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NATIONALADVISORYCOMMITTEEFORAERONAUTICS —

TECHNICAL NOTE 3623

CORRELATIONOFSUPERSONICCONVECTIVEHEAT-TRANSFER

COEFFICIENTSFROMMEASUREMENTSOFTHESKIN

TEMPERATUREOFA PARABOLICBODY

OFREVOLUTION(NACAmvl-10)

By LeoT. ChauvinandCarlosA. deMoraes

Ia.ngleyAeronauticalLaboratoryImgley Field,Va.

WashingtonMarch1956

d

. . . . . . . ---- . . ... . . . . . . .

TECHLIBRARYKAFB,NM

1P, NATIONALADVISORYCOMMITTEEFORAERONAUTICS Illlllulu!llllllllflnll

00bb432

mmmcmNom3623

CORREWI’IONOFSUPERSONICCONVEHTVEHEAT-TRANSFER

COEFI?ICIENTSEROMi&summm OFTHESKIN

TWHRMWW OFA PARABOLZCBODY

OFREVOLUTION(NACAm-lo)1

ByLeoT.ChauvinandCsrlosA. delloraes

Localcoefficientsof convectiveheattransferhavebeenevaluatedfromskintemperaturesmeasuredalongthebodyofanNACAresearchmis-siledesignatedtheRM-10.Thegeneralshapeofthebodywasa parabolaofrevolutionoffinenessratio12.2. Heat-trsnsferdataarepresentedfora Machnumberrangeof1.02to2.48andfora Reynoldsnuniberrangeof3.18x 106ta163.85x 106basedontheaxial&l.stancefromthenosetothepointatwhichtemperaturemeasurementsweremade.

ResultsfromthedataobtainedarepresentedastheproductofNusseltnuder NNUReynoldsnumberRurementsweremade.s.rylayerona flat

showntobe ingood

andthe-1/3powerofnsmdtlnmnberNn againstbasedonsxi.al.distancetothestationwherethemeas-Theequationforheattransferfora turbulentound-

(-1/3= 0.0296R

J0.8 isplateh subsoticflow NN#R

agreementwiththetestresultswhentheheat-transferparametersarebasedonthetemperaturejustoutsidetheboundarylayer.Basingthecorrelationofheat-transferparametersonairpropertiescal-culatedatthewalltemperaturegaveresultsthatwereingoodagreementwiththeequationforconvectiveheattransferforconesina supersonicfl~ NNUNW‘1/3= ooo34R0”8.Heat-transfercoefficients”fromthe

V-2testscorrelatedona Nusselt,Prandtl,andReynoldsnuniberrelationgavevaluesthatwereapproximately15percentlowerthantheresultsobtainedontheRM-10researchmissile,forconditionswheretheparam-eterswerebasedonthetemperaturejustoutsidetheboundarylsyer,oronthewalltemperature.Valuesofrecoveryfactorwereobtainedforthestationsatwhichtemperaturemeasurementsweremadeandareinagreementtiththeoreticalvaluesofrecoveryfactorsfora flatplate.

%qersedesdeclassifiedNACAResearchMemorandumL~lA18byIeoT.ChauvinandCarlosA. deMoraes,1951.

.— —.-——..— —z- -.---–-—.

2

IIWRODUCTION

Aerodynamicheatinginsupersonicflighthaslongbeenrecognizedasa.majorprobleminthedesignof supersonicaircraft,andexperimentalheat-transferdataforhighMachnumbersandReynoldsnumbersarein greatdemsnd.ExceptforsomeworkdoneontheV-2,alloftheconvectiveheat-transferworkhasbeendoneinwindtunnelsutilizingsteady-statecondi-tions;however,theresultspresentedhereinareforthetransientcondi-tionsencounteredalongthetrajectory.

Inasmuchastheproblemofaerodynamicheatingiscloselyrelatedwiththatof skin-frictiondrag,investigationsofthesetwophenomenaarebeingcsrriedoutsimultaneouslyby theLangleyPilotlessAircraftResearchDivisionasa partofanNACAprogramonsupersonicaerodynamics.Modelsofa specificconfiguration,designatedNACARM-10,wereflight-testedatthePilotlessA&craftResearch”StitionatWallopsIsland,Va.

Heat-trsnsfercoefficientsobtainedfromdatameasuredontwoRM-10testvehiclesarepresentedherein.Thetransientconditionsencounteredduringtheflightofa rocket-propelledtestvehicleareparticularlysuitedforobtainingaerodynamicheatingandheat-transferdata. Thesti temperaturemeasuredalongthebodyby resistance-typethermonterscementedtotheinnersurfaceoftheskinwascontinuouslytelemeteredtoa groundreceivingstationduringthetimeofflight.Fromthesedatatheskintemperature,timerateofchangeof skintem-perature,adiabaticwalltemperature,andconvectiveheat-transfercoef-ficientweredetermined.

TheMachnuniberrangecoveredinthesetestswasappro-tely 1.0to2.5. TheReynol&numberramge,basedonfree-streamconditionsanddistancealongtheaxisofthemissilefromthenosetotheteststation,was approdmatdy3.18x 106ta163.85x 106.

