CALIBRATION EXPERIMENTS OF A NEW ACTIVE FAST RESPONSE HEAT FLUX SENSOR TO MEASURE TOTAL TEMPERATURE FLUCTUATIONS

Transcription

1 CALIBRATION EXPERIMENTS OF A NEW ACTIVE FAST RESPONSE HEAT FLUX SENSOR TO MEASURE TOTAL TEMPERATURE FLUCTUATIONS PART II. PRELIMINARY MEASURES FOR A PERFORMANCE OF COMPARATIVE EXPERIMENTAL AND THEORETICAL HEAT FLUX DETERMINATIONS WITH AN ALTP H. Knauss, U. Gaisbaur, and S. Wagnr IAG, Stuttgart Univrsity, Grmany D.Buntin,A.Maslov,andB.Smorodsky ITAM, Novosibirsk, Russia J. Btz FORTECH, Grmany 1. Comparativ Hat Flux Rfrnc Mthods Simultanously with hat flux masurmnts dscribd in [1] with a nw ALTP snsor [] thr additional procdurs wr usd to dtrmin th stagnation hat transfr rat and compard with on anothr for accuracy: a) Th thin film hat transfr gaug tchniqu as a ral xprimntal altrnativ. b) Th Fay & Riddll [3] corrlation. c) A computation of th complt BL dvlopmnt from th stagnation point rgion and furthr downstram around th total prob body with full BL quations. In th procdurs b) and c) th prssur distribution P (s) along th prob body contour s is ncssary as initial boundary condition for dtrmining stagnation point vlocity gradint and to dfin an outr boundary condition for BL computation rspctivly. This was found onc by taking th surfac prssur masurmnts of th corrsponding prob body from wind tunnl tsts as wll as by two Eulr cods citd latr blow.. Th Thin Film Hat Transfr Gaug Tchniqu.1. Working principl Th oprating principls for thin film hat transfr masurmnts ar dtaild in [4]. From th tim history of th prob surfac tmpratur T w th hat flux may b obtaind. It is assumd that th thin film gaug has ngligibl hat capacity i.. film tmpratur T w and substrat tmpratur T FS in th intrfac ar th sam at ach tim. Undr such simplifid supposition, th govrning quations can b solvd to giv surfac (substrat) tmpratur T w (t) and hat flux q w (t)tothsurfacas t 1 qw ( τ) t ρλ W () c dt ( τ) d τ T t = dτ 1 π ρcλ (1a) and qw () t = dτ (1b) 1 0 ( t τ) π 0 ( t τ) rspctivly and whr ( ρcλ) 1 is th thrmal product of th substrat. Intgrating by parts (1b) yilds to a form of solution () which is most convnint for data analysis whn th hat transfr rat is not constant. Th singularity in th intgral trm at t = τ can b avoidd whn th Cook-Fldrmann algorithm is usd as dscribd in [15]. Convrting th surfac tmpratur chang T W (t) to th corrsponding thin film output voltag chang E(t) by using E() t α R E0 = TW () t,whre o is th initial output voltag with balancd bridg and α R th tmpratur cofficint of th nickl film rsistanc undr corrsponding tmpratur, () rsults in (3) H. Knauss, U. Gaisbaur, S. Wagnr, J. Btz, D. Bountin, A. Maslov, and B. Smorodsky, 00 93

2 t ρλ c T () t T() t T( τ ) qw () t = + dτ 3 π t 0 ( t τ) () t ρλ c E() t 1 E() t E( τ ) qw () t = + dτ 3 R E πα 0 t 0 ( t τ) (3) and lads finally, using th Cook-Fldrmann algorithm, to th numrical xprssion q () t E( ti) E( ti 1) ( ) ( ) n ρλ c (4) W,num 1 1 αre0 π i= 1 tn ti + tn ti 1 Th pr-factor of (4) is dfind by th cofficint α R and th thrmal product (ρcλ) 1/ which hav both to b dtrmind... Th DANTEC Flush Mounting Prob (FMP) For comparativ hat flux masurmnts a DANTEC FMP 55R45 was usd. It has bn installd analogus in th cntr of th flat front sid of a corrsponding prob body lik that of th ALTP snsor (s [], Fig. 4). So, convctiv hat flux rat cofficint α is idntical for both probs and undr sam flow conditions. Th FMP was opratd by a DANTEC 56C0 tmpratur plug-in unit in a DANTEC 56C01 CTA systm with a constant