heat transfer in the vicinity of a 15” compression corner...

C.P. No. 965

MINISTRY OF TECHNOLOGY

AERONAUTICAL RESEARCH COUNCIL

CURRENT PAPERS

Heat Transfer in the Vicinity of a 15” Compression Corner at

Mach Nu n nbers from 2.5 to 4.4 DERA lnfommtton Centre No 1 BulldIng DERA Clapham Tel 01234 225099 Bedford FL% 01234225011 MK41 BAE ICE Hurry Pat

Please return lhls publcabon to the lnformabon Centre. or request a renewal, by the date last stamped below

by , C. S. Brown and Susan Atkmson

t MAJESTY’S STATIONERY OFFICE

1967

E SEVEN SHILLINGS NET

U-D-C. No. 533.6.011.6 : 536.55 : 533.6.011.5 : 532.552

C.P. No. 965' June 1966

IEAT TRANSFER 22 THE VIGEG~1Y OF A 15°COiGPRESSION CORP!!R kT I:WX EULEE3 FROX 2.5 To 4.4

by

2. C. Hastings C. S. Brown

Sdsan Atkinson

Comercxdly wallable heatmeters have been used to measure the steady- state heat transfer rates in the viclnlty of a corn-pressmn corner. Results at all l&xzh numbers are qualltatlvely si.mzlar u? that, bclk ahead. and d~wstream of the corner, tne measured heat trrmsfer rate ~'a6 laxer than expected.

In the oompress~an region clcse to the corner, the adubatlc wall tcmjxra-

lures were also low.

The measuring technique is discussed end sax potential sources cf error

are mdlcated.

* Replaces R.A.E. Technical Report No. 66171 - 4.R.C. 28406.

CONTENTS

I l3Zi?~ODlJCTICN 2 A TECKKIQUE FOR~YLEASIJRIX STEADY33AT FLOW

3 EX.FERDI~F~U'T~L~~~'US 3.1 hkdel

3.2 ikxisl cooling equlpnent 3.3 Wind tunnel

3.4 Data recordiny facllitxs

4 DESCRIPTION Oi? I'ESTS

5 DATA RZBXTION Am THEORY 6 ImYJLTS

6.1 Pressure 6.2 tieat flow at%, = 4.36

6.2.1 Region upstream of corner compression 6.2.2 Region near corner 6.2.3 Region downstream of corner compression

6.3 Effects of reducmg L'iach number ahead of corner 6.4 Effects of unsteadiness in surfact: tmperature on

heat flow

7 G%W DIsGussIoN 8 COKCJ.XSIONS Table I Positions of znstrumented stations Table2 Summary of test conditions

SpIllIdS

References Illustrations Detachable abstract cards

s 3 3 4 4

5 5 5 6

7 IO IO

10

11

11

11

12

12

13 15

16

17

18 Plgures l-14

3

1 IXTRODUCTION

Heat transfer rates have been measured 1~1 the nelghbourhocd of a 15'

compression corner. The Kach number of the flu?/ approaching the corner was varied fran 2.5 to 4.36, corresponding to aReynolds number range of 13.25 to 8.33 x d per foot.

The tests were undertaken with applications such as multi-shock mtakes In mind. The corner angle was ohosen so that it would generate a shock wave which, while fairly strong, would not separate a turbulent boundary layer.

Heat transfer rates were measured by the steady state technique doveloped by Naysmith'. The present state of this method 1s discussed 111 data11 suxe It b-ars on the conduct of the tests and the valldlty of tr,e results presented here.

2 TKXXIQIJ~ FOR i.Z3L4S~EJG STEXDY FEAT FLW

The bnsls of the method 1s that sens17;lvc heatmeters, commercially available, arc embedded, together with surface-temprature '&ermocoupLs, 111 the shn of an internally cooled model. Rate of hont flow into the skin and skin surface temperature can then be related. The arrangensnt 1s shcvn in Frg.T(a) and 3(b) is a diagram of a he&meter 2xc.

The hcatmeter discs, developed by Hatfxeld', glvc an eleotrxal signal when subJected to heat flow u a dlrectlon wnlch prxiuces a temperature &ffer-

once between theu opposite faces. ?he signal 1s generated tharmo-clectrxally at the Junctions between copper eluctrcdes and the faces of the tolluruxn-srlver disc. The hqh sznsltivlty of these metsrs compared for example with a meter

conslstmg of a constantan disc wvlth copper eleotrcdes, is due to two factors, nsmcly a tenfold rncrease 121 thermo-electric power and a decrease of the same order in thermal conductivity. The manufacturer supplles a calibration factor with each heatmeter, giving the voltage output for umt heat flow normal to the faces of the disc. This callbratlon relates to fatly small heat flms, about 0.1 CHU per sq ft per socond, at a tcin?erature cf about 15'C. ArIsing from the

tests reported here, there are some doubts about the ap$lcability of these calzbratlons to heatmetcrs mounted 117 cold models.

The thermal conductivity and thermo-electrlo po#er of a sample of

tellurium-silver alloy, about 3 inches dumeter by $ inch thick, wore measured

ln the Basic Physics Dlvlsum of thd National Physxal Laboratory under the supernslon of Dr. R.W. Powell flhose assistance LS gratefully ackna<vledgcd. The

conductivity was found to be I.9 x low4 C3U per ft second 'C nt 30'S rind

4

2.3 x lO-4 CJIU per ft second "C at -6O'C. The thermo-electric emf generated at a mnction between the sample and a copper wire chuged at a rate of 450 PV per 'C m the range -190°C to 4O'C. This sample was of course much larger than the ordinary heatmeter disc (the size was dictated by the method of measuring the

conductivity) and the material was found to be harder and more brittle than that used III the heatmeters. It is not bown what effect these differences may have

had on the thermal and electrical behaviour.