SYME!OIS

area,sq ft

specificheatofair,Btu/slug/%

specificheatofwall,Btu/lb/%

localeffectiveconvectiveheat-transfercoefficient,Btu/(sec)(sqft)(%)

NACATN3623 3

k thermalconductivityofair,Btu/(sec)(sqft)(OF/ft)

1 distancefromthenosealongtheaxisofthebody,ft

‘Nu Nusseltnumber,~Z/k, dimensionless

NR Prandtlnumber,C$/k, dimensionless

Q cpanti~ofheat,Btu

R Reynoldsnumber,pV1/p, dimensionless

RF recoveryfactor

T temperature,OF orOR

t timefromstartofflight,sec

v velocity,ft/sec

7~ specificweightofwall,lb/cuft

P viscosityofair,slugs/ft-sec

P densityofair,slugs/cuft

T thickness,ft

Subscripts:

aw adiabaticwall.

w conditionsofmaterialpertainingtoWSJJ

o undisturbedfreestreamaheadofmodel

6 isentropicstagnation

v justoutsideboundarylayer

TESTVEHICLES

ThegeneralconfigurationandbodyequationoftheRM-10areshowninfigure1. Figure2 isa photographofthetestvehicleonthelauncher.Thebodieswerebasicallyparabolasofrevolutionhavinga maximumdiameter

.— . . . . . . —.. —.. ——. —.—–—

4 NACATN 3623

of12inchesanda finenessratioof1>;however,thesternwascutoffat81.3percentoffuKllengthto snow fortheinstallationoftherocketmotor.Thisdecreasein lengthresultedin anactualfbnessratioof12.2.Fouruntqeredstabilizin&finswereequallyspacedaroundthesfterbody.Theyweresweptback60°witha totalaspectratioof2.o4andhada 10-percent-thickcircular-arccrosssectionnormaltotheleadingedge. Thedesignwaschosentoattaina highdegreeofstabilitywhichinsuredtestingat zeroangleofattack.

TheRM-10testvehiclesweredesignedforheat-transferinvestiga-tionscoveringlargeMachnurtiberandReynoldsnumberranges.Aminimumofinternalstructurewaaaccomplishedby internallypressurizingthemodels.Figure3 showstheint.-ernslconstructionofthemodels.

Thetestvehicleswereallmetalin construction,utilizingspun_esium sJ-@YS- md cast~sium alloYtailsectionstowhichthefinswerewelded.Theskinthicknessusedforeachstationistab-ulatedintableI. Allthesurfacesweresmoothsmdhighlypolishedatthetimeofflight.

Bothmodelswerepropel.ledbya 6.2~-inchABLDeaconrocketmotorcarriedinternally.Thecaseoftherocketmotorhasa temperatureriseof50°F whichwasnotsufficienttoaffecttheaccuracyofthetests.Thissmallrisein temperatureis dueto theinternslburningofaDeaconrocketmotor;thatis,theburningstartsinthecenterandworksoutwardtowardthecasesothatthepowderandtheinhibitoractasinsulatorsbetweentheflimesndtherocketcase.

INS~ON ANDTESTS

Skintemperaturesweremeasuredlymeansofresistance-typether-mometerscementedtotheinnersurfaceoftheskin.Thesethermometersweremadeoffineplatinumwire0.0(X)2inchindiameter.Reference1describesthethermometersmorecompletely.

~ermometerswerelocatedatstations8.9,17.8,36.2,49.9,86.1,and123.5ononetestvehicle(modelA) smdatstations14.3,18.3,and85.3ontheothertestvehicle(modelB). Reference1 showsthatthesethermmnetershada timelagof 3 milliseconds,correspondingto a maximumtemperatureerrorof0.3°F forthetestconditionswheretheheattransferisthegreatest.Tbiserrorwasconsideredtobenegligiblecomparedwiththe3.2°F errorduetothethiclmessoftheskin.continu-oustemperaturereadingsweretelemeteredtogroundreceivingstations.

Themodeb werelaunchedfroma zero-lengthlauncheratanelevationangleof55°. Ea.tawereobtainedduringthedeceleratingportionof the .

NACATN 3623 5

flighttrajectory.TrajectoryandatmosphericdatawereobtainedfromtheNACAmodifiedSCR584radartheodoliteandby radiosondeobsenations.Thethe historyof thefUght velocitywasobt-ed fromthecontinuous-waveI@plertheodoliteradarunit(asdescribedinref.2). Thermody-namicpropertiesoftheairshowninfigure4 wereobtainedfromrefer-ence3. Thespecificheatof themagnesiumwallpresentedinfigure5wasobtainedfromreference4.