currnt of I=1mA and an xcitation of U=0 1W. Th dimnsions dfining th activ ara of th snsor ar about on ordr of magnitud smallr compard to that of th actual ALTP probs as shown also in [], Fig. 4. To us this prob for hat flux masurmnts a static and dynamic calibration of th FMP had to b prformd to dtrmin th nickl thin film tmpratur cofficint of rsistanc k = ρcλ. α R and th thrmal product ( ) 1.3. Dynamic Calibration to dtrmin Figur of Mrit Du to possibl intrpntration that can occur at th intrfac btwn th thin film and th substrat th physical quantitis λ, ρ and c ar not proprtis of th (pur) bulk matrial, strictly spaking. Thrfor it is not advisabl to dtrmin th figur of mrit for an accptabl dgr of accuracy by a standard stady stat tchniqu or vn by proprty valus givn in litratur (and as writtn in Tabl of []), but by an mploymnt of a transint tchniqu. Thrfor th standard lctrical discharg calibration tchniqu proposd in [4] was applid. An lctronic dvic KIEHL 1/01 was built in th lctronic lab at IAG to raliz this dynamic tchniqu for obtaining th thrmal product. Th instrumnt allows passing a constant currnt through th gaug itslf for a short tim (about 0,1 ms) so that ohmic hating within th film producs a chang in rsistanc. A doubl lctrical discharg calibration was prformd to liminat rrors introducd by th masurmnts of film ara othrwis ncssary. Th procdur consists in masuring onc th tim rspons of th prob to th puls in air and onc immrsd in liquid. Th thrmal product was thn calculatd from th rlationship { 1} ( c ) ( c ) ( Et ) ( Et ) ρ λ = ρ λ (5) sub liq air liq To incras accuracy fiv masurmnts wr carrid out in both mdiums air and liquid and an avraging was mad to dfin a man valu. Th first 500 µs of th tim signal hav 94

3 U, V -,7 -,7 -,74 -,76 -,78 -,8 -,8 -,84 -,86 Uair Uglyc 0,034 0,034 0,0344 0,0346 0,0348 t, s Fig.1: FMP dynamic calibration: tim rspons of prob to a currnt puls in air and immrsd in glycrin. Uair and Uglyc, V -,7 -,74 -,76 -,78 -,8 -,8 -,84 -,86 Figur of mrit Uair Uglyc 0 0,005 0,01 0,015 0,0 0,05 (t-t0) 1/,s 1/ Fig. : Data plotting of Fig. 1 vrsus squar rout of tim for a linar rgrssion to dtrmin thrmal product. Fig. 3. FMP snsor: calibration diagram for α R dscription. Fig. 4. HW snsor: calibration diagram for α R dscription. bn usd for data procssing. Bcaus tim dpndncy of th figur of mrit is not linar but of squar root natur, a dtrmination of th first point from which currnt bcoms constant is vry important. Bcaus of lctronic nois it was impossibl to dtrmin this point unambiguously. Thrfor a data procssing for ach tst was prformd for diffrnt starting points and rsulting valus wr thn avragd to rciv th most likly thrmal product for this tst. Figur 1 shows th FMP rspons signal in air and liquid rspctivly and Fig. corrsponding linar rgrssions vrsus squar root of t. Th rfrnc thrmal product was dtrmind according to th proportions of th mixtur componnts and rsultd in (ρcλ) 1/ liq=109.5 J/m²Ks 1/.ForFMPitwasfound(ρcλ) 1/ sub=1600±.5% in comparison to (ρcλ) 1/ sub=1530 J/m²Ks 1/ givn in [4]. For a tmpratur cofficint dtrmination of α R a sam procdur and dvic was applid for th hot-film as wll as a hot-wir prob. Th tmpratur cofficint is rlatd to th quation R/R 0 =1+α R (T T 0 )whrr 0 is th rfrnc rsistanc assignd to th corrsponding rfrnc tmpratur T 0. It was found for th tmpratur cofficint of hot-film α R =0,0048 1/K in comparison to givn by DANTEC and for HW prob α R = (s Figs.3, 4). 95

