UFDC Home  Search all Groups  World Studies  Federal Depository Libraries of Florida & the Caribbean  Vendor Digitized Files  Internet Archive   Help 
Material Information
Subjects
Notes
Record Information

Full Text 
iCA L q5 W:a:..An&Xt RETURN TO Dept of Aeronautical Engineering ROOM 5 ARMORY UNIVERSITY OF MINNESOTA ARR No. 4A22 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED January 1944 as Advance Restricted Report iA22 EFFECTS OF HEATCAPACITY LAG IN GAS DYNAMICS By Arthur Kantrowitz Langley Memorial Aeronautical Langley Field, Va. Laboratory WASHINGTON NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were pre viously held under a security status but are now unclassified. Some of these reports were not tech nically edited. All have been reproduced without change in order to expedite general distribution. . L 457 DOCUMENTS DEPARTMENT _ :~UIYC CLC~LI i.l;'~F~i~l~~ ~ ;;I; Digitized by Ihe Inlernel Archive in 2011 with funding from University ol Florida, George A. Smathers Libraries wiLh support from LYRASIS and the Sloan Foundation hltp: www.archive.org details effectsolhealcapOOlang iATIOI'AL ADVISORY COi;TTTrTTE FOR AERO.AUTICS ADVAIUCE R3STRLICTD R:?PORT C'FE'CTS OFP HEATCAPCITY L".C Ili CAS DYIITATCS By ,rthur Ksntrowitz The existence of energy dissipations in gas dynanics, which must be attributed to a q'r in the vibratjonsal _henn capacity of the ras has been established both theoreti cally and experimentally. The fl,',i about a very s.'all i.:,act t, be is discussed. It is shown that total;ead defect due to ,ieatcapacity lag during and after the cc'c.s ion )f tle g'as at theV nose of an impact tube are to be a.tic ipted. Lxperi ments quanti t'.Lively verifyin,, these ant.cipations in carbon dioxide : are d'.sci;use A C 2,e.;l tleo of the dissipations in a inre eiier'il lo'.' r.lrm l developed and applied to sie special c.*.ses. It is rjoirntcd out tjiat energy ,lssliat 'C 3 dcle to this e.'fct jare to be ant ci :.te, in turt', e. Diipslr ions _f ti C ;:ind night also inc~ odrce errr in cas'.s in Jhich the flo\: of rne gas is used in an al.tep)t to ir'ulate th { fli .: of another gas. UTiforturatcl'i, tue relaxa.ioi t s of t gases of EnginceriLcg i:.i. r'tance have not been studied. A ne, method of retss.rinr the relaxation tine of gas3s is intr . n ':.ch the total.radc defects cb served with a ?sec.'orili"' ha'icd .ir.pact ti'Le are co.napred with theoreLical 2'oi. ilerations. a parar.ster is t.ius evaluated in hic.i the only ,ir.'rn'\n qua:.ltit is3 the re laxatini tine of thec a?. T'.1 msthrld :.as bcee applied to carbon dio.:l de 'nd .,as ,iven c';nsist r.nt re..ults 'cr two impact tubes at a variety of gas velocities. I'TT GDJCTIOIl The heat content of gases 13 nri'arily three fcrms of molecular riechmnical enerfy. First, there is the translational kineti.c encer'y 0"' ich is tT, where I 2 is the gas constant and T is the absolute temperature. Secondld there is the rotational kinetic energy<, For all gases near or above room temperature, the n1 rota tional degrees of freed.on involving moments of inertia due to the separation of atomic neuclei have energy states cloce enough together that the rotational internal energy is close to the classical value nRT. The third prin cipal form of internal energy is the vibrvtional energy of the molecules. If the frequencies of the normal mr'..co of vibration of the rmolecule are known (say, from spectra), the vibrational heat capacity car be computed bte the Pethods of statistical t..echanics. (See, for e'arrple, reference 1.) The possibilit of dispersion and absorption of sound diau to parts of the heat capacity lagfing behind the raid temperature changes accoI.panying the propaga tion of a sound wave in a gas was first r'iscucsed theo r.tscally by Jeanr and Einsteln. Dispersion and ab sorftion in carbon dioxide obcrved by Pierce v'erc shown by Herzfeld and Rice to be attributable to laFring of the vibrational heat capacity of t.he gas. Kescer was able to account quantib t.tivl:l for dispersion and absorption in Co e.nd oxyoen on the assumption that the vibrati,nal cat capacity laged. The disper.icn and absorption of sound in several gares have been inve tiatcd and r. fairly complete bibliograp,.n is availabic in reference 2. It is found, in generral, that disp:r.ion and an:orption many times larger than thse attributable to vicozity and heart conduction are to be c:.rpected in gases with vibrational heat capacity. These cffecs t can et described by rela tions such as those rgivn biy Tnesc'r and can be attributed to the vibra.tional heat cap .rity of the gas. All the rc:asurrm,:nt.r c. dIpcrsion and abs)rption h've demonstrated that most impuritic markedly reduce thc rcla:;ati.cn timn of a 07 c; for example, Kneer and 7.nudscen (fterE.ncev 5 and 4) concluded that the adjust ment of the vibr..tional heat capacity of oxygen vas depcndent entir.l on the action of impurities. Various e:.mcrimeuts vith CO4 hv.e r.hown that, at room tempraturr', collisions with \ltcr molecule : are 500 times as effective as collisions with COmolecules in exciting; vibration in C02molecules. This strong dependence on purity has :ro.Duccd rrat discre.panlcies among the relaxation tinev neas.rreci by the various vwor:ers in this field. There ,has been much better agreement aronr the measurements of te effe': ienless." f 'im[.urities. Sonic reasurenenits in CO.G are discussed in appendix 41. I quanttunrechanical tlheory of relax.:.tion tinres developed by Landau and Teller is discuse, in appendix 3. Tvw. conclusions, which are verified b; t;.e so.i,'c work in C02, are important to the present rper: (1) All the vibra tional states 7f a single normal .,ide adjust v.'ith the same rela:atio; tile and (2) the loo.rith:n f the relaxation time (expressed in m.,lecu.ar collisions) is proportional I to 7 Verification of conclusion (i) is presented in figure 1. Dr. Vannevar 3Bu'h helped to initiate tlis cork by asking the v.riter a etimulatin.r quetiocn. The author als is very .r.ateful to Prcfes~o.r 7. Teller for helpful discussions. 7:F".C'7CS T" r2J .""..:':SC In the flw.':: f gases ato'lt obte.cl 7., conpressio.rns and rarefact iZoS. acor:panied b ter :,c.rature cha ntes occur. T7e ti.re .i '"ilc': t"esc te,!perat'ire chaines ta'e place is contrilledl b th': di,ensi ns cof the ob stacles and the velocit" of flo'w. If these tire inter vals are comparable wit' cr sn'ter a t.an tlhe time re quiredc for the Cas to ab'.orb its full heat cpcity, thie as will depart frI. its equilibri;um .iZt'...'n of energy. In this csE the transfer of ener:rv ^or.:1 parts of tl.e heat carp.acit.y; tiiat ha.v mor'e than th .eir rp.are to parts that ha"e less tan t:a .eir share :.il be an irre versible process and ,'ill in.crea e tre Ei.trop, f the ras. If the time intervals involve are comnrou.ble with the rela::ation time of the pas, this increase in entropy can be used to measure the rela::ation time of the ;s (refer ence 5). Turbinew.orkinp fluids such a stean, air, and ex haust gas have aprreciablc vi'ratinal heat capacity at hirh temperatures. If these gases have relaxation times comparable with or bshnrter.'than the intervals during which temperature chianes,. occur in th ,gas, losses .  