NASA NACA-TN-3819-1957 Base pressure at supersonic speeds on two-dimensional airfoils and on bodies of revolution with and without fins having turbulent boundary layers《二维机翼和带有及不带有.pdf

1、?L. *WCA. Ttlf3E?f/ _TECHNICALBASE PRESSURE.AT SUPERSONICNOTE 3819SPEEDS ONTWO-DIMENSIONALAIRFOILSAND ON BODIES OF REVOLUTION WITH ANDWITHOUT FINSHAVING TURBULENTBOUNDARY LAYERSByEugeneS.LoveLmgleyAeronauticalLaboratoryLangleyField,Va.WashingtonJanuary1957Provided by IHSNot for ResaleNo reproduction

2、 or networking permitted without license from IHS-,-,-TECHLIBRARYKAFB,NMlM NATIONALADVISORYCOMMITTEEBASEPRESSUREATAIRFOILSANDFORAERONAUT 11111111111011bL7KLTECWCALNOTE3819SUPERSONICSPEEDSONIWO-DIMENSIONALONBODIESOFREVOLUTIONWITHANDWITHOUTFINSHAVINGTURBULENTBOUNDARYLAYERS1ByEugeneS.LoveSUMMARYAnsaaly

3、sishasbeenmadeofavailableexperimentaldatatoshowtheeffectsofmostofthevariablesthataremorepredominantindetermining. basepressureatsupersonicspeeds.Theanalysiscoversbasepressuresfortwo-dimensionalairfoilsandforbodiesofrevolutionwithandwith-outstabilizingfinsandisrestrictedtoturbulentboundarylayers.Thep

4、resentstatusofavailableexperimentalinformationissummarizedasaretheexistingmethodsforpredlctirigbasepressure.A simplesemiempiricalmethodispresentedforestimatingbasepres-swe. Fortwo-dhnsionalbases,thismethodstemsfromananalogyestablishedbetweenthebase-pressurephenomenaandthepeakpressureriseassociatedwi

5、ththeseparationoftheboundarylayer.AnanalysismadeforaxiallysymmetricflowindicatesthatthebasepressureforbodiesofrevolutionissubJecttothesameanalogy.Baseduponthemethodspresented,estimationsaremadeofsucheffectsasMachnumber,angleofattack,boattailing,finenessratio,andfiris.Theseestima-tionsgivefairpredict

6、ionsofexperimentalresults.INTRODUCTIONTheproblemofpredictingthebasepressureatsupersonicspeedshasreceivedconsiderableattentioninrecentyearsandseveral“methodshavebeenadvancedrecently(refs.1 to5),someofwhichgivemuchmoresatis-factoryresultsthantheoldermethods(refs.6 to8). TheworkofCroccoandLees(ref.l)”g

7、ivessatisfactoryqualitativepredictionsthroughouttheReynoldsnumberrangeandmayultimatelygivesatisfactoryquantita-tivevaluesiftheproblemofpredictingtheReynoldsnwnberoftransitionlSupersedesdeclassifiedNACAResearchMemorandumL53C02byEugeneS.Love,1953.-11Provided by IHSNot for ResaleNo reproduction or netw

8、orking permitted without license from IHS-,-,-2 NACATN3819inboundarylayersandfreewakesissufficientlyovercomeandifsome .reliablebasicendvalueofthebasepressurecanbeusedasa startingpointinthecalculations.ThesemiempiricalmethodofChapman(ref.2)hasprovedsatisfactoryforthepredictionofthebasepressureonboat-

9、 *tailbodiesandairfoilswhentheboundarylayerIsturbulent.Thismethod(ref.2)utilizesexperimentaldataonprofileswithoutboat-tailing.EdgarCortrightandAlbertSchroederoftheLewisFlightPropulsionLaboratoryhaveproposedamethodforestimatingthebasepressureonaboattailbodyhavinga turbulentboundarylayerthatuti-lizesa

10、nydatawhichprovidetheseparationangleatthebaseasafunctionofMachnumberaheadofthebase.Existingcomparisonsbetweenthismethodandthatofreference2 appeartoindicatethatbothmethodsgive,ingeneral,reasonableagreementwithexperimentalmeasurementsofboattaileffectsforbodiesof-revolutionandfortwo-dimensiomlair-foils

11、. ThemethodofCope(ref.4)doesnotappeartogiveassatisfac-toryapredictionasthatofChapmanand,asCopehaspointedout,theapproximationsandassumptionsinvolvedresultina firstapproximationonly. LittleisknownbythepresentauthoroftherecentmethodofGabeaudbeyondtheinformationgiveninreference3; therefore,thelimitsofit