!Mmehistoriesofthemeasuredskintemperaturepresentedinfigure6wereobtainedas thevehiclescoastedfroma Machnunberofappro~tely2.5 to 1.0. At thetimeofrocketmotorburnout,whichwasapproximately3.2secondsafterthestartofflight,thetestvehicleswereattheirnmdmnnnvelocityandMachnuniber.No skintemperaturemeasurementswereobtainedthroughouttheinitial3.2seconds,theperiodofpoweredflight,duringwhichtimethetelemetersignalwasumatisfactory.PropertiesoftheairintheundisturbedfreestreamaheadofthemodelssndMachnum-berformodelsA andB areshowninfigure7 plottedagainsttime.Reyn-oldsnumberperfoot,basedonfree-streamconditions,is showninfig-ure8 plottedsgainstMachnumber.The&l.fferenceinReynoldsnumberbetweenthetwomodelsisattributedto differencesinatmosphericcon-ditionsandperformanceofthe‘rocketmotors.

METHOIEANDPROCEDURES

Thetransientconditionsencounteredduringthepoweredtestvehicleresultina heatingoftheskinduringthefirstpartoftheflightanda coolingofboundarylayerduringthelatterpartoftheflight.peratureincreasesduringtheheatingperiod,passes‘ad

the

flightoftherocket-by theboundarylayertheSkinby theThus, theskintem-througha maxhmn,

decreasesduringthe-remainderofthefl&#rb.

Consideringradiationandconductionasnegligible,theheatlostbyboundarylayerisequaltotheheatabsorbedby thesldnofthemodel.the rateofheatexchangebetweentheboundarylayerandtheskinis

~ = W=w(Taw- ‘w) (1)

thethe rateof changeoftheheatcontainedintheskinis

$ = ywT& ~ (2)

—___ __ .-. . —..—_.——. .—. —.z —— —— —-—

6 NACATN3623

Equatingequations(1)and(2)andsolvtngfortheeffectiveheat-transfercoefficientresultsin

(3)

Thepropertiesofthewallmaterialareknownandtherateof changeofwalltemperatureistheslopeofthemeasuredthe historyoftheskintemperature.ToobtainthetemperaturedifferenceTaw- ~ itisfirstnecessarytodefinethsrecoveryfactor.

RECOVERYFACTOR

Recoveryfactordefinedherehasbeendiscussedinreferences5 and6 andisbrieflydefinedasthefractionofstagnationtemperaturerise,abovethetemperaturejustoutsidetheboundarylayer,attsdnedby aninsulatedwall. As thestagnationtemperatureisconstsntthroughouttheflow,therecoveryfactormaybewrittenas

.

T - TvRF= aw

T - Tvso

(4)

~ theabsenceofradiationandconductionatthepeakoftheskin-temperaturecurve,noheatisbeingtransferredandtheskintemperatureandadiabaticwalltemperaturecoincide.Itisfromthispointthattherecoveryfactorisdetermined.Trajectoryandradiosondedatayieldthefree-stresmstaticandstagnationtemperatures.Thetemperatureoutsidetheboundarylayerisobtainedfromthefree-streamstatictemperatureby correctingforthelocalpressureonthebody.

Assumingthisrecoveryfactortobe constantduringthedeceleratingportionof tieflight,eqtition(4)maybehistoryoftheadiabaticwalltemperature

Taw (=TV+RFT -‘o

re-solvedto-yieldthetime -

)Tv (5)

.

NACATN 3623

Thisadiabaticwalltemperatureiswouldhavethroughoutthetestrangeif

Thetransfer

ACCURACY

errorintroducedinevaluating

thetemperaturethattheskinithadno heatcapacity.

thelocalconvectiveheat-coefficientsis causedeitherby inaccuratemeasurementof the

dataorby th6assumptionsmadeintheanalysis.ListedintableII arethemaximumvaluesexpectedoftheseerrors.Asthemaximmsdonotoccuratthesametime,theseerrorscombinetogivea probablemaximmerrorinevaluatingconvectiveheat-transfercoefficientsof*6percentforthetimeduringwhichthedatawereused.

Duringthetimeofflight,astheskintemperatureapproachesitspeak,therateofchangeof skinteqeratureapproacheszero,asdoesthetemperaturedifferenceTaw- ~ . Thus,~ becumesindete?mdnate.As therateof changeofskintemperatureandthetemperaturedifferenceTaw - ~ approachzero,anyerrorineitherquantitycausesan increasingerrorin ~, andthescatterinthecurveof & againsttimebecomeslarge(ascanbe seeninfig.9). Therefore,onlythedataonthesmoothportionof thecurve,wheretheprobablemaximumerrorwaswrittent6per-cent,wereused.

It canbe noticedfromfigures12 and13thatthescatterbetweenresultsobtainedfromsimilarstationsontwotifferentmodelsis 3 per-cent,orthescatterof+J~percentfromthemeanvalues.

2Ittherefore

appearsthattheactualerrorsaresubstantiallylessthanthemaximumshownby theprecedinganalysis.