4 3. Dtrmination of Stagnation Point Vlocity Gradint 3.1. Prsntation of Exprimntal and Thortical Surfac Prssur Distributions Th knowldg of static prssur distribution along th prob body contour (dfind in Fig. 4 of []) from th stagnation point downstram givs information about furthr flow quantitis. W can us this prssur distribution P(s)=P (s) also as an initial boundary condition for BL computations. By 1D isntropic rlations [5] w can driv Mach numbr M (s) and vlocity U (s) distributions at th BL outr dg. Th stagnation point vlocity gradint K which is important for slf-similar computations was dtrmind as K=U (s)/s. Th BL conditions at th BL outr dg ar rquird for any kind of th BL and th wall hat flux calculations as dscribd in sction IV and hav bn dtrmind for our problm in two ways: xprimntally and thortically. Exprimntal masurmnts hav bn prformd on th a prob body modl in th HMMS tunnl [] for.0 M 3.0. For M=.5 undr HMMS flow conditions, Rynolds numbr basd on D=40mm is R HMMS = For th SWK xprimnts [1], corrsponding Rynolds numbrs basd on prob body diamtr D=0 mm for stats Z1/Z has bn R SWKZ1 = and R SWKZ = rspctivly which ar clos to th HMMS valu. Th scond way to dfin P (s) was a numrical dtrmination by mans of th intgration of axisymmtrical Eulr quations undr adiabatic wall conditions with two diffrnt Eulr cods from two indpndnt rsarch groups. Cod-1: R.Fortnbach & T.Schwarzkoppf, IAG, Stuttgart, hav usd an Instationary Finit Volum Eulr Equation Solvr of fourth and scond ordr accuracy in spac and tim rspctivly on adaptiv unstructurd grids. Cod-: B.Rinartz, SFB 55 TP, Aachn, has usd th DLR FLOWr cod (vrsion 116.7); a finit volum procdur on block structurd grids and contour adaptd coordinats [6]. Most important problm is hr a prcis approximation of P (s). From xprimnt as wll as from numrical procdurs th distribution is givn in a mor or lss discrt form. Thrfor a functional curv fitting must b adaptd to th physical conditions spcially in th stagnation point. Approximation of an inviscid prssur distribution has bn don in a following mannr. From Eulr quations which govrns th inviscid flow at th BL outr dg, w hav dp = ρ U du. Intgrating this quation from th stagnation point and taking into account an incomprssibility of th low spd stagnation flow in th vicinity of s=0 w can obtain P P U t = ρt ρ, that is U ( s) = ( Pt P( s) ) t. (6) Th vlocity gradint in th vicinity of stagnation point: du dp ds = ds ρ P P s ( ( )) t t. (7) Now w must fit th scattrd P (s) with a propr function at s 0. For that w will considr P P = t Using this xpansion for (7) 6 P s = 0 = 0 and 3 Taylor sris xpansion: P ( s) P Ps s s w will obtain that ( ) 96

5 K du ds ( s 0) = = = ( s 0) P = ρ t, (8) that mans th stagnation point vlocity gradint K is proportional to th squar root of th scond drivativ of th xtrnal prssur distribution at th stagnation point. Thus w hav arrivd to a conclusion that th simpl parabolic approximation has to b usd for P (s). Practical computations hav shown that for xprimntally obtaind prssur distribution th bst corrlation of P (s) with parabola by mans of last squars mthod taks plac for th first 4 masurd points (0 s 3.5 mm) of a prob body modl dscribd in th nxt chaptr 3.. In th rang of xprimntal points No.4 to 40 (4 s 40 mm) a smoothing splin routin has bn usd to fit th data. For th two numrical data sts w hav applid th sam stratgy: parabolic fit function has bn usd for th stagnation point nighborhood and a smoothing splin fit - furthr downstram. 