12、sapplicabilityareunknown.Gabeauddoesappeartoconfinehiscom-parisonstoexperimentaldatafrombodiesofrevolutionwithfinsbut,sincetheequationasgiveninreference3includesnotermstocoverfineffects,thevalueofthemethodremainsinquestion.ThemethodofKurzweg(ref.)appearsinadequatesinceitgivesidenticalresultsforbotha

13、irfoilsandbodiesofrevolution.Todate,considerableexperimentalworkhasbeendevotedtoinvesti-gationsofbasepressureatsupersonicspeeds.Thereportedinvestiga- .tionsaretoonumeroustomakereferencetoallherein,butreferences9to 29, inadditiontocertainofthosepreviouslymentioned,areexamples -ofworkthathasbeendoneto

14、determinetheeffectsofvariousvariablesuponbasepressure.References2,15,16,and23reportinvestigationsinwhichtheeffectsofsupportinterferenceuponbasepressurehavebeenstudied.References2 and15includeinvestigationsoftheeffectsofdisturbancesenteringthewake(ref.2withstingsupportandref.15withoutstingsupport).A

15、nmnberofthereferencesshowthevariationofbasepressurewithReynoldsnumberata constantMachnumber.(Seerefs.2,5,9, lk, 15, 23, 27, and28, forexample.)Theseandotherreferencesshowtheeffectsforbodiesofrevolutionofsuchinfluencingvariablesasthepresenceoffins,locationoffins,jetflow,noseandbaseshapes,andboattaila

16、ngle.Reference10andpartsofreferences25and29areexamplesofstudiesdevotedtoessentiallytwo-dimensionalbasepressures.Withthisaccumulationofexperimensldataandthecom-pilationsofdatanowinexistence,particularlythosecontributedbyDeanR.Chapman,readyassessmentmaybemadeoftheeffectsofmostoftheprimaryinfluencingva

17、riablesaswellasanevaluationofanymethod .advmcedtoprecttheseeffects.However,astillbeshown,thereisstillaneedforexperimentalinformationontheeffectsofcertainvari-ables,particularlythoseassociatedwithfineffectsonbodiesof “revolution.!-l_Provided by IHSNot for ResaleNo reproduction or networking permitted

18、 without license from IHS-,-,-NACATN3819 3.,Inthepresentinvestigation,onlybodiesandwingshavingturbulentboundarylayersaheadoftheirbasesareconsidered.Thisrestrictiontoturbulentboundarylayersisnotsevereforpracticalapplicationsince,atReynoldsnumbersforfull-scaleaircraftormissiles,thelikelihoodofrealizin

19、glsminarflowovertheentirebodyorwingisremote,particu-larlysoforthebody;inaddition,thepresenceofstabilizingfinscausestransitionevenatlowReynoldsnunibers:(Seeref.15.) TheadvantageofthisrestrictionisthatitpermitseffectsofReynoldsnumbertobeignored.References2,10,12,and27,forexsmple,haveshownthat,oncea fu

20、llyturbulentboundarylayerexistsaheadofthebase,thevariationinbasepressurewithincreasingReynoldsnunberissmall.Thepurposeofthisinvestigationistomakea summaryanalysisofavailableexperimentaldata,includingsomeresultsobtainedrecentlyintheLsmgleyg-inchsupersonictunnel,toshowtheeffectsofmostofthevariablestha

21、taremorepredominantininfluencingbasepressureandtoadvance,wherepossible,simplesemiempiricalmethodsforthepredictionoftheseeffects.Thesemethods,whiletheymaynotbesignificantlyadvantageousoverormuchdifferentfrommethodsnowinexistence,arebelievedtoshowamoredirectrelationbetweenwskeandbodygeometry.Furthermo

22、re,a tiscousanalogyisestablishedbetweenthetrailingshockandthepeakpressureriseassociatedwiththesepationoftheboundarylayer.Thefirstpartofthispaperdealswithtwo-dimensionalbasepressures.Thesecondpartdealswiththebasepressureonbodiesofrevolutionwithandwithoutfins.SYM60LSangleofattackfree-stresmMachmmiberM

23、achnwnberaheadofbasestaticpressureaheadofbasedynsmicpressureaheadofbaseMachnumberalm+adoftrai15theseshocksapparentlyarisefromthetendencyoftheflowtooverexpandinitiallyasitturnsthecorner,sothata shockisrequiredtoturntheflowintheCtLrectiondeterminedbythemixingboundariesoftheso-calleddead-airregionassho

24、wninfiguren(a). Theinclinationsofthemixingboundariesandthelipshocksare,therefore,directlyrelatedand,asshowninfigure12,theirinclinationsvarywithReynoldsnumberuntilafullyturbulentboundarylayerexistsaheadofthebase. (Althoughtwo-dimensionalbasesfacili-tatetheobservationoftheseweaklipshocks,itisofinteres

