332a8bd
498751cb4f06989527bc0bc6610d04164c2ed732
27696 F20101207_AAAIEO nozaki_y_Page_136.QC.jpg
939738b0a258e9b52b84def657b284d8
10277ccf04ced534804f613da810516f5cb98399
76839 F20101207_AAAHAY nozaki_y_Page_030.jpg
24270736ad97c9bc0f913403374afb0e
43c66fffaa4910ff2d4bcc935270b7bbd1a2adac
1672 F20101207_AAAHZI nozaki_y_Page_100.txt
caabed68ebca9d63e5830160c01142b5
3fe2ca0654536d155683aca16224277453c57f51
1049 F20101207_AAAHYU nozaki_y_Page_086.txt
344b397a17a21473896ea999c69570e7
4d1f3c87629eeae761f8cfa58e427987dc49902d
53077 F20101207_AAAHCB nozaki_y_Page_061.jpg
49d77b6f5377793d30a6a4bf26a3c276
2b6b85829241d775dbd341cdc08c59d692072d3d
29369 F20101207_AAAHBM nozaki_y_Page_046.jpg
ff131c3943680f6cb27f9f99d6dcaaf0
5d06193196a45592c55799702fcf7b092173b0fc
8703 F20101207_AAAIFE nozaki_y_Page_034thm.jpg
02684fbf5a5cc0a9bbb39fe2436261e2
7d37fb9d59700ccab06feb8c4cbd938e3bad86aa
5671 F20101207_AAAIEP nozaki_y_Page_043thm.jpg
9a69e3337f00880d5c75757529656b38
02f08f6d18539d350f3af741d126daee869a6fb9
79918 F20101207_AAAHAZ nozaki_y_Page_032.jpg
9bf1e220ccd79041564655db1c606ed5
ff49deefc6479225150db5367d2d552714884d32
725 F20101207_AAAHZJ nozaki_y_Page_101.txt
afc8c11b835d3aec81bd24189131cf11
36997a2f9c4584b99e315ee137b4a396bdd04ab1
1239 F20101207_AAAHYV nozaki_y_Page_087.txt
20fdca26373eaae2e8c77f4af0b05dbf
65686584bc2a5ab6b962bdf54d0a05154177af67
53751 F20101207_AAAHCC nozaki_y_Page_062.jpg
9837d680663be40d8d5a2c3b82cd8bee
44844dc11454ff4b7047f843341295abb4d468b7
103557 F20101207_AAAHBN nozaki_y_Page_047.jpg
a020f6d45e2a4d1594df86d18047f975
fbed298ccee4dd1b56cfcd6467eee5d57fc0c5b1
6932 F20101207_AAAIFF nozaki_y_Page_105thm.jpg
a58b68304ae0582848a4eec850d2b974
7b180fabc1ff0d5cb40c24254578238ba067c82e
3010 F20101207_AAAIEQ nozaki_y_Page_037thm.jpg
f8d8a2d8c2e0e7b1ca9750db1367b145
a8ddd39936ab4b082a9cda3f40cf6d47ddba9668
732 F20101207_AAAHZK nozaki_y_Page_102.txt
64597bd273c16ec2ef3f80648263191b
f86e124fcbf2e50932583b276460e2d8efd5e5ef
1268 F20101207_AAAHYW nozaki_y_Page_088.txt
0de6dcbe214aab3889f1182043869b98
461a3dc6680664725f0de72e4456541fcb3d33ca
54966 F20101207_AAAHCD nozaki_y_Page_063.jpg
3f849c43fd2a7e80bba217a27be77e06
e8e1030fb0f18141f07edb4cb2d8176276617938
64209 F20101207_AAAHBO nozaki_y_Page_048.jpg
72810de2148ad8ad73695aecaca52571
64ee4fc01a7cc242132a4c603796f16fc79e94e0
23646 F20101207_AAAIFG nozaki_y_Page_068.QC.jpg
c2e131f4f7201e0cf84f879f42837d63
8f6d16f13f7da57602d3fd966912fbe08d039894
17912 F20101207_AAAIER nozaki_y_Page_089.QC.jpg
03dd5d41a0fa24ec772adf4950211c92
f3cea18f9e119c580741dfb593d4435aa8c4445b
905 F20101207_AAAHZL nozaki_y_Page_103.txt
d20c56bdf92ff40687af39d3f50d8332
7bd907fa206820fc1a2a85cfba842917f5f1d5f8
998 F20101207_AAAHYX nozaki_y_Page_089.txt
415243a749225be0892cd433ed497522
6cc18cf23150b8447de714b000f0495f4f5f0444
53173 F20101207_AAAHCE nozaki_y_Page_064.jpg
25449bbf413ff9b157b3f3fa9c843168
d8f52f1302bddbe83dab011809a546a55489dc78
81894 F20101207_AAAHBP nozaki_y_Page_049.jpg
7f083bbd4a08f920a0efef4f5a5f34e9
ffe33abf2d57670be6851303517bae130bd4a43e
6124 F20101207_AAAIFH nozaki_y_Page_131thm.jpg
ffe784fd8431d584c2ddc9980e0e36dd
11ca37a61f81a2a732b881837446c9a0062c2feb
6289 F20101207_AAAIES nozaki_y_Page_112thm.jpg
c29cfe2cf42dc298ce6edf785ee42248
abcd0ed0909ae4be63b4c24d314d276c28ab2857
1301 F20101207_AAAHZM nozaki_y_Page_104.txt
125d134dcbf51571725f5d125248c5c5
2f0a1c64aad7ccab8ee2a2fa88d7f693e1be3b6d
979 F20101207_AAAHYY nozaki_y_Page_090.txt
48899ac7b84c8dde6333db03aaec923a
764cdc4f3473fcf5819bfa14932a8f87b109d197
58337 F20101207_AAAHCF nozaki_y_Page_065.jpg
7a1f5bb8761dcfd046955b9af8edaece
f4c37b4cedf4c5fbd2028dd8e47e7b4e0eacaca6
108388 F20101207_AAAHBQ nozaki_y_Page_050.jpg
5c9d70d4183b58eacf6b551b061a0c4c
8c689d564a2469134e99990fb8dd261fb93c3332
5858 F20101207_AAAIFI nozaki_y_Page_067thm.jpg
7c10dfca7375be7a4fd6375e2a528137
cb3fa15b12af3b59c8279fc4feab753045b7a145
17494 F20101207_AAAIET nozaki_y_Page_061.QC.jpg
744abeebdeb32c34ccb983813fac204b
dd9085d242a5b01ec2485a02cbf42ab370d6e38b
1599 F20101207_AAAHZN nozaki_y_Page_105.txt
8cb6f75f28f952471cd97f6dc3f491a3
323cbb6ec26c284b0a29e695fb52705baee41e03
F20101207_AAAHYZ nozaki_y_Page_091.txt
29f57625ee90518f7bd30e043d135e69
76844d47ba22c66077219a5a3aad306c5954b45b
46076 F20101207_AAAHCG nozaki_y_Page_066.jpg
6868f4247310b89f7e81c6478a8f44a5
05f0d45488ca857dbfdc0b866b4cecd5abfaf3b1
99690 F20101207_AAAHBR nozaki_y_Page_051.jpg
df8d1c359e1586dbd05d4360b9c76adc
cb9ea7e5df706f18a903b26a5d466b8143c2d8a7
9200 F20101207_AAAIEU nozaki_y_Page_143.QC.jpg
1ff0f47522347166d1885670b1b6cdd4
c1e6043c866a1a02679100eeeafdf06503535d7e
1776 F20101207_AAAHZO nozaki_y_Page_106.txt
a82689dbdf34def235581016796b9fe6
8bee4f7a664db794dafdba5e72623c754380bbbf
86375 F20101207_AAAHBS nozaki_y_Page_052.jpg
ab3c715683da38d814851e15ba1f366f
0423feaaa40440303e5b81ee4aeefe2879e167f6
7491 F20101207_AAAIFJ nozaki_y_Page_076thm.jpg
bf4dbab2cd3c96792c0be5c7a77ee924
9fdab73496466fcd2ca84a743bc5e12792edcd12
24703 F20101207_AAAIEV nozaki_y_Page_085.QC.jpg
d4a35c2d46f8f13705a8befddac1fde7
f6e8f5039796c0914d7eafb4c8e0e8cfc44762ce
1692 F20101207_AAAHZP nozaki_y_Page_107.txt
647b0861a5cc883428d28bf23dc1b572
ece151f8e39ffbafee4fe9e422719f9d1a645b89
59333 F20101207_AAAHCH nozaki_y_Page_067.jpg
43ae80cdfb0dd2e9b0089c3159a8cccb
9737c051f0593f0252408f45062b4397efeeafbb
100588 F20101207_AAAHBT nozaki_y_Page_053.jpg
5540500930c82ccb4eaea81d14f8d4c9
69a5450f6b4e3dbb3011520a4437cf2677f4e53b
31678 F20101207_AAAIFK nozaki_y_Page_042.QC.jpg
298c29c0d6ea28ac5e308b31f9b67c6b
2c4bbec9ed2a222a839f5cc930bc80ddb555b6d8
6616 F20101207_AAAIEW nozaki_y_Page_068thm.jpg
8d565ef01db7d0009db7f4ab8c70e349
02cc7606289df87054f3f42a462101cb37ed75ed
1451 F20101207_AAAHZQ nozaki_y_Page_108.txt
0032fdee1cc60f7e203f57699ba5823a
906995e700a1a4a505a74276f6c8720494d1a946
72102 F20101207_AAAHCI nozaki_y_Page_068.jpg
e7e164d48d42f0822394e5f3ebc8f77d
3fb1fdec7ffb8fd185958bd94810f2398aeb0300
106659 F20101207_AAAHBU nozaki_y_Page_054.jpg
70d36776b9f1baa8cd20d0e7441cd2be
98db0441ccbbfcad98ca215498ebba7a2ce91bf7
6894 F20101207_AAAIGA nozaki_y_Page_113thm.jpg
f34a44e3d545ab6d3bea14bdf42194ab
7d83dd49bbf5964e17f941d1f1e5188f0df80ca9
2993 F20101207_AAAIFL nozaki_y_Page_103thm.jpg
4c6aa85191937b35cde01b598121bdb1
e9f53856c8d2d7fde74fc1ac7efd0658ee96cd2d
17073 F20101207_AAAIEX nozaki_y_Page_091.QC.jpg
3363c41914c07825c2d3269142c784e9
77161af40337ce1890369f25bdf0d74e356b41e4
1765 F20101207_AAAHZR nozaki_y_Page_109.txt
c39480a5109065e5f9386602747994cb
da45633010d5895bcb73942f4c5dfb2aae3c5365
70225 F20101207_AAAHCJ nozaki_y_Page_069.jpg
d0ab44e92fbab68bba36792499acd017
49d7b46b86514b839faf881fbf616ff8eabbf3dd
103335 F20101207_AAAHBV nozaki_y_Page_055.jpg
260cca2af7da62f53a6f27c7acd86292
140c106111616806614a62a801bd0575034f7bca
6518 F20101207_AAAIGB nozaki_y_Page_110thm.jpg
78478332d7c00541875763ee823abfc3
0ebf8b4bf4967e5326e69eea4e98f976ed4a5393
9328 F20101207_AAAIFM nozaki_y_Page_054thm.jpg
ff70d140e3af27df3b5f8fcd32721b62
e99d4bbd000b2eb8323554b76758fb7370b6d39c
5257 F20101207_AAAIEY nozaki_y_Page_063thm.jpg
5000ad5ccfc27f31a04debd647cf5f3c
6a80258cb5a5cf90d88ca163a6b0c1c4255d86a4
2152 F20101207_AAAHZS nozaki_y_Page_110.txt
63d20df85a8272983de60c1ec9c57766
dd2acb0198528779408ba2929d6f5a6d7e366049
54158 F20101207_AAAHCK nozaki_y_Page_070.jpg
ad7826b371d397c6f308cbc79178a446
bd53d3f18a1c702dac3b0002e526fd45007ba033
92605 F20101207_AAAHBW nozaki_y_Page_056.jpg
d0eafb1dfd385bc6d28d2cad08de4ff2
d54040745cb55505223271a059c3af58d616e63c
23546 F20101207_AAAIGC nozaki_y_Page_019.QC.jpg
3606bfc462c89cf43bb5a9f9c7bdfa22
69547eac45b12e4f8adef397fff1dae225eaf8d6
23918 F20101207_AAAIFN nozaki_y_Page_119.QC.jpg
86e49a0d1f7fbc51e40f5bb49350a322
c10a4da12c295c600d1e7dc37e21441c2c0ddb69
28525 F20101207_AAAIEZ nozaki_y_Page_123.QC.jpg
ab2c95ff6853d02580b1d30fa4690f84
17fd565a8dc18b644919d846c12f7a6efddcdb75
1848 F20101207_AAAHZT nozaki_y_Page_111.txt
e340e4a58c2dcb44b31d04d21aa9c577
5b426842e0ae1063650cd9982a03d2693fab84f6
77950 F20101207_AAAHDA nozaki_y_Page_086.jpg
4aacbead082cbd82a66a369cda71cac4
8a6b8fbcadfc6d4f28f4531dfbad0ab61cb907c4
54125 F20101207_AAAHCL nozaki_y_Page_071.jpg
657f601f1234947ae4d8a0d1dde764ac
e31068393caea7e8f2d5675cf34e77a6b06435ae
101345 F20101207_AAAHBX nozaki_y_Page_057.jpg
3838d62f3fe4137e42be5a9197557e62
10851fb9dd647f59ff82364b0b6084a335e02870
4282 F20101207_AAAIGD nozaki_y_Page_097.QC.jpg
cf8b9e328b62a09079d91ceafc51122d
bbca6124bcbcd774d8e586f7ff737afeefa60a01
8465 F20101207_AAAIFO nozaki_y_Page_001.QC.jpg
85de17f05418360462d90a071eeefb0a
3a566dbdb93791c9f089e04751b952848d5a895f
1627 F20101207_AAAHZU nozaki_y_Page_112.txt
1439021d24a2f6937672dcb814765070
591c84a8aee1599b9b9378836ca8a2a135c152b9
69899 F20101207_AAAHDB nozaki_y_Page_087.jpg
5e69448ba5dff9f8e457ca0fb76b991b
11c3fe1db14f503111a4ac6536e5c4067c287860
55806 F20101207_AAAHCM nozaki_y_Page_072.jpg
68085e859df0a53b033fb021feaefaac
07db36edd43c219216606afccefb566278e3ab0c
74779 F20101207_AAAHBY nozaki_y_Page_058.jpg
8535ffa0b8ac202cf1a8f0dc5caa6242
7b9b96d7ecdb2beae5bbf2043c48e60daf283029
8527 F20101207_AAAIGE nozaki_y_Page_047thm.jpg
4b9041d1df2b8216248e2b06ce288adc
9e94f780ab812d00ee9c29440988880233c31ad6
32636 F20101207_AAAIFP nozaki_y_Page_055.QC.jpg
45291a83da2f97d19c910677f004e850
357441288a99df4ce2a08975052d14e7bf009b21
2085 F20101207_AAAHZV nozaki_y_Page_113.txt
3a0a90564d1aedadaa99a09db30a657d
db7c40d2337457f0c70063b4fe7268408a5bd4ed
54382 F20101207_AAAHDC nozaki_y_Page_088.jpg
0e99b505a33ee339cee464c2e8c85ed7
fff63d98852deb5e40ba3834a5692934e9f8e028
51112 F20101207_AAAHCN nozaki_y_Page_073.jpg
970e67c7f2791bc6e212126211d0be28
440eeee4e1fab6bd813c2bd283f0c796b6fd4a63
75718 F20101207_AAAHBZ nozaki_y_Page_059.jpg
d1483fe8855fefde018c51d32a790181
2a5878a1f055d8370b302dfd24193fda5a6b7dc6
4480 F20101207_AAAIGF nozaki_y_Page_004.QC.jpg
97372d294abb06bdabe668e51b736bff
a303709b0b1ba8fd391d4ba06cc694842db48349
1663 F20101207_AAAIFQ nozaki_y_Page_021thm.jpg
23d17f6db627c5bbed781b96c47d18c9
8ec3390ce36a042b1756d5ceb50f6d5515dddd67
1437 F20101207_AAAHZW nozaki_y_Page_114.txt
e99031eb0afe37f6b552f227ae00b785
92caea342be6811b04f1cabf7f63e94b15744bd6
55293 F20101207_AAAHDD nozaki_y_Page_089.jpg
989bafe9ce766cfdc30f9530c7b1bfb8
9b7b3f32c50165c074a68e23b76d1de04932ac0f
59077 F20101207_AAAHCO nozaki_y_Page_074.jpg
0446a5ef4f401bd0c095ca54ca236cd1
59807027a598c33ebedcdb9594158e3048090b06
9907 F20101207_AAAIGG nozaki_y_Page_102.QC.jpg
19f2ff373d5df3026e71fd46e5c3316f
9e10b6d839d71732e2543d909911245ff3121e77
5636 F20101207_AAAIFR nozaki_y_Page_083thm.jpg
cced4cff9b3c9fa0bb38b7e534e17baa
a12b0b22e8f7e5b2bf19338afed473cf8ea18236
1801 F20101207_AAAHZX nozaki_y_Page_115.txt
916745c14df0ac5b99a784cc78f3a154
9eca2e88fb9a059bcf1128f72cc151e29d79aadb
57786 F20101207_AAAHDE nozaki_y_Page_090.jpg
876710f5bfc331ba3b9b3961df9981e8
5a18524e4cea1306ba6b75ccff546b8db57034de
55349 F20101207_AAAHCP nozaki_y_Page_075.jpg
f97ead848ce6d8ad1554ae91d96aa372
9746fdd1c7d3114f0ca2f8bfb9c8e687977d0a26
17537 F20101207_AAAIGH nozaki_y_Page_060.QC.jpg
34b236143b9961d3810aa27419bef99c
ec6ed59dfe8b438342467be331bc7b0a49b500dd
6987 F20101207_AAAIFS nozaki_y_Page_106thm.jpg
3f1c2fa61e5d2ec1bd0f89f77afff7fd
cd099ff43784f722795498ba4feee7de5144a8dd
1869 F20101207_AAAHZY nozaki_y_Page_116.txt
8cf30c668afd4d93679d1658d59c3358
34e8188058d69fa14f57c124f693a5c45f49860f
51619 F20101207_AAAHDF nozaki_y_Page_091.jpg
3701e7ee8f9491a5b05ebe8fbefd3ad3
e6ff99e55625c7d5d32390fb66127498235dfc36
83443 F20101207_AAAHCQ nozaki_y_Page_076.jpg
98c6e146b81630997684e2da615d8ced
b9ff50bbf5689e0e96351217524dcc47db4adfe3
14832 F20101207_AAAIGI nozaki_y_Page_006.QC.jpg
494225cf1a62e1146eb35dab6da7b40e
11c35c15980cf740a67c165aa167e57447ffd3bc
5674 F20101207_AAAIFT nozaki_y_Page_114thm.jpg
3019b6e19397bf68cf40b937f519bc7f
146e976eb7c078d9d2e070725533be81e1fef0fd
57861 F20101207_AAAHDG nozaki_y_Page_092.jpg
7d3cdc3425523bad0f7bc31ce4316e8c
b50410d9dd9d7ead902ee9b9b9a7fd2c9361c42e
81389 F20101207_AAAHCR nozaki_y_Page_077.jpg
beba5c1b55c4a8de1e25c75e51e6815f
06cb08a2e340f0d013be4b716b23c2b8ed430644
835 F20101207_AAAHZZ nozaki_y_Page_117.txt
345c934303b18117c7f553e21783e41b
95884a780edecc2b75eed70e7f24111d82c82350
5534 F20101207_AAAIGJ nozaki_y_Page_115thm.jpg
0294d27b0c374c43e1b0b58b5a6b4b95
91decbad9cf7b16037287a97fb7a6de092d63f36
35386 F20101207_AAAIFU nozaki_y_Page_050.QC.jpg
da69850c5447294c91e9c16317439b7f
7f50aec7bef063642ff94e7a4309811751670676
52474 F20101207_AAAHDH nozaki_y_Page_093.jpg
65b5d6764bbe65db1b66e90639594340
f1f4fc9a5301d43064adfa398ecab946b911d8c7
71716 F20101207_AAAHCS nozaki_y_Page_078.jpg
0e8d40195b654201a207b2906e2fe5db
81c98cae77a40c510f4a029428a3b95c1c58c2b3
32726 F20101207_AAAIFV nozaki_y_Page_008.QC.jpg
03215012393a451b84ae8fff92e1852d
69b1583a1ab65efc4fe8ea4e263bb2bcbfac0374
55762 F20101207_AAAHCT nozaki_y_Page_079.jpg
cc7ae5bee0ef122cd9a79c7e4b3be7a9
0e3d650c3cb4adab621567cffa06063f89a38dc2
16956 F20101207_AAAIGK nozaki_y_Page_082.QC.jpg
ac9ceb9b7e2fee0edd18a95ffb043733
4e88ce1862cb147acfe6b27943495d662cb6f8e2
32685 F20101207_AAAIFW nozaki_y_Page_026.QC.jpg
a7b31cac20ff2b44975c633b73652120
7b1c3e3bd07c4ada1d9f20f3b3d82104816a7fff
17658 F20101207_AAAHDI nozaki_y_Page_094.jpg
283402ce50e413a1cad3a33538c632b4
17acdba8eabe57a1bde1ecc31cb99dec9b9b4275
57093 F20101207_AAAHCU nozaki_y_Page_080.jpg
c236f82c1bfe5bce0c12295a50952693
03b8053b10698a5034b7de077d21feb8e5e9d016
22603 F20101207_AAAIHA nozaki_y_Page_015.QC.jpg
56769a673a859cdefd00c4c15029e0e2
a429cca3d85c29d6b2ec4d6763a7c571cbce05d8
7904 F20101207_AAAIGL nozaki_y_Page_017thm.jpg
3c8722b172bd3b8f4707403d5d4c8e51
58465193fa3ee18d9b25fadb22cc2e39a2393f6a
18619 F20101207_AAAIFX nozaki_y_Page_127.QC.jpg
5728926381e1f264cdec272ddf39218c
dd14d3be7dec9b946fb14f72ac118d4d4209b798
108787 F20101207_AAAHDJ nozaki_y_Page_095.jpg
cd9ccb6f890f9dd2af1acf5defeca390
0c8f16ef6ae8f7edfe90c8d709d31e329500c12d
56767 F20101207_AAAHCV nozaki_y_Page_081.jpg
03acc1f9cc8c529ff833455e26ef35cc
44de6a56ffda20264bfbe1f2e4e50482537b4e6b
30964 F20101207_AAAIHB nozaki_y_Page_016.QC.jpg
9f712acd4db54180c6754dcbc52cdf61
9192b46ac5e5877101e981e3d9939f0fe981a261
30596 F20101207_AAAIGM nozaki_y_Page_124.QC.jpg
158963cffa28d745170082d567a12607
9bc644c4e3ec4e4e786eca9773b367950ec029dd
26443 F20101207_AAAIFY nozaki_y_Page_131.QC.jpg
a13e697771c00d26b172ef17d496b66f
0dd48d3245da552a647f7d8a51c511064ec38909
101938 F20101207_AAAHDK nozaki_y_Page_096.jpg
78d7bc04d2f1cf6684be166374f7ac59
adf6b66886ffcf342ef6feb0d14571c0c924ef50
51644 F20101207_AAAHCW nozaki_y_Page_082.jpg
c780643bec5318ff957348a0a4c31099
456f5022e3d58ce45379a1fc2bed986b93a9fb96
31050 F20101207_AAAIHC nozaki_y_Page_017.QC.jpg
04dec9e6098828f35a533ed5a1518b0c
0e18f76af28f7c9fcd92c25804e48c87d4137dd6
213935 F20101207_AAAIGN UFE0020862_00001.xml FULL
95337605eb0c576bae18bd23a4fa1db3
a9f198a72050384f09bc7582fc5ca338cfc03bb7
24698 F20101207_AAAIFZ nozaki_y_Page_028.QC.jpg
1a1543a46817913188296114ff21d075
d85baab41ed6d2e30eba5dd9d319ec66057801da
59139 F20101207_AAAHCX nozaki_y_Page_083.jpg
5b6ef3b6d628728d7f030ceb05972c91
74d6183f6df2010af3cbdfa3b1d487b4a9f73981
85266 F20101207_AAAHEA nozaki_y_Page_112.jpg
23fb74088b523bbff09954190e2bc5fb
f38ec762aa1cd8770749f577f8c2333d8c5da069
11259 F20101207_AAAHDL nozaki_y_Page_097.jpg
eefece1ad632f9c9ccf94db996fce75c
2458fe9bb4f7edb86f2705a03c55d2edf97a9689
30586 F20101207_AAAIHD nozaki_y_Page_018.QC.jpg
7b3d443cb67283ca2eb70d1fdedbb868
ce6ed4f3ffc4fdf16395946929a93a58adfdd980
1400 F20101207_AAAIGO nozaki_y_Page_003thm.jpg
8c7c577825a9625ad87b4e22d8a4eee0
d98be5ebce00f24d6eb079eeae1989207e984e04
56890 F20101207_AAAHCY nozaki_y_Page_084.jpg
6e025768561828e43adcf2b4afac9c1f
943251d04a1ad2eb973c231ad39667818d943976
104697 F20101207_AAAHEB nozaki_y_Page_113.jpg
e8539ca7929bb5fe9192341cfdb03322
551c109d8e45b0e76e54a1e37d014a96cd0ed853
96944 F20101207_AAAHDM nozaki_y_Page_098.jpg
727299ddd85326f9d555e7eb234dd68e
529af0c6fced2c84fb67765eed74f62d8b251f68
7834 F20101207_AAAIHE nozaki_y_Page_020thm.jpg
f246f6c7dd93833bd8daed884f64d048
406a3ee042de8943245a45ab2087cd4c4c24239f
26212 F20101207_AAAIGP nozaki_y_Page_005.QC.jpg
d62132a18cdd64cf11cc3492f40e7c41
fd580b4ed631b80b79d5ea3719f99d6e180c206c
75084 F20101207_AAAHCZ nozaki_y_Page_085.jpg
93bc57ca21037c8095bc4a8e6e9f5bd7
23c07ca002feea1ee4465801833147af48871334
71483 F20101207_AAAHEC nozaki_y_Page_114.jpg
c944f671a2e0b5f7621686b153a23644
f3d736d0e4960e493c3aba4d64dc454ba7f08b63
108423 F20101207_AAAHDN nozaki_y_Page_099.jpg
4284b48e796c6d675c1b3c08fb359098
d94ed90a99baefcb9de67e77f65b5d322b397a4a
33522 F20101207_AAAIHF nozaki_y_Page_020.QC.jpg
45c0d6dd07c2ce40e94b18a03f2e8f62
d0e135e3872f24fe2777b84b1900d09b27751b7d
2862 F20101207_AAAIGQ nozaki_y_Page_007thm.jpg
5579c691b4cb9efecc3466305b291395
29379b51ed636a8a92f19c0152fb71c2ab5d0928
88541 F20101207_AAAHED nozaki_y_Page_115.jpg
ef71a089a791b4c7eb53a2f358813bbc
d72db50c1a799383705c3ad601e82de1aebda0f8
76401 F20101207_AAAHDO nozaki_y_Page_100.jpg
0c5b337da22abcca8b7bb0ad73f07338
243ff8753b074573776887fa1e73d4dd51a16e68
5533 F20101207_AAAIHG nozaki_y_Page_021.QC.jpg
693c14a91a5fd095b88197d42340233c
13fe802a206d2ca67415f666875b35948bcfbd70
9417 F20101207_AAAIGR nozaki_y_Page_010thm.jpg
a664d8528261d861c8df84558674a521
a2b206fe9a39b8e6ac3aca041ea99d9afa604fe8
100784 F20101207_AAAHEE nozaki_y_Page_116.jpg
8f5287cb0e8c7e3cf35ffbe6c6ca942b
ab0b587ab146e8efcb530e3e16e184d89f914f60
36081 F20101207_AAAHDP nozaki_y_Page_101.jpg
7ab57b2ac45af583d9e4f87914778874
d7183149db81f62a06ea99c3ec2c6b3055519266
31659 F20101207_AAAIHH nozaki_y_Page_022.QC.jpg
9482a79ff074472f93ce38552bd99014
9e5e9ca8ddbab0aac4265c14e4a068a547d4a9f0
35091 F20101207_AAAIGS nozaki_y_Page_010.QC.jpg
f64600f5d84c19b32d2351c24692d1ba
4379e367c0ee6012cac7327200c6550e7e134e31
42024 F20101207_AAAHEF nozaki_y_Page_117.jpg
f17d8d91cdaa99a24566f9933f2e5b69
dcf08c8863a4372dd9905dc96501cee067a97e45
39121 F20101207_AAAHDQ nozaki_y_Page_102.jpg
cf56329d1cbf99570752b43165d807f0
ef4c7c4e06b8c84fba88fb553aa393c463808fd4
6812 F20101207_AAAIHI nozaki_y_Page_024thm.jpg
5f2c861d9d5388b8764afcbd26c5fd5c
cc393fabd342686518493f2aef63bc657925c261
9707 F20101207_AAAIGT nozaki_y_Page_011thm.jpg
dc17d99539893ab3fb03d21d5b665d0d
f84041de95a698214607bae6136fa5ba27104581
73301 F20101207_AAAHEG nozaki_y_Page_118.jpg
3ae729024864d293aa3e9f95e1c74fb0
fa7c898bed80905b30eafcbb3c9f466c2ae8de65
50320 F20101207_AAAHDR nozaki_y_Page_103.jpg
9e99b932d49ff9c2716b09f38a9886eb
1dd3cfe284cc005b0f91c716a9d2436f7cda3c51
27036 F20101207_AAAIHJ nozaki_y_Page_024.QC.jpg
deb42f956e6f3e1525c776f7a6231652
93c922dce3f360e4d967afd35914309301acacb2
40913 F20101207_AAAIGU nozaki_y_Page_011.QC.jpg
8c3bdb1859a7a811069423cadc6d0199
0f9528918a6c01035753d8bae37402b62d6d5d33
85182 F20101207_AAAHEH nozaki_y_Page_119.jpg
9c2d77e93d1d7ff9a2b976306ab9578b
c39ec5d053c2ca225ac21bdf5ca56d1824504e20
68662 F20101207_AAAHDS nozaki_y_Page_104.jpg
43e8569d2b47ac6cea9c8896d7948435
352bc4eefeb6421be657049314a3ab0cebfef43a
7922 F20101207_AAAIHK nozaki_y_Page_025thm.jpg
ef5bc92b3611bb7549d64e5dcb9bff89
e043f34554d6f709184de38832f3351cae97f13c
9797 F20101207_AAAIGV nozaki_y_Page_012thm.jpg
1712fec542418e70963c879db5875b60
0f1480339e8c4e36e85c16107b6a6dd6029cd141
89185 F20101207_AAAHEI nozaki_y_Page_120.jpg
30bf550331a84ec1737bd92f9f777e3d
3e431cf8f065e1ba14c4d90c96d4ae30bd289418
83592 F20101207_AAAHDT nozaki_y_Page_105.jpg
6cf81c7a322e0fa2f78934ca83a95aeb
9555b449f756a8feee5312608f5ae72802e56d79
39605 F20101207_AAAIGW nozaki_y_Page_012.QC.jpg
5e8ba5022f8675067676ab8891cb2018
55b23109e6a395149e164e35d5f21af4b6ef2176
95935 F20101207_AAAHDU nozaki_y_Page_106.jpg
577841bd8bf64cee5a91a5c46108911d
56ad2229caa08a9ee73020df35364aeb73803957
2848 F20101207_AAAIIA nozaki_y_Page_046thm.jpg
5c37ca42101d21cfc0156721137f7070
38a203b653f917e9bc4cdba3d552076b700cf40f
6784 F20101207_AAAIHL nozaki_y_Page_027thm.jpg
937f24a2274f1c9135c363967f13e912
288c933983ae1738b3bceae096f35f739a69bf72
8635 F20101207_AAAIGX nozaki_y_Page_013thm.jpg
f6e2e10e1552cd4721f988e92d8c1ffd
218bcf0b3b763197344985eb841b520ac3e30825
89940 F20101207_AAAHEJ nozaki_y_Page_121.jpg
a19dfb15a11bc0c75aaf69554bf66bcc
4068728e3aabb9a3f71f1a5c9285574142833649
92225 F20101207_AAAHDV nozaki_y_Page_107.jpg
ba9180d4118efa864742a44283f8db49
33ed37e5aa0fcd4fc8d28c5e91f340bda13fe766
9444 F20101207_AAAIIB nozaki_y_Page_046.QC.jpg
7517f9b1030e2813a4e38103710726ba
8363619da4252b461e1d73c7fa2ec7d3d14bd397
29013 F20101207_AAAIHM nozaki_y_Page_029.QC.jpg
98fa558cfc8cad87812d37814a7ff704
4add698fee7025578bf60cdde827f15286845d81
9131 F20101207_AAAIGY nozaki_y_Page_014thm.jpg
888f99d41504a33d430afc0f2437c6ff
7b68c9baeabc9147665888bf5b703eba8a7c167e
95247 F20101207_AAAHEK nozaki_y_Page_122.jpg
80ef55d64261299d233f1ed4a180eba8
51d95afcb23a36aec24db2e0b13fb035a4833fa8
76763 F20101207_AAAHDW nozaki_y_Page_108.jpg
72f056173849720b0db26a9caaaadf05
0a1764ce4a09ff6f49350c103f160a6b9b4101fb
6163 F20101207_AAAIIC nozaki_y_Page_048thm.jpg
00d8b85515479e3807846eef44d53bdf
a18b9025079cba0a13ee3c074465f014c61ceef9
26010 F20101207_AAAIHN nozaki_y_Page_030.QC.jpg
143bc920b5c77884996ebc974a600adf
abd7015317e5dbf6f4507ad5420169dd31044161
40074 F20101207_AAAIGZ nozaki_y_Page_014.QC.jpg
92a3b027346ad859eb1467eba33f3dac
054b188aabd757471a09edef3aab81c92746ae16
111443 F20101207_AAAHFA nozaki_y_Page_138.jpg
fecba77b9d06c718eb8831330c6a1ab9
ecd427f55ce5bb45245c3e8963aa015cc63d2483
102085 F20101207_AAAHEL nozaki_y_Page_123.jpg
eb094906b8f0014c138cf8d5e7bca78b
7086f09340ed64d97d18a76f84c72508dc6f3bde
3054 F20101207_AAAGZF nozaki_y_Page_139.txt
264b2df7d38177b3d18d028fbe42fdc4
a7e171671444337eec072649ecdb517ab77e12b5
88631 F20101207_AAAHDX nozaki_y_Page_109.jpg
8e5a781d0fc780bc7413406e2a4fc165
334208b1921bceec7e1f295c6d8358c1c4e03470
7576 F20101207_AAAIID nozaki_y_Page_049thm.jpg
37db3ef0e495965a7b43eb8d482eb143
8e579131ed4a79fddbfa31bccf7448ca6bfde3e8
7885 F20101207_AAAIHO nozaki_y_Page_033thm.jpg
05426c5d78cbddd6884d65cebddb76d9
0179aa6b794a17f4bef1192e0fdc50a70d7cdc04
128624 F20101207_AAAHFB nozaki_y_Page_139.jpg
5ae14264d231df0625139bb506077e6d
b04333ab29d3e7ae760bb7dcf7597bac0dcdc2f5
107358 F20101207_AAAHEM nozaki_y_Page_124.jpg
0ba8752d7458a472ef16607ac22f0cad
e194e3491d2ba10b027c569b8de018f7bc390954
99444 F20101207_AAAGZG nozaki_y_Page_045.jpg
1bb480f8fdfa4f55df8fe8bd244faabe
4ee40b2a9a27349295fc35588ca8e50ae5e265db
111215 F20101207_AAAHDY nozaki_y_Page_110.jpg
23a6caf638d324d24e62eeb26477f6b6
a69a10ab4c749bc5e27d9cf21d32feb048109928
26970 F20101207_AAAIIE nozaki_y_Page_049.QC.jpg
3ec5536af29efb6326c3822f3fdb8330
460522d7e5b285794552bc9779b911263d0c1c3d
34958 F20101207_AAAIHP nozaki_y_Page_034.QC.jpg
2b7e99b318c66d3104c138256c043162
0408f74b46034fcbf1aaeed71a87a425ef5583db
F20101207_AAAHFC nozaki_y_Page_140.jpg
a2c0f8cdece3250d0c40545572fda691
881d6be2d5b2551eacd93ee954eebea38a490e8b
103131 F20101207_AAAHEN nozaki_y_Page_125.jpg
33d8b5a857b1bfa287f549e8ca0e413b
33cfb77cf4111ee3813bd98f77c28d8adf7cc227
2138 F20101207_AAAGZH nozaki_y_Page_049.txt
3c58670f2c80574ddba140bd36afd3d7
b04fb77e441df48789dc0fa2ec7092b2795b289a
97629 F20101207_AAAHDZ nozaki_y_Page_111.jpg
7ba0dff5abe6431cc2c86fc1cf31c553
bc49aeee87adb124d4bbb3a2cab2aec9a33c5354
9094 F20101207_AAAIIF nozaki_y_Page_051thm.jpg
de5eedec52a8c4520a7e81cb305fbde4
6e2b4e8903668a41bd433670161934c42dba92bb
9181 F20101207_AAAIHQ nozaki_y_Page_037.QC.jpg
0c2e7b7d0ffc5aa89890b1cbc95667f4
da1de20e7ccf326c104143b754e940bcda6d7bf8
64556 F20101207_AAAHFD nozaki_y_Page_141.jpg
edbaa38b827fd3776fbc01575828dc1a
798ba11bdbbe4d3c449692278585fe1b337ffa87
102228 F20101207_AAAHEO nozaki_y_Page_126.jpg
1af2786de08a585706c5f11217c01988
86555322ef0b055a4920fb858e524253b310b7f9
8573 F20101207_AAAGZI nozaki_y_Page_008thm.jpg
b7752113d05539ca29262af19a257f3d
a9a7100cc993da3c76b8c33d9371dab2da0e9c9e
31520 F20101207_AAAIIG nozaki_y_Page_051.QC.jpg
efe03e56441020d2fed1e69a9a0968a7
779ea7c02e2c13b49db7c780a22a2dee73559a1e
13269 F20101207_AAAIHR nozaki_y_Page_038.QC.jpg
9d0043149373ee2d88ad1f986b0d9cb7
3b82c112a48f2dbe2a9ed79c48dae9acca6952a9
103531 F20101207_AAAHFE nozaki_y_Page_142.jpg
be315b0d02882065660d1e98545cdf32
c7b5b34a33b42c813f4773ff27112a3fd7abda44
63164 F20101207_AAAHEP nozaki_y_Page_127.jpg
0bef1f41b748d07176300f095c699497
097b6b56753b230ed40ac18753ce599f31430dbc
19712 F20101207_AAAGZJ nozaki_y_Page_043.QC.jpg
948a8a6c6c4f7e3f58169b7d47ef40ce
48f17f0712c5b91ac06c3da33355001e8ee2c2c2
31039 F20101207_AAAIIH nozaki_y_Page_052.QC.jpg
40c7f494e8896aa8c879530f1bda8327
95d99e70dbcd83ff8b7c8da2d89a3faf3188aab0
16207 F20101207_AAAIHS nozaki_y_Page_039.QC.jpg
65a875d83917eded47c878d056607a52
224c7a20bb6f6f8eb7d52b58523da5aad87d74a3
28523 F20101207_AAAHFF nozaki_y_Page_143.jpg
d3cc958a00fee2d40513716274733eba
cdc7755fd1cd4b59a7d4e3bd4e99082b44be9b47
51742 F20101207_AAAHEQ nozaki_y_Page_128.jpg
e1c8c17896c2599621ae1b01cd219953
2323f6049340ee2e1ab32115eaa172081075699a
22938 F20101207_AAAGZK nozaki_y_Page_128.pro
a7c748b1d0b4182d3ad04319f34e4e68
5860aead6be6561a6c9f8fcdf71ca4006a2cc30c
33740 F20101207_AAAIII nozaki_y_Page_053.QC.jpg
a2ad9222b7fee8f310a522ca7ef6b57a
264b028fc0febad1efa89a98d60abc082a84a389
16411 F20101207_AAAIHT nozaki_y_Page_040.QC.jpg
e7dc0aac4f1862a938a8c983bbd8f33d
06c96de70b6c280daefc544dd88f25423d1d845d
24948 F20101207_AAAHFG nozaki_y_Page_001.jp2
b08fcf017f5712d91699ec68c31d4750
d82684b7c87f61dadf24316c959a794fbd345e9b
109343 F20101207_AAAHER nozaki_y_Page_129.jpg
283aea2bb7e34f1ae32710b9c8087549
2d3b9d1f92a14d45b423a968fb5b66a19eb0f235
129316 F20101207_AAAGZL nozaki_y_Page_138.jp2
124d0b34260dc042b059f42b6e7829ea
f5539f85b7ef4eb85a5a1cd7e467d7559627fa06
34783 F20101207_AAAIIJ nozaki_y_Page_054.QC.jpg
7aaf32cc0d3442bc6e82bdbb361fa150
95914794770bfe49a77ec17902c11ac53193590d
5258 F20101207_AAAIHU nozaki_y_Page_041thm.jpg
f57b88093834587671814e1618efee30
fd36cd33edc17dbbf2d30350fc7e3badf864e1f0
5295 F20101207_AAAHFH nozaki_y_Page_002.jp2
318acbe21522aab669d68c61dac77b58
f1f0006ee3855b1fd1dd5cdafcd8de149de6a427
120720 F20101207_AAAHES nozaki_y_Page_130.jpg
f2d05d8dbb428709832dbaf8721fc9b5
a2e82e95a76817cfff3ad04c0cf66ca08ad219c5
5194 F20101207_AAAGZM nozaki_y_Page_040thm.jpg
1b7b95989e084c99af9ee21e62745f32
3d4f54416ee3eaca22f1f07ff2706f7cca3d9fb7
8839 F20101207_AAAIIK nozaki_y_Page_055thm.jpg
67d60c42e0a76552c878675592cb6b51
31632abbf3b9f75ba31d3ef72b27a2cbf002f4dd
17207 F20101207_AAAIHV nozaki_y_Page_041.QC.jpg
e399594d6771ef6037abd540f9008e28
2a8345b7fcb996b59c7ceb596c76cf5f6d685c75
15410 F20101207_AAAHFI nozaki_y_Page_003.jp2
73fc4b4a3fa107f97c9ade669d83dfd2
fe9147ce35b2afd4bb6ee30342d3aabc3182a9bf
91267 F20101207_AAAHET nozaki_y_Page_131.jpg
c428f2b18ceb10d4954164af99c1f219
d9532a7e7fbf36a000e4adad82fa4076611baa82
F20101207_AAAGZN nozaki_y_Page_038.tif
3cdc5e127c3e326916d58da85adf3089
a67f8c9607f029ef366a27d4a3e207865b935673
7770 F20101207_AAAIIL nozaki_y_Page_056thm.jpg
5da57c67164707d00178c2fdae92873f
d368cfda917f506793fef00eba43c35700f22785
7449 F20101207_AAAIHW nozaki_y_Page_044thm.jpg
ec0e61c29fb108bb06ac8be80c1dff54
216bf531c93e511257416d043361160dd2b0264a
14795 F20101207_AAAHFJ nozaki_y_Page_004.jp2
589db2116b6000f75fc6c55b69bc1b45
7f983204e13983ba159b5b38b05395ede54d3a7b
115545 F20101207_AAAHEU nozaki_y_Page_132.jpg
28534ba123a4d15cd5368eed358bcbef
d9af157845e8ca7c704e8d9cbd4466276a6fa70b
3823 F20101207_AAAGZO nozaki_y_Page_003.QC.jpg
cecb70b3c5da378076550987a9f36f82
81e4921e920f0872451a3ee156a743ce1a812f5b
5051 F20101207_AAAIJA nozaki_y_Page_070thm.jpg
dbff2b0f49766aea94a61b9b839ca464
ba09935e8eaa031479c53af3ef61b28ca854b974
27122 F20101207_AAAIHX nozaki_y_Page_044.QC.jpg
69e7d19147e36e98ebaaf992d750559e
430fc7c7187444aa2ac6a18fd955dad2442f161f
26138 F20101207_AAAHEV nozaki_y_Page_133.jpg
39bacf5df88fb524b9c5163ec1e660db
77c104d485264109ed4410a2731fd4b36d7edf52
F20101207_AAAGZP nozaki_y_Page_075.tif
26388c2854cc80f0836efa1f8e1f15fb
3663497aba3d0c0f663436434ef06f818091274c
17140 F20101207_AAAIJB nozaki_y_Page_070.QC.jpg
da475f2b034e74f06c265188b88abf0e
111faafc8234a6ab048b91868375c8e8349dec6a
8273 F20101207_AAAIIM nozaki_y_Page_057thm.jpg
dbb95f625479e373fb157423d7db209e
7f765d59465c559bc842b134c4bd68843fe1688d
8341 F20101207_AAAIHY nozaki_y_Page_045thm.jpg
3d5f1ae06bc032840db2a145ef5058bb
043e06f5f3876df9ed82c2a10d4fc88066b886db
1051947 F20101207_AAAHFK nozaki_y_Page_005.jp2
54795ba2a8108e446e390aa27a720305
f1afc96bf893eaa8cbb75864445caf9d04cac75e
86081 F20101207_AAAHEW nozaki_y_Page_134.jpg
183d5fedbe53ced2e446053471ea1bb2
df26e1eb5a823e9279c8d45087dacae6c11941db
86091 F20101207_AAAGZQ nozaki_y_Page_031.jpg
6a998305f964e05aab7531b76de9e029
340a95b1da42d2657eec75fce8d3f86e206faa7c
17791 F20101207_AAAIJC nozaki_y_Page_072.QC.jpg
f1d7f515082a1d6a5910f3e1baa9c733
254e07d14782cbb525a1a8c3eab61f4199aa9ed2
7032 F20101207_AAAIIN nozaki_y_Page_058thm.jpg
60e27b08e9cd6ef731d3cba2f32c1973
c35b90c99549fb3ad17ecf7f7c790d866353dff6
29747 F20101207_AAAIHZ nozaki_y_Page_045.QC.jpg
9a19ab9d825a3bf2e205f7d503b02f1d
82f528266b423fbd064a53b1d979e2edda7c3321
886019 F20101207_AAAHFL nozaki_y_Page_006.jp2
cdf9570bc8ed162a10112e1a43a2a357
b41d8a5d19d6d4fdf9d16be17e6c4f29fbd90790
85933 F20101207_AAAHEX nozaki_y_Page_135.jpg
d642df861920d0ecbe9c33cc1f45be8a
015beb7fcc4f6c3f33b1f0f385186c8ebb2e84fd
113668 F20101207_AAAGZR nozaki_y_Page_034.jp2
984146f36f6bccfa7b109d78de5b7b04
8b5f450a04689cf5347862125b936f8e760ae9f2
152859 F20101207_AAAHGA nozaki_y_Page_021.jp2
dde3121243a43a2ebe158fc3ef3cab69
7e55703f959d9ca1188bcbad00e50d239bcf319f
5047 F20101207_AAAIJD nozaki_y_Page_073thm.jpg
27a2782fcb97a9a615e9199b4ea7e1ab
68fd472eb4dbf125f36fc9ff9abecca5bb872952
24718 F20101207_AAAIIO nozaki_y_Page_058.QC.jpg
45b55cc55a0ec21eeff9d2014eaa82d8
d4673b4d5e190bc20f1f6cb92b5854d4dfe276c4
633106 F20101207_AAAHFM nozaki_y_Page_007.jp2
41d586427dad0152d8cc22e890b1e00c
ca0ccc9f4ae4d78d8b922faef1e50d6baf565246
87035 F20101207_AAAHEY nozaki_y_Page_136.jpg
fe481dfedd65a0303b0318b068476a8f
e2da44e6399c10069489eba5dd52ef796b6db82a
165226 F20101207_AAAGZS UFE0020862_00001.mets
c6e4169be6878dcd1e9934e3ee85df1b
e1a88bfe79aee1bb59290e7a334da4bd2612e198
102605 F20101207_AAAHGB nozaki_y_Page_022.jp2
49ac50d2487c1803a49f747531ffc448
b976fde337fbe4948a2f96752d9dda1491ff6bb0
16667 F20101207_AAAIJE nozaki_y_Page_073.QC.jpg
3e906acd3ecc345bcc067692610f4073
fe17d3861186facf70e727a35ded4d65f9b995fe
6457 F20101207_AAAIIP nozaki_y_Page_059thm.jpg
06437c079176123c85d324c17c84a1a5
dcb3e09436017347e25e6b20e591807af7453135
1051915 F20101207_AAAHFN nozaki_y_Page_008.jp2
b9d28406b8eaeef707db2abb97aa480e
7fc848b3fe7644cf8173bfce90436fde718dc526
81194 F20101207_AAAHEZ nozaki_y_Page_137.jpg
fac6b2b0f3450365dba46acf1c4a9610
a08bfb7fd7f65f2beeccd1b7d5362c2bb04e2873
92984 F20101207_AAAHGC nozaki_y_Page_023.jp2
e278348ad259ad6157d0e8096302b80c
5a56c3ee72b5bf137f69f74d8c6a37fe50ddcd54
5524 F20101207_AAAIJF nozaki_y_Page_074thm.jpg
c51d935c86abee0e9e4a374c38a3557b
57a66e74ed870009530c39502ec86f6fd49a3359
24447 F20101207_AAAIIQ nozaki_y_Page_059.QC.jpg
434b8b4f553c91caa379e3c848bef408
0a289f095302ac7738f3d1e6df966334865d7d34
1051986 F20101207_AAAHFO nozaki_y_Page_009.jp2
eb58654cc91ff1f3e9169ac922e043c5
150c0c71e6d61493b5b245472c1b03f93a63b218
84043 F20101207_AAAHGD nozaki_y_Page_024.jp2
64102c0ff8ef3ec7ff18dee275a2a3d7
f18b87bd097d47e5bc2b9bddd22c3a9312edb655
6829 F20101207_AAAIJG nozaki_y_Page_075thm.jpg
a6c6097a23ed1b81a9015e1f35117b19
5e2c21fb058233c391f77a9aff4d9594dfafb4a2
5151 F20101207_AAAIIR nozaki_y_Page_061thm.jpg
ca11e6e843c95d78f58fdbe2e61cb342
155093c4bc6f961790559e99cd56373717f68883
1051985 F20101207_AAAHFP nozaki_y_Page_010.jp2
0d734722a6e871af479ac0a8b1463bf9
6c4bccf999beb22700eb64f821a82c5a5c5196a0
25806 F20101207_AAAGZV nozaki_y_Page_001.jpg
fdc013e1615c04f2e25aec8f2826e4c7
2bc9069ed192329c3c380b59da7c756b58152451
98057 F20101207_AAAHGE nozaki_y_Page_025.jp2
2c760c6bfc2daa4cece57953e337d9b6
8853680c6995d47a303271c69e4eb894b2d572f7
20576 F20101207_AAAIJH nozaki_y_Page_075.QC.jpg
4083915fe53ededa3325016597b01b46
25d9671c4e0265269732057bde887498ad9ad21d
18520 F20101207_AAAIIS nozaki_y_Page_062.QC.jpg
66d680da2fd4086610b5258c3a290319
31817227c3a57e69c80fa108b31d6f3eca3d7540
1051945 F20101207_AAAHFQ nozaki_y_Page_011.jp2
f0411c0792d78db718057d4c3f8c4d32
c1e0e2ecbb769f7113d0183f8350c1a667d593d1
3960 F20101207_AAAGZW nozaki_y_Page_002.jpg
bd0d52b94bf18bb00312e2c0c802061c
71b913ff600e8af0a84cdc04e0fc94c72103c729
105121 F20101207_AAAHGF nozaki_y_Page_026.jp2
41f0fc885b22b028ff0e63bd47196755
6438b3f8eb9db33dd71c1fe4040cd408edb3a032
25362 F20101207_AAAIJI nozaki_y_Page_076.QC.jpg
7b7c2de9f8ed52d89d0ff009990a0262
c1b643ae7d84da4d7bf6d5379e1f036601fbe82c
17410 F20101207_AAAIIT nozaki_y_Page_063.QC.jpg
8984c77cde319c8c817a8f27aeb7b483
0acc6043cd18ac4da3522c6f6ad3a962414bbedc
1051974 F20101207_AAAHFR nozaki_y_Page_012.jp2
aa58581a8cf6514842591e2e37b25a4c
78cb2bfc3c5f2e8359804fd174dcbda29dafaeec
15601 F20101207_AAAGZX nozaki_y_Page_003.jpg
0324411df3c36ab80d70ae987872db75
cea91afe0d9b0439f5d98d91d798c7c044bfa735
79479 F20101207_AAAHGG nozaki_y_Page_027.jp2
5df09078408dbcae7a111f966be4397d
ccd44d5fb2d03c65fd04353786369bc0af17fe9e
6762 F20101207_AAAIJJ nozaki_y_Page_077thm.jpg
494ee9f0b9c9abb1f16c9d499ca4a990
13880dbbd7b2108a5242b879191e860356d89461
5489 F20101207_AAAIIU nozaki_y_Page_064thm.jpg
6302454d4c4d9063898a462132dcc935
c13bcbd44dbf6549dc8b69e5818d412dac2bd9e0
1051975 F20101207_AAAHFS nozaki_y_Page_013.jp2
0741e725bcbeceb750c1a4464ae57a98
d3b9fb2d33e0da8a16da187d954395acdafa2f91
13416 F20101207_AAAGZY nozaki_y_Page_004.jpg
d50abe58cc32638af2d104442c053d72
f82515bbcb11100ab6d1ce916fba2633b4141f33
80826 F20101207_AAAHGH nozaki_y_Page_028.jp2
e3b4f8337123b42b562c82ef7b7d8afe
0c26966a2b647bf5accbe939b976259d3ca5ffbc
26267 F20101207_AAAIJK nozaki_y_Page_077.QC.jpg
58ec2ecac3465679e01bc6d40c685904
3abea9daeb90365dda60fe47570a0188dba753d8
17356 F20101207_AAAIIV nozaki_y_Page_064.QC.jpg
a46b36e44a844c9b82afb093ed5de32e
c3cba34e6a5f8ec5c5b2661401dc229950ec2915
1051980 F20101207_AAAHFT nozaki_y_Page_014.jp2
ca3be8eb8aed3c3ae08c26fa02f594bd
632ea3f379704e00e3ce7a89e7d02e6ba192b3a3
104978 F20101207_AAAGZZ nozaki_y_Page_005.jpg
f01fb27626e1fea306de254a7ffa1d14
87cbc7ec256bbf804b9572ec26ebb67d1491706f
89880 F20101207_AAAHGI nozaki_y_Page_029.jp2
c00f5da75dbe995214ff80bd1ea33846
d339f315e390e9151fa893871f7e4800b5726a14
22962 F20101207_AAAIJL nozaki_y_Page_078.QC.jpg
7f815efcd2bb8c7252b8ef74d996e8b0
1697d561e11eb322ee534afeb1f71b754ab127fe
5261 F20101207_AAAIIW nozaki_y_Page_065thm.jpg
d78faca49648f1a7cb22d7446ee09631
a20d9a23a2aeff17b067003e473286b2ccd25c2c
1051981 F20101207_AAAHFU nozaki_y_Page_015.jp2
a49a72e49ac5219a991bc13c24b06b74
82ff7c07b22deb45dcde46e29f667686503f4907
81464 F20101207_AAAHGJ nozaki_y_Page_030.jp2
715610f732b9f9d78832e420721ac5cc
93ad975afaef19c799d20b6dc940a5fac5918c76
18492 F20101207_AAAIKA nozaki_y_Page_092.QC.jpg
b30f5ce3917d8e8b146ed8fe8283f0e8
c1fb049d8969692054a3200f8039331fd0c31989
5271 F20101207_AAAIJM nozaki_y_Page_079thm.jpg
b472e8591b1e06a79b27d91350bb2f30
5fec9de4726d3b0c44809ebc18cd8fb05b18584d
17168 F20101207_AAAIIX nozaki_y_Page_066.QC.jpg
086225fc281e368f688b712cbf39cf0f
1592472e10e807ca45e7e4300f94bc6bf563919a
102426 F20101207_AAAHFV nozaki_y_Page_016.jp2
abd24695d929e9398d1a52dbd5e3db41
db703bbe979f1237fe70a5b316c620ff1e81b78f
92788 F20101207_AAAHGK nozaki_y_Page_031.jp2
1d1b492eeed1d71622e527f17c1ea89c
939db6def64bbb14449969322575c463da96655e
6715 F20101207_AAAIKB nozaki_y_Page_093thm.jpg
cf573a0ce0b0e1b4637b2328970526ee
6dd564d51e2b54368333c32da84809022b5fe414
20842 F20101207_AAAIIY nozaki_y_Page_067.QC.jpg
61c8a82726ac39731c491d481690d9d8
6706f04a99a4a4d74b8d0239919b487966ff7035
97966 F20101207_AAAHFW nozaki_y_Page_017.jp2
8a6d9cf0cb0fa66de245e5b7259d326f
761ee557a7a6cdda92f11604f455ec01fd52bb3f
6045 F20101207_AAAIKC nozaki_y_Page_094.QC.jpg
3eb1baa9a14aba7688d63995b132f52e
e22f61d6c7389dc84bbd26dc895a98246e991287
5566 F20101207_AAAIJN nozaki_y_Page_080thm.jpg
f669f2cf364ca939336c8d2f19453d33
0fe412745ad9453f46b081f9fdc6052006a85b41
6095 F20101207_AAAIIZ nozaki_y_Page_069thm.jpg
b60a215089387c98e6cb9457b3c5ea09
7a0b62495e9f3502a789676ce78f5e0f01fac1b8
97815 F20101207_AAAHFX nozaki_y_Page_018.jp2
7f5ebac12dd7dbf6a5b5bde477dc80e0
560d87e528a5b9649a532b7c30ea35143fdf75bc
68181 F20101207_AAAHHA nozaki_y_Page_048.jp2
b4360b43f2bee1cf3390f2c80deb7486
0bd6a9c5aff3f25adef7354a917e0e5ad4b5378d
86546 F20101207_AAAHGL nozaki_y_Page_032.jp2
bf234d590c020268e58515299fee91dd
cdbd5e84a4fdc782185f17d4cf465945abc9b8a5
35412 F20101207_AAAIKD nozaki_y_Page_095.QC.jpg
94f73d24857207008bbf0cf8d7e9c0c2
62b15e07706ce4204cd64264acab0a140b089f03
18145 F20101207_AAAIJO nozaki_y_Page_080.QC.jpg
9e7826d66c9c73d99858f18f008ba992
cd102b069c2f936b37b0f68a64a0f67212500822
80663 F20101207_AAAHFY nozaki_y_Page_019.jp2
17a33ee94f1c211a06b3067f29ad88e4
4365b8c8352c954a96ca7c064ab36a43205aa351
87259 F20101207_AAAHHB nozaki_y_Page_049.jp2
b06702be81a2f1d00f7bb0e5af273038
32cc2ee92f779e0b852040e79c41e83c8440b0c2
96675 F20101207_AAAHGM nozaki_y_Page_033.jp2
b7db3088ff514d3d0b22eb6074e6ab67
d3993e1a1d711149d112e9cec4b4b0eed6543214
32721 F20101207_AAAIKE nozaki_y_Page_096.QC.jpg
b932905d6d9bab29891f0c7baa320f10
0fce664d63e7230046a51475a6dcecf02b875456
5268 F20101207_AAAIJP nozaki_y_Page_081thm.jpg
ff783ba0a68cfe9e692d0b733a7d9e98
3789c610f18845c85c28a88317398b8285dda809
108839 F20101207_AAAHFZ nozaki_y_Page_020.jp2
157b45245d970badeb29113e3b3ae2bf
1644e6c498c9197a792f78b0e15b71dd4e00d69a
115876 F20101207_AAAHHC nozaki_y_Page_050.jp2
cbb580dd2918aa999e447ddac8d0ec8b
ddd5f3f8f23563f1f8694ab75ac2ab10435ebeb1
105568 F20101207_AAAHGN nozaki_y_Page_035.jp2
9190b7d9b377ef1f54d3a618309fec2d
ba6d5dcf800989879096feb91d351da799f2ce9f
1121 F20101207_AAAIKF nozaki_y_Page_097thm.jpg
1212d8d51431454382cd2ce2f35aa1e2
088dbbce226951bb81a2f5e8191d4f0a99578381
18947 F20101207_AAAIJQ nozaki_y_Page_081.QC.jpg
b11c5cf5c93ba59b28c11d4e049b22e2
d708a103c37e36ae4d6557ec1ab6f355d38b2ba4
109719 F20101207_AAAHHD nozaki_y_Page_051.jp2
974b0a09a1f7562bea3326b7804c6229
04c013f899471d788258798fbdccb466be00f5c7
84538 F20101207_AAAHGO nozaki_y_Page_036.jp2
26c23d7f851de5503c9f4a780bb20162
407b17803eef1ad67656c2b3b803273433c42030
6060 F20101207_AAAIKG nozaki_y_Page_098thm.jpg
c5ce389b53628f2a5631db8e172db566
a01e8cc7d4ed80a58093d80e7621aae54438080d
5230 F20101207_AAAIJR nozaki_y_Page_082thm.jpg
c03bc220704f292accdbb12edb6b6fbb
3c30bad6b2821dc3c586fc1196dd6e1ffaf17bb1
95105 F20101207_AAAHHE nozaki_y_Page_052.jp2
e2f2240d84a93ee43919b305d3b16a10
675e0a38b42353edbcff99dbc37b06d88ae10a27
304648 F20101207_AAAHGP nozaki_y_Page_037.jp2
1383000202157f1e534a98d7845e8cfb
93739608c7b92b1ed6cdbb27839c224be35d979d
28239 F20101207_AAAIKH nozaki_y_Page_098.QC.jpg
705c9628279843cc634c8904d6ff2043
c0ce7eb600f5cd04e0a7dd93866185280b6ca394
6835 F20101207_AAAIJS nozaki_y_Page_084thm.jpg
76a3b802ded2b4e0f2179334441da61a
ebfe74a1e43c6acd44c81c1002c0813aa636dd8d
111056 F20101207_AAAHHF nozaki_y_Page_053.jp2
a1af9a83bc089679ba443552dc34c267
421c647269955b498ab31a6f8a151fed66c66729
571655 F20101207_AAAHGQ nozaki_y_Page_038.jp2
88645a6eeac15fe92763bc2361b25a43
0f2e8824b9ed2d81c9d8d469a188a23339fa690d
5307 F20101207_AAAIKI nozaki_y_Page_100thm.jpg
709c5a7ad9e5e7e9e9b0a0a45bc2cd89
47f5467d9dea88972ebc6f321e40cb620ec17e04
20571 F20101207_AAAIJT nozaki_y_Page_084.QC.jpg
c944f3eff86bb359892b4efdd0aee5d8
8419201624b7d8fe2e4828d1a0b870a24fd59d4d
114600 F20101207_AAAHHG nozaki_y_Page_054.jp2
983de4ff5e9904d120ed9495dfaf0997
f440a69b31aa4326fb5812a20c2b5b05185dd7d5
400835 F20101207_AAAHGR nozaki_y_Page_039.jp2
6839972b4b200006284990802cc9df54
661a24ad86277f7d76c9416290e69c8124a59ec5
21968 F20101207_AAAIKJ nozaki_y_Page_100.QC.jpg
416c3dcf8c46b3a6a16d1a49560e9e8d
410ebd6d354f6e4e29237e0967a5d09b7b25f75c
7418 F20101207_AAAIJU nozaki_y_Page_085thm.jpg
cb51b4582790df99dac78945dde678df
76f30334d3cc6b3345347cc2635a60ab7931f25f
109665 F20101207_AAAHHH nozaki_y_Page_055.jp2
c148d9b91bc7841bc57ac80af0aa5335
eafeae73460592ad24de0b5c765e10f0e0abb06d
463719 F20101207_AAAHGS nozaki_y_Page_040.jp2
53e73339af42e0db3b94dc46bdb01da2
50468640b9495eb3e876a803b5e2f5e2ce45c270
9862 F20101207_AAAIKK nozaki_y_Page_101.QC.jpg
fe4bd289f3af2ff9abc13ca477b7a55c
52bf18ecbeeee3738c178ae3248bc7733b8bf2a9
6787 F20101207_AAAIJV nozaki_y_Page_086thm.jpg
53a24dc236aa1bfa8bd82664929ff1f1
f0f23f056ea6fd8ac0bc579fad338dc98a2ee8ed
99714 F20101207_AAAHHI nozaki_y_Page_056.jp2
6f1c312bea7f7b0d4a30bfe0ea8a3b07
63629b7e149aaa0296e8327a8f9c4ddbb043911b
426459 F20101207_AAAHGT nozaki_y_Page_041.jp2
b73bf02b7cdc84bd443ce7bf31460408
5c9e18952676d526f2cc8702f6a68414515498c3
4700 F20101207_AAAIKL nozaki_y_Page_104thm.jpg
dad5fd4a028d97acbf721cd943af56a6
b1b5ab40c97c68042b00db0d584de90cf40ffbcd
25375 F20101207_AAAIJW nozaki_y_Page_086.QC.jpg
ba419eb62d877d40e28f65b14d405f35
4e81c0228d3a1e6097d1711f53a2b06017aa4e54
1011882 F20101207_AAAHHJ nozaki_y_Page_057.jp2
d14505dd14c675011f1ed96c4547f001
7a320b3ebac672a8b71188f920f2770dfb0a7ffc
104745 F20101207_AAAHGU nozaki_y_Page_042.jp2
6780879be05cba712bf71be4b4d3116f
968d75640f51c412957fce3876e00c77dda8e2a0
25079 F20101207_AAAILA nozaki_y_Page_120.QC.jpg
49e63a663a1039b6eac28c286ff7927e
49c5fd433726a3daa4ce5e74e7729c81189f40c1
25676 F20101207_AAAIKM nozaki_y_Page_105.QC.jpg
9c0aea2b69c8f220be55e741bb6ec5a4
e7cab2a7ee77e70062afe026d9a73ee96db9e58d
F20101207_AAAIJX nozaki_y_Page_090thm.jpg
ab22d3878fa52e355dedeedf8155f156
71e5a251eeb122f07a997b485e8e333e38951a7b
734723 F20101207_AAAHHK nozaki_y_Page_058.jp2
2ad14aae36ca8df787747f9476fc12f1
d80caf52079e6ea046582478867c60e577418318
66587 F20101207_AAAHGV nozaki_y_Page_043.jp2
3b47e824e0be6b3b5256c12470a08d07
1b3b6c3fc4568eb04e8ee84227b46b91c19540ee







REDUCING SKIN FRICTION AND HEAT TRANSFER OVER A HYPERSONIC CRUISING
VEHICLE BY MASS INJECTION





















By

YOSHIFUMI NOZAKI


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

2007



































2007 Yoshifumi Nozaki


























To my parents, Yoshikazu Nozaki and Keiko Nozaki, and my brother, Toshihiro Nozaki. You
have inspired me to become who I am today. Thank you for always supporting and believing in
me. I dedicate this to you.









