1、C*1 ,1NATIONALADVISORYCOMMITTEEFORAERONAUTICSTECHNICALNOTE3344TIIEORETICALANDEXPERIMENTALINVESTIGATIONOFAERODYNAMIC-HEATINGANDISOTHERMALHEAT-TRANSFERPARAMETERSONA HEMISPHERICALNOSEWITHLAMTNARBOUNDARYJL%YERAT SUPERSONICMACHNUMBERSBy HowardA. StineandKentWanl.assAmesAeronauticalLaboratoryMoffettField,
2、 CaYf.UOAcX3PY:RETURRAFWL(DOGL)KIRTLANDAFB,N.IProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECHUBRARYKAFB,NMNATIONALADVISORYCOMMITTEEFORAEIJONAUT1Iilllllllllllllllllllllllll-001sL07iTECHNICALNOTE3344THEORETICALANDEXPERIMENTALINVESTIGATIONOFAERODYN
3、AMIC-13?ATINGANDISOTHERMALHEAT-TRANSFERPARAMETERSONA HEMISPHERICALNOSEWITHLAMINARBOUNDARYIJNERATSUPERSONICMACHNUMBERSByHowardA.StineandKentWanlassSUMMARYTheeffectofa strong,negativepressuregradientuponthelocalrateofheattransferthrougha laminarboundarylayerontheisothermalsurfaceofanelectricallyheated
4、,cylindricalbodyofrevolutionwithahemisphericalnosewasdeterminedfromwind-tunneltestsataMachnuniberof1.97. Theinvestigationindicatedthatthelocalheat-transferpara-meter,Nu/, basedonflowconditionsjustoutsidetheboundarylayer,decreasedfromavalueof0.65*O.1Oatthestagnationpointofthehemi-spheretoavalueof0.43
5、K).0atthejunctionwiththecylindrical.afterbody.Becausemeasurementsofthestaticpressuredistributionoverthehemisphereindicatedthatthelocalflowpatterntendedtobecomestationaryasthefree-streamMachnumberwasincreasedto3.8, thisdis-% tributionofheat-transferparameterisbelievedrepresentativeofallMachnumbersgre
6、aterthan1.97andoftemperatureslessthanthatofdis-sociation.Thelocalheat-transferpsrameterwasindependentofReynoldsnu?iberbasedonbodydiameterintherangefrom0.6xIto2.3x106.IThemeasureddistributionofheat-transferparameteragreedwithin*I8percentwithSJIapproximatetheoreticaldistributioncalculatedwithforelmowl
7、edgeonlyofthepressuredistributionaboutthebody.Thismethod,applicabletoanybodyofrevolutionwithanisothermalsurface,combinestheManglertransformation,Stewsrtsontransformation,andthermalsolutionstotheFallmer-Skanwedge-flowproblem,andthusevaluatestheheat-transferrateinaxisymmetriccompressibleflowintermsoft
8、heknownheat-transferrateinanapproximatelyequivalenttwo-dimensionalincompres-sibleflow.Measurementsofrecovery-temperaturedistributionsatMachnumbersof1.97and3.04yieldedlocalrecoveryfactorshavinganaveragevalueof0.823+0.012onthehemispherewhichincreasedabruptlyattheshouldertoanaveragevalueof0.840*C).012o
9、nthecylindricalafterbody.Thisresultsuggeststhattheusual,representationofthelsminarrecoverya71factorasthesquarerootofthePrandtlnumberisconservativeinthepresenceofa strong,acceleratingpressureadient.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2INTR
10、ODUCTIONNACATN3344Duetotheprocessesoffrictionandcompression,abodymovingthroughtheatmosph=eaccumulatesasthermaleneraportionofitsmechanicalenerofmotion.Thephysiological,structural,andaero-dynamicramificationsofthiswell-knownfactintherealmofhigh-speedflightconstitutetheaerodyrmnicheatingproblem.Thepres
11、entstatusofknowledgeinsofarastheaerodynamicaspectssreconcernedwillbediscussedinthefollowingsection.Itissufficientnowtostateonthebasisofareviewofselectedliterature”(refs.1 through25)thattheheattransferthroughthesurfaceofa supersonicvehiclecanbepre- dietedwithconfidenceonlywhentheheatpathisthroughregi
12、onsoflaminarflowandsmallpressuregradient.Becauseinsupersonicflowaconstant-pressuresurfacehasa shsrpleadingedgewhichisdifficult,ifnotimpossibletocool(refs.15and16), thepracticalvehicleforsustainedsupersonicflightmay,ofnecessity,beblunt.Althoughfavor- abletothepromotionoflsminarflow,theseverepressureg