RESULTSANDDISCUSSION

Recoveryfactorsshowninfigure10wereobtainedfor&l theteststatio~onmodelsA andB. Stations8.9onmodelA and18.3onmodelBhadrecoveryfactorsof0.835,whilestation14.3ofmodelB hadarecoveryfactorof0.841.!thesewereingoodagreementwiththerecovery

(factorof0.8k-6predictedby thetheoryofreference5 RI’= N- )1/2 for

laminsxboundaxylayers.RecoveryfactorsobtainedfortheotherteststationsWee withthevalueof0.894predictedby theoryinreference7

( )1/3 forturbulentboundarylayers.RF=NR I@orderb evaluatethese

theoretical.recoveryfactors,thethermodynamicpropertiesofairin thePrandtlnumberwerebasedonthetemperaturejustoutsidetheboundarylayer.

-..— _. ——.. -——

8 NACA~ 3623

Althoughtherecoveryfactorsobtainedatthreeofthestationsagreewiththetheoreticalvaluefora lminarboundarylayer,onlystation8.9onmodelA hasa Reynoldsnuntmrrsngethatislikelytoaccompanyalaminarboundarylayer.Alltheheat-transfercoefficientswereofthesameorderofmsgnitudeandwereof a magnitudeexpectedfora turbulentboundary.kyer. Thissuggeststhatthesethreestationswereina transi-tionregionwhereitmsyhavebeenpossibletoobtainlsminsrrecoveryfactorsin conjunctionwithturbulentheattransfer.Thistiewis sup-portedby Eber’stestson cones,atl.fachnmbersfroml.2to 3.1(ref.8),inwhichtheheat-transferdataindicatedthattransitionoccurredon thecones,butthemeasuredrecoveryfactorsalongtheconeswereequaltothevaluespredictedbythetheoryforlaminarflow.

Timehistoriesofthemeasuredskintemperaturesandthecalculatedadiabaticwalltemperaturesareshowninfigure11forstations8.9and123.5ofmodelA. Theskin-temperaturecurvesshowthevariationin themsgnitudeandtimeof occurrenceofthemaximumskintemperaturemeasuredat theextremeteststationsonthebody;thatis,a madmumskintemper-atureof398°F at 5.35secondsforstation8.9anda maximumskintemper-atureof279°F at7.94secondsforstation123.5.Thegreaterrateofheattransferandthinnerskinattheforwardstationcausetheskintem-peraturetheretorisefasterandreacha higherpeskthanattheaftstation,eventhoughtheadiabaticwalltemperatureattheforwardsta-tionis lessthanthatattheaftstation.Duringthecookingpartoftheflight,whentheadiabaticwalJtemperatureislowerthantheskintemper-atureata givenstation,thegreaterrateofheattransferandthinnerskinat station8.9resultin a higherrateof skincoo~ngat station8.9thanatstation123.5.

Theheat-transferdataobtainedinthepresenttestarepresentedinfigure12intermsofNusselt,Prandtl.,andReynoldsnumbers.Thetem-peratureusedtoevaluatetheviscosity,conductivity,density,velocity,andspecificheatoftheairintheaforementionedparametersisthetem-peraturejustoutsidetheboundarylayer Tv. Theflowconditionsjustoutsidetheboundarylayerweredeterminedby correctingthefree-streamconditionsforthetheoreticalpressuredistribution,whichwasobtainedfrmnreference9. (Althoughtheoretical,thepressuredistributionsthusobtainedhavebeensubstantiatedby thewind-tunneltestofref.10.)

As canbe seenfromfigureU!,theheat-transferparsmeterNNuN~-1/3

isprimarilya functionofReynoldsnuniberratherthanbodystation;thatis,resultsobtainedat differentbodystationswerethesamewhentheReynoldsnmiberswereequal.Althoughitisexpectedthatthebodycon-tourwouldhavesomeeffectontheheattrsnsfer,therewasno apparenteffectonthehigh-fineness-ratiobodyusedforthisinvestigation.

Itwouldbe moreconvenientinreducingtheheat-transferdatafor ‘engineeringpurposestobasetheheat-transferparameters,Nusselt,

NACATN 3623 9

Prandtl,andReynoldsnumbers,onconditionsof theairintheundis-turbedfreestrea aheadofthemodel.Theresultsthusobtainedareshowninfigure13. Thiscorrelationis ingoodagreementwiththecorrelationbasedonlocalconditions,probablybecausethefree-streamconditionsarenotverydifferentfromlocalconditionsforthishigh-fineness-ratiobody.

Theeqyationforthermalconductanceforturbulentflowovera flat

plateat subsonicspeedsisgivenas 0.8NNU= 0“.0296R NR 1/3 inrefer-enceXl. Thisequationresultsfromfrictionaldragmeasurementson aflatplateinparallelturbulentflowas correlatedby Colburn(ref.12)usingq momentumheat-transferanalo&y.Thedashedlineshowninfig-uresli?and13representstheprecedingeqwtion. Thislinefallsremarkablyclosetothetestdataobtainedontheparabolicbodyofrevolutionat supersonicspeedsandis inagreementwiththetestresultscorrelatedeitheronflowconditionsjustoutsidetheboundqylayeroronfree-stresmconditions.WhiletheagreementisbetteratthehigherReynoldsnumber,thisequationcouldbe usedtoevaluatetheheat-transfercoefficientwithfairaccuracyovertheentirerangeofReynoldsnumbersshown.