ACKNOWLEDGMENTS

I gratefully acknowledge the support provided by Dr. Pasquale M. Sforza, Professor of

Mechanical and Aerospace Engineering at the University of Florida.









TABLE OF CONTENTS

page

A CK N O W LED G M EN T S ................................................................. ........... ............. .....

L IS T O F T A B L E S .................................................................................7

LIST OF FIGURES .................................. .. ..... ..... ................. .8

A B S T R A C T ......... ....................... ............................................................ 16

CHAPTER

1 IN V ISC ID A N A L Y SIS ............................ .................................................. ......................17

Introduction ................................... .. .. ....... .................... 17
Local Surface Inclination M ethod ................................................. ............................. 17
Inviscid A erodynam ic Forces and M om ents .................................. ...................................... 19

2 VISCOUS AND HIGH TEMPERATURE CONSIDERATIONS.......................................22

In tro d u ctio n ................... ...................2...................2..........
L local R eynolds N um ber ............................................................................... .. ............. 22
L o c al S k in F rictio n .................................................................................................................2 6
Local H eat Transfer .................. ................................. .............. .... ........ 28
T total F forces A acting on the V vehicle ......................................................................... ...............3 1
Discussion of Results without any Cooling Methods..........................................................32

3 M A SS IN JECTION EFFECTS ........................................... .................. ............... 42

In tro d u ctio n ............................................................................................. .. 4 2
Effects of Mass Injection on the Boundary Layer ....................................... ...............43
General Behavior of Reducing Skin Friction and Heating................. .............................44

4 R E SU L T S ...........................................................................................4 7

In tro d u ctio n ................... ...................4...................7..........
The Range Equation .......................... ..................... ... .............. 47
Comparison of Range, L /D, and Heat Transfer Variance ....... ......... ...............................49

5 C O N C L U SIO N S ................. ......... ................................ .......... ........ ..... .... ...... .. 95

Conclusions of this Study ..................................... .............. ......... 95
F future W ork ......... ................................................................. 96

APPENDIX

A MATLAB CODE TO COMPUTE FLIGHT PERFORMANCE OF X24C.........................98









B MATLAB CODE (FUNCTION) TO COMPUTE TEMPERATURE ........... .....................129

C MATLAB CODE (FUNCTION) TO COMPUTE DENSITY ............................................132

D MATLAB CODE (FUNCTION) TO COMPUTE VOSCOSITY ........................................134

E MATLAB CODE (FUNCTION) TO COMPUTE PRANDTL NUMBER ..........................136

F MATLAB CODE (FUNCTION) TO COMPUTE ENTHALPY ........................................138

G MATLAB CODE (FUNCTION) TO COMPUTE MACH NUMBER FOR PRANDTL-
M A Y ER E X PA N SIO N .............................. .................. ......... ............................141

L IST O F R E F E R E N C E S ......... .. ............... ................. ........................ ..................................142

B IO G R A PH IC A L SK E T C H ........................................... ......... ................... .......................... 143









LIST OF TABLES


Table page

2-1. C oefficients in E q.(2-18) .............. ........................ .................. .. ...... 36

2-2. Comparison of aerodynamic forces and L/D .........................................................36

2-3. Configuration of X 24C studied.................................................................. .....................36

2-4. The effect of the base pressure on aerodynamic forces and L/D........................... 36

4-1. Comparison of flight parameters at M = 6 and 30000m altitude. The panels that have
q,, of more than 50000 W/m2 are cooled by the mass injection rate: 0, 0.001,
0 .0 1 (kg /m 2s) ........................................................................................57









LIST OF FIGURES


Figure page

1-1. General body surface panel showing the unit normal vector along with the locations
of the four corner points ............ ...... ............ .......... ....................... .. 21

2-1. Expansion w ave. ..................................... ... .. ........... ......... .... 37

2-2. D election angle at the corner. ........................................ .........................................37

2-3. Schem atic diagram of stagnation region....................................... ......................... 37

2-4. X-24C configuration. Note that this is a representation of the right half of the
aircraft. ................................................. 38

2-5. X-24C's LID as a function of angle of attack........................... ...... ............... 38

2-6. X-24C's aerodynamic force coefficients as a function of angle of attack.......................39

2-7. X-24C's pitching moment coefficients as a function of angle of attack .........................39

2-8. Heating distribution along windward symmetry plane of Space Shuttle Orbiter at
34.8 of angle of attack, M = 9.15, and 47.7km altitude................................40

2-9. Comparison of surface pressure distributions around the X-24C fuselage at the
farthest dow stream station. ..................................................................... ...................40

2-10. Comparison of heat transfer around the X-24C fuselage at the farthest downstream
station n ............... .............................. ................................................4 1

2-11. Comparison of streamwise surface pressure distribution along the windward and
leeward symmetry lines of the X-24C. .................... ................ ..............41

3-1. Effects of mass injection on L/D with different angle of attack for a flat plate
(6m x 6m square plate) at a M ach number of 6................. ............................................ 45

3-2. Effects of mass injection on heat transfer with angle of attack for a flat plate
(6m x 6m square plate) at a M ach number of 6................. ............................................ 46

4-1. Distribution of panel area with a given heat transfer, q,, (W/m2) at M = 6 and
3 0 0 0 0m altitu d e ............................. ........................................................... ............... 57

4-2. Distribution of the number of panels with a given heat transfer, q,w (W/m2) at
M = 6 and 30000m altitude............................................. ........................................ 58









4-3. Mass injection effect on the flight time at M = 6 and 30000m altitude. The panels to
be cooled are determined by q,, (W / m2). .......................... ........... ............... 58

4-4. Mass injection effect on L/D at M = 6 and 30000m altitude. The panels to be cooled
are determ ined by q (W /m 2). .................................... ............................... ...............59

4-5. Mass injection effect on reduction of heat power at M = 6 and 30000m altitude. The
panels to be cooled are determined by q,, (W/m2)......... ......... ............... 59

4-6. Normalized reduction of heat power v.s. normalized injected mass at M = 6 and
30000m altitude with 0.001 kg/m2 s of mass injection. The panels to be cooled are
determ ined by q (W m 2)...................................................................................... 60

4-7. Flight time v.s. normalized injected mass at at M = 6 and 30000m altitude with
0.001 kg/m2 s of mass injection. The panels to be cooled are determined by
q ,w ( W / 2 ) ...................................... ................................................ 6 0

4-8. Flight time v.s. normalized reduction of heat power at M = 6 and 30000m altitude
with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined by
q (W / 2) .................................................................................................... 6 1

4-9. Reduction of heat power (kW) v.s. injected mass rate (kg/ s) at M = 6 and 30000m
altitude with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined
b y q ,w (W / m 2) ...................................... ............................... ................ 6 1

4-10. Reduction of heat energy (kJ) v.s. injected mass (kg) at M = 6 and 30000m altitude
with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined by
q (W / 2) .................................................................................................... 62

4-11. Flight time v.s. reduction of heat energy (kJ) at M = 6 and 30000m altitude with
0.001 kg/m2 s of mass injection. The panels to be cooled are determined by
q (W / 2) .................................................................................................... 62

4-12. Normalized reduction of heat power v.s. normalized injected mass at M = 6 and
30000m altitude with 0.01 kg/m2 s of mass injection. The panels to be cooled are
determ ined by q (W /m 2)................................................................................. ..... 63

4-13. Flight time v.s. normalized injected mass at at M = 6 and 30000m altitude with
0.01 kg/m2 s of mass injection. The panels to be cooled are determined by
q ( W m 2 ) ............................................................................................... ..................... 6 3









4-14. Flight time v.s. normalized reduction of heat power at M = 6 and 30000m altitude
with 0.01 kg/ m2 s of mass injection. The panels to be cooled are determined by
S(W / m 2 ) ...................................................................................................... 6 4

4-15. Reduction of heat power (kW) v.s. injected mass rate (kg/ s) at M = 6 and 30000m
altitude with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined
b y q (W / m 2) ............................................... ........................................... 64

4-16. Reduction of heat energy (kJ) v.s. injected mass (kg) at M = 6 and 30000m altitude
with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined by
qc,. ( W /m 2 ) ...................................... ................................................. 6 5

4-17. Flight time v.s. reduction of heat energy (kJ) at M = 6 and 30000m altitude with
0.01 kg/m2 s of mass injection. The panels to be cooled are determined by
qc,. ( W /m 2 ) ...................................... ................................................. 6 5

4-18. Bottom view of X24C with 50000 W/m2 of allowable q,, at 30000m altitude ..............66

4-19. Side view of X24C with 50000 W/m2 of allowable q ,at 30000m altitude....................66

4-20. Top view of X24C with 50000 W/m2 of allowable q, at 30000m altitude. ...................66

4-21. Distribution of panel area with a given heat transfer, Q (, (W) at M = 6 and 30000m
altitude.............. ........................ ..................................................... 67

4-22. Distribution of the number of panels with a given heat transfer, Q, (W) at M = 6
and 30000m altitude...................... .................................... 67

4-23. Mass injection effect on the flight time at M = 6 and 30000m altitude. The panels to
be cooled are determined by Q0 (W )............ .... ......................... ......... ......68

4-24. Mass injection effect on L/D at M = 6 and 30000m altitude. The panels to be cooled
are determ ined by Q (W ). .............................................................. ........................ 68

4-25. Mass injection effect on reduction of heat power at M = 6 and 30000m altitude. The
panels to be cooled are determined by Q, (W) ............................................. 69

4-26. Normalized reduction of heat power v.s. normalized injected mass at M = 6 and
30000m altitude with 0.001 kg/m2 s of mass injection. The panels to be cooled are
determ ined by Q0 (W ). ........................................................................ ............ 69









4-27. Flight time v.s. normalized injected mass at M = 6 and 30000m altitude with
0.001 kg/m2 s of mass injection. The panels to be cooled are determined by Qc,w
(W ) ..................................................................................................... ...................... 70

4-28. Flight time v.s. normalized reduction of heat power at M = 6 and 30000m altitude
with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined by Qc,
( W ) ...... ..................... ............................................................................. ........................... 7 0.......... ...... .. 7 0

4-29. Reduction of heat power (kW) v.s. injected mass rate (kg/ s) at M = 6 and 30000m
altitude with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined
by Q (W ). ......................................................................................7 1

4-30. Reduction of heat energy (kJ) v.s. injected mass (kg) at M = 6 and 30000m altitude
with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined by Qc,
( W ) ...... ..................... ........................................................................................................ 7 1.......... ..... .. 7 1

4-31. Flight time v.s. reduction of heat energy (kJ) at M = 6 and 30000m altitude with
0.001 kg/m2 s of mass injection. The panels to be cooled are determined by Q,.
(W ) ..................................................................................................... ...................... 72

4-32. Normalized reduction of heat power v.s. normalized injected mass at M = 6 and
30000m altitude with 0.01 kg/m2 s of mass injection. The panels to be cooled are
determ ined by Q (W ). ....................................................................... ...................... .. ... 72

4-33. Flight time v.s. normalized injected mass at M = 6 and 30000m altitude with
0.01 kg/m2 s of mass injection. The panels to be cooled are determined by Qc, (W ).....73

4-34. Flight time v.s. normalized reduction of heat power at M = 6 and 30000m altitude
with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined by Qc,
(W ). ....................................................................................................... . ....................... 7 3

4-35. Reduction of heat power (kW) v.s. injected mass rate (kg/ s) at M = 6 and 30000m
altitude with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined
b y Q ( ). ...................................................................................... 74

4-36. Reduction of heat energy (kJ) v.s. injected mass (kg) at M = 6 and 30000m altitude
with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined by Qe,
( W ) ...... ..................... ........................................................................................................ 7 4.......... ...... .. 7 4

4-37. Flight time v.s. reduction of heat energy (kJ) at M = 6 and 30000m altitude with
0.01 kg/m2 s of mass injection. The panels to be cooled are determined by Qw (W).....75









4-38. Bottom view of X-24C with 40000 W of allowable Q, at M = 6 and 30000m
altitude................. ....................... .................................. .................. 75

4-39. Side view of X-24C with 40000 W of allowable Qcw at M = 6 and 30000m altitude......75

4-40. Top view of X-24C with 40000 W of allowable Qc, at M = 6 and 30000m altitude.......76

4-41. Distribution of panel area with a given heat transfer, q,, (W/m2 ) at M = 6 and
3 50 0 0m altitu d e ............................. .......................................................... ............... 7 6

4-42. Distribution of the number of panels with a given heat transfer, q,, (W/ m2) at
M = 6 and 35000m altitude............................................ ........................................ 76

4-43. Mass injection effect on the flight time at M = 6 and 35000m altitude. The panels to
be cooled are determined by qc,, (W /m2). ............. .... ..... ......... ...............77

4-44. Mass injection effect on L/D at M = 6 and 35000m altitude. The panels to be cooled
are determ ined by q, (W / m ). ....................................... ............................... ...............77

4-45. Mass injection effect on reduction of heat power at M = 6 and 35000m altitude. The
panels to be cooled are determined by q,, (W/m 2)............... ............ .............. 78

4-46. Normalized reduction of heat power v.s. normalized injected mass at M = 6 and
35000m altitude with 0.001 kg/m 2 s of mass injection. The panels to be cooled are
determ ined by q (W 2) ................................................................................. ..... 78

4-47. Flight time v.s. normalized injected mass at at M = 6 and 35000m altitude with
0.001 kg/m2 s of mass injection. The panels to be cooled are determined by
q ( 2 ) .................................................................................................... 7 9

4-48. Flight time v.s. normalized reduction of heat power at M = 6 and 35000m altitude
with 0.001 kg /m2 s of mass injection. The panels to be cooled are determined by
q ( 2 ) .................................................................................................... 7 9

4-49. Reduction of heat power (kW) v.s. injected mass rate (kg/ s) at M = 6 and 35000m
altitude with 0.001 kg /m2 s of mass injection. The panels to be cooled are determined
b y q c, ( W / m 2) ...................................... ............................... ................ 8 0

4-50. Reduction of heat energy (kJ) v.s. injected mass (kg) at M = 6 and 35000m altitude
with 0.001 kg /m2 s of mass injection. The panels to be cooled are determined by
q (W / 2) .....................................................................................................80









4-51. Flight time v.s. reduction of heat energy (kJ) at M = 6 and 35000m altitude with
0.001 kg/m2 s of mass injection. The panels to be cooled are determined by
q ,, ( W /m 2) ...................................... .................................................. 8 1

4-52. Normalized reduction of heat power v.s. normalized injected mass at M = 6 and
35000m altitude with 0.01 kg/m2 s of mass injection. The panels to be cooled are
determ ined by q,, (W m 2) ................................................................................. ..... 8 1

4-53. Flight time v.s. normalized injected mass at at M = 6 and 35000m altitude with
0.01 kg/m2 s of mass injection. The panels to be cooled are determined by
q (W / 2) .....................................................................................................82

4-54. Flight time v.s. normalized reduction of heat power at M = 6 and 35000m altitude
with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined by
(W / 2) .....................................................................................................82

4-55. Reduction of heat power (kW) v.s. injected mass rate (kg/ s) at M = 6 and 35000m
altitude with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined
b y q ,, (W /m 2 )....................................... ......... ................... ................ 8 3

4-56. Reduction of heat energy (kJ) v.s. injected mass (kg) at M = 6 and 35000m altitude
with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined by
q (W / 2) .....................................................................................................83

4-57. Flight time v.s. reduction of heat energy (kJ) at M = 6 and 35000m altitude with
0.01 kg/m2 s of mass injection. The panels to be cooled are determined by
q ,w ( W /m 2) ...................................... ................................................. 8 4

4-58. Bottom view of X-24C with 30000W/m2 of allowable q,, at 35000m altitude. ............84

4-59. Side view of X-24C with 30000 W/m2 of allowable q,, at 35000m altitude. .................84

4-60. Top view of X-24C with 30000 W/m2 of allowable q,, at 35000m altitude ..................85

4-61. Distribution of panel area with a given heat transfer, Q0, (W) at M = 6 and 35000m
altitude................. ....................... .................................. .................. 85

4-62. Distribution of the number of panels with a given heat transfer, Q, (W) at M = 6
and 35000m altitude .......................... ........... ................ ....... 85









4-63. Mass injection effect on the flight time at M = 6 and 35000m altitude. The panels to
be cooled are determ ined by Qc, (W ) ................ ............. .................. .... ................. 86

4-64. Mass injection effect on L/D at M = 6 and 35000m altitude. The panels to be cooled
are determ ined by Q (W ). .............................................................. ............... ..... 86

4-65. Mass injection effect on reduction of heat power at M = 6 and 35000m altitude. The
panels to be cooled are determined by Q0 ,w (W ) .............. ........................................... 87

4-66. Normalized reduction of heat power v.s. normalized injected mass at M = 6 and
35000m altitude with 0.001 kg/m2 s of mass injection. The panels to be cooled are
determined by Q, (W ). ....................................................................................................87

4-67. Flight time v.s. normalized injected mass at M = 6 and 35000m altitude with
0.001 kg/m2 s of mass injection. The panels to be cooled are determined by Q,.
(W ) ..................................................................................................... ...................... 88

4-68. Flight time v.s. normalized reduction of heat power at M = 6 and 35000m altitude
with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined by Qc,
(W ) ..................................................................................................... ...................... 88

4-69. Reduction of heat power (kW) v.s. injected mass rate (kg/ s) at M = 6 and 35000m
altitude with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined
by Q (W ). ...................................................................................... 89

4-70. Reduction of heat energy (kJ) v.s. injected mass (kg) at M = 6 and 35000m altitude
with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined by Qc,
(W ) ..................................................................................................... ...................... 89

4-71. Flight time v.s. reduction of heat energy (kJ) at M = 6 and 35000m altitude with
0.001 kg/m2 s of mass injection. The panels to be cooled are determined by Q,.
(W ). .................................................................................................................................. 90................ .. 90

4-72. Normalized reduction of heat power v.s. normalized injected mass at M = 6 and
35000m altitude with 0.01 kg/m2 s of mass injection. The panels to be cooled are
determ ined by Q (W ). ......................... .................................... ................. ........90

4-73. Flight time v.s. normalized injected mass at M = 6 and 35000m altitude with
0.01 kg/m2 s of mass injection. The panels to be cooled are determined by Q,, (W ).....91









4-74. Flight time v.s. normalized reduction of heat power at M = 6 and 35000m altitude
with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined by Qc,
(W ). ....................................................................................................... . ............... 9 1

4-75. Reduction of heat power (kW) v.s. injected mass rate (kg/ s) at M = 6 and 30000m
altitude with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined
by Q (W ). ...................................................................................... 92

4-76. Reduction of heat energy (kJ) v.s. injected mass (kg) at M = 6 and 35000m altitude
with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined by Qe,
(W ). .................................................................................................................................. 92................ .. 92

4-77. Flight time v.s. reduction of heat energy (kJ) at M = 6 and 35000m altitude with
0.01 kg/m2 s of mass injection. The panels to be cooled are determined by Q,, (W).....93

4-78. Bottom view of X-24C with 20000 W of allowable Qe, at 35000m altitude ..................93

4-79. Side view of X-24C with 20000 W of allowable Q,w at 35000m altitude......................93

4-80. Top view of X-24C with 20000 W of allowable Qc, at 35000m altitude.........................94









Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

REDUCING SKIN FRICTION AND HEAT TRANSFER OVER A HYPERSONIC CRUISING
VEHICLE BY MASS INJECTION

By

Yoshifumi Nozaki

August 2007

Chair: Pasquale M. Sforza
Major: Aerospace Engineering

Demonstrating technologies for hypersonic aircraft that cruise at speeds greater than Mach

5 is one of the long-term visions of many agencies, like NASA. Reducing skin friction and heat

transfer on the surface of hypersonic cruising vehicles has been a focus of constant

attention.General methods for estimating the aerodynamic forces and heat transfer around a

hypersonic vehicle are used to evaluate the reduction in skin friction and heat transfer on the

surface of a hypersonic vehicle by mass injection. Particular attention was paid to the X-24C

configuration because of the existence of experimental data of X-24C performance against which

the predictions can be compared. The local surface inclination method and the flat plate

reference enthalpy methods for laminar and turbulent flow were used to find aerodynamic forces

and heat transfer. High temperature effects were included by using a classical approximation of

thermodynamic properties. Although this analysis is based on many approximations, these

methods worked well and flow properties were reasonably predicted. Reducing skin friction and

protecting surfaces from heating by injecting mass did result in a penalty in the form of

decreased flight time of the vehicle, and therefore flight range. These penalties were often very

light. Also, as more mass is injected, the effect of mass injection grows, but more slowly.









CHAPTER 1
INVISCID ANALYSIS

Introduction

Hypersonic flow is complicated because of physical aspects of hypersonics such as high-

temperature chemically reacting, thin shock layer, etc. Such complex phenomena cannot be

described by a simple linear system. Even without these phenomena, the basic theory of inviscid

compressible flow, when the Mach number is very large, does not yield aerodynamic theories

which are mathematically linear. By using supersonic thin airfoil theory, the pressure coefficient

on the surface is obtained from

M20,
2c= (1-1)


where M0 is the free stream Mach number, and 0, is flow inclination. Eq.(1-1) is a classical

result from inviscid, linearized, two-dimensional, supersonic flow theory.1 This method is called

the local surface inclination method, and it is very simple and easy to use to predict cp. This

method does not need a detailed solution of the complete flowfield. This simplicity is very

useful, but unfortunately, it is not valid for hypersonic speeds since nonlinear effects become

important at high Mach number. However, there are other valid local surface inclination

methods, and some of those are presented, which are applied to our hypersonic bodies.

Local Surface Inclination Method

As M. approaches oo and y approaches 1, the shock layer becomes coincident with the

body surface. This is because the density ratio across the shock approaches zero, and since the

density behind the shock is so high the shock layer becomes thinner and thinner. Therefore, it

looks as if the incoming flow is directly impinging on the wedge surface, and then is running

parallel to the surface downstream. Under these conditions, Newtonian theory is used to find c .









For blunt bodies the modified Newtonian theory should be used, and such results usually

produce acceptable accuracy. In contrast, Anderson2 suggests that Newtonian results for slender

bodies should use the straight Newtonian theory. Newtonian theory works reasonably well alone

and lends itself to application to arbitrary slender body shapes. In the Newtonian model of fluid

flow, the particles in the free-stream impact only on the frontal area of the body; they cannot curl

around the body and impact on the back surface. Hence, for that portion of a body which is in the

"shadow" of the incident flow, no impact pressure is left, so over this "shaded" region the

Newtonian theory is inaccurate. Therefore the Newtonian theory is described by the following

equations:


cp = 2 .- for V1. < 0 (1-2)

c, =0 for V17 nh>0 (1-3)

where h is unit outward normal vector on the body surface. The above equations are locally

applicable to every surface panel on a smooth body. In order to have more accurate results,

Prandtl-Meyer expansion theory should be applied for the surface panel at which the Newtonian

method is inaccurate. In this study, we use Newtonian theory for all surface panels except for the

part in the "shadow", at which we applied Prandtl-Meyer expansion theory. In practice, the body

surface of a vehicle is subdivided into a number of individual panels and each panel is treated

separately to determine the pressure force acting. In this study, the surface of the X-24C vehicle

is divided into 284 panels as described subsequently. The normal vector of each panel can be

found by the cross-product of the P and Q vector as shown in Figure 1-1.

N=PxQ (1-4)

n = (1-5)









1- 1-
dA = = (1-6)
2 2

where dA is differential area of individual panel. Once having the unit normal to the surface

element, the pressure force acting on each panel can be found by:

dFpr. =-(cq +P ).dA. (1-7)

q=PV2 (1-8)
2

where dF.... is the pressure force acting on individual panel and q is the dynamic pressure.

Inviscid Aerodynamic Forces and Moments

Before determining differential lift(adL ) and drag(iD ) on each panel, the angle of attack

must be accounted for the flow condition. In this analysis, the angle of attack is defined as the

angle between the free stream velocity vector (or x-axis) and the fuselage reference line of the

vehicle. Therefore, each node point must be rotated with respect to y-axis as the angle of attack

increases (the origin of the coordinate is located at the nose of the vehicle). The following

equations are used to change each node on the surface according to variable angle of attacks:


x'= 2 + Zcos tan -a (1-9)

y'=y (1-10)

z'= z2 sin tan z -a (1-11)

(x,y,z): a node at a = 0
(x', y', z'): a node at nonzero a

Having the differential pressure force acting on each panel with an accounting for the angle

of attack, differential lift(dL) and drag(dD ) on each panel are found as:

dL ... =dFpe (1-12)
dD .....= dFp ..... (1-13)
dF = dFpe + dFpj + dF k (1-14)
pd=des (-press,
dF = dP (1-15)









where dL,,,,,, and dD,,,,.. are differential lift and drag caused by only the pressure acting on the

vehicle. Note that the free stream is always directed in the positive x-direction, and the vehicle

rotates with respect to y-axis and the free stream flow direction never changes even though the

angle of attack changes. Therefore, lift (L) and drag (D) are always directed in the z-direction

and x-direction, respectively. However, the angle of attack changes the normal vector on each

surface since the P and Q vectors of each surface change with angle of attack.

The differential moment of each panel about a reference point, say the center of mass, due

to the differential force on a particular body surface element is given by:

dM,= FxdF'= [(x" -x +(y" -y,)j +(z"-z,)k]xdF' (1-16)
dMo = dli + dm + dnk (1-17)
(l,m,n): (rolling moment, pitching moment, yawing moment)
(x,,y,,z,): reference point at zero angle of attack (e.g. center of gravity)

The vehicle in free flight has three rotational degrees of freedom. Three rotational
disturbances must be originated at a reference point of the vehicle. However, the coordinate
system is not set to the vehicle body, so a vector transformation is necessary as following:
x" = x cosa zc sina (1-18)
y"= yc (1-19)
z" = x sin a+ zcosa (1-20)
d = (dFx cos a dF, sin a)i + dFyj + (dF cos a + dFx sin a) (1-21)
(x", y", z"): center of each panel in the transformed coordinate system
(x, zC ): center of each panel computed by Eq.(1-9) (1-11)

The differential force dF' calculated by Eq.(1-21) is used in Eq.(1-16). In order to have

more accurate pressure force, Prandtl-Meyer expansion theory should be applied for the surface

in the "shadow region," in which the Newtonian theory is inaccurate. This theory will be

discussed in the next chapter since Prandtl-Meyer expansion theory is used to aid in

determining thermodynamic properties such as viscosity on the shaded surface.
















normal


Figure 1-1. General body surface panel showing the unit normal vector along with the locations
of the four corer points.









CHAPTER 2
VISCOUS AND HIGH TEMPERATURE CONSIDERATIONS

Introduction

In the preceding analysis the fluid dynamic effects of high Mach number is emphasized,

without the added complications of viscous and high temperature effects. However, the matter of

friction and thermal conduction should not be neglected since high speed flow is slowed by

viscous effects within the boundary layer, and lost kinetic energy is transformed in part into

internal energy. This extreme viscous effect can create very high temperatures high enough to

excite vibrational energy within molecules, and to cause dissociation and even ionization within

the gas. The geometric layout of the body surface panels, the pressure on each panel, and the

determination of the velocity component tangential to the body surface panels all are used in an

approximate analysis of the skin friction and heat loads experienced by the vehicle during

hypersonic flight. In order to calculate skin friction for both laminar and turbulent flows, the flat

plate reference enthalpy method and Reynolds' analogy with heat transfer are used. For very

large hypersonic Mach number, the assumption that the pressure is constant in the normal

direction through a boundary layer is not always valid. However, for vehicles designed to fly at

around M = 6 a constant pressure in the normal direction is the case.

Local Reynolds Number

One of the major parameters used in the analysis is the Reynolds number based on the

local tangential velocity, temperature, and distance, s, from the stagnation point, that is


Res,e Pes (2-1)
Pe

The variable s denotes the distance along the surface of the vehicle measured from the

relevant stagnation point or stagnation line, while the subscript e indicates that these variables









are conditions at the outer edge of the boundary layer. The tangential component of the free

stream velocity is denoted by u,, and that is found by the preceding inviscid analysis as

ii, = 17 (1. ) (2-2)

If the x component of the unit vector is positive, and the panel of a body is in the "shadow"

of the incident flow, the Prandtl-Meyer expansion relations are applied locally since the

Newtonian formula on merely has c, = 0 everywhere in the shadow region. Now consider the

centered Prandtl-Meyer expansion around a corer of deflection angle 0, as sketched in Figure 2-

1. Upstream of the wave is the windward area of a body and the downstream is the shadow area

of a body. The Mach numbers upstream and downstream of the wave are M1 and M,,

respectively. From basic compressible flow, the relation between 0, M1 and M, is given by:

0= v(M,) v(M) (2-3)

where v is the Prandtl-Meyer function:

v(M)= 1tan -l -1) -tan-'1 M21 (2-4)
Y -1 y+l

From the equation above, the value of v corresponding to M1, and M2 is found by the

tangential components of the free stream velocity u, at the outer edge of boundary layer. Figure

2-2 shows a 3-dimensional sketch of the flow around the corner. The deflection angle 0 is found

from the following relation:

0 = sin Uel XUe2 =sin (^el x ue2) (2-5)
uel Ue2

where Uel and u2 are the tangential component of the free stream velocity Ue at the outer edge

of boundary layer of upstream and downstream respectively. Both Ue, and ue2 are found by

Eq.(2-2) although ue2 obtained by Eq.(2-2) is not real outer edge velocity. In order to find the









deflection angle 0, only the directions of ue and ue2 must be found, so Eq.(2-2) is used only to

find the unit vector of u,2. Now 0 and M1 are known, so M2 can be found by using Eq.(2-3) and

Eq.(2-4), and the real ue2 and downstream thermodynamic properties are given by:3

ue2 =M2 yRT2 (2-6)
1+ 2 2
T2 T1 (2-7)
1+ 2 2
72 ;-1

P2 Pi T (2-8)
1 \ -1

P=2 A 1 (2-9)


In order to find the downstream thermodynamic properties, the upstream thermodynamic

properties must be known.

For a specific value of y, the Prandtl-Meyer function v asymptotically approaches the

maximum value vmax as Mach number increases. Thus, if v(M2) > vma, an infinite Mach number

is generated and the pressure falls to zero. Expansion at such condition would, according to the

pressure theory, lead to a vacuum adjacent to the wall. Of course, in reality, the continuum and

ideal gas assumption become invalid long before this situation is reached. However, panels

whose v may be greater than vmax won't have high heat exchange or skin friction. What we need

for this study is identifying those surface panels whose total heat transfer is not negligible, so an

accurate analysis for these special cases of large expansion angles is not necessary.

In order to evaluate the density and viscosity, the pressure and temperature are required.

Since the pressure is assumed to be constant in the direction normal to the panel, the pressure on









the panels may be obtained from the pressure coefficients obtained in chapter 1 or Eq.(2-8) for

the shaded panels, and that is

P. = P =cq + Po
or P = P, = P2 by Eq.(2-8) for shaded panels (2-10)

Temperature may be obtained by using the energy equation along a streamline


total =h + V2 =h + e2 (2-11)
2 2

Therefore,

he = h + V2-u2 1 e2: o =C +1 V2 e2 (2-12)


where Cp,, is constant pressure specific heat at temperature of To The assumption here is that

kinetic energy carried in the normal component of velocity is transformed into internal energy by

adiabatic compression. In order to find the temperature from enthalpy, it is necessary to use

tables or models for the thermodynamic and transport properties of high temperature air. Here

Hansen's "Approximations for the Thermodynamic and Transport Properties of High-

Temperature Air"4 is used to evaluate the behavior of thermodynamic and transport properties at

high temperature.

Numerical codes are used to predict temperature, compressibility, density, viscosity, and

Prandtl number. Prandtl number is not used to find Reynolds number, but will be used to find

skin friction later, so the code computing Prandtl number is introduced here. The code for

computing the temperature needs only inputs of enthalpy and pressure which are already known.

The other codes computing compressibility, density, viscosity, and Prandtl number need inputs

of pressure and temperature which is obtained from the code computing temperature. However,

in order to find the temperature from pressure and enthalpy, the compressibility must be known

since temperature is defined as a function of enthalpy, pressure, and compressibility in Hansen,









and inversely compressibility is obtained from pressure and temperature. Pressure and enthalpy

are known, and therefore the temperature is guessed, and an iteration is carried out until the

given enthalpy matches the enthalpy computed from guessed temperature. This approach

establishes the following five functions.

T = T(P,h) (2-13)
Z = Z(P,T) (2-14)
p = p(P,T) (2-15)
u = u(P,T) (2-16)
Pr = Pr(P, T) (2-17)

To find the distance s, the stagnation point (stagnation line for the wing) must be specified.

Here it is assumed that for typical vehicles, like the X-24C that will be studied in this paper,

there is one stagnation point for the fuselage while the two-dimensional cross section of the

wings (airfoils) have stagnation lines. We can set the stagnation point at the center of the panel

whose outward normal vector is the closest to the opposite vector of free stream. In this study,

the vehicle has only low angles of attack, so the stagnation points are always located at the most

windward panel. The most windward panel is so small that s of other panels do not change much

even if the stagnation point and line are shifted to the nose of the fuselage and leading edge of

the wing. Therefore, the stagnation point and line are set to the nose point of the fuselage and

leading edge of the wings, respectively for convenience. The distance s is assumed to be the

distance from the stagnation point to the center of the panel under consideration.

Local Skin Friction

The Van Driest II method for turbulent boundary layers is probably the most accurate

generally applicable equation for skin friction, but it is too complicated for the entire surface of a

vehicle. Another simpler method uses a reference value of temperature at which the density and

physical properties of the fluid are evaluated and used in the available constant density, constant









property boundary layer solutions to provide an adequate approximation to the actual, variable

density, variable property flow. That value of the temperature is called the reference temperature,

T* In this study, the flat plate reference enthalpy method is utilized to determine local surface

heat transfer and Reynolds' analogy with heat transfer for laminar and turbulent flow is used to

determine friction on panels. The flat plate panels considered here have approximately constant

pressure over the skin surface, and thus permits this approach. The Nusselt number is given by


Nu = AP \ Re e\ ) (2-18)


The coefficients in Eq.(2-18) are listed in Table 2-1. The reference enthalpy and the

adiabatic wall enthalpy are given by

h* = 0.28h + 0.5h, +0.22haw (2-19)
2
haw = he + Prem u (2-20)
2

where he and h, are the enthalpies at the edge of the boundary layer and at the wall,

respectively, and Pre is the Prandtl number evaluated at the edge of boundary layer. The quantity

m is 1/2 for laminar flow and 1/3 for turbulent flow. It is noted that the skin friction coefficient

and the Nusselt number are related. This observation can be formalized an generalized for non-

slip condition, u, = 0, and the relation is

1 c
Nu Re Pr3 (2-21)
2

or


cf(S)= pr 3 pe b Re (2-22)


where cf(s) is the local skin friction coefficient.









Local Heat Transfer

From Eq.(2-21) and Eq.(2-22), the local heat transfer can be found since the definition of

the Nusselt number is


Nu = S(2-23)
ke (T, -T.)

where qc,w is the convective heat transfer at the wall, and is obtained from the relation


cf(s) Pre3 Re,, k-(T )(2-24)
,w = 2s

The subscripts w and e denote conditions at the wall and the edge of the boundary layer.

Eq.(2-24) provides reasonable values for the heat transfer, except for the extremely high value at

the region near the stagnation point, since the distance from the stagnation point, s is very small

around the stagnation point. Thus, the blunt body heat transfer method is applied to the region

near the stagnation point. Fay and Riddell 6, a first carried out a rigorous study of stagnation point

convective heat transfer at hypersonic speeds and provided the following result


q,s = 0.76Pr- 6 (Pe, ) 04 (Pww )l )O1 (h, -hw) I-(Le'05 21) j1 (2-25)


In Eq.(2-25), the term in square brackets represents the effects of equilibrium chemical

reactions occurring in the stagnation region and


Le =PD1 (2-26)
k

hD =C,hf,, (2-27)
i=1

The gas considered here is air, which can be considered to be a binary mixture. This

mixture is made up of two species: oxygen and nitrogen atoms (O and N) and molecules (02 and


a Taken from "Space Access Vehicle Design Handbook" (Sforza, P. M.)









N2). The quantity D12 is the binary diffusion coefficient. The quantities c, and Ah1,> are the

molar concentrations of the individual species (0, 02, N, and N2) and the chemical heat of

formation of each species, respectively. The Lewis number for an air-like mixture given by

Eq.(2-26) is close to unity, Le-1.4, so that the quantity (Le 52 -1) 0.19, and the contribution of

the chemical reaction term can be often be safely neglected.

The velocity gradient at the stagnation point in Eq.(2-25) may be found by

due 1 /2(P_ -P o)
S1 2 (2-28)
ds R, Pe

In the Newtonian approximation this becomes

due V2 (2-29)
ds Rb

Then Eq.(2-25) is simplified to

0.9038 CC ( (2-3 0)
q,,- 14 (- Pr )Rb Pr )

In Eq.(2-30) the variable C, = p,~ /p, p, is the Chapman-Rubesin factor and the Prandtl

number is calculated at the stagnation conditions at the edge of the boundary layer. The

stagnation enthalpy behind the shock as well as the density ratio across the shock can be

determined from the shock relations for equilibrium air chemistry. A schematic diagram of

stagnation region is shown in Figure 2-3.

A stationary normal shock wave is considered here. The shock is so strong that the

temperature behind the shock is high enough to ensure that vibrational excitation and chemical

reactions occur behind the shock front. It is assumed that local thermodynamic and chemical

equilibrium conditions hold behind the shock, and all conditions ahead of the shock wave are

known. The governing equations for the flow across a normal shock are









Continuity p1u = pu2 (2-31)

Momentum P2 = P + pu2, !- (2-32)


Energy h, = hI + "1 1 )P1 (2-33)
2 P2

In addition, the equilibrium thermodynamic properties for the high-temperature gas are

known from the numerical techniques introduced by Eq. (2-13) and Eq.(2-15). The codes used

here are

T, =T(P2,h,) (2-34)
p2 = p(P,,T,) (2-35)

Since all the upstream conditions, pl, ul, P,, h,, etc., are known, Eq.(2-32) and Eq.(2-33)

express P2 and h2, respectively, in terms of only one unknown p,/p2 This establishes the basis

for an iterative numerical solutions introduced by Anderson2, as follows

1. Assume a value for p /p2 (A value of 0.1 is usually good first guess.)

2. Compute P2 from Eq.(2-32) and h2 from Eq.(2-33)

3. Using the values of P2 and h2 obtained, compute T2 from Eq.(2-34) and p2 from Eq.(2-35).

4. Form a new value of p,/p2 from the value of p2 obtained in step 3.

5. Use this new value of p,/p2 in Eq.(2-32) and Eq.(2-33) to obtain new values of P, and h2,

respectively. Then repeat step 2 through 5 until convergence is obtained, i.e., until there is

only a negligible change in p,/p2 from one iteration to the next.

6. At this stage, the correct values of P2, h2, T,, and p, are obtained. Using Eq.(2-31), obtain

the correct value of u2.

By means of step 1 through 6 above, all properties behind the shock wave are found for

given properties in front of the wave.









Now the stagnation point heat transfer is obtained by Eq.(2-30) and thermodynamic

properties behind the shock. For hypersonic flow conditions over blunt bodies, it is considered

that the flow along an inviscid streamline emerging from the stagnation region as if that

streamline were everywhere a local surface of the vehicle. The following is good approximation

of the local heat transfer on the surface of blunt bodies derived by Lees.7 b

IP e ,lUe 'r
1q\ P 1 P ) (2-36)
qc = qc,s (2-36)
n+1 / ~ / ~
2 e PeI e e2nds
(dx -[ Jro ds


where r0 is radius of cross section of bodies of revolution and n is 1 for bodies which are like

bodies of revolution and 0 for two dimensional bodies. The subscript s indicates computation at

the stagnation point and should not be confused with the variable s, the distance from the

stagnation point.

Total Forces Acting on the Vehicle

Now that the pressure and skin friction distribution around the body is known, the forces

acting on the vehicle may be determined. We already know the inviscid aerodynamic forces,

L..s, and Dl,.s.by summing the contributions of all the panel differential inviscid forces dLn,,s

and dD ..s. over all the panels. However, these differential forces do not include expansion

effects for the shaded panels. In order to recalculate the accurate inviscid aerodynamic forces, the

pressure computed in this chapter (Eq.(2-8) or Eq.(2-10)) should be used as follows,

dFpress = dF prss,, + dFpress,y + dFpress, k = -Pe dA n (2-37)
dL.. = dFpess, (2-38)
dD = dFpess, (2-39)


b Taken from "Space Access Vehicle Design Handbook" (Sforza, P. M.)









Inviscid aerodynamic forces mean the forces caused by only the pressure acting on the

vehicle. So far we know the local skin friction coefficients, so we can find the aerodynamic

forces including viscous effects. The differential skin friction forces for turbulent flow on the

plates can be found from,

dFf,,, = Cftub .q.dA.ue,x (2-40)
dFfc,j = Cftub -qdA u e,y (2-41)
dFf,, ,k= c ft q dA -u (2-42)

where u^,x, ue,, and u^, are the x, y, and z component of the unit vectors of the outer edge flow

velocity of the panel. The dynamic pressure of the free stream is q, the differential area of the

panel is dA, and Cf,tub is the local skin friction coefficient of the turbulent boundary layer. When

the laminar boundary layer is considered, Cf,tub is simply replaced by Cf,lam. Aerodynamic forces

including skin friction are found from the following:

dL = dL,,,,s +dFf,,, (2-43)
dD =dD,,,,,, + dFfc,x (2-44)
L = dL (2-45)
D = dD (2-46)

Discussion of Results without any Cooling Methods

We have just established a method to compute the total forces acting on the body surface

as well as the heat transfer. Aerodynamic forces can be found by summing the contributions of

all the panel differential forces (L, D) and moments can be found by summing the moment

contributions of all the panel differential data (dL dD, and dMo). The aerodynamic forces and

moments are expressed in term of dimensionless force and moment coefficients:8


CD -- D- :drag coefficient (2-47)
1P 2S
2 p Sref









L
CL = L :lift coefficient (2-48)
2p 2Sref

Cm = m :pitching moment coefficient (2-49)
21 2Sr

where Sref is the reference area, which is the planform area in this study and c is the fuselage

length. Unlike hypersonic gliders like the Space Shuttle Orbiter, hypersonic cruising vehicles

have relatively slender bodies and fly at low angles of attack. Therefore, here we analyze only

low angles of attack, in which skin friction effects on flight performance are more pronounced

than in high angles of attack.

The X-24C configuration is chosen for study here and is illustrated in Figure 2-4 with the

surface features being approximated by 284 panels. Table 2-2 shows comparisons of computed

lift and drag coefficients and L/D with experimental data. The flight condition of the X-24C

studied here is a Mach number of 5.95, an angle of attack of 6, a characteristic unit Reynolds

number of 1.64 x 107 /m, and a turbulent boundary layer, which are the same conditions as the

available experimental data.9-11' The base pressure, P, e is set to the same value as the ambient

pressure, which is probably an optimistic choice for the cruising vehicle. In this study, we

confine our attention to the X-24C vehicle. The configuration details are shown in table 2-3.

The results for the aerodynamic forces are slightly underpredicted, but they agree

reasonably well with experimental data. Figure 2-5 and 2-6 show L/D and aerodynamic forces

coefficients for various a, respectively. Viscous effects on L/D and CD are obvious, but not for

CL because at low angles of attack friction doesn't affect normal forces. Figure 2-7 shows the


Reference 9 and 10 are taken from Reference 11









pitching moment coefficient. The reference point is located at the center of gravity of the

vehicle (x = 9.706, y = 0, z = 0).

Table 2-4 shows the effect of base pressure on the aerodynamic forces. C, does not change

with P,,, since the base pressure does not have an effect on the lift much when the angle of

attack is relatively low. On the other hand, the predicted CD depends on Pba, and therefore so

does L/D. At PbA, = 0, CD is the closest to the experimental data, while at Pbae = 0.2P., the

predicted L/D gives the best agreement with the experiment. In order to have good agreement

with the experimental data, we should set Pb~, to 0 or 0.2P,. However, this value is too small for

cruising vehicle, and C, has the best agreement with the experiment when Pbae = P, so it is not

easy to find the appropriate Pb~, here. For the present study, the latter assumption Pbe = P, is

used.

We have introduced two methods to calculate the local heat transfer, the flat plate

reference enthalpy method and the blunt body solution method. At stagnation points, the flat

plate reference enthalpy method provides extremely high values of the heat transfer, so the blunt

body solution should be used for panels around the stagnation point or line. Although the flat

plate reference enthalpy method and the blunt body solution method give different values of heat

transfer, at least both solutions have similar behavior. In order to find the location where we may

start to use the flat plate reference enthalpy method, a heat transfer comparison is carried out for

the Space Shuttle Orbiter since there are more experimental data for that configuration than for

the X-24C. Figure 2-8 shows comparison of heating distribution along windward symmetry

plane of the Orbiter between the present method (the flat plate reference enthalpy method and the

blunt body solution method) and actual flight data.12 In this figure, s/L is the distance from the

stagnation point normalized by total length of the windward symmetry plane line. The flat plate









reference enthalpy method agrees with actual flight data except for the region around the

stagnation point. Therefore, around the stagnation point or line, the blunt body heat transfer

method is to be used, and the heat transfer calculated by both methods should be analyzed for

each stream line. There is a panel at which two methods provide the same or very close heat

transfer, and there we must switch the methods to use. In Figure 2-8, for example, the blunt body

heat transfer method should be used for the panels at which s/L = 0 and 0.0173. For the panels

downstream from s/L = 0.0864, the flat plate reference enthalpy method should be used. Mass

injection through the surface is used for cooling, which causes additional mixing in the boundary

layer. Since the boundary layer is approximated to be turbulent, we use the flat plate reference

enthalpy method for turbulent flow to find the heat transfer.

Since most of the experimental data9' 10, 12 for the X-24C was measured at several

streamwise stations, the format of comparison is constructed accordingly. Typical results are

given by abscissas in the form of normalized arc length. This length is calculated from the

leeward symmetry (top) plane toward the windward (bottom) counterpart and scaled by the total

arc length of each individual cross section. Surface pressure and the Stanton number distribution

comparisons with experimental measurements at the body furthest downstream station

(x/r, = 104.75 ) of the X-24C are shown in Figures 2-9 and 2-10, respectively. Our vehicle

configuration does not use very many panels, so we cannot show the results at exactly the same

stations. Thus surface pressure and Stanton number are computed at the furthest downstream

station (x/r, = 90.2 ) in our vehicle model. In Figure 2-9, we define the Stanton number as:1


St = q (2-50)
pj.(h, hJ)









The agreement in surface pressure and heat transfer distribution is reasonable. The

windward and leeward pressure distributions along the symmetry plane are given in Figure 2-11.

The present results slightly underpredict the experimental data at most points, but the theory

seems applicable for analyzing the flow properties around the X-24C. In order to find

aerodynamic forces and heat transfer over the X-24C vehicle, therefore it is reasonable to use the

methods introduced in Chapters 1 and 2.

Table 2-1. Coefficients in Eq.(2-18)
Type of flow A a b c j
laminar 0.3320Prl/3 0.5000 0.5000 0.5000
turbulent 0.0296Prl/3 0.8000 0.2000 0.8000
flat plate 0.0000
axisymmetric -- 1.0000

Table 2-2. Comparison of aerodynamic forces and L/D.
CL CD L/D
Experimental data 0.0368 0.0317 1.16
Present results 0.0332 0.0253 1.31
Percent error -9.78 -20.2 13.1

Table 2-3. Configuration of X24C studied.
Parameter Value
Reference area (m2) 57.2
Fuselage (m) 14.7
Wingspan (m) 7.38
Surface Temperature (K) 317.0

Table 2-4. The effect of the base pressure on aerodynamic forces and L/D.
Base /P CL error in C, CD error in CD L/D error(%) in L/D
0 0.0327 -11.0 0.0294 -7.21 1.11 -4.00
0.2 0.0328 -10.8 0.0286 -9.82 1.15 -1.00
0.4 0.0329 -10.6 0.0278 -12.4 1.18 2.21
0.6 0.0330 -10.3 0.0270 -15.0 1.22 5.62
0.8 0.0331 -10.1 0.0261 -17.6 1.27 9.25
1.0 0.0332 -9.82 0.0253 -20.2 1.31 13.1










/P-M expansion wave


Ml



Front region of a body
Shadow region on the
leeward side of a body


Figure 2-1. Expansion wave.


Figure 2-2. Deflection angle 0 at the corner.


Shock wave


V
-^ -> i


Edge of boundary
layer

/-Rb


Figure 2-3. Schematic diagram of stagnation region.




























Figure 2-4. X-24C configuration. Note that this is a representation of the right half of the aircraft.


2.5

2

1.5

1

0.5

0

-0.5

-1

-1.5


angle of attack (deg)


Figure 2-5. X-24C's L/D as a function of angle of attack.


SL/D inviscid

SL/D viscous









1 3 4 5 6 7 8 9 1.











0.08


0.06


0.04


0.02


0
-0.02 2 3 4 5 6 7 8
-0.02


-0.04

angle of attack (deg)



Figure 2-6. X-24C's aerodynamic force coefficients as a function of angle of attack.


0.003

0.002

0.001

0
U
-0.001

-0.002

-0.003

-0.004


-- Cminv

Cm vis




1 2 3 4 5 '.7 8 9







angle of attack (deg)


Figure 2-7. X-24C's pitching moment coefficients as a function of angle of attack.










1000000




100000


C 10

10000




1000


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
s/L (m)


Figure 2-8. Heating distribution along windward symmetry plane of Space Shuttle Orbiter at
34.8 of angle of attack, M =9.15, and 47.7km altitude.


6






06.20 0------------.6 0.8
A present results
5 o data ofRef 9

4

3 0






0 0.2 0.4 0.6 0.8 1
Normalized Arc Length

Figure 2-9. Comparison of surface pressure distributions around the X-24C fuselage at the
farthest downstream station.


-- present results (the flat plate
reference enthalpy method)
-- present results (the blunt
bodies solutions)
o flight data (Ref 12)




















-3.5

-4


-4.5

-;


Normalized Arc Length


Figure 2-10. Comparison of heat transfer around the X-24C fuselage at the farthest downstream
station.


IL
-- windward
10
10 leeward

8 A data ofRef 9 (windward)

S6 o data of Ref 9 (leeward)

4
A A A A A A A A

0 0 -


0 30 60 90 120 150
x/Rn


Figure 2-11. Comparison of streamwise surface pressure distribution along the windward and
leeward symmetry lines of the X-24C.


