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