Investigationssimilarto thosedescribedinthispaperwerecon-ductedontwoV-2researchmissiles.Figure4 ofreference13 showstheresultsfromtheheat-transfertestson theV-2researchmissilescomparedwithEber’scorrelation(ref.8),thatis,as a plotofNusseltnmibersgainstReynoldsnumber.Forconvenience,theletterdesignationsforthestationsareidentifiedwiththoseusedinreference13. Thesesta-tionsininchesfromthenoseareasfollows:

Configuration

v-2 NO. 27

V-2No.19

Station Distancefromnose,in.

AcGHKM

2.56.012.o12.O(trip)84.4121.4

--- I 41.71

Thethermalconductivimandviscosityoftheairwerebasedonthea~abaticTTSU temperatureandthedensityandvelocityon conditionsjustoutsidetheboundarylayer.Theseresultsarereproducedinfig-ure14. Thelinefairedthroughthepointsis40percentabovethe

—- -.—. -.— ———— —— .. .. .— ——.— .— .. ._ __ ___ _________ . -f

10 NACATN 3623

EberUne. ForfurthercomparisontheRM-10heat-transferdata,basedonthesameflowproperties,arealsoshown.A linefairedthroughtheRM-10testresultsisabovetheV-2line.

Resultsfromtheure15as NNUNR-1/3tiom oftheair$lst

approximately60percentaboveEberor20percent

V-2testsshowninfigure14areexpressedin fig-plottedagainstReynoldsnumberbasedon condi-outsidetheboundarylayer.Reference13states

thatthedecreaseat lowerReynoldsnumberinthepointsM sad K fortheV-2No.27 andforthepointofV-2No.19isattributedtopartialtransition.NeglectingthesepointsatthelowReynoldsnumber,theV-2heat-transferdataareapproximately15percentlowerthantheRM-10datarepresentedby thesolidcurve’.ThecorrelationNNuN~‘1/3. 0.0296RO”8 is shownasa dashedlineandfallsapproxi-mately20percenthigherthantheV-2points.

In figureI-6,theheat-transferparametersNNUN=‘1/3 frm theRM-10dataareplottedagainstReynoldsnumiber.Thethermalconductiv-ity,viscosity,andspecificheatof airarebasedon adiabaticwalltemperature,andthedensityisbasedonconditionsjustoutsidetheboundarylayer.Forthistemperaturebasis,somewhatgreaterscattercanbe seeninthetestpoints.Thefairedlinethroughthetestpointsfallsapproximately20percentlowerthantheflat-platecorrelation

%&r‘1/3. oQ)2g6R0”80

TIEv-2dataareexpressedtothessmebasisas infigure16 and zareshowninfigure17. Forccmpsrison,theRM-10fairedcurveandthe

0.8-1/3. ().0296Rflat-platecorrelationNNuNn arealsoshowninthisfigure.TheV-2pointsfallabout15percentlowerthantheRM-10fairedcurveandapproximately35percentlowerthantheflat-plateeqpation.

‘1/3 fortheRM-10dataareplottedHeat-transferparsmsters~uNW(fi.g.18)againstReynoldsnumber.Tbethermalconductivity,viscosity,anddensityoftheairarebasedonthewalltemperature.Thesolidline “inthefigureisthefairedcurveoftheRM-10points.Reference14givesa theoryforheattransferonconesin a supersonicturbulent

(‘1/3. ()O% RO*8)thatiS approdmatel.y7 perCf311tbo~ds.rylayerNNUN= .

lowerthanthecurvedlinerepresentingtheRM-10points.Theflat-0.8-1/3= 0.0296RplateequationNNuNn isshowninthefigureas a

dashedlineandisaypro~tely 20percentlowerthantheRM-10fairedcurve.

NACA~ 3623 U

In figure19,theV-2heat-~ansferparamtersareplottedagainstReynoldsnumber.me thermalconductivity,viscosity,anddensitiarebasedonwalltemperature.Disregardingagainforlow“ReynoldsnuniberthepointsK and M andV-2No.19showstheV-2heat-transferdatatobe roughly15percentlowerthantheRM-10fairedcurvere reducedfrom

figure18. (A linerepresentingtheconetheov ~uN~ r‘13 = 0.03 R0”8)faJJ.sapproximately8 percentabovethev-2&ta. ‘lheflat-platecorre-

-1-/3. o.0@6Rl.ationNNUNW 0.8 is shownbya dashedlineapproximately6 percentlowerthan-theV-2pofits.

TheagreementbetweenthesameapprodlmtestationsonmodelsA.andB iswellwithintheestimatedaccuracy.ltromthevariousmethodsofcorrelationitappearsthatbybming thepropertiesoftheaironthetemperaturejustoutsidetheboundarylayerud onwalltemperaturegaveresultsth@ wereapproximately15percentabovetheV-2heat-trsmsferdataandalsowereingoodagreementwiththereferencedequations.

CONCLUSIONS

SupersonicconvectiveheattransferhasbeenmeasuredinflAghtontwomodelsoftheNACARM-10missile.TheMachnumberscoveredbythetestswerefrom1.02to2.4-8andtheReynoldsnuniberswerefrom3.18x 106to163.85x 106basedontheaxial-distancefromthenosetothestationswheretheskin-temperaturemeasurementsweremade.