13、radients .associatedwithbluffbodiescanresultinheat-transferratesquitedif-ferentfromthoseonconstant-pressuresurfaces.Theheat-transferchar-acteristicsofthecompressibleboundarylayeronbluffbodiessrethere-forerequired.Thepresentinvestigationhasasitspurposethemeasurementin .supersonicflowofhminsr-boundary
14、-layertemperature-recoveryfactorsandlocalheat-transfercoefficientsontheuniformlyheatedsurfaceofa.hemisphere-cylinder.Theexperimentalresultsme comparedwithanewly #developedmethodofapproximatepredictionwhichutilizesexistingsolu-tionstotheboundary-layerproblem,andwhichbodyofrevolutionwithanisothermalsu
15、rface.JWIIIYSISStatusofKnowledgeisapplicabletoanybluffTheultimaterateofheattransfer-througha giventypeofboundarylayer(i.e.,laminarorturbulent)hasbeenfoundtodependuponthefluidflowconditionscharacterizedbyMachnumberandReynoldsnumber,thefluidpropertiesspecifiedbyPrandtlnumber,thesurfacetemperaturedistr
16、ibution,andthebodyshape.Inordertocalculatetheheat-transferratefromboundary-layertheory,thebodysurfaceiscommonlyassumedto _bea flatplateoraxisymmetric.Effectsofbodycurvatureuponthepres-suredistributionnormaltothesurfaceareneglected,andbody-shapeeffectsareassumedtodependonthestreamwisepressuredistribu
17、tionalone.Whendealin”gwithbodiesofrevolution,anadditionalshapeparam-etermustbeconsideredwhichaccountsforthevariationofcircumferencealongtheaxis.HoWever,becausethisadditionalshapeparsmeterhasbeenshowntorelatetheaxisyrmnetricboundary-layerflowwithanassociateda“.-.aProvided by IHSNot for ResaleNo repro
18、duction or networking permitted without license from IHS-,-,-NACATN 3344 3s two-dimensionalflow(ref.2),itispossible,withoutlossingenerality,toapplytwo-dimensionalresultstoaxisymmetricbodies.*A representativesampleoftheextensiveliteraturedealingwithlaminar-boundary-layerheat-transfertheoryisgiveninre
19、ferences3throughXL.Thelargebodyofemlysisbaseduponintegralmethodsofsolutionhasbeenexcludedfromthissurveypartlyintheinterestsofbrevity,andpartlybecausetheaccuracyoftheseintegralanalysesisjudgedbycomparisonwithsolutionssuchasthoseofreferences3through11. Fluid-propertyandflow-psraetereffectsarestressedi
20、nreferences3, k, and5.Nonisothermalsurfacesareconsideredinreference6. Pres-suregradienteffectsarestudiedinreferences7 and8. Effectsofsmallpressureandwall-temperaturegradientssreinvestigatedinreference9.Bothpressure-gadientandfluid-propertyvariationsareconsideredinreference10,andpressure-gradientandw
21、all-temperatureeffectsaredis-cussedinreferenceIL. Theresultsofthesestudiessuggestthatfluid-propertyandflow-psrsmetervariationsexerta relativelymildinfluenceonthelocalheat-trsnsfercoefficient.Pressureandwall-temperaturegradients,ontheotherhand,canproducelocalheat-transfercoefficientswhichdepartsignif
22、icantlyfromtheisobaricendisothermalpredictions.Theinfluenceofshapeisillustrat+iinreference12-which,inciden-tally,presentsanexcellentaccountofmethodsemployedtopredictheattransfer-whereinaprocedureisdevelopedfortheChowever,sincethedataofreference20wereobtainedundertransientconditionsinthepresenceofa s
23、urfacetemperaturetendingtobecomenonisothermal,thevalidityoftheseresultsisuncertain.HeatTransfer.AccordingtotheNewtonianLawofheattransfer,thethermalflowthroughaunitareaofthefluidincontactwithanisothermalsmfaceisproportionaltothedifferencebetweentheactualskintemperatureandtheskintemperaturecorrespondi
24、ngtonoheatflow.ThefactorofProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 NACATN3344proportionality,calledthelocalheat-transfercoefficient,depends, *fn.casesofforcedconvection,upontheboundary-layertype,andtheflow,fluid-property,andpressure-gradient
25、parametersmentionedpre- Vviously.Forlsminsrflow,thelocalNusseitnumberformedfromthelocalheat-tramfercoefficient,thelengthofboundary-layerrun, andthelocalfree-streamthermalconductivitycube combinedwiththelocalReynoldsnumberinto a localheat-transferpersmeter,definedastheratiooftheNusseltnumbertothesqua
