NATIONALr~m

ADVISORYCOMMITTEE‘aFORAERONAUTICS

TECHNICAL NOTE 3461

TURBULENT-HEAT-TRANSFERMEASUREMENTSAT

A MACHNUMBEROF 1.62

ByMauriceJ.BrevoortandBernardRashis

LangleyAeronauticalLaboratoryLangleyField,Va

WashingtonJune1955

https://ntrs.nasa.gov/search.jsp?R=19930084195 2018-05-27T21:05:35+00:00Z

TECHLIBRARYKAFB,NM

of

NATIONALADVISORYc(MMmTEE

TECENICfLNOTE

1!111[1111“FORAERONAU’TCCS 00bb57q”

3461

TUWUHNT-HEAl!-TRANSFER~ AT

A MACHNUIBEROF

ByMauriceJ.Brevoorts@

1.62

BernardhShiS

Turbulent-heat-transfermeasurementswereobtainedthroughtheuseau axialJ..Ysymmetricannularnozzlewhichcmsistsofan inner,shaped--

centerbcdyandan outercyltidricalsleeve.Measurementstaken~ong-theoutersleevegaveessentiallyfl-at-plateresultsthatarefreefromwallinterferenceandcornereffectsfora Machnrmiberof1.62andfora Reynoldsnuiberrangeof7.22x 10~to 1.20x 108. Theheat-transfercoefficientsareingoodagreanentwiththeoretical.resultsfora WchnuuiberofI.60 * fora ratioof inner-surfaceto free-stresmtemper-

P atureof1.60. Thetemperature-recoveryfactorsareontheaverage1.~ percentlowerthanthefactorsobtainedfora Machnumberof2.4.

J

INTRODUCTION

Thedesignof supersonicaircraftandmissilesrequiresengineeringinformationaboutheat-transfercoefficientsandtemperature-recoveryfactorsforsuperscmicspeedsthatex%nd overa widersngeofReynoldsnlmiber● BIreferences1 and2,localturbulent-heat-transfermeasurementswerepresentedforI&chnumbersof3.03and2.06Jrespectively.

Thepurposeofthisinvestigationisto extendtheworkofrefer-ences1 and2,withthesametypeofapparatusandmethodofreduchgthedata,to a Machnuniberof1.62. ThersngeofReynoldsnmber forwhichmeasurementswereobtainedisfrom?.22x 105to 1.20x 108. Theresultscovera temperaturedifferenceofapproxhately10oat 40 secondsafterstsrthgto a~roximately1°at 200secondsafterstarting.Theaveragevalueoftheratioof inner-surfacetemperatureto free-streamtemperatureT+~m was1.60.

2 NAC!ATN3461

sYMmLs

c

%

~

h

k

M

Nil

Pr

R

St

‘rav

Te

%?

l!=

t

v

w

x

specificheatof sleevematerial,Btu/lb-%

specificheatofairat constantpressure,Btu/lb-%

accelerationdueto gravity,ft/sec2

heat-transfercoefficient,Btu/ft2-sec-%

heatconductivity,Btu/ft-sec-%

Mach?miber

IVusseltrnmiber,l+

Prandtlnuniber,W@

Reynoldsnwiber,pvx/p

Stantonnwiber,@R - = @J~g 7

averagewalltemperature,%‘2

effectivestreamairtemperatureatwall;sanetemperaturewhichgivesthermalpotentialwhichisindependentofheat-transfercoefficienth, %

stagnationtemperature,%

inside-surfaceteqeratureofnozzlesleeve,%

free-stresmtemperature,%

time,sec

free-streamvelocity,ft/sec

specificweightof sleevematerial,lb/sqft

longitudinaldistancealongsleeve,ft (unlessindicatedotherwise)