In order that heatmeters can correctly measure heat flow to the surface of

a model, the model skin should have a thermal conductivity close to that of the meters. This condition has been achieved by embedding the meters in a surface coating of epoxy resin, loaded with about 1.2 times its own weight of fine aluminium particles. The losr conductivity of this coating has the advantage that it reduces conductivity along the skin, so enabling sharp peaks in heat flow (e.g. near re-attachment in rearward-facmg step floxs') to be measured. This same property hog;ever limits heat flow into the model for a given internal

coolant temperature and it is thus desirable to keep skin thickness to a minimum. The limit on skin thickness together %;ltn the need to study non-uniform dls- tributxani of heat flow lead to a requirement for small, thin heatmeters. Such meters are currently being developed and improved methcds of calibration are

being sought*,whxh in future should cover wider ranges of heat flow and temperature. It is hoped to make calibration easier and quicker by reducing the thermal inertia inherent in calibrators based on Hatfield's criginal design2.

3 EXFERIlvlENTAL AFF'NfATUS

3.1 Model

Flg.1 shows the general arrangement of the mcdel%itii leading dimensions, while Fig.2 shows in cross-section the internal construction.

A gunmetal casting provides a manifold for the coolant, together with inlet

and outlet passages. A perforated brass plate codgers the manifold and fcrms the bottom of the coolant chamber. The top of the coolant chamber is alother brass

plate, which, on its outer surface, carries the resin skin, and the instrumentation.

Static pressure tubes were sweated to the brass plate, while heatmeters

were attaohed to it by a thin flLm of resin. With these campcnents in place the resin skin was first cast on, then worked to give a smooth, flat surface.

Thermocouples were installed as shown in F&3.3(a), and finally 0.020 inch

dismeter pressure holes were drilled through the skin into the hypaiermic tubes. * See foctnote to p. 14.

5

PressWe tubes and electrical lea& were ali t&en out spanwise without or~s&g the Ch~~ilrrl~e scntrc-lme ln crder to mlnim~se mterferer.oe nith heat transfer near this lint. The positions of the pressure orlfloes, hcat;neters and thermocouples are listed in Table 1.

The span of the model was large enough to enswe that the reglcn (at ieast outsick the boundary layer) influenced by tho tips rcmamcd several inches clear of the chord?lise centre-lme. T!IXS is indicated IJI Fig.1.

3.2 ILo& coolmp: equipmnt

The circuit diagram of the cquqmnent used for cooling the model 1s sham m Fig.& Tile equlpmcnt 1s only sllgntly dlffercnt frcm '310°C used by Naysmjth and descrioca by hm I.II Ref.5. Non-uG%unmzblc trichlorocthyicne is now used III plact, of dc0:101 3s the i.32L* 'ur~020r~ me.eli~%, nuzcssltatpg the rcplaocment of all rubber parts suoh as seals, flcs~bl~ hosts otc, by sunilar psrts made from nylon.

The tcqerature of' the clrculatmg fluid ar.3 ticrofore the mai&, 1s controlled by solzctlng the proportIon of tho t&s1 flu:: nllovwl ii 7l-n t.hrou&

tic coclm. The cooler zts~lf is slnply a toll of copper tub? umcrscd m a

tank contamug a mixture of sclLi c-bon d~oxuk. and truAloroethylcne.

3.3 3uxl tunnel

The tests were made I.II the kIqh Supersonx Speed Vlnd Tunnel atiLA.3. EdfOrd. ,Pizs 1s a closed clrcurt, contuuous flow tunnel wth a warking sectun

4 ft by j ft. At tnc tmc of the tzsts a vrocdcn nozzlx provticd a furcd Ikch number nominally q&l tc 4. Stngnatxon prcssxre can bc var~~?. ~G+XK%X 15 and

220 img.

Thx. facl1lt.y has been d.zscrlbeJ in d&all m ;iefs. 3 and 4.

3.4 Data rccordmK frlc~llti~s

Fressure tubes were lcu to the iiixlvocd' stilf-baiancmg capstile mznomcters,

vrhlch are standard anc~llar~cs to 'dx t-01. Thcsc mstrumcnts mzaswc

absolute pressures q> to 60 m;ig, with m ~CCXCL-~C;- of 50.02 inHg on digltlscd

output.

Thermocouple and hoatmcter volta, ves were mensurod by the silf-balmcmg

d.c. potentlcmcters normal$ us& 111 conJur,ctlon vuth stram-gaugs forCC

balances. For heat transfer tssts csciyl potcntlometcr has been f'lttzd 1~1th a

tiiolvc--my witch vhlch IS scanned automatically. The tvcivc posltlons are covered m aboEt 20 seconds. \?~ll,h tzn pottintuxxters available for simultaneous

6

scanning, this is the total time required to record fro12 z.ny number up to 60

measuring stations. (Each ntatlon requires a channel for a thermocouple and another for o. hcatmctcr.) Ranges of 1, 2, L+ . . . . . . 32 mllivolts are available, with an accuracy better than 4;; of full-scale.

Izformatlon frcm digitxers, fitted to '3~ nwlometsrs and potentiometers, is punoned on to cards whhlch constltutc both the data record xnd the input to an automatic computer.