26、rerootoftheReynoldsnumber: .hx/klj% “JKXILl(1)(ForNotation,seeAppendixA.)Onthebasisofavailabletheoryforisothermalsurfaces,moderateMachnumber,andsmalltemperaturedifferences,onecanreasonthatthe .localleminarheat-transferparameteronthebluntnoseofabodyofNu/fiO.30. Thehighervalue(atthestagnationpointofa
27、sphere)ispredicted(foru =0.7)inreference22byneglectingcompressibility;thelowerfigureisappli-cabletoa flatplateorahollowcylinderwithsurfacep=alleltotheairstream. a71Noexact,simpleexpressioncanbewrittentopredictthelocalheat-transferpsrsmeterforpointsonthesurfaceofabodylyinginregions Mofarbitrarypressu
28、regradients,althoughanumberofapproximatemethodsareavailable(refs.12,23,and24forexample).Anotherapproximatemethod-anadaptationofatechniquedescribedinreference22-whichiseasytoapplytouybody ofrevolutionandpromisestobefairlyaccurateforuniformsurfacetemperaturesnotgreatlydifferentfromthestagnationtempera
29、ture-wasdevelopedinconjunctionwiththepresentexperimentalinvestigation.Thismethodhastheadvantagethatnoknowl-edgeisrequiredofthevelocityortemperatureprofilesintheboundarylayer;onlythepressuredistributionaboutthebodyneedbeknown.Themainresultsofthisanalysissresummarizedinthefollowingparagraphs;thedetail
30、scanbefoundinAppendixB.Briefly,themethodmakesuseofthetransformationsofMangler,(ref.2)andStewartson(ref.25)toremovetheproblemfromtheexisym-metriccompressibleplanetotheapproximatelyequivalenttwo-dimensionalincompressibleplane.Thelocalheat-transferpsnuneterontheaxisym-metricbodyincompressibleflow,IVu/a
31、nd,consequently,thedistributionofaxisymmetriccompressibleheat-transferparsmeterNu/fi canbeestablished.Inthepresentinvestigation,thelocalheat-transfer-parameterdistributiononthesurfaceofahemisphere-cylinderiscalculatedusingtheexpertientallydeterminedpressure-gradientparameter,m,accordingtotheforegoin
32、gmethod.RecoveryTemperatureandRecoveryFactorWhenabodymovesthroughtheatmospherethesurfacetendstoassumea temperaturedistribution,calledtheequilibriumtemperaturedistribu-tion,suchthatthelocalheattransferateachpointisaminimum.Intheabsenceofradiationandinternalheatflowtheminimumheattransferiszero;thisequ
33、ilibriumdistributioniscalledtherecovery-temperaturedistribution,andthebmlyissaidtobeinsulated.Sincea spotonthesurfacecanassumea temperaturenogreaterthanitslocalrecoverytem-perature,thequestionofhowhotabodycanpossiblybecomeforgivenflightvelocityandambienttemperaturecanbeansweredbyinvestigatingtheprop
34、ertiesofinsulatedbodies.Therecoverytemperatureatapointonaninsulatedbodyisspecifiedbythesumofthelocalfree-streamtemperaturejustoutsidetheboundarylayerandthetemperatureriseacrosstheboundarylayer.Thetemperatureriseacrosstheboundarylayerdependsupontheboundary-layertypeandthedimensionlessflow,fluidproper
35、ty,andbody-shapeparametersmentionedpreviously.Itisconvenientto comparetheactualtemperatureriseacrosstheboundarylayerwiththerisewhichwouldoccurifthelocalfreestreamwerebroughttorestadiabatically.InthenotationofAppendixA,theratiosoobtainedcanbewrittenTr-T1Cr=Tt-T1 (8)ThefactorCr iscalledtheferentvaluef
36、orlaminarthan. Withtheaidofanaloguetemperature-recoveryfactorandhasadif-puterssmdnumericalinteations,thelocallaminarrecoveryfactorson-aninsulatedflatplatefiairIthemaiimumrateofdecreaseis. abouthoFperminute.Althoughthermalequilibriumisneverachieved,itispossibletoobtainvalidtemperaturedataundercertain
37、operatingconditions.WindtunnelNo.2wasusedforsomeofthetestsbecauseitprovideshigherMachnuribersandReynoldsnumbersthanwindtunnelNo.1.TestBodyA hemisphericalnoseshapewasselectedforthetestbodyinthepresentinvestigation.Considerationsofexperimentalconvenience(suchaseaseofconstruction,mounting,andtesting)an
