1、r-1I,I/REYIfJOIiDSNUMBERcMsmIKuDmuMENTEFFECTS FOR A SERLESMACHNUMBERSINVESTIGATIONOFOF CONE-CYLINDER BODIESATOF 1.62,1.93,AND 2.41By Carl E. GrigsbyandEdmundL. OgburnLangleyAeronauticalLaboratoryLangleyField, Va,NATIONALADVISORY COMMITTEEFOR AERONAUTICSWASHINGTON .October7, 1953Provided by IHSNot fo
2、r ResaleNo reproduction or networking permitted without license from IHS-,-,-IIi- -.-._. - - . . . . . . . . - _ - - ,. . . . . . . _ IIIW,r.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-ID NACARML53H21 - /coNFIhowever,theseforcesarebelievedtobesma
3、ll,especiallyformcdel2.PrecisionofDataA1l-mcdelsweremaintainedwithin0.15ofzeropitchandyawwithrespecttothetunnelsidewalkandcenterline,respectively.Previousmeasurementsoftheflowangularityinthetunneltestsectionhaveshownnegligibledeviations.Theetiimatedaccuraciesofthetestvariablesandmeasuredcoefficients
4、aregiveninthesubsequenttable.Valuesaregivenforatunnelstagnationpressureof30in. Hg. Theaccuraciesofthecoefficientsarefunctionsofthestagnationpressureandincreasewithdecreasingstagnationpressm.Machnmber,M. . . . . . . . . . . . . . . . . 0.01Reynoldsnumber,R,perin. . . . . . . . . . . . to.oo)+xIobTota
5、l-dragcoefficient, . . . . . . . . . . . . . . . . 0.003Forebdypressure-dragcoefficient, . . . . . . . . . . 0.(x12Base-dragcoefficient,c. a71 . . . . . . . . . . . . . . . . .30.002RESULTSANDDISCUSSIONTotalad BaseDragThetotal-dragcoefficientsforallmodelsareshownforvaryingReynoldsnmtirat M . 2.41 in
6、figure3. ThesedataaretypicsloftheresultsobtainedattheothertestMachnunibers.Thecorrespondingbase-dragcoefficientsareshowninfigure4. Formodel8, the reflected=3. . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 -” -c5iiimFmmL .-”J NACARML53H21nosesh
7、ockenteredthewakeatapositionsuchthatthebasedragwasaffected(seeref.10). Thevariationofboththebase-andtotal-dragcoefficientswithReynoldsnumberistypicalofthevariationshowninpreviousresultsforthistypeofconfiguration.Theeffectsofbothmcdelfinenessratioandhkchnumberuponbasepressureforthesecon-figurationsha
8、vebeendiscussedinreference9.ForebodyPressureDragTypicalpressuredistributionsovertheconicalportionofmodel8at M =2.41 areshowninfigure. ThesedistributionsateachReynoldsnumberwereintegratedtoobtaintheforebodypressure-dragcoefficientsshowninfigure6. Itcanbeseenthattheforebodypressuredragisrela-tivelyind
9、ependentofReynoldsnumberattheMachnumberstested.TheexperimentalresultsarealsocomparedwiththevaluesfromthetablesofsolutionstothetheoryofTaylorandMaccollgiveninreferenceI-1.Theexperimentalresultsareabout6 percenthigherthantheoreticalresultsat M = 1.62, “in goodagreementat M = 1.93 andabout4percentlower
10、at M = 2.41.Skin-FrictionCoefficientTheskin-frictiondataresultsleftmuchtobedesiredwithregardtoaccuracyandscatteroftheresults;consequently,onlytypicslresultsat M = 2.41willbepresented.Theskin-frictioncoefficientswereobtainedinthe-followingmsmner:(1)Theresultsat M = 2.41 areshowninfigurel.Alsoshowninf
11、igure7are the followingtheoreticalresultsforlaminarflow:theflat-plateincompressibleresultofBlasius,thecompressibleresultofChapmanandRubesin,andtheflat-platevaluescorrectedtothecone-cylinderbytheformula-giveninreference2.2 J(s+a)(s+3a% ftplates+2a (2)Provided by IHSNot for ResaleNo reproduction or ne
12、tworking permitted without license from IHS-,-,-NACARML53H21 m 7-. where s istheslantheightoftheconeaud a isthelengthofthecylindricalsfterbody.TMs formulafollowsfromthetransformationbyMangleranddoesnotconsiderchangesinpressureslongthebody.Theincompressible,turbulent,skin-frictioncoefficientisalsopre