4 iX%XRIFTION OF T&Sii

Because the free stream Liach number 1~1 the high-su;;ersonlc rilnd tunnel was at the time of these tests fixed ntk = 4, a range of dtiferentlk3ch numbers

upstream of the corner was obtained by pitching the mOae1. At each lkch number the model temperature was changed ~1 a serxs of st0ps alid at each constant temperatwc heat f'lcw and temperature were recorded.

At the bsgm?mg of th0 tests, befor an operating tcchnlque for the cool- lng plant had been establxhed, scme dlfr'xulty was cxpcrienced U-I maintaining constant temperatures.. This is raflecttid In thi: scatter of data crt the lcwcst Kach number, which was the first of the series. To gauge tic 33,portance of

temperature variation, so~lc data w0re cbtaxned lawr ~:~th contvlwusly vary&g tempcretwe.

Becwsc of the possib11ity of f311ux of xx model skin, 00012.ng was

limited in the first test to about IO'C b&x recovery tc;~~xrnture. In subsc- qucnt tests the mod01 was cooled progrcssivcly further, fwally reaching about

30°C below recovery (i.e. about -lO°C).

The mnximua rat0 of heat trzns?,-r did not, howcvcr, chang0 very much from one test to another, and was of the ordsr of 0.1 CkN per square foot per second.

Test condition s xe sarxkscd in Table 2, which also gives the approxi- mate total pronsures above :ihich no boundary layycr zcpamtxn on tho model was

visible on the schlxren screen.

All data were obtained at a tot-1 >ressurc of 220 tiig s.nd n total

tsr.pcraturc of &O°C as measured III the tuxncl settling chardbcr.

.Phe specific hmidity of MC alrstrczn was bctwoen I:+0 .-sld 200 parts per million by weight. The rcfcrence Jun5tlcn.s of the thamocouples were maintarned

at 50°C 111 a tcqerature controlled water bath.

7

5 DATA RZDUCTIO~ AN'2 THEORY

In rcduc~n.g the heat flew and tcmwrature results, &vantagge has been taken of the capacity of autcxnntw cmqutmg in m&r to runowz sme sources of error. The cm&or ~jrogrsmme allows non-linear callbratums for both thernc- couples and hcatmetws to bo used and ensures that both heat flow and tenpora- ture at cwh ah pcmt, iirc ncn-clunensumallscd iv1t.h the ala of tdd pcsmrc and tmperaturc measured at the xme tune.

At tInis stage of the prowess, the data are a~allabl~ as:-

z = ha , a non-duansloml tmpcratwe

nhcre Q = heat transfm rate per unit area

P = a~ aznslty u = an velocity T = o.2.r static temperature

T w = model surface tel?perntLrc c p = spcclfic h03t of au at constant presswe

ana suffix a dcnotcs a rcfmenoe flew ccnditmn usca m forming non-cimensicnal varubles.

Tha reference oondltion, whhlch must be oonstmt, is computed autcmatlc~Ltly fran free stream total pressure and total tompcrature, lr rcfcrcncc I;ach nurAbc:r and the ratio of free strear? total prossure to total ?rossurc at the rzfcrcncc state, ar~ suppha t0 the ccqd5 The data, 2.n this form, can bc plotted nachanxally

as gra_nhs of ?T versus z for each ncas~rmg statlon.

Tne final results a?~ cbtamca fran a stialght lmc, fitted by the "lcast- SqUard m&h, to the K md T data. Firstly the slope of the lxx, and the value of z at 7i = 0; L.C. ccro heat tranof2r, arc found. I"rcm these, Stanton

number an& rccovmy factor corrcnpondmg to thu reference Lnch n&cr Ii,, are c~pda.

By defimtmn:- Q = pucp ST@

r -TV) ,

lf T = r

reccvcry tcmperatu?x (tenpc'"~Llr" at zero heat transfer)

and s T = Stantoll nwxxz .

8

Hence, if Q is linearly related to T,,

so that

if

sL= aT -put s

w PT'

The recovery factor, r, is defined by:-

Ls!p= 1 ( > 2 1+=--I-M , 2

so that (da = [b)& - 11 (y -'I) hi: *

The ccanputer output consists of (ST). and (r)a for each measuring statmn along

the model, together with values of (T)a and "unit" Reynolds number [?)a

averaged over all the data points making up a complete run.

Figs.5 and 6 show the linearity of the heat flow versus temperature rela-

tlons measured in the tests. The examples have been chosen to cover the whole

test Each number range, and various flow oonditxns along the chord of the model. For the transitional boundary layer, Flg..5(a), there is a slight suggestion of non-lmearlty. The paucity and poor quality of the data J.II F~y.6(n), arise frcm

their having been obtained from the first run (see section 4).

Stanton numbers were estimated by an ~termediate temperature EletnOd, for the folkwing conditions:-

(a) Ahead of the corner I

(i) The laminar boundary layer on en ideal flat plate with a thin, sharp leading edge.

(il) The flat plate turbulent bxndary layer, with effective origxn at the leading edge.

(b) Aft of the corner

The flat plate turbulent boundary layer approprxate to the Xach number and unit Reynolds number downstream of the unglt?, oblique shock wave; the manentum thlc'kness umwxllately behind the shock was calculated front the momentum thickness of (a)(li) above at the corner, allcwancc bang made fm the pressure jump at the shock wave.