3. Exprimntal and Thortical Surfac Prssur Distributions A prob body of a 40 mm rfrnc diamtr was manufacturd for surfac prssur distribution masurmnts in th HMMS. An nlargmnt of th body was ncssary to incras th rsolution in th prssur distribution. Totally 40 prssur taps hav bn arrangd on a kind of a spiral lin on th body surfac to attain a spacing of nighbord prssur taps of about 0.5 mm. Such an arrangmnt compnsats systmatic rrors causd by spatial fixd irrgularitis of th tst sction flow and avoids intraction btwn succssiv prssur tap ovrflows. Evry ffort was mad in th prssur masurmnts bcaus two basic problms ar ncountrd in th xprimntal dtrmination of stagnation point vlocity gradint on blunt bodis. First th vlocity in th stagnation rgion is rlativly low, and th prssur and vlocity gradints ar low compard to thos of lss blunt shaps. Th rsult is that dtrmination of small prssur gradints at rlativly high prssur lvls is rquird, a fact which could not b ralizd in th prsnt HMMS suck-down wind tunnl. Scondly blunt modl prssur distributions ar distortd by rlativly small fr-stram flow non-uniformitis in th ara of th modl nos. Svral stps wr takn to ovrcom ths problms: modl prssurs wr rcordd by a singl prssur transducr, thrby liminating individual transducr non-linaritis and zro shifts. By mans of th Schlirn tchniqu th fr-stram in th tst sction was analyzd to find th most (narly) uniform flow without any shimmring Mach wavs (s Fig. 5). This procdur nabld tsting of th modl in svral almost disturbanc fr rgions. Furthr ffort to nullify any rmaining ffcts of fr-stram flow non-uniformitis was mad by rolling th modl about its axis to obtain data from anothr svral diffrnt plans bsids thos capturd by th 3-dim. tap arrangmnt. Data obtaind from th modl in this mannr wr thn avragd to provid th most likly prssur distribution. Extnsiv prssur masurmnts hav bn prformd and ar documntd in D. Buntin [7, 8]. Essntially hr w confin ourslvs to th most rlvant data and in particular to Machnumbr.5. But it is alrady shown in Fig. 6, whr th normalizd prssur P/Pt (stagnation prssur Pt ) vrsus normalizd surfac coordinat s/s* (s*=sonic lin) is dpictd, that thr is no grat dpndnc from th Mach numbr in th rlvant rgion around th stagnation point. This rsults ar also from data procssing, whn K-valus ar outlind as shown in Tabl 3. Mach numbr M vlocity gradint K (1/s) xp. uncrtainty % ±13 ±7 ±7 ±7 Tabl 3 97

6 P(s )/Pt 1, 1 0,8 0,6 0,4 0, 0 M= M=.5 M=.5 M= s /s * Fig. 5. Schlirn pictur of approaching HMMS flow M=,5 flow and around th prob body nos. Comparison of bow shock shap, its position and that of th sonic lin with thory (CODE-1,). P/P t P Masurd = Cod-1 Cod Expr. Fit Cod-1 Fit Cod- Fit s/d Fig. 7. Comparison of thortical and xprimntal prssur distributions in th vicinity of th stagnation point. Fig. 6. Normalizd prssur distribution along th surfac contour masurd for diffrnt Machnumbrs. It is sn that th gradints for M=.0,.5 and 3 ar approximatly th sam and clos to a man valu of K=9080 s 1. Th dviation for M=.5 couldn t bxplaind, but th diffrnc lis in th rang of xprimntal uncrtainty. Dpnding on two diffrnt kind of rgrssion functions, from th sam data st for M=.5, R=0, basd on rfrnc diamtr 40 mm, a stagnation point vlocity gradint btwn K= s 1 could b dfind. This span is about % of th avragd valu. Taking into account th half diamtr of th snsor prob body, (D=0mm), th corrsponding xprimntally found vlocity gradint is dfinitly dcidd to b K=18545 s 1 with an inhrnt xprimntal rror of ±7%. Anothr outr potntial prssur distributions hav bn gnratd by th two Eulr