Resultsofthetestsindicatithat:

1.Heat-transferparametersfromtheRM-10datawhencorrelatedonaNusselt,Prandtl,and.Reynoldsnumberrelation,basedon conditionsjustoutsidetheboundarylayer,showedthattheequationforconvectiveheat

(0.8-1/3=o.&X36Rtransferona flatplateina subsonicflow NNUNR )

wasingoodagreementwiththetestresults,andtheresultsfromtheV-2testswereapproximately15percentlowerthantheRM-10data.

2. Correlationoftheheat-transferte~eratureshowedthattheequationfor

inagoodwere

supersonicturbulentboundarylayeragreementwiththetestresultsandapproximately15percentlowerthan

3.TheRM-10heat-transferdataareEber’sempirical.equation.

parametersfortheFM-10onwallconesforconvectiveheattramsfer

(IN ‘1/3= o.o~R0”8u% ) wasin

theresultsfromtheV-2teststheRM-10data.

approximately60percenthigher

—- . . - -- —. . .—- -- -—.——. .— —— ----- --— ——— -.. + -—-——- .. . . .

12

k. Goodagreementwasobtainedbetweenthemdels A andB andthescatteriswithinthepercent. -

NACA‘IN3623.

heat-transfercoefficientsestimatedaccuracyof

5. Recoveryfactorsmeasuredalongthebodyarein agreementwiththeflat-platetheory.

6. No evidenceofboundsry-lsyertransitionwasapparentintheheat-transferdata.

LangleyAeronauticalLaboratory,NationalAdvisoryComitbeeforAeronautics,

LangleyField,Vs.,Jsmusry18,1951.

.

-. —

NACATN 3623

INFERENCES

13

1.

2.

3.

4.

6.

7*

8.

9.

10.

11.

Fricke,CliffordL.,sadSmith,?hW.IICiSB.: Skin-TemperatureTele-meterforDeterminingBoundary-LayerHeat-~snsferCoefficients.NACARML50J17,1951.

Morrow,JohnD.,andKatz,Ellis:Flight12ivestigationatMachNm-bersFrom0.6 to 1.7ToDetermineDragandlksePressureson,aBlunt-Trailing-EdgeAirfoilsadDrsgofDis.mendandCirc@-ArcAirfoilsatZeroLift.NACATN 354-8,1955. (SupersedesNACARM L50E19a.)

Keenan,JosephH.,andKaye,Joseph:ThermodynamicPropertiesofAirIncludingPol.ytropicFunctions.JohnWiley& Sons,Inc.,1945.

Kelly,K.K.: ContributionstotheEataonTheoreticalMetaI1.urgy.II.Hi.gh-TemperatureSpecific-HeatEquationsforInorganicSub-stances.Bulletin371,Bur.Mines,1934,p. 32.

Wimbrow,Will.ismR.: ExperimentalInvestigationofTemperatureRecoveryFactorsonBod3.esofRevolutionatSupersonicSpeeds.NACATN 1975,1949●

Staider,JacksonR.,Rubesin,MorrisW.,and!l?endeland,Thorval:AIJsterminationoftheIaminar-,Transitional-,andTurbulent-Boundary-LsyerTemperature-RecoveryFactorsona FlatPbte insupersonicFlow. NACATN2077,1950.

Squire,H.B.: HeatTransferCalculationforAerofoils.R.& M.NO.1986,EmitishA.R.c.,1946.

Eber,[G.]: ExperimentalResearchonl%cictionTemperatureandHeatTransferforSimpleBodiesatSupersonicVelocities.Rep.GTR22,ChanceVoughtAircraft!bmslationjI&Y20,1946.

Jones,RobertT.,andMargolis,Kenneth:FlowOvera SlenderBodyofRevolutionatSupersonicVelocities.NACATN1081,1946..

Esenwein,l?redT.,Obery,LeonardJ.jandSchuel.ler,CarlF.: Aero-dymmicCharacteristicsofNACARM-10Missilein8-by 6-FootSupersonicWindTunnelatMachNumbersl?rom1.49to1.98. II -PresentationandAnalysisofForceMeasurements.NACARM E50D28,1950.

Johnson,H.A.,Rubesin,M.W.,et al.: A DesignManualforDeter-mnI theMF TRNo.1947.

fiermalCkacter~sticsofHighS@ed5632,AirMaterielCommand,U. S.Air

Aircrsft(Reprint).Force,Sept.10,

...__ .—____ .—._. _ __ . . .. . _.— —. — .— —. . ...—--— .. . . .. . .—. —— -———

14 NACA~ 5623

12.Colburn,A.lls.nP.: A MethodofCorrelatingForcedConvectionHeat‘IWnsferDataanda CmnyarisonWithFluidFriction.Trans.Am.Inst.Chem.Eng.,VO1.~, 1933,pp. l’j’4-210.