25、ttonotethatlipshockshavebeenobservedintheflowaboutthebaseofabodyofrevolution.Anexampleofthisisshowninfiguren(b)fora 15cone-cylindertestedinaballisticrsngeintheLangleygasdynsmicslaboratory.Inaxiallysymmetricflowthelipshocksareseentobecurved.)Noattemptismadetoaccountforthepresenceoftheseweakshocksinth

26、eestimatesofbasepressureinthisreport.Onthebasisoftheconfigurationemployedandtheresultsshowninfigure8, an analogymaybedrawnforthebaseseparatingtwosupersonicstresmshavingdifferentMachnumbersanddifferentstaticpressuresjustaheadofthebase. (Forexample,at =2.41 and a.=20,M.= 3.40ontheuppersurfaceand1.58on

27、thelowersurface.)IftheparticularvaluesoftheMachnmbersandstaticpressuresoneithersideofabasearesuchthattheycs.nberesolvedtoessentiallythesameMachnumberand -staticpressurebysuperimposingangleofattack,thenthebasepressuremaybeestimatedbythepresentmethod.Generalremarks.-Inviewofthereasonablycloseanalogyth

28、athasbeenshowntoexistbetweentwo-dhensionalbasepressuresandthepeakpressurerisethrougha shockassociatedwiththeseparationoftheboundarylayerfromaflatplate,thereverseoftheproceduremaybeapplied;thatis,measurementsofbasepressuresmaybeacceptedasameansofestimatingthepeakpressurerisewithseparationoftheboundar

29、ylayer.Investigationofthisanalogyforlsmlnarboundarylayersandlaminarwakesmight,withtheadditionalconsiderationofReynoldsnumber,leadto,anestablishmentoftheReynoldhowever,acceptingtheideathatthepeakpressurerisedeterminesthebasepressurepermitsa qualitativesmalogytobedrawn.Figure13 presentsa sketchofthefl

30、owphenmnenaatthebaseofabodyofrevolutionforwhichthevaxiationinMachnumberonthebodysur-faceiszero.Theconvergwake(AtoB)isessentiallyconicalandmustexperiencea recompressionalongAB;whereas,fortwo-dimensional,flowtheconvergenceofthewakewouldcausenochangeinpressurefromthatcorre-spondingtothecompletedexpansi

31、onat A. Forthebodyofrevolution,therefore,thereisa decreaseinMachnumberalongAB suchthatimmedi-atelyaheadof B thelocalMachnmiberisconsiderablylessthsmwouldbethecasefora two-dimensionalbasewiththessmevalueofMachnumberat A. Exactlyat B theturningoftheflowmayb.econsideredtwo-d3mensional;consequently,thet

32、wo-dimensionalpressure-risecoefficientwouldapplyexactlyat B andthevalue.of Ml wouldbethatimmediatelyaheadof B. Itbecomesobtious,therefore,thatinordertorealizethesamevalueof Mljustaheadofthebaseofthetrailingshockfora two-dimensionalbaseandforthebaseofabodyofrevolution,eachhaving .-thesamedegreeofwake

33、convergence,thevalueoftheMachnuuiberaheadofthebase M. mustbeconsiderablygreaterforthebodyofrevolution.Fromtheforegoingreasoningandinviewofthevsriationof b with showninfigure4,thebasepressuresonbodiesofrevolutionwouldbeexpectedtobeconsiderablyhigherthanthoseontwo-dimensionalbodiesatlowandmoderatesupe

34、rsonicspeedsandequaltoorslightlylessthanthoseontwo-dimensionalbodiesathighsupersonicspeeds.Althoughexperimentalbase-pressureresultstendtoconfirmthepre-cedingqualitativeanalysis,quantitativeconfirmationthroughcalculationsbasedon Pr isdesirable;however,itwouldbenecessarytoknowthedistanceN (seefig.13).

35、beforeanyreversecalculationcouldbemadeoftheMachnumbervariationfrcmB to A.ThisdistancewouldofnecessityhavetobemeasuredfromexperimentalresultsandthelocationofthepointB mightbesubjecttoconsiderableerror.Forthisreasonandfromconsiderationoftheinherenterrorsinvolvedina reversecalculationofthistype(methodo

36、fcharacteristics),noattempthasbeenmadetoapply. thisapproach.Instead,measurementshavebeenmade,frompublishedschlierenphotographsandshadowgraphs,oftheanglee (seefig.13).Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-12 l!lACATN3819betweenfree-streamdir