cods 1 (IAG) and (Aachn). In Fig. 7 a comparison of masurd and computd prssur distributions is shown along th blunt body. Th ssntial discrpancy, as shown in Fig. 7, xists in th vicinity of th stagnation point, which is th actual rgion of importanc. A dtaild analysis of ths computd and xprimntal prssur distributions by B. Smorodsky [9] rsults in K-valus, givn in Tabl 4. Also th assumd paramtrs, dfining th stagnation point condition of a typical SWK xprimnt, as dscribd in [1] ar givn in this tabl. Stat 6 R 10 P (s) from Cod-1 Cod- Exprimnt IAG Aachn Z1 Z 0,5 0,8 K-valus K-valus P L =1,3bar;T L = 95 K; T 0Z1 = 88 K; T 0Z = 74 K; T w 300K. Tabl 4 98

7 Th maximal discrpancy found in this analysis of th vlocity gradint is 1 K Cod-1 /K Exp 9% for th stady stats Z1/Z compard to corrsponding 7% with CODE-. It sms that th most rliabl prssur distribution for M=.5 is givn by CODE- (whil for M= th masurd P (s) is bttr). Whn w dfin an actual xprimntal valu of KD/U 0,677 (xmplary for SWK Z1 condition with U =576 m/s), w s that Whit [10] (Fig. 7-6, pag 517), has don for a flat nosd body a vry good stimat, assuming a valu of KD/U 0,57, whn taking into account th prsnt uncrtainty of about 9% btwn thory and xprimnt. 4. Exact Boundary Layr Computation in th Stagnation Point Lt us considr th BL past an axisymmtric modl in a comprssibl flow. W will us common notations, whr x dnots th downstram dirction (paralll to th undisturbd inviscid outr flow), s varis along th body contour lin, y is dirctd normal to th modl surfac. Th BL quations can b dducd from th full systm of quations of motion for viscous hat conducting prfct gas (Navir Stoks quations, continuity, nrgy and stat) by introducing Ls-Dorodnitsyn variabls [11]: j ( ) ( ) ( ) ( ) S su s sr sds, 0 ξ= ρ µ ρur η= ρ j y dy ξ, (9) 0 ρ whr ρ, µ and U ar dnsity, viscosity and stramwis vlocity (along th body surfac) rspctivly. Subscript dnots corrsponding valu at th BL outr dg, j=1 for th cas of axisymmtric modl, with th contour dfind by th radius r=r(x). Th BL quations can b writtn by mans of th nw variabls (9) in th following form: ρ ( ) ( ) f f Cf + ff +βη f = ξ f f ρ ξ ξ,(10) C ( 1) M 1 g f g fg C 1 f f + + f g = ξ Pr 1+ ( γ 1) M Pr ξ ξ, (11) whr th prim dnots th partial drivativ with rspct to η; γ th ratio of spcific hats, Pr Prandtl numbr, M =M (ξ) th local Mach numbr at th BL outr dg, C = ρµ ρ µ and β H = ( ξ U)( du dξ ) th prssur gradint (Hartr) paramtr. Hr nondimnsional static nthalpy g= g( ξ, η ) = h h ( ξ) and stramwis vlocity f = f ( ξ, η ) = U U ( ξ) ar introducd. Th BL quations (10,11) inourcashavtobsolvdundrthfollowingboundary conditions: f = f = 0, g = gw ( η= 0 ), f 1, g 1, ( η ), (1) that mans fixd wall tmpratur. This assumption is valid bcaus of th short tim scal ( 110 ms) of th SWK run. Outr potntial flow prssur distribution P (s) rprsntsalsoa vry important boundary condition for computations of th BL dvlopmnt on th basis of systm (10-1), bcaus th corrsponding vlocity distribution U (s) can b dducd from P (s) by mans of rlations for isntropic flow [5]. For th local hat transfr rat at th wall (nrgy pr scond pr unit ara) q w on can us q = k dt dy.hrk is th thrmal conductivity th Fourir quation for hat conduction: w [ ] w 99