Same the surface terr.peratures in the tests were never far from recovery

temi)erature, estunates were made only for recovery surface temperatures. The formulae used m the estimates were those recanmended in Ref.7. The specific heat of au? was assumed constant. For both 1amux.r and turbulent flow, the intermediate temperature (TX) YIBS taken as:-

4 1. = Ts + Od(T,, - TF?) + 0.22(Tr - Te) ,

TX = Te + 0.72(T r - Tc) ;

1.e.

with ii e = ZIach nwber just outside the boundary layer.

The recovery factor, r, 1s given by:-

1' = (E$ ,

for 1aana.r layers, l?: being the Frandtl number at temperature TX; and

r = 0.89

for turbulent layers.

Reynolds analogy factors between Stanton numbers (ST) and skin frlctlon cooffzcxnts (of) were assumed, giving final farmulac, for an isothermal wail:-

10

-Z/J ST = 0.332 < 0 for laminar flow ,

sT = 0.288 x 0.61 @-10g,~ (kx 2 s)] -2'45 for turbulent flow . TXL \TuX

In these formulae, Rx is the Reynolds number fcrmed frcm fluid properties just outside the boundary layer and the distance x from the origin of the layer. The coefficient of viscosity of air is, as usual, denotea by p.

The ratios of the momentum thicknesses (h2) on either side of the corner shock wave were ootsined f'ra Nash's 8 formula:-

where ( 1, ana ( )2 denote conditions upstream and downstream of the shock wave.

Of several available formulae quoted by Cooke', tnis 1s the simplest.

6 REZJLTS

6.1 Frcssure

h-essures were scaled by taking the averag,e pr~ssuix wll ahead of the corner as unity. Since this study concerns heat transfer rather than pressure distributions, Mach numbers, donsities, and velocities wore taken from measured

pressures rather than nominal flw conditions. Flm changes across the corner correspond to a corner angle of 15.1' +_O.l', %,hich agrc~s satisfactorily with the geometrical angle.

The pressure distributions, which confirm the absence of any significant scRsration at the tost Reynolds numbers, arc illustrated in Pig.-/.

6.2 Heat Plum at:.+ = 4.36

Since the results of all test are qualitatively similar, detailed description will be confined to one test, nawly that illust=atcd 313 Pig.8, for nhicn li , = 4.36.

11

6.2.1 zk!&G&n ahead of oorner con~sion A--

The reoovary factors shown in Pig.S(b) rise to a Peak before falling away towards the turbulent boundary layer value of 0.89. This behaviour, which is a chsraoteristic of transition regions bctw-ieon laminsr and turbulent flow 10

> =s broadly consistent rith the Stanton nuxioers of Flg.8(c). In the s~?xne region, Stanton numbers rise from values appropriate to a laminar layer, finally roaching some '753 of the estimated values for a turbulent layer. Comparison of recovery factors and Stanton number suggests i&at transition nffects the former earlier than the latter, and recovery factor; continue to be slightly sffeoted after Stanton numbers have apparently rcnchcd their final level.

6.2.2 Ikgion near oorncr _,---_-

Keoovel~ factors, whethLr derived using uistream Mach nussbcr (M,) and

corresgponding statlo temPorature (T,) or conditions at the loner Mach numbers associated with the corner compression, foJ1 aPPrioiably rcoshing a minimum slightly downstream of the corner. Stanton numbers on the other hand, rise

sharply if defined using density and velocity asc,ad of tnc ccnprcssion, but remain constant if estimated ioccl density and velocity arc used. Local density

and velocity were estimated by assuring Chat b!lncql --I--~ was tne sa3e function of

(P) local PI Y

PI as it would be if the Pressure rise from p

1 to (p4osol wcrc produced by a single oblique shock. Tnus (p~)~~~~ x:trc fcund by using tables of flon chalgcs through oblique shosks in i:c,ljunctz.on with tlr.e Pressure distributions of Fl.g.7. l& may bc seen from the 1cw.r lint 5.3 Zig.E(a), riall texaPcraturc rose appreciably through the: compression region when heat was being traosferrcd to the model.

6.2.3 lieglon downstream of corner oomorcs&og -

Both recovery factor and Stanton number rise initially, the Tormcr tending

to return to the normal level fcr a turbulent boundary layer. St,anton numbers based on loc,al density and velocity tend on avora& to some 8% of the estimated

values behind the corner shock wave. f~pinparcntly-, the Proportionate increase of

Stanton number through the shock agrees fairly well rnth thz theoretical estimate excePt in the immcdictc neighbcurhood -.f the ~ornci'. On botn sides of the

compressmn regim, however, the St,, --ton nwnbcr l~vcls fr?n exparimcnt are below

tho estimctes.

In the f@rward Psrt of the reg~n especially, the true dimcrsional rate Of

heat transfer is nuch lower than would be estimated for the measured surface tcnyerature because of the ccmbined zffect of lcw Stanton number and low recovery

factor.

12

6.3 Effects of reducing Mach number ahead of Corner -

Test results for M, ranging from 3.97 to 2.4Y5 are shown in Egs.9 to 12. Reduction of Mach number ahead of the corner tends to move transiticn nearor to

the leading edge of the model. Rcpolds number at the end of transition, as

indicated by recovery factors, falls slightly from about 4.5 x ,06 at Ei 1

= 4.36

to 3.9 x 106 at :d, = 3.59. At the remaining llncil numhrs, Id, = 3.23, 2.495, transition appesrs to be ahead of the first instrumented station. This inplies that transition is complete at Reynolds numbers below 3.3 x 106.

Ahead of the corner Stanton numbers fall further belo?{ the estimates as 14, is reduced, until at iA, = 2.495 they are ority about 503 of expcoted values.

