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  • IC AS Paper No. 68-09

    DETAILED EXPLORATION OF THE COMPRESSIBLE,VISCOUS FLOW OVER TWO-DIMENSIONAL AEROFOILSAT HIGH REYNOLDS NUMBERS

    by

    M. C. P. Firmin and T. A. CookAerodynamics DepartmentRoyal Aircraft EstablishmentFarnborough, U. K.

    TheSixthCongressofMe

    InternationalCouncilofMeAeronauticalSciences

    DEUTSCHES MUSEUM, MUNCHEN, GERMANY/SEPTEMBER 9-13, 1968

    Preis: DM 2.00

  • DETAILED EXPLORATION OF THE COMPRESSIBLE,VISCOUS FLOW OVER

    TWO DIMENSIONAL AEROFOILS AT HIGH REYNOLDS NUMBERS

    M. C. P. Firminand T. A. CookRoyalAircraftEstablishment,Farnborough,Hampshire,England

    Abstract

    Wind-tunnelinvestigationsintotheflowovertwo-dimensionalaerofoilsare discussedwithparti-cularemphasison the influenceof viscouseffectson aerodynamiccharacteristics.The experimentalworkwas undertakenusinglarge-chord-modelsspan-ning tunnelsboth withsolidand slottedwallsattheRoyalAircraftEstablishment.ThemeasurementsweremadewithReynoldsnumbersup to 15 x 106 andspeedsup to high subsonicwithmodelshavingaspan-to-chordratioof about3.

    Measurementsof boundarylayerand wakedevelopmentare presentedwithmoredetailedmeasurementsin theregionof thetrailing-edgeofthe wings. The resultsare comparedwithmethodsof estimation,and wind tunnelwallcorrectionsarediscussed.

    Introduction

    The designof aircraftforflightat highsub-sonicspeedshas resultedin shapesthathaveasweptwinglayout. In general,thesweepanglesaresuchthattheflowoverthe wingsis sensiblysimi-lar to thatovertwo-dimensionalsections,andcurrenttrendswouldsuggestthatthissituationwillcontinuebut withsectionsthatmorecloselyapproachtheboundariesimposedby viscosityandcompressibility.As it is notyet possibleto makeexactcalculationsof theviscouscompressibleflowaboutaerofoils,predictionmethodsrelyon soundexperimentalbacking; yet as we explainin thispaper,evenexperimentson two-dimensionalsectionsare by no meansas simpleas thetheoreticalmodelmightimplysincetheyrequireparticularlycarefulplanningandmeticulousattentionto detail.

    In thepast,it has notbeenpossibleat speedswherecompressibilitywas significant,to determinethe influenceof viscosityon thepressuredistri-butionoveran aerofoilas no generalsqlytionforpotential-flowexisted. RecentlySells0) hasobtainednumericalsolutionsfor theexactinviscidcompressibleflow overaerofoilsectionsat sub-criticalspeeds. Thisis an importantstepforwardand meansthatany differencebetweenmeasuredandtheoreticalpressuredistributions,suchas thatshownin Figure1 at highsubsonicspeeds,mustnowbe limitedto theviscouseffectswhichwe wishtoinvestigateandany undesirableenvironmentaleffectsdue to the conditionsunderwhichmeasure-mentsare made. Theseenvironmentalproblemsincludetheconstraininginfluenceof thewind-tunnelwallsand viscouseffects,bothof whichmaydetractfrom the two-dimensionalityof thetests.Theseproblemshaveto be overcomebeforetheinfluenceof theviscouseffectson two-dimensionalaerofoilscanbe determinedaccurately.An exampleof someexperimentalresultsis givenin Figure1and theyhavebeencorrectedfor theincreasedvelocityoverthe aerofoildue to thepresenceofthe wind-tunnelwallswhenthe aerofoilis at zerolift (i.e.theblockagecorrection)but notforotherwind-tunnelwallcorrections,whichwouldincreasethe differencein the quotedliftcoef-ficientsby about0.03assumingfirstorder

    theoreticalwall correctionsapply. The inviscidflowcalculationsfor thisfigurehaveinvolvedanextrapolationfrom justbelowthe criticalspeedwhichcannotbe justifiedon purelytheoreticalgrounds,but sincethemeasurementsthemselvesarewhollysubcriticalthisis consideredreasonable.

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    Viscouseffectsof course,occurdue to flowinregionsof high shearsuchas in theboundarylayerand in the wake. At highReynoldsnumbers,theflowin theseviscousregionsis usuallyturbulentandconsequentlynot amenableto theoreticaltreatmentunlesssimplifyingassumptionsaremade. Theviscouslayershave thusto be determinedexperi-mentally. It shouldbe possiblehoweverto treattheselayersas normalboundarylayersandwakeswithconstantstaticpressurenormalto thesurface,exceptnearthe trailingedgeof an aerofoi;wheretheflow curvaturemaybe large. nchemannk2)evensuggestsit is possiblefor theinfluenceof vorti-cityin the curvedflownearthetrailing-edgetocauseearlierseparationthanwouldotherwisebeexpected.Consequently,detailedmeasurementsof theflowin sucha regionareparticularlydesirable.

    Whenconsideringtheoverallforceson an aero-foil,the contributionto theliftfrom thefric-tionalforcescan usuallybe neglectedand theliftdeterminedfromsurfacepressuresalone,but fordragthefrictionalforcesareimportant.The aero-foildragis made up in twoparts; theformdrag,obtainedfrom the surfacepressureson thewinganddue to the displacementeffectof theboundarylayer,and thefrictionaldragwhichhas to be measuredbysomeothermeans. Waketraversemethods,in whichconvenientassumptionsaremadeabouttheflow,canbe usedto determineoveralldrag,but doubtsstillremainabouttheaccuracyof suchmethodsso directmeasurementsof the dragarealsodesirable.