8 and th drivativ dt/dy can b xprssd in trms of g ( x,0). Th lattr valu can b obtaind from th solution of th Eqs. (10,11) for th complt flowfild insid th BL, taking into account th propr boundary conditions (1). Thr is no way to obtain g at th wall dirctly and only a complt solution of th BL will provid th rsults at th wall. In th prsnt work th actual solution of BL quations has bn prformd numrically. For that purpos th systm of coupld nonlinar partial diffrntial quations (PDE) has bn intgratd as a two-point boundary-valu problm by mans of an implicit fourth ordr numrical schm. Th numrical algorithm and computr cod for BL computations usd hr ar dscribd in a mor dtail in [1]. 5. Th Mthod by Fay and Riddll as a Slf Similar Solution In th clos vicinity of a stagnation point, whr th flow can b tratd as incomprssibl (M =0), PDE (10,11) can b significantly simplifid and rducd to a st of ODE [11]. Inth nighborhood of stagnation point rlationship, (9) can b valuatd xplicitly as 4 s ρ ξ = ρ µ K, η = K y, βh = µ Hr th xtrnal flow vlocity clos to th stagnation point was approximatd as U = Ks, whr K is th vlocity gradint in th stagnation point at th xtrnal BL dg. Thn systm (10,11) taks th form: ( Cf ) + ff = 1 ( f ) g, C g + fg = Pr 0, (13) with corrsponding boundary conditions: f ( 0) = f ( 0) = 0, g( 0 ) = cptw, f ( ) = g( ) = 1. (14) Systm (13-14) was solvd numrically by Fay & Riddll [3] which hav approximatd th rsulting stagnation point wall hat flux by a following corrlation: ρ wµ w qw = B Pr ρµ K cp ( T Tw), ρµ (15) whr B=0.763 for axisymmtric blunt body with sphrical nos. Th actual valus of B wr dtrmind thortically on th basis of Nwton thory for a stagnation flow [10]. Wcans from (15) that th K valu dtrmind abov is a vry important paramtr govrning th wall hat transfr and its accurat dtrmination is ncssary for th hat flux computations. In th prsnt papr Eqs. (13,14) hav bn intgratd numrically by mans of classic fourth ordr Rung Kutta numrical schm. Shooting tchniqu and Nwton itrations wr usd for th calculations. W hav assumd that th viscosity-tmpratur rlation for (10,11) and µ = µ T = T 3 T (13) is providd by th Suthrland formula: ( ) ( ) 6. Rsults Figur 8 shows th BL dvlopmnt (BL thicknss δ(s) and displacmnt thicknss δ * (s)) and th wall hat flux q w (s) along blunt prob body surfac in normalizd coordinat s/d (D=0 mm). Computations hav bn prformd for conditions of th ral tst run No.38 in th SWK with ALTP snsor: M=.54, P L =1.31 bar, T L =9.77 K, T w =T ALTP =96.35 K. Masurd P (s) hav bn usd. Dashd lins rprsnt rsults for stady stat Z1 whil solid lins ar for Z. 100

9 Edgs of ALTP snsor (a) δ.5.0 Edgs of ALTP snsor (b) δ [mm] Body shouldr δ q w [W/cm ] s/d 0.5 Body shouldr s/d Fig. 8. Thortical BL dvlopmnt (a) and th wall hat flux (b) along blunt body surfac. In th narrow vicinity of th stagnation point (0 s/d<0.1) th prssur gradint (Hartr) paramtr of th stagnation flow β H const=0.5 and th BL thicknss δ(s) const. Furthr downstram along th body surfac, th outr inviscid flow prssur distribution dviats from th parabolic law, th BL acclration is incrasing and as a rsult th thicknss of th BL bcoms smallr (0.1<s/D<0.5, Fig. 8a). Clos to th body shouldr th footpoint of th sonic lin is situatd (s/d 0.8), and a minimal BL thicknss lads to th growth of a tmpratur gradint across th BL and as a consqunc th wall hat flux has a maximum at this point (Fig. 8b). In this xampl th ratio q w (0.8)/q w (0).5 for Z1. Thus it was found that for th prsnt blunt body in such a modrat-suprsonic-flow with small valus of driving tmpratur diffrnc (stagnation-to-th-wall) th thrmal load on th body shouldr is highr than at th stagnation point. Furthr downstram (s/d>0.3), whr th suprsonic outr potntial flow alrady xists, a fast growth of th suprsonic