Downstream of the corner, the Grinoipal effect of %ach number reduction is to delay the return of reocvcry f',aotcr to the flat-plate boundary layer level. For M, d 3.59 this return does not occur !,ithin tho length of the model. The probable reason for this low-Tech number behavicx is that the 15' corner angle is then close to the limiting angle for attached flow. Acsordirg, to Kuehn 11 ,

this limiting angle fjLls from about 23" Khcn h:, z 4. to I-(' wllen M, = 2.5 at

relevant Reynolds numbers.

6.4 Rffect of unsteadiness in ourfaoe temperature on heat flcv --

During the M, = 3.97 run, data were.r aoorded at frequent intervals during a period when coolant temperature was allowed to vary. Time histories of heat flow and model surface temperature arc shown in Fie;.13. In Fig.14 these measurements are compared with the mean relation between heat flew and tempera-

ture for nominslly steady conditions: Anclysis of the deviations of heat flows from the steady-state relaticn shows that, at given temperature, the error in a heat flow measurement. correlates no11 vnth the mean rate of change of tcmpernture

during some 5 or 6 minutes preceding the acquisition of the data; that 1s in Fig.13, a slope A-A rather thsn B-B, determines the error of the data at tint C. A moan change of $'C per minute in model surface tcm+?raturc, preceding time C produces an error of about 2 x low5 in non-dimensional heat flow measured at -that time. This numerical result is not gencrsl: it mould be expected to depend on the thermel properties of th2 thermocouple, skin and heat&tcr to xrhich the

measurements relate.

7 &&Wl%AL DISCUSSION

The most striking result of these tests is that on both sides of the corner, heat transfer through thti turbulent bcund‘ary layers appcors to be much lower than

one would ewect. This and the considerable scatter of the Stanton numbers foster

suspiaion of the aoouraoy of the heatmettr calibreticns. A brief attempt

13

to calibrate come of the cctcrs m the mcde? mtixtcd That, in tnis enviroment, these meters mcy be some 1O,4 loss sensitive thsL1 in the mnl;er's csllbr,?tir.g appaatus. Even if the Stcnton numbtirs acre rnisu3 by this zmour,t, they :iOdd still 1s considerably belox the estimates".

It is thought that errors in the neeswwent of surface temperature would not be large enough to expic:ln the remauing drscrcpa~cy. sLE.1 errors woux, howcvor, ba in the correct sense, baczuse the thcrmocou?lcs would tend to measure the lower temperature at some point within the skin, If they fnllod to incasure surface temperatwe. Some indl-,ation of the possibl e size of these errors may be gained from the fact that the temperature gradknt in the resin skin is some 40-50°C per inch ct. a heat flow of 0.1 CHU/ft2 sot. The progressive divergence betwen theory and experiment as Mach number falls 1s cowistent with error in the temperature measurements. This is becnusc the: dz.ffcrcnce bctwx% rccov<~ry and surface temperatwcs nwdcd to generate R given hw.t transfer, foJ.[ls with X;noh number; consequently uca;uremcnt errors become more importnnt at the lower Minoh nmbers.

The exporinentnl results hc.vc been proscntcd as tnoy wrc obixincd: vrith neither heat flux no? ~31 tcmpercture constant along the model. Reiiable metiiods for relatrng StznT;on nwbers XI com&essibl o flax Et nr.oitrzry uall oondltz.olls to Stanton numbb3rs at standard conditions s~;c;l 3s ZI ~smhermi w.ll do not, to tho authors lcnourkdgc, exist. Swh wthods xc necdtid in order that hczt trzns- fer rates and nail temperatures for real vehicles may be wJcuinted, since the temperature and heat flow dxtributions will dopcnd ‘lot oii~y on acrodpanic (convective) heat txansfcr, but also on intemcl end e::zerncJ mdlation, internal heat paths prcvided by the struoture, and the coolers ?r he,?t sirks contuned

therein. The mnterxtion of these factors oan correctly be obtained orJy if heat trusfer coefficlcnts approprlnte to any arbitrary wJ.l conditions arc known.

In incol;pressiblti flow, nc'c~ods have bcxzu developed. for the effects of vnriable ~4.1 temperature (actuai dlstributxns being approxuzkxl by comb.blnations of "step" rind linear "rmp" changes of tcr~qxxhre 12 ), cud fou the ci"i‘cots of trmsltlon'3. For co!?prass~.ble flow the effect of 5 step chnngc in wall tempcra- ture is examined m Ref.14.

0 CONCLUSIOh%

Heat transfer measurements U-I the viclr~ty of D 15' compression corner,

with approach Ms&h numbers ranging from 2.495 to 4.36 hzve shown the follorring

features:-

0 See footnote tc p. II+.

14

(I) Measured Stanton numbers for turbulent flw c.re lower thsn had been estimated; the accuracy of these measurenents zs, however, uncertain*.

(2) Away fron the iswdinte vicinity of the owner, ratios of Stanton numbers upstream and &ovmstream of the oonpression cre as eqeotcd.

-(3) Low recovery factors in the inmediate ncighbourhocd of the sompression lead to low heat transfer; this region extends furthest at the lowest approach b&oh numbers where the corner shock w8ve is nealy strong cnowh to sepzrate the boundary layer. The lneasurad recovery factors nre probably rclioble, since heat oonductxon from tempercture czd heat sensors, a likely source of error in the tests ns a whole, should becow uninpcrtant cs rccwcry tenpernture is spproaohed.