T - T@recoveryfactor,~

Tt - Tm

NACATN3461

ev dynamicviscositycoefficient,lb-sec/sqft

3

k P free-streamdensityofah, slugs/cu

APPARATUSAlil)METHOD

ft

Theapparatusconsistedofan axiallysymnetricannularnozzlewhichwasdirectlyconnectedto thesettlingcha?iberof oneofthecold-airblowdowzljetsoftheLangleygasdynamicskboratory.Thenozzlehada shapedwocdencenterbodyandtwooutersleeves.Onesleevewasconstructedof 8-inch-diameter,extraheavy,sesmlesscarbon-steelpipe,andtheotherwasconstructedofl/16-inchstainlesssteelwhichwasrolledintoa cylinderandwelded;bothcylindersweresurface-machinedinsideandoutsidetowsXLthicknessesof0.388inchand0.060inch,respectively.Thecoordinatesofthetier bodyaregivenintableI.

A detaileddrawingoftheapparatusis showninfigure1 whichgivesthelocationofthethermocouplesandstatic-pressureorifices.Detailsofthethermocouples,thestatic-pressure-orificeinstallations,

* thetemperature-recordingequilynent,andtheprecisionof instrumentationaregiveninreferences1 and2.

. TheWch nuniberdistributionis showninfigure2. Theal-inementoftheflowwascheckedat severalstationsby meansoforificeslocatedaroundthesleeve.Thelocationofthesemeasurementsis shownhfigure2.

Thetestprocedureisgiveninreferences1 and2. Forthisinves-tigationtestrunsweremadeforsettli.ng-chauberpressuresof0.4,57,and196lb/sqin.gage. Thetestat a pressureof0.4Xb/sqin.gagewasmadewitha sleeve0.060inchthick,andthetestsetupwasevacuatedto an absolutepressureof1.0inchofmercury.Excludingthefirst20 seconds,thepressuresweremaintainedconstantforeachtestrun.Thestagnationtemperaturestwtedat essentiallyrocantemperatureanddecreasedasthepipingwascooled,as illustratedinfigure3 wherestagnationtemperatureisplottedagainsttimefora sett+g-chauiberpressureof 196lb/sqin.gage. Thewalltemperaturealsostartedatessentiallyrocmtemperatureandtendedto approachtheequilibriumtemperaturewhichwas approx5nately22°R beluwsta~tion temperate.Thisvariationis showninfigureh wherewaXLtemperatureat stations12and18 isplottedagainsttimefora settling-chsmiberpressureof196lb/sqin.gage.

0 In figure~ areplotted,forvarioustimesdurx thetestrun,thevaluesofwalltemperatureagainstlongitudinaldistancealongthecylinder.Thesevalueswereusedto determinetherateofchangeof8

4

d2Tavthelongitudinalconductionk —

&weretakenonlyforthelengthofthe

REDUCTION

NACATN 3461

alongthecylinder.Testresults

cylinderfor

OFDATA

Themethodofreducingthedataiscompletelyences1 and2. Briefly,theequationsusedare

h ..c%L1~-Te

d%avwhich k —

d? ‘0”

describedinrefer-

(1)

(2)

(3)

Themethodconsistssimplyof selectinga recoveryfactorandthenobtainingTe frcmequation(3). Thisvalueof Te is stistitutedintoequation(2)andvaluesof h forclifferentheat-flowratiosareobtained.Thesevalues of h arethenstistitutedintoequation(l). Thetruevaluesof Te) ~~ and St areobtainedwhen St isconstantwithtime(fordifferentheat-flowratios).Figure6 showsthevalues usedindeterminingtheStantonnwber andrecoveryfactorat station12forasettling-chmiberpressureof196lb/sqin.gage.

Thevaluesof specificheatandspecificweightofthesleevemate-rialweretakenfromreference3. ThevaluesofPrandtlnuuiber(0.71)andviscosityofairwerealsotakenfromreference3 andwerebasedupon ~. Thevslueof ~ usedwasthevaluemeasured80secondsafterstarting.