4 sttributable to heatcar:acitr 1 v ,l.st be anticipated. A rurFh esti.iLoP 'as indic.tr:. tPat, unless the rela:a tion times of tle .'orlinr fluids acre very rhort, the losses at hi.i te.peis.tures dl to .eatcapacity lag can be conpaseble vwth the losses due to skin friction. U',fortunately, no measurement: of the relaxation tines of the u?,sial turbinev ork :. nr 'luid rs e:ist. Various persons have prcocd, in vrndtunnel tests a:l in tests of rotat:.in r,'c ..n:Per,, the substitution of ,gaes that ihave Frol'ertirs en"bliln tests to be made more cnvcn ienfltl at a riven l'ch nri..ber_ or Reynolds number tha.n with the actual vorl,:r.r luid. TI s.ich cases, care nmst be takein to er.svre t':at ar error du'. to dif ferences in heatcj ac itlaej hehavior of t:he fluid used and the vor:ir.inp fluid is rnot 'iLtro,.uced. For example, .according to a roubh calcui.at.or., a win, in pure C02 mi.'ht have a drag coefficient t"'ice as large as the same winr in air at the seae ":ach n'.:ocr and e:'nolds nu..ber. In the follow;lnr: discur'..on, the e:ristence of these dir.sinaticons in ias d:'n!'.cs '.s Jeronrtrated and a gas d :r!iaics retIho of reacirin, te rc.laation tines is develocpd. 'he appllcatio. of th.is mret.od to the meas urL.'ent of the relsa:xation tin %. of J ss of engineering importance is pr;p.:se'.. P:,O'. ABOUT A. VT'.R'' T:LL I?;:.& TJR.. As a first e::a.nle of the energy dissipations to be expected from heatcannc'.ty lag, consider the total head measured by an impact tube In a perfect gas. For defi niteness, consider the naparatus Illustrated schenatically in firs:re 2. The raQ enters t'.e c'Lnter and settles at the pressure p.1 and t!.e ter'perature T,. It then ex pands to a pressure pl and a ',prn .rrature _1 o'i.t of the faired orifice, which h .: s dez.rned t? give a temperature drop praldual enoJii.] that the ey.ansion thorough the orifice is ise tropic. Tie ,~s that flov"s alonr the axial stream line of the impact tube is then brought to rest at the nose of the tube nd, during: thi". process, its pressure rises to p2 and its tcmpc:'ature rises to T2. If this second process is sl:vr enou'r1 to be isentropic also, the en*4rory and th'e f.ervy of c'e r s that has reached equi librium at the nrose of the 'r,.'ct tube are equal to the values in the chamber and hence the pressure p, equals pO and the reading on the alcohol nmanometer is zero. Consider, however, the other extreme case in which the compression time that is, the time required for the gas to undergo the greater part of its temperature rise  at the nose of the impact tube is small compared with the time required for the gas to absorb its full heat capacity. The orif'.ce is concidercd larrc enough that, during the expansion through it, the gas maintains equilibrium. A part of the heat capacity of the gas Cvib does not follow the rise in temperature during the compression as the gas is brouji':t to rest at the nose of the inopact tube and adjusts .rrlvcrsibly after the compression is over. The resultant increase f entropy in this case r'cans that the pressure P2 is lower than pp. This increase in entropy is now crlculatcd. All temper'turo changes arc assumed small .'nc.ugh that the heat capacities of the gas can be taken ac constant., At tie bcrinning of the adjurtment, the lagilng part of the heat capacltTV cvi It still in rquilbri.un with a thermoicter at t'.h tcnperati.re n;1 '.:h1ile the transla tional and other dclrce, olf freed ;:.ri7h heat capncitics totLling c', thl;c rcla:ation timc of which h can be neg lected, are' in c.qullib'iun1 vith a the ;,rnc ter al some highe1 r impc? .ture T. 1.rcr,3 thcn flovws from the heat cap?.ci t ce o the heat capacity c,.,,I, increasin the temiperature Tvb assocf.tcd "th ev1ib fr.omI T1 to the f'.nal cquil2'rilu temecrature, "i'ich i" TO. Con.,crvation of ,.c.r'.T7 jgves the follov' ilr rolPtion between T and Tvib Cvib' vlb + cp'T = cpT3 (1) where Cp is the total heat c:.pacity at contant pres sure. The entropy increase v.'~tn an lecr.ent of energy dq flows from T to Tvib is dS dq dq d / 2 Tb ."  cvib vib ITi Tvib vLb T  6 Eliminating T in equation (2) from equation (1) and in tegrating over the whole process gives AS = vib dTvib co T + SpTo CvibTvib T og vib P v/ (3) T1 1 S vilb TO Equation (3) gives the entropy difference between the gas in the chamber and the gas at equilibrium at the nose of the impact tube. Because the energy and hence the temperature is the same at the beginning and at the end of the process, the ratio of chamber pressure to impacttube pressure can readily be computed from the perfect gas relation S = Cp log T R log p + Constant which gives AS = R log  P2 and c : Cvib Cvib To It may be instructive to derive this relation by considering the isentropic parts of the process. During the slow expansion, the enthalpy theorem (see appendix C) 1 2 gives cpT + fu = Constant (u is flow velocity) and, during the instantaneous compression, Cp'T + 1u = Constant, cvib being omitted because it tak:es no part in the com rression. Combining thle equation? gives cpTo0 TI.) Cp'(T2 T1) (5) where T2 i' the tFmpeC t,..'re re',ch1ed L"' the translational degrees of frecdorn before the adjustLr.ent period starts. The adcin tb cticcoriirssion relc.tion can be applied to both the exr"..:.ion dr.:l the comr.re:s."ion vith the appropriate heat cS.acltie; to calculate p2; thus, E FR 1) \1/ lT Comlbining eqigtinotl (E) and (f') gI es, after several mani;:ulci l io.ns c. i, 7 which 1s of cour'e ientical with cu'J1: ). S. ,P.2 The percentage 'otslhesad defect 10' is ''0 "1 plotted against ceimner pressure c,'. in f ureu 5 for Cp' = 3.5R. The p arEatus scher;ati Led in f.rure 2 v", used to chtmc. equation (4) for CC verc. tie vibra tional Ieat car:.acit wjould be expcted to Ir rhe orifice was a hole in a inch plate with its dia;meter variation desir:;ed f.r constant tir,e ;ate of t e.;pcrat'ire drop. The last 1/16 ir:ch of' the flot passage w.s straight in order that the strea.lirLes in the jet would be straight and axial and I.ence the static pressure at the orifice exit would equal at:o.spheric. pressure. The glass impact tube wa3? O.C00 inch in diareter and its end N ~ 8 were between 300 and 600 fe t per second. The expansion therefore took place in times ranging between 1.4 x 104 and 2.8 x 10 second. The compression at the nose of an impact tube takes place while