* After this Report was first issued, further oalibraticns of single heatmeters were performed by staff of the 8 ft Superscnic Tunnel at R.A.E. Bedfcrd. The new calibrations indicate that the calibrating technique evclved by Hatfleld2 and used by heatmeter manufacturers cverestmtes heatmeter sensitzvity by cne- third. Complete acceptance of the new callbraticns, which shculd be more accurate than those mentioned on page 13, wculd brin& the Stultxn numbers cf this experiment much closer to estlnated values.

'I'able 1 -e"--

~os2.tions of ~nskr~mcnted. stctions __-," --- -- (Distances fron lading cdgo we CaJonp the cArsme~t surface.) Is.~-.Ae _I_,. I" w---L - -

Dist=cc from lading edge

(inches)

2.9

4.0 5.1

5.35

5.6

5.85

6.1

6.35

6.6

6.85

7.1

(7.25)

7.4

7.65

7.9

a.15

9.25

10.35 - “L

1--_1--s. Static prcsuure tap

(offset: port or starboard)

(inches) -.

0.6 s 0.6 P 0.6 s

0.6 s 0.6 P

0.6 P 0.6 :, 0.6 P 0.6 3 cc ornw) 0.6 ? 0.6 s 0.6 P 0.6 s

0.6 s -_--l_l_- !

Hciltrneter and. thermocouple (offset: port or starboard)

(inches) n-e

0.4 P 0.i s 0.4 P 0.4 s 0.4 P 0.4 s 0.1, P c.4 s

O.l!. s 0.4 P

0.4 s 0.4 P 0.4 s 0.4 P 0.4 s 0.4 P

---

ITote:- SpcLces 5.n the table denote st&ons where Lmtrunents wre unscrvlocnble; add~t~onctlly, at &.I5 inches fron lecding edge:, no heat flow data w?rc obtai~ud in the test at ;,I

1 = 4.36.

16

Table 2

Summary of test co~titlons Nominal total pressure of free stream 220 inHg Nominal total temperature of free stream 4.0%

Ahead of corner Aft of corner hlnx. free strem

1.87 16.33 x d 45

2.41 17.70 x IO6 45

2.65 15.73 x 106 47

2.91 13.18 x 106 70

, 3.20-I 11.58 x 40' , 100

Sf!,lBOLS ----

specific heat of air at cox?,tznt pressure

Mach number heat transfer rate >er unit area

P, ue x Reynolds number = -P--

e recovery factor Stanton number = Q/puC (T - T,,)

P r temperature total temperature in main stream

air velocity distance from virtual origin of boundaq layer

rat10 of specific neat3 for air momentum thickness of boundary layer ooefficient of viscosity for air non-dimensional. heat flon rate air density non-8.imensional surface texpersture

C

MP

Q

% r

sT T

*0

u

x

Y

62 P *

P 7

Superscript. x

Suffixes

a e r pi 1

2

intermediate temperature

reference condition outer edge of bouwlary layer zero convective heat trensfer model surface ahead of corner oomprcsslon downstream of corner coqression

No.

1

2

3

4

5

6

7

a

9

IO

11

Author A. Naysnith

H.S. Hatfield P.J. I!ilkim

J. Poole

D.R. Anarens

A.C. Browning J.F.W. Crme R.J. Monaghan

G.F. Midwood R.\:. Hayward

L.F. Crabtree R.L. Domett J.G. i'loodley

J.F. Nash

J.C. Cooke

J.L. Potter J.D. Qhihrtfield

M. Rxhn

PLEBRlQJCCS ------

rtls et0 Heat transfer ad boundary layer neasurenents in a region 0f SU~C~SO~O flow separation ad reettaohment.

R.A.X. Tech. Note Aero 2558,(a.s.c. 20601) td;ry 1958 I

A new heat flow meter.

J. of Scientific Instrulllents, V01.27, Jan. 1950

A description of the R.B.X. high supersonic sped tunnel. R.A.Z. Tech. Kate Aero 2678, 1960

Some notes on the model testing fttcilities afforded by

the high s@ersonio srze& mnd tunnel at R.k.ti:. Bedford.

R.B.E. Tech. Note Aero 2582, (L.R.C. 20922) JhqgSt 1958

&osurments of the effect of surfcse cooling on boundary

layer trzuisition on a 15' cone. Part I. Tests at M = 2 and 3 in an 8 inch x 9 inch v&d

tunnel at X.A.E. Bedford. -4.X.C. 1983h, Cd?. 381, Sqt.. 1957

m automatic self-balancing capstie mmnomcter. A.?.C. 7.P. 231, July 1355

Estimation df heat transfer to flat plates, cones and blunt bodies.

R.h.E. Tech. Report So.65137 (L.R.C. 27233), July 1965

An analysis of two-dimensional turbulent base flow, includmg t'ne effect of the apprcsching boundmy layer.

:,.R.C. R.md X. 3344, July 1962

sepmha SU+~FSOI~C flq~r.

R . . ..E. Tech. Note iiero 2379 (a,.R.C. 24Y35), March 1963

Wfects of urdt Reynolds number, nose bluntaess,Eyld mugmess on bomrlzy layer transition. XXD Repart X0.256, April 1960

Expermcntal investigation of the pressure rise required

for the incipient separation of turbulent boundary layers

m two-dimensional sup&sonic flow.