0.2 0.4 0.6 0.8

0 0 0
o o O O O

o
0 /
000


I- present results
o data ofRef 9 & 10









CHAPTER 3
MASS INJECTION EFFECTS

Introduction

Reducing skin friction and heat transfer is one of the most challenging areas of research in

hypersonic aerodynamics. Attention has been focused on surface suction to delay transition to

the turbulent flow region which produces relatively large skin friction. However, even a very

small protuberance can cause laminar flow to transition into turbulent flow. Also, laminar flow is

more susceptible to flow separation than turbulent flow. Therefore this technique of using

suction still remains in the research stage. One of the drag reduction methods that has been

ignored is surface mass injection because researchers believed that the penalty associated with

mass injection is very large because of the susceptibility of flow separation. Despite this

shortcoming, many experiments were conducted in 1970's on mass injection on a flat plate with

no pressure gradient. It was well established that mass injection significantly reduced skin

friction with respect to the skin friction of the same porous plate with no injection.13

Thus far in the present study we have discussed only boundary layers for which the normal

component of velocity at the surface, v, is zero. Nonzero values of v, can occur if the wall is

porous and mass is injected into the boundary layer. Mass injection from the surface is one of

several cooling methods for protecting the surface from an extremely high-temperature stream. It

is assumed that the boundary layer over the body is turbulent everywhere in order to maintain a

conservative evaluation of the heating load. In addition, the transition location is not known even

for the zero injection case, so to be consistent we have focused on purely turbulent flow.

Dominant parameters are angle of attack and ratio of the mass flow rate of the cooling gas to air

of free stream.









Effects of Mass Injection on the Boundary Layer

In order to examine the effect of injecting gas into the boundary layer, we use reviews of

the effects of transpiration on the turbulent boundary layer presented by Kays and Crawford.14

They introduced a simple algebraic Couette flow solution which has the virtue of fitting the

additional experimental data. The effect of porous surface injection on Stanton number and skin

friction coefficient at the same Reynolds number based on distance s are described as follows:

St ln( + B) (3-1)
St, B,

cf ln(1+Bf) (3-2)
(3-2)
cf, Bf

where


Bh Pww/eUe (3-3)
St

B, =P Pv/Pe (3-4)
cf/2

In the above equations, p, is the density of injected gas, and vis the normal velocity

component at the surface. The subscript 0 refers to the case with zero injection, that is, Bh = 0

and Bf = 0. Because of the implicit nature of such equations, it is frequently more convenient to

use other blowing parameters than Bh and Bf, such as:


bh = Pv Pe/P (3-5)
Sto

b, =P Pe e (3-6)
Cf,o/2

We find that bh = ln(1 + B) and bf = ln(1 + B), and then


St_ bh (3-7)
Sto ebh 1
Cf bf (3-8)
f,o ebf -1









If comparison is made at the same Reynolds number based on streamwise distance s for the

case of constant free-stream velocity, the above equations fit the experimental data remarkably

well. The Nusselt number is related to the Stanton number as follows:


St= Pre Nu (3-9)
Res,e

where Pre and Res,e are constant at the same location (or in our case panel) for any values of Bh

and bh, so the Couette flow analysis above can be developed in the same manner for the Nusselt

number as for the Stanton number.

Nu ln(1+Bh) bh
Nuo Bh ebh -1

From Eq.(2-23) and Eq.(2-24), the convective heat transfer at the wall can be found to be


qC,w =-h ,,,0 (3-11)
eh -1

Eq.(3-1 1) is to be evaluated at the same k,, T,, and T0w for injected and non-injected

cases.

A limiting case occurs for large values of blowing when the friction coefficient tends to

zero and boundary layer is literally blown off the surface, an occurrence similar to the separation

of a boundary layer in an adverse pressure gradient. Two commonly used rules of thumb for

"blow-off" are as follows: if pvw/Peue = 0.01 and/or bf =4.0, then is safe to assume that "blow-

off" has occurred.

General Behavior of Reducing Skin Friction and Heating

Unlike hypersonic gliders such as Space Shuttle Orbiter, hypersonic cruising vehicles have

relatively slender bodies and fly at low angles of attack. Therefore, here we consider only low

angles of attack in which skin friction effects on flight performance are more pronounced than at









high angles of attack. In order to illustrate the general effects of mass injection, the case of a flat

plate in hypersonic flight is briefly discussed, in which, without loss in generality, we neglect

forces acting on the upper surface. Figure 3-1 shows the effects of mass injection on the lift to

drag ratio by plotting (L/D),cooed(LD)o with different angle of attack. (L/D)coo.ed is L/D with

some mass injection, and (L/D)o is the LID ratio without any mass injection. Figure 3-2 shows

the effects of mass injection on the heat transfer on the surface by show qcooid /q as a function

of mass injection for different angles of attack here. qcooied is heat transfer with some mass

injection, and q0 is the heat transfer without any mass injection.

In general, the lower a is, the more mass injection reduces skin friction and protects the

surface from heating, and even a small amount of injected mass is effective to improve flight

performance. Figure 3-1 and 3-2 show that merely increasing the amount of injection for

reducing skin friction and heat transfer is not very effective because the improvement of L/D

and the reduction in q are more pronounced for small amounts of injection. Also, the beneficial

effects of injection are larger for lower a than for higher a.



2 deg
2 1.8 e 4 deg-
6-- 6 deg
1.6 8 deg
-o- 10 deg
8 1.4

p1.2 X X X

1
0 0.05 0.1 0.15 0.2 0.25 0.3
mass injection (kg/m2-s)

Figure 3-1. Effects of mass injection on L/D with different angle of attack for a flat plate
(6m x 6m square plate) at a Mach number of 6.























0.05


1 0.15 0.:
mass injection (kg/m2-s)


0.25


Figure 3-2. Effects of mass injection on heat transfer with angle of attack for a flat plate
(6m x 6m square plate) at a Mach number of 6.


22 deg
44 deg
~-6 deg
~t8 deg
S10 deg









CHAPTER 4
RESULTS

Introduction

In the preceding chapters, we discussed inviscid flow, viscous flow, and reducing skin

friction and heat transfer on a hypersonic cruising vehicle by using mass injection and

established a theory for finding flow properties whether or not we use mass injection. In this

chapter, we show the advantages and penalties associated with the mass injection cooling

method. The coolant injected may be a part of the total fuel load or different material (but a gas)

from the fuel. In both cases, the critical parameter in analyzing the reduction of skin friction and

heat transfer as discussed in the previous chapter is the injected mass flux pv, and therefore the

density of the coolant (p ) and the velocity of the coolant (v ) are not individually important. In

this chapter, "fuel" is defined as the fuel used only for producing thrust, and "coolant" is defined

as the material (although it may be the same material as the fuel) to be injected through portions

the vehicle's surface to reduce viscous and heating effects. In order to evaluate the advantages

and penalties of mass injection, the total mass of fuel and coolant consumed is kept constant no

matter how much coolant is injected. For instance, if the total mass of the fuel and the coolant

consumed is set to 100kg and the mass of the coolant is 10kg, then the mass of the fuel is 90kg. If

the mass of the coolant is increased to 20kg, then the mass of the fuel is 80kg. Our perspective is

that injecting mass (coolant) from the vehicle's surface reduces viscous effects, reducing the heat

transfer on the surface (advantage) even though it may decrease the flight range (or flight time)

since the amount of the fuel used for the thrust is decreased (penalty).

The Range Equation

One of important performance metrics for cruising aircraft is the flight range, the total

distance that an aircraft can travel on a given amount of fuel. Simple flight behavior is assumed









so that the thrust vector is assumed to be aligned with the flight path and the flight path angle, the

angle between the flight trajectory and the local horizontal, is very small. For equilibrium flight

we have the following relations:

F, =D (4-1)
L=W (4-2)

where F, is thrust and W is weight of the vehicle. The rate at which the fuel and the coolant are

consumed in quasi-steady flight is the summation of the weight flow rate of fuel used to produce

the needed thrust and the weight flow rate of the coolant injected from the surface.[16] This may

be written as follows:

dW dWo d w + C,
dW dWconsumed dC FT (p.v g)Acooled (4-3)
dt dt dt 3600

where WfV, is weight of the fuel, Wcooa,, is weight of the coolant, and Acooled is total area to be

cooled by injection. The quantity C, is the specific fuel consumption and may also be written as

3600
I' (4-4)
C.

where IJ is the specific impulse, measured in thrust produced per unit weight of fuel consumed

per unit time. Now Eq.(4-3) becomes

dW F W
dt in, Acooled L- A njAcooled (4-5)


where w,, = pvwg Therefore, Eq.(4-5) is written as

dW
dt = (4-6)

I (L D) "AJ cooled









The horizontal speed V. = dx/dt, so Eq.(4-6) may be integrated from the initial time to the

final time, assuming that Ip, L/D, and wjAcooled are constant, as follows:

W finl
tfinj R R dW finIn mn Acooled + (+ D) W
f d =v f = R f- W d ( p ( LID) (4-7)
t-1-d 0 n. t ci Wvi, Acooled
i; D s(L D) r(LD) 't

+A final
L dW 1AWnj'.cooled + (LD7
Vootin = R = -I p L In Wp cool) (4-8)
Dua A | "rital
nj cooled + (LnaD)
4isp ID)

where tina is the flight time and R is the flight range. Here Wfina is the weight of the vehicle

after all the fuel and coolant are consumed during the cruising flight and W,,,,, is the weight of

the vehicle when carrying full fuel and full coolant. Eq.(4-8) is used to find the flight range

starting with a constant initial amount of fuel and coolant. Note that no matter how much coolant

is used for surface injection, Eq.(4-8) gives the flight range or flight time with the given amount

of fuel and coolant being completely consumed. As already discussed, L/D depends on both w,,

and Acooled. The weight of the vehicle before it uses any fuel and coolant, Wn,,,~ is set to:


Wt'al = L, = CL,0 2 yP M 2Sef (4-9)

where CL, is the lift coefficient without mass injection. The total weight of the fuel and the

coolant is:

Wnital Wfina = Wiue + Wcoolant (4-10)

Comparison of Range, L /D, and Heat Transfer Variance

Since we have already established methods to find the aerodynamic forces including skin

friction, heat transfer, effects of mass injection, and flight range for hypersonic flow. We are now









ready to show the advantages and penalties arising from injecting mass through the surface of a

hypersonic cruising vehicle. In this study, the characteristic Reynolds number is used, and it is

defined as: Rehar, = pV lpu Our theories were applied to an X-24C vehicle assumed to be

flying at Mach number of 6.00 with angle of attack of 6 at 30000m (Rehar = 2.21x106 /m and

q = 29500Pa) altitude and 35000m (Reh,, = 9.95 x 105 /m and q = 14000Pa) altitude. The surface

temperature is assumed to be constant with or without injection. For the case at which we do not

use mass injection, some unspecified internal cooling system may accomplish constant surface

temperature assumption by absorbing the thermal power. For injected surface, surface

temperature may remain constant temperature of coolant that is being injected through the panel

surface. The fuel used here is assumed to be hydrocarbon, with I = 1000s The material injected

through the surface of vehicle is not specified, but it is at least a gas. Wfin, is the weight of the

vehicle after 100s of cruising flight with zero mass injection. Therefore, Eq.(4-8) provides the

flight time for which the aircraft can cruise when the total amount of the fuel and coolant is the

same as Wi,,a Wina whether or not we use mass injection.

Injecting on the windward panels on the forward section of the fuselage, where q,, is

relatively high, reduces heat transfer with a small rate of mass injection. However, each of these

individual panels has a relatively high angle of attack with respect to the free stream direction,

therefore the effect of mass injection may be relatively smaller than other panels in reducing

drag. Cooling aft panels, where qc,, is relatively low, reduces heat transfer less effectively, and

the required mass injection rate is relatively large. However, each of these panel's angle of attack

is lower than the ones of the forward panels, and each has a large area, so it is not simple to

choose the panels to be cooled so that the mass is used most effectively.









Therefore, the panels to be cooled were determined by two aspects of the heat transfer

experienced by each panel: the thermal power transfer, Qc, (W), and the heat flux, q,,w (W / m2).

Around the nose of body and the leading edge of the wings, each panel has relatively high q ,,,

but low Qe, because of the small area of the individual panels. On the other hand, the aft panels

have low q,, but high Q, since each panel has relatively large area.

Figure 4-1 shows the distribution of panel area as a function of the panel's heat transfer,

q,, (W/m2) at M = 6 and 30000m altitude for no injection. The total area of panels whose

uncooled heat transfer qc,, is between 0 and 5000 W/m2 is slightly larger than 25 m2, and there

is 35 m2 area of panels that have uncooled q,, between 5000 and 10000 W/m2. Figure 16 is

slightly different as it shows the distribution of the number of panel as a function of the panel's

uncooled heat transfer, q,,w (W/m2) at M = 6 and 30000m altitude. For example, there are 14

panels whose uncooled heat transfer q,, is between 0 and 5000 W/m2, while there are over 50

panels with uncooled q,, >100000W/m2.

Figures 4-3 to 4-5 show the effect of mass injection on the flight time, and therefore the

range, L/D, and reduction of heat power (normalized heat power), respectively at M = 6 and

30000m altitude. Normalized heat power is defined as Q/Qo. Q is heat power absorbed by all

panels when we do not use any mass injection, and Q is heat power absorbed by all panels with

mass injection. When thm, is zero, Q= Qo. The panels to be cooled are determined by the heat

transfer, qc,, experienced by the individual panels without injection. As we increase the rate of

mass injection, the flight range decreases and this effect is more pronounced for cases in which

there is a larger area to be cooled. As discussed in the previous chapter, mass injection reduces









skin friction and heat transfer. Therefore, we get an advantage in reducing the heat transfer but

with the penalty of decreasing flight range.

For instance, consider the case of a mass injection rate of 0.005 kg /m2s atM = 6 and

30000m altitude. Figure 4-3 shows that the flight time is 85.16s when all panels are cooled by the

selected mass injection rate of 0.005 kg/m2s The flight time is 89.97s when only the panels that

have q,,w of more than 10000W/m2 are cooled by the selected mass injection rate of

0.005 kg/m2s Figure 4-4 shows that L/D is 1.245 when all panels are cooled by the mass

injection rate of 0.005 kg /m2s and L/D is 1.236 when only the panels that have q,,w of more

than 30000 W/m2 are cooled by the mass injection rate of 0.005kg/m2s Figure 4-5 shows that

normalized heat power is 0.8936 when all panels are cooled by the mass injection rate of

0.005kg/m2s However, the normalized heat power is 0.9517 when the panels that have q,,, of

more than 50000 W/m2 are cooled by the mass injection rate of 0.005 kg/m2s .

Before Figures 4-6 to 4-11 are discussed, two normalized parameters: normalized injected

mass and normalized reduction of heat power are introduced. Normalized injected mass is

defined as:

SmjA cooled Acooled (4-11)
injAtotal Atotal

where thn is the rate of mass injected and Ao,,, is the total surface area of the vehicle.

Normalized reduction of heat power is defined as:


Q =Q- (4-12)
Q0

In order to show more details of the advantages and penalties associated with mass

injection, Figures 4-6 to 4-11 show the relation between injected mass, reduction of heating, and









reduction of flight range at the relatively low mass injection rate of 0.001 kg/m2s Figures 4-12

to 4-17 show results at mass injection rate an order of magnitude greater, i.e. 0.01 kg/m2s .

For instance, the case of mass injection rate of 0.001 kg/m2s at M = 6 and 30000m altitude

is introduced. Figure 4-6 shows that normalized reduction of heat power is 0.02091 when

normalized injected mass is 0.8482 and when the panels that have q,,w of more than 5000 W/m2

are cooled by the mass injection rate of 0.001 kg/m2s Figure 4-7 shows that the flight time is

97.14s when normalized injected mass is 0.8482 and when the panels that have q,, of more than

5000 W/m2 are cooled by the mass injection rate of 0.001 kg/m2s Figure 4-8 shows that the

flight time is 97.14s when normalized reduction of heat power is 0.02091 and when the panels

that have q,,w of more than 5000 W/m2 are cooled by the mass injection rate of 0.001 kg/m2s .

Figure 4-9 shows that reduction of heat power is 71.46kWwhen injected mass rate is

0.1427kg / s and when the panels that have q,,w of more than 5000 W/m2 are cooled by the mass

injection rate of 0.001 kg/ m2s Figure 4-10 shows that reduction of heat energy is 16700kJ when

injected mass is 13.86kg and when the panels that have q,,w of more than 5000 W/m2 are cooled

by the mass injection rate of 0.001 kg /m2s Figure 4-11 shows that flight time is 97.14s when

reduction of heat energy is 16700kJ and when the panels that have q,,, of more than 5000 W/m2

are cooled by the mass injection rate of 0.001 kg/m2s .

Figures 4-6 and 4-12 show the effect of normalized injected mass on normalized reduction

of heat power. Figures 4-7 and 4-13 show the effect of normalized injected mass on the flight

time, while Figures 4-8 and 4-14 show the effect of normalized reduction of heat power on the

flight time. Figures 4-9 and 4-15 show the effect of injected mass rate on the reduction of heat









power. The effect of injected mass on the reduction of heat energy is shown in Figures 4-10 and

4-16. Finally, Figure 4-11 and 4-17 show the advantage (reduction of heat transfer) we have for

the penalty (reduction of flight time). The data labels attached to the lines are the allowable heat

transfer, qc,, of the panels. For instance, a data label, "50000 Wi?2 means that all panels

whose heat transfer is above 50000 W/m2 (the allowable heat transfer) are cooled by mass

injection.

Figures 4-6 and 4-12 show a concave downward curve, which indicates that choosing the

highly heated panels for cooling reduces total heat transfer more effectively than cooling all

panels. Figures 4-7 and 4-13 show an almost linear relation between normalized mass and flight

time. Therefore, as more mass injected, the more the flight time (therefore flight range) decreases

at an almost constant rate. Figures 4-8 and 4-14 show a concave downward curve relation

between reduction of heat power and flight time. Thus, injecting on too many panels is

increasingly apt to decrease flight time. Figures 4-9 and 4-15 show the actual reduction in heat

power with various mass injection rates (kg /s). Figures 4-10 and 4-16 show the reduction in

heat energy with various mass injection (kg). These figures give a slightly concave downward

relation between the reduction of heat energy and the mass injection. Figures 4-11 and 4-17 give

a slightly concave downward curve. Again, this indicates that cooling only panels whose heat

transfer, qc,, is relatively high gives the most effective advantage (reduction of heat transfer) by

mass injection.

Figures 4-18 to 4-20 show the X-24C vehicle whose panels are to be cooled if the heat

transfer qc,, is more than 50000 W/n2 at M = 6 and 30000m altitude. The shadings (red panels)

are the panels cooled. In general, the nose, the vertical fin, and the leading edges of the wing and

the off-center fin have high q ,,. The bottom panels also have high heat absorption. The panels









around the nose of the fuselage and the leading edge of the wings have the highest heat

absorption.

Figures 4-21 to 4-40 are analogous to Figures 4-1 to 4-20. They are at the exactly same

conditions except for that the panels to be cooled are determined by heat power, Qc,w of

individual panels in Figures 4-21 to 4-40. Also, Figure 4-41 to 4-60 are analogous to Figures 4-1

to 4-20. Figures 4-41 to 4-60 are results for M = 6 and 35000m altitude, and the cooled panels

are chosen by heat transfer, qc,w of the individual panel. Finally, Figures 4-61 to 4-80 are also

analogous to Figures 4-1 to 4-20. Figures 4-41 to 4-80 are results for M = 6 and 35000m altitude,

and the panels to be cooled are determined by the heat power, Qe, of individual panels.

Figures 4-23 to 37 show results very similar to those of Figures 4-3 to 4-17. There is little

of difference to note within difference between Figures 4-3 to 4-17 and 4-23 to 4-37. Therefore,

whether we choose the panels to be cooled by taking those with the higher heat transfer, q,,, or

the higher heat power, Q, of individual panels, cooling only some of the highest heated panels

gives the most effective advantage. Figures 4-38 to 4-40 show that we have panels whose heat

power is higher in the aft portion of the vehicle although the front panels have the higher heat

transfer, q, ,. This is because aft panels have larger area, and the heat power Qcw absorbed by

each panel is defined as q,, dA.

Figures 4-43 to 4-57 also show the same behavior as Figures 4-3 to 4-17. Comparing

Figures 4-6, 4-7, 4-12 and 4-13 and Figures 4-46, 4-47, 4-52, and 4-53, we find that the effect of

mass injection (normalized injected mass) on reducing flight time and heat transfer (normalized

reduction of heat power) is larger for the case at 35000m altitude. Comparing Figure 4-48 and 4-

54 with Figure 4-8 and 4-14, the same value of normalized reduction of heat power gives slightly









greater reduction in flight time at 35000m altitude. This is because of lower dynamic pressure at

higher altitude. Comparing Figures 4-9, 4-10, 4-15, and 4-16 and Figures 4-49, 4-50, 4-55, and

4-56, it is found that the effect of mass injection on the reduction of heat power and heat energy

is slightly larger at 35000m altitude or almost same for both cases. This argument may look as if

it conflicts with the comparison of Figures 4-6 and 4-46, but this is because the total heat power

and heat energy absorbed by the vehicle are larger for the case at 30000m than the case at

35000m.

Figures 4-63 to 4-77 show similar behavior and values to those of Figures 4-43 to 4-57 and

we have seen that Figures 4-23 to 4-37 do not change much from Figures 4-3 to 4-17. In general,

choosing the panels to be cooled by taking the higher heat transfer, qc, gives more effective

advantage (reduction of heat transfer) than by taking the higher heat power, Q, of individual

panel. However, the X-24C has the highest qc,, around the nose where the panels have relatively

high angle of attack. On the other hand, the aft panels have the highest QC, and relatively low

angle of attack. The effect of mass injection on reducing heat transfer and increasing L/D is

generally more pronounced at the panels whose angle of attack is low as we have seen in figure

3-1 and 3-2. Therefore, for the X-24C there is not much difference results between choosing the

panels by using qc, and Q, of each panels. As a brief result, table 4-1 shows comparison of

critical flight parameters for various mass onjection rate.

One of the parameters that indicates how the vehicle is slender (or "fat") is the volume-

surface parameter, r defined as:

V2/3
V=- (4-13)
S









where V is the volume of the vehicle, and S is the spanwise area of the vehicle. The smaller r

is, the more slender the vehicle. For the X-24C aircraft, r = 0.18 which is relatively high value

for a cruising vehicle. A more slender body would have a higher L/D than the X-24C because the

contribution of aerodynamic forces caused by pressure is smaller. The fraction of skin friction

force in total drag force is therefore larger, which makes the increment of L/D by mass injection

larger. Therefore, it is expected that reduction of flight range by mass injection decreases or that

flight time increases for a more slender body.

Table 4-1. Comparison of flight parameters at M = 6 and 30000m altitude. The panels that have
qc, of more than 50000 W/m2 are cooled by the mass injection rate: 0, 0.001,
0.01 (kg/m2s).
Parameter 0(kg/m2s) 0.001 (kg/m2s) 0.010(kg/ m2s)
final (s) 100.0 96.65 74.04
L/D 1.225 1.227 1.240
Q/Qo 1.000 0.990 0.906
Acooled /Atota 0.000 0.3634 0.3634
reduction of heat power (kW) 0.000 33.76 320.8
reduction of heat energy (MJ) 0.000 7.585 66.851
W ,el (kg) 442.7 436.8 397.4
Wolant (kg) 0.000 5.909 45.27


40
35
30
25
20
15
10






panels' heat transfer (W/m2) range

Figure 4-1. Distribution of panel area with a given heat transfer, q,, (W/m2) at M = 6 and
30000m altitude.












C)
Cl
c)
C)


60
50
40
30
20
10
0 ii Bil 1.


panels' heat transfer (W/m2) range


Figure 4-2. Distribution of the number of panels with a given heat transfer, q w (W/m2) at M= 6
and 30000m altitude.



100


95


85


80


75


70


0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
mass injection rate (kg/m2-s)



Figure 4-3. Mass injection effect on the flight time at M = 6 and 30000m altitude. The panels to
be cooled are determined by q,,, (W/m2).


-o- all panels are cooled (168.244m2)
- 5000W/m2 and more (142.7m2)

- 10000W/m2 and more (108m2)
- 30000W/m2 and more (88.719m2)
-- 50000W/m2 and more (61.143m2)











1.27


1.26 10000W/m2 and more (108m2)

-- 30000W/m2 and more (88.719m2)
1.25 -- 5000W/m2 and more (61.143m2)


1.24


1.23


1.22
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
mass injection rate (kg/m2-s)


Figure 4-4. Mass injection effect on L/D at M = 6 and 30000m altitude. The panels to be cooled
are determined by qc, (W m2).


1
0.98
0.96
0.94
0.92
0.9
0.88
0.86
0.84
0.82
0.8


-o-all panels are cooled (168.244m2)
-- 5000W/m2 and more (142.7m2)
-e- 1000W/m2 and more (108m2)
-- 30000W/m2 and more (88.719m2)
-- 50000W/m2 and more (61.143m2)


0 0.001 0.002 0.003 0.004 0.005 0.006 0.007
mass injection rate (kg/m2-s)


0.008 0.009 0.01


Figure 4-5. Mass injection effect on reduction of heat power at M = 6 and 30000m altitude. The
panels to be cooled are determined by q,,, (W/m2).











0.025pane
0.02 5000W
S05000W/m2
-5 s 0.015
N 0 3000W/m2
S0.01
g 50000W/m2
0.005


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
normalized injected mass


Figure 4-6. Normalized reduction of heat power v.s. normalized injected mass at M = 6 and
30000m altitude with 0.001 kg/m2 s of mass injection. The panels to be cooled are
determined by qc,W (W/m2).


100

99
o 50000W!/
98 ---37 vvOO;OOW /m2-- -----.....
98 105000W/m2
E 97
all pane
96
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
normalized injected mass


Figure 4-7. Flight time v.s. normalized injected mass at at M = 6 and 30000m altitude with
0.001 kg/m2 s of mass injection. The panels to be cooled are determined by
qc,. (WIm2).











100


.~ 98

97

96


0 0.005 0.01 0.015 0.02 0.025
normalized reduction of heat power


Figure 4-8. Flight time v.s. normalized reduction of heat power at M = 6 and 30000m altitude
with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined by
qc, (WIm2).


100
80

60

40

20
0


0 0.02 0.04 0.06 0.08


0.1 0.12 0.14 0.16 0.18


injected mass rate (kg/s)


Figure 4-9. Reduction of heat power (kW) v.s. injected mass rate (kg/s) at M = 6 and 30000m
altitude with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined
by q,,.(W/m2).


50000W/m2
I10000W/m2
~- 5000W/m2

all panels


all panels

__--__0_10000W-- OW
W/m2OOOOW/m2











S20000

" 15000

S10000

= 5000

0
0 0


all panels


OOOOW/m2
0 2-4-68 .00 W 2 141618
2 4 610 2OOW/m2




0 2 4 6 8 10 12 14 16 18


injected mass (kg)


Figure 4-10. Reduction of heat energy (kJ) v.s. injected mass (kg) at M = 6 and 30000m altitude
with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined by

q,w (W/m2).


100

99 50000W/m2
_-3o 0 30000W/m2
98 1 OOOOW/m2
S--10000 5000W/m2
97
all panels


0 2000 4000 6000


8000 10000 12000 14000 16000 18000 20000
reduction of heat energy (kJ)


Figure 4-11. Flight time v.s. reduction of heat energy (kJ) at M = 6 and 30000m altitude with
0.001 kg/m2 s of mass injection. The panels to be cooled are determined by
q,,. (W/m2).













S0.15 a-. oow, 2
S|,--30000W/m2
P a0.15

00 O050000W/m2
0.0 05

0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
normalized injected mass


Figure 4-12. Normalized reduction of heat power v.s. normalized injected mass at M = 6 and
30000m altitude with 0.01 kg/m2 s of mass injection. The panels to be cooled are
determined by qc, ( W/m2).


100
95
90
S85 5 000)0W!W
o 3 0000 7m2^l 0000W/m2
80
75
70 ,allf panel
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
normalized injected mass


Figure 4-13. Flight time v.s. normalized injected mass at at M = 6 and 30000m altitude with
0.01 kg/m2 s of mass injection. The panels to be cooled are determined by
q,.(W/m2).











100
95
90
S85000(
85 3000 0000W/m2

75 500
70 all panels
0 0.05 0.1 0.15 0.2
normalized reduction of heat power


Figure 4-14. Flight time v.s. normalized reduction of heat power at M = 6 and 30000m altitude
with 0.01 kg /m2 s of mass injection. The panels to be cooled are determined by

qc, (W/m2).


S800
7 all panels
S600 ---"m2W/

S400000
S00 50000W/m2
a 200 /n-

0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
injected mass rate (kg/s)


Figure 4-15. Reduction of heat power (kW) v.s. injected mass rate (kg/s) at M = 6 and 30000m
altitude with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined
by q,,.(W/m2).










51 1all panels
S140000 5000W/m2-
o 120000 00 m
S100000 .O
a, 80 0 -------------^ ^ O W /m ?-------
80000
0000 OOOOW/m2
60000
40000
20000
0
| 0 l 10-------
0 10 20 30 40 50 60 70 80 90 100 110 120 130
injected mass (kg)


Figure 4-16. Reduction of heat energy (kJ) v.s. injected mass (kg) at M = 6 and 30000m altitude
with 0.01 kg /2 s of mass injection. The panels to be cooled are determined by

qc, (WIm2).


100
95
90 50000W/m2
S 085 30000W/m2
80 0000W/m2
75 5000W
70 allpane
0 20000 40000 60000 80000 100000 120000 140000
reduction of heat energy (kJ)


Figure 4-17. Flight time v.s. reduction of heat energy (kJ) at M = 6 and 30000m altitude with
0.01 kg/m2 s of mass injection. The panels to be cooled are determined by
q,. (W/m2).












Figure 4-18. Bottom view of X24C with 50000 W/m2 of allowable q,,w at 30000m altitude.





Figure 4-19. Side view of X24C with 50000 W/m2 of allowable q,, at 30000m altitude.


Figure 4-20. Top view of X24C with 50000 W/m2 of allowable q,,, at 30000m altitude.


"qqq%











60
50
R 40
30
t 20
10
0
60 S-----------------------------------------------








panels' heat transfer (W) range

Figure 4-21. Distribution of panel area with a given heat transfer, Q~ (W) at M= 6 and
30000m altitude.


100
80
60
40
S20






panels' heat transfer (W) range



Figure 4-22. Distribution of the number of panels with a given heat transfer, Qe, (W) at M = 6
and 30000m altitude.




























0 0.001 0.002 0.003 0.004 0.005 0.006
mass injection rate (kg/m2-s)


0.007 0.008


0.009 0.01


Figure 4-23. Mass injection effect on the flight time at M = 6 and 30000m altitude. The panels to
be cooled are determined by Qc, (W).


1.27
-o-all panels are cooled (168.244m2)
-a- 10000W and more (102.13m2)
1.26 -e- 20000W and more (86.749m2)
-- 30000W and more (67.747m2)
-x- 40000W and more (61.202m2)
1.25


1.24


1.23


1.22
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
mass injection rate (kg/m2-s)


Figure 4-24. Mass injection effect on L/D at M = 6 and 30000m altitude. The panels to be
cooled are determined by Qc, (W).


-o-all panels are cooled (168.244m2)
-- 10000W and more (102.13m2)
--- 20000W and more (86.749m2)
-- 3000W and more (67.747m2)
- 40000W and more (61.202m2)











1
0.98
0.96
g 0.94
S0.92
0.9
0.88 -0-allpanels are cooled (168.244m2)
S .86 10000W and more (102.13m2)
0.86
0.8 -e- 20000W and more (86.749m2)

-0.82 30000W and more (67.747m2)
0.82
x- 40000W and more (61.202m2)
0.8
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
mass injection rate (kg/m2-s)


Figure 4-25. Mass injection effect on reduction of heat power at M = 6 and 30000m altitude. The
panels to be cooled are determined by Q, (W).


0.025pane

I 0.02

0. 0.015
30000W 0W10000W
0.01 0.0
S40000W
S0.005

0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
normalized injected mass


Figure 4-26. Normalized reduction of heat power v.s. normalized injected mass at M = 6 and
30000m altitude with 0.001 kg/m2 s of mass injection. The panels to be cooled are
determined by Q, (W).










100
99.5 5 0
S50000W
99
S98.5 30000 WV10000W
98
S97.5
97
96.5 all pane
96
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
normalized injected mass


Figure 4-27. Flight time v.s. normalized injected mass at M = 6 and 30000m altitude with
0.001 kg/m2 s of mass injection. The panels to be cooled are determined by Qw (W).



100
99.5
99
S98.5 40000 0000W
S 98 30000 10000W
S 97.5
S97
96.5 all panels
96
0 0.005 0.01 0.015 0.02 0.025
normalized reduction of heat power


Figure 4-28. Flight time v.s. normalized reduction of heat power at M = 6 and 30000m altitude
with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined by Qc
(W).










100

g 80

o 60

I 40
4.
S20

O 0


0.12 0.14 0.16 0.18


Figure 4-29. Reduction of heat power (kW) v.s. injected mass rate (kg/s) at M = 6 and 30000m
altitude with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined
by Q, (W).


20000

15000

S10000

o 5000

0
C)


all panels

f o oooow
------------------- -- O OO W---------
^30000W
04 40000W



0 2 4 6 8 10 12 14 16 18


injected mass (kg)


Figure 4-30. Reduction of heat energy (kJ) v.s. injected mass (kg) at M = 6 and 30000m altitude
with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined by Qc,
(W).


0 0.02 0.04 0.06 0.08 0.1
injected mass rate (kg/s)


all panels




3000OW
40000W










100
99.5
940000W
99
^* _4 30000W
o 98.5 000 0000W
98 10000W
-. 97.5
2 97
96.5 al panels
96
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
reduction of heat energy (kJ)


Figure 4-31. Flight time v.s. reduction of heat energy (kJ) at M = 6 and 30000m altitude with
0.001 kg/m2 s of mass injection. The panels to be cooled are determined by c, (W).


0.2

0.15

S0.1

0.05
C


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
normalized injected mass


Figure 4-32. Normalized reduction of heat power v.s. normalized injected mass at M = 6 and
30000m altitude with 0.01 kg/m2 s of mass injection. The panels to be cooled are
determined by Qc, (W).


10000W
30000W 20000W

4--- 0000W










100
95
90
90 40000 0 20000W
S85 0000-2000OWMO
80
75
70 all_ panel
70
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
normalized injected mass


Figure 4-33. Flight time v.s. normalized injected mass at M = 6 and 30000m altitude with
0.01 kg/m2 s of mass injection. The panels to be cooled are determined by Ocw (W).



100
95
9040000
0 40000 20000W
85 W10000W
80
75
70 ,all pa els
0 0.05 0.1 0.15 0.2
normalized reduction of heat power


Figure 4-34. Flight time v.s. normalized reduction of heat power at M = 6 and 30000m altitude
with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined by O,
(W).










800
700
600
S500
S400
S 300
200
S100
0


0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8


injected mass rate (kg/s)


Figure 4-35. Reduction of heat power (kW) v.s. injected mass rate (kg/s) at M = 6 and 30000m
altitude with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined
by Q, (W).


140000
120000
100000
80000
60000
40000
20000
0


0 10 20 30 40 50 60 70 80 90 100 110 120 130
injected mass (kg)


Figure 4-36. Reduction of heat energy (kJ) v.s. injected mass (kg) at M = 6 and 30000m altitude
with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined by Oc
(W).


all panels


20000W
0000W
40000W










100
95
90 40000W
^85 7 00W20000W
85
80 -
75
70 all pane


20000


40000


60000


80000 100000 120000 140000


reduction of heat energy (kJ)


Figure 4-37. Flight time v.s. reduction of heat energy (kJ) at M = 6 and 30000m altitude with
0.01 kg/m2 s of mass injection. The panels to be cooled are determined by Qw (W).


Figure 4-38. Bottom view of X-24C with 40000 W of allowable Q,w at M = 6 and 30000m
altitude.


Figure 4-39. Side view of X-24C with 40000 W of allowable Q,, at M = 6 and 30000m altitude.























Figure 4-40. Top view of X-24C with 40000W of allowable Q, at M = 6 and 30000m altitude.


45
40
35
30
S25
20
15
10
5
0


panels' heat transfer (W/m2) range


Figure 4-41. Distribution of panel area with a given heat transfer, qc,w (W/m2) at M = 6 and
35000m altitude.


40
S35
30
25
S20
15
10
5
0



oz C^ W Ce ^ WP bs WP CY^ W W Ce; e 'o
panels' heat transfer (W/m2) range



Figure 4-42. Distribution of the number of panels with a given heat transfer, q,,, (W/m2) at
M = 6 and 35000m altitude.


Eu EE~


'00











100

95
90

85
80

75
70
S -o- all panels are cooled (168.244m2)
65 5000W/m2 and more (126.79m2)
60 -e- 10000W/m2 and more (104.3m2)
-a- 20000W/m2 and more (84.58m2)
x- 30000W/m2 and more (57.119m2)
50
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01

mass injection rate (kg/m2-s)


Figure 4-43. Mass injection effect on the flight time at M = 6 and 35000m altitude. The panels to
be cooled are determined by qc, (W/m2).


1.26

1.25

1.24

1.23

1.22

1.21

1.2

1.19

1.18


0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01

mass injection rate (kg/m2-s)



Figure 4-44. Mass injection effect on L/D at M = 6 and 35000m altitude. The panels to be
cooled are determined by qc, (W /m2 ).


- all panels are cooled (I 68.244m2)
ia 500OW/m2 and more (126.79m2)
e IOOOOW/m2 and more (104.3m2)
6- 2000OW/m2 and more (84.58m2)
xt 3000OW/m2 and more (57.119m2)











1

0.96

a 0.92

0.88

- 0.84
N
0.8

S0.76


0.72

n KQ


VJ.UO
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01

mass injection rate (kg/m2-s)

Figure 4-45. Mass injection effect on reduction of heat power at M = 6 and 35000m altitude. The
panels to be cooled are determined by qc, (W/m2).


0.05

0.04

3 0.03

2 0.02

0.01
C


0 0.1 0.2 0.3 0.4 0.5 0.6
normalized injected mass


0.7 0.8 0.9 1


Figure 4-46. Normalized reduction of heat power v.s. normalized injected mass at M = 6 and
35000m altitude with 0.001 kg/m2 s of mass injection. The panels to be cooled are
determined by qc, (W/m2).


-o-allpanels are cooled (168.244m2)
-- 5000W/m2 and more (126.79m2)
--10000W/m2 and more (104.3m2)
-- 20000W/m2 and more (84.58m2)
-x- 30000W/m2 and more (57.119m2)


all panelI
10000W/m2
50000m2
20000W/m2

30000W/m2










U.U3
o all panels
C.*- 0.04
10000W/m2 --
S0.03 00WA5000W/m2
0 o OOW/m2
2 0.03
S02 30000W/m2
0 '0.0 1


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
normalized injected mass

Figure 4-47. Flight time v.s. normalized injected mass at at M = 6 and 35000m altitude with
0.001 kg/m2 s of mass injection. The panels to be cooled are determined by

qc, (W/m2).


100
99
98
97 30000
S96 20000 WA 10000W/m2
95 *5000W/m2
95
94
93 all pane'
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045
normalized reduction of heat power

Figure 4-48. Flight time v.s. normalized reduction of heat power at M = 6 and 35000m altitude
with 0.001 kg /m2 s of mass injection. The panels to be cooled are determined by
q_. (W/m2).










100

80

S60

" 40

20

0


0 0.02 0.04 0.06 0.08 0.1
injected mass rate (kg/s)


0.12 0.14 0.16 0.18


Figure 4-49. Reduction of heat power (kW) v.s. injected mass rate (kg/s) at M = 6 and 35000m
altitude with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined
by q,, (W/m2).


S25000

S20000

15000

S10000

* 5000
0
C.


8 10 12 14
injected mass (kg)


Figure 4-50. Reduction of heat energy (kl) v.s. injected mass (kg) at M = 6 and 35000m altitude
with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined by
qc,. (WIm2).


all panels

m3000W/m2
--OW/m0000W/m2


3000OW/m2


all pane

OW/m2OW/m2
'~10000W/m2
O000W/m2
30000W/m2










100
99 --
S98 30000W/m2
9o 20000W/m2
7 10000W/m2
S9 5 OW2-~ 5000W/m2

94
93 allpa
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000
reduction of heat energy (kJ)


Figure 4-51. Flight time v.s. reduction of heat energy (kJ) at M = 6 and 35000m altitude with
0.001 kg/m2 s of mass injection. The panels to be cooled are determined by
qc, (W/m2).


0.4
o 0.35 allpanel
0.3

*^g0.25 ------------OOW200Wm-----------
0.25
~ 0.2 20000W/n2

Ca 0.1 30000W/m2
0.1
o 0.05
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
normalized injected mass


Figure 4-52. Normalized reduction of heat power v.s. normalized injected mass at M = 6 and
35000m altitude with 0.01 kg/m2 s of mass injection. The panels to be cooled are
determined by qc, (W/m2).










100 *


0 0.1 0.2 0.3 0.4 0.5 0.6
normalized injected mass


0.7 0.8 0.9 1


Figure 4-53. Flight time v.s. normalized injected mass at at M = 6 and 35000m altitude with
0.01 kg/m2 s of mass injection. The panels to be cooled are determined by

q, (Wm2).

I n O 0-------------------------


0.05


0.15 0.2
normalized reduction of heat power


0.25


0.35


Figure 4-54. Flight time v.s. normalized reduction of heat power at M = 6 and 35000m altitude
with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined by
q,,. (WIm2).


30000W/ n .. 000W
200010000W/m2

all20000W/m2 pan
all panel


30000W/m2
30000W 20000W 0000W/m2
50alaW/m2

all panels










700
600
S500
400
- 300
S200
* 100
S 0


0 0.2 0.4 0.6 0.8 1
injected mass rate (kg/s)


1.2 1.4 1.6 1.8


Figure 4-55. Reduction of heat power (kW) v.s. injected mass rate (kg/s) at M = 6 and 35000m
altitude with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined
by q,, (W/m2).


140000
120000
100000
80000
60000
40000
20000
0


0 10 20 30 40 50 60 70 80 90 100
injected mass (kg)


Figure 4-56. Reduction of heat energy (kJ) v.s. injected mass (kg) at M = 6 and 35000m altitude
with 0.01 kg/ m2 s of mass injection. The panels to be cooled are determined by
q,. (W/m2).


all panels

00--_OOOW/m2
20000W/m2 10000W/m2

30000W/m2


all pane


oo000W/m2
20000W/m2
30000W/m2













- 30000W/m2
--- 20000W/m2
S 10000W/m2
5000W

all pane


20000


400(


0 60000 80
reduction of heat energy (kJ)


1000


100000


120000


Figure 4-57. Flight time v.s. reduction of heat energy (kJ) at M = 6 and 35000m altitude with
0.01 kg/m2 s of mass injection. The panels to be cooled are determined by

q,,w(W/m2).


Figure 4-58. Bottom view of X-24C with 30000 W/m2 of allowable q,,w at 35000m altitude.















Figure 4-59. Side view of X-24C with 30000 W/m2 of allowable q,, at 35000m altitude.






















Figure 4-60. Top view of X-24C with 30000W/m2 of allowable q,,w at 35000m altitude.


60
50
Ri 40
a 30
% 20
10
60 im 1 1 1 iN im iM im imi I I M-i






panels' heat transfer (W) range


Figure 4-61. Distribution of panel area with a given heat transfer, Q (W) at M = 6 and 35000m
altitude.


120
100
80
o

S60
40
20
0







panels' heat transfer (W) range

Figure 4-62. Distribution of the number of panels with a given heat transfer, Qc (W) at M = 6
and 35000m altitude.




















-o- all panels are cooled (168.244m2)
-- 2500W and more (156.64m2)
-- 5000W and more (116.8m2)
-- 10000W and more (88.768m2)
-x- 20000W and more (64.485m2)


0 0.001 0.002 0.003 0.004 0.005 0.006
mass injection rate (kg/m2-s)


0.007 0.008 0.009


Figure 4-63. Mass injection effect on the flight time at M = 6 and 35000m altitude. The panels to
be cooled are determined by Qc, (W).


1.27

1.26

1.25

1.24

1.23

1.22

1.21

1.2

1.19

1.18


0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
mass injection rate (kg/m2-s)



Figure 4-64. Mass injection effect on L/D at M = 6 and 35000m altitude. The panels to be
cooled are determined by Qc, (W).


-o-all panels are cooled (168.244m2)
-- 2500W and more (156.64m2)
-- 5000W and more (116.8m2)
-*- 10000W and more (88.768m2)
-x- 20000W and more (64.485m2)













0.96

S 0.92

S0.88

0.84

S0.8

0.76


0.72

0.68


0 0.001 0.002 0.003 0.004 0.005 0.006 0.007
mass injection rate (kg/m2-s)


0.008 0.009 0.01


Figure 4-65. Mass injection effect on reduction of heat power at M = 6 and 35000m altitude. The
panels to be cooled are determined by Qc, (W).


0.05


0.04

S0.03

a 0.02

- 0.01
o


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

normalized injected mass


Figure 4-66. Normalized reduction of heat power v.s. normalized injected mass at M = 6 and
35000m altitude with 0.001 kg/m2 s of mass injection. The panels to be cooled are
determined by Q0, (W).


- all panels are cooled (168.244m2)
2500W and more (156.64m2)
e 5000W and more (116.8m2)
*-- 10000W and more (88.768m2)
-- 20000W and more (64.485m2)


all par

5000W 2500W

0 00W0W
____________^ T OO W____NOW____










100
99
98
97 20000W 1
96 10000
96 5000W
S95
94 ___2500W
93 alley
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
normalized injected mass


Figure 4-67. Flight time v.s. normalized injected mass at M = 6 and 35000m altitude with
0.001 kg/m2 s of mass injection. The panels to be cooled are determined by Qw (W).


100
99
98
97 20000W :000W
4 96
95 2500W
94-*allpane$
93
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045
normalized reduction of heat power


Figure 4-68. Flight time v.s. normalized reduction of heat power at M = 6 and 35000m altitude
with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined by Q,
(W).










100

) 80

a 60

S40

20

0


0 0.02 0.04 0.06 0.08 0.1
injected mass rate (kg/s)


0.12 0.14 0.16 0.18


Figure 4-69. Reduction of heat power (kW) v.s. injected mass rate (kg/s) at M = 6 and 35000m
altitude with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined
by Q, (W).


S25000

S20000

15000

10000

* 5000
S 0


8
injected mass (kg)


10 12 14


Figure 4-70. Reduction of heat energy (kJ) v.s. injected mass (kg) at M = 6 and 35000m altitude
with 0.001 kg/m2 s of mass injection. The panels to be cooled are determined by Q,
(W).


all panels

50! OO 2500W


00W 00 O


all pane

2500W
5000W
00 0000W
20000W










100
99
98
97
96
95
94
93


0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000
reduction of heat energy (kJ)

Figure 4-71. Flight time v.s. reduction of heat energy (kJ) at M = 6 and 35000m altitude with
0.001 kg/m2 s of mass injection. The panels to be cooled are determined by ()w (W).


0.35
0.3
0.25
0.2
S0.15
1 0.1
o 0.05
0


0 0.1 0.2 0.3 0.4 0.5 0.6
normalized injected mass


0.7 0.8 0.9 1


Figure 4-72. Normalized reduction of heat power v.s. normalized injected mass at M = 6 and
35000m altitude with 0.01 kg/m2 s of mass injection. The panels to be cooled are
determined by Qw (W).


0000W
000W
5000W
2500W
all pa










100
90
80
70
60
50


0 0.1 0.2 0.3 0.4 0.5 0.6
normalized injected mass


0.7 0.8 0.9 1


Figure 4-73. Flight time v.s. normalized injected mass at M = 6 and 35000m altitude with
0.01 kg/m2 s of mass injection. The panels to be cooled are determined by c,, (W).


0.15 0.2
normalized reduction of heat power


0.25


Figure 4-74. Flight time v.s. normalized reduction of heat power at M = 6 and 35000m altitude
with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined by Qc,
(W).


20000 W 1000W

5000W~ 2500W

all pan(


100


20000W5
--------------------"---1 0 O OWW----
52A500W
all panels





















0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
injected mass rate (kg/s)


Figure 4-75. Reduction of heat power (kW) v.s. injected mass rate (kg/s) at M = 6 and 30000m
altitude with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined
by Q, (W).


140000
7, all panels


120000
100000
80000
60000
40000
20000
0


0 10 20 30 40 50 60 70 80 90 100
injected mass (kg)


Figure 4-76. Reduction of heat energy (kJ) v.s. injected mass (kg) at M = 6 and 35000m altitude
with 0.01 kg/m2 s of mass injection. The panels to be cooled are determined by Qc,
(W).


5000W 02500W
10000W
20000W










100

90
80 20000W
10000W
70 5000W

60
I aH pane


20000


4000


)0 60000 8
reduction of heat energy (kJ)


000


100000


120000


Figure 4-77. Flight time v.s. reduction of heat energy (kJ) at M = 6 and 35000m altitude with
0.01 kg/m2 s of mass injection. The panels to be cooled are determined by Qw (W).


Figure 4-78. Bottom view of X-24C with 20000 W of allowable Qc, at 35000m altitude.


Figure 4-79. Side view of X-24C with 20000 W of allowable Q,w at 35000m altitude.




















Figure 4-80. Top view of X-24C with 20000 W of allowable Qcw at 35000m altitude.









CHAPTER 5
CONCLUSIONS

Conclusions of this Study

The local surface inclination method (Newtonian theory) was shown to reasonably predict

the pressure around a flight vehicle like the X-24C. The flat plate reference enthalpy method for

laminar and turbulent flow was utilized, along with a classical approximation of thermodynamic

properties for considering high temperature effects, to calculate heat transfer over a hypersonic

vehicle. This method provided good agreement with available heat transfer measurements.

However, around a stagnation point or line, the flat plate reference enthalpy method gave

extremely high values, much higher than experimental data. Therefore, around stagnation points

or lines, the blunt body heat transfer method was used since it gave reasonable solutions. For

surfaces on which the two methods give the same or close heat transfer, the flat plate reference

enthalpy method was preferred. These simple methods are based on many approximations, but

for preliminary design considerations, they are sufficiently accurate tools to compute the flow

properties including aerodynamic forces, moments, and heating.

In order to reduce skin friction and heat transfer on a vehicle surface, we used an existing

simple algebraic Couette flow solution since it has the virtue of fitting the experimental data. The

effect of mass injection is relatively large for the lower a. Also, the more mass is injected, the

less the effect of blowing grows. Therefore, even a small amount of injected mass is effective in

improving flight performance (L/D) and thermal protection (less heating). Even though the

amount of fuel is reduced in favor of carrying the coolant for surface injection, the fuel still

provides the necessary thrust so that flight time is not reduced much, because blowing reduces

the total drag. Reducing flight range is the penalty of mass injection, while reducing heat transfer

is the advantage of mass injection. It has been shown that choosing the panels to be cooled by









taking the panels whose heat transfer, q,, or Q,, are the highest gives the most advantage for

the least penalty. This illustrates the conclusion that simply providing injection on all panels is

not an efficient cooling method.

The X-24C vehicle has relatively high pressure forces because of the fuselage shape. Using

mass injection on a more slender cruising vehicle which has a higher fraction of viscous drag

than the X-24C will have less penalty (reduced flight range) or even zero penalty (constant or

increasing flight range), in addition to reducing heat transfer.

Future Work

In this study, we considered the effects of mass injection only on the boundary layer over

the plates through which injection occurs. However, in reality, the injected mass effects a change

in flow structures downstream of the injected plates. The injected gas has a normal component of

profile velocity, which makes the boundary layer profile less full and therefore the gradient of

tangential velocity in normal direction becomes smaller than the boundary layer with zero

injection. In general, the shear stress is linearly dependent on this gradient, and the skin friction

would be the integrated value of local shear stress. This is the physics describing why injected

gas reduces skin friction. The "less full" boundary layer profile cannot rapidly return to the

original equilibrium profile just downstream of the injected plate. The injected gas, therefore,

will reduce the skin friction on regions downstream of the injected plate.

Eventually, the "less full" boundary layer returns to the equilibrium profile at a certain

point, after which the injected gas has no effect. Establishing the method that predicts how much

skin friction and heat transfer are reduced is a logical extension to this study. The more accurate

analysis of viscous effect reduction given by this method will make the results more reliable.









Furthermore these downstream effects will show that the current results are actually conservative

and that even better performance should be possible.