the gas flows a distance of the order of 1 tube radius. (See fig. 5.) The com pression times then ranged between 7 x 107 and 14 x 10" second. Commercial CO2 was used and, be cause it was fairly dry, a relaxation time of the order of C05 second was expected.. It seomed likely, therefore, that thick setup would approach the case of an isentropic expansion and an instantaneous compression closely enough for the results to bear at least a qualitative resemblance to equation (4). Preliminary to the investigation of heatcapacity las., it was necessary to iake sure that hydrodynamic effects other than heatcapacity lag would not produce a reading on the alcohol manometer. Air and later nitrogen ail room temperature were therefore substituted for CO2 at the beginning of each run. It was always found in these preliminary tests that, v.hen the tube was properly alined, the difference in pressure measured by the alcohol manometer ,7aS vcry small and could be accounted for entirely ty lags in the small vibrational heat capacity of eir (at'rit 0.02P). Carbon dio .ide w.prs then introduced into the apparatus and t.he observations chown in fiure 4 vcrc. made. The ras. was heated before cr.toring the chamber, and its ten~pc.raturo vas measured by n small thermocouple inserted in the jet close to the impact tube. In accordance with acrodynamic experience, the temperature measured by the thermoccuple was cr.s!sicd to be 0.9TO + O.1T1. The dif ference betvw'en Tr and T1 was" always less than 300 F, corresponding to a difference in Cvib of less than 8 percent, and v;wc. thus considered accurate enough to assu:ie a constant cvi and to compute this value at a T + temperature T L The pressure pO p, was read by the mercury manoneter, pl, by a barom;cter, and pO P2 by the alcohol manometer, which was fitted with a microscope to make possible readings to 0.001 inch, In figure 4 the reading of the alcohol manometer is plotted against the chamber pressure PO/p,. The ex perimental values at both temperatures agree with the theoretical values more closely than could have been anticipated. It will become clear later that the theo retical and experiri:nrtal values agreed soo clo.cly because smrn]l entropy increases in the oriffice, attributahle to toorap'id e:p.nrsion, just about compensated for tbc fact t'at the ccToprecssionr was not anite Instantaneous compared w'th the relao.:atin time of thbo pac. It should be pointed out that ordinary h;rdrodyncamic c 'ffcts such as inldalinemnent of the impact tube v'r.nld bc expected to pro duce a totalhead defect ,.hich would vary directly as Pn  1 . 1 G7i;ER.AL TI71,T7 o w7 i!C DISCFTTIOIIS. IN GASES EhIFITTIG HEr CAPAC. LAG In the general case in ',nhich the temperature changes nay be neither t verve, i. sl. ::' compared with the relaxation ir'ic of th? gas, the teir.pcrature history of a gas particle a: it floeves alon] strea.mline n'ust be con sidered. The problc,! ~ rc greatly siinlified if the effect of hcatcapacity lag on vclocity dilsributi'on is neglected in order to .*:et the cffcct of the 1,. on energy dissipation. This *;rocicLurc cin be recardo.1 aj the first step in an iteration procers "nd is .robahly aice quate for tlie applications no'v c .nt !nrlatc. 'Th re striction t1lrt the tc.r;crat,.re changes involv:rd :'.n the flo" are sr'all Lemu1.: for ti.c '.acnt capacitiec to bc con sidered constant is also retaiicd. Assume, therefore, that t;,. velocity distribution in the field of floi is dctcrmincd by standard gasdynamics nrethods. Tlio velocity distribution is usually given as a function of space cocrdinrtcs u(x,:y,z) or along the ':trc '.r'.lire s s(i) '. re s is the distance along the r:trcanlinrc. Ths cxprc ssion can be converted to a function of ti;. v n ,(t) b: integration of dt = d uT 7T 10 along a streamline. The function ua(t) is taken for granted and the entropy increase in the flow along a streamline is determined, Ly introducing the variable c, which represents the excess energy penr unit mass in the lagging heat capacity over the energy at equilibrium partition at the translational temperature T, it is seen that 1 o c T + u + E= Constant (7) P 2 The assaunption is now introduced that there is only one type of heat energy in the gas Evib which lags appreciably behind the translation temperature and that its time rate of adjustment is proportional to its de parture from equ.iibri'u.i; that is, Svib= I, E dt This asi'mptlon is in areement w.th the sonic theories previor.sly dircuss~d, From the definition of , C E~ c T vib vib because cvibTvib is t.e eCvil.l.bViun valve of Evib measurede d from an arbitrary zero). By combining these eqi.ations, Evib can be eliminated to yield dc c dT dt vib dt k The meaning of 1: carn be made clear if the variation of e ,with time is e::ar.icd for the case in which the total heat energy of the gas remains constant. In this case, c T + C = Constant P Equation (8) then becomes at c P or L.t T ' from '.'.ich I, is the reciprocal of the relaxation P tie T of the gas. It will 1t' seen that these equa ti:,.s are 'restricted to gases with on.r' onne relaxation time. In orner to sirmlif7 later 'r:'re3s1n. and to clarify their phTvical meiening, there are introduced the dimrensionless variables F r~t l c = ti " ,an I ci "' / ' Cp' where h Rnrd L arc a tr'rctl len, th and a t'nical velocity in tha f'lol ard I is a dil..ensi less araneter that is a rieasiure. of t,e rat io of the t1r.ie. n r v'hi,li temperature c.:afre3 c'cur .:. the .cas to the rela:"ation ti'ie of the !as It vill be seen later that C' is de fined to r.ale It becor.e .ul'.ty .aftc E: inst.,ttaneous ex pansion "hich starts fro', rsct 'it equ .ltlbri 6 '.: er partition and ~cns %'th the ?elociY T" Lli:'.nat ig T betvecn equttioris (7) and (0) and introdicinc the non dimenioinal quanti :ies rives S+ Ec (10) ,:t' t' If u'(t') is Ikno\rn, the inte,'ral of equation (10) can be written as K I 12 IKdt' du'2 ,/Kdt' t = e t 'I e dt' + Constant (11) Th rate of entropy increase in the flow can now be calcu lated from equation (11). The rate of heat flow from the temperature Tvib to T is k.; hence, d.s = r I (12) dt \, Tvib/ Tw C = Cevib ( ib T\ and equation (12) can be written as dS /1 1 1 dt T +  \ cvib/ The entvnpy increase along the strea rlrine in question bet:ecn the startin. time t and the tirme t is ;it 1 1 AS \ d t (13) C. T + i SvO ib, In order to obtain the total entropy increase, equa tion (13) v:ould have to be ir:.regrrated over all the strea:mlincs in the flo', '~it: the uce of equation (7). Similari.t: Law for Lov:Velocity Flows The calculation of energy dissipstions can be simpli fied if the restriction to flows involving pressure and te;riprature clharnes that are small compared. w3th ambient pressure nd tcmncuratuLe is adopted. The greatest ad vantag: of third prre i :rei i that the flow pna ttern ob tained in an incofiirsc.tle fluid can b' used as ani ap proximnation. Thi_ fa.ct is important because few compres sible fluid flows are kcn:wn accurately. If this restriction is accepted, k and hence K can be assumed co',rtant for the flow. Equation (11) then becomes t duy Kt' E1 e ( dt' + Constan (14) .dt ' Now both  and variations of T are small compared cvib with T and equation (13) becomes AS = k e2 dt (15) Cvib.T2 t (15) to It is now shown that there is a simple relation among the dependencies of the energy dissipation in a lowvelocity flow on the scale of the flow, on the typical velocity, and on the rela:.tion tiie of .he rar. This relation i.s that the entropy increase, reduced to non dimensional form, depend, in ecmietrically sinmlar flovs cn a single parameter K. Equation (15) can be rewritten as c E U2 cvib 2 .. 