13.Fischer,W.W.: SupersonicConvectiveHeatTransferCorrelationsFromSkin-TcakperatureMeasurementsDuringFlightsofV-2RocketsNo.27 andNo.19. Rep.No.55258,Gen.Elec.Co.,July1949.

14.Gazley,C.,Jr.: TheoreticalEvaluationoftheTurbulentSkin-FrictionandHeatTransferona ConeinSupersonicFlight.Rep.No.R49A0524,Gen.Elec.Co.,Nov.1949.

.

NACA’I!N3623 15

TABLEI.-SKINTHICKNESSNt?TESTSTATIONS

Model station Skinthickness,

(1) in.

A 8.9 0.058717.8 .058736.2. .092749.9 .081686.1 “.0933123.5 .0863

B 14.3 0.059118.3 .0591“85.3 .0935

1Stationnumberdenotesaxialdis-tancefromnosemeasuredin inches.

TABLEII.- ACCURACY

MaAmum errorin

Sourcesoferror convectiveheat-transfercoefficient,

percent

A possibleerrorin measuredskintemperaturesofti perceqtofmmimum skintemperatureat thatstation

Summationof temperaturelagthroughtheskinandof thethermometer

PossibleK? percenterrorinskinthickness +Q

Neglectedheatflowsinmak.fmgheatbalances Q

2

*4

—. —. . — —.—— .—— .. . . ..-

I

Sta

r Circular-arc profileK

thickness ratio =O.10’

19

d4

9.060° ‘1

I v==-- — .+ ..-j_—_ — —

L x\

Sta Sta S to

o 90 146.5Ymax=6.0 y=?I.IjzG

.

- ~.- @nerd configoxatlonmd body equation d tk IWCAW-10.D@miona m in iIlCh9S . 13tation number denotm axial W3bancefrom m6e in inches. 130dYProfile eqution Y = 6.cGo - 0.W@lq’X?

3PNACA‘IN3623 17

ii /4/’/

,,/0?“

,/,.

d

-J.‘4

, .. —__ _- ..— Ii

Figure2. Photographofmodel“inlaunchingposition.

------ ——-—— —----- -. .—__ _ ._.. -_ .- —__ —-. —.. . _.

IS$ m $

Stole

Figure 3.- Intaml. construction of the NACA RM-10.

I

I

\

ItI

,

Figure 4.- Thermodynamic properties of air.

G

Temperature, ‘f

Figure 5.- Specific heat of magnesium.

i

I

I

i

I

,

440

400

360 //

320 - \___/“

.- -.

$280/’ =.

/’ ./” —— __m“ ‘..

/- -

~ /’-” \ -.--- -

:240 / ‘./

2/ ‘ -- \\

/’ k

~200 //

— mmms.9-——––~*.9————Erbti 4.5

16CI

\~o

60

40 I2345678 10 I 12 13 14 15

Tl:e, SeC16 17

(a) Mcdel A.

Figure 6.- Skin-temperature time history; ‘P

Q4:

LOCI\

360 =-.

/

j: ~ \---- --- ----//”

-.=/~~:j . ,/ =..--— ——_

/ / “ — . ‘.

// / \ .

24G /)7

/,/

Y ‘-.~ti 11,*——-——-mum .4 ,9

11 / ——. Swrma!.1

:~~

l/

.

//

160 -/

/,)/

120 1?

,180 /

-=fS=-40 ~

3 4 5 6 7 8Tln?e, sec

10 II 12 13 14 15 16 I“’

(a) Concluded.

Figure 6.- Continueii.

440

400

360

320

280L!-0a: 240

&

:r 200

160

120

80

[

k3

/\

8titi I&3

\

\

I

I

=+2I

5T$ne (se<onds)

8 9 10 II 12 13 14

5’=

(b) Model B.

Figure 6.- Continued.

440

400

360

320

160

I20

80

,--- -\

,/’ ./ ‘\

/ ‘\\t/ \

/ \/’ x

‘-.~.

-\.— . ‘.. -

‘\,,- . .

/ ---- ~bti la.)— ~ 85.$

2 3 4 5 6 7 8 9 10 II 12 13 14ilme (seconds)

Iv-r=

(b) CODChlded.

Figure 6.- Concluded.

2.s 510

2.4 !300

2.0 490

1,6

12

0

.4

0

Time (seconds)

(a) Wdel A.

Figure 7.- Free-stream parameters.

‘G

z.e 550

2,4 540

2(3 530

z-0.

16 w 520

0 480

26

-7\

24 ~<-,

\mah !nmhr

c ~ —————— m-baa ~tan%——— — n@-9-9&lm IMIEitg

$22 ‘“

~m

-

*O 20 I\

\\

x \\

h\

.!- \ \

.- \u-l \.s 18

$\ \

EQ

‘:’, ‘i,<,

Q 16 \ \~In \\ - ‘“ .,

a)\ \

‘-..\

‘w \

t ,4\ \ \

\‘.

y12

0 2 4 6 8 10 12 14

Time (seconds)

(b) Model B.

Figme 7.- Concluded.

.