APPENDIX A
MATLAB CODE TO COMPUTE FLIGHT PERFORMANCE OF X24C



%code name: x24c0012
%written by: Yoshifumi Nozaki
%date: 3/20/2007
%This code computes the x-24c cruising vehicle flight performance
%center off fin & wing has NACA0012 airfoil.
%Inviscid and viscous hypersonic flow field can be solved by using
%the modified Newtonian method and Reynolds' analogy approximation
%This code works with other code
%**************************************************************************

%****** Flow Properties *********** *********
% ro: air density (kg/m3)
% Pinf: atmospheric pressuer (N/m2)
% Rair: gas constant of air (287J/kg-K)
% Tinf: free stream temperature (K)
% cpinf: specific heat constant pressure of free stream (J/g-K or kJ/kg-K)
% M: Mach number
% gamma: specific heat ratio
% Vinf: free stream velocity (m/s)
% a: speed of sound (m/s)
% qinf: dynamic pressure (kN/m2)


%***** Orbiter Characteristics ********************************************
% aoa: angle of attack (deg.)
% Sref: wing planform area (m2)
% chord: chord length (m)
% b: wing span (m)
% ep: density ration across shock wave for hypersonic flow
% dlel: left elavon 1 deflection (deg.)
% d2_el: left elavon 2 deflection (deg.)
% dler: right elavon 1 deflection (deg.)
% d2_er: right elavon 2 deflection (deg.)
% dr: rudder deflection (deg.)
% ref: reference point e.g. center of gravity
% refa: reference point accounting angle of attack
%**************************************************************************

%***** Flight Performance *******************
% Lift: lift (N)
% Drag: drag (N)
% LD: L/D ratio (inviscid)









% L D vis L/D ratio (viscous without cooling)
% LDcool L/D ratio (viscous with cooling)
% rolling: rolling moment (N-m)
% pitching: pitching moment (N-m)
% yawing: yawing moment (N-m)
% CL: lift coefficient
% CD: drag coefficient
% C m: pitching moment coefficient
% C 1: rolling moment coefficient
% C n: yawing moment coefficient
% CN: normal force coefficient
% CA: axial force coefficient


%***** Computing Arrays***************************************************
% nod_o: original point coordinate node (left side)
% nod: point coordinate at some angle of attack (left side)
% nodr_o: original point coordinate node (right side)
% nodr: point coordinate at some angle of attack (right side)
% Pvec: P vector of each panel
% Qvec: Q vector of each panel
% Nvec: N vector of each panel
% nunit: n (N unit) vector of each panel
% Area: area of each panel (m2)
% cp: local pressure coefficient of each panel
% dF: differential force (pressure force) acting on each panel
% dL: differential lift force acting on each panel
% dD: differential drag force acting on each panel
% cent: panel center point centroidd)
% radi: radius vector w.r.t. reference
% d 1: differential rolling moment on each panel
% d m: differential rolling moment on each panel
% d n: differential rolling moment on each panel
% Pvecr: P vector of each panel (right side)
% Qvecr: Q vector of each panel (right side)
% Nvecr: N vector of each panel (right side)
% nunitr: n (N unit) vector of each panel (right side)
% Arear: area of each panel (m2) (right side)
% cpr: local pressure coefficient of each panel (right side)
% dFr: differential force (pressure force) acting on each panel (right side)
% dLr: differential lift force acting on each panel (right side)
% dDr: differential drag force acting on each panel (right side)
% center: panel center point centroidd) (right side)
% radir: radius vector w.r.t. reference (right side)
% d lr: differential rolling moment on each panel (right side)
% d mr: differential rolling moment on each panel (right side)









% d nr: differential rolling moment on each panel (right side)
%**************************************************************************

% input data
ro = 0.014283 % air density (kg/m3) Z=36000m or 31500m
Pinf = 935.425354 % atmospheric pressuer (N/m2)
Rair = 287 % gas constant of air (287J/kg-K)
Tinf = 228.15 % free stream temperature (K)
cpinf= 1006 % specific heat constant pressure of free stream (J/kg-K)
M = 6.00 % Mach number
gamma = 1.4 % specific heat ratio
ref = [9.0932 0] % reference point e.g. center of gravity

% flow properties computaion
a = (gamma*Rair*Tinf)A0.5 % speed of sound (m/s)
Vinf = M*a % free stream velocity (m/s)
qinf = 0.5*ro*VinfA2 % dynamic pressure (N/m2)

% flight condition (input)
aoa = 6.0 % angle of attack (deg.)
Sref = 57.20 % vehicle planform area (m2)
chord = 14.7066 % chord length (m)
b = 7.37616 % wing span (m)
ep = (gamma-1)/(gamma+l) % density ration across shock wave for hypersonic flow

% reference point accounting angle of attack
refa = [((ref(1,1)A 2+ref(1,2)2)A0.5)*cos(atan(ref(1,2)/ref(1,1))-aoa*3.14159265359/180) 0
((ref(l1,1)A2+ref(1,2)A2)A0.5)*sin(atan(ref(1,2)/ref(1,1))-aoa*3.14159265359/180)]

% original point coordinate system left side
nod_o =0.0254*[0 0 0;
41 0-8.3;
41 2.0-8.1;
41 5.0 -7.5;
41 7.5 -5.0;
41 9.0 -3.0;
41 10.3 0;
41 10.3 5.0;
41 8.5 8.0;
41 5.0 11.0;
41 1.0 12.3;
41 0.75 12.4;
41 0.50 12.4;
41 0.25 12.4;
41 0 12.4;
120 0 -12.4;










120 5.0 -12.4;
120 15.5 -12.4;
120 25.0 -12.4;
120 27.9 -9.0;
120 27.9 0;
120 27.0 8.0;
120 23.0 18.0;
120 13.0 27.0;
120 2.0 29.0;
120 1.5 29.0;
120 1.0 29.0;
120 0.5 29.0;
120 0 29.0;
145 0-13.7;
145 5.5 -13.7;
145 18.0 -13.7;
145 31.0 -13.7
145 34.1 -10.5;
145 34.1 0;
145 33.0 8.5;
145 29.0 19.0;
145 21.0 29.0;
145 12.0 34.0;
145 10.0 38.0;
145 8.0 42.0;
145 4.0 44.5;
145 0 45.5;
178 0-15.4;
178 6.5 -15.4;
178 20.5 -15.4;
178 38.0 -15.4;
178 41.4 -12.0;
178 41.4 0;
178 40.0 9.5;
178 36.0 20.0;
178 29.0 31.0;
178 21.0 37.0;
178 17.0 43.5;
178 12.0 48.0;
178 6.0 49.5;
178 0 49.7;
215 0-17.3;
215 7.5 -17.3
215 24.0 -17.3;
215 46.0 -17.3;
215 49.7 -14.0;









215 49.7 0;
215 48.0 10.0;
215 45.0 22.0;
215 39.0 33.0;
215 32.0 42.0;
215 26.0 48.0;
215 18.0 51.0;
215 10.0 53.0;
215 0 54.0;
331 0-23.3;
331 10.5 -23.3;
331 34.0 -23.3;
331 69.0 -23.3;
331 74.5 -19.0;
331 74.5 0;
331 73.0 12.0;
331 67.0 26.0;
331 59.0 37.5;
331 48.0 47.0;
331 37.0 52.0;
331 24.0 54.0;
331 11.0 54.0;
331 0 54.0;
385 0-26.1;
385 12.0-26.1;
385 39.0 -26.1;
385 86.9 -26.1;
385 86.9 -22.0;
385 86.9 0;
385 82.0 14.0;
385 76.0 27.0;
385 71.0 40.0;
385 66.0 54.0;
385 46.0 54.0;
385 24.0 54.0;
385 11.0 54.0;
385 0 54.0;
480 0-31.0;
480 14.5 -31.0;
480 46.0 -31.0;
480 86.9 -31.0;
480 86.9 -28.0;
480 86.9 0;
480 82.0 14.0;
480 76.0 27.0;
480 71.0 40.0;










480 66.0 54.0;
480 46.0 54.0;
480 24.0 54.0;
480 11.0 54.0;
480 0.0 54.0;
579 0 -4.1;
579 14.5 -4.1;
579 46.0 -4.1;
579 86.9 -4.1;
579 86.9 -2.0;
579 86.9 0;
579 82.0 14.0;
579 76.0 27.0;
579 71.0 40.0;
579 66.0 54.0;
579 46.0 54.0;
579 24.0 54.0;
579 11.0 54.0;
579 0 54.0;
478 0 54;
594 10.5 54;
548 0 108;
583 3.15 108;
507 62 54;
511.776418 64.631838 54;
516.584952 65.342358 54;
525.361858 65.720558 54;
537.945254 65.285752 54;
550.710744 64.241238 54;
569 62 54;
511.776418 59.368162 54;
516.584952 58.657642 54;
525.361858 58.279442 54;
537.945254 58.714248 54;
550.710744 59.758762 54;
542 89 84;
545.312677 90.825307 84;
548.647628 91.318087 84;
554.734837 91.580387 84;
563.462031 91.278828 84;
572.315516 90.554407 84;
585 89 84;
545.312677 87.174693 84;
548.647628 86.681913 84;
554.734837 86.419613 84;
563.462031 86.721172 84;









572.315516 87.445593 84;
385 86.9 -25;
403.720477 86.9 -14.684893;
422.566828 86.9 -11.900113;
456.966637 86.9 -10.417813;
506.285431 86.9 -12.121972;
556.317916 86.9 -16.215793;
628 86.9 -25;
403.720477 86.9 -35.315107;
422.566828 86.9 -38.099887;
456.966637 86.9 -39.582187;
506.285431 86.9 -37.878028;
556.317916 86.9 -33.784207;
530 149 19;
537.935017 149 23.372247;
545.923388 149 24.552627;
560.504377 149 25.180927;
581.409051 149 24.458588;
602.616236 149 22.723347;
633 149 19;
537.935017 149 14.627753;
545.923388 149 13.447373;
560.504377 149 12.819073;
581.409051 149 13.541412;
602.616236 149 15.276653]

num nod = 178+1 %the number of nod
num_panel = 142

for i=l:numnod %To make y-component of each nod to the negative
nod_o(i,2) = -1.0*nod_o(i,2)
end

% point coordinate at some angle of attack left & right side
nod(l,1)=0; nod(1,2)=0; nod(1,3)=0

for i = 2:num nod
nod(i,1)= ((nod_o(i, 1)A2+nod_o(i,3)A2)0.5)*cos(atan(nod_o(i,3)/nod_o(i, 1))-
aoa*3.14159265359/180)
nod(i,2) = nod_o(i,2)
nod(i,3)= ((nod_o(i, 1)A2+nod_o(i,3)A2)0.5)*sin(atan(nod_o(i,3)/nod_o(i,1))-
aoa*3.14159265359/180)
end

% Pvec: P vector of each panel
% Pvec of body panels (panel 1-117)









fori = 1:13
Pvec(i, )=nod(i+1,1)-nod(l,l); Pvec(i,2)=nod(i+1,2)-nod(1,2); Pvec(i,3)=nod(i+1,3)-nod(1,3)
end
for i = 14:26
Pvec(i,1)=nod(i+2,1)-nod(i- 11,1); Pvec(i,2)=nod(i+2,2)-nod(i- 11,2); Pvec(i,3)=nod(i+2,3)-
nod(i-11,3)


end
for i = 27:39
Pvec(i, 1)=nod(i+3,1)-nod(i-10,1); Pvec(i,2)
nod(i-10,3)
end
for i = 40:52
Pvec(i,1)=nod(i+4,1)-nod(i-9,1); Pvec(i,2)=
9,3)
end
for i = 53:65


=nod(i+3,2)-nod(i-10,2); Pvec(i,3)=nod(i+3,3)-



nod(i+4,2)-nod(i-9,2); Pvec(i,3)=nod(i+4,3)-nod(i-


Pvec(i,1)=nod(i+5,1)-nod(i-8,1); Pvec(i,2)=nod(i+5,2)-nod(i-8,2); Pvec(i,3)=nod(i+5,3)-nod(i-
8,3)


end
for i = 66:78
Pvec(i,1)=nod(i+6,1)-nod(i-7,1); Pvec(i,2)
7,3)
end
for i = 79:91
Pvec(i,1)=nod(i+7,1)-nod(i-6,1); Pvec(i,2)
6,3)
end
for i = 92:104
Pvec(i,1)=nod(i+8,1)-nod(i-5,1); Pvec(i,2)


=nod(i+6,2)-nod(i-7,2); Pvec(i,3)=nod(i+6,3)-nod(i-



=nod(i+7,2)-nod(i-6,2); Pvec(i,3)=nod(i+7,3)-nod(i-



=nod(i+8,2)-nod(i-5,2); Pvec(i,3)=nod(i+8,3)-nod(i-


end
fori = 105:117
Pvec(i,1)=nod(i+9,1)-nod(i-4,1); Pvec(i,2)=nod(i+9,2)-nod(i-4,2); Pvec(i,3)=nod(i+9,3)-nod(i-
4,3)
end
%Pvec center fin panels(panel 118)
Pvec(118,1)=nod(129, 1)-nod(130,1); Pvec( 118,2)=nod(129,2)-nod(130,2);
Pvec(118,3)=nod(129,3)-nod(130,3)
%Pvec off center fin panels(panel 119-130)
Pvec(119,1)=nod(145,1)-nod(132,1); Pvec(119,2)=nod(145,2)-nod(132,2);
Pvec(119,3)=nod(145,3)-nod(132,3)
for i= 120:123
Pvec(i, 1)=nod(i+26,1 )-nod(i+13,1); Pvec(i,2)=nod(i+26,2)-nod(i+ 13,2);
Pvec(i,3)=nod(i+26,3)-nod(i+13,3)
end









Pvec(124,1)=nod(150,1)-nod(137,1); Pvec(124,2)=nod(150,2)-nod(137,2);
Pvec(124,3)=nod(150,3)-nod(137,3)
Pvec(125,1)=nod(144,1)-nod(139,1); Pvec(125,2)=nod(144,2)-nod(139,2);
Pvec(125,3)=nod(144,3)-nod(139,3)
for i= 126:129
Pvec(i, 1)=nod(i+25,1)-nod(i+14,1); Pvec(i,2)=nod(i+25,2)-nod(i+14,2);
Pvec(i,3)=nod(i+25,3)-nod(i+ 14,3)
end
Pvec(130,1)=nod(155,1)-nod(138,1); Pvec(130,2)=nod(155,2)-nod(138,2);
Pvec(130,3)=nod(155,3)-nod(138,3)
%Pvec wing panels(panel 131-142)
Pvec(131,1)=nod(168,1)-nod(157,1); Pvec(131,2)=nod(168,2)-nod(157,2);
Pvec(131,3)=nod(168,3)-nod(157,3)
for i= 132:135
Pvec(i, 1)=nod(i+3 7,1 )-nod(i+26,1); Pvec(i,2)=nod(i+3 7,2)-nod(i+26,2);
Pvec(i,3)=nod(i+37,3)-nod(i+26,3)
end
Pvec(136, 1)=nod(173,1 )-nod(162, 1); Pvec(136,2)=nod(173,2)-nod(162,2);
Pvec(136,3)=nod(173,3)-nod(162,3)
Pvec(137,1)=nod(175,1)-nod(156,1); Pvec(137,2)=nod(175,2)-nod(156,2);
Pvec(137,3)=nod(175,3)-nod(156,3)
for i= 138:141
Pvec(i, 1)=nod(i+38,1)-nod(i+25,1); Pvec(i,2)=nod(i+38,2)-nod(i+25,2);
Pvec(i,3)=nod(i+38,3)-nod(i+25,3)
end
Pvec(142,1)=nod(174,1)-nod(167,1); Pvec(142,2)=nod(174,2)-nod(167,2);
Pvec(142,3)=nod(174,3)-nod(167,3)

% Qvec of body panels (panel 1-117)
fori = 1:13
Qvec(i, 1)=nod(i+2,1)-nod( 1,1); Qvec(i,2)=nod(i+2,2)-nod(1,2); Qvec(i,3)
nod(l,3)


end
for i = 14:26
Qvec(i, 1)=nod(i+3,1)-nod(i-12,1); Qvec(i,2)
nod(i-12,3)
end
for i = 27:39
Qvec(i, 1)=nod(i+4, 1)-nod(i-11,1); Qvec(i,2)
nod(i-11,3)
end
for i = 40:52
Qvec(i, l)=nod(i+5,1)-nod(i-10,1); Qvec(i,2)
nod(i-10,3)
end
for i = 53:65


=nod(i+2,3)-


=nod(i+3,2)-nod(i-12,2); Qvec(i,3)=nod(i+3,3)-



=nod(i+4,2)-nod(i- 11,2); Qvec(i,3)=nod(i+4,3)-



=nod(i+5,2)-nod(i-10,2); Qvec(i,3)=nod(i+5,3)-









Qvec(i, 1)=nod(i+6,1)-nod(i-9,1); Qvec(i,2)
nod(i-9,3)
end
for i = 66:78
Qvec(i, 1)=nod(i+7,1)-nod(i-8,1); Qvec(i,2)
nod(i-8,3)
end
for i = 79:91
Qvec(i, 1)=nod(i+8,1)-nod(i-7,1); Qvec(i,2)
nod(i-7,3)
end
for i = 92:104
Qvec(i, 1)=nod(i+9,1)-nod(i-6,1); Qvec(i,2)
nod(i-6,3)


=nod(i+6,2)-nod(i-9,2); Qvec(i,3)=nod(i+6,3)-



=nod(i+7,2)-nod(i-8,2); Qvec(i,3)=nod(i+7,3)-



=nod(i+8,2)-nod(i-7,2); Qvec(i,3)=nod(i+8,3)-



=nod(i+9,2)-nod(i-6,2); Qvec(i,3)=nod(i+9,3)-


fori = 105:117
Qvec(i, )=nod(i+10,1)-nod(i-5,1); Qvec(i,2)=nod(i+10,2)-nod(i-5,2); Qvec(i,3)=nod(i+10,3)-
nod(i-5,3)
end
%Qvec center fin panels(panel 118)
Qvec(118,1)=nod(131,1)-nod(128,1); Qvec(118,2)=nod(131,2)-nod(128,2);
Qvec(118,3)=nod(131,3)-nod(128,3)

%Pvec off center fin panels(panel 119-130)
Qvec(l 19,1)=nod(144, 1)-nod(133,1); Qvec( 119,2)=nod(144,2)-nod(133,2);
Qvec(119,3)=nod(144,3)-nod(133,3)
for i= 120:123
Qvec(i, 1)=nod(i+25,1)-nod(i+14,1); Qvec(i,2)=nod(i+25,2)-nod(i+14,2);
Qvec(i,3)=nod(i+25,3)-nod(i+14,3)


Qvec(124,1)=nod(149,1)-nod(138,1); Qvec(124,2)=nod(149,2)-nod(1 38,2);
Qvec(124,3)=nod(149,3)-nod(138,3)

Qvec(125,1)=nod(151,1)-nod(132,1); Qvec(125,2)=nod(151,2)-nod(132,2);
Qvec(125,3)=nod(151,3)-nod(132,3)
for i= 126:129
Qvec(i, 1)=nod(i+26,1)-nod(i+13,1); Qvec(i,2)=nod(i+26,2)-nod(i+13,2);
Qvec(i,3)=nod(i+26,3)-nod(i+13,3)
end
Qvec(130,1)=nod(150,1)-nod(143,1); Qvec(130,2)=nod(150,2)-nod(143,2);
Qvec(130,3)=nod(150,3)-nod(143,3)

%Pvec wing panels(panel 131-142)
Qvec(131,1)=nod(169,1)-nod(156,1); Qvec(131,2)=nod(169,2)-nod(156,2);
Qvec(131,3)=nod(169,3)-nod(156,3)
for i= 132:135









Qvec(i, 1)=nod(i+38,1)-nod(i+25,1); Qvec(i,2)=nod(i+38,2)-nod(i+25,2);
Qvec(i,3)=nod(i+38,3)-nod(i+25,3)
end
Qvec(136, 1)=nod(174,1)-nod(161,1); Qvec(136,2)=nod(174,2)-nod(161,2);
Qvec(136,3)=nod(174,3)-nod(161,3)

Qvec(137,1)=nod(168,1)-nod(163,1); Qvec(137,2)=nod(168,2)-nod(163,2);
Qvec(137,3)=nod(168,3)-nod(163,3)
for i= 138:141
Qvec(i, 1)=nod(i+37,1)-nod(i+26,1); Qvec(i,2)=nod(i+37,2)-nod(i+26,2);
Qvec(i,3)=nod(i+37,3)-nod(i+26,3)
end
Qvec(142,1)=nod(179,1)-nod(162,1); Qvec(142,2)=nod(179,2)-nod(162,2);
Qvec(142,3)=nod(179,3)-nod(162,3)

% Nvec: N vector of each panel

for i=l: num_panel
Nvec(i,1) = Pvec(i,2)*Qvec(i,3)-Pvec(i,3)*Qvec(i,2)
Nvec(i,2) = Pvec(i,3)*Qvec(i, 1)-Pvec(i, 1)*Qvec(i,3)
Nvec(i,3) = Pvec(i, 1)*Qvec(i,2)-Pvec(i,2)*Qvec(i, 1)
end

% nunit: n (N unit) vector of each panel
for i=l:num_panel
nunit(i, 1)=Nvec(i, 1)/(Nvec(i, 1)A2+Nvec(i,2)A2+Nvec(i,3)A2)A0.5
nunit(i,2)=Nvec(i,2)/(Nvec(i,1)A2+Nvec(i,2)A2+Nvec(i,3)A2)A0.5
nunit(i,3)=Nvec(i,3)/(Nvec(i,1)A2+Nvec(i,2)A2+Nvec(i,3)A2)A0.5
end

% Area: area of each panel (m2)
for i=l:num_panel
Area(i, 1) = 0.5 (Nvec(i, 1)A2+Nvec(i,2)A2+Nvec(i,3)A2)A0.5
end

% cp: local pressure coefficient of each panel
for i=l:num_panel
if nunit(i, 1)<0
cp(i,l) = (2.0-0.0)*nunit(i, 1)^2
else
cp(i, 1)= 0
end
end

% dF: differential force (pressure force) acting on each panel
for i=l:numpanel









dF(i, 1)
dF(i,2)
dF(i,3)
end


-cp(i, 1)*qinf*Area(i, 1)*nunit(i, 1)
-cp(i,1)*qinf*Area(i, 1)*nunit(i,2)
-cp(i,1)*qinf*Area(i, 1)*nunit(i,3)


% dL: differential lift force acting on each panel
% dD: differential drag force acting on each panel
% dLr: differential lift force acting on each panel (right side)
% dDr: differential drag force acting on each panel (right side)
for i=l:num_panel
dL(i, 1)= dF(i,3)
dD(i,1)= dF(i,1)
end

% cent: panel center point centroidd)
% center: panel center point centroidd) (right side)

fori= 1:13
cent(i,1)=(nod(i+1,1)+nod(i+2,1))/3; cent(i,2)=(nod(i+1,2)+nod(i+2,2))/3;
cent(i,3)=(nod(i+l,3)+nod(i+2,3))/3
end
for i= 14:26
cent(i, 1)=(nod(i+2,1 )+nod(i+3,1 )+nod(i-12,1 )+nod(i-11,1 ))/4
cent(i,2)=(nod(i+2,2)+nod(i+3,2)+nod(i-12,2)+nod(i-11,2))/4
cent(i,3)=(nod(i+2,3)+nod(i+3,3)+nod(i-12,3)+nod(i-11,3))/4
end
for i= 27:39
cent(i, 1)=(nod(i+3,1 )+nod(i+4,1 )+nod(i- 11,1 )+nod(i-10,1 ))/4
cent(i,2)=(nod(i+3,2)+nod(i+4,2)+nod(i- 11,2)+nod(i-10,2))/4
cent(i,3)=(nod(i+3,3)+nod(i+4,3)+nod(i- 11,3)+nod(i-10,3))/4
end
for i= 40:52
cent(i, 1)=(nod(i+4,1 )+nod(i+5,1 )+nod(i-10,1 )+nod(i-9,1 ))/4
cent(i,2)=(nod(i+4,2)+nod(i+5,2)+nod(i-10,2)+nod(i-9,2))/4
cent(i,3)=(nod(i+4,3)+nod(i+5,3)+nod(i-10,3)+nod(i-9,3))/4
end
for i= 53:65
cent(i, 1)=(nod(i+5, 1)+nod(i+6, 1)+nod(i-9, 1)+nod(i-8,1))/4
cent(i,2)=(nod(i+5,2)+nod(i+6,2)+nod(i-9,2)+nod(i-8,2))/4
cent(i,3)=(nod(i+5,3)+nod(i+6,3)+nod(i-9,3)+nod(i-8,3))/4
end
for i= 66:78
cent(i, 1)=(nod(i+6, 1)+nod(i+7,1 )+nod(i-8, 1)+nod(i-7,1))/4
cent(i,2)=(nod(i+6,2)+nod(i+7,2)+nod(i-8,2)+nod(i-7,2))/4
cent(i,3)=(nod(i+6,3)+nod(i+7,3)+nod(i-8,3)+nod(i-7,3))/4
end









for i= 79:91
cent(i, 1)=(nod(i+7, 1)+nod(i+8,1 )+nod(i-7, 1)+nod(i-6,1))/4
cent(i,2)=(nod(i+7,2)+nod(i+8,2)+nod(i-7,2)+nod(i-6,2))/4
cent(i,3)=(nod(i+7,3)+nod(i+8,3)+nod(i-7,3)+nod(i-6,3))/4
end
for i= 92:104
cent(i, 1)=(nod(i+8, 1)+nod(i+9, 1)+nod(i-6, 1)+nod(i-5,1))/4
cent(i,2)=(nod(i+8,2)+nod(i+9,2)+nod(i-6,2)+nod(i-5,2))/4
cent(i,3)=(nod(i+8,3)+nod(i+9,3)+nod(i-6,3)+nod(i-5,3))/4
end
for i= 105:117
cent(i, 1)=(nod(i+9,1 )+nod(i+10,1 )+nod(i-5,1 )+nod(i-4,1 ))/4
cent(i,2)=(nod(i+9,2)+nod(i+ 0,2)+nod(i-5,2)+nod(i-4,2))/4
cent(i,3)=(nod(i+9,3)+nod(i+ 10,3)+nod(i-5,3)+nod(i-4,3))/4
end
%cent center fin panels(panel 118)
forj=l:3
cent(118,j)=(nod(128,j)+nod(129,j)+nod(130,j)+nod(131,j))/4
end
%cent off center fin panels(panel 119-130)
cent(119,1)=(nod(132,1)+nod(133,1)+nod(144,1)+nod(145,1))/4
cent( 119,2)=(nod( 132,2)+nod( 133,2)+nod(144,2)+nod(145,2))/4
cent(119,3)=(nod(132,3)+nod(133,3)+nod(144,3)+nod(145,3))/4
for i= 120:123
cent(i, 1)=(nod(i+13,1 )+nod(i+14,1 )+nod(i+25, 1)+nod(i+26,1))/4
cent(i,2)=(nod(i+13,2)+nod(i+14,2)+nod(i+25,2)+nod(i+26,2))/4
cent(i,3)=(nod(i+ 13,3)+nod(i+14,3)+nod(i+25,3)+nod(i+26,3))/4
end
cent(124,1)=(nod(137,1)+nod(138,1)+nod(149,1 )+nod(150,1))/4
cent( 124,2)=(nod( 13 7,2)+nod( 13 8,2)+nod( 149,2)+nod( 150,2))/4
cent(124,3)=(nod(137,3)+nod(138,3)+nod(149,3)+nod(150,3))/4
cent(125,1)=(nod(132,1)+nod(139,1)+nod(144,1)+nod(151,1))/4
cent(125,2)=(nod( 132,2)+nod( 139,2)+nod(144,2)+nod( 151,2))/4
cent(125,3)=(nod(132,3)+nod(139,3)+nod(144,3)+nod(151,3))/4
for i= 126:129
cent(i, 1)=(nod(i+25, 1)+nod(i+26, 1)+nod(i+13,1 )+nod(i+14,1))/4
cent(i,2)=(nod(i+25,2)+nod(i+26,2)+nod(i+13,2)+nod(i+14,2))/4
cent(i,3)=(nod(i+25,3)+nod(i+26,3)+nod(i+13,3)+nod(i+14,3))/4
end
cent(130,1)=(nod(143,1)+nod(138,1)+nod(155,1)+nod(150,1))/4
cent( 130,2)=(nod(143,2)+nod( 138,2)+nod( 155,2)+nod( 150,2))/4
cent(130,3)=(nod(143,3)+nod(138,3)+nod(155,3)+nod(150,3))/4

%cent wing panels(panel 131-142)
cent(131,1)=(nod(156,1)+nod(157,1)+nod(168,1)+nod(169,1))/4
cent(131,2)=(nod( 156,2)+nod( 157,2)+nod( 168,2)+nod( 169,2))/4









cent(131,3)=(nod(156,3)+nod(157,3)+nod(168,3)+nod(169,3))/4
for i= 132:135
cent(i, 1)=(nod(i+25, 1)+nod(i+26, 1)+nod(i+37,1 )+nod(i+3 8,1))/4
cent(i,2)=(nod(i+25,2)+nod(i+26,2)+nod(i+37,2)+nod(i+38,2))/4
cent(i,3)=(nod(i+25,3)+nod(i+26,3)+nod(i+37,3)+nod(i+38,3))/4
end
cent(136,1)=(nod(173,1)+nod(174,1)+nod(161,1)+nod(162,1))/4
cent( 136,2)=(nod(173,2)+nod( 174,2)+nod(161,2)+nod(162,2))/4
cent(136,3)=(nod(173,3)+nod(174,3)+nod(161,3)+nod(162,3))/4
cent(137,1)=(nod(156,1 )+nod(163,1)+nod(168,1)+nod(169,1))/4
cent( 137,2)=(nod( 156,2)+nod( 163,2)+nod( 168,2)+nod( 169,2))/4
cent(137,3)=(nod(156,3)+nod(163,3)+nod(168,3)+nod(169,3))/4
for i= 138:141
cent(i, 1)=(nod(i+25, 1)+nod(i+26, 1)+nod(i+37,1 )+nod(i+3 8,1))/4
cent(i,2)=(nod(i+25,2)+nod(i+26,2)+nod(i+37,2)+nod(i+38,2))/4
cent(i,3)=(nod(i+25,3)+nod(i+26,3)+nod(i+37,3)+nod(i+38,3))/4
end
cent( 142,1)=(nod(167,1 )+nod( 162,1)+nod(179,1 )+nod( 174,1))/4
cent( 142,2)=(nod( 167,2)+nod( 162,2)+nod( 179,2)+nod( 174,2))/4
cent(142,3)=(nod(167,3)+nod(162,3)+nod(179,3)+nod(174,3))/4

%Arc length (only body)
arc =0
arc(1,1)=-cent(1,2)
for i= 2:13
arc(i,1)=arc(i-1)+((cent(i,2)-cent(i-1,2))A2+(cent(i,3)-cent(i-l,3))A2)O0.5
end
totalarcl=arc(13,1)-cent(13,2)
arc(14,1)=-cent(14,2)
for i= 15:26
arc(i,1)=arc(i-1)+((cent(i,2)-cent(i-1,2))A2+(cent(i,3)-cent(i-l,3))A2)A0.5
end
totalarc2=arc(26, 1)-cent(26,2)
arc(27,1)=-cent(27,2)
for i= 28:39
arc(i,1)=arc(i-1)+((cent(i,2)-cent(i-1,2))A2+(cent(i,3)-cent(i-l,3))A2)A0.5
end
totalarc3=arc(39, 1)-cent(39,2)
arc(40,1)=-cent(40,2)
for i= 41:52
arc(i,1)=arc(i-1)+((cent(i,2)-cent(i-1,2))A2+(cent(i,3)-cent(i-l,3))A2)A0.5
end
totalarc4=arc(52, 1)-cent(52,2)
arc(53,1)=-cent(53,2)
for i= 54:65
arc(i,1)=arc(i-1)+((cent(i,2)-cent(i-1,2))A2+(cent(i,3)-cent(i-l,3))A2)O0.5









end
totalarc5=arc(65,1 )-cent(65,2)
arc(66,1)=-cent(66,2)
for i= 67:78
arc(i,1)=arc(i-1)+((cent(i,2)-cent(i-1,2))A2+(cent(i,3)-cent(i-l,3))A2)A0.5
end
totalarc6=arc(78, 1)-cent(78,2)
arc(79,1)=-cent(79,2)
for i= 80:91
arc(i,1)=arc(i-1)+((cent(i,2)-cent(i-1,2))A2+(cent(i,3)-cent(i-l,3))A2)O0.5
end
totalarc7=arc(91,1 )-cent(91,2)
arc(92,1)=-cent(92,2)
for i= 93:104
arc(i,1)=arc(i-1)+((cent(i,2)-cent(i-1,2))A2+(cent(i,3)-cent(i-l,3))A2)O0.5
end
totalarc8=arc(104,1)-cent(104,2)
arc(105,1)=-cent(105,2)
for i= 106:117
arc(i,1)=arc(i-1)+((cent(i,2)-cent(i-1,2))A2+(cent(i,3)-cent(i-l,3))A2)0.5
end
totalarc9=arc( 17,1)-cent(117,2)

% radi: radius vector w.r.t. reference
for i=l:num_panel
radi(i,1) = (cent(i,1)*cos(aoa*3.14159265359/180)-cent(i,3)*sin(aoa*3.14159265359/180))-
ref(1,1)
radi(i,2) = cent(i,2)-ref(l,2)
radi(i,3) = (cent(i,3)*cos(aoa*3.14159265359/180)+cent(i,1)*sin(aoa*3.14159265359/180))-
ref(1,3)
end

for i=l:num_panel
d_m(i,1) =-
(radi(i,1)*(dF(i,3)*cos(aoa*3.14159265359/180)+dF(i,1)*sin(aoa*3.14159265359/180))-
radi(i,3)*(dF(i,1)*cos(aoa*3.14159265359/180)-dF(i,3)*sin(aoa*3.14159265359/180)))
end
pitching = sum(dm)*2
C_m = pitching/qinf/Sref/chord

%****** Viscous consideration *******************************************
%From here viscous effect is accounted into flow field
%In order to find the skin friction and heat transfer, local Reynolds'
%analogy is used. (Approximate analysis)
%ue : tangential component of velocity on each panel (m/s)
%u er : tangential component of velocity on each panel (m/s) right side









%u_eunit : unit vector of tangential component of velocity on each panel
%u_eunitr: unit vector of tangential component of velocity on each panel right side
%PMang : Prandtl-Meyer expansion angle (rad)
%psi : deflection angle (rad)
%he : enthalpy at edge of boundary layer (this is known in
% thermodynamic property code (ThermPropAir.m)
% unit: J/kg, change unit to J/g so that h_e can be used in
% ThermPropAir.m
%her : enthalpy at edge of boundary layer right side
%s : the distance along the surface of the vehicle measured from
% relevant stagnationpoint for body (panel 1 40 & 75)
% for wing section 1 (panel 43 53)
% for wing section 2 (panel 54 64)
% for wing section 2 (panel 65 74)
% for rudder (panel 41 & 42)
%l s :the distance between two centroids
%sr : the distance along the surface of the vehicle measured from
% relevant stagnationpoint for right body (panel 1 40 & 75)
% for right wing section 1 (panel 43 53)
% for right wing section 2 (panel 54 64)
% for right wing section 2 (panel 65 74)
% for right rudder (panel 41 & 42)
%ls r :the distance between two centroids for right side


%tangential component of velocity on each panel
for i=l:num_panel

u_e(i,1) = Vinf (Vinf*nunit(i, 1))*nunit(i, 1)
u_e(i,2) = 0 (Vinf*nunit(i,1))*nunit(i,2)
u_e(i,3) = 0 (Vinf*nunit(i,1))*nunit(i,3)
end
u_e(numpanel+l,1)=Vinf; u_e(numpanel+l,2)=0; u_e(numpanel+l,3)=0
for i=1 :num_panel+1
%u_eunit : unit vector of tangential component of velocity on each panel
u_eunit(i,1) = u_e(i,1)/(u_e(i, 1)A2+u_e(i,2)A2+u_e(i,3)A2)0.5
u_eunit(i,2) = u_e(i,2)/(u_e(i, 1)2+u_e(i,2)A2+u_e(i,3)A2)0.5
u_eunit(i,3) = u_e(i,3)/(u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)A2)0.5
end

%enthalpy at edge of boundary layer
%computed by using energy equation
h_inf = Tinf* 1006 %cp = 1006 J/kg-K at T = 250K
for i=l:num_panel
h_e(i,1) = 0.5*VinfA2 + h_inf- 0.5*(u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)A2) %unit: J/kg or m2/s2
end










%s : the distance along the surface of the vehicle measured from
% relevant stagnationpoint for body (panel 1 40 & 75)
% for wing section 1 (panel 43 53)
% for wing section 2 (panel 54 64)
% for wing section 2 (panel 65 74)
% for rudder (panel 41 & 42)
%l s : the distance between two centroids

nosevector = -1.0*cos(aoa*3.14159265359/180)

for i=1:117
forj=i:117
l_s(ij)=((cent(i, 1)-cent(j,1))A2 + (cent(i,2)-cent(j,2))A2 + (cent(i,3)-cent(j,3))A2)^0.5
end
end
for i=119:130
forj=i:130
l_s(ij)=((cent(i, 1)-cent(j,1))A2 + (cent(i,2)-cent(j,2))A2 + (cent(i,3)-cent(j,3))A2)^0.5
end
end
for i=131:142
forj=i:142
l_s(ij)=((cent(i, 1)-cent(j,1))A2 + (cent(i,2)-cent(j,2))A2 + (cent(i,3)-cent(j,3))A2)^0.5
end
end

% for body (panel 1 117)
for i= 1:13
s(i,1) = (cent(i, 1)A2+cent(i,2)A2+cent(i,3)A2)^0.5 0.205 + 0.10110667
end
for i= 14:117
s(i,1) =s(i-13,1) + l_s(i-13,i)
end
s(118,1) ((cent( 18, 1)-(nod(128,1)+nod(130,1))/2)A2+(cent(1 18,3)-
(nod(128,3)+nod(130,3))/2)A2)A0.5
s(119,1) = ((cent(119,1)-(nod(132,1)+nod(144,1))/2)A2+(cent( 19,3)-
(nod(132,3)+nod(144,3))/2)A2) 0.5
s(125,1) = ((cent(125,1)-(nod(132,1)+nod(144,1))/2)A2+(cent(125,3)-
(nod(132,3)+nod(144,3))/2) 2) 0.5
for i= 120:124
s(i,1) = s(i-l,1) + l_s(i-l,i)
end
for i= 126:130
s(i,1) = (i-1) + l_s(i-l,i)
end









s(131,1)= ((cent(131,1)-(nod(156,1)+nod(168,1))/2)A2+(cent(131,3)-
(nod(156,3)+nod(168,3))/2)A2)A0.5
s(137,1) = ((cent(137,1)-(nod(156,1)+nod(168,1))/2)A2+(cent(137,3)-
(nod(156,3)+nod(168,3))/2)A2)A0.5
for i= 132:136
s(i,1) = s(i-1,1) + l_s(i-l,i)
end
for i= 138:142
s(i,1) = s(i-l,1) + l_s(i-l,i)


s(num_panel+1,1)=0
%***** Thermodynamic properties **********************************************
%Now u e, h e, and s are known.
%Pin = input P (atm)
knownn = input h (J/g or kJ/kg)
%Tout = input T (K)
%**********************************************
%T_e is found by temperature (Pin, known)
%ro is found by density (Pin, Tout)
%mu is found by viscosity (Pin, Tout)
%Pr is found by prandtl (Pin, Tout)
%**************************************************************************


%***** Reynolds number and skin friction

%The flat plate reference enthalpy method is used in each panel, using
%Reynonds' analogy with heat transfer to calculate slin friction for both
laminarr and turbulent cases
%
%Res : Reynolds number based on the local tangential velocity (u_e).
% temperature (T_e), and distance (s) from the stagnation point
%Res =ro e u e s / mu e
%
%cf : local skin friction coefficient
%cf = 2AA/(Pr_eA(1/3)) (roref/ro_e)Asa (muref/mu_e)sb R
%AA = 0.332*PrA(1/3) --------laminar
% 0.0296*PrA(1/3) -------------turbulent
%sa = 0.5 ---------------------laminar
% 0.8 ---------------------turbulent
%sb = 0.5 ---------------------laminar
% 0.2 ---------------------turbulent
%sc = 0.5 ---------------------laminar
% 0.8 ---------------------turbulent
%sj =0 ---------------------flat plate
% 1 ---------------------axisymmetric


s^(sc-1) (3Asj)A0.5


I









%
%Pin : the pressure computed by inviscid analysis for each panel (input for function)
knownn : enthalpy at edge of boundary layer for each panel (input for function)
%Tout : temperature at edge of boundary layer for each panel (input for function)
%he : enthalpy at edge of boundary layer for each panel
%Te :temperature at edge of boundary layer for each panel
%roe :air density at edge of boundary layer for each panel
%mue : viscosity at edge of boundary layer for each panel
%Pre : Prandtl Number at edge of boundary layer for each panel
%href :enthalpy at edge of boundary layer for each panel
%Tref :reference temperature at edge of boundary layer for each panel
%ro ref :reference air density at edge of boundary layer for each panel
%mu ref : reference viscosity at edge of boundary layer for each panel
%Pr ref :reference Prandtl Number at edge of boundary layer for each panel
%hw :enthalpy at wall
%haw :adiabatic wall enthalpy


%****** Flow Properties (again) *******************
% ro: air density (kg/m3)
% Pinf: atmospheric pressuer (N/m2)
% Rair: gas constant of air (287J/kg-K)
% Tinf: free stream temperature (K)
% cpinf: specific heat constant pressure of free stream (J/g-K or kJ/kg-K)
% M: Mach number
% gamma: specific heat ratio
% Vinf: free stream velocity (m/s)
% a: speed of sound (m/s)
% qinf: dynamic pressure (kN/m2)



% Reynolds Number and skin friction for left side
T_e(num_panel+1,1)=Tinf
P_e(num_panel+1,1)=Pinf/101325
cp(num_panel+l, 1)=0.0

for i=1 :num_panel+1
Pin = (cp(i,1)*qinf + Pinf)/101325 % must be in unit ofatm
P_e(i,1)= Pin
known = (0.5*Vinf^2 + Tinf*cpinf- 0.5*(u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)A2))/1000 %unit
of J/g

h_e(i,1) = h known
Tout = temperature (Pin, known)
if i == numpanel+1









Tout=Tinf
end
T_e(i, 1)= Tout

ro_out = density (Pin, Tout)
ro_e(i,1) = ro_out

mu_out = viscosity (Pin, Tout)
mu_e(i,1) = mu_out

Prout = prandtl (Pin, Tout)
Pr e(i, 1)= Prout

end

%tangential component of velocity on "shadow" panel is found by P-M expansion

fori= 1:13
jj(i, 1) = num_panel+1
end
for i= 14:117
jj(i,1) = i-13
end
jj(118,1)= 104
jj(119,1) = num_panel+l
jj(125,1) = num_panel+l
for i= 120:124
jj(i,1) = i-i
end
for i= 126:130
jj(i,1) = i-i
end
jj(131,1) = num_panel+l
jj(137,1) = num_panel+l
for i= 132:136
jj(i,1) = i-i
end
for i= 138:142
jj(i,1) = i-i
end

for i = 1:num_panel
if nunit(i,1) > 0
j=jj(i,1)
Ml = ((u_e(j,1)A2+u_e(j,2)A2+u_e(j,3)A2)/(gamma*Rair*T_e(j,1)))A0.5 %M ofj panel
if MK<









M2 =M1
else
M2 = shadowM (i,jj,u_eunit, T_e, u_e, gamma, ep, Rair) %M of i panel
T_e(i, 1) =T_e(j, 1)*(1+((gamma-1)*M1A2)/2)/(l+((gamma-1)*M2A2)/2)
P_e(i,l) =P_e(j,1)*(T_e(i, 1)/Te(j, 1))A(gamma/(gamma-1))
ro_e(i, 1) = ro_e(j, 1)*(T_e(j, 1)/T_e(i, 1))A( 1/(gamma-1))
Pin = P_e(i,1); Tout=T_e(i,1)
h_e(i,1) =enthalpy (Pin, Tout)
u_e(i,1) = (M2*(gamma*T_e(i,1)*Rair)A0.5)*u_eunit(i,1)
u_e(i,2) = (M2*(gamma*T_e(i,1)*Rair)O0.5)*u_eunit(i,2)
u_e(i,3) = (M2*(gamma*T_e(i,1)*Rair)A0.5)*u_eunit(i,3)
end
end
end

for i=l:num_panel
dF(i, 1) = -P_e(i, 1)*101325*Area(i, 1)*nunit(i, 1)
dF(i,2) = -P_e(i, 1)*101325*Area(i, 1)*nunit(i,2)
dF(i,3) = -P_e(i, 1)*101325*Area(i, 1)*nunit(i,3)
end


for i=l:num_panel
dL(i, 1)= dF(i,3)
dD(i,1)= dF(i,1)


% Lift:
% Drag:
% L D:
Lift inv


lift (N)
drag (N)
L/D ratio
= sum(dL)*2


Draginv = sum(dD)*2
LD inv = Liftinv/Draginv %inviscid
CLinv = Liftinv/qinf/Sref
CDinv = Draginv/qinf/Sref
CNinv= CLinv*cos(aoa*3.14159265359/180)+CDinv*sin(aoa*3.14159265359/180)
CAinv = CDinv*cos(aoa*3.14159265359/180)-CLinv*sin(aoa*3.14159265359/180)
for i=l:num_panel
d_m(i,1) =-
(radi(i,1)*(dF(i,3)*cos(aoa*3.14159265359/180)+dF(i,1)*sin(aoa*3.14159265359/180))-
radi(i,3)*(dF(i,1)*cos(aoa*3.14159265359/180)-dF(i,3)*sin(aoa*3.14159265359/180)))
end
pitching = sum(dm)*2
C_minv = pitching/qinf/Sref/chord

for i=1 :num_panel+1
if s(i, 1) == 0









s(i,1) = 0.000001 %zero Reynolds Number provides NaN heat transfer, so s is set to very
small number like 0.000001
end
Res(i,1) = ro_e(i,1)*((u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)A2)A0.5)*s(i,1)/mu_e(i,1) % Reynolds
Number based on s
end

%to make jj array has the same index
jj(num_panel+1) = 0

% local skin friction
for i=1 :num_panel+1
%hw : enthalpy at wall
%haw : adiabatic wall enthalpy
%href : reference enthalpy
h_aw(i,1) = h_e(i,1) + (Pre(i,1)A0.5)*0.5*(u_e(i, 1)2+u_e(i,2)A2+u_e(i,3)A2)/1000
h_awtub(i,1) = h_e(i,1) + (Pre(i,1)A(1/3))*0.5*(u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)A2)/1000
% here, wall temperature is set to adiabatic wall temperature. hw can
% be also set to the cold case (0 K)
h w(i,1) = 319.5 %h_aw(i,1) (Tw = 314.5K)

h_ref(i,) = 0.28*h_e(i,l) + 0.5*h w(i,1) + 0.22*h_aw(i,1)
h_reftub(i,1) = 0.28*h_e(i,1) + 0.5*h w(i,1) + 0.22*h_awtub(i,1)
%Tref : reference temperature at edge of boundary layer for each panel
%ro ref : reference air density at edge of boundary layer for each panel
%mu ref : reference viscosity at edge of boundary layer for each panel
%Pr ref : reference Prandtl Number at edge of boundary layer for each panel
Pin = P_e(i,1)
%Laminar
h_known = href(i, 1)
Tout = temperature (Pin, known)
T_ref(i,1)= Tout
ro_out = density (Pin, Tout)
roref(i,1) = ro_out
mu_out = viscosity (Pin, Tout)
muref(i, 1) = mu_out
Prout = prandtl (Pin, Tout)
Pr ref(i,1)= Prout
%Turbulent
h_known = hreftub(i,1)
Tout = temperature (Pin, known)
T_reftub(i,1)= Tout
ro_out = density (Pin, Tout)
roreftub(i,1) = ro_out
mu_out = viscosity (Pin, Tout)
mu reftub(i,1) = mu out









Prout = prandtl (Pin, Tout)
Prreftub(i,1)= Prout

%******* skin friction *************************************************
%cf: local skin friction coefficient laminarr)
%cftub : local skin friction coefficient (turbulent)
%***********************************************************************
AA = 0.332*Pre(i,1)A(1/3) %--------------laminar
AAtub = 0.0296*Pre(i, 1)^(1/3) %-------------turbulent
sa = 0.5 %-------------------------laminar
satub = 0.8 %-------------------------turbulent
sb = 0.5 %-------------------------laminar
sbtub = 0.2 %-------------------------turbulent
sc = 0.5 %-------------------------laminar
sctub = 0.8 %-------------------------turbulent
sj = 0 % -------------------------flat plate

cf(i,1) = 2*AA/(Pre(i, 1)(1/3)) (ro_ref(i,1)/ro_e(i, 1))sa (mu_ref(i,1)/mu_e(i, 1))sb *
Res(i, 1)(sc-1) (3Asj)A0.5
cf tub(i,1) = 2*AAtub/(Pre(i, 1)(1/3)) (roreftub(i, 1)/ro_e(i,1))Asatub *
(mureftub(i, 1)/mu_e(i, 1))sbtub Res(i,1)A(sctub-1) (3Asj)A0.5
end

%******** heat transfer (ref enthalpy) ********************************
%q_cw en: Local Heat Transfer by using flat plate reference enthalpy methods (J/s-m2)
%Nu = q_cw*s/(ke *(T w T_aw)) --> q_cwen = cf*Pr_eA(1/3)*Res*ke*(T w -
T_aw)/(2* s)
%***********************************************************************

for i=1 :num_panel+1
Pin = P_e(i,1)
Tout = T_e(i, 1)
k_con = conductivity (Pin, Tout)
k_e(i,1)= kcon % (J/m-sec-K)
end
for i=1 :num_panel+1
known = h w(i,1)
Pin = P_e(i,1)
T_w(i, 1) = temperature (Pin, known)
h_known = h_aw(i,1)
T_aw(i, 1) = temperature (Pin, known)
h_known = h_awtub(i,1)
T_awtub(i, 1) = temperature (Pin, known)
q_cwen(i,1) = -cf(i,1)*(Pr e(i,1)A(1/3))*Res(i,1)*ke(i,1)*(T w(i,) T_aw(i,1))/(2*s(i,1))
% W/m2 J/s-m2,









q_cw en tub(i,1) = -cf tub(i,1)*(Pr_e(i,1)A(1/3))*Res(i,1)*ke(i,1)*(T w(i,1) -
T_awtub(i,l))/(2*s(i,1)) % W/m2 J/s-m2,
end

%********** heat transfer (blunt body)

%q_cw bl : Local Heat Transfer by using blunt body method (J/s-m2)
%q_cw bl(s=0) = (0.9038/(ep^0.25)) (C w/Pre)A0.1 (ro*Vinf*mu_e/Rb/Pr e)^0.5 (h_e
- h w) % at stagnation point, so e : se here
%Cw = (ro w*muw/(ro_e*mu_e)) % e : se here
%Cws = (ro_e*mu_e/(ro_se*mu_se))
%q_cw bl(s) = q_cw bl(s=0) C ws u_e*rbodyAjq / (2A(jq+l) (u_e(i)-u_e(i-1))/(s(i)-s(i-
1)))^0.5 SUM(i=1-->i,C ws(i)*u_e(i)*rbodyA(2*jq)*(s(i)-s(i-1))
%rbody : radius of cross section of bodies of revolution
%jq : 1 for bodies, 0 for 2-D
%**************************************************************************

for i=l:num_panel

z_original=((cent(i, 1)A2+cent(i,3)A2)A0.5)*sin(aoa*3.14159265359/180+atan(cent(i,3)/cent(i, 1))
)
rbody(i, 1)=(cent(i,2)A2+z_original^2)^0.5
end
rbody(num_panel+l1,1)=0.001

%Find stagnation M, ue, T_e for equilibrium condition

rolro2 = 0.1 % step 1: first guess of ro_l/ro_2

press_l = Pinf
temp_l = Tinf
ro 1 = ro
vel 1 = Vinf
enth_l = enthalpy (press_1/101325, temp_l)
error equi = 1
while errorequi > 0.0001
press_2 = press_l + ro_l*(vel_l)A2*(1-rolro2) % step 2: obtain p2
enth_2 = enth_l + (0.5/1000)*(vel_1)A2*(1-rolro2A2) % step 2: obtain h2 (J/g)
P_stag = press_2/101325
temp_2 = temperature (P_stag, enth_2) % step 3: obtain T2
ro_2 = density (P_stag, enth_2) % step 3: obtain ro_2
rolro2new = ro_l/ro 2 % step 4: obtain new rolro2
error equi = abs(rolro2 rolro2new)
rolro2 = rolro2new
end
vel 2 = rolro2 vel 1









M_stag = vel_2/((gamma*temp_2*Rair)A0.5) %Mach number at stagnation point
P_stag = press_2/101325 %Pressure at stagnation point (atm)
T_stag = temp_2 % Temperature at stagnation point (K)
h_stag = enth_2 % enthalpy at stagnation point

u_stag_e = vel_2

P_stag; T_stag; T_sw=temperature (P_stag, h w(1,1)); Pin = P_stag
ro_sw = density (Pin, T_sw); mu_sw = viscosity (Pin, T_sw)
rose = ro/rolro2; mu_se = viscosity (Pin, T_stag)
Prse = prandtl (Pin, T_stag)
h_se = enthalpy (Pin, T_stag); h_sw= enthalpy (Pin, T_sw)
C_w01 = (ro_sw*mu_sw)/ro_se/mu_se
R_b01 = 0.3048%0.10110667%((l+((nod(8,3)-nod(1,3))/(nod(8,1)-
nod(l, 1)))A2)A 1.5)/abs((nod(8,3)-2*nod(1,3)+nod(2,3))/(nod(8, l)-nod(1,1 ))/(nod(2,1 )-nod(l, 1)))
q_cw bl01 = 1000*(0.9038/(epA0.25)) (C w01/Prse)A0.1 *
(ro*Vinf*mu_se/Rb01/Prse)A0.5 (h_se h_sw) % at stagnation point(body) W/m2 J/s-m2, so
e : se here
q_cw bl nose= q_cwbl01

s(num_panel+1,1)=0
u_e(num_panel+l,1)=u_stag_e; u_e(num_panel+l,2)=0; u_e(num_panel+l,3)=0
rbody(num_panel+1,1)=0.0001 %radius of cross section of body
ro_e(num_panel+ 1,1)=ro_se
mu_e(num_panel+1,1)=mu_se
C ws(num_panel+1,1)=1.0

fork= 1:13
SUMq = 0
fori =k:13:117
j=jj(i,1)
C ws(i,1) = (ro_e(i,1)*mu_e(i,l))/(ro_se*mu_se)
f s_l(i,1)= (Cws(i,1)*(u_e(i, 1)2+u_e(i,2)A2+u_e(i,3)A2)0.5)*(rbody(i,1)A2)
f s_0(i,1)= (C ws(j,1)*(u_e(j,1)A2+u_e(j,2)A2+u_e(j,3)A2)A0.5)*(rbody(j,1)A2)
SUMq = SUMq + (fs_0(i,1) + f s_l(i,l))*(s(i,l)-s(j,l))/2
q_cw bl(i,1) = (SUMqA-
0.5)*q_cwbl01*C ws(i,1)*(u_e(i, 1)2+u_e(i,2)A2+u_e(i,3)A2)0.5*rbody(i,1)/((4*(((u_e(k,1)A
2+u_e(k,2)A2+u_e(k,3)A2) 0.5-u_stag_e)/(s(k,1))))A0.5)
end
end

for i=119:130
rbody(i, 1)=1.0 %for two dimensional
end
for i=131:142
rbody(i, 1)=1.0 %for two dimensional











P_stag; T_stag; T_sw=temperature (P_stag, h w(119,1)); Pin = P_stag
ro_sw = density (Pin, T_sw); mu_sw = viscosity (Pin, T_sw)
rose = density (Pin, T_stag); mu_se = viscosity (Pin, T_stag)
Prse = prandtl (Pin, T_stag)
h_se = enthalpy (Pin, T_stag); h_sw= enthalpy (Pin, T_sw)
C_w01 = (ro_sw*mu_sw)/ro_se/mu_se
R_b01 = 0.018548985 %15.17 % ((l+((nod(8,3)-nod(1,3))/(nod(8,1)-
nod(l, 1)))A2)A 1.5)/abs((nod(8,3)-2*nod(1,3)+nod(2,3))/(nod(8, l)-nod(1,1 ))/(nod(2,1 )-nod(l, 1)))
q_cw bl011 = 1000*(0.9038/(epA0.25)) (C wO1/Prse)A0.1 *
(ro*Vinf*mu_se/R_b01/Prse)A0.5 (h_se h_sw) % at stagnation point(wing) W/m2 J/s-m2, so
e : se here

s(num_panel+1,1)=0
u_e(num_panel+l,1)=Vinf; u_e(num_panel+l,2)=0; u_e(num_panel+l,3)=0
%u_e(121,1)=u_stag_e; u_e(121,2)=0; u_e(121,1)=0
%q_cw bl(53,1) = q_cw bl01

SUMq = 0
for i =119:124
j=jj(i,1)
C ws(i,1) = (ro_e(i,1)*mu_e(i,l))/(ro_se*mu_se)
f s_l(i,l) = Cws(i,1)*(u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)A2)A0.5
f s_0(i,l) = Cws(j,l)*(u_e(j,1)A2+u_e(j,2)A2+u_e(j,3)A2)^0.5
SUMq = SUMq + (fs_0(i,1) + f s_l(i,l))*(s(i,l)-s(j,l))/2
q_cw bl(i,1)= (SUMqA-
0.5)*q_cwbl011*C ws(i,1)*(u_e(i, 1)2+u_e(i,2)A2+u_e(i,3)A2)A0.5/((2*(((u_e(121, 1)2+u_e(1
21,2)A2+u_e(121,3)A2)A0.5-u_stag_e)/(s(121,1))))A0.5)
end
SUMq = 0
for i =125:130
j=jj(i,1)
C ws(i,1) = (ro_e(i,1)*mu_e(i,l))/(ro_se*mu_se)
f s_l(i,1)= Cws(i,1)*(u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)^2)0.5
f s_0(i,l) = Cws(j,1)*(u_e(j,1)A2+u_e(j,2)A2+u_e(j,3)A2)A0.5
SUMq = SUMq + (fs_0(i,1) + f s_l(i,l))*(s(i,l)-s(j,l))/2
q_cw bl(i,1)= (SUMqA-
0.5)*q_cwbl011*C ws(i,1)*(u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)A2)A0.5/((2*(((u_e(127,1)A2+u_e(1
27,2) 2+u_e(127,3) 2) 0.5-u_stag_e)/(s(127,1))))A0.5)
end

P_stag; T_stag; T_sw=temperature (P_stag, h w(137,1)); Pin = P_stag
ro_sw = density (Pin, T_sw); mu_sw = viscosity (Pin, T_sw)
rose = density (Pin, T_stag); mu_se = viscosity (Pin, T_stag)
Pr se = prandtl (Pin, Tstag)









h_se = enthalpy (Pin, T_stag); h_sw= enthalpy (Pin, T_sw)
C_w01 = (ro_sw*mu_sw)/ro_se/mu_se
R_b01 = 0.061123322 % ((1+((nod(8,3)-nod(1,3))/(nod(8,1)-
nod(l, 1)))A2) 1.5)/abs((nod(8,3)-2*nod(1,3)+nod(2,3))/(nod(8, l)-nod(1,1 ))/(nod(2,1 )-nod(l, 1)))
q_cw bl012 = 1000*(0.9038/(epA0.25)) (C w01/Prse)A0.1 *
(ro*Vinf*mu_se/Rb01/Prse)A0.5 (h_se h_sw) % at stagnation point(wing) W/m2 J/s-m2, so
e : se here

s(num_panel+1,1)=0
u_e(num_panel+l, 1)=Vinf u_e(num_panel+,2)=0; u_e(num_panel+l,3)=0

SUMq = 0
for i =131:136
j=jj(i,1)
C ws(i,1) = (ro_e(i,1)*mu_e(i,l))/(ro_se*mu_se)
f s_l(i,l) = Cws(i,1)*(u_e(i, 1)A2+u_e(i,2)A2+u_e(i,3)A2)A0.5
f s_0(i,l) = Cws(j,1)*(u_e(j,1)A2+u_e(j,2)A2+u_e(j,3)A2)A0.5
SUMq = SUMq + (fs_0(i,1) + f s_l(i,l))*(s(i,l)-s(j,l))/2
q_cw bl(i,1)= (SUMqA-
0.5)*q_cwbl012*C ws(i, )*(u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)A2)A0.5/((2*(((u_e(121,1)A2+u_e(1
21,2)A2+u_e(121,3)A2)A0.5-u_stag_e)/(s(121,1))))A0.5)
end
SUMq = 0
for i =137:142
j=jj(i,1)
C ws(i,1) = (ro_e(i,1)*mu_e(i,l))/(ro_se*mu_se)
f s_l(i,l) = Cws(i,1)*(u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)A2)A0.5
f s_0(i,l) = Cws(j,1)*(u_e(j,1)A2+u_e(j,2)A2+u_e(j,3)A2)A0.5
SUMq = SUMq + (fs_0(i,1) + f s_l(i,l))*(s(i,l)-s(j,l))/2
q_cw bl(i,1)= (SUMqA-
0.5)*q_cwbl012*C ws(i,l)*(u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)A2)A0.5/((2*(((u_e(127,1)A2+u_e(l
27,2)A2+u_e(127,3)A2)A0.5-u_stag_e)/(s(127,1))))A0.5)
end

%***** heat transfer choice

%
% q_cw : heat transfer at each panel (J/m-s2)
%
% q_cw en: Local Heat Transfer by using flat plate reference enthalpy methods (J/s-m2)
% q_cw bl : Local Heat Transfer by using blunt body method (J/s-m2)
%
% Around the stagnation points, the flat plate reference enthalpy method provides
% extremely high value of the heat transfer as discussed before, so the blunt bodies
% solutions should be used for the panels around the stagnation points. For far
% panels from the stagnation points, the both methods agree closely, and at least









% both have the similar behavior. Therefore, the flat plate reference enthalpy method
% is used to find the heat transfer for far surface of the body and wings.
%
% *around the stagnation point or leading edge: stagnation point(panel) next panel
% otherwise, far from the stagnation points
%
% tangential component of velocity on "shadow" panel is found by P-M expansion
% sb =[nosevector; nunit(6,1); nunit(12,1); nunit(18,1); nunit(24,1); nunit(30,1)]
% swl =[nunit(53,1); nunit(52,1); nunit(51,1)]
% sw2 =[nunit(64,1); nunit(63,1); nunit(62,1)]
% s w3 =[nunit(74,1); nunit(73,1)]
%****************************************************************************
**********

q_cw = q_cwen tub %set q_cw to q_cw en here, and q_cw bl will be applied to around the
stagnation later

for i=l:num_panel
St2(i,1) = q_cw(i,1)/(ro*Vinf)/(h_se h w(i,1))/1000
end
Pin=Pinf/101325; Tout=Tinf
mu_e(num_panel+l,1) = viscosity (Pin, Tout)
Reinf = ro*Vinf/mu_e(num_panel+l, 1) %Reynolds number divided by certain characteristic
length
%Use blunt body scheme is applied only for the stagnation points(body and
%wing) and the the most downstream panel of each stream.