'v vi2 \ 2 ct '' CpCvib \2t Introducing the nondimensional entropy increase A3' by dividing AS by the entropy increase followirr an "instantaneous" conp;ressicn .ilves AS' = 2K ,2 dr' (16) From equation (14), it is 1LA':'n thst e and hens AS' depends only on K for similar flo. s. Appro::irations for Large an'l :r.all Values of . The integration of equations (14) and (1.) are sometimes difficult to perfl rn analtically and laborious to evaluate nurerlcall. For the special cases in which the relaxation tine is either lonr or short compared with the times in w,:hich temperature changes ta!:e place in the gas, it is possible to use approxirimations that consider ably reduce the numerical labor. In these cases, it is possible to express AS' in terms of integral in which K 14 K does not appear under the integral sign; thus, these integral need be evaluated only once to determine AS' for all values of K for which the approximation is valid. The case of short relaxation time, when K is large, will be treated first. In order to avoid confusion, the symbol tVa is introduced into equation (14), which becomes 'a C'(t'a) = f du'2 K(t'at') e dt' dt' (17) For a large value of K, most of the contribution to this integral cones from values of t' so close to t'a that the following approximations can be made: du'2 du'2 dt' \dt'/a u12 ,a2 S a t' t'a (du,2 dut' d dt' /a and the lower limit of the integral in equation (17) be replaced by c Equation (17) then becomes u'a2 e'(t'a) = f/ 1:'+,3 exp d, u'a2) du'2 dt' )a where the sign of the lover limit is opposite that of (du'a. Hence, for K >> 1, ' a)dt 'a 2_ 2 f 2du2 AS' = Kjdt' dt Kf it, ) The case of long relaxation time, when K is small compared with 1, is now considered. In the usual flow problem, the gas velocity changes appreciably during a certain time interval say, from 0 to t'1 and then can (18) settles to e new steady. value. Te problem can be divided into two parts: 0 < t' < tI1 and t' > t'l. If I is small enough., the ch'aive in Er due to the c'terr in equation (10) is small co'.pered with'the change due to the dtterl anc can be neglected in dt' the calculation of the entrpy increase AS' during the first interval; tlhus, c' = u ,. where u'IO" is the velccity o'l.rd. at t' = . rt' AS'I = 21: % 0 r tI ' dtat = 2 : '. u ,? )2 dt' In trCder to c: r e the value : c' t t'l, the total contribution onf th . . in eq.ration (10) is added to the tot~ 1 lanhc In t:I sq:;r' cf the velocity during the first i"t.rval ui". '1 = Au'2 ': /t I. 1 T t1 e' .tt' = u' . J,i 1(u,' u'o' )dt' In the period after t' n ntCt' i) i a' tC 'C(tl and the entrcpy incrcr.:,e in this seccn,' eriod z53'2 is as 3' = 2 1t'l S ,'" 1) "t 1 (t ) The total ertro: i!:rease in th.E flo i.s ter:c.e, fcr K << 1, enice, 1'us, N ~a' 16 AS' = 2K 1 u'O u2 2 dt' + I: (u'02 u'2) dt' + Au12 Calculation of TotalHead Defect in Flow about a "SourceShaped" Impact Tube The totalhead defect to be anticipated in a com pression at the nose of an inr'act tube of a special shape is calculated to be used In the measurement of the re laxation time of gases. The restriction to lov veloci ties adopted previously is retained, chiefly to permit the use of incotrpressiblefluid theory and of the simi larity theorem. The flow about bodies of revolution in a uniform stream is usually calculated b' considering` the flow about sources in the fluid. (Comoare reference 6, p. 146.) It is possible to find a surface in the flow across which no fluid flo:s. If a solid body shaped like this surface is suoztituted for the sources, no alteration outside the surface occurs; the flov' about the solid body is thus identical with that about the sources. The flow about a single source in a uniform flow is calculated in reference 6 and the corresponding shape is plotted in figure 5. The totalhead defect to be anticipated for a tube of this shape is calcu lated as follows: The velocity along the central streamline is re quired. This velocity is given on page 147 of refer ence 6 and is plotted in figure 5 as u(x) = U1 2 16 26 17 where x distance along central streamline from source U velocity far from body d diameter of impact tube This expression can be converted to the following non dimensional forn by usinr U as the typical velocity and d as the typical dimension: u'(x') = 1 (19) The next sten is to find u'(t'). The quantity t' can be found as a function of u' tb integrating dx 1 du' dt' I =  11' (x') o .l /2 Sxu' (1 u' ) The choice of the zero of t' is arbitrary. For con venience, if t' = 0 when u' = 0.99, then 1 du' = 1eg + 2 2 1 (20) 1 i u7' i u' The next step is to determine e '(c) froi e',uLation (14). Then, by use of equation (19), du'2 /u,2 =16u'2x u')3 2 (21) dt'. : (21 Because c is zero initially (t' = c) and remains zero until u' begins to vary rapidly with tire, if ; is not too small, the lagging heat capacity can be assumed to follow the temperature changes in the gas up to the point u' = 0.99; that is, E' = 0 can be used for t' = 0. Combining this fact with equations (14) and (21) yields '(t') = eKt' 16u'2(1 u)3/2eKt dt' (22) In view of the partly transcendental nature of equa tion (20), it was necessary to integrate equation (22) numerically. Equation (20) was plotted (fig. 6) in such a way that the valued of u' corresponding to regularly spaced values of t' could be found easily. By Sirmpson's rule, E'(t') was then fcund for a series of values of K. An example of the result of such a calculation is Fiven in figure C for K = 3. The entropy increase alonr the central streamline was then found front: equation (16). Values of AS' found frcr.i inteirrating equation (22) by Simpson's rule and equation (16) with a planimeter are ;lotted in figure 7 and are given in the following table: RESULTS OF ITUIERICAL CALCULATIOIIS OF AS' FOR SOURlCESIHAPED IMPACT TUBL SC AS' nf i 10 0.1685 3 .405 2 .516 1 .676 .3 .868 .1 .952 For large and small values of K, the approximations