    There was, therefore,a need to design anexperiment in which as much information as possibleis obtained about the detailedflow characteristics.

    1

  • The workmustobviouslybe at highReynoldsnumbers(sothatboundarylayertransitionproblemsarereducedas muchas possible)andat thehighsub-sonicspeedsrelevantto presentsweptwingdesigns.Alsoit is essentialthattheconditionsunderwhichthe wingsare testedbe knownaccurately,inparticulartheeffectsof windtunnelwallinter-ference,whichare knownto increaserapidlyat thehighersubsonicspeeds,mustbe determinedcarefully.

    In thispaperwe willgivedetailsof aselectionof themeasurementsmadeso far at R.A.E.,indicatewheredifficultiesin measuringtechniqueshaveoccurredand makecomparisonswithexistingtheorieswherethisis useful. A completeanalysisof all thesemeasurementshasnotyetbeenmadeandfurtherexperimentalworkstillneedsto be done.Someof the theoriesused,particularlyfor theboundary-layerdevelopment,willtendtobe some-whatparochialsincecomputerprogrammesareusuallyinvolvedand onlythosereadilyavailableto us havethusbeenused.

    ActualMeasurements

    For measurementsof the tyTementionedabove,windtunnelswithlargeworking-sectionsarerequiredto enablereasonablylargechordmodelstobe usedwithoutinvokingserioustunnelinterferencedifficultiesas regardsboth chord-to-heighteffectsand end-wall(i.e.low aspect-ratio)effects. Withlargechordmodels,accurateanddetailedboundary-layerand wakesurveyscanbe madeat realistically-highReynoldsnumbersand increasedprecisionis possiblein modelmanufacture.Ourworkwas,in fact,done in the8 ft x 8 ft (2.4m x2.4m) closed-walltunnelat Bedfordand the 8 ft x6 ft (2.4m x 1.8m) slotted-walltunnelatFarnboroughusingmodelsof up to 76 cm chord. Thus,both themodelspan-to-chordand tunnelheight-to-chordratioswere3 (orgreater)whilethe trailing-edgeboundary-layerthicknessesweretypically1 to3 cm.

    In the 8 ft x 8 ft (2.4m x 2.4m) tunnel,awingwasmountedas shownin Figure2. Boundarylayerand wakemeasurementsweremadeusingrear-mountedtraversingprobes. The wingwas splitintosevensimilarspanwisepartseachindividuallymounted,so thatit was possibleto makeoverallforcemeasurementson a centralsegmentof the wingusinga straingaugebalance. The smallgapsbetweenthe segmentsweresealedotherthanwhenoverallforcemeasurementswerebeingmade. In the 8 ft x6 ft (2.4m x 1.8m) tunnelthe wingwasmountedverticallyas shownin Figure3. Boundary-layerandwakeprobesweremountedfromwithinthe thicknessof wingand traversedby remotelycontrolleddrives.Enlargementsare shownof the probesprotrudingfromthe wing. Measurementsin thewakefurtherdown-streamthan10% of thechordbehindthe wingweremadeusingrear-mountedtraversingprobes. Thisarrangementmadesure thatthe influenceof theprobesand theirsupportson theflow averthe wingwaskept to an absoluteminimumand thattheloca-tionof the probeswasknownaccuratelyevenformeasurementsin the wakecloseto the trailing-edgeof the wing. The wallslotarrangementwas alteredfor thiswork,the open-arearatioof thewallsparallelto a spenwisegeneratorbeingvariedbyusingadditionalplatesbehindtheusualslots,andtheslotsin thewallsnormalto a spanwisegeneratorwereclosedexceptfor a regionwell

    downstreamof thewing. Anotherwingwas testedwiththe samesectionbut havingabouthalfthechordso thattunnelinterferenceeffectsoouldbeinvestigated.The smallerwingdidnothavepro-visionfor makingboundarylayermeasurements,however.

    Fig.2: Aerofoil mounted in 8 ft x 8 ft 12,4 m x 2,4 m I wind tunnel

    Fig.3: Aerofoil mounted in 8 ft x 6 ft (2,4 m x 1,8 m) wind tunnel

    showing remotely controlled boundary layer probes

    In all theworkcomprehensivemeasurementsofsurfacepressuresweremadewhilesurfacetubetechniqueswereusedfor skinfrictionmeasurements.

    On themodels,boundary-layertransitionprob-lemshaveas far as possiblebeenavoidedby fixingtransitionwitha sparsedistributionof smallspheres('ballotini')stuckontothe wingsurfacein a thinband at about5%chordbackfromtheleadingedge. At theReynoldsnumbersof the teststhe diameterof thesphereswasverysmallcomparedwiththe wingchord,a diameter-to-chordratioof0.00015beingtypical.Thisapproachavoidedthelocationof the transitionregionhavingto bedeterminedfor eachcombinationof free-streamMachnumberand wingincidence,and it alsoensuredtransitionwouldoccurneartheleading-edgeof thewingsat an almostconstantlocationon the chord,thushelpingto ensuretwo-dimensionalflow.

    2

  • Although there is some uncertaintyabout thetransitionprocess itself, it is thoughtthatinterms of the chord the boundary-layerflow sqtlesdown to a truly turbulent layerquite quickly0)after transit

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