%***** cooling analysis

%
% cf: local skin friction coefficient laminarr)
% cftub : local skin friction coefficient (turbulent)
% cfcool : local skin friction coefficient of cooled condition. This array
% includes cf at non-cooled panels also.
%
% q_cw : Local Heat Transfer (J/s-m2); reference enthalpy method or blun body method
% q_cw_cool : local heat transfer (J/s-m2) of cooled condition. This array
% includes q_cw at non-cooled panels also.
%
% nunit: n (N unit) vector of each panel
% Area: area of each panel (m2)
% roe : air density at edge of boundary layer for each panel (kg/m3)
% ue : tangential component of velocity on each panel (m/s)
% vw : normal velocity at the wall of each panel (m/s)
% ro w : injected gas density at the wall (kg/m3)
%









% Lift vis: lift (N) (viscous without cooling)
% Liftviscool: lift (N) (viscous with cooling)
% Dragvis: drag (N) (viscous without cooling)
% Dragviscool: drag (N) (viscous with cooling)
% L D vis: L/D ratio (viscous without cooling)
% L D viscool: L/D ratio (viscous with cooling)
% dF f: differential friction force (N) acting on each panel (without cooling)
% dF fcool: differential friction force (N) acting on each panel (with cooling)
% dLr: differential lift force acting on each panel (right side)
% dDr: differential drag force acting on each panel (right side)
%****************************************************************************
****************

%*** Total L/D ratio of viscous case without cooling *********

for i=l:num_panel
qinf e(i, 1)= ro_e(i,1)*(u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)A2)/2.0
dFfx(i, 1)=
cf tub(i,1)*qinf e(i,1)*Area(i,1)*u_e(i,1)/((u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)A2)0.5)
dF_fy(i,1)=
cf tub(i, )*qinf e(i,1)*Area(i,1)*u_e(i,2)/((u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)A2)A0.5)
dF fz(i, 1)=
cf tub(i,1)*qinf e(i,1)*Area(i,1)*u_e(i,3)/((u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)A2)0.5)

end

Lift_vis = (sum(dL)+sum(dFfz(:,1)))*2
Drag vis = (sum(dD)+sum(dFfx(:,1)))*2
LD vis = Liftvis/Drag vis
CLvis = Lift vis/qinf/Sref
CDvis = Drag vis/qinf/Sref
CNvis = CLvis*cos(aoa*3.14159265359/180)+CDvis*sin(aoa*3.14159265359/180)
CAvis = CDvis*cos(aoa*3.14159265359/180)-CLvis*sin(aoa*3.14159265359/180)

for i=l:num_panel
d_mvis(i,1)= -
(radi(i, )*((dF(i,3)+dF fz(i, ))*cos(aoa*3.14159265359/180)+(dF(i, )+dFfx(i,1))*sin(aoa*3.1
4159265359/180))-radi(i,3)*((dF(i,1)+dF_fx(i,1))*cos(aoa*3.14159265359/180)-
(dF(i,3)+dFfz(i,1))*sin(aoa*3.14159265359/180)))
end
pitching vis = sum(dmvis)*2
C_mvis = pitching vis/qinf/Sref/chord

%*** Determine the panel cooled ***********************************
% panel around the bottom noze: [8,9,10,11,12,13,14] (not stagnation point)
%









% Injected Gas properties:
% H2: 0.08078kg/m3 (T=300K)
%******************************************************************

intbf = 11 %the number of step of 0.1 in bf. (intbf 1)*0.1 = max ofbf
massrate_step = 0.001 %kg/m2-s

%partial bottom panels are cooled
for i=l:num_panel
forj=l:intbf
cfcool(ij) = cf tub(i,1)
end
end

for i=l:num_panel
Nu(i,) = -q_cw(i, )*s(i,1)/(ke(i,1)*(T w(i, )-T_aw(i,1)))
end

for i=l:num_panel
St(i, 1) = Pre(i,l)*Nu(i,1)/Res(i,1)
end

for i=l:num_panel
forj=l:intbf
q_cw cool(i,j) = q_cw(i,1)
end
end

A cool2 =0
for i= 1:1:num_panel
if q_cw(i,1)>0 %Choose panels to be cooled here by setting the minimum value of allowable
heat trans.
cooled_panel2(i, 1)=1.0
A_cool2 = A_cool2+Area(i,1)
%l:num_panel%all panels
forj = 1:intbf
m_inj(i,j)=mass_rate_step*(j-1)
bf2(ij)=m_inj(ij)/(0.5*cf tub(i,1)*ro_e(i,1)*(u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)A2)A0.5)
bh2(ij)= minj(ij)/(St(i,1)*ro_e(i,1)*(u_e(i, 1)A2+u_e(i,2)A2+u_e(i,3)A2)A0.5)
ifj==1
cfcool(ij) = cf tub(i,1)
q_cw cool(i,j) = q_cw(i,1)
else
cfcool(ij) = cftub(i, )*(bf2(ij)/(exp(bf2(ij))-1))
q_cw cool(ij) = q_cw(i,1)*(bh2(ij)/(exp(bh2(ij))-1))
end









end
else
end
end

for i=l:num_panel
qinf e(i,1) =ro_e(i,1)*(u_e(i,1)A2+u_e(i,2)A2+u_e(i,3)A2)/2.


forj=l:int bf
dF fxcool(ij) =
cfcool(ij)*qinf e(i,1)*Area(i,1)*u_e(i,1)/((u_
dFfycool(ij) =
cfcool(ij)*qinf e(i,1)*Area(i,1)*u_e(i,2)/((u
dF fzcool(ij) =
cfcool(ij)*qinf e(i,1)*Area(i,1)*u_e(i,3)/((u_
end
end

Q total=0.0
for i=l:num_panel
Q_total = Qtotal + q_cw(i,1)*Area(i,1)
end


e(i, 1)A2+u_e(i,2)A2+u_e(i,3)^2)A0.5)

e(i,1)A2+u_e(i,2)A2+u_e(i,3)^2)A0.5)

e(i,1)A2+ue(i,2)A2+ue(i,3)A2)A0.5)


forj=l:intbf
Liftviscool2(j,) = (sum(dL)+sum(dFfzcool(:j)))*2
Drag viscool2(j,) = (sum(dD)+sum(dF_fxcool(:,j)))*2
L D viscool2(j,1) = Liftviscool2(j,1)/Drag viscool2(j,1)
L_Dimprovement2(j,1)=L D viscool2(j,1)/L D vis
Q total cool=0.0
for i=l:num_panel
Q_total_cool = Qtotal_cool + q_cwcool(i,j)*Area(i, 1)
end
q_cwimprovement2(j, 1)=Q_total_cool/Qtotal
end









APPENDIX B
MATLAB CODE (FUNCTION) TO COMPUTE TEMPERATURE



%code thermoproperty (temperature)
%This code compute thermodynamic property of air as function of T an P
%Thermodynamic property includes:
compressibilityy Z(T, P)
%temperature T(P, h)
%density ro(T, P)
%viscocity mu(T,P)
%Prandtl number Pr
%Inputs are: entahlpy and pressure, so h and P must be known
%output of this code is accurate but not exact solution


%****** Input *************************************************************
%Pin : Pressure input, this value must be known unit:atm
knownw: enthalpy input, this value must be known unit:J/g or kJ/kg

function [Tout] = temperature (Pin, known)

%Pin = 0.01 %Pressure input, this value must be known unit:atm
knownn = 11054.6 %enthalpy input, this value must be known unit:J/g or kJ/kg


%****** Compressibility ***************************************************
%computed by using interp2 function with known Hansen's data (T and P)
%inter2 is function of 2-D data interpolation
%T : temperature
%P : pressure
%Tin : input temperature
%Pin : input pressure
%ZTP : compressibility table
%Z : compressibility of air as f(Tin, Pin)


T = 0:500:15000 %Temperature range OK --> 15000K
P = [100 10 1 0.1 0.01 0.001 0.0001 0] %Pressure range Oatm --> 0.0001atm --> 100atm
ZTP =[1.000 1.000 1.000 1.000 1.000 1.000 1.003 1.012 1.033 1.071 1.118 1.159 ...
1.189 1.214 1.243 1.284 1.341 1.418 1.512 1.616 1.718 1.807 1.876 1.927 1.965 ...
1.993 2.017 2.039 2.062 2.086 2.113
1.000 1.000 1.000 1.000 1.000 1.001 1.009 1.035 1.089 1.149 1.186 1.208 ...
1.235 1.279 1.351 1.457 1.590 1.727 1.838 1.914 1.962 1.993 2.018 2.042 2.067 ...
2.098 2.135 2.180 2.233 2.297 2.372
1.000 1.000 1.000 1.000 1.000 1.004 1.026 1.092 1.165 1.196 1.214 1.248 ...









1.316 1.437 1.607 1.778 1.896 1.959 1.993 2.018 2.042 2.071 2.111 2.163 2.232 ...
2.318 2.426 2.553 2.700 2.861 3.028
1.000 1.000 1.000 1.000 1.001 1.011 1.072 1.167 1.198 1.213 1.252 1.348 ...
1.529 1.752 1.904 1.971 2.001 2.023 2.050 2.090 2.149 2.234 2.351 2.505 2.694 ...
2.910 3.135 3.347 3.527 3.667 3.769
1.000 1.000 1.000 1.000 1.002 1.033 1.149 1.197 1.208 1.245 1.359 1.599 ...
1.849 1.961 1.997 2.017 2.044 2.090 2.166 2.286 2.462 2.700 2.983 3.272 3.520 ...
3.700 3.818 3.889 3.932 3.957 3.973
1.000 1.000 1.000 1.000 1.005 1.088 1.192 1.203 1.228 1.337 1.622 1.898 ...
1.983 2.006 2.027 2.067 2.144 2.284 2.510 2.832 3.202 3.526 3.745 3.867 3.931 ...
3.963 3.979 3.988 3.993 3.996 3.997
1.000 1.000 1.000 1.000 1.016 1.163 1.200 1.211 1.287 1.577 1.910 1.990 ...
2.008 2.032 2.088 2.210 2.446 2.826 3.282 3.645 3.843 3.932 3.969 3.985 3.993 ...
3.996 3.998 3.999 3.999 4.000 4.000
1.000 1.000 1.000 1.000 1.016 1.163 1.200 1.211 1.287 1.577 1.910 1.990 ...
2.008 2.032 2.088 2.210 2.446 2.826 3.282 3.645 3.843 3.932 3.969 3.985 3.993 ...
3.996 3.998 3.999 3.999 4.000 4.000]


%****** Temperature *******************************************************
%Z function is known, T and h relation is computed by using interp2 function with
%known Hansen's data (h, P, and Z)
%Now, P and h are known. Set P known and assume T and iterate to match h
%given by T and h relation
%T : temperature (K)
%P : pressure (atm)
%h : enthalpy (J/g)
knownn : enthalpy known (input enthalpy) (J/g)
%Z : compressibility
%R : universal gas constant (J/mol-K)
%MWair : molecular weight (g/mol)
%ZH RT : dimensionless enthalpy (Zh/RT) table givenin Hansen's
%ZHRT : dimensionless enthalpy (Zh/RT) as function of (T, P)
%Tin : input temperature (guessed temperature)
%Pin : input pressure
%ZTP : compressibility table
%Z : compressibility of air as f(Tin, Pin)


T = 0:500:15000 %Temperature range OK --> 15000K
P = [100 10 1 0.1 0.01 0.001 0.0001 0] %Pressure range Oatm --> 0.OOO1atm --> OOatm
ZHRT = [3.52 3.52 3.65 3.80 3.92 4.01 4.13 4.34 4.70 5.20 5.73 6.13 6.38 6.62 6.95 7.44 8.16

9.10 10.20 11.36 12.42 13.23 13.77 14.08 14.22 14.28 14.30 14.31 14.34 14.40 14.49
3.52 3.52 3.65 3.80 3.92 4.03 4.25 4.75 5.56 6.29 6.62 6.80 7.11 7.72 8.76 10.24 11.99 13.63









14.79 15.40 15.61 15.64 15.60 15.58 15.62 15.74 15.96 16.28 16.71 17.26 17.92
3.52 3.52 3.65 3.80 3.92 4.09 4.61 5.75 6.74 6.98 7.10 7.58 8.70 10.64 13.20 15.48 16.73
17.09 17.04 ...
16.91 16.84 16.90 17.13 17.57 18.24 19.16 20.32 21.72 23.29 24.98 26.66
3.52 3.52 3.65 3.80 3.93 4.27 5.55 7.08 7.28 7.33 7.96 9.73 12.93 16.46 18.34 18.66 18.43
18.17 ...
18.09 18.29 18.85 19.84 21.31 23.28 25.69 28.36 30.99 33.27 34.97 36.02 36.53
3.52 3.52 3.65 3.80 3.97 4.81 7.13 7.62 7.53 8.14 10.48 15.14 19.30 20.35 20.01 19.54 19.34

19.60 20.49 22.17 24.78 28.28 32.31 36.13 39.01 40.66 41.26 41.17 40.69 40.01 39.24
3.52 3.52 3.65 3.80 4.07 6.16 8.02 7.77 8.09 10.55 16.68 21.58 21.97 21.24 20.69 20.72 21.65

23.85 27.66 33.00 38.79 43.28 45.57 46.09 45.64 44.74 43.69 42.61 41.55 40.53 39.57
3.52 3.52 3.65 3.80 4.41 8.02 8.19 8.03 9.82 16.80 23.46 23.58 22.54 21.93 22.29 24.26 28.65

35.75 43.74 49.15 50.96 50.64 49.48 48.07 46.64 45.26 43.97 42.76 41.64 40.58 39.60
3.52 3.52 3.65 3.80 4.41 8.02 8.19 8.03 9.82 16.80 23.46 23.58 22.54 21.93 22.29 24.26 28.65

35.75 43.74 49.15 50.96 50.64 49.48 48.07 46.64 45.26 43.97 42.76 41.64 40.58 39.60]

%P and h are known. Set P known and assume T and iterate to match h
%given by T and h relation above
R = 8.3144 %universal gas constant unit:J/K-mol
MWair = 29
cp_0 = 1.0 % specific heat constant pressure at T = OK
Tin = hknown/cp_0 %guess temperature, unit:K
dh = -1 % initialize difference between hi and h known
while dh < 0
Z = interp2(T, P, ZTP,Tin, Pin)
ZHRT = interp2(T, P, ZH RT,Tin, Pin)
hi = ZHRT*R*Tin/Z/MWair %enthalpy i unit:J/g
dh = h known hi
Tin = Tin 5
end
Tout = Tin + 5 %unit:K










APPENDIX C
MATLAB CODE (FUNCTION) TO COMPUTE DENSITY


o%**************************************************************************
%code thermoproperty
%This code compute thermodynamic property of air as function of T an P
%Thermodynamic property includes:
compressibilityy Z(T, P)
%temperature T(P, h)
%density ro(T, P)
%viscocity mu(T,P)
%Prandtl number Pr
%Inputs are: entahlpy and pressure, so h and P must be known
%output of this code is accurate but not exact solution
0%**************************************************************************

%****** Input*************************************************************
%Pin : Pressure input, this value must be known unit:atm
%h_known : enthalpy input, this value must be known unit:J/g or kJ/kg
%**************************************************************************
function [ro] = density (Pin, Tout)


T = 0:500:15000 %Temperature range OK --> 15000K
P = [100 10 1 0.1 0.01 0.001 0.0001 0] %Pressure range Oatm --> 0.OOO1atm --> 00atm
ZTP =[1.000 1.000 1.000 1.000 1.000 1.000 1.003 1.012 1.033 1.071 1.118 1.159...
1.189 1.214 1.243 1.284 1.341 1.418 1.512 1.616 1.718 1.807 1.876 1.927 1.965 ...
1.993 2.017 2.039 2.062 2.086 2.113
1.000 1.000 1.000 1.000 1.000 1.001 1.009 1.035 1.089 1.149 1.186 1.208 ...
1.235 1.279 1.351 1.457 1.590 1.727 1.838 1.914 1.962 1.993 2.018 2.042 2.067 ...
2.098 2.135 2.180 2.233 2.297 2.372
1.000 1.000 1.000 1.000 1.000 1.004 1.026 1.092 1.165 1.196 1.214 1.248 ...
1.316 1.437 1.607 1.778 1.896 1.959 1.993 2.018 2.042 2.071 2.111 2.163 2.232 ...
2.318 2.426 2.553 2.700 2.861 3.028
1.000 1.000 1.000 1.000 1.001 1.011 1.072 1.167 1.198 1.213 1.252 1.348 ...
1.529 1.752 1.904 1.971 2.001 2.023 2.050 2.090 2.149 2.234 2.351 2.505 2.694 ...
2.910 3.135 3.347 3.527 3.667 3.769
1.000 1.000 1.000 1.000 1.002 1.033 1.149 1.197 1.208 1.245 1.359 1.599 ...
1.849 1.961 1.997 2.017 2.044 2.090 2.166 2.286 2.462 2.700 2.983 3.272 3.520 ...
3.700 3.818 3.889 3.932 3.957 3.973
1.000 1.000 1.000 1.000 1.005 1.088 1.192 1.203 1.228 1.337 1.622 1.898 ...
1.983 2.006 2.027 2.067 2.144 2.284 2.510 2.832 3.202 3.526 3.745 3.867 3.931 ...
3.963 3.979 3.988 3.993 3.996 3.997
1.000 1.000 1.000 1.000 1.016 1.163 1.200 1.211 1.287 1.577 1.910 1.990 ...
2.008 2.032 2.088 2.210 2.446 2.826 3.282 3.645 3.843 3.932 3.969 3.985 3.993 ...
3.996 3.998 3.999 3.999 4.000 4.000
1.000 1.000 1.000 1.000 1.016 1.163 1.200 1.211 1.287 1.577 1.910 1.990 ...
2.008 2.032 2.088 2.210 2.446 2.826 3.282 3.645 3.843 3.932 3.969 3.985 3.993 ...
3.996 3.998 3.999 3.999 4.000 4.000]
R = 8.3144 %universal gas constant unit:J/K-mol










MWair = 29


%****** density *******************
%density is found by using simple equation of state with compressibility
%ro = P*MWair/(Z*R*T)
%ro : density (kg/m3)
%/Z compressibilityy
%MWair : molecular weight (g/mol)
%R : universal gas constant (J/mol-K)
%T : temperature computed above (K)
%**************************************************************************

Z = interp2(T, P, ZTP,Tout, Pin)
ro = Pin* 101325*MWair/R/Tout/1000










APPENDIX D
MATLAB CODE (FUNCTION) TO COMPUTE VOSCOSITY


%**************************************************************************
%code thermo_property (viscosiy)
%This code compute thermodynamic property of air as function of T an P
%Thermodynamic property includes:
compressibilityy Z(T, P)
%temperature T(P, h)
%density ro(T, P)
%viscocity mu(T,P)
%Prandtl number Pr
%Inputs are: entahlpy and pressure, so h and P must be known
%output of this code is accurate but not exact solution
%**************************************************************************

%****** Input *************************************************************
%Pin : Pressure input, this value must be known unit:atm
%h_known: enthalpy input, this value must be known unit:J/g or kJ/kg
%**************************************************************************
function [mu] = viscosity (Pin, Tout)

%Pin = 0.01 %Pressure input, this value must be known unit:atm
%h_known = 11054.6 %enthalpy input, this value must be known unit:J/g or kJ/kg


%****** Compressibility ***************************************************
%computed by using interp2 function with known Hansen's data (T and P)
%inter2 is function of 2-D data interpolation
%T :temperature
%P :pressure
%Tin : input temperature
%Pin : input pressure
%ZTP : compressibility table
%Z : compressibility of air as f(Tin, Pin)
%**************************************************************************

R = 8.3144 %universal gas constant unit:J/K-mol
MWair = 29

%****** Viscosity ***************************************************
%computed by using interp2 function with known Hansen's data (T and P)
%inter2 is function of 2-D data interpolation
%T :temperature
%P :pressure
%Tout : input temperature (computed above)
%Pin : input pressure
%Cmu : viscousity ratio (mu/nuO) given in Hansen's
%mu0 : reference viscosity
%mu : viscosity (gm/cm-s)










o/**************************************************************************

T = 0:500:15000 %Temperature range OK --> 15000K
P = [100 10 1 0.1 0.01 0.001 0.0001 0] %Pressure range Oatm --> 0.OOO1atm --> 10Oatm
Cmu= [1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.003 1.010 1.022 1.036 1.050 1.072 1.089
1.112 ...
1.143 1.185 1.238 1.298 1.361 1.418 1.467 1.509 1.549 1.577 1.581 1.594 1.599 1.601 1.604
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.001 1.008 1.022 1.036 1.052 1.067 1.090 1.124 1.175
1.238 ...
1.307 1.368 1.418 1.468 1.496 1.501 1.511 1.520 1.516 1.508 1.492 1.468 1.415 1.387
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.003 1.016 1.029 1.043 1.060 1.090 1.139 1.208 1.283
1.342 ...
1.386 1.425 1.438 1.445 1.448 1.442 1.424 1.394 1.342 1.274 1.187 1.082 0.940 0.828
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.006 1.020 1.033 1.051 1.086 1.148 1.229 1.294 1.332
1.371 ...
1.386 1.396 1.393 1.375 1.335 1.267 1.168 1.040 0.881 0.711 0.547 0.408 0.268 0.212
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.010 1.022 1.033 1.051 1.086 1.148 1.229 1.294 1.332
1.347 ...
1.343 1.314 1.251 1.143 0.983 0.782 0.571 0.387 0.249 0.158 0.100 0.067 0.042 0.016
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.010 1.024 1.055 1.128 1.209 1.257 1.286 1.303 1.307
1.280 ...
1.207 1.068 0.853 0.595 0.361 0.200 0.108 0.063 0.036 0.024 0.018 0.015 0.013 0.012
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.011 1.032 1.096 1.181 1.227 1.256 1.271 1.264 1.210
1.072 ...
0.826 0.517 0.261 0.118 0.055 0.029 0.018 0.012 0.009 0.008 0.007 0.007 0.008 0.008
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.011 1.032 1.096 1.181 1.227 1.256 1.271 1.264 1.210
1.072 ...
0.826 0.517 0.261 0.118 0.055 0.029 0.018 0.012 0.009 0.008 0.007 0.007 0.008 0.008]

mu0 = 1.462*((Tout)^0.5)/(1+112/Tout)*10^-5
mu = interp2(T, P, Cmu, Tout, Pin)*mu0/10










APPENDIX E
MATLAB CODE (FUNCTION) TO COMPUTE PRANDTL NUMBER


%**************************************************************************
%code thermo_property (Prandtl number)
%This code compute thermodynamic property of air as function of T an P
%Thermodynamic property includes:
compressibilityy Z(T, P)
%temperature T(P, h)
%density ro(T, P)
%viscocity mu(T,P)
%Prandtl number Pr
%Inputs are: entahlpy and pressure, so h and P must be known
%output of this code is accurate but not exact solution
%**************************************************************************

%****** Input *************************************************************
%Pin : Pressure input, this value must be known unit:atm
%h_known: enthalpy input, this value must be known unit:J/g or kJ/kg
%**************************************************************************
function [Pr] = prandtl (Pin, Tout)

%Pin = 0.01 %Pressure input, this value must be known unit:atm
%h_known = 11054.6 %enthalpy input, this value must be known unit:J/g or kJ/kg


%****** Compressibility ***************************************************
%computed by using interp2 function with known Hansen's data (T and P)
%inter2 is function of 2-D data interpolation
%T :temperature
%P :pressure
%Tin : input temperature
%Pin : input pressure
%ZTP : compressibility table
%Z : compressibility of air as f(Tin, Pin)
%**************************************************************************


%****** Prandtl number ***************************************************
%computed by using interp2 function with known Hansen's data (T and P)
%inter2 is function of 2-D data interpolation
%T :temperature
%P :pressure
%Tout : input temperature (computed above)
%Pin : input pressure
%Prtable : Prandtl number given in Hansen's
%Pr : Prandtl number

T = 0:500:15000 %Temperature range OK ***************************************-> 15000K
T = 0:500:15000 %Temperature range OK --> 15000K










P = [100 10 1 0.1 0.01 0.001 0.0001 0] %Pressure range 0 atm --> 0.0001atm --> lOOatm
Prtable =[0.738 0.738 0.756 0.767 0.773 0.762 0.740 0.678 0.640 0.654 0.702 0.748 0.763 0.610 0.593
0.595 ...
0.620 0.666 0.730 0.806 0.886 0.937 0.955 0.947 0.908 0.728 0.525 0.438 0.421 0.401 0.394
0.738 0.738 0.756 0.767 0.773 0.751 0.680 0.631 0.662 0.743 0.767 0.620 0.592 0.592 0.620 0.688
0.788 ...
0.891 0.961 0.966 0.872 0.532 0.463 0.434 0.412 0.396 0.383 0.369 0.360 0.349 0.341
0.738 0.738 0.756 0.767 0.773 0.696 0.627 0.660 0.762 0.752 0.611 0.583 0.602 0.673 0.796 0.927
0.983 ...
0.943 0.807 0.497 0.429 0.404 0.382 0.369 0.355 0.343 0.333 0.319 0.302 0.277 0.253
0.738 0.738 0.756 0.767 0.766 0.645 0.636 0.744 0.759 0.610 0.581 0.617 0.738 0.906 0.986 0.969
0.648 ...
0.411 0.382 0.364 0.348 0.339 0.327 0.312 0.292 0.263 0.227 0.185 0.144 0.0986 0.0819
0.738 0.738 0.756 0.767 0.724 0.611 0.740 0.737 0.619 0.578 0.624 0.785 0.969 0.955 0.830 0.424
0.387 ...
0.363 0.348 0.336 0.319 0.295 0.254 0.201 0.146 0.101 0.0688 0.0470 0.0345 0.0245 0.0129
0.738 0.738 0.756 0.767 0.668 0.654 0.745 0.658 0.580 0.611 0.799 0.989 0.891 0.464 0.404 0.371
0.351 ...
0.335 0.316 0.279 0.216 0.145 0.0877 0.0524 0.0346 0.0238 0.0190 0.0162 0.0149 0.0130 0.0120
0.738 0.738 0.756 0.767 0.614 0.771 0.714 0.606 0.587 0.764 0.993 0.871 0.455 0.392 0.361 0.342
0.322 ...
0.279 0.200 0.114 0.0576 0.0314 0.0213 0.0167 0.0143 0.0129 0.0121 0.0110 0.0108 0.0109 0.0110
0.738 0.738 0.756 0.767 0.614 0.771 0.714 0.606 0.587 0.764 0.993 0.871 0.455 0.392 0.361 0.342
0.322 ...
0.279 0.200 0.114 0.0576 0.0314 0.0213 0.0167 0.0143 0.0129 0.0121 0.0110 0.0108 0.0109
0.0110]

Pr = interp2(T, P, Pr table, Tout, Pin)










APPENDIX F
MATLAB CODE (FUNCTION) TO COMPUTE ENTHALPY


oV**************************************************************************
%code enthalpy
%This code compute thermodynamic property of air as function of T an P
%
%Inputs are: temperature and pressure, so T and P must be known
%output of this code is accurate but not exact solution
0V**************************************************************************

%****** Input *************************************************************
%****** Input
%Pin : Pressure input, this value must be known unit:atm
%Tout : Temperature input, this value must be known unit:K
0V**************************************************************************
function [h known] = enthalpy (Pin, Tout)


%****** Compressibility ***************************************************
%computed by using interp2 function with known Hansen's data (T and P)
%inter2 is function of 2-D data interpolation
%T :temperature
%P :pressure
%Tin : input temperature
%Pin : input pressure
%ZTP : compressibility table
%Z : compressibility of air as f(Tin, Pin)
0 **************************************************************************

T = 0:500:15000 %Temperature range OK --> 15000K
P = [100 10 1 0.1 0.01 0.001 0.0001 0] %Pressure range Oatm --> 0.OOO1atm --> 00atm
ZTP =[1.000 1.000 1.000 1.000 1.000 1.000 1.003 1.012 1.033 1.071 1.118 1.159...
1.189 1.214 1.243 1.284 1.341 1.418 1.512 1.616 1.718 1.807 1.876 1.927 1.965 ...
1.993 2.017 2.039 2.062 2.086 2.113
1.000 1.000 1.000 1.000 1.000 1.001 1.009 1.035 1.089 1.149 1.186 1.208 ...
1.235 1.279 1.351 1.457 1.590 1.727 1.838 1.914 1.962 1.993 2.018 2.042 2.067 ...
2.098 2.135 2.180 2.233 2.297 2.372
1.000 1.000 1.000 1.000 1.000 1.004 1.026 1.092 1.165 1.196 1.214 1.248 ...
1.316 1.437 1.607 1.778 1.896 1.959 1.993 2.018 2.042 2.071 2.111 2.163 2.232 ...
2.318 2.426 2.553 2.700 2.861 3.028
1.000 1.000 1.000 1.000 1.001 1.011 1.072 1.167 1.198 1.213 1.252 1.348 ...
1.529 1.752 1.904 1.971 2.001 2.023 2.050 2.090 2.149 2.234 2.351 2.505 2.694 ...
2.910 3.135 3.347 3.527 3.667 3.769
1.000 1.000 1.000 1.000 1.002 1.033 1.149 1.197 1.208 1.245 1.359 1.599 ...
1.849 1.961 1.997 2.017 2.044 2.090 2.166 2.286 2.462 2.700 2.983 3.272 3.520 ...
3.700 3.818 3.889 3.932 3.957 3.973
1.000 1.000 1.000 1.000 1.005 1.088 1.192 1.203 1.228 1.337 1.622 1.898 ...
1.983 2.006 2.027 2.067 2.144 2.284 2.510 2.832 3.202 3.526 3.745 3.867 3.931 ...
3.963 3.979 3.988 3.993 3.996 3.997
1.000 1.000 1.000 1.000 1.016 1.163 1.200 1.211 1.287 1.577 1.910 1.990 ...










2.008 2.032 2.088 2.210 2.446 2.826 3.282 3.645 3.843 3.932 3.969 3.985 3.993 ...
3.996 3.998 3.999 3.999 4.000 4.000
1.000 1.000 1.000 1.000 1.016 1.163 1.200 1.211 1.287 1.577 1.910 1.990 ...
2.008 2.032 2.088 2.210 2.446 2.826 3.282 3.645 3.843 3.932 3.969 3.985 3.993 ...
3.996 3.998 3.999 3.999 4.000 4.000]


%****** Temperature *******************************************************
%Z function is known, T and h relation is computed by using interp2 function with
%known Hansen's data (h, P, and Z)
%Now, P and h are known. Set P known and assume T and iterate to match h
%given by T and h relation
%T : temperature (K)
%P : pressure (atm)
%h : enthalpy (J/g)
%h_known : enthalpy known (input enthalpy) (J/g)
%Z compressibilityy
%R : universal gas constant (J/mol-K)
%MWair : molecular weight (g/mol)
%ZHRT : dimensionless enthalpy (Zh/RT) table givenin Hansen's
%ZHRT : dimensionless enthalpy (Zh/RT) as function of (T, P)
%Tin : input temperature (guessed temperature)
%Pin : input pressure
%ZTP : compressibility table
%Z : compressibility of air as f(Tin, Pin)
0V**************************************************************************

T = 0:500:15000 %Temperature range OK --> 15000K
P = [100 10 1 0.1 0.01 0.001 0.0001 0] %Pressure range Oatm --> 0.OOO1atm --> OOatm
ZHRT = [3.52 3.52 3.65 3.80 3.92 4.01 4.13 4.34 4.70 5.20 5.73 6.13 6.38 6.62 6.95 7.44 8.16 ...
9.10 10.20 11.36 12.42 13.23 13.77 14.08 14.22 14.28 14.30 14.31 14.34 14.40 14.49
3.52 3.52 3.65 3.80 3.92 4.03 4.25 4.75 5.56 6.29 6.62 6.80 7.11 7.72 8.76 10.24 11.99 13.63 ...
14.79 15.40 15.61 15.64 15.60 15.58 15.62 15.74 15.96 16.28 16.71 17.26 17.92
3.52 3.52 3.65 3.80 3.92 4.09 4.61 5.75 6.74 6.98 7.10 7.58 8.70 10.64 13.20 15.48 16.73 17.09 17.04

16.91 16.84 16.90 17.13 17.57 18.24 19.16 20.32 21.72 23.29 24.98 26.66
3.52 3.52 3.65 3.80 3.93 4.27 5.55 7.08 7.28 7.33 7.96 9.73 12.93 16.46 18.34 18.66 18.43 18.17 ...
18.09 18.29 18.85 19.84 21.31 23.28 25.69 28.36 30.99 33.27 34.97 36.02 36.53
3.52 3.52 3.65 3.80 3.97 4.81 7.13 7.62 7.53 8.14 10.48 15.14 19.30 20.35 20.01 19.54 19.34 ...
19.60 20.49 22.17 24.78 28.28 32.31 36.13 39.01 40.66 41.26 41.17 40.69 40.01 39.24
3.52 3.52 3.65 3.80 4.07 6.16 8.02 7.77 8.09 10.55 16.68 21.58 21.97 21.24 20.69 20.72 21.65 ...
23.85 27.66 33.00 38.79 43.28 45.57 46.09 45.64 44.74 43.69 42.61 41.55 40.53 39.57
3.52 3.52 3.65 3.80 4.41 8.02 8.19 8.03 9.82 16.80 23.46 23.58 22.54 21.93 22.29 24.26 28.65 ...
35.75 43.74 49.15 50.96 50.64 49.48 48.07 46.64 45.26 43.97 42.76 41.64 40.58 39.60
3.52 3.52 3.65 3.80 4.41 8.02 8.19 8.03 9.82 16.80 23.46 23.58 22.54 21.93 22.29 24.26 28.65 ...
35.75 43.74 49.15 50.96 50.64 49.48 48.07 46.64 45.26 43.97 42.76 41.64 40.58 39.60]

%P and h are known. Set P known and assume T and iterate to match h
%given by T and h relation above
R = 8.3144 %universal gas constant unit:J/K-mol
MWair = 29










%cp_0 = 1.0 % specific heat constant pressure at T = OK
%hin = cp_0*Tout %guess temperature unit:K
%dT = 1 % initialize difference between hi and h known
%while dh < 0
Z = interp2(T, P, ZTP,Tout, Pin)
ZHRT = interp2(T, P, ZHRT,Tout, Pin)
h_known = ZHRT*R*Tout/Z/MWair %enthalpy i unit:J/g
%dh = h known hi
%Tin =Tin 10
%end
%Tout = Tin + 10 %unit:K










APPENDIX G
MATLAB CODE (FUNCTION) TO COMPUTE MACH NUMBER FOR PRANDTL-
MAYER EXPANSION


function [M2] = shadowM (i,jj,ueunit, T e, ue, gamma, ep, Rair)

%function [Te, i] = temp(i,jj,nunit, T e, ue, gamma, ep, Rair)
%This function will compute the Mach number (M2) of shadow panel
%from the data of the panel in front of shadow panel

j =jj(i,1)
PMang_guess =0
aaa= [ueunit(j,1) u eunit(j,2) ueunit(j,3)]; bbb= [ueunit(i,1) ueunit(i,2)
u_eunit(i,3)]
ccc = cross(aaa,bbb) %a:unit normal vector ofjth panel; b:unit vector ofith panel
cc = (ccc(1)A2+ccc(2)A2+ccc(3)A2)A0.5
aa = (aaa(1)A2+aaa(2)A2+aaa(3)^2)^0.5
bb = (bbb(1)A2+bbb(2)A2+bbb(3)A2)^0.5
psi = asin(cc/(aa*bb)) %deflection angle (rad)
M = ((ue(j,1)A2+u_e(j,2)A2+u_e(j,3)A2)/(gamma*Rair*T e(j,1)))0.5 %Mach
number ofj panel
PMang2 = psi + (ep^(-0.5))*atan((ep*(Ml^2-1))^0.5)-atan((M1^2-1)^0.5)
maxPMang = (((gamma+1)/(gamma-1))^0.5-1)*3.14159265359/2
if PMang2 >= maxPMang
M2 = 1000
else
M2 = M1-0.01 %M2 is Mach number ofi panel and this is initial guess
while PMang2 > PMang_guess
PMang_guess = (epA(-0.5))*atan((ep*(M2A2-1))^0.5)-atan((M2A2- 1)0.5)
M2 = M2 + 0.01

%aaa
%bbb
%ccc
%aa
%bb
%cc
%M1
%PMang2
end
end
M2 =M2-0.01









LIST OF REFERENCES

1. Liepmann, H. W., Roshko, A.: Elements of Gasdynamics, Wiley, New York, 1957

2. Anderson, J. D.: Hypersonic and High Temperature Gas Dynamics, McGraw-Hill, New
York, 1989

3. Oosthuizen, P. H., Carscallen, W. E.: Compressible FluidFlow, McGraw-Hill, New York,
1997

4. Hansen, C. F.: Approximationsfor the Thermodynamic and Transport Properties ofHigh-
Temperature Air, NASA Technical Report R-50, 1959

5. Schetz, J. A.: Boundary Layer Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1993

6. Fay, J. A. and Riddell, F. R.: "Theory of Stagnation Point Heat Transfer in Dissociated
Air", Journal of the Aeronautical Sciences, vol.25, no.2, February, 1958, pp. 73-85

7. Lees, L.: "Laminar Heat Transfer over Blunt-Nosed Bodies at Hypersonic Flight Speeds",
Jet Propulsion, vol.26, 1956, pp. 259-269, 274

8. Phillips, W. F.: Mechanics ofFlight, John Wiley & Sons, Inc., Hoboken, NJ, 2004

9. Wannemwetsch, G D.: "Pressure Tests of the AFFDL X-24C-10D Model at Mach Number
of 1.5, 3.0, 5.0 and 6.0," von Karman Gas Dynamics Facility, Arnold Engineering
Development Center, TN, AEDC-DR-76-92, Nov. 1976.

10. Neumann, R. D., Patterson, J. L., and Sliski, N. J.: "Aerodynamic Heating to the
Hypersonic Research Aircraft X24C," AIAA Paper 78-37, 1978.

11. Shang, J. S., Scherr, S. J.: "Navier-Stokes Solution for a Complete Re-Entry Configuration,"
Journal of Aircraft, vol.23, No.12, Dec. 1986, pp. 881-888

12. Hamilton J. T., Wallace R. O., Dill C.C., "Launch vehicle aerodynamic data base
development comparison with flight data," NASA CP-2283, Pt. 1, 1983, pp. 19-36

13. Hwang, D. P.: "A Proof of Concept Experiment for Reducing Skin Friction By Using a
Micro-Blowing Technique," 35th Aerospace Sciences Meeting and Exhibit, Reno, Nevada,
January 6-9, 1997.

14. Kays, W. M., Crawford, M. E.: Convective Heat andMass Transfer, McGraw-Hill, New
York, 1980









BIOGRAPHICAL SKETCH

Yoshifumi Nozaki was born in Kochi, Japan, in 1981. He graduated from Tosa High

School in 2000. He received his Bachelor of Science in Mechanical Engineering from Utah State

University in May of 2004. He entered the graduate program at the University of Florida in

August of 2005 under Dr. Pasquale M. Sforza in the Department of Mechanical and Aerospace

Engineering to obtain his Master of Science.





PAGE 1

1 REDUCING SKIN FRICTION AND HEAT TRANSFER OVER A HYPERSONIC CRUISING VEHICLE BY MASS INJECTION By YOSHIFUMI NOZAKI A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2007

PAGE 2

2 Yoshifumi Nozaki

PAGE 3

3 To my parents, Yoshikazu Nozaki and Keiko No zaki, and my brother, Toshihiro Nozaki. You have inspired me to become who I am today. Thank you for always supporting and believing in me. I dedicate this to you.

PAGE 4

4 ACKNOWLEDGMENTS I gratefully acknowledge the s upport provided by Dr. Pasquale M. Sforza, Professor of Mechanical and Aerospace Engineeri ng at the University of Florida.

PAGE 5

5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........7 LIST OF FIGURES................................................................................................................ .........8 ABSTRACT....................................................................................................................... ............16 CHAPTER 1 INVISCID ANALYSIS..........................................................................................................17 Introduction................................................................................................................... ..........17 Local Surface Inclination Method..........................................................................................17 Inviscid Aerodynamic Forces and Moments..........................................................................19 2 VISCOUS AND HIGH TEMPERATURE CONSIDERATIONS.........................................22 Introduction................................................................................................................... ..........22 Local Reynolds Number.........................................................................................................22 Local Skin Friction............................................................................................................ .....26 Local Heat Transfer............................................................................................................ ....28 Total Forces Acting on the Vehicle........................................................................................31 Discussion of Results wit hout any Cooling Methods.............................................................32 3 MASS INJECTION EFFECTS..............................................................................................42 Introduction................................................................................................................... ..........42 Effects of Mass Injection on the Boundary Layer..................................................................43 General Behavior of Reducing Skin Friction and Heating.....................................................44 4 RESULTS........................................................................................................................ .......47 Introduction................................................................................................................... ..........47 The Range Equation............................................................................................................. ..47 Comparison of Range, L /D, and Heat Transfer Variance.....................................................49 5 CONCLUSIONS....................................................................................................................95 Conclusions of this Study...................................................................................................... .95 Future Work.................................................................................................................... ........96 APPENDIX A MATLAB CODE TO COMPUTE FLI GHT PERFORMANCE OF X24C...........................98

PAGE 6

6 B MATLAB CODE (FUNCTION) TO COMPUTE TEMPERATURE.................................129 C MATLAB CODE (FUNCTION) TO COMPUTE DENSITY.............................................132 D MATLAB CODE (FUNCTION) TO COMPUTE VOSCOSITY........................................134 E MATLAB CODE (FUNCTION) TO COMPUTE PRANDTL NUMBER..........................136 F MATLAB CODE (FUNCTION) TO COMPUTE ENTHALPY.........................................138 G MATLAB CODE (FUNCTION) TO CO MPUTE MACH NUMBER FOR PRANDTLMAYER EXPANSION........................................................................................................141 LIST OF REFERENCES.............................................................................................................142 BIOGRAPHICAL SKETCH.......................................................................................................143

PAGE 7

7 LIST OF TABLES Table page 2-1. Coefficients in Eq.(2-18)................................................................................................ ...36 2-2. Comparison of aerodynamic forces and D L....................................................................36 2-3. Configuration of X24C studied..........................................................................................36 2-4. The effect of the base pressure on aerodynamic forces and D L......................................36 4-1. Comparison of flight parameters at 6 M and 30000 m altitude. The panels that have w cq, of more than 500002/ m W are cooled by the ma ss injection rate: 0, 0.001, 0.01) / (2s m kg.....................................................................................................................57

PAGE 8

8 LIST OF FIGURES Figure page 1-1. General body surface panel showing the unit normal vector along with the locations of the four corner points.....................................................................................................21 2-1. Expansion wave........................................................................................................... ......37 2-2. Deflection angle at the corner.........................................................................................37 2-3. Schematic diagram of stagnation region............................................................................37 2-4. X-24C configuration. Note that this is a representation of the right half of the aircraft....................................................................................................................... .........38 2-5. X-24Cs D L as a function of angle of attack...................................................................38 2-6. X-24Cs aerodynamic force coefficients as a function of angle of attack.........................39 2-7. X-24Cs pitching moment coefficients as a function of angle of attack............................39 2-8. Heating distribution along windward sy mmetry plane of Space Shuttle Orbiter at 8 34of angle of attack, 15 9M, and 47.7 km altitude.....................................................40 2-9. Comparison of surface pressure distri butions around the X-24C fuselage at the farthest downstream station...............................................................................................40 2-10. Comparison of heat transfer around the X24C fuselage at the farthest downstream station........................................................................................................................ .........41 2-11. Comparison of streamwise surface pre ssure distribution along the windward and leeward symmetry lines of the X-24C...............................................................................41 3-1. Effects of mass injection on D L with different angle of attack for a flat plate (m m6 6 square plate) at a Mach number of 6..................................................................45 3-2. Effects of mass injection on heat transfer with angle of attack for a flat plate (m m 6 6 square plate) at a Mach number of 6..................................................................46 4-1. Distribution of panel area with a given heat transfer, w cq,(2/m W) at 6M and 30000 m altitude..................................................................................................................57 4-2. Distribution of the number of pa nels with a given heat transfer, w cq,(2/m W) at 6 M and 30000 m altitude................................................................................................58

PAGE 9

9 4-3. Mass injection effect on the flight time at 6 M and 30000 m altitude. The panels to be cooled are determined by w cq,(2/ m W).........................................................................58 4-4. Mass injection effect on D L at 6 M and 30000 m altitude. The panels to be cooled are determined by w cq,(2/ m W)..........................................................................................59 4-5. Mass injection effect on reduction of heat power at 6 M and 30000 m altitude. The panels to be cooled are determined by w cq,(2/ m W)..........................................................59 4-6. Normalized reduction of heat pow er v.s. normalized injected mass at 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)................................................................................................60 4-7. Flight time v.s. normalized injected mass at at 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)........................................................................................................................60 4-8. Flight time v.s. normalized reduction of heat power at 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/ m W)........................................................................................................................61 4-9. Reduction of heat power ( kW ) v.s. injected mass rate () /s kgat 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)...................................................................................................................61 4-10. Reduction of heat energy ( kJ ) v.s. injected mass ()kgat 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)........................................................................................................................62 4-11. Flight time v.s. reduction of heat energy ( kJ ) at 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)........................................................................................................................62 4-12. Normalized reduction of heat pow er v.s. normalized injected mass at 6M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/ m W)................................................................................................63 4-13. Flight time v.s. normalized injected mass at at 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)........................................................................................................................63

PAGE 10

10 4-14. Flight time v.s. normalized reduction of heat power at 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/ m W)........................................................................................................................64 4-15. Reduction of heat power ( kW ) v.s. injected mass rate () /s kgat 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/ m W)...................................................................................................................64 4-16. Reduction of heat energy ( kJ ) v.s. injected mass ()kgat 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)........................................................................................................................65 4-17. Flight time v.s. reduction of heat energy ( kJ ) at 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)........................................................................................................................65 4-18. Bottom view of X24C with 500002/m W of allowable w cq, at 30000 m altitude...............66 4-19. Side view of X24C with 500002/ m W of allowable w cq, at 30000 m altitude....................66 4-20. Top view of X24C with 500002/m W of allowable w cq, at 30000 m altitude....................66 4-21. Distribution of panel area with a given heat transfer, w cQ, (W) at 6M and 30000 m altitude....................................................................................................................... .........67 4-22. Distribution of the number of pa nels with a given heat transfer, w cQ, (W) at 6 M and 30000 m altitude...........................................................................................................67 4-23. Mass injection effect on the flight time at 6 M and 30000 m altitude. The panels to be cooled are determined by w cQ, (W)..............................................................................68 4-24. Mass injection effect on D L at 6 M and 30000 m altitude. The panels to be cooled are determined by w cQ, (W)..............................................................................................68 4-25. Mass injection effect on reduction of heat power at 6 M and 30000 m altitude. The panels to be cooled are determined by w cQ, (W)...............................................................69 4-26. Normalized reduction of heat pow er v.s. normalized injected mass at 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W)....................................................................................................69

PAGE 11

11 4-27. Flight time v.s. normalized injected mass at 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).............................................................................................................................. ......70 4-28. Flight time v.s. normalized reduction of heat power at 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).............................................................................................................................. ......70 4-29. Reduction of heat power ( kW ) v.s. injected mass rate () /s kgat 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).......................................................................................................................71 4-30. Reduction of heat energy ( kJ ) v.s. injected mass ()kgat 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).............................................................................................................................. ......71 4-31. Flight time v.s. reduction of heat energy ( kJ ) at 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).............................................................................................................................. ......72 4-32. Normalized reduction of heat pow er v.s. normalized injected mass at 6M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W)....................................................................................................72 4-33. Flight time v.s. normalized injected mass at 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).....73 4-34. Flight time v.s. normalized reduction of heat power at 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).............................................................................................................................. ......73 4-35. Reduction of heat power ( kW ) v.s. injected mass rate () /s kgat 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).......................................................................................................................74 4-36. Reduction of heat energy ( kJ ) v.s. injected mass ()kgat 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).............................................................................................................................. ......74 4-37. Flight time v.s. reduction of heat energy ( kJ ) at 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).....75

PAGE 12

12 4-38. Bottom view of X-24C with 40000W of allowable w cQ, at 6 M and 30000 m altitude....................................................................................................................... .........75 4-39. Side view of X-24C with 40000W of allowable w cQ, at 6 M and 30000m altitude......75 4-40. Top view of X-24C with 40000W of allowable w cQ, at 6 M and 30000 m altitude.......76 4-41. Distribution of panel area with a given heat transfer, w cq,(2/m W) at 6 M and 35000 m altitude..................................................................................................................76 4-42. Distribution of the number of pa nels with a given heat transfer, w cq,(2/m W) at 6 M and 35000 m altitude................................................................................................76 4-43. Mass injection effect on the flight time at 6 M and 35000 m altitude. The panels to be cooled are determined by w cq,(2/m W).........................................................................77 4-44. Mass injection effect on D L at 6 M and 35000 m altitude. The panels to be cooled are determined by w cq,(2/m W)..........................................................................................77 4-45. Mass injection effect on reduction of heat power at 6 M and 35000 m altitude. The panels to be cooled are determined by w cq,(2/m W)..........................................................78 4-46. Normalized reduction of heat pow er v.s. normalized injected mass at 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)................................................................................................78 4-47. Flight time v.s. normalized injected mass at at 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)........................................................................................................................79 4-48. Flight time v.s. normalized reduction of heat power at 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)........................................................................................................................79 4-49. Reduction of heat power ( kW ) v.s. injected mass rate () /s kgat 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)...................................................................................................................80 4-50. Reduction of heat energy ( kJ ) v.s. injected mass ()kgat 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)........................................................................................................................80

PAGE 13

13 4-51. Flight time v.s. reduction of heat energy ( kJ ) at 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)........................................................................................................................81 4-52. Normalized reduction of heat pow er v.s. normalized injected mass at 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)................................................................................................81 4-53. Flight time v.s. normalized injected mass at at 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)........................................................................................................................82 4-54. Flight time v.s. normalized reduction of heat power at 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)........................................................................................................................82 4-55. Reduction of heat power ( kW ) v.s. injected mass rate () /s kgat 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)...................................................................................................................83 4-56. Reduction of heat energy ( kJ ) v.s. injected mass ()kgat 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)........................................................................................................................83 4-57. Flight time v.s. reduction of heat energy ( kJ ) at 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W)........................................................................................................................84 4-58. Bottom view of X-24C with 300002/m W of allowable w cq, at 35000 m altitude.............84 4-59. Side view of X-24C with 300002/m W of allowable w cq, at 35000 m altitude..................84 4-60. Top view of X-24C with 300002/m W of allowable w cq, at 35000 m altitude...................85 4-61. Distribution of panel area with a given heat transfer, w cQ,(W) at 6M and 35000 m altitude....................................................................................................................... .........85 4-62. Distribution of the number of pa nels with a given heat transfer, w cQ,(W) at 6 M and 35000 m altitude...........................................................................................................85

PAGE 14

14 4-63. Mass injection effect on the flight time at 6 M and 35000 m altitude. The panels to be cooled are determined by w cQ, (W)..............................................................................86 4-64. Mass injection effect on D L at 6 M and 35000 m altitude. The panels to be cooled are determined by w cQ, (W)..............................................................................................86 4-65. Mass injection effect on reduction of heat power at 6 M and 35000 m altitude. The panels to be cooled are determined by w cQ, (W)...............................................................87 4-66. Normalized reduction of heat pow er v.s. normalized injected mass at 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W)....................................................................................................87 4-67. Flight time v.s. normalized injected mass at 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).............................................................................................................................. ......88 4-68. Flight time v.s. normalized reduction of heat power at 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).............................................................................................................................. ......88 4-69. Reduction of heat power ( kW ) v.s. injected mass rate () /s kgat 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).......................................................................................................................89 4-70. Reduction of heat energy ( kJ ) v.s. injected mass ()kgat 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).............................................................................................................................. ......89 4-71. Flight time v.s. reduction of heat energy ( kJ ) at 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).............................................................................................................................. ......90 4-72. Normalized reduction of heat pow er v.s. normalized injected mass at 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W)....................................................................................................90 4-73. Flight time v.s. normalized injected mass at 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).....91

PAGE 15

15 4-74. Flight time v.s. normalized reduction of heat power at 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).............................................................................................................................. ......91 4-75. Reduction of heat power ( kW ) v.s. injected mass rate () /s kgat 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).......................................................................................................................92 4-76. Reduction of heat energy ( kJ ) v.s. injected mass ()kgat 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).............................................................................................................................. ......92 4-77. Flight time v.s. reduction of heat energy ( kJ ) at 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).....93 4-78. Bottom view of X-24C with 20000W of allowable w cQ, at 35000 m altitude...................93 4-79. Side view of X-24C with 20000W of allowable w cQ, at 35000 m altitude........................93 4-80. Top view of X-24C with 20000W of allowable w cQ, at 35000 m altitude.........................94

PAGE 16

16 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science REDUCING SKIN FRICTION AND HEAT TRANSFER OVER A HYPERSONIC CRUISING VEHICLE BY MASS INJECTION By Yoshifumi Nozaki August 2007 Chair: Pasquale M. Sforza Major: Aerospace Engineering Demonstrating technologies for hyp ersonic aircraft that cruise at speeds greater than Mach 5 is one of the long-term visions of many agenci es, like NASA. Reducing skin friction and heat transfer on the surface of hypersonic cruising vehicles has been a focus of constant attention.General methods for estimating the ae rodynamic forces and heat transfer around a hypersonic vehicle are used to evaluate the reduc tion in skin friction a nd heat transfer on the surface of a hypersonic vehicle by mass injection. Particular atte ntion was paid to the X-24C configuration because of the existence of experi mental data of X-24C performance against which the predictions can be compared. The local su rface inclination method and the flat plate reference enthalpy methods for lami nar and turbulent flow were us ed to find aerodynamic forces and heat transfer. High temperat ure effects were included by usi ng a classical approximation of thermodynamic properties. Although this analys is is based on many approximations, these methods worked well and flow pr operties were reasonably predic ted. Reducing skin friction and protecting surfaces from heating by injecting ma ss did result in a penalty in the form of decreased flight time of the vehicle, and therefor e flight range. These pe nalties were often very light. Also, as more mass is injected, the eff ect of mass injection grows, but more slowly.

PAGE 17

17 CHAPTER 1 INVISCID ANALYSIS Introduction Hypersonic flow is complicated because of physical aspects of hypersonics such as hightemperature chemically reacting, thin shock la yer, etc. Such complex phenomena cannot be described by a simple linear system. Even withou t these phenomena, the basi c theory of inviscid compressible flow, when the Mach number is ve ry large, does not yield aerodynamic theories which are mathematically linear. By using supers onic thin airfoil theory, the pressure coefficient on the surface is obtained from 1 22 M ci p (1-1) where M is the free stream Mach number, and i is flow inclination. E q.(1-1) is a classical result from inviscid, linearized, twodimensional, supersonic flow theory.1 This method is called the local surface inclination method, and it is very simple and easy to use to predict pc. This method does not need a detailed solution of the complete flowfield. This simplicity is very useful, but unfortunately, it is not valid for hypersonic speeds since nonlinear effects become important at high Mach number. However, ther e are other valid local surface inclination methods, and some of those are presented, which are applied to our hypersonic bodies. Local Surface Inclination Method As Mapproaches and approaches 1, the shock layer becomes coincident with the body surface. This is because the density ratio across the shock approaches zero, and since the density behind the shock is so high the shock laye r becomes thinner and thinner. Therefore, it looks as if the incoming flow is directly im pinging on the wedge surface, and then is running parallel to the surface downstream. Under these conditions, Newtonian theory is used to find pc.

PAGE 18

18 For blunt bodies the modified Newtonian theo ry should be used, and such results usually produce acceptable accuracy. In contrast, Anderson2 suggests that Newtonian results for slender bodies should use the straight Newtonian theor y. Newtonian theory work s reasonably well alone and lends itself to application to arbitrary slender body shapes. In the Newtonian model of fluid flow, the particles in the free-st ream impact only on the frontal ar ea of the body; they cannot curl around the body and impact on the back surface. Hen ce, for that portion of a body which is in the shadow of the incident flow, no impact pressure is left, so over this shaded region the Newtonian theory is inaccurate. Therefore the Newtonian theory is described by the following equations: V V n V cp 2 2 for 0 n V (1-2) 0pc for 0 n V (1-3) where n is unit outward normal vector on the body surface. The above equations are locally applicable to every surface panel on a smooth b ody. In order to have more accurate results, Prandtl-Meyer expansion theory should be appl ied for the surface panel at which the Newtonian method is inaccurate. In this study, we use Newtonian theory for all surface panels except for the part in the shadow, at which we applied Pra ndtl-Meyer expansion theo ry. In practice, the body surface of a vehicle is subdivided into a number of individual panels and each panel is treated separately to determine the pressure force acti ng. In this study, the surf ace of the X-24C vehicle is divided into 284 panels as described subse quently. The normal vector of each panel can be found by the cross-product of the P and Q vector as shown in Figure 1-1. Q P N (1-4) N N N n (1-5)

PAGE 19

19 N Q P dA 2 1 2 1 (1-6) where dA is differential area of i ndividual panel. Once having th e unit normal to the surface element, the pressure force acting on each panel can be found by: n dA P q c F dp press (1-7) 22 1 V q (1-8) where pressF d is the pressure force act ing on individual panel and q is the dynamic pressure. Inviscid Aerodynamic Forces and Moments Before determining differential lift(dL) and drag(dD) on each panel, the angle of attack must be accounted for the flow condition. In this an alysis, the angle of attack is defined as the angle between the free stream velocity vector (o r x-axis) and the fuselage reference line of the vehicle. Therefore, each node point must be rotated with respect to y-axis as the angle of attack increases (the origin of the coordinate is lo cated at the nose of the vehicle). The following equations are used to change each node on the surface according to variable angle of attacks: x z z x x1 2 2tan cos (1-9) y y (1-10) x z z x z1 2 2tan sin (1-11) z y x ,: a node at 0 z y x ,: a node at nonzero Having the differential pressure force acting on each panel with an accounting for the angle of attack, differential lift(dL) and drag(dD) on each panel are found as: z press inviscdF dL, (1-12) x press inviscdF dD, (1-13) k dF j dF i dF F dz press y press x press (1-14) P d F d (1-15)

PAGE 20

20 where inviscdL and inviscdD are differential lift and drag caused by only the pressure acting on the vehicle. Note that the free stream is always di rected in the positive xdirection, and the vehicle rotates with respect to y-axis and the free stream flow directio n never changes even though the angle of attack changes. Therefore, lift ( L ) and drag ( D ) are always directed in the z-direction and x-direction, respectively. However, the angl e of attack changes the normal vector on each surface since the P and Q vectors of each surface change with angle of attack. The differential moment of each panel about a re ference point, say the center of mass, due to the differential force on a partic ular body surface element is given by: F d k z z j y y i x x F d r M d 0 0 0 0 (1-16) k dn j dm i dl M d 0 (1-17) n m l ,: (rolling moment, pitching moment, yawing moment) 0 0 0, z y x: reference point at zero angle of attack (e.g. center of gravity) The vehicle in free flight has three rota tional degrees of freedom. Three rotational disturbances must be originated at a reference point of the vehicle. Ho wever, the coordinate system is not set to the vehicle body, so a v ector transformation is necessary as following: sin cosc cz x x (1-18) cy y (1-19) cos sin z x zc (1-20) k dF dF j dF i dF dF F dx z y z x sin cos sin cos (1-21) z y x ,: center of each panel in the tr ansformed coordinate system c c cz y x ,: center of each panel comput ed by Eq.(1-9) (1-11) The differential force F d calculated by Eq.(1-21) is used in Eq.(1-16). In order to have more accurate pressure force, Prandtl-Meyer e xpansion theory should be applied for the surface in the shadow region, in which the Newtonian theory is inaccurate. This theory will be discussed in the next chapter since Prandtl-Meyer expansion theory is used to aid in determinning thermodynamic properties such as viscosity on the shaded surface.

PAGE 21

21 Figure 1-1. General body surface panel showing th e unit normal vector along with the locations of the four corner points.