developed earlier were used to reduce the labor of cal culations and yieldedd the result AS' = 1.743/K when K is large and AS' = 1.452K + (1 1.008K)2 when K is small. These results are plotted in figure 7; this figure thus indicates the range of applicability of these approximations. Calculation of Entropy Increase in Flow through a Nczzle of Srecial DCsign For the mnas'irc';ents of the relaxation time in COp, a nozzle is employed in which the gases expand and ac colerate before ime.tin the impact tube. This expansion cannot always bLt 'made slow enough that is, the nozzle lar.:e c louh! that t.he oxranicn through the nozzle in volves a rc;..:ll n..lJgi'e e'itropy incrsese; hcnce, the results orf ficLroe rmist be corret.'d for the entropy increasoc: in the r.,c.zzle. In order to simplify the cal culations,T the r.zz).e vwas so dc'.im.eCd that t '.ic tine rate of temeniratirture daop v.3 constC.nt. It c..n be shovrn that the entropy incre.sc ini nozale of thi design is S + 3 I! 7. whro = iKs tv:ir fi:a .!;locity attained b, th f'.. : t'c r',:1l Tt uv.t b. reen'ebercd that the ca7.L':'.L n. ?r .:: ~.e t o"nc c". umcd to be zero in t'a '..t. cn, i tio.n th? cae. only if 1. >> a,.' c , t;i cal uil....t'..i giv,. n ,re is val'd only for tLd c0. Prom the da'1in.r ons of K "nd Dh, it is soon that Kf K n hnce the tot.l entrzrpy increase AS' = 3'" + t3' can bc ex>.ressed . a fun:.tilcn of :K nalon fo given I/d. This total cntiop:' increa. is plotted in fig ure 8 against K fo r th tv.'o valn.u.: of 1/C. us';d in these cxpori..nents ai, for 7./d = . MrP.ASUTPR..E:T OF RTLAXAITICt' TI:.iE OF C02 The thcor :'ill rov ::,' e arlc l j. to n: t r aea,.reatent of the rela;::st on btir of 00. This ''.or:k Tas underlta. :n o :,i, t' test the theory and to .dc:vclop a 20 technique that would supplement the sonic methods pre v.ously used for measuring relaxation tines. The method essentially consists in expanding the gas through a knovn pressure ratio in a nozzle and compressing it again at the nose of a sourceshaped impact tube. The resultant totalhead loss is divided by the totalhead loss that would be obtained in a very slow expansion and a fast compression (equation (4)). This nondimensional totalhead loss is compared with a theoretical result such as is shown in figure and the value of K appro priate to the flo. is found. From this value of K, the relaxation time of the gas canbe easily computed if the velocity before compression and the diameter of the impact tube are know. During the compression of the gas, the temperature and pressure rise from T1 .nd p. to T2 and P2, rosectively. The relaxation time and the heat capacity of the gas thus charge along a streamline. The pro cedure previously outlined then gives an average relaxa tion tine for the flow. It is assumed Lhat this average relaxation time ic the relaxation time appropriate to conditions halfway between compressed and expanded con ditions. Because po is clp.oe to p. and T2 = T these conditions p and T can be found from PO +Pl p 2 and TO + T1 T =  2 The errors introduced in this '.tay certainly are no greater than those due to the lowvelocity assumption introduced in the theory upon which figure 8 is based. Gas The qas used in these experiments was commercial "bonedry' C02. This gas was dried by passing it through calcium chloride and then dehydrite while it 21 was at a pressure greater than 40 atmospheres. The puri fication procedure was not so thorough as methods used in some previous investigations, and it is to beexpected that somewhat shorter relaxation times would be obtained. The primary object of this vrork is to establish the self consistency of this test method rather than to obtain an accurate relaxation time for pure CO2. Apparatus The apparatus used is essentially the same as that schematized in figure 2. A longitudinal section through a chamber of the most recent design is shown in figure 9. (The chamber used in the tests discussed in the next sec tion did not incorporate the liner and the gas entered from the bottom.) The gas enters through three holes that were made small to stabilize the ras flow Into the chamber. The glass wool is necessary to remove turbu lence from the ras in the chamber and contributes materi ally toward reducing the totalhead defects obtained in gases without heatcapacity lag. It was found that totalhead defects traceable to nonuniformities in tem perature existed and could be reduced by the u.se of the lined chamber shown. The fact that the gas flows around the inner chamber before entering helps to keep the gas in the inner chamber at uniform temperature, The temperature nonuniformities can be almost elimi nated if the gas entering the outer chamber is at the same temperature as the chamber. A mechanism was used to adjust the alinement of the impact tube without moving the tip from the center of the nozzle. The impact tube must be adjustable in order that small errors in shape near the hole will not give spurious totalhead defects (in helium, for example). The gas and the chamber were heated electrically and a thermocouple inside the chamber was used to measure the gas temperature. The nozzle used had a circular cross section, was 1.6 inches long, and was designed according to the methods previously described to give a constant tine rate of du2 temperature drop; that is, = Constant for the first dt 1.5 inches, the last 0.1 inch being straight. The radius of the nozzle r is plotted against the distance along the center line x in figure 10. N 22 Two impact tubes with diameters 0.0299 inch and 0.0177 inch were used in these experiments. They were made by drawing out glass tubing until a piece of ap propriate diameter and hole was obtained. The hole was kept larger than about 0.004 inch and the fine section not too long (=1/4 in.) to prevent the response of the alcohol manometer from being too sluggish. The ends of the tubes were ground to a source sb&pe (fig. 5) on a fine stone. During the grinding process, a silhouette of the tube was cast on the screen of a projecting micro scope and the contour superimposed on a sourceshaped curve. By this technique the contour could be ground to the source shape within 0.0005 inch, except for the hole, in a short time. Tests and Computations The totalhead defect in CO2 was measured with the two impact tubes over a range of chamber pressures. The consistency of relaxation times obtained at various pres sure ratios and vith various impact tubes serves as a check on this method of measuring relaxation tine and on the theory on which the method is based. Before each series of measurements nitrogen, which has only a negligible vibrational heat content at room temperature, was run through the chamber to be sure that no spurious effects and leaks were present. In the re sults