37、ectionandtheclearlydefinedouterboundaryof .theconvergentwake.ThemainpartofthesemeasurementswasobtainedfrcznshadowgraphsmadebytheBallisticResearchLaboratories(BRL),AberdeenProvingGround,examplesofwhichareshowninreference2. The -resultsareshownhereininfigure14.Several valuesof f3and M. fromfigure14wer

38、eutilizedinattemptstocalculatethech numbervariationalongthesurfaceofaconereplacingtheconvergentwakeinordertodeterminewhetherareasonableapproximationoftherequiredvalueof Ml couldbeobtainedatsomestationaheadofthetipofthecone.Themethodofcharacter-isticswasusedfirstinthesecalculations.Alltheresultsshowe

39、dthat,ifreliablepressuresweretobeobtainedovertherearportionofthecone,increasinglymorepointsmustbeaddedtothecharacteristicnetastheconetipisapproached.Becauseofthiscomplication,thecalcula-tionswereconfinedto M.=2.00 and e =10.33;theresultsareshowninfigure15. Thethirdrefinementtothecalculations,whichga

40、ve44pointsalongtheconesurface,gavea valueof Ml ofapproxtely1.6oattheconetipascomparedwiththecriticalvalueofabout1.58determinedfrom Pr.Itisdifficulttoestimatewhetherfurtherrefine-mentstothecharacteristiccalculationswouldlowerthecalculatedvalueof Ml muchfurther,butthefactthatthevaluethuscalculatedandt

41、hevaluedeterminedfrom Pr areofthessmeorderwouldseemtooffer,atleast,supportforthequalitativeanalogypresentedpreviously.ThelessexactmethodofsmallMsturbanceswasusedinseveral30-pointcalculationsand,excludingtherearward5 to10percentoftheconewherethepredictedvaluesbegintoincreaserapidlytowardinfinitepress

42、ureatthetip,theseresultsalsogavevalues of Ml ofthesameorderasthosedeterminedfromPr. Furthermore,theresultsofrefer-ence15wouldappeartoindicatethatthetheoreticallypredictedposi-tivepressuresovertherearofaparabolicconvergentafterbodyarereallzedexperimentally.RecentlyjmeasurementshavebeenmadeintheLangle

43、y9-inchsuper-sonictunneloftherecompressionalongthesurfaceofa 10conicalafterbodyprecededbya cylindricalsectionandwitbinthewakebehindthebaseofa cylindricalsemibodyofrevolutionmountedona.boundary-layer-removalplate.Theresultsforthe10conicalafterbodyarepre-sentedinfigure16andshowclearlythattherecompress

44、ionalongtheconesurfacereachedpositivevaluesandisoftheorderofmagnitudepredictedtheoretically.Figure17presentsthewskepressuresmeasuredonthesurfaceoftheboundary-layerplateforwhichorificeswerelocatedalonganextensionofthebodycenterlineandalonga 10oraypassingthroughtheshoulderofthebase.Althoughthewakepres

45、suresthusmeasuredaresubjecttotheeffectsofthepresenceoftheplate.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN3819 13surface,theyarebelievedtorepresenta reasonablyaccuratepictureofthetruevariationofthewskepressureswiththepossibleexceptionofreg

46、ionsveryclosetothebase.At M = 1.93 a directcomparisonmaybemadebetweentheresultsoffigures16and17since,asshowninfigure14,thevalueof e at M = 1.93 isverycloseto10. Sucha cmnparisonshowsthattherecompressionalongthewakeboundaryisverysimilartothatontheconicalafterbodyandthattherecompressiontendstobeslight

47、lygreaterforthewakeboundary;thus,thecalculatedrecompressionat M.=2.00 presentedpreviouslywouldappeartobea conservativeestimate.Theseresultscoupledwiththeprecedinganalysistendtosub-stantiatetheideathatthepeakpressureriseassociatedwiththesepa-rationoftheboundarylayeristhepredominantfactorindetermimlmg

48、thebasepressureinaxiallysymmetricaswellastwd-dimensionalflow.me resultsoffigure17 appeartobeofadditionalthattheresultsatallMachnumbersshowthattheoftenofconstantpressurewithintheconvergentwakebehindationisnotpermissible.Simplifledrelationtowakeconvergence.-Theuppersignificanceinusedasstionbodyofrevol

49、u-curveoffig-ure14,throughaMachnumberofabout4,isfairedthrouthemeasuredexperimentalvaluesofwakeconvergence13presentedasa functionoftheMachnumberaheadofthebase.Thedoublesymbolfora givenmeasurementrepresentsthelimitsofmeasurementof “f3frombothsidesofthewake.Allexperimentalpointsrepresentthecaseofzeroboat-tailing,andnomeasurementsweremadeforbodieshatingfinenessratioslessthan5.Ifthecylindricalafterbodywasnotsufficientlylongtoal