PAGE 22

22 CHAPTER 2 VISCOUS AND HIGH TEMPERATURE CONSIDERATIONS Introduction In the preceding analysis the fluid dynamic effects of high Mach number is emphasized, without the added complications of viscous and high temperature e ffects. However, the matter of friction and thermal conduction sh ould not be neglected since high speed flow is slowed by viscous effects within the boundary layer, and lost kinetic energy is transformed in part into internal energy. This extreme viscous effect can create very high temperatures high enough to excite vibrational energy within molecules, and to cause di ssociation and even ionization within the gas. The geometric layout of the body surface panels, the pressure on each panel, and the determination of the velocity component tangential to the body surface panels all are used in an approximate analysis of the skin friction a nd heat loads experienced by the vehicle during hypersonic flight. In order to calc ulate skin friction for both lamina r and turbulent flows, the flat plate reference enthalpy method and Reynolds analogy with heat transfer are used. For very large hypersonic Mach number, the assumption that the pressure is constant in the normal direction through a boundary layer is not always valid. However, fo r vehicles designed to fly at around 6 M a constant pressure in the no rmal direction is the case. Local Reynolds Number One of the major parameters used in the an alysis is the Reynolds number based on the local tangential velocity, temperature, and dist ance, s, from the sta gnation point, that is e e e e ss u ,Re (2-1) The variable s denotes the distance along the surface of the vehicle measured from the relevant stagnation point or sta gnation line, while the subscript e indicates that these variables

PAGE 23

23 are conditions at the outer edge of the boundary layer. The tangential component of the free stream velocity is denoted by eu, and that is found by the pre ceding inviscid analysis as n n V V ue (2-2) If the x component of the unit vector is positive, and the pa nel of a body is in the shadow of the incident flow, the Prandtl-Meyer expa nsion relations are applied locally since the Newtonian formula on merely has 0 pc everywhere in the shadow region. Now consider the centered Prandtl-Meyer expansion ar ound a corner of deflection angle as sketched in Figure 21. Upstream of the wave is the windward area of a body and the downstream is the shadow area of a body. The Mach numbers upstream and downstream of the wave are 1M and 2M, respectively. From basic compressible flow, the relation between 1M and 2Mis given by: ) ( ) (1 2M M (2-3) where is the Prandtl-Meyer function: 1 tan 1 1 1 tan 1 12 1 2 1 M M M (2-4) From the equation above, the value of corresponding to 1M, and 2M is found by the tangential components of the free stream velocity eu at the outer edge of boundary layer. Figure 2-2 shows a 3-dimensional sketch of the fl ow around the corner. The deflection angle is found from the following relation: ) ( sin sin2 1 1 2 1 2 1 1 e e e e e eu u u u u u (2-5) where 1 eu and 2 eu are the tangential component of the free stream velocity eu at the outer edge of boundary layer of upstream and downstream respectively. Both 1 eu and 2 eu are found by Eq.(2-2) although 2 eu obtained by Eq.(2-2) is not real outer edge velocit y. In order to find the

PAGE 24

24 deflection angle only the directions of 1 eu and 2 eu must be found, so Eq.(2-2) is used only to find the unit vector of 2 eu. Now and 1M are known, so 2M can be found by using Eq.(2-3) and Eq.(2-4), and the real 2 eu and downstream thermodynamic properties are given by:3 2 2 2T R M uair e (2-6) 2 2 2 1 1 22 1 1 2 1 1 M M T T (2-7) 1 1 2 1 2 T T P P (2-8) 1 1 1 2 1 2 T T (2-9) In order to find the downstream thermodyna mic properties, the upstream thermodynamic properties must be known. For a specific value of the Prandtl-Meyer function asymptotically approaches the maximum value max as Mach number increases. Thus, if max 2) ( M, an infinite Mach number is generated and the pressure falls to zero. Expa nsion at such condition would, according to the pressure theory, lead to a vacuum adjacent to th e wall. Of course, in reality, the continuum and ideal gas assumption become inva lid long before this situation is reached. However, panels whose may be greater than max wont have high heat exchange or skin friction. What we need for this study is identifying those surface panels whos e total heat transfer is not negligible, so an accurate analysis for these special cases of large expansion angles is not necessary. In order to evaluate the density and viscosit y, the pressure and temp erature are required. Since the pressure is assumed to be constant in the direction normal to the panel, the pressure on

PAGE 25

25 the panels may be obtained from the pressure coe fficients obtained in chapter 1 or Eq.(2-8) for the shaded panels, and that is P q c P Pp e w or 2P P Pe w by Eq.(2-8) for shaded panels (2-10) Temperature may be obtained by using the energy equation along a streamline 2 22 1 2 1e e totalu h V h h (2-11) Therefore, 2 2 2 22 1 2 1 2 1 2 1e p e eu V T C u V h h (2-12) where ,pC is constant pressure specific heat at temperature of T. The assumption here is that kinetic energy carried in the normal component of ve locity is transformed in to internal energy by adiabatic compression. In order to find the temp erature from enthalpy, it is necessary to use tables or models for the thermodynamic and tran sport properties of high temperature air. Here Hansens Approximations for the Therm odynamic and Transport Properties of HighTemperature Air4 is used to evaluate the behavior of thermodynamic and transport properties at high temperature. Numerical codes are used to predict temperat ure, compressibility, density, viscosity, and Prandtl number. Prandtl number is not used to find Reynolds number, but will be used to find skin friction later, so the code computing Pr andtl number is introduced here. The code for computing the temperature needs only inputs of enthalpy and pressure which are already known. The other codes computing compressibility, dens ity, viscosity, and Prandt l number need inputs of pressure and temperature which is obtained fr om the code computing temperature. However, in order to find the temperature from pressure and enthalpy, the compressibility must be known since temperature is defined as a function of en thalpy, pressure, and comp ressibility in Hansen,

PAGE 26

26 and inversely compressibility is obtained from pressure and temp erature. Pressure and enthalpy are known, and therefore the temperature is guess ed, and an iteration is carried out until the given enthalpy matches the enthalpy computed from guessed temperature. This approach establishes the followi ng five functions. ) ( h P T T (2-13) ) ( T P Z Z (2-14) ) ( T P (2-15) ) ( T P (2-16) ) Pr( Pr T P (2-17) To find the distance s, the sta gnation point (stagnation line for the wing) must be specified. Here it is assumed that for typical vehicles, like the X-24C that wi ll be studied in this paper, there is one stagnation point for the fuselage while the two-dimensional cross section of the wings (airfoils) have stagnation lines. We can set the stagnation point at the center of the panel whose outward normal vector is the closest to the opposite vector of fr ee stream. In this study, the vehicle has only low angles of attack, so the stagnation points are always located at the most windward panel. The most windward panel is so sm all that s of other panels do not change much even if the stagnation point and line are shifted to the nose of th e fuselage and leading edge of the wing. Therefore, the stagnation point and line are set to the nose point of the fuselage and leading edge of the wings, resp ectively for convenience. The dist ance s is assumed to be the distance from the stagnation point to the center of the panel u nder consideration. Local Skin Friction The Van Driest II method for turbulent boundary layers is probably the most accurate generally applicable equation for sk in friction, but it is too complicat ed for the entire surface of a vehicle. Another simpler method uses a reference value of temperature at which the density and physical properties of the fluid ar e evaluated and used in the avai lable constant density, constant

PAGE 27

27 property boundary layer solutions to provide an adequate approximation to the actual, variable density, variable property flow. That value of th e temperature is called th e reference temperature, T .5 In this study, the flat plate reference enthal py method is utilized to determine local surface heat transfer and Reynolds analogy with heat transfer for laminar and turbulent flow is used to determine friction on panels. The flat plate panels considered here have approximately constant pressure over the skin surface, and thus permits this approach. The Nusselt number is given by j c e s b e a eA Nu 3 Re, (2-18) The coefficients in Eq.(2-18) are listed in Table 2-1. The reference enthalpy and the adiabatic wall enthalpy are given by aw w eh h h h 22 0 5 0 28 0* (2-19) 2 Pr2 e m e e awu h h (2-20) where eh and wh are the enthalpies at the edge of the boundary layer and at the wall, respectively, and ePr is the Prandtl number evaluated at th e edge of boundary layer. The quantity m is 2 1 for laminar flow and 3 1 for turbulent flow. It is noted that the skin friction coefficient and the Nusselt number are related. This observa tion can be formalized an generalized for nonslip condition, 0 wu, and the relation is 2 Pr Re3 1 fc Nu (2-21) or j c e s b e a e fA s c 3 Re Pr 2 ) (1 3 1 (2-22) where ) ( s cf is the local skin friction coefficient.

PAGE 28

28 Local Heat Transfer From Eq.(2-21) and Eq.(2-22), th e local heat transfer can be found since the definition of the Nusselt number is aw w e w cT T k s q Nu (2-23) where w cq, is the convective heat transfer at th e wall, and is obtained from the relation s T T k s c qaw w e e s e f w c2 ) ( Re Pr ) (, 3 1 (2-24) The subscripts w and e denote conditions at the wall and the edge of the boundary layer. Eq.(2-24) provides reasonable values for the heat transfer, except for the extremely high value at the region near the stagnation point, since the di stance from the stagnation point, s is very small around the stagnation point. Thus, the blunt body h eat transfer method is applied to the region near the stagnation po int. Fay and Riddell 6, a first carried out a rigorous study of stagnation point convective heat transfer at hypersonic speeds and pr ovided the following result e s D w e s s e w w e e s ch h Le h h ds du q, 52 0 1 0 4 0 6 0 ,) 1 ( 1 ) ( ) ( ) ( Pr 76 0 (2-25) In Eq.(2-25), the term in square brackets represents the effects of equilibrium chemical reactions occurring in th e stagnation region and k c D Lep 12 (2-26) n i i f i Dh c h1 (2-27) The gas considered here is air, which can be considered to be a binary mixture. This mixture is made up of two species: oxygen and n itrogen atoms (O and N) and molecules (O2 and a Taken from Space Access Vehicle Design Handbook (Sforza, P. M.)

PAGE 29

29 N2). The quantity 12Dis the binary diffusion coefficient. The quantities ic and i fh, are the molar concentrations of the individual species (O, O2, N, and N2) and the chemical heat of formation of each species, respectively. The Lewis number for an air-like mixture given by Eq.(2-26) is close to unity, Le~1.4, so that the quantity 19 0 ~ ) 1 (52 0 Le, and the contribution of the chemical reaction term can be often be safely neglected. The velocity gradient at the stagna tion point in Eq.(2-25) may be found by e e b eP P R ds du) ( 2 1 (2-28) In the Newtonian approximation this becomes b eR V ds du2 (2-29) Then Eq.(2-25) is simplified to ) ( Pr Pr 9038 0, 1 0 4 1 w e s b s w s ch h R V C q (2-30) In Eq.(2-30) the variable s s w w wC is the Chapman-Rubesin factor and the Prandtl number is calculated at the stagnation condi tions at the edge of the boundary layer. The stagnation enthalpy behind the shock as well as the density ratio ac ross the shock can be determined from the shock relations for equilibrium air chemistry. A schematic diagram of stagnation region is shown in Figure 2-3. A stationary normal shock wave is considered here. The shock is so strong that the temperature behind the shock is high enough to ensure that vibr ational excitation and chemical reactions occur behind the shock front. It is assumed that local thermodynamic and chemical equilibrium conditions hold behi nd the shock, and all conditions ahead of the shock wave are known. The governing equations for the flow across a normal shock are

PAGE 30

30 Continuity 2 2 1 1u u (2-31) Momentum 2 1 2 1 1 1 21 u P P (2-32) Energy 2 2 1 2 1 1 21 2 u h h (2-33) In addition, the equilib rium thermodynamic properties for the high-temperature gas are known from the numerical techni ques introduced by Eq. (2-13) a nd Eq.(2-15). The codes used here are ) (2 2 2h P T T (2-34) ) (2 2 2T P (2-35) Since all the upstream conditions, 1 1u, 1P, 1h, etc., are known, Eq.(2-32) and Eq.(2-33) express 2P and 2h, respectively, in terms of only one unknown 2 1 This establishes the basis for an iterative numerical solutions introduced by Anderson2, as follows 1. Assume a value for 2 1 (A value of 0.1 is usually good first guess.) 2. Compute 2P from Eq.(2-32) and 2h from Eq.(2-33) 3. Using the values of 2P and 2h obtained, compute 2T from Eq.(2-34) and 2 from Eq.(2-35). 4. Form a new value of 2 1 from the value of 2 obtained in step 3. 5. Use this new value of 2 1 in Eq.(2-32) and Eq.(2-33) to obtain new values of 2P and 2h, respectively. Then repeat step 2 through 5 until convergence is obtained, i.e., until there is only a negligible change in 2 1 from one iteration to the next. 6. At this stage, the correct values of 2P, 2h, 2T, and 2 are obtained. Using Eq.(2-31), obtain the correct value of 2u. By means of step 1 through 6 above, all pr operties behind the shoc k wave are found for given properties in front of the wave.

PAGE 31

31 Now the stagnation point heat transfer is ob tained by Eq.(2-30) and thermodynamic properties behind the shock. For hypersonic flow c onditions over blunt bodies it is considered that the flow along an inviscid streamline em erging from the stagnation region as if that streamline were everywhere a local surface of the vehicle. The following is good approximation of the local heat transfer on the surf ace of blunt bodies derived by Lees.7, b 2 1 0 2 0 0 2 1 2 1 ,2 1 s n e s s e e n e s s e e s e n s c cds r u r u dx du q q (2-36) where 0r is radius of cross section of bodies of re volution and n is 1 for bodies which are like bodies of revolution and 0 for two dimensional bodi es. The subscript s indi cates computation at the stagnation point and should not be confused with the vari able s, the distance from the stagnation point. Total Forces Acting on the Vehicle Now that the pressure and skin friction di stribution around the body is known, the forces acting on the vehicle may be determined. We already know the inviscid aerodynamic forces, inviscL and inviscDby summing the contributions of all the panel differential inviscid forces inviscdL and inviscdD over all the panels. However, these diffe rential forces do not include expansion effects for the shaded panels. In order to recal culate the accurate inviscid aerodynamic forces, the pressure computed in this ch apter (Eq.(2-8) or Eq.(2-10)) should be used as follows, n dA P k dF j dF i dF F de z press y press x press press (2-37) z press inviscdF dL, (2-38) x press inviscdF dD, (2-39) b Taken from Space Access Vehicle Design Handbook (Sforza, P. M.)

PAGE 32

32 Inviscid aerodynamic forces mean the for ces caused by only the pr essure acting on the vehicle. So far we know the local skin fricti on coefficients, so we can find the aerodynamic forces including viscous effects. The differentia l skin friction forces fo r turbulent flow on the plates can be found from, x e tub f x fricu dA q c i dF, (2-40) y e tub f y fricu dA q c j dF, (2-41) z e tub f z fricu dA q c k dF, (2-42) where x eu,, y eu,, and z eu, are the x, y, and z compone nt of the unit vectors of the outer edge flow velocity of the panel. The dynamic pressure of the free stream is q, the differential area of the panel is dA and tub fc, is the local skin friction coefficient of the turbulent boundary layer. When the laminar boundary layer is considered, tub fc, is simply replaced by lam fc,. Aerodynamic forces including skin friction ar e found from the following: z fric inviscdF dL dL, (2-43) x fric inviscdF dD dD, (2-44) dL L (2-45) dD D (2-46) Discussion of Results wi thout any Cooling Methods We have just established a method to compute the total forces acting on the body surface as well as the heat transfer. Aerodynamic for ces can be found by summing the contributions of all the panel differential forces ( L, D ) and moments can be found by summing the moment contributions of all the panel differential data (dL,dD, and 0dM). The aerodynamic forces and moments are expressed in term of dimens ionless force and moment coefficients:8 ref DS V D C22 1 :drag coefficient (2-47)

PAGE 33

33 ref LS V L C22 1 :lift coefficient (2-48) c S V m Cref m 22 1 :pitching moment coefficient (2-49) where refS is the reference area, which is the planform area in this study and c is the fuselage length. Unlike hypersonic gliders like the Space S huttle Orbiter, hypersonic cruising vehicles have relatively slender bodies and fly at low an gles of attack. Therefor e, here we analyze only low angles of attack, in which skin friction effects on flight performance are more pronounced than in high angles of attack. The X-24C configuration is chosen for study here and is illustrated in Figure 2-4 with the surface features being approximated by 284 panels Table 2-2 shows comparisons of computed lift and drag coefficients and D L with experimental data. The flight condition of the X-24C studied here is a Mach number of 5.95, an angle of attack of 6, a characteristic unit Reynolds number of m / 10 64 17, and a turbulent boundary layer, which are the same conditions as the available experimental data.9-11, c The base pressure, baseP is set to the same value as the ambient pressure, which is probably an optimistic choi ce for the cruising vehicle. In this study, we confine our attention to the X-24C vehicle. The configuration details are shown in table 2-3. The results for the aerodynamic forces ar e slightly underpredicted, but they agree reasonably well with experimental data. Figure 2-5 and 2-6 show D L and aerodynamic forces coefficients for various respectively. Viscous effects on D L and DC are obvious, but not for LC because at low angles of attack friction doesn t affect normal forces. Figure 2-7 shows the c Reference 9 and 10 are taken from Reference 11

PAGE 34

34 pitching moment coefficient. The reference poin t is located at the center of gravity of the vehicle0 0 706 9 z y x. Table 2-4 shows the effect of base pressure on the aerodynamic forces. LC does not change with baseP since the base pressure does not have an effect on the lift much when the angle of attack is relatively low. On the other hand, the predicted DC depends on baseP and therefore so does D L. At 0 baseP, DC is the closest to the experimental data, while at P Pbase2 0, the predicted D L gives the best agreement with the expe riment. In order to have good agreement with the experimental data, we should set baseP to 0 or P 2 0. However, this value is too small for cruising vehicle, and LC has the best agreement with the experiment when P Pbase, so it is not easy to find the appropriate baseP here. For the present study, the latter assumption P Pbase is used. We have introduced two methods to calculate the local heat tran sfer, the flat plate reference enthalpy method and the blunt body solu tion method. At stagnation points, the flat plate reference enthalpy method provi des extremely high values of th e heat transfer, so the blunt body solution should be used for panels around th e stagnation point or li ne. Although the flat plate reference enthalpy method a nd the blunt body solutio n method give different values of heat transfer, at least both solutions have similar behavior. In order to find the location where we may start to use the flat plate refe rence enthalpy method, a heat transf er comparison is carried out for the Space Shuttle Orbiter since there are more expe rimental data for that configuration than for the X-24C. Figure 2-8 shows comparison of h eating distribution along windward symmetry plane of the Orbiter between the present method (t he flat plate reference enthalpy method and the blunt body solution method) and actual flight data.12 In this figure, L s is the distance from the stagnation point normalized by total length of the windward symmetry plane line. The flat plate

PAGE 35

35 reference enthalpy method agrees with actual flight data except for the region around the stagnation point. Therefore, ar ound the stagnation point or line the blunt body heat transfer method is to be used, and the heat transfer calculated by both methods should be analyzed for each stream line. There is a panel at which two methods provide the same or very close heat transfer, and there we must switc h the methods to use. In Figure 2-8, for example, the blunt body heat transfer method should be used for the panels at which 0 L s and 0173 0. For the panels downstream from 0864 0 L s, the flat plate reference enth alpy method should be used. Mass injection through the surface is used for cooling, which causes additional mixing in the boundary layer. Since the boundary layer is approximated to be turbulent, we use the flat plate reference enthalpy method for turbulent flow to find the heat transfer. Since most of the experimental data9, 10, 12 for the X-24C was measured at several streamwise stations, the format of comparison is constructed accordingly. Typical results are given by abscissas in the form of normalized ar c length. This length is calculated from the leeward symmetry (top) plane toward the windward (bottom) counterpart and scaled by the total arc length of each individual cross section. Surfac e pressure and the Stanton number distribution comparisons with experimental measuremen ts at the body furthest downstream station ( 75 104 nr x) of the X-24C are shown in Figures 2-9 and 2-10, respectively. Our vehicle configuration does not use very many panels, so we cannot show the results at exactly the same stations. Thus surface pressure and Stanton num ber are computed at the furthest downstream station ( 2 90 nr x) in our vehicle model. In Figure 29, we define the Stanton number as:11 w s ch h V q St (2-50)

PAGE 36

36 The agreement in surface pressure and heat transfer distribution is reasonable. The windward and leeward pressure di stributions along the symmetry plane are given in Figure 2-11. The present results slightly underpredict the expe rimental data at most points, but the theory seems applicable for analyzing the flow pr operties around the X-24C. In order to find aerodynamic forces and heat transfer over the X-24C vehicle, therefore it is reasonable to use the methods introduced in Chapters 1 and 2. Table 2-1. Coefficients in Eq.(2-18) Type of flow A a b c j laminar 3 1Pr 3320 0 0.5000 0.5000 0.5000 turbulent 3 1Pr 0296 0 0.8000 0.2000 0.8000 flat plate 0.0000 axisymmetric 1.0000 Table 2-2. Comparison of aerodynamic forces and D L. LC DC D L Experimental data 0.0368 0.0317 1.16 Present results 0.0332 0.0253 1.31 Percent error -9.78 -20.2 13.1 Table 2-3. Configuration of X24C studied. Parameter Value Reference area (2m) 57.2 Fuselage (m) 14.7 Wingspan (m) 7.38 Surface Temperature ( K ) 317.0 Table 2-4. The effect of the base pressure on aerodynamic forces and D L. P Pbase LC error in LC DC error in DC D L error(%) in D L 0 0.0327 -11.0 0.0294 -7.21 1.11 -4.00 0.2 0.0328 -10.8 0.0286 -9.82 1.15 -1.00 0.4 0.0329 -10.6 0.0278 -12.4 1.18 2.21 0.6 0.0330 -10.3 0.0270 -15.0 1.22 5.62 0.8 0.0331 -10.1 0.0261 -17.6 1.27 9.25 1.0 0.0332 -9.82 0.0253 -20.2 1.31 13.1

PAGE 37

37 Figure 2-1. Expansion wave. Figure 2-2. Deflection angle at the corner. Figure 2-3. Schematic diag ram of stagnation region.

PAGE 38

38 Figure 2-4. X-24C configuration. Note that this is a representation of the right half of the aircraft. -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 012345678910 angle of attack (deg)L/D L/D inviscid L/D viscous Figure 2-5. X-24Cs D L as a function of angle of attack.

PAGE 39

39 -0.04 -0.02 0 0.02 0.04 0.06 0.08 012345678910 angle of attack (deg)CL, CD CL inviscid CL viscous CD inviscid CD viscous Figure 2-6. X-24Cs aerodynamic fo rce coefficients as a function of angle of attack. -0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 012345678910 angle of attack (deg)Cm Cm_inv Cm_vis Figure 2-7. X-24Cs pitching moment coeffici ents as a function of angle of attack.

PAGE 40

40 1000 10000 100000 1000000 00.10.20.30.40.50.60.7 s/L (m)q (W/m2) present results (the flat plate reference enthalpy method) present results (the blunt bodies solutions) flight data (Ref. 12) Figure 2-8. Heating distribution along windward symmetry plane of Space Shuttle Orbiter at 8 34of angle of attack, 15 9 M, and 47.7 km altitude. 0 1 2 3 4 5 6 00.20.40.60.81 Normalized Arc Lengthp/p_in f present results data of Ref. 9 Figure 2-9. Comparison of surface pressure distributions around the X-24C fuselage at the farthest downstream station.

PAGE 41

41 -5 -4.5 -4 -3.5 -3 -2.5 -2 00.20.40.60.81 Normalized Arc LengthLOG(St) present results data of Ref. 9 & 10 Figure 2-10. Comparison of heat transfer around th e X-24C fuselage at th e farthest downstream station. 0 2 4 6 8 10 12 0306090120150 x/Rnp/p_in f windward leeward data of Ref. 9 (windward) data of Ref. 9 (leeward) Figure 2-11. Comparison of streamwise surface pressure distribution along the windward and leeward symmetry lines of the X-24C.

PAGE 42

42 CHAPTER 3 MASS INJECTION EFFECTS Introduction Reducing skin friction and heat transfer is one of the most challenging areas of research in hypersonic aerodynamics. Attention has been focuse d on surface suction to delay transition to the turbulent flow region which pr oduces relatively la rge skin friction. However, even a very small protuberance can cause laminar flow to trans ition into turbulent flow. Also, laminar flow is more susceptible to flow separation than turb ulent flow. Therefore th is technique of using suction still remains in the research stage. On e of the drag reduction methods that has been ignored is surface mass injection because researcher s believed that the pe nalty associated with mass injection is very large b ecause of the susceptibility of flow separation. Despite this shortcoming, many experiments were conducted in 1970's on mass injection on a flat plate with no pressure gradient. It was well established that mass injection significantly reduced skin friction with respect to the skin friction of the same porous plate with no injection.13 Thus far in the present study we have discu ssed only boundary layers for which the normal component of veloc ity at the surface, wv is zero. Nonzero values of wv can occur if the wall is porous and mass is injected into the boundary laye r. Mass injection from the surface is one of several cooling methods for protec ting the surface from an extremely high-temperature stream. It is assumed that the boundary layer over the body is turbulent everywhere in order to maintain a conservative evaluation of the hea ting load. In addition, the transi tion location is not known even for the zero injection case, so to be consiste nt we have focused on purely turbulent flow. Dominant parameters are angle of attack and ratio of the mass flow rate of the cooling gas to air of free stream.

PAGE 43

43 Effects of Mass Injection on the Boundary Layer In order to examine the effect of injecting gas into the boundary laye r, we use reviews of the effects of transpiration on the turbulent boundary layer pr esented by Kays and Crawford.14 They introduced a simple algebraic Couette fl ow solution which has the virtue of fitting the additional experimental data. The effect of por ous surface injection on Stanton number and skin friction coefficient at the same Reynolds number based on distan ce s are described as follows: h hB B St St 1 ln0 (3-1) f f f fB B c c 1 ln0 (3-2) where St u v Be e w w h (3-3) 2f e e w w fc u v B (3-4) In the above equations, w is the density of injected gas, and wvis the normal velocity component at the surface. The subscript 0 refe rs to the case with zero injection, that is, 0 hB and 0 fB. Because of the implicit nature of such equations, it is frequently more convenient to use other blowing parameters than hB and fB, such as: 0St u v be e w w h (3-5) 20 ,f e e w w fc u v b (3-6) We find that h hB b 1 ln and f fB b 1 ln, and then 10 hb he b St St (3-7) 10 fb f f fe b c c (3-8)

PAGE 44

44 If comparison is made at the same Reynolds number based on streamwise distance s for the case of constant free-stream velocity, the above equations fit the experimental data remarkably well. The Nusselt number is related to the Stanton number as follows: Nu Ste s e,Re Pr (3-9) where ePr and e s,Re are constant at the same location (or in our case panel) for any values of hB and hb, so the Couette flow analysis above can be developed in the same manner for the Nusselt number as for the Stanton number. 1 1 ln0 hb h h he b B B Nu Nu (3-10) From Eq.(2-23) and Eq.(2-24), th e convective heat tr ansfer at the wall can be found to be 0 ,1w c b h w cq e b qh (3-11) Eq.(3-11) is to be evaluated at the same ek, wT, and awT for injected and non-injected cases. A limiting case occurs for large values of blowing when the friction coefficient tends to zero and boundary layer is literally blown off the surface, an occurrence similar to the separation of a boundary layer in an adverse pressure gr adient. Two commonly used rules of thumb for blow-off are as follows: if e e w wu v 0.01 and/or fb4.0, then is safe to assume that blowoff has occurred. General Behavior of Reducing Skin Friction and Heating Unlike hypersonic gliders such as Space Shuttle Orbiter, hypersonic cruising vehicles have relatively slender bodies and fly at low angles of attack. Therefore, here we consider only low angles of attack in which skin friction effects on flight performance are more pronounced than at

PAGE 45

45 high angles of attack. In order to illustrate the general effects of mass injection, the case of a flat plate in hypersonic flight is br iefly discussed, in which, without loss in generality, we neglect forces acting on the upper surface. Figure 3-1 show s the effects of mass injection on the lift to drag ratio by plotting 0) (D L D Lcooled with different angle of attack. cooledD L) ( is D L with some mass injection, and 0) ( D Lis the D L ratio without any mass in jection. Figure 3-2 shows the effects of mass injection on the h eat transfer on the surface by show 0q qcooled as a function of mass injection for different angles of attack here. cooledq is heat transfer with some mass injection, and 0q is the heat transfer w ithout any mass injection. In general, the lower is, the more mass injection reduces skin friction an d protects the surface from heating, and even a small amount of injected mass is effective to improve flight performance. Figure 3-1 and 3-2 show that me rely increasing the amount of injection for reducing skin friction and heat transfer is no t very effective because the improvement of D L and the reduction in q are more pronounced for small amounts of injection. Also, the beneficial effects of injection are larger for lower than for higher 1 1.2 1.4 1.6 1.8 2 00.050.10.150.20.250.3 mass injection (kg/m2-s)(L/D)cooled/(L/D)0 2 deg 4 deg 6 deg 8 deg 10 deg Figure 3-1. Effects of mass injection on D L with different angle of attack for a flat plate (m m6 6 square plate) at a Mach number of 6.

PAGE 46

46 0 0.2 0.4 0.6 0.8 1 00.050.10.150.20.250.3 mass injection (kg/m2-s)qcooled/q0 2 deg 4 deg 6 deg 8 deg 10 deg Figure 3-2. Effects of mass injection on heat tran sfer with angle of attack for a flat plate (m m6 6 square plate) at a Mach number of 6.

PAGE 47

47 CHAPTER 4 RESULTS Introduction In the preceding chapters, we discussed invi scid flow, viscous fl ow, and reducing skin friction and heat transfer on a hypersonic cruising vehicle by using mass injection and established a theory for finding fl ow properties whether or not we use mass injection. In this chapter, we show the advantag es and penalties associated wi th the mass injection cooling method. The coolant injected may be a part of the to tal fuel load or different material (but a gas) from the fuel. In both cases, the critical paramete r in analyzing the reduction of skin friction and heat transfer as discussed in the prev ious chapter is the injected mass flux w wv and therefore the density of the coolant (w ) and the velocity of the coolant (wv) are not individually important. In this chapter, fuel is defined as the fuel used only for produ cing thrust, and coolant is defined as the material (although it may be the same material as the fuel) to be in jected through portions the vehicles surface to reduce viscous and heating effects. In order to evaluate the advantages and penalties of mass injection, th e total mass of fuel and coolant consumed is kept constant no matter how much coolant is injected. For instance, if the total mass of the fuel and the coolant consumed is set to 100 kg and the mass of the coolant is 10 kg then the mass of the fuel is 90 kg If the mass of the coolant is increased to 20 kg then the mass of the fuel is 80 kg Our perspective is that injecting mass (coolant) from the vehicles surface reduces viscous eff ects, reducing the heat transfer on the surface (advantage) even though it may decrease the flight range (or flight time) since the amount of the fuel used for the thrust is decr eased (penalty). The Range Equation One of important performance me trics for cruising aircraft is the flight range, the total distance that an aircraft can trav el on a given amount of fuel. Simp le flight behavior is assumed

PAGE 48

48 so that the thrust vector is assume d to be aligned with the flight pa th and the flight path angle, the angle between the flight trajectory and the local ho rizontal, is very small. For equilibrium flight we have the following relations: D FT (4-1) W L (4-2) where TF is thrust and W is weight of the vehicle. The rate at which the fuel and the coolant are consumed in quasi-steady flight is the summation of the weight flow rate of fuel used to produce the needed thrust and the weight flow rate of th e coolant injected from the surface.[16] This may be written as follows: cooled w w T j coolant fuel consumedA g v F C dt W W d dt dW dt dW 3600 (4-3) where fuelW is weight of the fuel, coolantW is weight of the coolant, and cooledA is total area to be cooled by injection. The quantity jC is the specific fuel consumption and may also be written as j spC I 3600 (4-4) where spI is the specific impulse, measured in thrust produced per unit weight of fuel consumed per unit time. Now Eq.(4-3) becomes cooled inj sp cooled inj sp TA w D L I W A w I F dt dW (4-5) where g v ww w inj Therefore, Eq.(4-5) is written as cooled inj spA w D L I W dW dt (4-6)

PAGE 49

49 The horizontal speed dt dx V so Eq.(4-6) may be integrated from the initial time to the final time, assuming that spI, D L, and cooled injA w are constant, as follows: final initial final initial final initialW W sp sp cooled inj W W cooled inj sp R t tD L I D L I W A w A w D L I W dW V R V dx dt 1 ln0 (4-7) D L I W A w D L I W A w V D L I R t Vsp initial cooled inj sp final cooled inj sp final ln (4-8) where finalt is the flight time and R is the flight range. Here finalW is the weight of the vehicle after all the fuel and coolant are cons umed during the cruising flight and initialW is the weight of the vehicle when carrying full fuel and full coolan t. Eq.(4-8) is used to find the flight range starting with a constant initial amount of fuel a nd coolant. Note that no matter how much coolant is used for surface injection, Eq.(4-8) gives the fl ight range or flight time with the given amount of fuel and coolant being complete ly consumed. As already discussed, D L depends on both injw and cooledA. The weight of the vehicle before it uses any fuel and coolant, initialW is set to: ref L initialS M P C L W2 0 02 1 (4-9) where 0 ,LC is the lift coefficient wit hout mass injection. The total we ight of the fuel and the coolant is: coolant fuel final initialW W W W (4-10) Comparison of Range, L /D, and Heat Transfer Variance Since we have already established methods to find the aerodynamic forces including skin friction, heat transfer, effects of mass injection, and flight range for hypersonic flow. We are now

PAGE 50

50 ready to show the advantages and penalties aris ing from injecting mass through the surface of a hypersonic cruising vehicle. In th is study, the characteristic Reynolds number is used, and it is defined as: Vchar.Re. Our theories were applied to an X-24C vehicle assumed to be flying at Mach number of 6.00 with angle of attack of 6 at 30000 m (mchar/ 10 21 2 Re6 and Pa q29500 ) altitude and 35000 m (mchar/ 10 95 9 Re5 and Pa q14000 ) altitude. The surface temperature is assumed to be constant with or without injection. For the case at which we do not use mass injection, some unspecified internal cooling system may accomplish constant surface temperature assumption by absorbing the ther mal power. For injected surface, surface temperature may remain constant temperature of coolant that is being in jected through the panel surface. The fuel used here is assumed to be hydrocarbon, with s Isp1000 The material injected through the surface of vehicle is not sp ecified, but it is at least a gas. finalW is the weight of the vehicle after 100 s of cruising flight with zero mass inje ction. Therefore, Eq.(4-8) provides the flight time for which the aircraft can cruise when the total amount of the fuel and coolant is the same as final initialW W whether or not we use mass injection. Injecting on the windward panels on the fo rward section of the fuselage, where w cq, is relatively high, reduces heat transf er with a small rate of mass injection. However, each of these individual panels has a relatively high angle of attack with resp ect to the free stream direction, therefore the effect of mass inje ction may be relatively smaller than other panels in reducing drag. Cooling aft panels, where w cq, is relatively low, reduces heat transfer less effectively, and the required mass injection rate is relatively large. However, each of these panels angle of attack is lower than the ones of the forward panels, an d each has a large area, so it is not simple to choose the panels to be cooled so th at the mass is used most effectively.

PAGE 51

51 Therefore, the panels to be cooled were de termined by two aspects of the heat transfer experienced by each panel: the thermal power transfer, w cQ,(W), and the heat flux, w cq,(2/m W). Around the nose of body and the leading edge of the wings, each pane l has relatively high w cq,, but low w cQ, because of the small area of the individual panels. On the other hand, the aft panels have low w cq,, but high w cQ, since each panel has relatively large area. Figure 4-1 shows the distribution of panel area as a function of the panels heat transfer, w cq,(2/m W) at 6 M and 30000 m altitude for no injection. Th e total area of panels whose uncooled heat transfer w cq, is between 0 and 50002/m W is slightly larger than 252m, and there is 352marea of panels that have uncooled w cq, between 5000 and 100002/m W. Figure 16 is slightly different as it shows th e distribution of the number of pa nel as a function of the panels uncooled heat transfer, w cq,(2/m W) at 6 M and 30000 m altitude. For example, there are 14 panels whose uncooled heat transfer w cq, is between 0 and 50002/m W, while there are over 50 panels with uncooled 2 ,/ 100000m W qw c. Figures 4-3 to 4-5 show the effect of mass in jection on the flight time, and therefore the range, D L, and reduction of heat power (norma lized heat power), respectively at 6 M and 30000 m altitude. Normalized heat power is defined as 0Q Q 0Q is heat power absorbed by all panels when we do not use any mass injection, and Q is heat power absorbed by all panels with mass injection. When injm is zero, 0Q Q The panels to be cooled are determined by the heat transfer, w cq, experienced by the individual panels wit hout injection. As we in crease the rate of mass injection, the flight range d ecreases and this effect is more pronounced for cases in which there is a larger area to be cooled. As discusse d in the previous chapter, mass injection reduces

PAGE 52

52 skin friction and heat transfer. Th erefore, we get an advantage in reducing the heat transfer but with the penalty of decreasing flight range. For instance, consider the case of a mass injection rate of 0.005s m kg2/ at 6 M and 30000 m altitude. Figure 4-3 shows that the flight time is 85.16 s when all panels are cooled by the selected mass injection rate of 0.005s m kg2/. The flight time is 89.97 s when only the panels that have w cq, of more than 100002/m W are cooled by the selected mass injection rate of 0.005s m kg2/. Figure 4-4 shows that D L is 1.245 when all panels are cooled by the mass injection rate of 0.005s m kg2/ and D L is 1.236 when only the panels that have w cq, of more than 300002/m W are cooled by the mass injection rate of 0.005s m kg2/. Figure 4-5 shows that normalized heat power is 0.8936 when all panels are cooled by the mass injection rate of 0.005s m kg2/. However, the normalized heat power is 0.9517 when the panels that have w cq, of more than 500002/m W are cooled by the mass injection rate of 0.005s m kg2/. Before Figures 4-6 to 4-11 are discussed, two normalized parameters: normalized injected mass and normalized reduction of heat power are introduced. Normalized injected mass is defined as: total cooled total inj cooled injA A A m A m m ~ (4-11) where injm is the rate of mass injected and totalA is the total surface area of the vehicle. Normalized reduction of h eat power is defined as: 0 0 ~ Q Q Q Q (4-12) In order to show more deta ils of the advantages and pe nalties associated with mass injection, Figures 4-6 to 4-11 s how the relation between injected mass, reduction of heating, and

PAGE 53

53 reduction of flight range at the rela tively low mass injection rate of 0.001s m kg2/. Figures 4-12 to 4-17 show results at mass injection rate an order of magnit ude greater, i.e. 0.01s m kg2/. For instance, the case of ma ss injection rate of 0.001s m kg2/ at 6 M and 30000 m altitude is introduced. Figure 4-6 shows that normali zed reduction of heat power is 0.02091 when normalized injected mass is 0.8482 and when the panels that have w cq, of more than 50002/m W are cooled by the mass injection rate of 0.001s m kg2/. Figure 4-7 shows that the flight time is 97.14 s when normalized injected mass is 0.8482 and when the panels that have w cq, of more than 50002/m W are cooled by the mass injection rate of 0.001s m kg2/. Figure 4-8 shows that the flight time is 97.14 s when normalized reduction of heat power is 0.02091 and when the panels that have w cq, of more than 50002/m W are cooled by the mass injection rate of 0.001s m kg2/. Figure 4-9 shows that reduc tion of heat power is 71.46 kW when injected mass rate is 0.1427s kg/ and when the panels that have w cq, of more than 50002/m W are cooled by the mass injection rate of 0.001s m kg2/. Figure 4-10 shows that reduc tion of heat energy is 16700 kJ when injected mass is 13.86kg and when the panels that have w cq, of more than 50002/m W are cooled by the mass injection rate of 0.001s m kg2/. Figure 4-11 shows that flight time is 97.14 s when reduction of heat energy is 16700 kJ and when the panels that have w cq, of more than 50002/m W are cooled by the mass injection rate of 0.001s m kg2/. Figures 4-6 and 4-12 show the effect of nor malized injected mass on normalized reduction of heat power. Figures 4-7 and 4-13 show the ef fect of normalized injected mass on the flight time, while Figures 4-8 and 4-14 show the effect of normalized reduction of heat power on the flight time. Figures 4-9 and 4-15 show the effect of injected ma ss rate on the reduction of heat

PAGE 54

54 power. The effect of injected mass on the reducti on of heat energy is shown in Figures 4-10 and 4-16. Finally, Figure 4-11 and 4-17 show the advantag e (reduction of heat transfer) we have for the penalty (reduction of flight time). The data la bels attached to the lines are the allowable heat transfer, w cq, of the panels. For inst ance, a data label, 2/m W means that all panels whose heat transfer is above 500002/m W (the allowable heat tr ansfer) are cooled by mass injection. Figures 4-6 and 4-12 show a c oncave downward curve, which indicates that choosing the highly heated panels for cooling reduces total h eat transfer more effectively than cooling all panels. Figures 4-7 and 4-13 show an almost lin ear relation between norma lized mass and flight time. Therefore, as more mass injected, the more th e flight time (therefore flight range) decreases at an almost constant rate. Figures 4-8 a nd 4-14 show a concave downward curve relation between reduction of heat power and flight time. Thus, injecting on too many panels is increasingly apt to decrease fli ght time. Figures 4-9 a nd 4-15 show the actual reduction in heat power with various mass injection rates () /s kg. Figures 4-10 and 4-16 show the reduction in heat energy with various mass injection (kg). These figures give a slightly concave downward relation between the reduction of heat energy an d the mass injection. Figures 4-11 and 4-17 give a slightly concave downward curve. Again, this i ndicates that cooling only panels whose heat transfer, w cq, is relatively high gives the most effec tive advantage (reduction of heat transfer) by mass injection. Figures 4-18 to 4-20 show the X-24C vehicle w hose panels are to be cooled if the heat transfer w cq, is more than 500002/m W at 6 M and 30000 m altitude. The shadings (red panels) are the panels cooled. In general, the nose, the vertical fin, and the lead ing edges of the wing and the off-center fin have high w cq,. The bottom panels also have high heat absorption. The panels

PAGE 55

55 around the nose of the fuselage and the leadi ng edge of the wings have the highest heat absorption. Figures 4-21 to 4-40 are anal ogous to Figures 4-1 to 4-20. Th ey are at the exactly same conditions except for that the panels to be cooled are determined by heat power, w cQ, of individual panels in Figures 4-21 to 4-40. Also, Figure 4-41 to 4-60 are analogous to Figures 4-1 to 4-20. Figures 4-41 to 4-60 are results for 6 M and 35000 m altitude, and the cooled panels are chosen by heat transfer, w cq, of the individual panel. Finall y, Figures 4-61 to 4-80 are also analogous to Figures 4-1 to 4-20. Fi gures 4-41 to 4-80 are results for 6 M and 35000 m altitude, and the panels to be cooled ar e determined by the heat power, w cQ, of individual panels. Figures 4-23 to 37 show results very similar to those of Figures 4-3 to 4-17. There is little of difference to note within difference between Figures 4-3 to 4-17 and 4-23 to 4-37. Therefore, whether we choose the panels to be cooled by taking those with the higher heat transfer, w cq, or the higher heat power, w cQ, of individual panels, cooling only so me of the highest heated panels gives the most effective advantage. Figures 4-38 to 4-40 show that we have panels whose heat power is higher in the aft portion of the vehicl e although the front panels have the higher heat transfer, w cq,. This is because aft panels have larger area, and the heat power w cQ, absorbed by each panel is defined as dA qw c,. Figures 4-43 to 4-57 also show the same behavior as Figures 4-3 to 4-17. Comparing Figures 4-6, 4-7, 4-12 and 4-13 a nd Figures 4-46, 4-47, 4-52, and 4-53, we find that the effect of mass injection (normalized injected mass) on reduc ing flight time and heat transfer (normalized reduction of heat power) is larger for the case at 35000 m altitude. Comparing Figure 4-48 and 454 with Figure 4-8 and 4-14, the same value of no rmalized reduction of heat power gives slightly

PAGE 56

56 greater reduction in flight time at 35000 m altitude. This is because of lower dynamic pressure at higher altitude. Comparing Fi gures 4-9, 4-10, 4-15, and 4-16 and Figures 4-49, 4-50, 4-55, and 4-56, it is found that the effect of mass injection on the reduction of heat power and heat energy is slightly larger at 35000 m altitude or almost same for both cases. This argument may look as if it conflicts with the comparison of Figures 4-6 and 4-46, but this is because the to tal heat power and heat energy absorbed by the vehi cle are larger for the case at 30000 m than the case at 35000 m Figures 4-63 to 4-77 show similar behavior and values to those of Fi gures 4-43 to 4-57 and we have seen that Figures 4-23 to 4-37 do not ch ange much from Figures 4-3 to 4-17. In general, choosing the panels to be cooled by taking the higher heat transfer, w cq, gives more effective advantage (reduction of heat transfer) than by taking the higher heat power, w cQ, of individual panel. However, the X-24C has the highest w cq, around the nose where the panels have relatively high angle of attack. On the other ha nd, the aft panels have the highest w cQ, and relatively low angle of attack. The effect of mass inject ion on reducing heat tr ansfer and increasing L/D is generally more pronounced at the pa nels whose angle of attack is low as we have seen in figure 3-1 and 3-2. Therefore, for the X-24C there is no t much difference results between choosing the panels by using w cq, and w cQ, of each panels. As a brief resu lt, table 4-1 shows comparison of critical flight parameters for various mass onjection rate. One of the parameters that indicates how the vehicle is slender (or fat) is the volumesurface parameter, defined as: S V3 2 (4-13)

PAGE 57

57 where V is the volume of the vehicle, and S is the spanwise area of the vehicle. The smaller is, the more slender the vehicle. For the X-24C aircraft, 18 0 which is relatively high value for a cruising vehicle. A more slender body would have a higher L/D than the X-24C because the contribution of aerodynamic forces caused by pressure is smaller. The fraction of skin friction force in total drag force is therefore larger, which makes the increment of L/D by mass injection larger. Therefore, it is expected that reduction of flight range by mass injection decreases or that flight time increases for a more slender body. Table 4-1. Comparison of flight parameters at 6 M and 30000 m altitude. The panels that have w cq, of more than 500002/m W are cooled by the ma ss injection rate: 0, 0.001, 0.01) / (2s m kg. Parameter 0) / (2s m kg 0.001) / (2s m kg 0.010) / (2s m kg finalt(s) 100.0 96.65 74.04 D L 1.225 1.227 1.240 0Q Q 1.000 0.990 0.906 total cooledA A 0.000 0.3634 0.3634 reduction of heat power (kW) 0.000 33.76 320.8 reduction of heat energy (MJ) 0.000 7.585 66.851 fuelW(kg) 442.7 436.8 397.4 coolantW(kg) 0.000 5.909 45.27 0 5 10 15 20 25 30 35 400-5000 5 00 0-100 0 0 10 000 -15 000 15 0 00-20 0 00 20 000-2 5 000 25 00030 000 30 00 0-35 00 0 3 5 000-40000 40 00045 000 45 00 0-50 00 0 5 0 000-55000 55 00060 000 60 00 0-65 00 0 6 5 000-7 0 000 70 00075 000 75 0 00-80 0 00 80000-85 0 00 85 00090 000 90 00 0-95 000 95000-100000 10 000 0-panels' heat transfer (W/m2) rangearea (m2) Figure 4-1. Distribution of panel ar ea with a given heat transfer, w cq,(2/m W) at 6 M and 30000 m altitude.

PAGE 58

58 0 10 20 30 40 50 600-50 00 5 000-100 00 10000150 00 15000-20000 20000-25000 25000-30000 30000-35000 35000-40000 40000-450 0 0 45000-500 0 0 500 00-550 00 550 00-600 00 600 00-650 00 650 00-700 00 700 00-750 00 7500 0-800 00 8000 0-850 00 85000900 00 90000950 00 95000100 000 100 000 -panels' heat transfer (W/m2) rangethe number of panel Figure 4-2. Distribution of the number of panels with a given heat transfer, w cq,(2/m W) at 6 M and 30000 m altitude. 70 75 80 85 90 95 100 00.0010.0020.0030.0040.0050.0060.0070.0080.0090.01 mass injection rate (kg/m2-s)flight time (s) all panels are cooled (168.244m2) 5000W/m2 and more (142.7m2) 10000W/m2 and more (108m2) 30000W/m2 and more (88.719m2) 50000W/m2 and more (61.143m2) Figure 4-3. Mass injection eff ect on the flight time at 6 M and 30000 m altitude. The panels to be cooled are determined by w cq,(2/m W).

PAGE 59

59 1.22 1.23 1.24 1.25 1.26 1.27 00.0010.0020.0030.0040.0050.0060.0070.0080.0090.01 mass injection rate (kg/m2-s)L/D all panels are cooled (168.244m2) 5000W/m2 and more (142.7m2) 10000W/m2 and more (108m2) 30000W/m2 and more (88.719m2) 50000W/m2 and more (61.143m2) Figure 4-4. Mass injection effect on D L at 6 M and 30000 m altitude. The panels to be cooled are determined by w cq,(2/m W). 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 00.0010.0020.0030.0040.0050.0060.0070.0080.0090.01 mass injection rate (kg/m2-s)normalized heat power all panels are cooled (168.244m2) 5000W/m2 and more (142.7m2) 10000W/m2 and more (108m2) 30000W/m2 and more (88.719m2) 50000W/m2 and more (61.143m2) Figure 4-5. Mass injection effect on reduction of heat power at 6 M and 30000 m altitude. The panels to be cooled are determined by w cq,(2/m W).

PAGE 60

60 5000W/m2 all panels 10000W/m2 30000W/m2 50000W/m2 0 0.005 0.01 0.015 0.02 0.025 00.10.20.30.40.50.60.70.80.91 normalized injected massnormalized reduction of heat power Figure 4-6. Normalized reduction of heat power v.s. normalized injected mass at 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W). all panels 5000W/m2 10000W/m2 30000W/m2 50000W/m2 96 97 98 99 100 00.10.20.30.40.50.60.70.80.91 normalized injected massflight time (s) Figure 4-7. Flight time v.s. norma lized injected mass at at 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W).

PAGE 61

61 5000W/m2 all panels 10000W/m2 30000W/m2 50000W/m2 96 97 98 99 100 00.0050.010.0150.020.025 normalized reduction of heat powerflight time (s) Figure 4-8. Flight time v.s. normali zed reduction of heat power at 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W). all panels 5000W/m2 10000W/m2 30000W/m2 50000W/m2 0 20 40 60 80 100 00.020.040.060.080.10.120.140.160.18 injected mass rate (kg/s)reduction of heat power (kW) Figure 4-9. Reduction of heat power ( kW ) v.s. injected mass rate () /s kgat 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W).

PAGE 62

62 all panels 5000W/m2 10000W/m2 30000W/m2 50000W/m2 0 5000 10000 15000 20000 024681012141618 injected mass (kg)reduction of heat energy (kJ) Figure 4-10. Reduction of heat energy ( kJ ) v.s. injected mass ()kgat 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W). all panels 5000W/m2 10000W/m2 30000W/m2 50000W/m2 96 97 98 99 100 02000400060008000100001200014000160001800020000 reduction of heat energy (kJ)flight time (s) Figure 4-11. Flight time v.s. reduction of heat energy ( kJ ) at 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W).

PAGE 63

63 50000W/m2 30000W/m2 10000W/m2 all panels 5000W/m2 0 0.05 0.1 0.15 0.2 00.10.20.30.40.50.60.70.80.91 normalized injected massnormalized reduction of heat power Figure 4-12. Normalized reduction of heat power v.s. normalized injected mass at 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W). 50000W/m2 30000W/m2 10000W/m2 5000W/m2 all panels 70 75 80 85 90 95 100 00.10.20.30.40.50.60.70.80.91 normalized injected massflight time (s) Figure 4-13. Flight time v.s. nor malized injected mass at at 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W).

PAGE 64

64 50000W/m2 30000W/m2 10000W/m2 all panels 5000W/m2 70 75 80 85 90 95 100 00.050.10.150.2 normalized reduction of heat powerflight time (s) Figure 4-14. Flight time v.s. normali zed reduction of heat power at 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W). all panels 5000W/m2 10000W/m2 30000W/m2 50000W/m2 0 200 400 600 800 00.20.40.60.811.21.41.61.8 injected mass rate (kg/s)reduction of heat power (kW) Figure 4-15. Reduction of heat power ( kW ) v.s. injected mass rate () /s kgat 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W).

PAGE 65

65 50000W/m2 30000W/m2 10000W/m2 5000W/m2 all panels 0 20000 40000 60000 80000 100000 120000 140000 0102030405060708090100110120130 injected mass (kg)reduction of heat energy (kJ) Figure 4-16. Reduction of heat energy ( kJ ) v.s. injected mass ()kgat 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W). 50000W/m2 30000W/m2 10000W/m2 5000W/m2 all panels 70 75 80 85 90 95 100 020000400006000080000100000120000140000 reduction of heat energy (kJ)flight time (s) Figure 4-17. Flight time v.s. reduction of heat energy ( kJ ) at 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W).

PAGE 66

66 Figure 4-18. Bottom view of X24C with 500002/m W of allowable w cq, at 30000 m altitude. Figure 4-19. Side view of X24C with 500002/m W of allowable w cq, at 30000 m altitude. Figure 4-20. Top view of X24C with 500002/m W of allowable w cq, at 30000 m altitude.

PAGE 67

67 0 10 20 30 40 50 6005000 5000-10000 100015000 150 0 0-20000 2000 0-2500 0 25000-30000 3000 0-35 000 350 0 0-40000 4000 045000 4 500 0-50000 5000 055000 55 00 0-60000 6000 065000 6500 0-70000 70000-panels' heat transfer (W) rangearea (m2) Figure 4-21. Distribution of panel ar ea with a given heat transfer, w cQ, (W) at 6 M and 30000 m altitude. 0 20 40 60 80 1000 -5000 5 0001 000 0 100 0150 0 0 15000-20 0 00 2 000 0250 0 0 25 00 0-3 00 00 30000-35000 3 500 0 -400 0 0 40 00 0450 00 450 0 0-50 0 00 5000 0 -55000 55 00 0600 00 600 0 0-6 50 00 6500 0 -70000 7 0 000-panels' heat transfer (W) rangethe number of panel Figure 4-22. Distribution of the number of panels with a given heat transfer, w cQ, (W) at 6 M and 30000 m altitude.

PAGE 68

68 70 75 80 85 90 95 100 00.0010.0020.0030.0040.0050.0060.0070.0080.0090.01 mass injection rate (kg/m2-s)flight time (s) all panels are cooled (168.244m2) 10000W and more (102.13m2) 20000W and more (86.749m2) 30000W and more (67.747m2) 40000W and more (61.202m2) Figure 4-23. Mass injection eff ect on the flight time at 6 M and 30000 m altitude. The panels to be cooled are determined by w cQ, (W). 1.22 1.23 1.24 1.25 1.26 1.27 00.0010.0020.0030.0040.0050.0060.0070.0080.0090.01 mass injection rate (kg/m2-s)L/D all panels are cooled (168.244m2) 10000W and more (102.13m2) 20000W and more (86.749m2) 30000W and more (67.747m2) 40000W and more (61.202m2) Figure 4-24. Mass injection effect on D L at 6 M and 30000 m altitude. The panels to be cooled are determined by w cQ, (W).

PAGE 69

69 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 00.0010.0020.0030.0040.0050.0060.0070.0080.0090.01 mass injection rate (kg/m2-s)normalized heat power all panels are cooled (168.244m2) 10000W and more (102.13m2) 20000W and more (86.749m2) 30000W and more (67.747m2) 40000W and more (61.202m2) Figure 4-25. Mass injection effect on reduction of heat power at 6 M and 30000 m altitude. The panels to be cooled are determined by w cQ, (W). 10000W all panels 20000W 30000W 40000W 0 0.005 0.01 0.015 0.02 0.025 00.10.20.30.40.50.60.70.80.91 normalized injected massnormalized reduction of heat power Figure 4-26. Normalized reduction of heat power v.s. normalized injected mass at 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).

PAGE 70

70 all panels 10000W 20000W 30000W 50000W 96 96.5 97 97.5 98 98.5 99 99.5 100 00.10.20.30.40.50.60.70.80.91 normalized injected massflight time (s) Figure 4-27. Flight time v.s. normalized injected mass at 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W). 10000W all panels 20000W 30000W 40000W 96 96.5 97 97.5 98 98.5 99 99.5 100 00.0050.010.0150.020.025 normalized reduction of heat powerflight time (s) Figure 4-28. Flight time v.s. normali zed reduction of heat power at 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).

PAGE 71

71 all panels 10000W 20000W 30000W 40000W 0 20 40 60 80 100 00.020.040.060.080.10.120.140.160.18 injected mass rate (kg/s)reduction of heat power (kW) Figure 4-29. Reduction of heat power ( kW ) v.s. injected mass rate () /s kgat 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W). all panels 10000W 20000W 30000W 40000W 0 5000 10000 15000 20000 024681012141618 injected mass (kg)reduction of heat energy (kJ) Figure 4-30. Reduction of heat energy ( kJ ) v.s. injected mass ()kgat 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).

PAGE 72

72 all panels 10000W 20000W 30000W 40000W 96 96.5 97 97.5 98 98.5 99 99.5 100 02000400060008000100001200014000160001800020000 reduction of heat energy (kJ)flight time (s) Figure 4-31. Flight time v.s. reduction of heat energy ( kJ ) at 6 M and 30000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W). 40000W 30000W20000W all panels 10000W 0 0.05 0.1 0.15 0.2 00.10.20.30.40.50.60.70.80.91 normalized injected massnormalized reduction of heat power Figure 4-32. Normalized reduction of heat power v.s. normalized injected mass at 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).

PAGE 73

73 40000W 30000W 20000W 10000W all panels 70 75 80 85 90 95 100 00.10.20.30.40.50.60.70.80.91 normalized injected massflight time (s) Figure 4-33. Flight time v.s. normalized injected mass at 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W). 40000W 30000W 20000W all panels 10000W 70 75 80 85 90 95 100 00.050.10.150.2 normalized reduction of heat powerflight time (s) Figure 4-34. Flight time v.s. normali zed reduction of heat power at 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).

PAGE 74

74 40000W 30000W 20000W 10000W all panels 0 100 200 300 400 500 600 700 800 00.20.40.60.811.21.41.61.8 injected mass rate (kg/s)reduction of heat power (kW) Figure 4-35. Reduction of heat power ( kW ) v.s. injected mass rate () /s kgat 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W). 40000W 30000W 20000W 10000W all panels 0 20000 40000 60000 80000 100000 120000 140000 0102030405060708090100110120130 injected mass (kg)reduction of heat energy (kJ) Figure 4-36. Reduction of heat energy ( kJ ) v.s. injected mass ()kgat 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).

PAGE 75

75 40000W 30000W 20000W 10000W all panels 70 75 80 85 90 95 100 020000400006000080000100000120000140000 reduction of heat energy (kJ)flight time (s) Figure 4-37. Flight time v.s. reduction of heat energy ( kJ ) at 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W). Figure 4-38. Bottom view of X-24C with 40000W of allowable w cQ, at 6 M and 30000 m altitude. Figure 4-39. Side view of X-24C with 40000W of allowable w cQ, at 6 M and 30000m altitude.

PAGE 76

76 Figure 4-40. Top view of X-24C with 40000W of allowable w cQ, at 6 M and 30000 m altitude. 0 5 10 15 20 25 30 35 40 450 500 0 50001 0000 1 0 000-1 5 0 0 0 1 50 0 0 -2 0 0 00 2 0 000-2 5 0 0 0 2 5 00 0 -3 0 0 0 0 300 0 0 35000 3 5 00 0 -4 0 0 0 0 400 0 0 -4 5000 450 0 0 50000 5 0 000-550 0 0 550 0 0 60000 60000-65000 6 5 000-7 0 0 0 0 70000-75000 7 5 000-8 0 0 0 0 8 0 00 0 -8 5 0 0 0 850 0 0 -90000 9 0 00 0 -9 5 0 0 0 9 5 000-1 0 0 0 00 1 0 0 0 00-panels' heat transfer (W/m2) rangearea (m2) Figure 4-41. Distribution of panel ar ea with a given heat transfer, w cq,(2/m W) at 6 M and 35000 m altitude. 0 5 10 15 20 25 30 35 400-500 0 5 0 0 0 -1 0 00 0 1000 0 -1 5 00 0 1 5 000-20000 2000 0 -2 5 00 0 2 5 000-30000 30 0 0 0 -3 50 0 0 3 5 000-40000 40 0 0 0 -4 50 0 0 4 5 000-50000 50 0 0 05 50 0 0 5500 0 -6 0 000 6 0 0 0 0-650 0 0 6500 0 -7 0 000 7 0 000-750 0 0 7500 0 -8 0 00 0 8 0 000-85000 8500 0 -9 0 00 0 9 0 000-95000 9 5 000 -1 0 00 0 0 100000-panels' heat transfer (W/m2) rangethe number of panel Figure 4-42. Distribution of the number of panels with a given heat transfer, w cq,(2/m W) at 6 M and 35000 m altitude.