reported herein, the errors due to these effects were lept to less than 0.01 percent of the chamber pres sure; therefore, the resultant error in relaxation time due to these causes was less than 4 percent. In sub sequent work (not reported herein), it was found that most of these totalhead aberrations could be eliminated by ensuring uniform temperature in the issuing gases. If care is taken to eliminate ter rature nonuniformities, tube misalinements, and turbulence in the chamber, the totalhead aberrations can be reduced to 0.002 percent or less. The totalhead defects obtained were divided by the result of equation (4) to reduce them to nondimensional form. The appropriate value of K was found by refer ring to the appropriate curve in figure 8. The gas velocity was computed from the reading of the mercury manometer by the enthalpy theorem with adiabatic expansion assumed. The relaxation time was then computed from the definition of K by equation (9). The relaxation times thus obtained were expressed in collisions per molecule. The number of molecular collisions per second in C02 was assumed to be 8.888 x 190 at 150 C and 1 atmosphere by combining tables of pages 26 and 149 oV reference 7. At all other temperatures and pressures, the number of collisions was assumed to vary inversely with VT and directly with pressure. The number of molecular colli sions per second and the heat capacity of the gas were computed at temperature T and pressure p. The data obtained are given in tables I and II for the 3.0299 and 0.0177inch tubes, respectively. The result. are plotted in figure 11, which indi cates that the relaxation time in collisions is nearly independent of pressure ratio and impacttube size. This consistency constitutes the desired verification of this test method. It was expected that a variation at high pressure ratios would appear in view of the assumption of low velocity made at several points in the theoretical development. A large part of the scatter of the results in fig ure 11, in particular the apparent drop at low pressures, is attributed to the fact that in the tests the average temperature (halfway between chamber end expanded tem peratures) was not held constant during the run. The average number of collisions obtained with the 0.0299inch tube was 33,100; with the C.0177inch tube, 32,000. The final result at 1050 F thus is 32,C00, which is somewhat lower than the result of recent inves tigations in which the CO2 has been mum. more carefully purified than in the present investigation. (Compare with fig. 1.) IMPACTTUBE METHOD OF MNASURITNG RELAXATIONT TIr; OF GaSES The impacttube method of measuring the relaxation time of gases rests essentially on the fact that the totalhead defect not traceable to heatcapacity lag can be reduced to a very small value say, 0.002 percent. Very small dissipations due to heatcapacity lag are therefore measurable. For example, a gas having a ' 24 lagging heat capacity 0.1 with a relaxation time of 10" second could give a totalhead defect of 0.05 percent. If the gas had a lagging heat .capacity as large as R, a relaxation time as short as 108 second would be meas urable. This method seems to be easier to carry out than the sonic methods previously discussed and can be used to measure relaxation times vjjth comparable precision. The quantity of gas required to make a measurement will be larger than for the sonic methods (a standard tank of C02 lasts about 5 hr in this apparatus) and thus may make it more difficult to attain high purity. If the gas to be studied has a long relaxation time  greater than 50 microseconds, for example it should be possible to measure the relaxation time in an apparatus similar to the one discussed by comparing the totalhead defects obtained with a calculation of the entropy in crease in the nozzle. In this case, the time taken for the gas to flow through the nozzle is compared with the relaxation time of the gas. The shape of the impact tube would be uniiinportant in this case as long as it was small enough that K << 1. CONCLUSIONS The existence of energy dissipations in gas dynamics, which must be attributed to a lag in the vibrational heat capacity of the gas, has been established both theoreti cally and experimentally. An approximate method of calculating the entropy in crease in a general flov problem has been developed. The special case in which a gas at rest expands out of a specially shaped nozzle and is compressed at the nose of a sourceshaped impact tube near the mouth of the nozzle has been treated, and the dependence of the resultant totalhead defect on the relaxation time of the gas has been found. The totalhead defect in this flow has been applied to measure the relaxation time of CO2. The results obtained with two impact tubes were in agreement within 25 about 3 percent. The consistency of these results is regarded as a check on the general theory developed and on this measurement method. Langley Memorial Aeronautical Laboratory, National Advisory Committee for Aeronautics, L~:.irley Field, Va. N. 26 AP1PECDIX A SOINIC ESTTRE.miTS I: R CARB~O DIO):ID Much careful work has been done on the lag in the vibrational heat capacity of CC2. Carbon dioxide is a linear molecule and thus has a translational and rota ticnal heat capacity of R. It has four norn.ial modes in vibration that are dieararnTed :with their frequencies as follows (data from reference 8): 09 C *0 v1 = 4.164 x 1013 0 0 U2 = 2.003 x 1013 2 modes 0 C) 0 U = 7.050 x 1013 The heat capacity of CO2 iF sormewih1at complicated by the fact that the second excited state of the oscil lation '2 has alrrost the sLrme energy as the first excited state of ul The near resonance results in a strong interaction through the firstord.er perturbation (the firstorder departure of the potential energy from the square law) between the two states involved, as was pointed out ~',:y 7err.i (reference 9). This perturbation produces significant disturbances (=0 cm1) of the levels involved but does not have a large effect on the heat capacity of the gas. The heat capacity of CO2 was computed by Kassel (reference 10) and his results are used in the present calculations. F'ucken and his cov'orlkers have carefully studied over a period of years the dispersion of sound in C02 (references 11 to 15). One conclusion of this work  that the vibrational energy levels in CO2 adjust with the same relaxation tire is demonstrated by showing that the dispersion curves obtained fit a simple dispersion formula suc' as 1neser's. KuiChler. for e::arple, obtained a simple dispersion curve at 410 C, at which appreciable heat capacity due to all three normal .iodes would be expected. Richards and Reid (reference 16) and others (see bibliography of reference 2) have maintained that the symmetrical valence vibration vu of CO de? not adjust at 9 kilocycles in some dirpersion nee.sure:;ens r3de near :ocm tewrnrcre tivre. As they pcint out, this fact I. re,..akable be cauc tihe second excitcted .ttee cf u2, strongly perturbs the first crcitcc state , U1. In any c.se, the con trihu.tion of thi!s nor:ml n;oce to th heat capacity is vert rc.l. at r:,oii. tLuirerarure and the eff'ects found are neasi tihe lli.'