N.;SA hkmo I-21-5911, February 1959

19

Title. etc _ Heat transfer m the turbulent incompressible boundary layer. III - Arb;traq wall temperature and heat flux. N&X Eeno 12-3-58V, December 1958

Heat transfer xn the turbulent incompressible boundary layer. IV - Effect of location of transitlon and pred;Lc- tion of heat transfer xn a known transition region. N&L I,emo 12-4-58W, Dcccmbcr 195P

Heat transfer measurements at a Mach number of 2 zn the turbulent boundary layer on a flat plate having a step- vase temperature distribution.

IL% TN D-159, Ncvimber 1959

NO -2 i,uthor 12 W.C. Reynolds

'I. Ii. my s S.J. IUlne

13 W.C. Reynolds W.M. Kays S.J. Kline

14 R.J. Conti

----hh / COOLANT / I Ii-A

PIPES ;‘ \ up\ STING1

I~UfATiON

THERMOCOUPLE LEADS /

‘HEATMETER LEADS

\

COOLED SURFACE (RESIN COVERED)

STEEL NOSE -CAP

T -. . . \ I

PLAN VIEW SHOWING TIP MACH LINES

_-

FIG. I GENERA; -ARRANGEMENT OF MODEL : ~

@ DENOTES THERMOCOUPLE AND HEATMETER POSITIONS + DENOTES PRESSURE TAP LISTED IN TABLEI

ALUM IN IUM LOADED RESIN SKIN 0*17,n THICK

W ITH CHOROW ISE TTER FINS

INSTRUMENTED

-1 - -

-ASTIC FoAI~~\Y IOOLANT IjQj - \INSULATIONC,\Y MANIFOLD BFEEOER IJ&I

- I INCH

FIG. 2 DETAILS OF MODEL

COPPER/CONSTANTAN

THERM0 COUPLE

SLOT FOR LEADS LOT h t4OLE REFILLED JTH LOADEO RESIN AFTER

THEMOCOUf’LE

>WIRE da 0.0048 in (40 5.W.G)

COOLANT CHAMBER COVER

FIG.3 (a) THERMOCOUPLE & HEATMETER MOUNTING

COLO JUNCTIPN

TELLURIUM - SILVER DISC

FIG.3 (b ) DIAGRAM OF HEATMETER

FIG.3 DETAILS OF INSTRUMENTATION

OPEN HEADER

TRI’XLOROETHYLENE ‘MODEL COOLANT

c XiCUlATIl$ PUMP P

COOLER BY-PASS

r COIL IN TANK FILLED WtTH TRICHLOROETHYLENE, COOLED BY ADDITION OF SOLID co2

u PRESSURE VAPOUR 3 BALANCE

+ SUPPLY TRAP

TO MODEL

FROM MODEL

FIG. 4 LINE DIAGRAM OF COOLING RIG

l-p- ,

/ Q (3

,

J In

. 0

\ a------ RECOVERY FACTOR 0 W- .

’ f ‘.

. 156 I.59 160 I.61 1 T2

+I 0

I c to.5 L

U

2

e \ O

-7

0

-05

.

I RECOVEFU FACTOR 08Bf

Y . . \<

YT x

+ 2-7 5 2.00 -. 2-85 I 9

FIG. 6(a) TURBULENT BOUNDARY LAYER CLOSE TO CORNER COMPRESSION; Ml= 2.495 , M2= l-87

FIG&(b) TURBULENT BOUNDARY LAYER WELL DOWNSTREAM OF CORNER COMPRESSION

POSITION: 9-25 in FROM LEADING EDGE Ml=436 ; % = 3-20

POSITION t IO*35in FROM LEADING EDGE

FIG.6 EXAMPLES OF MEASURED RELATIONS BETWEEN HEAT FLOW AND TEMPERATURE DOWNSTREAM OF CORNER

3.0

29

I.0 --

.^ 0 .2 4- b e I”

INCHES FROM LEAOlNGj EOC+

(ALONG AIRSWEPT SURFACE)

FIG. 7 PRESSURE DISTRIBUTIONS FOR ALL TESTS

0 2 + 6 8 IO DISTANCE : INCHES FROM LEAOINCJ EOC+

FIG. 8 (a) WALL TEMPERATURES

NATURE LAMINA TRANSITIONAL l-UR6ULENf

OF

FLOW NORMAL FLAT PLATE

BOUNOARY LAYER

0 2 4 6 0 DISTANCE: INCHES FROM LEAOINC\ El&E.

FIG. 8 (b) TEMPERATURE RECOVERY FACTORS

~1~8 TEST RESULTS FOR tdI = 4.36 (PART I)

