'R. &. .3-400'MINSTROFAVATOAgRONAUtIAREERHCJNUArri-D ^1j-V,44:i-ptc,^in,P.____Ati11m1imuV1YVILim~ %-FLA.L%A..andStalled Wings in a Closed Wind TunnelByE.C.MASKELLLONDON:HER~ MAJESTY'S STATIONERY OFFICE~t9g65smcATheory of theBlockageEffectsonBluff BodiesandStalledWingsin a ClosedWindTunnelByE.C.MASKELL,COMMUNICATEDBYTHEDEPUTYCONTROLLERAIRCRAFT(RESEARCHANDDEVELOPMENT),MINISTRYOFAVIATIONReportsand MemorandaNo.3400*November, 1963Sumtnwry.Atheoryofblockageconstraintontheflowpastabluffbodyinaclosedwindtunnelisdeveloped,usinganapproximaterelationdescribingthemomentumbalanceintheflowoutsidethewake,andtwoempiricalauxiliaryrelations.ThetheoryiswellsupportedbyexperimentandleadstothecorrectionformulaAq/q= cCDSI/CwhereAq istheeffectiveincreaseindynamicpressureduetoconstraint,andc isa blockagefactordependentonthemagnitudeofthe base-pressurecoefficient.Thefactorcis showntorangebetweenavaluealittlegreaterthan5J2 foraxi-symmetricflowtoa littlelessthanunityfortwo-dimensionalflow.Butthevariationfrom5/2isfoundtobesmallfor,spectratiosintherangeI to10.Thetheoryisextendedtostalledwings,andanappropriatetechniqueforthecorrectionofwind-tunneldataisevolved.LISTOFCONTENTSjAcessionForSectionTISGRA&II.IntroductionDTICTAB2.BluffBodies JUnatiou2.1Propertiesofthebluff-bodywake2.2Invarianceunderconstraint!;3Y31Distribution/2.3Conservation of momentumsAvailability Codes2.4Distortion of the wake IAvailand/or2.5Blockage correction AvistnSpecoial.2.6Discussion2.7Comparisonwithexperiment2.7.1A = 12.7.2A= oo2.7.3The effectofaspectratioUNANNOUNCEDReplacesRA.E.ReportNo.Acro. 2685--A.R.C.25730.CSLTEErLISTOFCONTENTS-continuedSection3.StalledWings3.1Propertiesof thewake3.2Recommendedforms of correction3.2.1Finitespan3.2.2Infinitespan4.ConcludingRemarksSymbolsReferencesIllustrations-Figs.Ito11DetachableAbstractCardsLISTOFILLUSTRATIONSFigure1.Modelofflow2.Invarianceof theratioCD /?k fornon-liftingsquareplates3.Theeffectofconstraintonthelateraldistributionof pressure1 4lbehinda squareflat plate4.Blockageeffectondragandbasepressurefornon-liftingsquareplates5.Blockageeffectondragandbasepressurefornon-liftingtwo-dimensionalplates6.Spanwisevariationofbasepressure(correctedforblockage)fornon-liftingrectangularplates7.Variationofblockagefactorwithaspectratiofornon-liftingrectangularplatesS.Draganalysisfora liftingwing9.Applicationoftheblockagecorrectionstodataobtainedwithtwosizesofaparticularwing-bodycombination(deltawingofA=3)10.Variationofbasepressurewithincidenceforsharp-edgedflatplatesintwo-dimeqsionalflow11.Variation,.oftheblockagefactorwithincidencefortwo-dimensionalplates1.Introduction.Theflowpasta symmetricalbodyimmersedinanairstreamboundedbyrigidwallsissubjecttipwhatiscommonlycalledblockageconstraint.TherigidboundariespreventafreelateraldisIdlacementoftheairflowbythebody,intheneighbourhoodof\hich\elocitiesarehigherthan2theywouldbeinanunlimitedstream.Thedominanteffectisusuallytakentobeequivalenttoasimpleincreasein thefree-streamvelocity,relatedinparttothevolumedistributionofthebodyitself(solidblockage),andinparttothedisplacementeffectof thewake(wakeblockage).Approrpriatecorrectonstomeobservedvelocityofthestreamcanbecalculatedbystandardmethods,providedthatthegivenbodygivesrise toanessentiallystreamlineflow.Little attentionhasbeengiventowallconstraintonthe non-streamlineflow past abluff bodyor,more generally,astalledwing, sinceGlauert's'treatmentof thetwo-dimensionalproblemin1933.Glauert'sinterestintheproblem appearstohavebeenstimulatedbytheexperimentsofFageandJohansen2, 3 ontheflowpastaninclinedflatplatespanningawindtunnel.Hepointedoutthenatureoftheblockageeffectassociatedwiththethickbluff-bodywake,andhisremarksledFageandJohansentotestseveralplatesofdifferentsizesandhence,byextrapolationtozerochord,toestablishthe dragcoefficientof atwo-dimensionalflatplatenormaltoanunlimitedstream.Mean-whileGlauertproposedatheory,basedinpart upontheHelmholtzmodelof theflowpastabluffbody,accordingtowhichthedragD,inanunlimitedstreamisrelatedtothedragDinthewindtunnel by %De=Dl-h]wheretisthethicknessofthebluffbase,h thetunnelheight,andqanempiricalfactor.Butthepresenceoftheempiricallydeterminedq reducesGlauert'sformulatoaninterpolationbetweenknownexperimentalresults,whicharenotsufficientlyaccuratetogiveadequatesupporttotheproposedfunctionaldependenceuponilh. Theformulaseemsnottohavebeenwidelyused,thewakeblockagecorrectionAqI CSq2(whereAqistheeffectiveincrementinthedynamicpressureoftheundisturbedstream,Stherepresei,,ativeareaonwhichtheprofiledragcoefficientCDoisbased,andC thecross-sectionalareaofthetunnel)generallybeingpreferredtoit.