. .f tuie accu~a,:; of .Richards and :eid. The relaxation tire of CO in rrolecular collisions, as J.veri by E.l:en .n h.'. cc'vrkers, is nobttcd against T 3 (T In 0K) in fl.rrc 1 for co.iarizon with the theory dirrursed in aupendi:. 1. Vani Itterleek, de Eruyn, arnd Mari r.n (rcfereence IT) 'measurep' the a' bsnrptSon at 590 kilo cyclee in very car.: f t. T lpr'i 'led C02. heir measure ment., ..'ich are aln l.en iln fi_.urc 1, hov: a longer re laxation tim th.ai .1. .c s.'rc.c ta of :"'.clir n and hi coworkers. Fy al .. ,t t'j'. incres'es. releaation time to careful po'v. fic.o n of i.'. a.:. All the riac..," ,' i h CO ; :ave indicated that the rol.xati3r' :" .: i ..cr.ely ri'opc& iortl to the pr r.. e ..of : ,: 1. t F n' er :T.: the process rosl lir: n'.' i c :r L:'. r'a.rcb .;C.rc .o *o" c '.ner t.tV:ecn vibra tional a.d ot.'.er d1.r. : forced. is bi'lecular. APFE:?DTX B TTEC2Y OF EX:CITATTIO 0P O OLECUTLA2 VIEtATION EY COLLISIONS LTarda:u and Teller (reference 1:) have riven an ap pro;xiaste calculation of the probability of the excita tion of a vibratior.al quantmini in a molecular collision. Arsur:iinr that the interaction nr.rr v.'hich induces the vibration dr. rendu lirn.arl: en the l' ori.al tcrdinate of a ina:r'o;nc vibration, tay:: n.sl:e a firstorder perturba tin.... eultt ion. The iatri.L 'clreent for the transi tijon from the lth to the (Z + 1)th or from the (Z + i)th tc te i Ith vibratli.Oal !..tte ic then pro portional to V/7 +1. The trarltil1rn robabilities k "i cre pro.oprvttional to the a v.aro of matrix elements anrd th: before I1' 12 lO:k,?1'32 = 1.:2:3 and, when i j A 1, :, 0. nThs result is shown "J i i referc..ice 1 t?. t . to te credlietion that all the &alloved tra,iti :n in a rive.. .' .1 mode have the same ar .a: io i l..rn a' a'nd ellcr ne:: examine the c ol is .n p rr.c s r.I c.r calrI, a :, tr7.n7 the interaction energy oet we' :. ra:l.::':iLn ir3d vi:,,ation to be prrpor L"ic'n. l o i whcre tIhe .f stance between the i" rl cul'c ainw.1 a i" an r.nd:. tcr::.inE.'i c..t ant. They al2 o ti..'i.u.;? ,t t t'. a:sl:: ti lonnl cner:. of the mole cucs tl ;. is, the co lisle, i' 1 idiabatic. The 'moic.unt of cncr"'' trans.'c.rd t.. ibra'tor. In a collision ?. then calci ]atr'.. on .1 d to :stir..a ..C che tians..tion lr'babi' t : anid I!.L 'lexatlon tre oi thc gas. _11 r; Thley concllide t'hat ti.:. ;c;rr:.:rt'bw variation 0O thc rc Colli. ions = ex') 7T where "I in molecular v.wirht. Tn : .re 1., exp'ri:.intal results for the relaxation tinre .:,1 collins o CC :1Vn? nitrous oxide 1I20 are 1 plotted against T T. The theoretical results are seen to be straight lines, within e::perimental error. The value of a can be found from the slope of the straight line. For C02 with u = 2.003 x 1013 a=0.22 x 10 cm and, for N20 with u = 1.773 x 1013, a= 0.36 x 10 cam. These reasonable values for a are a further check on this theory. It should be pointed out that the temperature varia tion of catalytic effects is Quite different from that of pure gases, the number of collisions required being nearly independent of temperature. (See Ku"bler, reference 15.) Various attempts have been made to associate the effective ness of catalysts with their Fhysical or chemical proper ties but no generally successful rule sefrs to have been proposed. Gases that have or.e chemical affinity, gases with large dipole moments, and gases with snall moments of inertia are usually rost effect ive.  ' 30 APPEIIJTX C THE EITHTALFY THEOREM If no energy is transmitted across the walls of a stream tube, the total energy (Internal energy E plus Kinetic energy per unit rma"z u 1 plue the work done by prezs.sres pV mist be the same at any cross section of the tube; that is, 2 E + + pV = Constant (C1) In the case of a perfect ims vith constant heat capacity and with 'cq1.illbriuml partition of ?nergy, equation (Cl) Lec ...:es c..T + u = Constarnt (C2) where cp is the heat capacity at constant pressure and T is the absolute Ltc.,,rrature. ,Whenever equilibrium partition exists, even though ronequiblibrium states have been passed through, equation (Cl) is aplicable in the absence of vl c..:s. 3aj,.; heat c..ndIction and equation (C2) can be at. lir;..i. t .c rif :'.t gases., provided the heat capacity of the gan ca. 1e considered' constant. REFERENCES 1. Fo.lrer, R. H., and Ouggenheim, F. A.: Statistical Thernodynaric The T'acmillsn Co., 1939. 2. Richard..:, V.ll am T.: Super.rnic PeIFnn'ena. Rev. 'Todern Ph:s., vol. 11, no. 1, .Jar. 1339, Tv. 3614. 3. :Inerer, I. C." Interpretation cf Anomalous Tound Absorption 1.n .ir and Oxygen in Terms cf ':olec.lar Collision". J.ur. Acous. 3oc. ri., vol. 5, no. 2, Oct. 1933, p.r. 122120. 4. Knudse.n, Vern C.: The Absorption of Sound In Air, in Cyv' env, and in TU'trogern E'ffect: of I;u.mirlitt, and 'CmcreI:el'r.tute. Jorir. Acous. Soc. Ar., vDl. 5, ni. 2, Oct. .1v, p. e,21,". 5. Kantro'vitz, Arthur: Fffects of Heat Canccit: T,a in Ca.s DyTn.aic Let. tm Td., Jou:. Cher. P)r'., vol. 1", n 2. 2, PIet. 142, i.. 1 . 6. Tietjens, 0. G.: ThGunda r!.ntl.s of ':yd i and Aerone chan ic. 'T"coral,4.ilol .'1. Co., ITc., 11954. 7. I"enrar'rd, Fanle I : Kin ti. The:.rc:, of ace c.cravr 11ill Fe'ok Co., Inc., 1238. E. Deinnison, David '.. The 'ibr'.tionJ..l Levels of Linecr i t .r trical 'rlo.to:ric 'ole o le Pr R.v., vil. 1'I, ::.. .3, e s t ., t. ,. 1, 1 v '', pp. 0 i' 12o. 9. Fcrrni, T.: a nls'. Effect in CCr. Ze.Itchr. ?. Phys., vol. ',], o. arnd 4, Aur. 15, 1931, Fp. C', ;;C 9. 10. jassol, r.. '.? T. 'ermoi :ra;n.~ .r Fruntion of :;itrous Oxide :nd Carbon Dioido. Jou... Am. Chet. Soc., vol. ,C, no. 9, Sept. 19,., ;p. 183C184:2. 11. Eu:len, A., and Bcl:er, P.: citcition of intra'.olec u]Lar l'ibrations in Gases al.d "ar: Mixtures ihy Coll].sioZ1 'oCed on :"ea.sre:!m. nt. of Sound Disper sion. Pe.li:.,'ra:; C'nLu..nhati,?.. 2c tschr. f. p'." Ch'..., Abt. ', vrl. 20, no. 5/6, April 1933, pc. 4: 7 , 12. Eucken, A., and Becker, R.: Excitation of Intra rmolecular Vibrations in Sases and Gas ?ii.;tures by %oliioens, 7ased on :easlurements of Sound Dislerision. Part TI. Ze.itccnr. f. phys. Chem., .:,. F, :ni. 27, njs. 3 and 4, Dec. 1934, pp. 5:"i:2. 13. Eucko, '., and Jancks, H.: Exr.itati.n of Tntra r'e '.a 'ibralions in Gases and GOs .1Mitures bt .'.1. lens, ,asod on :easurements of sound S:~~ si.. 3t T7. ZLetschr. f. phva. Chen., ..' 'l. 530, no". 