RESULTSANDDISCUSSION

Overthetestrange(seefig.5), thewalltemperaturesareconstantalong x. Intherelation

*

1?

dTav/dth—.wc%-Te

NACATN 3461 5

. wandc areconstant,and dTav/dtisconstantbecauseTV is con-stant.Therefore,ifthereistobe a variationof h withReynolds

d’ numberor x, Z’emUSt VSXY with X. The valueof T= obtainedforthetestat a settling-chamberpressureoflg6lh/sqin.gage,evaluated80 seconds.afterstarting,actuallydecreasesabout1°.

Figure7 showsthevariationoflocalNusseltnumberwithlocalReynoldsnumber.Thevalueof x usedinevaluatingthesenumbershasbeenadjustedfor x = O locations(theeffectivebeginningofthetur-bulentboundarylayer)bythemethodofreferences1 and2. The x = Olocationsarek.o and1.0inchesdownstreamoftheminimumstationforsettlQg-chsmberpressuresof 0.4and57 lb/sqin.gage,respectively,andattheminimumstationforthesettling-chamberpressureof@ lb/sqin.gage.

TheNusseltnumberswerefoundto vary frm 84oto 56,650fortheReynoldsnumberrangeof 7.22x 10~to 1.20x 108(basedonad~ustedx= O locations.)ForcomparisonthecurvebasedupontheVanDriestanalysis(ref.4) is shown.FortheVanDriestanalysis,Tw& WS

consideredto be 1.6o(theaveragevalue ofthetestresultspresentedm herein).

Thedatawerecomputedby usingfree-streamtemperatureto determine. thedensityandvelocity.Thewalltemperaturewasusedto determinethe

viscosityandthePrandtlnumber.Theagreementbetweenthetestresultsandthetheoryisgood.

Figure8 showsthevariationoflocaltemperature-recoveryfactorwithlocalReynoldsnmber. Thevariationisfrom0.880at 7.22x l@to 0.868at 1.2ox ld. Theresultsarecomparedwitha curvewhichrepresentsthefairingofthedataofreference5 fora Machnmnberof2.4. Theresultsobtainedinthisinvestigationareontheaverage1.5percentlowerthanthedataofreference5. Alsoincludedfor‘com-

1/3 and prl/2.parisonarethecurvesfortherecoveryfactorequl to PrThewalltemperaturewasusedto determinethePrandtlnumber.

.

d

6 NACATN 3461

CCINCLUDINGREMARKS.

vTurbulent-heat-transfermeasuremerrtsthatgaveessentiallyflat-

plateresultswereobtainedfora Machnumberof1.62andfora Reynoldsnumberrangeof 7.22x 105to 1.20x 108. TheNusseltmmibersagreewiththeoreticalresults.Thetemperature-recoveryfactorsareontheaver.age1.5percentlowerthanotheravailabledatafora Machnumberof2.4.

LangleyAeronauticalLaboratory,NationalAdvisoryCommitteeforAeronautics,

~ey Field,Vs.,lfarch~, 155.

REFIELENCES

1.Brevoort,MauriceJ.,andRashis,Bernard:Turbulent-HeatflransferMeasurementsat a MachNumberof3.03.NACATN3303,1954.

2.Brevocmt,MauriceJ.,andRashis,Bernard:Turbulent-Heat-TrensferMeasurementsat a MachNumberof2.06.NACATN 3374,1955.

3. Eckert,E.R. G. (WithAppendixby RobertM. Drake,Jr.): Introduc-tiontotheTransferofHeatandMass.Firstcd.,McGraw-HillBookCO. IU., l~o, PP. 266~ti 274.

4.VanDriest,E. R.: TheTurbulentBoundaryLayerforCompressibleFluidson a FlatPlateWithHeatTransfer.Rep.No.AL-997,NorthAmericanAviation,Inc.,Jan.27,1%0.

5. Staider,JacksonR.,Rubesin,MorrisW.,andTendeland,Thorval:ADeterminationoftheLsminar-,Transitional-,andTurbulent-Boundary-LayerTemperature-RecoveryFactorsona FlatPlatein SupersonicFlow. NACATN 2077,1%0.

r-.. .