PAGE 77

77 50 55 60 65 70 75 80 85 90 95 100 00.0010.0020.0030.0040.0050.0060.0070.0080.0090.01 mass injection rate (kg/m2-s)flight time (s) all panels are cooled (168.244m2) 5000W/m2 and more (126.79m2) 10000W/m2 and more (104.3m2) 20000W/m2 and more (84.58m2) 30000W/m2 and more (57.119m2) Figure 4-43. Mass injection eff ect on the flight time at 6 M and 35000 m altitude. The panels to be cooled are determined by w cq,(2/m W). 1.18 1.19 1.2 1.21 1.22 1.23 1.24 1.25 1.26 00.0010.0020.0030.0040.0050.0060.0070.0080.0090.01 mass injection rate (kg/m2-s)L/D all panels are cooled (168.244m2) 5000W/m2 and more (126.79m2) 10000W/m2 and more (104.3m2) 20000W/m2 and more (84.58m2) 30000W/m2 and more (57.119m2) Figure 4-44. Mass injection effect on D L at 6 M and 35000 m altitude. The panels to be cooled are determined by w cq,(2/m W).

PAGE 78

78 0.68 0.72 0.76 0.8 0.84 0.88 0.92 0.96 1 00.0010.0020.0030.0040.0050.0060.0070.0080.0090.01 mass injection rate (kg/m2-s)normalized heat powe all panels are cooled (168.244m2) 5000W/m2 and more (126.79m2) 10000W/m2 and more (104.3m2) 20000W/m2 and more (84.58m2) 30000W/m2 and more (57.119m2) Figure 4-45. Mass injection effect on reduction of heat power at 6 M and 35000 m altitude. The panels to be cooled are determined by w cq,(2/m W). 5000W/m2 all panels 10000W/m2 20000W/m2 30000W/m2 0 0.01 0.02 0.03 0.04 0.05 00.10.20.30.40.50.60.70.80.91 normalized injected massnormalized reduction of heat power Figure 4-46. Normalized reduction of heat power v.s. normalized injected mass at 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W).

PAGE 79

79 5000W/m2 all panels 10000W/m2 20000W/m2 30000W/m2 0 0.01 0.02 0.03 0.04 0.05 00.10.20.30.40.50.60.70.80.91 normalized injected massnormalized reduction of heat power Figure 4-47. Flight time v.s. nor malized injected mass at at 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W). 5000W/m2 all panels 10000W/m2 20000W/m2 30000W/m2 93 94 95 96 97 98 99 100 00.0050.010.0150.020.0250.030.0350.040.045 normalized reduction of heat powerflight time (s) Figure 4-48. Flight time v.s. normali zed reduction of heat power at 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W).

PAGE 80

80 all panels 5000W/m2 10000W/m2 20000W/m2 30000W/m2 0 20 40 60 80 100 00.020.040.060.080.10.120.140.160.18 injected mass rate (kg/s)reduction of heat power (kW) Figure 4-49. Reduction of heat power ( kW ) v.s. injected mass rate () /s kgat 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W). all panels 5000W/m2 10000W/m2 20000W/m2 30000W/m2 0 5000 10000 15000 20000 25000 0246810121416 injected mass (kg)reduction of heat energy (kJ) Figure 4-50. Reduction of heat energy ( kJ ) v.s. injected mass ()kgat 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W).

PAGE 81

81 all panels 5000W/m2 10000W/m2 20000W/m2 30000W/m2 93 94 95 96 97 98 99 100 0200040006000800010000120001400016000180002000022000 reduction of heat energy (kJ)flight time (s) Figure 4-51. Flight time v.s. reduction of heat energy ( kJ ) at 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W). 30000W/m2 20000W/m2 10000W/m2 all panels 5000W/m2 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 00.10.20.30.40.50.60.70.80.91 normalized injected massnormalized reduction of heat power Figure 4-52. Normalized reduction of heat power v.s. normalized injected mass at 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W).

PAGE 82

82 30000W/m2 20000W/m2 10000W/m2 5000W/m2 all panels 50 60 70 80 90 100 00.10.20.30.40.50.60.70.80.91 normalized injected massflight time (s) Figure 4-53. Flight time v.s. nor malized injected mass at at 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W). 30000W/m2 20000W/m2 10000W/m2 all panels 5000W/m2 50 60 70 80 90 100 00.050.10.150.20.250.30.35 normalized reduction of heat powerflight time (s) Figure 4-54. Flight time v.s. normali zed reduction of heat power at 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W).

PAGE 83

83 30000W/m2 20000W/m2 10000W/m2 5000W/m2 all panels 0 100 200 300 400 500 600 700 00.20.40.60.811.21.41.61.8 injected mass rate (kg/s)reduction of heat power (kW) Figure 4-55. Reduction of heat power ( kW ) v.s. injected mass rate () /s kgat 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W). 30000W/m2 20000W/m2 10000W/m2 5000W/m2 all panels 0 20000 40000 60000 80000 100000 120000 140000 0102030405060708090100 injected mass (kg)reduction of heat energy (kJ) Figure 4-56. Reduction of heat energy ( kJ ) v.s. injected mass ()kgat 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W).

PAGE 84

84 30000W/m2 20000W/m2 10000W/m2 5000W/m2 all panels 50 60 70 80 90 100 020000400006000080000100000120000 reduction of heat energy (kJ)flight time (s) Figure 4-57. Flight time v.s. reduction of heat energy ( kJ ) at 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cq,(2/m W). Figure 4-58. Bottom view of X-24C with 300002/m W of allowable w cq, at 35000 m altitude. Figure 4-59. Side view of X-24C with 300002/m W of allowable w cq, at 35000 m altitude.

PAGE 85

85 Figure 4-60. Top view of X-24C with 300002/m W of allowable w cq, at 35000 m altitude. 0 10 20 30 40 50 600-5 0 00 50 0 0-1 0 000 1000-15 0 00 15 000 -2 00 00 20000-25000 25 00 0-3 0 000 300003 500 0 35 0 00-4 0 000 4 0 000 -4 50 00 45 0 00-50000 50 00 0-5 50 00 550006 000 0 60 0 00-6 5 000 6 5 000 -7 000 0 70000-panels' heat transfer (W) rangearea (m2) Figure 4-61. Distribution of panel ar ea with a given heat transfer, w cQ,(W) at 6 M and 35000 m altitude. 0 20 40 60 80 100 1200-5000 5000-100 00 1000150 00 150002 0000 200002500 0 2500 030000 30000-35000 3500040000 40000-45000 450005 0000 5 000055000 5500 060000 60000650 00 650 0070000 700 00 -panels' heat transfer (W) rangethe number of panel Figure 4-62. Distribution of the number of panels with a given heat transfer, w cQ,(W) at 6 M and 35000 m altitude.

PAGE 86

86 50 55 60 65 70 75 80 85 90 95 100 00.0010.0020.0030.0040.0050.0060.0070.0080.0090.01 mass injection rate (kg/m2-s)flight time (s) all panels are cooled (168.244m2) 2500W and more (156.64m2) 5000W and more (116.8m2) 10000W and more (88.768m2) 20000W and more (64.485m2) Figure 4-63. Mass injection eff ect on the flight time at 6 M and 35000 m altitude. The panels to be cooled are determined by w cQ, (W). 1.18 1.19 1.2 1.21 1.22 1.23 1.24 1.25 1.26 1.27 00.0010.0020.0030.0040.005 0.0060.0070.0080.0090.01 mass injection rate (kg/m2-s)L/D all panels are cooled (168.244m2) 2500W and more (156.64m2) 5000W and more (116.8m2) 10000W and more (88.768m2) 20000W and more (64.485m2) Figure 4-64. Mass injection effect on D L at 6 M and 35000 m altitude. The panels to be cooled are determined by w cQ, (W).

PAGE 87

87 0.68 0.72 0.76 0.8 0.84 0.88 0.92 0.96 1 00.0010.0020.0030.0040.005 0.0060.0070.0080.0090.01 mass injection rate (kg/m2-s)normalized heat power all panels are cooled (168.244m2) 2500W and more (156.64m2) 5000W and more (116.8m2) 10000W and more (88.768m2) 20000W and more (64.485m2) Figure 4-65. Mass injection effect on reduction of heat power at 6 M and 35000 m altitude. The panels to be cooled are determined by w cQ, (W). 2500W all panels 5000W 10000W 20000W 0 0.01 0.02 0.03 0.04 0.05 00.10.20.30.40.50.60.70.80.91 normalized injected massnormalized reduction of heat power Figure 4-66. Normalized reduction of heat power v.s. normalized injected mass at 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).

PAGE 88

88 all panels 2500W 5000W 10000W 20000W 93 94 95 96 97 98 99 100 00.10.20.30.40.50.60.70.80.91 normalized injected massflight time (s) Figure 4-67. Flight time v.s. normalized injected mass at 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W). 2500W all panels 5000W 10000W 20000W 93 94 95 96 97 98 99 100 00.0050.010.0150.020.0250.030.0350.040.045 normalized reduction of heat powerflight time (s) Figure 4-68. Flight time v.s. normali zed reduction of heat power at 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).

PAGE 89

89 all panels 2500W 5000W 10000W 20000W 0 20 40 60 80 100 00.020.040.060.080.10.120.140.160.18 injected mass rate (kg/s)reduction of heat power (kW) Figure 4-69. Reduction of heat power ( kW ) v.s. injected mass rate () /s kgat 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W). all panels 2500W 5000W 10000W 20000W 0 5000 10000 15000 20000 25000 0246810121416 injected mass (kg)reduction of heat energy (kJ) Figure 4-70. Reduction of heat energy ( kJ ) v.s. injected mass ()kgat 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).

PAGE 90

90 all panels 2500W 5000W 10000W 20000W 93 94 95 96 97 98 99 100 0200040006000800010000120001400016000180002000022000 reduction of heat energy (kJ)flight time (s) Figure 4-71. Flight time v.s. reduction of heat energy ( kJ ) at 6 M and 35000 m altitude with 0.0012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W). 20000W 10000W 5000W all panels 2500W 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 00.10.20.30.40.50.60.70.80.91 normalized injected massnormalized reduction of heat power Figure 4-72. Normalized reduction of heat power v.s. normalized injected mass at 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).

PAGE 91

91 20000W 10000W 5000W 2500W all panels 50 60 70 80 90 100 00.10.20.30.40.50.60.70.80.91 normalized injected massflight time (s) Figure 4-73. Flight time v.s. normalized injected mass at 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W). 20000W 10000W 5000W all panels 2500W 50 60 70 80 90 100 00.050.10.150.20.250.30.35 normalized reduction of heat powerflight time (s) Figure 4-74. Flight time v.s. normali zed reduction of heat power at 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).

PAGE 92

92 20000W 10000W 5000W 2500W all panels 0 100 200 300 400 500 600 700 00.20.40.60.811.21.41.61.8 injected mass rate (kg/s)reduction of heat power (kW) Figure 4-75. Reduction of heat power ( kW ) v.s. injected mass rate () /s kgat 6 M and 30000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W). 20000W 10000W 5000W 2500W all panels 0 20000 40000 60000 80000 100000 120000 140000 0102030405060708090100 injected mass (kg)reduction of heat energy (kJ) Figure 4-76. Reduction of heat energy ( kJ ) v.s. injected mass ()kgat 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W).

PAGE 93

93 20000W 10000W 5000W 2500W all panels 50 60 70 80 90 100 020000400006000080000100000120000 reduction of heat energy (kJ)flight time (s) Figure 4-77. Flight time v.s. reduction of heat energy ( kJ ) at 6 M and 35000 m altitude with 0.012/m kgs of mass injection. The panels to be cooled are determined by w cQ, (W). Figure 4-78. Bottom view of X-24C with 20000W of allowable w cQ, at 35000 m altitude. Figure 4-79. Side view of X-24C with 20000W of allowable w cQ, at 35000 m altitude.

PAGE 94

94 Figure 4-80. Top view of X-24C with 20000W of allowable w cQ, at 35000 m altitude.

PAGE 95

95 CHAPTER 5 CONCLUSIONS Conclusions of this Study The local surface inclination me thod (Newtonian theory) was shown to reasonably predict the pressure around a flight vehicle like the X-24 C. The flat plate refe rence enthalpy method for laminar and turbulent flow was utilized, along wi th a classical approximation of thermodynamic properties for considering high temperature effects, to calculate heat transfer over a hypersonic vehicle. This method provided good agreement w ith available heat transfer measurements. However, around a stagnation point or line, the flat plate reference enthalpy method gave extremely high values, much higher than experime ntal data. Therefore, around stagnation points or lines, the blunt body heat tran sfer method was used since it gave reasonable solutions. For surfaces on which the two methods give the same or close heat transfer, th e flat plate reference enthalpy method was preferred. These simple methods are based on many approximations, but for preliminary design considerations, they are su fficiently accurate tools to compute the flow properties including aerodynamic fo rces, moments, and heating. In order to reduce skin friction and heat tran sfer on a vehicle surface, we used an existing simple algebraic Couette flow solution since it has the virtue of fitting the experimental data. The effect of mass injection is relatively large for the lower Also, the more mass is injected, the less the effect of blowin g grows. Therefore, even a small amount of injected mass is effective in improving flight performance ( L/D ) and thermal protection (le ss heating). Even though the amount of fuel is reduced in favor of carrying the coolant for surface in jection, the fuel still provides the necessary thrust so that flight time is not reduced much, because blowing reduces the total drag. Reducing flight ra nge is the penalty of mass inject ion, while reducing heat transfer is the advantage of mass injecti on. It has been shown that choosi ng the panels to be cooled by

PAGE 96

96 taking the panels whose heat transfer, w cq, or w cQ,, are the highest gives the most advantage for the least penalty. This illustrates the conclusion that simply providing inj ection on all panels is not an efficient cooling method. The X-24C vehicle has relatively high pressure forces because of the fuselage shape. Using mass injection on a more slender cruising vehicl e which has a higher fraction of viscous drag than the X-24C will have less penalty (reduced fli ght range) or even zero penalty (constant or increasing flight range), in addi tion to reducing heat transfer. Future Work In this study, we considered the effects of mass injection only on the boundary layer over the plates through which injection occurs. However, in reality, the injected mass effects a change in flow structures downstream of the injected pl ates. The injected gas has a normal component of profile velocity, which makes the boundary layer profile less full and ther efore the gradient of tangential velocity in normal direction beco mes smaller than the boundary layer with zero injection. In general, the shear stress is linearl y dependent on this gradient, and the skin friction would be the integrated value of local shear stress. This is th e physics describing why injected gas reduces skin friction. The less full boundary laye r profile cannot rapidly return to the original equilibrium profile just downstream of th e injected plate. The in jected gas, therefore, will reduce the skin friction on regions downstream of the injected plate. Eventually, the less full boundary layer return s to the equilibrium profile at a certain point, after which the inj ected gas has no effect. Establishing the method that predicts how much skin friction and heat transfer ar e reduced is a logical extension to this study. The more accurate analysis of viscous effect reduction given by th is method will make the results more reliable.

PAGE 97

97 Furthermore these downstream effects will show that the current results are actually conservative and that even better performance should be possible.

PAGE 98

98 APPENDIX A MATLAB CODE TO COMPUTE FLIGHT PERFORMANCE OF X24C %************************************************************************** %code name: x24c0012 %written by: Yoshifumi Nozaki %date: 3/20/2007 %This code computes the x-24c cr uising vehicle flight performance %center off fin & wing has NACA0012 airfoil. %Inviscid and viscous hypersonic flow field can be solved by using %the modified Newtonian method and Reynolds' analogy approximation %This code works with other code %************************************************************************** %****** Flow Properties *************************************************** % ro: air density (kg/m3) % Pinf: atmospheric pressuer (N/m2) % Rair: gas constant of air (287J/kg-K) % Tinf: free stream temperature (K) % cpinf: specific heat constant pressu re of free stream (J/g-K or kJ/kg-K) % M: Mach number % gamma: specific heat ratio % Vinf: free stream velocity (m/s) % a: speed of sound (m/s) % qinf: dynamic pressure (kN/m2) %************************************************************************** %***** Orbiter Characteristics ******************************************** % aoa: angle of attack (deg.) % Sref: wing planform area (m2) % chord: chord length (m) % b: wing span (m) % ep: density ration across shock wave for hypersonic flow % d1_el: left ela von 1 deflection (deg.) % d2_el: left ela von 2 deflection (deg.) % d1_er: right ela von 1 deflection (deg.) % d2_er: right ela von 2 deflection (deg.) % dr: rudder deflection (deg.) % ref: reference point e.g. center of gravity % refa: reference point accounting angle of attack %************************************************************************** %***** Flight Performance ************************************************* % Lift: lift (N) % Drag: drag (N) % L_D: L/D ratio (inviscid)

PAGE 99

99 % L_D_vis L/D ratio (viscous without cooling) % L_D_cool L/D ratio (viscous with cooling) % rolling: rolling moment (N-m) % pitching: pitching moment (N-m) % yawing: yawing moment (N-m) % CL: lift coefficient % CD: drag coefficient % C_m: pitching moment coefficient % C_l: rolling moment coefficient % C_n: yawing moment coefficient % CN: normal force coefficient % CA: axial force coefficient %************************************************************************** %***** Computing Arrays *************************************************** % nod_o: original point c oordinate node (left side) % nod: point corrdinate at so me angle of attack (left side) % nodr_o: original point c oordinate node (right side) % nodr: point corrdinate at so me angle of attack (right side) % Pvec: P vector of each panel % Qvec: Q vector of each panel % Nvec: N vector of each panel % nunit: n (N unit) vector of each panel % Area: area of each panel (m2) % cp: local pressure coefficient of each panel % dF: differential force (p ressure force) acting on each panel % dL: differential lift force acting on each panel % dD: differential drag force acting on each panel % cent: panel center point (centroid) % radi: radius vector w.r.t. reference % d_l: differential rolling moment on each panel % d_m: differential rolling moment on each panel % d_n: differential rolling moment on each panel % Pvecr: P vector of each panel (right side) % Qvecr: Q vector of each panel (right side) % Nvecr: N vector of each panel (right side) % nunitr: n (N unit) vector of each panel (right side) % Arear: area of each panel (m2) (right side) % cpr: local pressure co efficient of each panel (right side) % dFr: differential force (pressure force) acting on each panel (right side) % dLr: differential lift fo rce acting on each panel (right side) % dDr: differential drag force acting on each panel (right side) % centr: panel center point (centroid) (right side) % radir: radius vector w.r.t. reference (right side) % d_lr: differential rolling moment on each panel (right side) % d_mr: differential rolling moment on each panel (right side)

PAGE 100

100 % d_nr: differential rolling moment on each panel (right side) %************************************************************************** % input data ro = 0.014283 % air density (kg/m3) Z=36000m or 31500m Pinf = 935.425354 % atmospheric pressuer (N/m2) Rair = 287 % gas constant of air (287J/kg-K) Tinf = 228.15 % free stream temperature (K) cpinf= 1006 % sp ecific heat constant pressure of free stream (J/kg-K) M = 6.00 % Mach number gamma = 1.4 % specific heat ratio ref = [9.0932 0 0] % reference point e. g. center of gravity % flow properties computaion a = (gamma*Rair*Tinf)^0.5 % speed of sound (m/s) Vinf = M*a % free stream velocity (m/s) qinf = 0.5*ro*Vinf^2 % dynamic pressure (N/m2) % flight condition (input) aoa = 6.0 % angle of attack (deg.) Sref = 57.20 % vehicle planform area (m2) chord = 14.7066 % chord length (m) b = 7.37616 % wing span (m) ep = (gamma-1)/(gamma+1) % dens ity ration across shock wave for hypersonic flow % reference point accounting angle of attack refa = [((ref(1,1)^2+ref(1,2)^2)^0.5)*cos( atan(ref(1,2)/ref(1,1))-aoa*3.14159265359/180) 0 ((ref(1,1)^2+ref(1,2)^2)^0.5)*sin(atan (ref(1,2)/ref(1,1))-aoa*3.14159265359/180)] % original point coordinate system left side nod_o =0.0254*[0 0 0; 41 0 -8.3; 41 2.0 -8.1; 41 5.0 -7.5; 41 7.5 -5.0; 41 9.0 -3.0; 41 10.3 0; 41 10.3 5.0; 41 8.5 8.0; 41 5.0 11.0; 41 1.0 12.3; 41 0.75 12.4; 41 0.50 12.4; 41 0.25 12.4; 41 0 12.4; 120 0 -12.4;

PAGE 101

101 120 5.0 -12.4; 120 15.5 -12.4; 120 25.0 -12.4; 120 27.9 -9.0; 120 27.9 0; 120 27.0 8.0; 120 23.0 18.0; 120 13.0 27.0; 120 2.0 29.0; 120 1.5 29.0; 120 1.0 29.0; 120 0.5 29.0; 120 0 29.0; 145 0 -13.7; 145 5.5 -13.7; 145 18.0 -13.7; 145 31.0 -13.7 145 34.1 -10.5; 145 34.1 0; 145 33.0 8.5; 145 29.0 19.0; 145 21.0 29.0; 145 12.0 34.0; 145 10.0 38.0; 145 8.0 42.0; 145 4.0 44.5; 145 0 45.5; 178 0 -15.4; 178 6.5 -15.4; 178 20.5 -15.4; 178 38.0 -15.4; 178 41.4 -12.0; 178 41.4 0; 178 40.0 9.5; 178 36.0 20.0; 178 29.0 31.0; 178 21.0 37.0; 178 17.0 43.5; 178 12.0 48.0; 178 6.0 49.5; 178 0 49.7; 215 0 -17.3; 215 7.5 -17.3 215 24.0 -17.3; 215 46.0 -17.3; 215 49.7 -14.0;

PAGE 102

102 215 49.7 0; 215 48.0 10.0; 215 45.0 22.0; 215 39.0 33.0; 215 32.0 42.0; 215 26.0 48.0; 215 18.0 51.0; 215 10.0 53.0; 215 0 54.0; 331 0 -23.3; 331 10.5 -23.3; 331 34.0 -23.3; 331 69.0 -23.3; 331 74.5 -19.0; 331 74.5 0; 331 73.0 12.0; 331 67.0 26.0; 331 59.0 37.5; 331 48.0 47.0; 331 37.0 52.0; 331 24.0 54.0; 331 11.0 54.0; 331 0 54.0; 385 0 -26.1; 385 12.0 -26.1; 385 39.0 -26.1; 385 86.9 -26.1; 385 86.9 -22.0; 385 86.9 0; 385 82.0 14.0; 385 76.0 27.0; 385 71.0 40.0; 385 66.0 54.0; 385 46.0 54.0; 385 24.0 54.0; 385 11.0 54.0; 385 0 54.0; 480 0 -31.0; 480 14.5 -31.0; 480 46.0 -31.0; 480 86.9 -31.0; 480 86.9 -28.0; 480 86.9 0; 480 82.0 14.0; 480 76.0 27.0; 480 71.0 40.0;

PAGE 103

103 480 66.0 54.0; 480 46.0 54.0; 480 24.0 54.0; 480 11.0 54.0; 480 0.0 54.0; 579 0 -4.1; 579 14.5 -4.1; 579 46.0 -4.1; 579 86.9 -4.1; 579 86.9 -2.0; 579 86.9 0; 579 82.0 14.0; 579 76.0 27.0; 579 71.0 40.0; 579 66.0 54.0; 579 46.0 54.0; 579 24.0 54.0; 579 11.0 54.0; 579 0 54.0; 478 0 54; 594 10.5 54; 548 0 108; 583 3.15 108; 507 62 54; 511.776418 64.631838 54; 516.584952 65.342358 54; 525.361858 65.720558 54; 537.945254 65.285752 54; 550.710744 64.241238 54; 569 62 54; 511.776418 59.368162 54; 516.584952 58.657642 54; 525.361858 58.279442 54; 537.945254 58.714248 54; 550.710744 59.758762 54; 542 89 84; 545.312677 90.825307 84; 548.647628 91.318087 84; 554.734837 91.580387 84; 563.462031 91.278828 84; 572.315516 90.554407 84; 585 89 84; 545.312677 87.174693 84; 548.647628 86.681913 84; 554.734837 86.419613 84; 563.462031 86.721172 84;

PAGE 104

104 572.315516 87.445593 84; 385 86.9 -25; 403.720477 86.9 -14.684893; 422.566828 86.9 -11.900113; 456.966637 86.9 -10.417813; 506.285431 86.9 -12.121972; 556.317916 86.9 -16.215793; 628 86.9 -25; 403.720477 86.9 -35.315107; 422.566828 86.9 -38.099887; 456.966637 86.9 -39.582187; 506.285431 86.9 -37.878028; 556.317916 86.9 -33.784207; 530 149 19; 537.935017 149 23.372247; 545.923388 149 24.552627; 560.504377 149 25.180927; 581.409051 149 24.458588; 602.616236 149 22.723347; 633 149 19; 537.935017 149 14.627753; 545.923388 149 13.447373; 560.504377 149 12.819073; 581.409051 149 13.541412; 602.616236 149 15.276653] num_nod = 178+1 %the number of nod num_panel = 142 for i=1:num_nod %To make y-component of each nod to the negative nod_o(i,2) = -1.0*nod_o(i,2) end % point corrdinate at some angl e of attack left & right side nod(1,1)=0; nod(1,2)=0; nod(1,3)=0 for i = 2:num_nod nod(i,1) = ((nod_o(i,1)^2+nod_o(i,3)^2 )^0.5)*cos(atan(no d_o(i,3)/nod_o(i,1))aoa*3.14159265359/180) nod(i,2) = nod_o(i,2) nod(i,3) = ((nod_o(i,1)^2+nod_o(i,3)^2 )^0.5)*sin(atan(nod_ o(i,3)/nod_o(i,1))aoa*3.14159265359/180) end % Pvec: P vector of each panel % Pvec of body panels (panel 1-117)

PAGE 105

105 for i = 1:13 Pvec(i,1)=nod(i+1,1)-nod(1,1); Pvec(i,2)=nod (i+1,2)-nod(1,2); Pvec(i ,3)=nod(i+1,3)-nod(1,3) end for i = 14:26 Pvec(i,1)=nod(i+2,1)-nod(i-11,1); Pvec(i,2) =nod(i+2,2)-nod(i-11,2); Pvec(i,3)=nod(i+2,3)nod(i-11,3) end for i = 27:39 Pvec(i,1)=nod(i+3,1)-nod(i-10,1); Pvec(i,2) =nod(i+3,2)-nod(i-10,2); Pvec(i,3)=nod(i+3,3)nod(i-10,3) end for i = 40:52 Pvec(i,1)=nod(i+4,1)-nod(i9,1); Pvec(i,2)=nod(i+4,2)-nod(i9,2); Pvec(i,3)=nod(i+4,3)-nod(i9,3) end for i = 53:65 Pvec(i,1)=nod(i+5,1)-nod(i8,1); Pvec(i,2)=nod(i+5,2)-nod(i8,2); Pvec(i,3)=nod(i+5,3)-nod(i8,3) end for i = 66:78 Pvec(i,1)=nod(i+6,1)-nod(i7,1); Pvec(i,2)=nod(i+6,2)-nod(i7,2); Pvec(i,3)=nod(i+6,3)-nod(i7,3) end for i = 79:91 Pvec(i,1)=nod(i+7,1)-nod(i6,1); Pvec(i,2)=nod(i+7,2)-nod(i6,2); Pvec(i,3)=nod(i+7,3)-nod(i6,3) end for i = 92:104 Pvec(i,1)=nod(i+8,1)-nod(i5,1); Pvec(i,2)=nod(i+8,2)-nod(i5,2); Pvec(i,3)=nod(i+8,3)-nod(i5,3) end for i = 105:117 Pvec(i,1)=nod(i+9,1)-nod(i4,1); Pvec(i,2)=nod(i+9,2)-nod(i4,2); Pvec(i,3)=nod(i+9,3)-nod(i4,3) end %Pvec center fin panels(panel 118) Pvec(118,1)=nod(129,1)-nod(130,1); Pvec(118,2)=nod(129,2)-nod(130,2); Pvec(118,3)=nod(129,3)-nod(130,3) %Pvec off center fin panels(panel 119-130) Pvec(119,1)=nod(145,1)-nod(132,1); Pvec(119,2)=nod(145,2)-nod(132,2); Pvec(119,3)=nod(145,3)-nod(132,3) for i= 120:123 Pvec(i,1)=nod(i+26,1)-nod(i+13,1 ); Pvec(i,2)=nod(i+26,2)-nod(i+13,2); Pvec(i,3)=nod(i+26,3)-nod(i+13,3) end

PAGE 106

106 Pvec(124,1)=nod(150,1)-nod(137,1); Pvec(124,2)=nod(150,2)-nod(137,2); Pvec(124,3)=nod(150,3)-nod(137,3) Pvec(125,1)=nod(144,1)-nod(139,1); Pvec(125,2)=nod(144,2)-nod(139,2); Pvec(125,3)=nod(144,3)-nod(139,3) for i= 126:129 Pvec(i,1)=nod(i+25,1)-nod(i+14,1 ); Pvec(i,2)=nod(i+25,2)-nod(i+14,2); Pvec(i,3)=nod(i+25,3)-nod(i+14,3) end Pvec(130,1)=nod(155,1)-nod(138,1); Pv ec(130,2)=nod(155,2)-nod(138,2); Pvec(130,3)=nod(155,3)-nod(138,3) %Pvec wing panels(panel 131-142) Pvec(131,1)=nod(168,1)-nod(157,1); Pvec(131,2)=nod(168,2)-nod(157,2); Pvec(131,3)=nod(168,3)-nod(157,3) for i= 132:135 Pvec(i,1)=nod(i+37,1)-nod(i+26,1 ); Pvec(i,2)=nod(i+37,2)-nod(i+26,2); Pvec(i,3)=nod(i+37,3)-nod(i+26,3) end Pvec(136,1)=nod(173,1)-nod(162,1); Pvec(136,2)=nod(173,2)-nod(162,2); Pvec(136,3)=nod(173,3)-nod(162,3) Pvec(137,1)=nod(175,1)-nod(156,1); Pvec(137,2)=nod(175,2)-nod(156,2); Pvec(137,3)=nod(175,3)-nod(156,3) for i= 138:141 Pvec(i,1)=nod(i+38,1)-nod(i+25,1 ); Pvec(i,2)=nod(i+38,2)-nod(i+25,2); Pvec(i,3)=nod(i+38,3)-nod(i+25,3) end Pvec(142,1)=nod(174,1)-nod(167,1); Pv ec(142,2)=nod(174,2)-nod(167,2); Pvec(142,3)=nod(174,3)-nod(167,3) % Qvec of body panels (panel 1-117) for i = 1:13 Qvec(i,1)=nod(i+2,1)-nod(1,1); Qvec(i,2) =nod(i+2,2)-nod(1,2); Qvec(i,3)=nod(i+2,3)nod(1,3) end for i = 14:26 Qvec(i,1)=nod(i+3,1)-nod(i-12,1); Qvec(i, 2)=nod(i+3,2)-nod(i-12,2); Qvec(i,3)=nod(i+3,3)nod(i-12,3) end for i = 27:39 Qvec(i,1)=nod(i+4,1)-nod(i-11,1); Qvec(i, 2)=nod(i+4,2)-nod(i-11,2); Qvec(i,3)=nod(i+4,3)nod(i-11,3) end for i = 40:52 Qvec(i,1)=nod(i+5,1)-nod(i-10,1); Qvec(i, 2)=nod(i+5,2)-nod(i-10,2); Qvec(i,3)=nod(i+5,3)nod(i-10,3) end for i = 53:65

PAGE 107

107 Qvec(i,1)=nod(i+6,1)-nod( i-9,1); Qvec(i,2)=nod(i+6,2)-nod(i -9,2); Qvec(i,3)=nod(i+6,3)nod(i-9,3) end for i = 66:78 Qvec(i,1)=nod(i+7,1)-nod( i-8,1); Qvec(i,2)=nod(i+7,2)-nod(i -8,2); Qvec(i,3)=nod(i+7,3)nod(i-8,3) end for i = 79:91 Qvec(i,1)=nod(i+8,1)-nod( i-7,1); Qvec(i,2)=nod(i+8,2)-nod(i -7,2); Qvec(i,3)=nod(i+8,3)nod(i-7,3) end for i = 92:104 Qvec(i,1)=nod(i+9,1)-nod( i-6,1); Qvec(i,2)=nod(i+9,2)-nod(i -6,2); Qvec(i,3)=nod(i+9,3)nod(i-6,3) end for i = 105:117 Qvec(i,1)=nod(i+10,1)-nod(i-5,1); Qvec(i,2) =nod(i+10,2)-nod(i-5,2); Qvec(i,3)=nod(i+10,3)nod(i-5,3) end %Qvec center fin panels(panel 118) Qvec(118,1)=nod(131,1)-nod(128,1); Qv ec(118,2)=nod(131,2)-nod(128,2); Qvec(118,3)=nod(131,3)-nod(128,3) %Pvec off center fin panels(panel 119-130) Qvec(119,1)=nod(144,1)-nod(133,1); Qv ec(119,2)=nod(144,2)-nod(133,2); Qvec(119,3)=nod(144,3)-nod(133,3) for i= 120:123 Qvec(i,1)=nod(i+25,1)-nod(i+14,1 ); Qvec(i,2)=nod(i+25,2)-nod(i+14,2); Qvec(i,3)=nod(i+25,3)-nod(i+14,3) end Qvec(124,1)=nod(149,1)-nod(138,1); Qv ec(124,2)=nod(149,2)-nod(138,2); Qvec(124,3)=nod(149,3)-nod(138,3) Qvec(125,1)=nod(151,1)-nod(132,1); Qv ec(125,2)=nod(151,2)-nod(132,2); Qvec(125,3)=nod(151,3)-nod(132,3) for i= 126:129 Qvec(i,1)=nod(i+26,1)-nod(i+13,1 ); Qvec(i,2)=nod(i+26,2)-nod(i+13,2); Qvec(i,3)=nod(i+26,3)-nod(i+13,3) end Qvec(130,1)=nod(150,1)-nod(143,1); Qv ec(130,2)=nod(150,2)-nod(143,2); Qvec(130,3)=nod(150,3)-nod(143,3) %Pvec wing panels(panel 131-142) Qvec(131,1)=nod(169,1)-nod(156,1); Qv ec(131,2)=nod(169,2)-nod(156,2); Qvec(131,3)=nod(169,3)-nod(156,3) for i= 132:135

PAGE 108

108 Qvec(i,1)=nod(i+38,1)-nod(i+25,1 ); Qvec(i,2)=nod(i+38,2)-nod(i+25,2); Qvec(i,3)=nod(i+38,3)-nod(i+25,3) end Qvec(136,1)=nod(174,1)-nod(161,1); Qv ec(136,2)=nod(174,2)-nod(161,2); Qvec(136,3)=nod(174,3)-nod(161,3) Qvec(137,1)=nod(168,1)-nod(163,1); Qv ec(137,2)=nod(168,2)-nod(163,2); Qvec(137,3)=nod(168,3)-nod(163,3) for i= 138:141 Qvec(i,1)=nod(i+37,1)-nod(i+26,1 ); Qvec(i,2)=nod(i+37,2)-nod(i+26,2); Qvec(i,3)=nod(i+37,3)-nod(i+26,3) end Qvec(142,1)=nod(179,1)-nod(162,1); Qv ec(142,2)=nod(179,2)-nod(162,2); Qvec(142,3)=nod(179,3)-nod(162,3) % Nvec: N vector of each panel for i=1: num_panel Nvec(i,1) = Pvec(i,2)*Q vec(i,3)-Pvec(i,3)*Qvec(i,2) Nvec(i,2) = Pvec(i,3)*Q vec(i,1)-Pvec(i,1)*Qvec(i,3) Nvec(i,3) = Pvec(i,1)*Q vec(i,2)-Pvec(i,2)*Qvec(i,1) end % nunit: n (N unit) vector of each panel for i=1:num_panel nunit(i,1)=Nvec(i,1)/(Nvec(i ,1)^2+Nvec(i,2)^2+Nvec(i,3)^2)^0.5 nunit(i,2)=Nvec(i,2)/(Nvec(i ,1)^2+Nvec(i,2)^2+Nvec(i,3)^2)^0.5 nunit(i,3)=Nvec(i,3)/(Nvec(i ,1)^2+Nvec(i,2)^2+Nvec(i,3)^2)^0.5 end % Area: area of each panel (m2) for i=1:num_panel Area(i,1) = 0.5*(Nvec(i,1)^2 +Nvec(i,2)^2+Nvec(i,3)^2)^0.5 end % cp: local pressure coefficient of each panel for i=1:num_panel if nunit(i,1)<0 cp(i,1) = (2.0-0.0)*nunit(i,1)^2 else cp(i,1) = 0 end end % dF: differential force (p ressure force) acting on each panel for i=1:num_panel

PAGE 109

109 dF(i,1) = -cp(i,1) *qinf*Area(i,1)*nunit(i,1) dF(i,2) = -cp(i,1) *qinf*Area(i,1)*nunit(i,2) dF(i,3) = -cp(i,1) *qinf*Area(i,1)*nunit(i,3) end % dL: differential lift force acting on each panel % dD: differential drag force acting on each panel % dLr: differential lift for ce acting on each panel (right side) % dDr: differential drag force acting on each panel (right side) for i=1:num_panel dL(i,1) = dF(i,3) dD(i,1) = dF(i,1) end % cent: panel center point (centroid) % centr: panel center poin t (centroid) (right side) for i= 1:13 cent(i,1)=(nod(i+1,1)+nod(i+2,1)) /3; cent(i,2)=(nod(i+1,2)+nod(i+2,2))/3; cent(i,3)=(nod(i+1,3)+nod(i+2,3))/3 end for i= 14:26 cent(i,1)=(nod(i+2,1)+nod( i+3,1)+nod(i-12,1)+nod(i-11,1))/4 cent(i,2)=(nod(i+2,2)+nod( i+3,2)+nod(i-12,2)+nod(i-11,2))/4 cent(i,3)=(nod(i+2,3)+nod( i+3,3)+nod(i-12,3)+nod(i-11,3))/4 end for i= 27:39 cent(i,1)=(nod(i+3,1)+nod( i+4,1)+nod(i-11,1)+nod(i-10,1))/4 cent(i,2)=(nod(i+3,2)+nod( i+4,2)+nod(i-11,2)+nod(i-10,2))/4 cent(i,3)=(nod(i+3,3)+nod( i+4,3)+nod(i-11,3)+nod(i-10,3))/4 end for i= 40:52 cent(i,1)=(nod(i+4,1)+nod( i+5,1)+nod(i-10,1)+nod(i-9,1))/4 cent(i,2)=(nod(i+4,2)+nod( i+5,2)+nod(i-10,2)+nod(i-9,2))/4 cent(i,3)=(nod(i+4,3)+nod( i+5,3)+nod(i-10,3)+nod(i-9,3))/4 end for i= 53:65 cent(i,1)=(nod(i+5,1)+nod( i+6,1)+nod(i-9,1)+nod(i-8,1))/4 cent(i,2)=(nod(i+5,2)+nod( i+6,2)+nod(i-9,2)+nod(i-8,2))/4 cent(i,3)=(nod(i+5,3)+nod( i+6,3)+nod(i-9,3)+nod(i-8,3))/4 end for i= 66:78 cent(i,1)=(nod(i+6,1)+nod( i+7,1)+nod(i-8,1)+nod(i-7,1))/4 cent(i,2)=(nod(i+6,2)+nod( i+7,2)+nod(i-8,2)+nod(i-7,2))/4 cent(i,3)=(nod(i+6,3)+nod( i+7,3)+nod(i-8,3)+nod(i-7,3))/4 end

PAGE 110

110 for i= 79:91 cent(i,1)=(nod(i+7,1)+nod( i+8,1)+nod(i-7,1)+nod(i-6,1))/4 cent(i,2)=(nod(i+7,2)+nod( i+8,2)+nod(i-7,2)+nod(i-6,2))/4 cent(i,3)=(nod(i+7,3)+nod( i+8,3)+nod(i-7,3)+nod(i-6,3))/4 end for i= 92:104 cent(i,1)=(nod(i+8,1)+nod( i+9,1)+nod(i-6,1)+nod(i-5,1))/4 cent(i,2)=(nod(i+8,2)+nod( i+9,2)+nod(i-6,2)+nod(i-5,2))/4 cent(i,3)=(nod(i+8,3)+nod( i+9,3)+nod(i-6,3)+nod(i-5,3))/4 end for i= 105:117 cent(i,1)=(nod(i+9,1)+nod( i+10,1)+nod(i-5,1)+nod(i-4,1))/4 cent(i,2)=(nod(i+9,2)+nod( i+10,2)+nod(i-5,2)+nod(i-4,2))/4 cent(i,3)=(nod(i+9,3)+nod( i+10,3)+nod(i-5,3)+nod(i-4,3))/4 end %cent center fin panels(panel 118) for j=1:3 cent(118,j)=(nod(128,j) +nod(129,j)+nod(130,j)+nod(131,j))/4 end %cent off center fin panels(panel 119-130) cent(119,1)=(nod(132,1)+nod( 133,1)+nod(144,1)+nod(145,1))/4 cent(119,2)=(nod(132,2)+nod( 133,2)+nod(144,2)+nod(145,2))/4 cent(119,3)=(nod(132,3)+nod( 133,3)+nod(144,3)+nod(145,3))/4 for i= 120:123 cent(i,1)=(nod(i+13,1)+nod( i+14,1)+nod(i+25,1)+nod(i+26,1))/4 cent(i,2)=(nod(i+13,2)+nod( i+14,2)+nod(i+25,2)+nod(i+26,2))/4 cent(i,3)=(nod(i+13,3)+nod( i+14,3)+nod(i+25,3)+nod(i+26,3))/4 end cent(124,1)=(nod(137,1)+nod( 138,1)+nod(149,1)+nod(150,1))/4 cent(124,2)=(nod(137,2)+nod( 138,2)+nod(149,2)+nod(150,2))/4 cent(124,3)=(nod(137,3)+nod( 138,3)+nod(149,3)+nod(150,3))/4 cent(125,1)=(nod(132,1)+nod( 139,1)+nod(144,1)+nod(151,1))/4 cent(125,2)=(nod(132,2)+nod( 139,2)+nod(144,2)+nod(151,2))/4 cent(125,3)=(nod(132,3)+nod( 139,3)+nod(144,3)+nod(151,3))/4 for i= 126:129 cent(i,1)=(nod(i+25,1)+nod( i+26,1)+nod(i+13,1)+nod(i+14,1))/4 cent(i,2)=(nod(i+25,2)+nod( i+26,2)+nod(i+13,2)+nod(i+14,2))/4 cent(i,3)=(nod(i+25,3)+nod( i+26,3)+nod(i+13,3)+nod(i+14,3))/4 end cent(130,1)=(nod(143,1)+nod( 138,1)+nod(155,1)+nod(150,1))/4 cent(130,2)=(nod(143,2)+nod( 138,2)+nod(155,2)+nod(150,2))/4 cent(130,3)=(nod(143,3)+nod( 138,3)+nod(155,3)+nod(150,3))/4 %cent wing panels(panel 131-142) cent(131,1)=(nod(156,1)+nod( 157,1)+nod(168,1)+nod(169,1))/4 cent(131,2)=(nod(156,2)+nod( 157,2)+nod(168,2)+nod(169,2))/4

PAGE 111

111 cent(131,3)=(nod(156,3)+nod( 157,3)+nod(168,3)+nod(169,3))/4 for i= 132:135 cent(i,1)=(nod(i+25,1)+nod( i+26,1)+nod(i+37,1)+nod(i+38,1))/4 cent(i,2)=(nod(i+25,2)+nod( i+26,2)+nod(i+37,2)+nod(i+38,2))/4 cent(i,3)=(nod(i+25,3)+nod( i+26,3)+nod(i+37,3)+nod(i+38,3))/4 end cent(136,1)=(nod(173,1)+nod( 174,1)+nod(161,1)+nod(162,1))/4 cent(136,2)=(nod(173,2)+nod( 174,2)+nod(161,2)+nod(162,2))/4 cent(136,3)=(nod(173,3)+nod( 174,3)+nod(161,3)+nod(162,3))/4 cent(137,1)=(nod(156,1)+nod( 163,1)+nod(168,1)+nod(169,1))/4 cent(137,2)=(nod(156,2)+nod( 163,2)+nod(168,2)+nod(169,2))/4 cent(137,3)=(nod(156,3)+nod( 163,3)+nod(168,3)+nod(169,3))/4 for i= 138:141 cent(i,1)=(nod(i+25,1)+nod( i+26,1)+nod(i+37,1)+nod(i+38,1))/4 cent(i,2)=(nod(i+25,2)+nod( i+26,2)+nod(i+37,2)+nod(i+38,2))/4 cent(i,3)=(nod(i+25,3)+nod( i+26,3)+nod(i+37,3)+nod(i+38,3))/4 end cent(142,1)=(nod(167,1)+nod( 162,1)+nod(179,1)+nod(174,1))/4 cent(142,2)=(nod(167,2)+nod( 162,2)+nod(179,2)+nod(174,2))/4 cent(142,3)=(nod(167,3)+nod( 162,3)+nod(179,3)+nod(174,3))/4 %Arc length (only body) arc =0 arc(1,1)=-cent(1,2) for i= 2:13 arc(i,1)=arc(i-1)+((cent(i,2)-cen t(i-1,2))^2+(cent(i,3)-cent(i-1,3))^2)^0.5 end totalarc1=arc(13,1)-cent(13,2) arc(14,1)=-cent(14,2) for i= 15:26 arc(i,1)=arc(i-1)+((cent(i,2)-cen t(i-1,2))^2+(cent(i,3)-cent(i-1,3))^2)^0.5 end totalarc2=arc(26,1)-cent(26,2) arc(27,1)=-cent(27,2) for i= 28:39 arc(i,1)=arc(i-1)+((cent(i,2)-cen t(i-1,2))^2+(cent(i,3)-cent(i-1,3))^2)^0.5 end totalarc3=arc(39,1)-cent(39,2) arc(40,1)=-cent(40,2) for i= 41:52 arc(i,1)=arc(i-1)+((cent(i,2)-cen t(i-1,2))^2+(cent(i,3)-cent(i-1,3))^2)^0.5 end totalarc4=arc(52,1)-cent(52,2) arc(53,1)=-cent(53,2) for i= 54:65 arc(i,1)=arc(i-1)+((cent(i,2)-cen t(i-1,2))^2+(cent(i,3)-cent(i-1,3))^2)^0.5

PAGE 112

112 end totalarc5=arc(65,1)-cent(65,2) arc(66,1)=-cent(66,2) for i= 67:78 arc(i,1)=arc(i-1)+((cent(i,2)-cen t(i-1,2))^2+(cent(i,3)-cent(i-1,3))^2)^0.5 end totalarc6=arc(78,1)-cent(78,2) arc(79,1)=-cent(79,2) for i= 80:91 arc(i,1)=arc(i-1)+((cent(i,2)-cen t(i-1,2))^2+(cent(i,3)-cent(i-1,3))^2)^0.5 end totalarc7=arc(91,1)-cent(91,2) arc(92,1)=-cent(92,2) for i= 93:104 arc(i,1)=arc(i-1)+((cent(i,2)-cen t(i-1,2))^2+(cent(i,3)-cent(i-1,3))^2)^0.5 end totalarc8=arc(104,1)-cent(104,2) arc(105,1)=-cent(105,2) for i= 106:117 arc(i,1)=arc(i-1)+((cent(i,2)-cen t(i-1,2))^2+(cent(i,3)-cent(i-1,3))^2)^0.5 end totalarc9=arc(117,1)-cent(117,2) % radi: radius vector w.r.t. reference for i=1:num_panel radi(i,1) = (cent(i,1)*cos(a oa*3.14159265359/180)-cent(i,3) *sin(aoa*3.14159265359/180))ref(1,1) radi(i,2) = cent(i,2)-ref(1,2) radi(i,3) = (cent(i,3)*cos(a oa*3.14159265359/180)+cent(i,1)*sin(aoa*3.14159265359/180))ref(1,3) end for i=1:num_panel d_m(i,1) = (radi(i,1)*(dF(i,3) *cos(aoa*3.14159265359/180)+dF(i ,1)*sin(aoa*3.14159265359/180))radi(i,3)*(dF(i,1)*cos(aoa*3.14159265359/ 180)-dF(i,3)*sin(aoa*3.14159265359/180))) end pitching = sum(d_m)*2 C_m = pitching/qinf/Sref/chord %****** Viscous consideration ******************************************* %From here viscous effect is accounted into flow field %In order to find the skin friction an d heat transfer, local Reynolds' %analogy is used. (Approximate analysis) %u_e : tangential component of velocity on each panel (m/s) %u_er : tangential component of ve locity on each panel (m/s) right side

PAGE 113

113 %u_eunit : unit vector of tangential co mponent of velocity on each panel %u_eunitr: unit vector of tangential component of velocity on each panel right side %PMang : Prandtl-Meyer expansion angle (rad) %psi : deflection angle (rad) %h_e : enthalpy at edge of boundary layer (this is h_known in % thermodynamic property code (ThermPropAir.m) % unit: J/kg, change unit to J/g so that h_e can be used in % ThermPropAir.m %h_er : enthalpy at edge of boundary layer right side %s : the distan ce along the surface of th e vehicle measured from % relevant stagnationpoint for body (panel 1 40 & 75) % for wing section 1 (panel 43 53) % for wing section 2 (panel 54 64) % for wing section 2 (panel 65 74) % for rudder (panel 41 & 42) %l_s :the distance between two centroids %sr : the distance along the su rface of the vehicl e measured from % relevant stagnationpoi nt for right body (panel 1 40 & 75) % for right wing section 1 (panel 43 53) % for right wing section 2 (panel 54 64) % for right wing section 2 (panel 65 74) % for right rudder (panel 41 & 42) %l_s r :the distance between two centroids for right side %************************************************************************** %tangential component of velocity on each panel for i=1:num_panel u_e(i,1) = Vinf (Vinf*nunit(i,1))*nunit(i,1) u_e(i,2) = 0 (Vinf*nunit(i,1))*nunit(i,2) u_e(i,3) = 0 (Vinf*nunit(i,1))*nunit(i,3) end u_e(num_panel+1,1)=Vinf; u_e(num_pane l+1,2)=0; u_e(num_panel+1,3)=0 for i=1:num_panel+1 %u_eunit : unit vector of tangential component of velocity on each panel u_eunit(i,1) = u_e(i,1) /(u_e(i,1)^2+u_e(i,2 )^2+u_e(i,3)^2)^0.5 u_eunit(i,2) = u_e(i,2) /(u_e(i,1)^2+u_e(i,2 )^2+u_e(i,3)^2)^0.5 u_eunit(i,3) = u_e(i,3)/(u_e(i ,1)^2+u_e(i,2)^2+u_e(i,3 )^2)^0.5 end %enthalpy at edge of boundary layer %computed by using energy equation h_inf = Tinf*1006 %cp = 1006 J/kg-K at T = 250K for i=1:num_panel h_e(i,1) = 0.5*Vinf^2 + h_inf 0.5*(u_e(i,1)^ 2+u_e(i,2)^2+u_e(i,3)^2) %unit: J/kg or m2/s2 end

PAGE 114

114 %s : the distance along the su rface of the vehicle measured from % relevant stagnationpoint for body (panel 1 40 & 75) % for wing section 1 (panel 43 53) % for wing section 2 (panel 54 64) % for wing section 2 (panel 65 74) % for rudder (panel 41 & 42) %l_s : the distance between two centroids nose_vector = -1.0*cos(aoa*3.14159265359/180) for i=1:117 for j=i:117 l_s(i,j)=((cent(i,1)-cent(j,1))^2 + (cent( i,2)-cent(j,2))^2 + (cent( i,3)-cent(j,3))^2)^0.5 end end for i=119:130 for j=i:130 l_s(i,j)=((cent(i,1)-cent(j,1))^2 + (cent( i,2)-cent(j,2))^2 + (cent( i,3)-cent(j,3))^2)^0.5 end end for i=131:142 for j=i:142 l_s(i,j)=((cent(i,1)-cent(j,1))^2 + (cent( i,2)-cent(j,2))^2 + (cent( i,3)-cent(j,3))^2)^0.5 end end % for body (panel 1 117) for i= 1:13 s(i,1) = (cent(i,1)^2 +cent(i,2)^2+cent(i ,3)^2)^0.5 0.205 + 0.10110667 end for i= 14:117 s(i,1) = s(i-13,1) + l_s(i-13,i) end s(118,1) = ((cent(118,1)-(nod( 128,1)+nod(130,1))/2)^2+(cent(118,3)(nod(128,3)+nod(130,3))/2)^2)^0.5 s(119,1) = ((cent(119,1)-(nod( 132,1)+nod(144,1))/2)^2+(cent(119,3)(nod(132,3)+nod(144,3))/2)^2)^0.5 s(125,1) = ((cent(125,1)-(nod( 132,1)+nod(144,1))/2)^2+(cent(125,3)(nod(132,3)+nod(144,3))/2)^2)^0.5 for i= 120:124 s(i,1) = s(i-1,1) + l_s(i-1,i) end for i= 126:130 s(i,1) = s(i-1,1) + l_s(i-1,i) end

PAGE 115

115 s(131,1) = ((cent(131,1)-(nod( 156,1)+nod(168,1))/2)^2+(cent(131,3)(nod(156,3)+nod(168,3))/2)^2)^0.5 s(137,1) = ((cent(137,1)-(nod( 156,1)+nod(168,1))/2)^2+(cent(137,3)(nod(156,3)+nod(168,3))/2)^2)^0.5 for i= 132:136 s(i,1) = s(i-1,1) + l_s(i-1,i) end for i= 138:142 s(i,1) = s(i-1,1) + l_s(i-1,i) end s(num_panel+1,1)=0 %***** Thermodynamic properties ********************************************** %Now u_e, h_e, and s are known. %Pin = input P (atm) %h_known = input h (J/g or kJ/kg) %T_out = input T (K) %********************************************** %T_e is found by temperature (Pin, h_known) %ro is found by density (Pin, Tout) %mu is found by viscosity (Pin, Tout) %Pr is found by pr andtl (Pin, Tout) %************************************************************************** %***** Reynolds number and skin friction ************************************************ %The flat plate reference enthalpy me thod is used in each panel, using %Reynonds' analogy with heat transfer to calculate slin friction for both %laminar and turbulent cases % %Res : Reynolds number based on the local tangential velocity (u_e), % temperature (T_e), and distance (s) from the stagnation point %Res = ro_e u_e s / mu_e % %cf : local skin friction coefficient %cf = 2AA/(Pr_e^(1/3)) (ro_ref/ro_e )^sa (mu_ref/mu_e)^sb Res^(sc-1) (3^sj)^0.5 %AA = 0.332*Pr^(1/3) -------------laminar % 0.0296*Pr^(1/3) -------------turbulent %sa = 0.5 ------------------------laminar % 0.8 -----------------------turbulent %sb = 0.5 ------------------------laminar % 0.2 -----------------------turbulent %sc = 0.5 ------------------------laminar % 0.8 -----------------------turbulent %sj = 0 ------------------------f lat plate % 1 ------------------------ax isymmetric

PAGE 116

116 % %Pin : the pressure computed by invisc id analysis for each panel (input for function) %h_known : enthalpy at edge of boundary layer for each panel (input for function) %Tout : temperature at edge of bounda ry layer for each panel (input for function) %h_e : enthalpy at edge of boundary layer for each panel %T_e : temperature at edge of boundary layer for each panel %ro_e : air density at edge of boundary layer for each panel %mu_e : viscosity at edge of boundary layer for each panel %Pr_e : Prandtl Number at edge of boundary layer for each panel %h_ref : enthalpy at edge of boundary layer for each panel %T_ref : reference temperature at edge of boundary layer for each panel %ro_ref : reference air density at edge of boundary layer for each panel %mu_ref : reference viscosity at edge of boundary layer for each panel %Pr_ref : reference Prandtl Number at edge of boundary layer for each panel %h_w : enthalpy at wall %h_aw : adiabatic wall enthalpy %************************************************************************** %****** Flow Properties (again) ******************************************* % ro: air density (kg/m3) % Pinf: atmospheric pressuer (N/m2) % Rair: gas constant of air (287J/kg-K) % Tinf: free stream temperature (K) % cpinf: specific heat constant pressu re of free stream (J/g-K or kJ/kg-K) % M: Mach number % gamma: specific heat ratio % Vinf: free stream velocity (m/s) % a: speed of sound (m/s) % qinf: dynamic pressure (kN/m2) %************************************************************************** % Reynolds Number and skin friction for left side T_e(num_panel+1,1)=Tinf P_e(num_panel+1,1)=Pinf/101325 cp(num_panel+1,1)=0.0 for i=1:num_panel+1 Pin = (cp(i,1)*qinf + Pinf)/101325 % must be in unit of atm P_e(i,1) = Pin h_known = (0.5*Vinf^2 + Tinf*cpinf 0.5*(u_ e(i,1)^2+u_e(i,2)^2+u_e (i,3)^2))/1000 %unit of J/g h_e(i,1) = h_known Tout = temperature (Pin, h_known) if i == num_panel+1

PAGE 117

117 Tout=Tinf end T_e(i,1) = Tout ro_out = density (Pin, Tout) ro_e(i,1) = ro_out mu_out = viscosity (Pin, Tout) mu_e(i,1) = mu_out Pr_out = prandtl (Pin, Tout) Pr_e(i,1)= Pr_out end %tangential component of velocity on "shadow" panel is found by P-M expansion for i= 1:13 jj(i,1) = num_panel+1 end for i= 14:117 jj(i,1) = i-13 end jj(118,1) = 104 jj(119,1) = num_panel+1 jj(125,1) = num_panel+1 for i= 120:124 jj(i,1) = i-1 end for i= 126:130 jj(i,1) = i-1 end jj(131,1) = num_panel+1 jj(137,1) = num_panel+1 for i= 132:136 jj(i,1) = i-1 end for i= 138:142 jj(i,1) = i-1 end for i = 1:num_panel if nunit(i,1) > 0 j=jj(i,1) M1 = ((u_e(j,1)^2+u_e(j,2)^2+u_e(j ,3)^2)/(gamma*Rair*T_e(j,1)))^0.5 %M of j panel if M1<1