*However,thereislittledoubtthatthelattercorrectionholdsonlyforstreamlineflow,andthatthebluff-bodyproblemrequiresadifferenttreatment.Thispaperpresentsasimpletheoryoftheconstraintwhichiswellsupportedbyobservation.Interestintheproblem,especiallyinitsthree-dimensionalform,wasrevivedwhenmarkeddifferenceswerenoticedinthehigh-liftcharacteristicsofmodelsofaparticularaircrafttestedindifferentwindtunnels.Themodelsinquestionwerebasicallydeltawingsofmoderatelysmallaspectratio.Andfrom the onsetof stall,which beganat the wingtipsand then spreadinboardwithincreasingincidence,thedifferentsetsofresultscouldbereconciledonlythroughsomeformofwallinterferencegrosslybiggerthanthosecoveredbythe standardcorrections.Thepurposeof thepresentinvestigation,therefore,wastoestablishtheexistenceofsuchaninterferencemorecon-vincinglyandthentoprovideappropriatecorrectionsforit.Sinceitwasevident,fromtheoutset,thattheeffectwasconnectedwiththebreakdownofstreamlineflowover the wing,it seemedworthwhile toconcentrateattention,in thefirst instance,uponthe extremesituationoccurringwhenawing-likeshape-forexample,athinflatplate-is set* See,forexample,Pankhurstand Holder4.3(90995)A2normalto the windstream.The blockageconstraint onthis type of bluff-bodyflow ina wind tunnelwith solidwallsisthereforethe subjectof thefirst partof thispaper.A theoryisdevelopedwhichprovidesanestimateoftheeffectiveincreaseinthedynamicpressureq ofthestream,duetotheconstraint,intheformq_k2CDSqk,:'k 2-wherek2 =1 - C,,CI,bisthebase-pressurecoefficient,and wherethesuffixcreferstoeffective,orcorrected,quantities.Thetheoryisshowntobewellsupportedbyexperimentsonasetofsquareflatplatesin twodifferentwind tunnels.Andsince it is clearfrom thework ofFail,LawfordandEyre,,thatthtbase-pressurecoefficientforsquares,circlesandequilateraltriangles,isabout- 0.4,theblockagecorrectionappropriatetothisrangeofthree-dimensionalshapesfollowsasAqlq- (5/2)CjDSIC, i.e.roughlyfivetimesthecorrectionappropriatetothesamedragin stream-lineflow.Forthetwo-dimensionalflowstudiedexperimentallybyFageandJohansen,forwhichthecorrectedbase-pressurecoefficientismorenearly- 1,thepredictedblockagecorrectionisroughlyAq/q=CDSIC, i.e.onlytwicethecorrespondingcorrectionforstreamlineflow.rTiheremainderofthepaperisconcernedwiththeextensiontostalledwings,withparticularreferencetowings of moderateto small aspect ratiowhereboththe effectand its practicalsignificancearegreatest.Tomaketheextensionpossible,itisnecessarytoassumethatthebreakdownofathree-dimensionalstreamlineflowtendstogiverisetodiscreteregionsofnearlyaxi-symmetricfluw,closelysimilarinstructuretothe bluff-bodywakespreviouslyconsidered.This assumptionissuggestedbymeasurements,byKirbyandSpenceG,inthewakesbehindmodelsofparticulardelta-wingandswept-wingaircraft.Andit isfurthersupportedby theworkof Fail etal, whoshowthat evenwhena bluff-bodywakeis farfrom axi-symmetricnearitsorigin,the subsequenttendencytowardsaxialsymmetryis verystrong.Inconsequenceof this assumedpropertyof the generalflow,thetheorydevelopedfornon-liftingbluffbodiescontinuestohold,inprinciple.Anditsuggests,further,thatthe slowlyvaryingfactor1/(k,2- 1) intheexpressionfortheblockagecorrectionmayusuallybereplacedbytheempiricalconstant5/2.It remainsonly toidentify that part of themeasureddrag to beincludedin the blockageparameterCI) SIC. Forapartiallystalledliftingwingtherearethree contributionsto the totaldragcoefficient:theinduceddragCDp;theprofiledragassociatedwiththeregionsofstreamlineflow,C1O;andtheprofiledragassociatedwiththestalledregions,C,.Itis,ofcourse,thislastcontributionthathas to beidentified.Andacompositewake-blockagecorrectionformulaisproposed,withthe objectofensuringthatthehighcorrectionappropriatetotheeffectconsideredinthispaperisappliedautomaticallyastheneedarises.Thebulkof theworkonwhichthisreportisbasedwascompletedin1955,andtheprincipalformuladerivedwasgivena limitedcirculationatthattime.2.Bliff Bodies.2.1.Propertiesof the Bhiff-BodyWake.Fail,LawfordandEyre5 reportdetailedmeasurementsinthewakesbehindflatplatesoffinitespansetnormalto awindstream.Althoughtheflowishighlyunsteady,theydetect adistinctmeanflowstructure,whichislittleaffectedbyaspectratio(forA