NACATN3623

16x106

14r

12

Figure

—Model A——Model B

/ $

/

=s=

L6 2.0 2.4 2.8Mach number

8.- Reynoldsnumberperfoot(basedon the conditionoftheairintheundisturbedfreestreamaheadofthemodel).

E3c

oc

z’K

,

/

.

L+

,05 0~

,04

.,

,03

.02 - (

o

.0 I

o

n I

“o 2 4 6 8 10 12 14 16 18 *Time, sec E!

wCnFigure 9.-Typical veriation of heat-tramfer coefficientwith time. E

/.

I

.96

0 Model Ao Model B

,92 u

- –0 0-. LJ -.

.88z “-—Turbulent theory

o f

— .- ~Lam;nar theory

.84—-

A~ ‘+

RF= TQWTV.TO-T. =%=

.800 ‘20 40 60 80 100 /20 140 160

Station, in,

Figure 10.- Recovery factors obtained at the test stations on the vehicle,

~

{

.

30

—._ ..__

NACATN 3623

640—S? ation 8.9

\–––-Station123.5

560

-Adioba?icWOII temperature

480

400

Skin temperature

320

/“

240 /// -./

160 \.

80 \

yo-o 2 4

Figure11.- Typicaltime

6 8 10 12 14 j6 18lime, sec

historiesof skintemperatureandadiabaticwall.temperature.

NACATN 3623 31

.C‘&z

Z3

I

I

Figure1.2.- Correlationoutsidetheboundaryformula(ref.E?).

Reynoldsnumber

ofheat-transferdata(basedonlayer)withColburn’sturbulent

108

temperatureflat-plate

. . ..-— .——. . ———. —— __ .—. .. ——..+. .. .—— .--—.—.. ——. .— ———— —-— -

32

.

.

I09 I I I I I I I II II Model A Model B Station

R ~ 14.3*————— 17.8

~— 18.3 F

I04

I03106 ~ 107

——

———

—

—

—

/

Reynoldsnumber

Figure 13.- Correlationofheat-transferdata(basedonfree-stream

.

‘temperature)withColburn’sturbulentflat-pl.ateformula.

33

4X104‘STATION SYMBOL

(E

: +

1-V2No.27 ; xL I

K 4M e

I04-V-2N~J9

4

A \3 0

-:[

8.9 Q= sd 17.8 0

3‘Model A 36.2h

‘~ 5100

49.9Lx

z A86.1.

:n~ .c+z I03mwz b

●&lo2 k /

k +

Ebers correlationNNU=.00974, R“*2r

o

&/0..”

●.“

?o

/’

I02 I I I I I 1 I I I I I I I

2XI05 5XI05 106 5406 107QvvvzReynolds number, R= *W

Figure14.- CorrelationofV-2heat-transferdatawithIIber.

.

9107

———..—. .—-. – .—. —.—. — — . — —— . . . .. —- .. -—.— — . .——.-—

I 05

–\~

%10’2=

Reynolds number R= ~

Figure 15. - Correlation of IVACARM-10 and V-2 heat-tranafer data.

I07 I08

,

I 05

22:104

Zz

I I I I I

-1/3% ~PP = 0.a296 F(OOS-

Modal A Mmlel B Sktioil

n ——— ——— 8.9o— — -4.4.3

0 ——— ———~v.aa — — —18.3

Q —.— — — —36.2a ——— — — –43.9

o — — –$5.3——— —— –86.1

L—— —— +23.5

I

E‘<

/’P

/

/ /

//

I07 Q&LReynolds number R= ~Qw10s

Figure 16.- Correlation of WA IW-10 heat-tiansfer data (based onadlabatlc wall temperature)with flat-plate fornr.i&,

,.!

I I I I I I I II I I I I I-1/3

I I I I 1 I ‘W ‘Pr x o.@% R0”8 (fit Phti)

=

FM-lodata

I/

.

—

7-

/—

—

—

77

—

—

—

station 5*1

HKH

‘?-2 Ho. ~

V-2 Ho. 19

4

- —

-———

—

—E F,

k’Ak/2X1(?3

I06 I 07 I08Reynolds number, R= w

Figure 17.- Correlation of IWCA RK-10 heat-tramfer data (based on.@iabaticwall temperature)with V-2 and flat-plate formula.

,

I

I!

I

11,

I

I I I I I I I I%U %,-1’3” 0.034 R0”8(o~

I 1I I

Mdel A Ibid B station

d ———— ——— . 8“’~O—— ——LL3o

sAA

II

I

2.,,’

—— .

—— ————

—— ——— —

10’

——

—

?

7

—

——————

—

I

4, + — —

7‘

-1/3NNUNPr m 0.02% R0”8

1;< )/[/,’I06

Reynolds number R&&

Figure 18.- Correlatbn Of NACA FM-10 heat-tranafer data (based on W&KLtemperature)with turbulent flat-plate and cone formulas.

10’

!2

I

w I

-a

I

I

,“

\

106

.\foLtn.z~ 104

z

2xq-.. .

Figure 19.- Ccu@rlson of NACA RM-10 and V-2 heat-transfer data withturbulent flat-plate and cone formulas.