13、sentedtogetherwiththeextendedFrsnklandVoisheltheory.Thesetheoretical.predictionsforturbdentflowarepresentedonlyasamatterofrefer-encesincetherearenocomparableexperimentalresults.Theexperimentalresultscanbeseentoexhibitconsiderablescatter,particularlyinthetrsmitionrangewherethevaluesofskin-frictioncoe
14、fficientaresmallest.Nogeneralconclusioncanbedrawnfromtheresultsabouttheeffectsofvaryingmodelfinenessratiouponskin,friction. IReynoldsNumberforFromtheoreticalconsiderations,itTrsmsitioniswelllmownatsubsonic8peeds,theReweldsnumberfortransitionthat,forairfoilsisafunctionofwingReynoldsnumber.Thisdepende
15、ncyuponw5ngReynoldsnumberisaconsequenceofthefavorablepressuregradientexistingovertheforwardpositionoftheairfoil.Configurationshavingzeropressuregradient,suchasflatplates,havetransitionReynoldsnumberswlxichareinvariantwithwingReynoldsnumbers.Thus,itissurprisingwhentheresultsinreference7 forhollowcyli
16、ndersatsupersonicspeedsshowtransition-uReynoldsnumberswhichincreasewithincreasingstagnationpressure.(increasingstresmReynoldsnumber).Since,fora givenMachnumiber,Reynoldsnumberisafunctionoftemperaturesndpresswe,itwasnotclearthatsimilarresultscouldnothavebeenobtainedbyvariationsinstagnationtemperature
17、inwhichcasethetransitionReynoldsnumberswouldhavebeenshownasafunctionofReynoldsnuuiberperunitlengbh.However,unpublisheddataofthetransitionReynoldsnumberona 10conefromtheLangleyg-inchsupersonictunnelhaveindicatedthatdecreasingthestagnationtemperature(increasingstreamReynoldsnumiber)gaveslightlylowertr
18、ansitionReynoldsnumbers,whereasincreasingthestag-nationpressure(increasingstreamReynoldsnumber)gavehighertransi-tionReynoldsnwbers. Thus,itappearsthattheeffectcannotbeiso-latedasafunctionofReynoldsnumberperunitlength,butisafunctionofsomeparameterwhichisinfluencedbychangesinstagnationpressure.Schlier
19、enphotographsofmodel8 (steel)wereobtainedforseveralstagnationpressuresateachMachnumber;typicalresultsat M = 1.62srepresentedinfigure8. Pointsoftransitionweremeasuredateachstagnationpressurefromthephotographsandthecorrespondingtransition.Reynoldsnumbersweredetermined.ThesetransitionReynoldsnumberssre
20、showninfigure9 togetherwitha compilationofdatafromothersources.whichincluderesultsforseversllbodiesofrevolution,a coneandtwohollowcylinders(refs.2,3, 6, 7, andunpublishedresults).Tbe- Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 I?ACARML53H21baJ
21、listic-rangeresultsofreference2 areplottedwithambientpressureastheabscissa.Thewind-tunnelresultsshowninfigure9 representequilibriatemperateconditions.Therelativeturbulencelevelsofthevarioustunnelsarenotknown,andthepossibleeffectsofstagnationpressureupontheseturbulencelevelsanduponothertunnelconditio
22、nssuchasMachnumberandstreamangularitiesanddisturbances,cannotbedetenninad.Inthepressurizedbsllistic-rangetests(ref.2),anyeffectsoftunnelturbulencearepresumablyexcluded,althoughitispossiblethatheat-transfereffectsandeffectsofslightoscillationsinangleofattacksrepresent.Theresultsforthebodiesofrevoluti
23、oncontaineffectsofvaryingpressuregradientoverthecylindricalafterbody,anditalsoappearsthatconsiderationmustbegiventothelenhoftheadversepres-suregradientaswellastothevalueofthepressuregradient.However,inspiteofthevarietyofthetestconditionsandtech-niquesrepresentedinthesummaryofdata,a definiteincreasei
24、nReynoldsnumberfortransitionwithincreasingstaationpressureisevident.Thepresentresultsshowedanincreasewithincreasingstagnationpressurerangingfromabout3 x 106 at30in. Hgtoabout5 x 106 at 120 in.Hg.Itisalsointerestingtonotethattheresultsshownfortheconeandforthehollowcylinderswhichhaveessentiallyzeropre