38、dtheprecedentofcon-siderabletheoreticalbackgrounddealingwithflowaboutspherescombinedtosuggestthehemisphereasthetestbcdy.Thek-inchdiameterhemi-sphericalnosehadacylindricalafterbodywitha lengthlimitedto3inchestoavoidintersectingthereflectionofthebowshockwavefrmnthewind-tunnelwalls.Threesting-supported
39、modelsofthetestbodywereconstructed,eachhavingthessmeexternalsizeandshape,andsur-faceroughnesses(lessthanabout20microinches).Theinstrumentationhousedineachandthesting-supportdetails,however,weredifferent.0Pressure-distributionmodel.-Thepressure-distributionmodel(fig.l(a)madefromaluminum,hadawallthick
40、nessofone-halfinch.Twenty-two0.031-inch-diameterstatic-pressureorificesWereplacedonthesurfaceinaplanepassingthroughtheaxisofrevolution(meridianplane). BrassplugscontainingthedrilledorificeswerepressedProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10
41、 NACATN3344into3/16-inch-diameter,3/8-inch-deepholesinthealuminum.Copper-tubingattachedto-theplugspassedradiallythrough0.064-inch-dismeterholesintothemodelcavityandemergedthrougha2-inch-diameterhollow astingthreadedintothebase.Eachplugandtubewascoatedwithanalkydresinbeforeinsertiontopreventleaks-bet
42、weenthecavityandthesurface.Recovery-temperaturemodel.-Therecovery=tegperaturemodel(fig.l(b),madefromstainlesssteel,had,exceptfortheafterbody,a nominalwallthicknessof0.020inch.Thethicknessofthecylindricalportionincreasedlinearlyfrom0.020inchatitsjunctionwiththehemi-sphere(shoulder)to1/8inchatthepoint
43、of”attachmentofthel/2-inch-thickbasering.Thethinwallservedtominimizeboththeheatcapacityofthemodelandthelongitudinalheatconductionwithintheshell.Stainlesssteelwasusedbecauseofitslowthermalconductivityrelativetoothermetals.Twenty-fourconstantanwiresweresolderedintoholesinthesurfacelyinginarneridisnpla
44、ne,asshowninfigurel(b).Asinglestainless-steelwireconnectedtotheinsideoftheshellnearthebasecompletedthereturncircuitforthetwenty-fourstainless-steel-constantanthermocouples.Thethermocouplewireswerebroughtintothe2-inch-dibneterhollowstingthroughapressure-tightfittinginthebase.Theassemblywascalibratedi
45、na liquidbath.A coppertubecom-municatingwiththemodelcavitywasprovidedsothattheinternalairpressurecouldbereducedtolessthan400microns(0.016-inchHg)abso- *lutetominimizeinternalheattransferduetofreeconvection. Heat-transfermodel.”-Theheat-transfer-model(fig.l(c)wasastainless-steelshellwhichformedtheres
46、istanceeleme”ntofthelow- voltage,high-amperageelectricalcircuitusedtoheatthebody.Thecircuitwasarrangedsothata 60-cyclealternatingcurrentcouldbepassedlongitudinallythroutheshell,enteringthrougha copperbusbarimbed-dedinthenose,andleavingthrougha copper-collectorringwhichformedthebase.Theinteriorsurfac
47、eoftheshellwascontouredtoprovideaneffectivethicknessdistribution,andthereforearesistancedistributionwhichwasproportionaltotheexpectedheat-removalcapabilitiesoftheairstreamwhenthetemperaturewasuniform.Twenty-twocopper-constantanthermocouplesweresoft-solderedinholesdrflledthrougl”theshellinameridianpl
48、ane,withthethermocouplejunctionswithinl/32inchoftheoutersurface.Thespacingisindicatedinfigurel(c).Thewirester-minatedata selectorswitchoutsidethewindtunnelwhichwasarrangedsothat,onalternatesidesofthebody,suctieedtngpairs“ofthecopperwireswhichformedonesideofeachcopper-constantanthermocouplecir-cuitco
49、uld.beutilizedastapstomeasuretheA.C.voltagedropexistingalongany12arconthehemisphere.A simultaneousindicationoftem-peraturecouldbeobtainedfromthethermocouplelyingwithinthesameintervalbutdisplaced1800abouttheaxis.Thestationsontheafterbody .werespacedthesanedistanceapartaswerethoseonthehemisphere.Topreventheatgeneratedinthenosefromflowingbyconductionintothe3/thestaticpressureacrosstheboundary