.—

.

“

N.4CATN 3461 7

.

?

x, in.-10.00-4.70-4.%-4.00-3.00-2.50-2.00-1.X-1.00:::

-.40-.200

●10.20.30

TABLEI.- clm!m-BoDYcoommwlzs

Radius, in.2.0002.0002.0202*lm2.5002.7352.9703.1503.3003.3403●3753.4033.4253.43753.43643.43373.4298

t.x, in. Radius, in.0.442 3.4249

3.4190% 3.4L?2.70 3.4045●8O, 3.3961●9O 3.38~1.00 3.37761.10 3.36%1.20 3935a1.30 ;.344.1.40l.~ 3:33171.60 3.32381.70 3.31671.80 3.3103l.go 3.3@72.00 392997

x, in.2.102.202.302.4Q2.502.602.702.802.905.00

10.CO15,0020.0025.00S.oo35.0038.625

Radius, in.3=9553.29203.28913.2%83.28513.28393.28313.28273.28253.27203.2k703.22203.19703.17203.14703.12203.1059

C2

\

‘ ‘5’,,\

u 59

Fcmr thermocouple at stntlcmsO, 6, 12, 18, 24, ad 30 s~ced90° awrt. One only at eochof the other %tlons. Totalnumber of t hermoccuples, 36,

One sleeve 0.388 wall thicknessOne sleeve O.O&l wall thickness

Siognatlon

I,-’,,

I

--L 1=f? J /’

-“~—T” 1- Z@

// ;:_J

P

ur pressure oflflces ot stationsMahogany O, 4, 11, 25, and 31 spaced 9cP

/,/ - “P“ Stationo center body apart. One only at each of the

other %tkms. Total number of—.!”... . .

/

\

L------47premm 0rIIIGe8, x..

+SettUnq ctmmbtr

Figure 1.- Test arrangement. IMnksnsionsare in hche~.

,

%“

1.80-c Start of test section

o.60 ~ 7 m l-cl v 9 u n n

un

u

o ●

O Single orifice

~ I .40 “c)

● Four orifices .

c 90” apart

xu o; 1.20

I .Oqj2468101214161820 222426283032

Distance, x, in.

Figure 2.- Mach number distributionfor settling-chsmberpressure of1* Mjsq in. gage.

E 1 1 I ! ,

m0

H]120 140 160 180 200 220 240 2W 280 3CQ

Time, t, sac

Figure 3.-Variation of stagndiontemperatwe with time for settling-chsmber pressure of 196 lb/sq in. gage.

● ✎

Time, t , sec

Figure 4.-Varlationofwalltemperatuxewith thue forpressure of l% lb/sq in. gage.

settling-chsmber

G

5

5

lx

0.5

a)

Eal490

.

; 48002 4 6 8 10 12 14 16 [8 20 22 24 26 28 30

Distonce, x , in.

Figure ~.- Variation of ~ temperaturewith longilndhml distanceforsettling-chamberpressure of lx lb/sq in. gage.

.00I2

cI Recovery

.0010 factor, qrG

() o 0,871L’ ❑ .868

; .0008 () 6 .866t1

I1r 1

;

~ .0006<}

&{>

(>

.0004<>

40 80 120 160 200Time, t, sec

Figure 6.-Stanton number as a function of %ime and recovery factor atstation 12 for settling-chamberpresmwe of 15 lb/sq in. gage.

Reynolds number, R

Figure 7.- Variation of local Nusselt number with local Reynolds nuuiberfor ad$mted locations of x = O. Viscosityand Rrandtl number deter-mined for wall temperatures.

T, .

L ,

n~ oQ Q)‘~‘ o0‘ >0

G, I I I . .

Iu.u ‘ .)v .J.!.!’.!’!I I

‘.82 3 45.68 10 20X107

Reynolds number, R

Figure 8.-Vsxiation of local,recovery factor with local Reynoldsnumber for adjusted locations of x = O. Viscosity determinedfor wall temperatures.

G