25、ssungradientareinsubstantialagreementwiththeresultsforthebcdiesofrevolution.Uptothepresentthe, nosatisfactoryexplanationhasbeenfoundforthisphenomenon,butitisevidentthatcomparisonsofwind-tunnel-transitionresultsorattemptstoapplytheseresultstofreeflightmusttakeintoconsiderationthisphenomenon.Thevariat
26、ioninReynoldsnumberfortransitionatthebasewithMachnumberasdeterminedfromschlierenphotographsispresentedinfigure10togetherwitha smmaryofresultsforcone-cylinderbodiesofrevolution(refs.1,2,5, 6, 10,and12to 15). Theaveragesurfaceroughnessfortheseconfigurationsrangesfromabout8 to20rmsmicroinches.Eachpoint
27、representsa singlevalueofstagnationpressure;someeffectofstagnationpressureasdiscussedpreviouslymaybeseeninthepresentresultswherethelow-fineness-ratiobodieshavethelargestvaluesoftrfiitionReynoldsnuaiber.Inviewofthenuderoffactorswhichmayinfluencetransitionandwhichmayoccurasvariablesinthepresentcom-pil
28、ation,itisnotsurprisingthattheresultsshowconsiderablescatter.However,itmaybeseenthat,ingeneral,thevsriationofReynoldsnumberfortransitionwithllachnwnberistoincreasewithincreasingMachnumberand,then,reachapeakina rsngeofMachnmberfromabout2.0to2.5and,thereafter,decreasewithfurtherincreasesinMachnumber.T
29、hisdecreaseintrsmsitionReynoldsnumberwithMachnumberisconsistentwiththeoreticalresultsforthestabilityoftheIaminarboundarylayerincom-pressibleflow(see,forexample,ref.16). ItmightbenotedthathigherReynoldsnumbersfortransitionhavebeenobtatiedatthehigherMachnum-berswhereboundary-lsyercoolingwaspresent.For
30、exsmple,atransitionL “ -coNFmiyLProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2D-.NACARML53H21 Z!z=zl 9Reynoldsnumberofabout8.5 x 106hasbeenobtainedonahollowcylinderintheLangleyn-inchhypersonictunnelataMachnumberof6.9.Aninvestigationfrictiondragatz
31、eroCONCLUDINGREMARKSoftheReynoldsnumberfortransitionandtheskin-liftofeightcone-cylinderbdieshavingvaryingfinenessratioshasbeenmadeatMachnmhersof1.62, 1.93, and2.41overaReynoldsnumberrsmgefrom0.3 x 106to10x 106. Theaccuracyoftheskin-frictiondatawasnotsufficienttopermitanygeneralconclu-sionstobedrawn.
32、TheReynoldsnumberfortransitionwasindicatedtobeafunctionofsomeparameterwhichisinfluencedbychangesinstagnationpressure.Forthepresentresults,thetransitionReynoldsnumberincreasedwithincreasingstagnationpressurerangingfromabout3 x 106at30in. Hgtoabout5 X106 at120k. Hg. Uptothepresenttime,nosatisfactoryex
33、planationhasbeenfoundforthisphenomenon.-siS ofthepresenttestsresultstogetherwiththeresultsofothercone-cylinderbodiesofrevolutionhavingzero-heattransfershowedthattheReynoldsnumberfortransitionatthebaseincreasedwithincreasingWch numberandreachedapeakataWch numberfromabout2.0to2.5,and,thereafter,decrea
34、sedwithfurtherincreasesinMachnwiber.LangleyAeronauticalLaboratory,NationalAdvisoryCcmmritteeforAeronautics,LareyField,Vs.,August18, 1953. .- -z _Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 NACARML53H21REFERENCES1.2.3.4.5.6.7.8.9.10a71Potter,J.
35、L.: FrictionDragandTransitionReynoldsNumberonBodiesofRevolutionatSupersonicSpeeds.NAVOKDRep.2150,U.S.NavalOral.Lab.,whiteo106 Ar , _. . ,- . - .,.1T ,-. ,. -L-L7%nt of transltla ,4. . “.J RI_736x ,. i”r- #r- ”;:- - “will-, , .-. .-L-80291.Hgure 8.- Schlieren photographs of model 8 for varlouE Reyr.IoME numbersat M u 1.62.! IIProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I(iEWlles of revolutionO w e-cylln, Model 8 (st zero heat tranafer.I,t.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