0*0020

‘; 0~0015

‘; c

e “> 0~0010

e 0

II o-0005

l- ln

0

DOWNSTREAM OF COMPRESSION

0 2 4 6 8 IO

DISTANCE : INCHES FROM LEADING EDGE

FIG. 8 (c)STANTON NUMBERS

0

* *

CORNER CORNER

I I \ \ \( \(

PARTIAL COOLING PARTIAL COOLING

\ \

0 2 4 6 8


FIG. 8(d) HEAT TRANSFER RATES

IO

FIG.8 (CONCLD) TEST RESULTS FOR M,=4*36

FIG. 9 (a) WALL TEMPERATURES


e

z

z+ (, 0.0005 I / l- UY

/ \ oOWNSTfW

pu=p2Lb OF . COMPRESSIOI

0

FIG. 9 (c)STANTON NUMBERS

CORNER I I I I I I I I 0 2 4 6 8 IO 12

DISTANCE * INCHES FROM LEADING EDGE

FIG 9 TEST RESULTS FOR M,=3*97

FIG.10 (a) WALL TEMPERATURES

0’00 IS

0~00l0

O*OOOE

0

FIG.10 (b) TEMPERATURE RECOVERY FACTORS

FIG. IO (c) STANTON NUMBERS

CORNER I 1 I I , I I

0 2 4 6 8 IO 12


FIG.10 TEST RESULTS FOR M,= 3.59

FIG.11 (a) WALL TEMPERATURES

FIG II (b) TEMPERATURE RECOVERY FACTORS

‘; 45 u” 5 u I

ii- DOWNSTREAM OF

01 COMPRESSION

FIG II (c) STANTON NUMBERS

CORNER

I I I 1 1 , I I I I I I 1 0 2 4 6 a IO I2

DISTANCE: INCHES FROM LEADING EDGE

FIG. II TEST RESULTS FOR M,= 3.23

FlG.12 (a) WALL TEMPERATURES


FIG. 12 (cc STANTON NUM BERS

CORNER I 1 I 1 I I I I I I I I 1 0 e 4 6 8 10 12

DISTANCE. INCHES FROM LEADING EDGE

FIG. 12 TEST RESULTS FOR M, = 2-495

IO

Q*5

0

3.!

3,’

3.!

3

1

I 5 0

8 I I e-DENOTES COOLING RIG HEAOER

TEMPERATURE STEADY

e

IU ZU JU 4-J 3u . b

TIME mtn

! 0-- 7 ,

IO 20 30 40 5C TIME m,n

I 60

FIG. 13 TIME HISTORIES OF UNSTEADY HEAT FLOW 8, TEMPERATURE

I-a

0.8

O-6

-.. LINE FOR ‘STEADY’

N 6 :- TIMES MARKED BESIDE OATP

POINTS RECAlE THIS

I mln

I 3.6 3.1 -f-W /T

MODEL WALL TEMPERATURE

3.8

FIG. 14 COMPARISON OF ‘STEADY’ AND ‘UNSTEADY’ DATA

Printed tn Rnt-Iawi fo+ Eer Najorty’s Statlaasy Office by the Royal Aircraft E~tablt~hasnt, Pamboswfh. Dd.129528. X.U.

A.R.C. C.P. No. 965 June 1966 sast1ngs. R. c. Brcun, C. 8. Atkins”“. slsan

EAT IRAtEFEX IN TXE VICINITY OF A 15O CMlpREsSION CORNEX AT MACH WNBiYt(s FflOM 2.5 TO 4.4

533.6.011.6.: 536.55 : 533.6.011.5 : 532.5%

ccmaerc1al1y available heatmeters have be?” used tc meas.Ire the steady-state Ccmrerclally available heafmeters have bee” used tc mea=18 the steady-state tEat tmnsrer Iilte.s I” the vicinity OI a ccmpressicn corner. Results at heat transfer rates I” CtE vlcl”lcy or * compress1cn corner. Results at all Hach n-,-s are q,i?,lltaCively sitilar I” that, both ahead and do&n- all Mach nuwrs are qwalitatively simllar In that. both ahead and dom- SLIpam cl the ccmr, the measured heat tr’ansler rate ws lcmr tba” stream of the ccr+‘mr. the mea-d heat Lra”sfer rate IBS lmer than expcted. expected.

In the compression reglcn close tc the corner. the adiabatic wll tempera- C”reS were also lOA.

I” the compresslc” reglc” close ta the u)IIIa-, the adlabatlc -11 tempera- tln-cs ml-e also low.

The neararrlng technique 1s dIscussed and some pctentlal sources of ermr are lndlcated.

The meas”rlng technique is discussed and some pote”t.le.1 scurces cl e-r are lndlcated

I June 1966 Sast1nSs. il. c.

Atklnscn, &san

533.6.011.6 : 536.55 1 533.6.011.5 : S2.552

HEAT ‘DUWFSR IN l,lE VICINITY OF A 19 COhWK%ION CORNER AT NACH NlMBERs FRCt12.5 TO 4.4

A.R.C. C.P. NC. 965 June1966 NaStl”g.3. R. c. Br[~n. C. 9. AkInso”. m3an HEAT ?RAkEf= IN ?HE VICINITY OF A 150 CMpFtESSlON CORNlX AT MACH tARBEllS FRDM 2.5 lU 4.4

533.6.011.6 t 536.55 I 533.6.011.5 I 532.552

Commercially avallable heatmeCers have bee” used Cc mea- the steady-stat, heat tmsrer rates 1” the vlclnlcy Of a ccmpresslon ccnwr. Re.v.11~ *t all llach “rrmbers BIP qualitatively slmllar in that, both ahead and dorm- stream 01 the ccr”er, Che masued heat transfer rate ms lower than expcted.

In Che ccnpressic” r&on close tc the corner, ttx adlabatlc ~sll temperatures were alSO 10%

I

TW meaarl”B Technique Is discussed and some potential sources of erra- are Indicated.

I

C.P. No. 965

PublIshed by HUI MAJESTY’S STATIONERY OFIKE

To be purchased from 49 High Holborn, London w c 1 423 Oxford Street, London w 1 13~ Ca>tle Street. Edmburgh 2

109 St Mary Street, CardIt? Brazennose Street, Manchester 2

50 FaIrfax Street, Brlstol 1 35 Smallbrook, Rmgway, Blrmmgham 5

7-11 Lmenhall Street, Belfast 2 or through any bookseller

C.P. No. 965 50. CODE No. 23-9017-65

heat transfer in the vicinity of a 15” compression corner...

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