2 aiid 3, Oct. 1935, pp. 14. r"ck, ,/'.., .ard Irann, E.: Excitation of Tntra inCoiuila VioaL.'ions in jases and Gas Mixtures 'yy ".:. _.n. Part TV. Leitschr. f. phys. Ch, ,. t. vol. c, no. 3, July 1937, pp. l..,] .:,5. 15. ::ichler, .. t of TI tr:tLr'olocular Vibra tio:ns :i '.:seze and Gas .i:.:turev: by Collisions. F ,: V. z t. L.r. .f rc..v Cl'rF At 3, vol. 41, no. Z, C.t. 193%, pp. 1.'214. 16. P.ichardr, ,1 Re.d, J. A.: Acoistical St'.'ile. Part :i. II Rat.e of' Txc .tvtion of Vi,'at .c:al 'rer.Tr' in 1 C~, and SOs.Jour. :. . ., r.l. 2, no. , ,nril i....4, pp. 193 *.'.. ?:.'t l.1 .o.n E' Il' c. ll ie 3 of Vari oi "i .e 'ci 'inr t'e TLer Vibrational tctes .'.. cn".. .::nI ati. n of Fotat onal Encr ;,' 1 "r', c _ J.T '1 E.'' P:;ys.., vol. 2, uin 4, n.'l 1 2.T', pF. 27,e21?.. 17. v:an tter .rc.', .., de :ru:n, 2., an,' Mari6ns, P.: '".s .,.. .t t:. e ?.bs.:'rti.on of '.i.ud in COT ara nr". Iso in 'ixt:.i: of C a . Ph,sia, voIl. ., I'. 6, Juno 1.3 J, pF. &11518. 18. Lan, dqn.: Tel 1.e .: Thlcory of ound Dis ..i..Oi. y.:. l.eitsjb.r. der Sowjetunion, vol. 1.0, no. 1, 19'23, pp. 344, 0J CO u 0 r0 0 02 0 %ro OOO(D00000000000000000 wHH OOOOOOOOOOOOOOO o lEr 00 O ~ 00 HOC )0000000000 H rI ) 3% k f ft t ft t ft f t ft ft ft ft rI C.) i tL O '^ 4 LO CO)F Cto I ; tO o, U 4 t)N U PR ) t tototor t to to to to to to S0 C) H to mwtUon QLtoLaQ 4 VI Or H OHOH LOO torHto 0 0 N N1 DO 4,tIE toto L O D 1C4, (D .r'.), 0 3 0C Cd 1 C2m O 0 a C 0 0 0 0 0 cri ca Ca H 0 0 GO O OWo rl oOrOO Orfljc ..  i.* * M IO'HrOl DlHHHHHI r HHHrIrIMrI 03kv H3 1o 't C. O u0 D r c O D ( rq t0 LO F) il O wLO C' tO 4t3 Of) ri 0 tri di) c to DOtoN to (.D (Do Dto 0 4 00 *O E > ;i 0 E0 OH COtHmO4C O.) m L; LO 44 w O L Q r 0 H m ci N C1 H 0 H r N M O 0tOOi toOLMCOC;0OJOH o H CI O.0C 0)0 to IoC0 1 OCtn C L C m 0 ) 0 HN)O L .D r" A IC.U 001 .5 . C. 0) 5 ,I r0 r ,C ,4 r 4 r HHHH P J 0 I'm O4) 0 0 FO r c c< EO C,C0 tu F, e a a 0 0 e 0 6c . da) 0WtoCW0 2 C0 tos 10 L0HLm to OH I +0m *a ** *m SI H r.HJHHHHCCMC 03 l 0) 0I O OC 0 ) 0rtlo?4COOta)00 C3toLOtrtfO 3 0. 0 0H QC HN.w OtOtOa)3C0C2$OWLCO0 o03OC0 CH ) bO2 CO 1003 to 03C C) rV ,t to CO toO CM to r I" H to tO C tO ) o to ;J ,44 L O to L CO 4 0 .C 0 0 .* a a a a * P.D P . 4 1. a) 0 ft 0) 4 n\ O O ctf* ., *. .. .. 0d o ft rilrHddilrlil d llrl ft~ . ,) '"CC1 Om o H Omoo 0000000000000000000 4) <00000000000000000000 .1 , r( ] . L. 4 M a a N  0 u a I uO ti O 0 D 0 O a E I O qO CD 0 O Ot w O n c 'v 144 qv.Q C O SHO, 0 NC1 N 0 0F V lO tO n lO3 t O ti) to o I3 ) t OX 0) S II I I ,. 4.OOII 0 CO 0 0 V 0 0 CfOUrl HC ,MNiLlcOMGOO 0 (HHOlH 4lr4 Ha an 4 0 o .H H Dr L O O O rC o Q ot l m OLON Clm M LV 5o a0 C Lo" 1C (D 3 MM, O ) c Y. M.. c o.cC M M C Lm o ODnr t 1 m *D*****to *o(D*******o H UaCV I LO l 000 MOE >>t >0 ac 3r00 rD4 >C v i > _*i L tL L O C 04 0O 0 E i* I Ed 4 c H o rl M l LO ( Lc , % I Q) :: O M H 01 V C V)M tD (D D l qH 9I.4 (l) r Q4 F. O O H Q F. DI0400 a 1 v 4c ri rll 4) H H H H 1; 1: r: 9 r4 r4 1. 1: r; A >C_ Jo mcq0m. ol m0'ommooooo o H H Fu 4 0 4 3_ _ 0 0 ;4 Q r. HtjoQ0H a CH0 HH OOHHrO t . S 1 S __ 5 ; vm) Lo L to0 0HQ t LuO)too4 wr S4 O I I IC W LC tO Ol to 0) H CTWOO COW4'oCtV D iCOO H OI 4 U to 0 Ot NUOO 02T3LDO.(HU)OJ fK) OC)JOo JH Ov d .) C e. C a S a a S S S S a * 0 H H H HH HH HHH O O H E E 0 4> tCtOC COOJC'(O 0InutLOCLOF.M4? L .0 0 *** FIG. I LOOx10 C 02 O Present Investip ton  [ van Itterbeek, de Druyn, r  and Marlens (rEference 17)  A Richards and Reid (reference b)  N Eucken and coworkerr  (rFferences 11 to 15)  2 0 r0 2 0 Eucken and Jasck :  (reference 13)   1    + .11 0 S        .10 .11 .12 .15 .15 .16 .1 4_ T1 K1  . . . . ' := ... t.tt .i, ' ..10 .11 .12 .15 .4 i6 . 7 tt 7 TIL,(OYF 3 7i" ..  ____ : : __ ~. ~ ' 7 jii77F7V:Prk#1 Ple'ure 1 . Measur nents of r rlaxr i.:r time of CO2 and J20. . I . I . L .. L S 'r; j r r i 1_ NACA 'as supply Fig. 2 Mercury manometer Flpure 2 . Schematized experimental arranoement. 1.3 Chamber pressure, Plaure 3. Theoretcal. totalhead aefect in percent of dynamic for an instantaneous compression. (Linear molecules, cp'  essure ! 5.5R). P 4; " ::: fi;: NACA 10 r Fi '.4 9 1 1 I ___ I __/ 0 ExperITinntil values, 113' F P 0 Experimen~r l vIaluE, 2,1F P The3rTet tcs 'n .i s, e.lur;c'in i / 7 '/ ATONAL A RY COMMITTEE FOR AERONAUTICS r 7 1 4. In anano    ATIoNAfL AOVISOvY .....CO... MMITEf. FOR AERONAUTICS i. 1.1 i.L 1.? l.L ''1 Figure 4. Instarntaneous conmpressio3r, t:.eoretlc' 1 .n exc'.i eri'e:.'.i:L. Fig. 5 T4: IT I.T.. :_1..I.~." 1~ I I 1 1 1 I I I I I i I I I I I P. j _T. "" I i r : i ' 0. I'i ' I I I I C _ i   .... 3 i y', , , .. : 7.... Iz i i iK '' _! ~ ~ ~ ~ ! _ L. ..  4  __i ,.__i __ l_ i___ I  TK Fo ! NACA C c, ,2 I r, Z T L I4 71F I I I Fig. 6 1T7 J 0. 0. Io 1 I O  /p , ,c p q4   0 _I 0, 04. p p4 .I +3 Q 0 2 r cr     , 0 0   __ 02 ~   *     .0W _  i a  o Fig.?     i  r7 I as i .* *!i : i ;  2 .E _ .. ^... .. 7 T i 'Ir ,. :  o  _^  G  S 0? 3 as . .. .... .. ,: o" 1 w J C) .. 4:: ;. : 0 i D .  oc r4 V , ii  i 1  I / ~ 4 S ... .  11 :. : '   i I i _"_ _'_ ._ " ....  _____I ___________  +I4   /      mI ^ I I I . i_ ii  '4 .:,I i. , .. i I . 1,  : I  .; ... .....  o o ii ,o [ , F~Eli4rE3~Z4EEfl ~tt41+1H~ R+ H~i~v4J:, :+4tL t Tm ii TL. i  l.n, ll, : , ti "" r__ "T N r r .~ .  r    ___I  '   p  7"    o   : ___ : 7 : __=  ; _. .: _ ___:  i_; _]= ___T _  LAi II i ii! .  r I  ~ _.    T* 1% !c FACA l~L~ 1  Lfr;  r rEr" TiT U7 EM r = .. = T. 7_ L _ ` /_L; JF r =I~ ""' '"T~ Fig. 8  E ,a c I1 ,0 0 4. a N 0 0 0 Ct ci, . Lt,4 T  i I Fig. 9 To manometer Impact tube pivots about two horizontal axes through this point / Chamber pressure tap To manometers SHeating coil  Heat insulation Figure 9 . Longitudinal section through chamber. NACA A t _Fig. 10 I I I j II I I I I I 0 I I S_ I ._ I i ; ;  1 i oI  ..... j _..._ ^ . .__i . I ^ Si 'i I ............ ...._... .. T ... .. : .. y ^ " II I I o 1Ii / ..1. " io I I I ., Ui I I/ U II I .,.II o r> a r  _ n ' ,   , ,V ._ ~o e  T  f  \ \   c. r tZL. O 'To130" SSOJO TZ:r0' 30J STLTT':h NACA Fi.. 11 li i ; i ! II I 0 t [ i  r i  .. .... ... .t .... _...   . ... ,, SI I I ___ I I i n, C" I ir I I i I o .' i," I I I I i 0 S, I I .i     S.. i I I I I i ; ..... ,I .. .. .. r  "J .. , i' I I .. I I I ,." S. .' i 'r S_. .... ,,i L, .I 3 I . I ,I I C ' I I i .' C ' I I :o I r J !I I Io i I i ;J i i, i S. .. .I ......   .. ___. .. i *. _L ... .1 1 _ ^ I I __ o L l. 0 0 ," 0 euoisn^.o' N i 1 ii i UNIVERSITY OF FLORIDA i 31262 08104 994 UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE LIBRARY RO. BOX 117011 GAINESVILLE, FL 326117011 USA .A 4 "i Si. k.;?. , :jti: 
Full Text 
xml version 1.0 encoding UTF8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchemainstance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd INGEST IEID EOA5Q1STI_G6QH4D INGEST_TIME 20120302T21:36:32Z PACKAGE AA00009410_00001 AGREEMENT_INFO ACCOUNT UF PROJECT UFDC FILES 