4 nationaladvisorycommittee i foraeronautics d/67531/metadc... · techlibrarykafb,nm 1p,...
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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
. . . . . . . ---- . . ... . . . . . . .
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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- -.---–-—.
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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)(%)
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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
.— . . . . . . —.. —.. ——. —.—–—
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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 .
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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 —— —— —-—
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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)
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.
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.
-..— _. ——.. -——
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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,
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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
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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.
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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. [email protected] 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
—- . . - -- —. . .—- -- -—.——. .— —— ----- --— ——— -.. + -—-——- .. . . .
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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.
.
-. —
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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,
...__ .—____ .—._. _ __ . . .. . _.— —. — .— —. . ...—--— .. . . .. . .—. —— -———
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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.
.
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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
—. —. . — —.—— .—— .. . . ..-
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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?
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3PNACA‘IN3623 17
ii /4/’/
,,/0?“
,/,.
d
-J.‘4
, .. —__ _- ..— Ii
Figure2. Photographofmodel“inlaunchingposition.
------ ——-—— —----- -. .—__ _ ._.. -_ .- —__ —-. —.. . _.
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IS$ m $
Stole
Figure 3.- Intaml. construction of the NACA RM-10.
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I
I
\
ItI
,
Figure 4.- Thermodynamic properties of air.
G
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Temperature, ‘f
Figure 5.- Specific heat of magnesium.
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i
I
I
i
I
,
440
400
360 //
320 - \___/“
.- -.
$280/’ =.
/’ ./” —— __m“ ‘..
/- -
~ /’-” \ -.--- -
:240 / ‘./
2/ ‘ -- \\
/’ k
~200 //
— mmms.9-——––~*.9————Erbti 4.5
16CI
\~o
60
40 I2345678 10 I 12 13 14 15
Tl:e, SeC16 17
(a) Mcdel A.
Figure 6.- Skin-temperature time history; ‘P
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Q4:
LOCI\
360 =-.
/
j: ~ \---- --- ----//”
-.=/~~:j . ,/ =..--— ——_
/ / “ — . ‘.
// / \ .
24G /)7
/,/
Y ‘-.~ti 11,*——-——-mum .4 ,9
11 / ——. Swrma!.1
:~~
l/
.
//
160 -/
/,)/
120 1?
,180 /
-=fS=-40 ~
3 4 5 6 7 8Tln?e, sec
10 II 12 13 14 15 16 I“’
(a) Concluded.
Figure 6.- Continueii.
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440
400
360
320
280L!-0a: 240
&
:r 200
160
120
80
[
k3
/\
8titi I&3
\
\
I
I
=+2I
5T$ne (se<onds)
8 9 10 II 12 13 14
5’=
(b) Model B.
Figure 6.- Continued.
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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.
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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
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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.
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.
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
,
/
.
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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
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/.
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,
~
{
.
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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.
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NACATN 3623 31
.C‘&z
Z3
I
I
Figure1.2.- Correlationoutsidetheboundaryformula(ref.E?).
Reynoldsnumber
ofheat-transferdata(basedonlayer)withColburn’sturbulent
108
temperatureflat-plate
. . ..-— .——. . ———. —— __ .—. .. ——..+. .. .—— .--—.—.. ——. .— ———— —-— -
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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.
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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
———..—. .—-. – .—. —.—. — — . — —— . . . .. —- .. -—.— — . .——.-—
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I 05
–\~
%10’2=
Reynolds number R= ~
Figure 15. - Correlation of IVACARM-10 and V-2 heat-tranafer data.
I07 I08
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,
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&,
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,.!
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)
=
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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.
,
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Reynolds number R&&
Figure 18.- Correlatbn Of NACA FM-10 heat-tranafer data (based on W&KLtemperature)with turbulent flat-plate and cone formulas.
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w I
-a
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Figure 19.- Ccu@rlson of NACA RM-10 and V-2 heat-transfer data withturbulent flat-plate and cone formulas.