acclrating BL thicknss taks plac and th rsulting dcras in th wall hat flux. On can s on Fig. 8a that th BL thicknss for Z bcoms highr in comparison to Z1 bcaus of th rducd stagnation prssur P tz, whil th wall hat flux on Fig.8b bcoms highr bcaus of th incrasd driving tmpratur diffrnc. Horizontal lins at Fig. 8 rprsnt th rsults of th computations in a slf-similar approximation stablishd in (13,14). A good agrmnt of ths rsults with th data obtaind from th full BL quations (10-1) in th stagnation point rgion is obsrvd. It should b mntiond that th stimats mad on th basis of an approximat formula (15) also agr wll in th stagnation point rgion. It should b notd that paramtr B in th formula (15) dducd from our xact BL computations is always B const Of cours, th similarity solution (13,14) is unabl to prdict th radius of a constant hat flux in th stagnation point rgion (q w (s)=const for 0 s/d 0.1, that was found to b 40% of th body flat fac radius).so for our small prob body with flat fac radius of 5 mm, th siz of th snsor should not xcd ssntially 4 mm in width. It should b mphasizd that this rsult of th constant hat flux radius stimats can b obtaind only by mans of numrical intgration of full BL quations, but not in th slf-similar approximation. This justifis th prformd numrical fforts of th prsnt papr. 7. Conclusions and Aspcts Thr procdurs ar at a disposal now to prform comparativ hat flux masurmnts with th nw ALTP snsor dscribd in []. It was confirmd by th complt BL computations that th dsignd shap of th prob body, whr th snsor has bn installd, has a larg constant hat flux dnsity ara in th vicinity of th stagnation point. Thrfor a comparison b- 101

10 twnmasurdhatfluxinthstagnationpointbyfmpwithanactivaratwoordrofmagnitud smallr than th ALTP activ ara is approximatly justifid [1]. REFERENCES 1. Knauss H., Gaisbaur U., Wagnr S., Buntin D., Maslov A., Smorodsky B., Btz J. Calibration xprimnts of a nw activ fast rspons hat flux snsor to masur total tmpratur fluctuations. Part III. Hat flux dnsity dtrmination in a short duration wind tunnl // Intrn. Conf. on th Mthods of Arophys. Rsarch.: Proc. Pt III. Novosibirsk, 00. P Knauss H., Gaisbaur U., Wagnr S., Buntin D., Maslov A., Smorodsky B., Btz J. Calibration xprimnts of a nw activ fast rspons hat flux snsor to masur total tmpratur fluctuations. Part I. Introduction to th problm. // Intrn. Conf. on th Mthods of Arophys. Rsarch.: Proc. Pt. III. Novosibirsk, 00. P Fay J.A. and Riddll F.R. Thory of Stagnation Point Hat Transfr in Dissociatd Air. J. Aronaut. Sci., 1958, V. 5, P Schultz D.L. and Jons T.V. Hat Transfr Masurmnts in Short Duration Hyprsonic Facilitis. AGARDograph No Zucrow J.M, Hoffmann J.D. Gasdynamics, John Wily and Sons. WE Kroll N., Rossow C.C., Bck K. and Thil F. Th MEGA FLOW Projct Arospac Scinc Tchnology, Vol. 4, P. 3-37, Buntin D. Rport about th activitis during th first stay at th IAG, Stuttgart Univrsity, Buntin D. Rport about th activitis during th scond stay at th IAG, Stuttgart Univrsity, Smorodsky B. and Knauss H. Invstigations of Possibilitis of a Nw Activ Fast Rspons Hat Flux Snsor to Masur Total Tmpratur Fluctuations. Part II: Thortical procdur: IAG Intrim rport, Whit F.M. Viscous Fluid Flow / nd d., McGraw-Hill, Andrson J.D. jun. Hyprsonic and High-Tmpratur Gas Dynamics. McGraw-Hill Book Company, Harris J.E. and Blanchard D.K. Computr Program for Solving Laminar, Transitional, or Turbulnt Comprssibl Boundary-Layr Equations for Two-Dimnsional and Axisymmtric Flow: NASA TM