PAGE 118

118 M2 =M1 else M2 = shadowM (i,jj,u_euni t, T_e, u_e, gamma, ep, Rair) %M of i panel T_e(i,1) =T_e(j,1)*(1 +((gamma-1)*M1^2)/2)/(1+((gamma-1)*M2^2)/2) P_e(i,1) =P_e(j,1 )*(T_e(i,1)/T_e(j,1))^(gamma/(gamma-1)) ro_e(i,1) = ro_e (j,1)*(T_e(j,1)/T_e(i,1))^(1/(gamma-1)) Pin = P_e(i,1); Tout=T_e(i,1) h_e(i,1) =enthalpy (Pin, Tout) u_e(i,1) = (M 2*(gamma*T_e(i,1)*Rair)^0.5)*u_eunit(i,1) u_e(i,2) = (M 2*(gamma*T_e(i,1)*Rair)^0.5)*u_eunit(i,2) u_e(i,3) = (M 2*(gamma*T_e(i,1)*Rair)^0.5)*u_eunit(i,3) end end end for i=1:num_panel dF(i,1) = -P_e(i,1 )*101325*Area(i,1)*nunit(i,1) dF(i,2) = -P_e(i,1 )*101325*Area(i,1)*nunit(i,2) dF(i,3) = -P_e(i,1 )*101325*Area(i,1)*nunit(i,3) end for i=1:num_panel dL(i,1) = dF(i,3) dD(i,1) = dF(i,1) end % Lift: lift (N) % Drag: drag (N) % L_D: L/D ratio Lift_inv = sum(dL)*2 Drag_inv = sum(dD)*2 L_D_inv = Lift_inv/Drag_inv %inviscid CLinv = Lift_inv/qinf/Sref CDinv = Drag_inv/qinf/Sref CNinv = CLinv*cos(aoa*3.14159265359/ 180)+CDinv*sin(aoa*3.14159265359/180) CAinv = CDinv*cos(aoa*3.14159265359/180)-CLinv*sin(aoa*3.14159265359/180) for i=1:num_panel d_m(i,1) = (radi(i,1)*(dF(i,3) *cos(aoa*3.14159265359/180)+dF(i ,1)*sin(aoa*3.14159265359/180))radi(i,3)*(dF(i,1)*cos(aoa*3.14159265359/ 180)-dF(i,3)*sin(aoa*3.14159265359/180))) end pitching = sum(d_m)*2 C_minv = pitching/qinf/Sref/chord for i=1:num_panel+1 if s(i,1) == 0

PAGE 119

119 s(i,1) = 0.000001 %zero Reynolds Number provides NaN heat transfer, so s is set to very small number like 0.000001 end Res(i,1) = ro_e(i,1)*((u_e(i,1)^2+u_e(i ,2)^2+u_e(i,3)^2)^0.5)*s(i,1 )/mu_e(i,1) % Reynolds Number based on s end %to make jj array has the same index jj(num_panel+1) = 0 % local skin friction for i=1:num_panel+1 %h_w : enthalpy at wall %h_aw : adiabatic wall enthalpy %h_ref : reference enthalpy h_aw(i,1) = h_e(i,1) + (Pr_e(i,1) ^0.5)*0.5*(u_e(i,1)^2+u_e(i ,2)^2+u_e(i,3)^2)/1000 h_awtub(i,1) = h_e(i,1) + (Pr_e(i,1)^( 1/3))*0.5*(u_e(i,1)^2+u_e (i,2)^2+u_e(i,3)^2)/1000 % here, wall temperature is set to adiabatic wall temperature. h_w can % be also set to the cold case (0 K) h_w(i,1) = 319.5 %h_aw(i,1) (Tw = 314.5K) h_ref(i,1) = 0.28*h_e(i,1) + 0.5*h_w(i,1) + 0.22*h_aw(i,1) h_reftub(i,1) = 0.28*h_e(i ,1) + 0.5*h_w(i,1) + 0.22*h_awtub(i,1) %T_ref : reference temperature at edge of boundary layer for each panel %ro_ref : reference air density at edge of boundary layer for each panel %mu_ref : reference viscosity at edge of boundary layer for each panel %Pr_ref : reference Prandtl Number at edge of boundary layer for each panel Pin = P_e(i,1) %Laminar h_known = h_ref(i,1) Tout = temperature (Pin, h_known) T_ref(i,1) = Tout ro_out = density (Pin, Tout) ro_ref(i,1) = ro_out mu_out = viscosity (Pin, Tout) mu_ref(i,1) = mu_out Pr_out = prandtl (Pin, Tout) Pr_ref(i,1)= Pr_out %Turbulent h_known = h_reftub(i,1) Tout = temperature (Pin, h_known) T_reftub(i,1) = Tout ro_out = density (Pin, Tout) ro_reftub(i,1) = ro_out mu_out = viscosity (Pin, Tout) mu_reftub(i,1) = mu_out

PAGE 120

120 Pr_out = prandtl (Pin, Tout) Pr_reftub(i,1)= Pr_out %******* skin friction ************************************************* %cf : local skin friction coefficient (laminar) %cf_tub : local skin fricti on coefficient (turbulent) %*********************************************************************** AA = 0.332*Pr_e(i,1)^( 1/3) %--------------laminar AAtub = 0.0296*Pr_e(i,1)^(1/ 3) %-------------turbulent sa = 0.5 %-----------------------laminar satub = 0.8 %-----------------------turbulent sb = 0.5 %-----------------------laminar sbtub = 0.2 %-----------------------turbulent sc = 0.5 %-----------------------laminar sctub = 0.8 %-----------------------turbulent sj = 0 % -----------------------flat plate cf(i,1) = 2*AA/(Pr_e(i,1)^(1/3)) (ro_re f(i,1)/ro_e(i,1))^sa (mu_r ef(i,1)/mu_e(i,1))^sb Res(i,1)^(sc-1) (3^sj)^0.5 cf_tub(i,1) = 2*AAtub/(Pr_e(i,1)^( 1/3)) (ro_reftub(i,1)/ro_e(i,1))^satub (mu_reftub(i,1)/mu_e(i,1))^sbtub Res(i,1)^(sctub-1) (3^sj)^0.5 end %******** heat transfer (ref. enthalpy) ******************************** %q_cw_en: Local Heat Transfer by using flat plate referenc e enthalpy methods (J/s-m2) %Nu = q_cw*s/(k_e *(T_w T_aw)) --> q_c w_en = cf*Pr_e^(1/3)*Res*k_e*(T_w T_aw)/(2*s) %*********************************************************************** for i=1:num_panel+1 Pin = P_e(i,1) Tout = T_e(i,1) k_con = conductivity (Pin, Tout) k_e(i,1) = k_con % (J/m-sec-K) end for i=1:num_panel+1 h_known = h_w(i,1) Pin = P_e(i,1) T_w(i,1) = temp erature (Pin, h_known) h_known = h_aw(i,1) T_aw(i,1) = temperature (Pin, h_known) h_known = h_awtub(i,1) T_awtub(i,1) = temperature (Pin, h_known) q_cw_en(i,1) = -cf(i,1)*( Pr_e(i,1)^(1/3))*Res(i ,1)*k_e(i,1)*(T_w(i,1) T_aw(i,1))/(2*s(i,1)) % W/m2 J/s-m2,

PAGE 121

121 q_cw_en_tub(i,1) = -cf_tub(i,1)*(Pr _e(i,1)^(1/3))*Res(i,1)*k_e(i,1)*(T_w(i,1) T_awtub(i,1))/(2*s(i,1)) % W/m2 J/s-m2, end %********** heat transfer (blunt body) *************************************************************** %q_cw_bl : Local Heat Transfer by using blunt body method (J/s-m2) %q_cw_bl(s=0) = (0.9038/(ep^0.25 )) (C_w/Pr_e)^0.1 (ro*Vinf*mu_e/R_b/Pr_e)^0.5 (h_e h_w) % at stagnation point, so e : se here %C_w = (ro_w*mu_w/(ro_e *mu_e)) % e : se here %C_ws = (ro_e*mu_e/(ro_se*mu_se)) %q_cw_bl(s) = q_cw_bl(s=0) C_ws u_e*rbody^jq / (2^(jq+1) (u_e(i)-u_e(i-1))/(s(i)-s(i1)))^0.5 SUM(i=1-->i,C_ws(i)*u_e(i)*rbody^(2*jq)*(s(i)-s(i-1)) %rbody : radius of cross sect ion of bodies of revolution %jq : 1 for bodies, 0 for 2-D %************************************************************************** for i=1:num_panel z_original=((cent(i,1)^2+ cent(i,3)^2)^0.5)*sin(aoa*3.14159265359/180+ atan(cent(i,3)/cent(i,1)) ) rbody(i,1)=(cent(i,2)^2+z_original^2)^0.5 end rbody(num_panel+1,1)=0.001 %Find stagnation M, u_e, T_e for equilibrium condition ro1ro2 = 0.1 % step 1: first guess of ro_1/ro_2 press_1 = Pinf temp_1 = Tinf ro_1 = ro vel_1 = Vinf enth_1 = enthalpy (press_1/101325, temp_1) error_equi = 1 while error_equi > 0.0001 press_2 = press_1 + ro_1*(vel _1)^2*(1-ro1ro2) % step 2: obtain p2 enth_2 = enth_1 + (0.5/1000)*(vel_1)^ 2*(1-ro1ro2^2) % step 2: obtain h2 (J/g) P_stag = press_2/101325 temp_2 = temperature (P_sta g, enth_2) % step 3: obtain T2 ro_2 = density (P_stag, en th_2) % step 3: obtain ro_2 ro1ro2new = ro_1/ro_2 % step 4: obtain new ro1ro2 error_equi = abs(ro1ro2 ro1ro2new) ro1ro2 = ro1ro2new end vel_2 = ro1ro2 vel_1

PAGE 122

122 M_stag = vel_2/((gamma*temp_2*Rai r)^0.5) %Mach number at stagnation point P_stag = press_2/101325 %Pre ssure at stagnation point (atm) T_stag = temp_2 % Temperature at stagnation point (K) h_stag = enth_2 % en thalpy at stagnation point u_stag_e = vel_2 P_stag; T_stag; T_sw=temperature (P_stag, h_w(1,1)); Pin = P_stag ro_sw = density (Pin, T_sw ); mu_sw = viscosity (Pin, T_sw) ro_se = ro/ro1ro2; mu_s e = viscosity (Pin, T_stag) Pr_se = prandtl (Pin, T_stag) h_se = enthalpy (Pin, T_stag ); h_sw= enthalpy (Pin, T_sw) C_w01 = (ro_sw*mu_sw)/ro_se/mu_se R_b01 = 0.3048%0.10110667%((1+ ((nod(8,3)-nod(1,3))/(nod(8,1)nod(1,1)))^2)^1.5)/abs((nod(8,3)-2*nod(1,3)+nod(2,3) )/(nod(8,1)-nod(1,1 ))/(nod(2,1)-nod(1,1))) q_cw_bl01 = 1000*(0.9038/(ep^0.25)) (C_w01/Pr_se)^0.1 (ro*Vinf*mu_se/R_b01/Pr_se)^0.5 (h_se h_sw) % at stagnation point(body) W/m2 J/s-m2, so e : se here q_cw_bl_nose= q_cw_bl01 s(num_panel+1,1)=0 u_e(num_panel+1,1)=u_stag_e; u_ e(num_panel+1,2)=0; u_e(num_panel+1,3)=0 rbody(num_panel+1,1)=0.0001 %ra dius of cross section of body ro_e(num_panel+1,1)=ro_se mu_e(num_panel+1,1)=mu_se C_ws(num_panel+1,1)=1.0 for k= 1:13 SUMq = 0 for i =k:13:117 j=jj(i,1) C_ws(i,1) = (ro_e(i,1)*mu_e(i,1))/(ro_se*mu_se) f_s_1(i,1) = (C_ws(i,1)*(u_e(i ,1)^2+u_e(i,2)^2+u_e(i,3 )^2)^0.5)*(rbody(i,1)^2) f_s_0(i,1) = (C_ws(j,1)*(u_e(j ,1)^2+u_e(j,2)^2+u_e(j,3 )^2)^0.5)*(rbody(j,1)^2) SUMq = SUMq + (f_s_0( i,1) + f_s_1(i,1))*(s(i,1)-s(j,1))/2 q_cw_bl(i,1) = (SUMq^0.5)*q_cw_bl01*C_ws(i,1)*(u_e(i,1)^2+u_e(i,2)^2+ u_e(i,3)^2)^0.5*rbody(i ,1)/((4*(((u_e(k,1)^ 2+u_e(k,2)^2+u_e(k,3)^2)^0.5-u_s tag_e)/(s(k,1))))^0.5) end end for i=119:130 rbody(i,1)=1.0 %for two dimensional end for i=131:142 rbody(i,1)=1.0 %for two dimensional

PAGE 123

123 end P_stag; T_stag; T_sw=temperature (P_stag, h_w(119,1)); Pin = P_stag ro_sw = density (Pin, T_sw ); mu_sw = viscosity (Pin, T_sw) ro_se = density (Pin, T_stag ); mu_se = viscosity (Pin, T_stag) Pr_se = prandtl (Pin, T_stag) h_se = enthalpy (Pin, T_stag ); h_sw= enthalpy (Pin, T_sw) C_w01 = (ro_sw*mu_sw)/ro_se/mu_se R_b01 = 0.018548985 %15.17 % ((1+((nod(8,3)-nod(1,3))/(nod(8,1)nod(1,1)))^2)^1.5)/abs((nod(8,3)-2*nod(1,3)+nod(2,3) )/(nod(8,1)-nod(1,1 ))/(nod(2,1)-nod(1,1))) q_cw_bl011 = 1000*(0.9038/(ep^0.25)) (C_w01/Pr_se)^0.1 (ro*Vinf*mu_se/R_b01/Pr_se)^0.5 (h_se h_sw) % at stagnation point(wing) W/m2 J/s-m2, so e : se here s(num_panel+1,1)=0 u_e(num_panel+1,1)=Vinf; u_e(n um_panel+1,2)=0; u_e (num_panel+1,3)=0 %u_e(121,1)=u_stag_e; u_e(121,2)=0; u_e(121,1)=0 %q_cw_bl(53,1) = q_cw_bl01 SUMq = 0 for i =119:124 j=jj(i,1) C_ws(i,1) = (ro_e(i,1)*mu_e(i,1))/(ro_se*mu_se) f_s_1(i,1) = C_ws(i,1 )*(u_e(i,1)^2+u_e(i,2)^2+u_e(i,3)^2)^0.5 f_s_0(i,1) = C_ws(j,1 )*(u_e(j,1)^2+u_e(j,2)^2+u_e(j,3)^2)^0.5 SUMq = SUMq + (f_s_0( i,1) + f_s_1(i,1))*(s(i,1)-s(j,1))/2 q_cw_bl(i,1) = (SUMq^0.5)*q_cw_bl011*C_ws(i,1)*(u_e(i,1)^2+u_e(i,2)^2+ u_e(i,3)^2)^0.5/((2*(((u_e(121,1)^2+u_e(1 21,2)^2+u_e(121,3)^2)^0.5-u_stag_e)/(s(121,1))))^ 0.5) end SUMq = 0 for i =125:130 j=jj(i,1) C_ws(i,1) = (ro_e(i,1)*mu_e(i,1))/(ro_se*mu_se) f_s_1(i,1) = C_ws(i,1 )*(u_e(i,1)^2+u_e(i,2)^2+u_e(i,3)^2)^0.5 f_s_0(i,1) = C_ws(j,1 )*(u_e(j,1)^2+u_e(j,2)^2+u_e(j,3)^2)^0.5 SUMq = SUMq + (f_s_0( i,1) + f_s_1(i,1))*(s(i,1)-s(j,1))/2 q_cw_bl(i,1) = (SUMq^0.5)*q_cw_bl011*C_ws(i,1)*(u_e(i,1)^2+u_e(i,2)^2+ u_e(i,3)^2)^0.5/((2*(((u_e(127,1)^2+u_e(1 27,2)^2+u_e(127,3)^2)^0.5-u_stag_e)/(s(127,1))))^ 0.5) end P_stag; T_stag; T_sw=temperature (P_stag, h_w(137,1)); Pin = P_stag ro_sw = density (Pin, T_sw ); mu_sw = viscosity (Pin, T_sw) ro_se = density (Pin, T_stag ); mu_se = viscosity (Pin, T_stag) Pr_se = prandtl (Pin, T_stag)

PAGE 124

124 h_se = enthalpy (Pin, T_stag ); h_sw= enthalpy (Pin, T_sw) C_w01 = (ro_sw*mu_sw)/ro_se/mu_se R_b01 = 0.061123322 % ((1+((n od(8,3)-nod(1,3))/(nod(8,1)nod(1,1)))^2)^1.5)/abs((nod(8,3)-2*nod(1,3)+nod(2,3) )/(nod(8,1)-nod(1,1 ))/(nod(2,1)-nod(1,1))) q_cw_bl012 = 1000*(0.9038/(ep^0.25)) (C_w01/Pr_se)^0.1 (ro*Vinf*mu_se/R_b01/Pr_se)^0.5 (h_se h_sw) % at stagnation point(wing) W/m2 J/s-m2, so e : se here s(num_panel+1,1)=0 u_e(num_panel+1,1)=Vinf; u_e(n um_panel+1,2)=0; u_e (num_panel+1,3)=0 SUMq = 0 for i =131:136 j=jj(i,1) C_ws(i,1) = (ro_e(i,1)*mu_e(i,1))/(ro_se*mu_se) f_s_1(i,1) = C_ws(i,1 )*(u_e(i,1)^2+u_e(i,2)^2+u_e(i,3)^2)^0.5 f_s_0(i,1) = C_ws(j,1 )*(u_e(j,1)^2+u_e(j,2)^2+u_e(j,3)^2)^0.5 SUMq = SUMq + (f_s_0( i,1) + f_s_1(i,1))*(s(i,1)-s(j,1))/2 q_cw_bl(i,1) = (SUMq^0.5)*q_cw_bl012*C_ws(i,1)*(u_e(i,1)^2+u_e(i,2)^2+ u_e(i,3)^2)^0.5/((2*(((u_e(121,1)^2+u_e(1 21,2)^2+u_e(121,3)^2)^0.5-u_stag_e)/(s(121,1))))^ 0.5) end SUMq = 0 for i =137:142 j=jj(i,1) C_ws(i,1) = (ro_e(i,1)*mu_e(i,1))/(ro_se*mu_se) f_s_1(i,1) = C_ws(i,1 )*(u_e(i,1)^2+u_e(i,2)^2+u_e(i,3)^2)^0.5 f_s_0(i,1) = C_ws(j,1 )*(u_e(j,1)^2+u_e(j,2)^2+u_e(j,3)^2)^0.5 SUMq = SUMq + (f_s_0( i,1) + f_s_1(i,1))*(s(i,1)-s(j,1))/2 q_cw_bl(i,1) = (SUMq^0.5)*q_cw_bl012*C_ws(i,1)*(u_e(i,1)^2+u_e(i,2)^2+ u_e(i,3)^2)^0.5/((2*(((u_e(127,1)^2+u_e(1 27,2)^2+u_e(127,3)^2)^0.5-u_stag_e)/(s(127,1))))^ 0.5) end %***** heat transfer choice *********************************************************** % % q_cw : heat transfer at each panel (J/m-s2) % % q_cw_en: Local Heat Transfer by using flat plate referenc e enthalpy methods (J/s-m2) % q_cw_bl : Local Heat Transfer by using blunt body method (J/s-m2) % % Around the stagnation points, the flat plate reference enthalpy method provides % extremely high value of the heat transfer as discussed before, so the blunt bodies % solutions should be used for the pane ls around the stagnation points. For far % panels from the stagnation points, the both methods agree closely, and at least

PAGE 125

125 % both have the similar behavior. Therefor e, the flat plate reference enthalpy method % is used to find the heat transf er for far surface of the body and wings. % % *around the stagnation point or leading e dge: stagnation point( panel) next panel % otherwise, far from the stagnation points % % tangential component of velocity on "shadow" panel is found by P-M expansion % s_b =[nose_vector; nunit( 6,1); nunit(12,1); nunit(18,1); nunit( 24,1); nunit(30,1)] % s_w1 =[nunit(53,1); n unit(52,1); nunit(51,1)] % s_w2 =[nunit(64,1); n unit(63,1); nunit(62,1)] % s_w3 =[nunit(74,1 ); nunit(73,1)] %**************************************************************************** ********** q_cw = q_cw_en_tub %set q_cw to q_cw_en here and q_cw_bl will be applied to around the stagnation later for i=1:num_panel St2(i,1) = q_cw(i,1)/(ro*Vinf)/(h_se h_w(i,1))/1000 end Pin=Pinf/101325; Tout=Tinf mu_e(num_panel+1,1) = viscosity (Pin, Tout) Re_inf = ro*Vinf/mu_e(num_panel+1,1) %Reynol ds number divided by certain characteristic length %Use blunt body scheme is applied onl y for the stagnation points(body and %wing) and the the most downs tream panel of each stream. %***** cooling analysis ******************************************************************** % % cf : local skin friction coefficient (laminar) % cf_tub : local skin fricti on coefficient (turbulent) % cf_cool : local skin friction coeffi cient of cooled condition. This array % includes cf at non-cooled panels also. % % q_cw : Local Heat Transfer (J/s-m2); reference enthalpy method or blun body method % q_cw_cool : local heat transfer (J/s -m2) of cooled condition. This array % includes q_cw at non-cooled panels also. % % nunit: n (N unit) vector of each panel % Area: area of each panel (m2) % ro_e : air density at edge of boundary layer for each panel (kg/m3) % u_e : tangential component of velocity on each panel (m/s) % v_w : normal velocity at the wall of each panel (m/s) % ro_w : injected gas density at the wall (kg/m3) %

PAGE 126

126 % Lift_vis: lift (N) (viscous without cooling) % Lift_viscool: lift (N) (viscous with cooling) % Drag_vis: drag (N) (viscous without cooling) % Drag_viscool: drag (N) (viscous with cooling) % L_D_vis: L/D ratio (viscous without cooling) % L_D_viscool: L/D ratio (viscous with cooling) % dF_f: differential friction fo rce (N) acting on each pa nel (without cooling) % dF_fcool: differential friction for ce (N) acting on each panel (with cooling) % dLr: differential lift for ce acting on each panel (right side) % dDr: differential drag force acting on each panel (right side) %**************************************************************************** **************** %*** Total L/D ratio of viscous case without cooling ********* for i=1:num_panel qinf_e(i,1) = ro_e(i,1)*( u_e(i,1)^2+u_e(i,2)^2+u_e(i,3)^2)/2.0 dF_fx(i,1) = cf_tub(i,1)*qinf_e(i,1)*Ar ea(i,1)*u_e(i,1)/((u_e(i,1)^2 +u_e(i,2)^2+u_e(i,3)^2)^0.5) dF_fy(i,1) = cf_tub(i,1)*qinf_e(i,1)*Ar ea(i,1)*u_e(i,2)/((u_e(i,1)^2 +u_e(i,2)^2+u_e(i,3)^2)^0.5) dF_fz(i,1) = cf_tub(i,1)*qinf_e(i,1)*Ar ea(i,1)*u_e(i,3)/((u_e(i,1)^2 +u_e(i,2)^2+u_e(i,3)^2)^0.5) end Lift_vis = (sum(dL)+sum(dF_fz(:,1)))*2 Drag_vis = (sum(dD)+sum(dF_fx(:,1)))*2 L_D_vis = Lift_vis/Drag_vis CLvis = Lift_vis/qinf/Sref CDvis = Drag_vis/qinf/Sref CNvis = CLvis*cos(aoa*3.14159265359/180)+CDvis*sin(aoa*3.14159265359/180) CAvis = CDvis*cos(aoa*3.14159265359/180)-CLvis*sin(aoa*3.14159265359/180) for i=1:num_panel d_mvis(i,1) = (radi(i,1)*((dF(i,3)+dF_fz (i,1))*cos(aoa*3.14159265359/180)+(dF(i,1)+dF_fx(i,1))*sin(aoa*3.1 4159265359/180))-radi(i,3)*((dF(i,1)+d F_fx(i,1))*cos(aoa*3.14159265359/180)(dF(i,3)+dF_fz(i,1))*sin(aoa*3.14159265359/180))) end pitching_vis = sum(d_mvis)*2 C_mvis = pitching_vis/qinf/Sref/chord %*** Determine the panel cooled *********************************** % panel around the bottom noze: [8,9,10,11,12,13,14] (not stagnation point) %

PAGE 127

127 % Injected Gas properties: % H2: 0.08078kg/m3 (T=300K) %****************************************************************** int_bf = 11 %the number of step of 0.1 in bf. (int_bf 1)*0.1 = max of bf mass_rate_step = 0.001 %kg/m2-s %partial bottom panels are cooled for i=1:num_panel for j=1:int_bf cf_cool(i,j) = cf_tub(i,1) end end for i=1:num_panel Nu(i,1) = -q_cw(i,1)*s(i,1) /(k_e(i,1)*(T_w(i,1)-T_aw(i,1))) end for i=1:num_panel St(i,1) = Pr_e (i,1)*Nu(i,1)/Res(i,1) end for i=1:num_panel for j=1:int_bf q_cw_cool(i,j) = q_cw(i,1) end end A_cool2 =0 for i=1:1:num_panel if q_cw(i,1)>0 %Choose panels to be cooled he re by setting the minimum value of allowable heat trans. cooled_panel2(i,1)=1.0 A_cool2 = A_cool2+Area(i,1) %1:num_panel%all panels for j = 1:int_bf m_inj(i,j)=mass_rate_step*(j-1) bf2(i,j) = m_inj(i,j)/( 0.5*cf_tub(i,1)*ro_e(i,1)*(u_e(i,1 )^2+u_e(i,2)^2+u_e(i,3)^2)^0.5) bh2(i,j) = m_inj(i,j)/( St(i,1)*ro_e(i,1)*(u_e(i,1)^2 +u_e(i,2)^2+u_e(i,3)^2)^0.5) if j==1 cf_cool(i,j) = cf_tub(i,1) q_cw_cool(i,j) = q_cw(i,1) else cf_cool(i,j) = cf_tub(i,1 )*(bf2(i,j)/(exp(bf2(i,j))-1)) q_cw_cool(i,j) = q_cw(i ,1)*(bh2(i,j)/(exp(bh2(i,j))-1)) end

PAGE 128

128 end else end end for i=1:num_panel qinf_e(i,1) = ro_e(i,1)*( u_e(i,1)^2+u_e(i,2)^2+u_e(i,3)^2)/2. for j=1:int_bf dF_fxcool(i,j) = cf_cool(i,j)*qinf_e(i,1)*Ar ea(i,1)*u_e(i,1)/((u_e(i,1)^2 +u_e(i,2)^2+u_e(i,3)^2)^0.5) dF_fycool(i,j) = cf_cool(i,j)*qinf_e(i,1)*Ar ea(i,1)*u_e(i,2)/((u_e(i,1)^2 +u_e(i,2)^2+u_e(i,3)^2)^0.5) dF_fzcool(i,j) = cf_cool(i,j)*qinf_e(i,1)*Ar ea(i,1)*u_e(i,3)/((u_e(i,1)^2 +u_e(i,2)^2+u_e(i,3)^2)^0.5) end end Q_total=0.0 for i=1:num_panel Q_total = Q_tota l + q_cw(i,1)*Area(i,1) end for j=1:int_bf Lift_viscool2(j,1) = (sum(dL)+sum(dF_fzcool(:,j)))*2 Drag_viscool2(j,1) = (s um(dD)+sum(dF_fxcool(:,j)))*2 L_D_viscool2(j,1) = Lift _viscool2(j,1)/Drag_viscool2(j,1) L_Dimprovement2(j,1)=L_D_viscool2(j,1)/L_D_vis Q_total_cool=0.0 for i=1:num_panel Q_total_cool = Q_to tal_cool + q_cw_cool(i,j)*Area(i,1) end q_cwimprovement2(j ,1)=Q_total_cool/Q_total end

PAGE 129

129 APPENDIX B MATLAB CODE (FUNCTION) TO COMPUTE TEMPERATURE %************************************************************************** %code thermo_propert y (temperature) %This code compute thermodynamic prope rty of air as f unction of T an P %Thermodynamic property includes: %compressibility Z(T, P) %temperature T(P, h) %density ro(T, P) %viscocity mu(T,P) %Prandtl number Pr %Inputs are: entahlpy and pressu re, so h and P must be known %output of this code is a ccurate but not exact solution %************************************************************************** %****** Input ************************************************************* %Pin : Pressure input, th is value must be known unit:atm %h_known : enthalpy input, this value must be known unit:J/g or kJ/kg %************************************************************************** function [Tout] = temperature (Pin, h_known) %Pin = 0.01 %Pressure input, this value must be known unit:atm %h_known = 11054.6 %enthalpy input, this value must be known unit:J/g or kJ/kg %****** Compressibility *************************************************** %computed by using interp2 function w ith known Hansen's data (T and P) %inter2 is function of 2-D data interpolation %T : temperature %P : pressure %Tin : input temperature %Pin : input pressure %ZTP : compressibility table %Z : compressibility of air as f(Tin, Pin) %************************************************************************** T = 0:500:15000 %Tempera ture range 0K --> 15000K P = [100 10 1 0.1 0.01 0.001 0.0001 0] %Pressure range 0atm --> 0.0001atm --> 100atm ZTP =[1.000 1.000 1.000 1.000 1.000 1.000 1.003 1.012 1.033 1.071 1.118 1.159 ... 1.189 1.214 1.243 1.284 1.341 1.418 1.512 1.616 1.718 1.807 1.876 1.927 1.965 ... 1.993 2.017 2.039 2.062 2.086 2.113 1.000 1.000 1.000 1.000 1.000 1.001 1.009 1.035 1.089 1.149 1.186 1.208 ... 1.235 1.279 1.351 1.457 1.590 1.727 1.838 1.914 1.962 1.993 2.018 2.042 2.067 ... 2.098 2.135 2.180 2.233 2.297 2.372 1.000 1.000 1.000 1.000 1.000 1.004 1.026 1.092 1.165 1.196 1.214 1.248 ...

PAGE 130

130 1.316 1.437 1.607 1.778 1.896 1.959 1.993 2.018 2.042 2.071 2.111 2.163 2.232 ... 2.318 2.426 2.553 2.700 2.861 3.028 1.000 1.000 1.000 1.000 1.001 1.011 1.072 1.167 1.198 1.213 1.252 1.348 ... 1.529 1.752 1.904 1.971 2.001 2.023 2.050 2.090 2.149 2.234 2.351 2.505 2.694 ... 2.910 3.135 3.347 3.527 3.667 3.769 1.000 1.000 1.000 1.000 1.002 1.033 1.149 1.197 1.208 1.245 1.359 1.599 ... 1.849 1.961 1.997 2.017 2.044 2.090 2.166 2.286 2.462 2.700 2.983 3.272 3.520 ... 3.700 3.818 3.889 3.932 3.957 3.973 1.000 1.000 1.000 1.000 1.005 1.088 1.192 1.203 1.228 1.337 1.622 1.898 ... 1.983 2.006 2.027 2.067 2.144 2.284 2.510 2.832 3.202 3.526 3.745 3.867 3.931 ... 3.963 3.979 3.988 3.993 3.996 3.997 1.000 1.000 1.000 1.000 1.016 1.163 1.200 1.211 1.287 1.577 1.910 1.990 ... 2.008 2.032 2.088 2.210 2.446 2.826 3.282 3.645 3.843 3.932 3.969 3.985 3.993 ... 3.996 3.998 3.999 3.999 4.000 4.000 1.000 1.000 1.000 1.000 1.016 1.163 1.200 1.211 1.287 1.577 1.910 1.990 ... 2.008 2.032 2.088 2.210 2.446 2.826 3.282 3.645 3.843 3.932 3.969 3.985 3.993 ... 3.996 3.998 3.999 3.999 4.000 4.000] %****** Temperature ******************************************************* %Z function is known, T and h relation is computed by using interp2 function with %known Hansen's data (h, P, and Z) %Now, P and h are known. Set P known a nd assume T and iterate to match h %given by T and h relation %T : temperature (K) %P : pressure (atm) %h : enthalpy (J/g) %h_known : enthalpy known (input enthalpy) (J/g) %Z : compressibility %R : universal gas constant (J/mol-K) %MWair : molecular weight (g/mol) %ZH_RT : dimensionless enthal py (Zh/RT) table givenin Hansen's %ZHRT : dimensionless enthal py (Zh/RT) as function of (T, P) %Tin : input temper ature (guessed temperature) %Pin : input pressure %ZTP : compressibility table %Z : compressibility of air as f(Tin, Pin) %************************************************************************** T = 0:500:15000 %Tempera ture range 0K --> 15000K P = [100 10 1 0.1 0.01 0.001 0.0001 0] %Pressure range 0atm --> 0.0001atm --> 100atm ZH_RT = [3.52 3.52 3.65 3.80 3.92 4.01 4.13 4.34 4.70 5.20 5.73 6.13 6.38 6.62 6.95 7.44 8.16 ... 9.10 10.20 11.36 12.42 13.23 13.77 14.08 14.22 14.28 14.30 14.31 14.34 14.40 14.49 3.52 3.52 3.65 3.80 3.92 4.03 4.25 4.75 5.56 6.29 6.62 6.80 7.11 7.72 8.76 10.24 11.99 13.63 ...

PAGE 131

131 14.79 15.40 15.61 15.64 15.60 15.58 15.62 15.74 15.96 16.28 16.71 17.26 17.92 3.52 3.52 3.65 3.80 3.92 4.09 4.61 5.75 6.74 6.98 7.10 7.58 8.70 10.64 13.20 15.48 16.73 17.09 17.04 ... 16.91 16.84 16.90 17.13 17.57 18.24 19.16 20.32 21.72 23.29 24.98 26.66 3.52 3.52 3.65 3.80 3.93 4.27 5.55 7.08 7.28 7.33 7.96 9.73 12.93 16.46 18.34 18.66 18.43 18.17 ... 18.09 18.29 18.85 19.84 21.31 23.28 25.69 28.36 30.99 33.27 34.97 36.02 36.53 3.52 3.52 3.65 3.80 3.97 4.81 7.13 7.62 7.53 8.14 10.48 15.14 19.30 20.35 20.01 19.54 19.34 ... 19.60 20.49 22.17 24.78 28.28 32.31 36.13 39.01 40.66 41.26 41.17 40.69 40.01 39.24 3.52 3.52 3.65 3.80 4.07 6.16 8.02 7.77 8.09 10.55 16.68 21.58 21.97 21.24 20.69 20.72 21.65 ... 23.85 27.66 33.00 38.79 43.28 45.57 46.09 45.64 44.74 43.69 42.61 41.55 40.53 39.57 3.52 3.52 3.65 3.80 4.41 8.02 8.19 8.03 9.82 16.80 23.46 23.58 22.54 21.93 22.29 24.26 28.65 ... 35.75 43.74 49.15 50.96 50.64 49.48 48.07 46.64 45.26 43.97 42.76 41.64 40.58 39.60 3.52 3.52 3.65 3.80 4.41 8.02 8.19 8.03 9.82 16.80 23.46 23.58 22.54 21.93 22.29 24.26 28.65 ... 35.75 43.74 49.15 50.96 50.64 49.48 48.07 46.64 45.26 43.97 42.76 41.64 40.58 39.60] %P and h are known. Set P known and assume T and iterate to match h %given by T and h relation above R = 8.3144 %universal gas constant unit:J/K-mol MWair = 29 cp_0 = 1.0 % specific heat c onstant pressure at T = 0K Tin = h_known/cp_0 %guess temperature unit:K dh = -1 % initializ e difference between hi and h_known while dh < 0 Z = interp2(T, P, ZTP,Tin, Pin) ZHRT = interp2(T, P, ZH_RT,Tin, Pin) hi = ZHRT*R*Tin/Z/MWair %enthalpy i unit:J/g dh = h_known hi Tin = Tin 5 end Tout = Tin + 5 %unit:K

PAGE 132

132 APPENDIX C MATLAB CODE (FUNCTION) TO COMPUTE DENSITY %************************************************************************** %code thermo_property %This code compute thermodynamic property of air as function of T an P %Thermodynamic property includes: %compressibility Z(T, P) %temperature T(P, h) %density ro(T, P) %viscocity mu(T,P) %Prandtl number Pr %Inputs are: entahlpy and pressure, so h and P must be known %output of this code is accurate but not exact solution %************************************************************************** %****** Input ************************************************************* %Pin : Pressure input, this value must be known unit:atm %h_known : enthalpy input, this value must be known unit:J/g or kJ/kg %************************************************************************** function [ro] = density (Pin, Tout) T = 0:500:15000 %Temperature range 0K --> 15000K P = [100 10 1 0.1 0.01 0.001 0.0001 0] %P ressure range 0atm --> 0.0001atm --> 100atm ZTP =[1.000 1.000 1.000 1.000 1.000 1.000 1. 003 1.012 1.033 1.071 1.118 1.159 ... 1.189 1.214 1.243 1.284 1.341 1.418 1.512 1.616 1.718 1.807 1.876 1.927 1.965 ... 1.993 2.017 2.039 2.062 2.086 2.113 1.000 1.000 1.000 1.000 1.000 1. 001 1.009 1.035 1.089 1.149 1.186 1.208 ... 1.235 1.279 1.351 1.457 1.590 1.727 1.838 1.914 1.962 1.993 2.018 2.042 2.067 ... 2.098 2.135 2.180 2.233 2.297 2.372 1.000 1.000 1.000 1.000 1.000 1. 004 1.026 1.092 1.165 1.196 1.214 1.248 ... 1.316 1.437 1.607 1.778 1.896 1.959 1.993 2.018 2.042 2.071 2.111 2.163 2.232 ... 2.318 2.426 2.553 2.700 2.861 3.028 1.000 1.000 1.000 1.000 1.001 1. 011 1.072 1.167 1.198 1.213 1.252 1.348 ... 1.529 1.752 1.904 1.971 2.001 2.023 2.050 2.090 2.149 2.234 2.351 2.505 2.694 ... 2.910 3.135 3.347 3.527 3.667 3.769 1.000 1.000 1.000 1.000 1.002 1. 033 1.149 1.197 1.208 1.245 1.359 1.599 ... 1.849 1.961 1.997 2.017 2.044 2.090 2.166 2.286 2.462 2.700 2.983 3.272 3.520 ... 3.700 3.818 3.889 3.932 3.957 3.973 1.000 1.000 1.000 1.000 1.005 1. 088 1.192 1.203 1.228 1.337 1.622 1.898 ... 1.983 2.006 2.027 2.067 2.144 2.284 2.510 2.832 3.202 3.526 3.745 3.867 3.931 ... 3.963 3.979 3.988 3.993 3.996 3.997 1.000 1.000 1.000 1.000 1.016 1. 163 1.200 1.211 1.287 1.577 1.910 1.990 ... 2.008 2.032 2.088 2.210 2.446 2.826 3.282 3.645 3.843 3.932 3.969 3.985 3.993 ... 3.996 3.998 3.999 3.999 4.000 4.000 1.000 1.000 1.000 1.000 1.016 1. 163 1.200 1.211 1.287 1.577 1.910 1.990 ... 2.008 2.032 2.088 2.210 2.446 2.826 3.282 3.645 3.843 3.932 3.969 3.985 3.993 ... 3.996 3.998 3.999 3.999 4.000 4.000] R = 8.3144 %universal gas constant unit:J/K-mol

PAGE 133

133 MWair = 29 %****** density *********************************************************** %density is found by using simple equation of state with compressibility %ro = P*MWair/(Z*R*T) %ro : density (kg/m3) %Z : compressibility %MWair : molecular weight (g/mol) %R : universal gas constant (J/mol-K) %T : temperature computed above (K) %************************************************************************** Z = interp2(T, P, ZTP,Tout, Pin) ro = Pin*101325*MWair/R/Tout/1000

PAGE 134

134 APPENDIX D MATLAB CODE (FUNCTION) TO COMPUTE VOSCOSITY %************************************************************************** %code thermo_property (viscosiy) %This code compute thermodynamic property of air as function of T an P %Thermodynamic property includes: %compressibility Z(T, P) %temperature T(P, h) %density ro(T, P) %viscocity mu(T,P) %Prandtl number Pr %Inputs are: entahlpy and pressure, so h and P must be known %output of this code is accurate but not exact solution %************************************************************************** %****** Input ************************************************************* %Pin : Pressure input, this value must be known unit:atm %h_known : enthalpy input, this value must be known unit:J/g or kJ/kg %************************************************************************** function [mu] = viscosity (Pin, Tout) %Pin = 0.01 %Pressure input, this value must be known unit:atm %h_known = 11054.6 %enthalpy input, th is value must be known unit:J/g or kJ/kg %****** Compressibility *************** ************** *********** *********** %computed by using interp2 function with known Hansen's data (T and P) %inter2 is function of 2-D data interpolation %T : temperature %P : pressure %Tin : input temperature %Pin : input pressure %ZTP : compressibility table %Z : compressibility of air as f(Tin, Pin) %************************************************************************** R = 8.3144 %universal gas constant unit:J/K-mol MWair = 29 %****** Viscosity *************************************************** %computed by using interp2 function with known Hansen's data (T and P) %inter2 is function of 2-D data interpolation %T : temperature %P : pressure %Tout : input temperature (computed above) %Pin : input pressure %Cmu : viscousity ratio (mu/nu0) given in Hansen's %mu0 : reference viscosity %mu : viscosity (gm/cm-s)

PAGE 135

135 %************************************************************************** T = 0:500:15000 %Temperature range 0K --> 15000K P = [100 10 1 0.1 0.01 0.001 0.0001 0] %P ressure range 0atm --> 0.0001atm --> 100atm Cmu = [1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.003 1.010 1.022 1.036 1.050 1.072 1.089 1.112 ... 1.143 1.185 1.238 1.298 1.361 1.418 1.467 1.509 1.549 1.577 1.581 1.594 1.599 1.601 1.604 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.001 1.008 1.022 1.036 1.052 1.067 1.090 1.124 1.175 1.238 ... 1.307 1.368 1.418 1.468 1.496 1.501 1.511 1.520 1.516 1.508 1.492 1.468 1.415 1.387 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.003 1.016 1.029 1.043 1.060 1.090 1.139 1.208 1.283 1.342 ... 1.386 1.425 1.438 1.445 1.448 1.442 1.424 1.394 1.342 1.274 1.187 1.082 0.940 0.828 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.006 1.020 1.033 1.051 1.086 1.148 1.229 1.294 1.332 1.371 ... 1.386 1.396 1.393 1.375 1.335 1.267 1.168 1.040 0.881 0.711 0.547 0.408 0.268 0.212 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.010 1.022 1.033 1.051 1.086 1.148 1.229 1.294 1.332 1.347 ... 1.343 1.314 1.251 1.143 0.983 0.782 0.571 0.387 0.249 0.158 0.100 0.067 0.042 0.016 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.010 1.024 1.055 1.128 1.209 1.257 1.286 1.303 1.307 1.280 ... 1.207 1.068 0.853 0.595 0.361 0.200 0.108 0.063 0.036 0.024 0.018 0.015 0.013 0.012 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.011 1.032 1.096 1.181 1.227 1.256 1.271 1.264 1.210 1.072 ... 0.826 0.517 0.261 0.118 0.055 0.029 0.018 0.012 0.009 0.008 0.007 0.007 0.008 0.008 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.011 1.032 1.096 1.181 1.227 1.256 1.271 1.264 1.210 1.072 ... 0.826 0.517 0.261 0.118 0.055 0.029 0.018 0.012 0.009 0.008 0.007 0.007 0.008 0.008] mu0 = 1.462*((Tout)^0.5)/(1+112/Tout)*10^-5 mu = interp2(T, P, Cmu, Tout, Pin)*mu0/10

PAGE 136

136 APPENDIX E MATLAB CODE (FUNCTION) TO COMPUTE PRANDTL NUMBER %************************************************************************** %code thermo_property (Prandtl number) %This code compute thermodynamic property of air as function of T an P %Thermodynamic property includes: %compressibility Z(T, P) %temperature T(P, h) %density ro(T, P) %viscocity mu(T,P) %Prandtl number Pr %Inputs are: entahlpy and pressure, so h and P must be known %output of this code is accurate but not exact solution %************************************************************************** %****** Input ************************************************************* %Pin : Pressure input, this value must be known unit:atm %h_known : enthalpy input, this value must be known unit:J/g or kJ/kg %************************************************************************** function [Pr] = prandtl (Pin, Tout) %Pin = 0.01 %Pressure input, this value must be known unit:atm %h_known = 11054.6 %enthalpy input, th is value must be known unit:J/g or kJ/kg %****** Compressibility *************** ************** *********** *********** %computed by using interp2 function with known Hansen's data (T and P) %inter2 is function of 2-D data interpolation %T : temperature %P : pressure %Tin : input temperature %Pin : input pressure %ZTP : compressibility table %Z : compressibility of air as f(Tin, Pin) %************************************************************************** %****** Prandtl number *************************************************** %computed by using interp2 function with known Hansen's data (T and P) %inter2 is function of 2-D data interpolation %T : temperature %P : pressure %Tout : input temperature (computed above) %Pin : input pressure %Pr_table : Prandtl number given in Hansen's %Pr : Prandtl number %************************************************************************** T = 0:500:15000 %Temperature range 0K --> 15000K

PAGE 137

137 P = [100 10 1 0.1 0.01 0.001 0.0001 0] %Pressure range 0 atm --> 0.0001atm --> 100atm Pr_table =[0.738 0.738 0.756 0.767 0.773 0.762 0.740 0.678 0.640 0.654 0.702 0.748 0.763 0.610 0.593 0.595 ... 0.620 0.666 0.730 0.806 0.886 0.937 0.955 0.947 0.908 0.728 0.525 0.438 0.421 0.401 0.394 0.738 0.738 0.756 0.767 0.773 0.751 0.680 0.631 0.662 0.743 0.767 0.620 0.592 0.592 0.620 0.688 0.788 ... 0.891 0.961 0.966 0.872 0.532 0.463 0.434 0.412 0.396 0.383 0.369 0.360 0.349 0.341 0.738 0.738 0.756 0.767 0.773 0.696 0.627 0.660 0.762 0.752 0.611 0.583 0.602 0.673 0.796 0.927 0.983 ... 0.943 0.807 0.497 0.429 0.404 0.382 0.369 0.355 0.343 0.333 0.319 0.302 0.277 0.253 0.738 0.738 0.756 0.767 0.766 0.645 0.636 0.744 0.759 0.610 0.581 0.617 0.738 0.906 0.986 0.969 0.648 ... 0.411 0.382 0.364 0.348 0.339 0.327 0.312 0.292 0.263 0.227 0.185 0.144 0.0986 0.0819 0.738 0.738 0.756 0.767 0.724 0.611 0.740 0.737 0.619 0.578 0.624 0.785 0.969 0.955 0.830 0.424 0.387 ... 0.363 0.348 0.336 0.319 0.295 0.254 0.201 0.146 0.101 0.0688 0.0470 0.0345 0.0245 0.0129 0.738 0.738 0.756 0.767 0.668 0.654 0.745 0.658 0.580 0.611 0.799 0.989 0.891 0.464 0.404 0.371 0.351 ... 0.335 0.316 0.279 0.216 0.145 0.0877 0.0524 0.0346 0.0238 0.0190 0.0162 0.0149 0.0130 0.0120 0.738 0.738 0.756 0.767 0.614 0.771 0.714 0.606 0.587 0.764 0.993 0.871 0.455 0.392 0.361 0.342 0.322 ... 0.279 0.200 0.114 0.0576 0.0314 0.0213 0.0167 0.0143 0.0129 0.0121 0.0110 0.0108 0.0109 0.0110 0.738 0.738 0.756 0.767 0.614 0.771 0.714 0.606 0.587 0.764 0.993 0.871 0.455 0.392 0.361 0.342 0.322 ... 0.279 0.200 0.114 0.0576 0.0314 0.0213 0.0167 0.0143 0.0129 0.0121 0.0110 0.0108 0.0109 0.0110] Pr = interp2(T, P, Pr_table, Tout, Pin)

PAGE 138

138 APPENDIX F MATLAB CODE (FUNCTION) TO COMPUTE ENTHALPY %************************************************************************** %code enthalpy %This code compute thermodynamic property of air as function of T an P % %Inputs are: temperature and pressure, so T and P must be known %output of this code is accurate but not exact solution %************************************************************************** %****** Input ************************************************************* %Pin : Pressure input, this value must be known unit:atm %Tout : Temperature input, this value must be known unit:K %************************************************************************** function [h_known] = enthalpy (Pin, Tout) %****** Compressibility *************** ****************** ********** ******** %computed by using interp2 function with known Hansen's data (T and P) %inter2 is function of 2-D data interpolation %T : temperature %P : pressure %Tin : input temperature %Pin : input pressure %ZTP : compressibility table %Z : compressibility of air as f(Tin, Pin) %************************************************************************** T = 0:500:15000 %Temperature range 0K --> 15000K P = [100 10 1 0.1 0.01 0.001 0.0001 0] %P ressure range 0atm --> 0.0001atm --> 100atm ZTP =[1.000 1.000 1.000 1.000 1.000 1.000 1. 003 1.012 1.033 1.071 1.118 1.159 ... 1.189 1.214 1.243 1.284 1.341 1.418 1.512 1.616 1.718 1.807 1.876 1.927 1.965 ... 1.993 2.017 2.039 2.062 2.086 2.113 1.000 1.000 1.000 1.000 1.000 1. 001 1.009 1.035 1.089 1.149 1.186 1.208 ... 1.235 1.279 1.351 1.457 1.590 1.727 1.838 1.914 1.962 1.993 2.018 2.042 2.067 ... 2.098 2.135 2.180 2.233 2.297 2.372 1.000 1.000 1.000 1.000 1.000 1. 004 1.026 1.092 1.165 1.196 1.214 1.248 ... 1.316 1.437 1.607 1.778 1.896 1.959 1.993 2.018 2.042 2.071 2.111 2.163 2.232 ... 2.318 2.426 2.553 2.700 2.861 3.028 1.000 1.000 1.000 1.000 1.001 1. 011 1.072 1.167 1.198 1.213 1.252 1.348 ... 1.529 1.752 1.904 1.971 2.001 2.023 2.050 2.090 2.149 2.234 2.351 2.505 2.694 ... 2.910 3.135 3.347 3.527 3.667 3.769 1.000 1.000 1.000 1.000 1.002 1. 033 1.149 1.197 1.208 1.245 1.359 1.599 ... 1.849 1.961 1.997 2.017 2.044 2.090 2.166 2.286 2.462 2.700 2.983 3.272 3.520 ... 3.700 3.818 3.889 3.932 3.957 3.973 1.000 1.000 1.000 1.000 1.005 1. 088 1.192 1.203 1.228 1.337 1.622 1.898 ... 1.983 2.006 2.027 2.067 2.144 2.284 2.510 2.832 3.202 3.526 3.745 3.867 3.931 ... 3.963 3.979 3.988 3.993 3.996 3.997 1.000 1.000 1.000 1.000 1.016 1. 163 1.200 1.211 1.287 1.577 1.910 1.990 ...

PAGE 139

139 2.008 2.032 2.088 2.210 2.446 2.826 3.282 3.645 3.843 3.932 3.969 3.985 3.993 ... 3.996 3.998 3.999 3.999 4.000 4.000 1.000 1.000 1.000 1.000 1.016 1. 163 1.200 1.211 1.287 1.577 1.910 1.990 ... 2.008 2.032 2.088 2.210 2.446 2.826 3.282 3.645 3.843 3.932 3.969 3.985 3.993 ... 3.996 3.998 3.999 3.999 4.000 4.000] %****** Temperature ******************************************************* %Z function is known, T and h relation is computed by using interp2 function with %known Hansen's data (h, P, and Z) %Now, P and h are known. Set P known a nd assume T and iterate to match h %given by T and h relation %T : temperature (K) %P : pressure (atm) %h : enthalpy (J/g) %h_known : enthalpy known (input enthalpy) (J/g) %Z : compressibility %R : universal gas constant (J/mol-K) %MWair : molecular weight (g/mol) %ZH_RT : dimensionless enthalpy (Zh/RT) table givenin Hansen's %ZHRT : dimensionless enthalpy (Zh/RT) as function of (T, P) %Tin : input temperature (guessed temperature) %Pin : input pressure %ZTP : compressibility table %Z : compressibility of air as f(Tin, Pin) %************************************************************************** T = 0:500:15000 %Temperature range 0K --> 15000K P = [100 10 1 0.1 0.01 0.001 0.0001 0] %P ressure range 0atm --> 0.0001atm --> 100atm ZH_RT = [3.52 3.52 3.65 3.80 3.92 4.01 4.13 4.34 4.70 5.20 5.73 6.13 6.38 6.62 6.95 7.44 8.16 ... 9.10 10.20 11.36 12.42 13.23 13.77 14.08 14.22 14.28 14.30 14.31 14.34 14.40 14.49 3.52 3.52 3.65 3.80 3.92 4.03 4.25 4.75 5.56 6.29 6.62 6.80 7.11 7.72 8.76 10.24 11.99 13.63 ... 14.79 15.40 15.61 15.64 15.60 15.58 15.62 15.74 15.96 16.28 16.71 17.26 17.92 3.52 3.52 3.65 3.80 3.92 4.09 4.61 5.75 6.74 6.98 7.10 7.58 8.70 10.64 13.20 15.48 16.73 17.09 17.04 ... 16.91 16.84 16.90 17.13 17.57 18.24 19.16 20.32 21.72 23.29 24.98 26.66 3.52 3.52 3.65 3.80 3.93 4.27 5.55 7.08 7.28 7.33 7.96 9.73 12.93 16.46 18.34 18.66 18.43 18.17 ... 18.09 18.29 18.85 19.84 21.31 23.28 25.69 28.36 30.99 33.27 34.97 36.02 36.53 3.52 3.52 3.65 3.80 3.97 4.81 7.13 7.62 7.53 8.14 10.48 15.14 19.30 20.35 20.01 19.54 19.34 ... 19.60 20.49 22.17 24.78 28.28 32.31 36.13 39.01 40.66 41.26 41.17 40.69 40.01 39.24 3.52 3.52 3.65 3.80 4.07 6.16 8.02 7.77 8.09 10.55 16.68 21.58 21.97 21.24 20.69 20.72 21.65 ... 23.85 27.66 33.00 38.79 43.28 45.57 46.09 45.64 44.74 43.69 42.61 41.55 40.53 39.57 3.52 3.52 3.65 3.80 4.41 8.02 8.19 8.03 9.82 16.80 23.46 23.58 22.54 21.93 22.29 24.26 28.65 ... 35.75 43.74 49.15 50.96 50.64 49.48 48.07 46.64 45.26 43.97 42.76 41.64 40.58 39.60 3.52 3.52 3.65 3.80 4.41 8.02 8.19 8.03 9.82 16.80 23.46 23.58 22.54 21.93 22.29 24.26 28.65 ... 35.75 43.74 49.15 50.96 50.64 49.48 48.07 46.64 45.26 43.97 42.76 41.64 40.58 39.60] %P and h are known. Set P known and assume T and iterate to match h %given by T and h relation above R = 8.3144 %universal gas constant unit:J/K-mol MWair = 29

PAGE 140

140 %cp_0 = 1.0 % specific heat constant pressure at T = 0K %hin = cp_0*Tout %guess temperature unit:K %dT = 1 % initialize difference between hi and h_known %while dh < 0 Z = interp2(T, P, ZTP,Tout, Pin) ZHRT = interp2(T, P, ZH_RT,Tout, Pin) h_known = ZHRT*R*Tout/Z/MWair %enthalpy i unit:J/g %dh = h_known hi %Tin = Tin 10 %end %Tout = Tin + 10 %unit:K

PAGE 141

141 APPENDIX G MATLAB CODE (FUNCTION) TO CO MPUTE MACH NUMBER FOR PRANDTLMAYER EXPANSION function [M2] = shadowM (i,jj,u_eunit, T_e, u_e, gamma, ep, Rair) %function [T_e, i] = temp(i,jj,nunit, T_e, u_e, gamma, ep, Rair) %This function will compute the Mach number (M2) of shadow panel %from the data of the panel in front of shadow panel j = jj(i,1) PMang_guess =0 aaa= [u_eunit(j,1) u_eun it(j,2) u_eunit(j,3)]; bbb= [u_eunit(i,1) u_eunit(i,2) u_eunit(i,3)] ccc = cross(aaa,bbb) %a:unit normal vector of jth panel; b:unit vector of ith panel cc = (ccc(1)^2+ccc(2)^2+ccc(3)^2)^0.5 aa = (aaa(1)^2+aaa(2)^2+aaa(3)^2)^0.5 bb = (bbb(1)^2+bbb(2)^2+bbb(3)^2)^0.5 psi = asin(cc/(aa*bb)) %deflection angle (rad) M1 = ((u_e(j,1)^2+u_e(j,2)^2+u_e(j,3)^2)/(gamma*Rair*T_e(j,1)))^0.5 %Mach number of j panel PMang2 = psi + (ep^(-0.5))*atan((ep*(M1^2-1))^0.5)-atan((M1^2-1)^0.5) maxPMang = (((gamma+1)/(gamma-1))^0.5-1)*3.14159265359/2 if PMang2 >= maxPMang M2 = 1000 else M2 = M1-0.01 %M2 is Mach number of i panel and this is initial guess while PMang2 > PMang_guess PMang_guess = (ep^(-0.5))*atan((ep*(M2^2-1))^0.5)-atan((M2^2-1)^0.5) M2 = M2 + 0.01 %aaa %bbb %ccc %aa %bb %cc %M1 %PMang2 end end M2 =M2-0.01

PAGE 142

142 LIST OF REFERENCES 1. Liepmann, H. W., Roshko, A.: Elements of Gasdynamics Wiley, New York, 1957 2. Anderson, J. D.: Hypersonic and High Temperature Gas Dynamics McGraw-Hill, New York, 1989 3. Oosthuizen, P. H., Carscallen, W. E.: Compressible Fluid Flow McGraw-Hill, New York, 1997 4. Hansen, C. F.: Approximations for the Thermodynamic and Transport Properties of HighTemperature Air NASA Technical Report R-50, 1959 5. Schetz, J. A.: Boundary Layer Analysis Prentice-Hall, Englewood Cliffs, NJ, 1993 6. Fay, J. A. and Riddell, F. R.: Theory of St agnation Point Heat Transfer in Dissociated Air, Journal of the Aeronautical Sciences, vol.25, no.2, February, 1958, pp. 73-85 7. Lees, L.: Laminar Heat Transfer over Blunt-N osed Bodies at Hypersonic Flight Speeds, Jet Propulsion, vol.26, 1956, pp. 259-269, 274 8. Phillips, W. F.: Mechanics of Flight John Wiley & Sons, Inc., Hoboken, NJ, 2004 9. Wannernwetsch, G. D.: Pressure Tests of the AFFDL X-24C-10D Model at Mach Number of 1.5, 3.0, 5.0 and 6.0, von Karman Gas D ynamics Facility, Arnold Engineering Development Center, TN, AEDC-DR-76-92, Nov. 1976. 10. Neumann, R. D., Patterson, J. L., and Slis ki, N. J.: Aerodynamic Heating to the Hypersonic Research Aircraft X24C, AIAA Paper 78-37, 1978. 11. Shang, J. S., Scherr, S. J.: Navier-Stokes So lution for a Complete Re-Entry Configuration, Journal of Aircraft, vol.23, No.12, Dec. 1986, pp. 881-888 12. Hamilton J. T., Wallace R. O., Dill C.C ., Launch vehicle aerodynamic data base development comparison with flight data, NASA CP-2283, Pt. 1, 1983, pp. 19-36 13. Hwang, D. P.: A Proof of Concept Experiment for Reducing Skin Friction By Using a Micro-Blowing Technique, 35th Aerospace Scie nces Meeting and Exhibit, Reno, Nevada, January 6-9, 1997. 14. Kays, W. M., Crawford, M. E.: Convective Heat and Mass Transfer McGraw-Hill, New York, 1980

PAGE 143

143 BIOGRAPHICAL SKETCH Yoshifumi Nozaki was born in Kochi, Japa n, in 1981. He graduate d from Tosa High School in 2000. He received his Bachelor of Scien ce in Mechanical Engineering from Utah State University in May of 2004. He entered the gradua te program at the Univ ersity of Florida in August of 2005 under Dr. Pasquale M. Sforza in th e Department of Mechanical and Aerospace Engineering to obtain his Master of Science.