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NATIONALADVISORYCOMMI’M’EEFORAERONAUTICS
TECHNICALNOTE 2825
A COMPARATIVE EXAMINATION OF SOME MEASUREMENTS OF AIRFOIL
SECTION LIFT AND DRAG AT SUPERCRITICAL SPEEDS
By GeraldE. NitzbergandStewartM. Crandall
Ames AeronauticalMoffettField,
LaboratoryCalif.
Washington..—.November 1952
. ... . . . .. . . .. . . . . . . .. . . . . .. . . .. -. -,.. . . .. . . . ------ _, ----
https://ntrs.nasa.gov/search.jsp?R=19930083484 2018-07-16T20:16:46+00:00Z
TECHLIBRARYKAFi,NM
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N4zTow mnsoRY cohmtm FORAERONAUmCS
TECHNICALIWI!E2825
A COMPARATIVEEXAM12WTTONOF SOME~S OF‘AIRFOIL
SECTIONLIFTANDDRAGAT SUPERCRITICALSPEEDS
.
By GeraldE. NitzbergandStewartM. Cran@ ‘
SUMMARY
A studywasmadeoftheliftanddragcharacteristics>asdeter-minedfromwind-tunneltests=ofa numberof airfoilsectionsatsupercriticalMachnumbers.
Semiempiricalcorrelationsof supercriticaldragdataweremadefora familyof symmetricalairfoilsandforseveralseriesof camberedairfoilsat smallandmoderateanglesofattack.Thecorrelationsareofpressure-dragriseperunitchordlengthasa functionofMachnumler.Fortheairfoilscomidered,thereisan essenthlJyuniqueshapeofthedrag-risecurvewhentheangleofattackisthatformaximumdrag-divergenceMachnwnber.Theprimaryeffectof changingtheairfoilshapeapparentlyisto changetheMachnumberatwhi’chthedragrisebegins.Nomeanshavebeendevisedforappl@ngtheseresultstothepredictionof ~ercriticaldragcharacteristics.
Theliftstudyconsistedprimarilyof an examinationofthese’pa-ratenormal-forcecomponentsof theupperandlowersurfacesof severalairfoilsections.Oneof themostsignificantobservationstobemadeconcerningtheliftdatastudiedisthat?atmoderatipositiveanglesofattackandintherangeofMachnumbersforwhich’supersonicflowoccurredoveronlytheuppersurface,thereappeareda markedchangeintherateofvariationwith(1- M~-LPof theco~onentofthenormal-forcecoefficientcontribu~dby thelowersurfaceas thedrag-divergenceMachnumberwasexceeded.Thischangewasmostabruptforthickersectionsandistheprimarycauseof thelossofliftat supercritical.speeds.
IN’IRODUC!ITOTJ
Theoreticaltreatmentoftheflowofa compressiblefluidaboutanairfoilsectionat supercritical,stisonicspeedsina rigorousmannerhasmetwithgreatdifficulty.Furthermore,theimportanceof shock-waveboundary-layerinteractionintransonicflow mightinvalidateany
.
...— —.-...————- —— -.— —
—.— -.. —.— .—— -- ..— . . —
2 ,, micAm 2825
theorywhichassumestheexistenceof inviscidflow. Consequently,experimenthasbeentheprincipalsourceof informationconcerningthebehaviorofa-oil sectionsat supercritical.,wibsonicMachnunibers.Sectionforcecoefficientsfora Lxrgenuniberof airfoilsectionshavebeenmeasuredat supercriticslMachnumbers.Thesedataindicatethatbetweenairfoflsectionsthere~e importantdifferencesinthemia-tionwithMachnumber,at constantangleof attack,of liftanddragcoefficients.Fora givenairfoilsectiondifferencesexistbetweenthevariationofforcecharacteristicswithMachnrmiberatvariouaangleeof attack.Onepurposeofthisreportistopointoutsomesystematictrendsinthelift-anddrag-coefficientvariationwithMachmniberfora nwiberoffamiliesofairfoilsectionsat supercriticalfree-streamMachimibers.
Theflowchaugesassociatedwiththedragriseof airfoilsectionsat supercritic&L$subsonicspeedswerestudiedinreference1. Itwasfoundthattheinitialsupercritical.dr6grisewasprimarilyan increaseinpressuredragduetothevariationwithMachnumberoftheairfoilpressuredistributionovertheregionsurroundingthesonicpoint.Ameansforcoqsringthetransonicpotentialflowfieldsaboutthinwingshavingsimil=shapesbutdifferentthickness-chordratioshasbeenpresentedintheformof similsri~rules(e.g.,references2and3). In thisreportoneformof theses~ity rulesieappliedto thesectiondragdatameasuredfora familyofairfoilsat super-critical.,stisonicWch number-..Theshortcomingsof theserulesarediscussedanda semieqdricalcorrelationof&ragdataispresented..
Inreference1, itwassuggestedthattheliftbreskforairfoilsectionsat supercriticsl,subsonicspeedsandatpositiveanglesofattackmaybe duepr~~ @ pressure~stributionchangesonthe.lowersurface.Thelossinliftisnotproducedbythepressurealtera-tionsintheportionoftheflowfield(uppersurface)inwhichsuper-sonicvelocitiesexist.Theinitiallossinliftresultsfromlower-mrfacepressure+istributionchangeswhichweretentativelyattributedto effectsof thelargewakeaccompanyingthesupercriticaldragrise.If thishypothesisiscorrectthen,inasmuchas suchwakeeffectsarenotincludedinthepotentialtheoryonwhichthetransonicsimilarityrulesarebased,theseruleswouldnotbe expectedtobe usefulas aguidefordirectlycorrelatingsqpercriticallift@hsracteri.sties.Theliftstudyinthisreportconsistsprimarilyofan examinationoftheseparateliftcomponentsof theupperandlowersurfacesof severalairfoilsections.
zwcAm 2825
NoTA.moN
— ——
3
c
Cd
C%r
cdP
Acd
CT
c~
Cnz
Cnu
‘K
Kc~
M
%
%
Mk
.‘P
P.
chordofairfoilsection0
airfoil-sectiondragcoefficient -.
airfoil-sectiondragcoefficientat critic&LMachnuniber
airfoil-sectionpressure-dragcoefficient
incrementofairfoii-sectiondragcoefficient(cd- c~r)
airfoil-sectionliftcoefficient-
airfoil-sectionnormal-forcecoefficient
normal-forcecoefficientof-airfoil-sectionlowersurface
normal-forcecoefficientofairfoil-sectionupper~face
transonic.similsxityparameter
transonicshilarityparameterforcriticalMachnu@er.
free-stresmMachnumber -..
criticalMach’nuuiber
drag-divergenceMachntiber,free-streamMachnuuiberatwhich
dCd—has valueof 0.1m
correlationMachnumber
Machnumberatwhichsonicvelocityisreachedat airfoilcrest(pointon surfaceatwhichtangentto surfacei~infree-streamdirection)
totalpressure
9. free-streamdynamicpressure
. .
.—_ —. —’ — ————.—.. —
. _._— .—. .— —— —-——— --
4 NACAm 2825
t -imum thicknessofairfoilsection
x chordwisedistancefromairfoilleadingedge
Y ordinateof atioti
a airfoil-sectionangleofattack
% angleof attackatwhichairfoilsectionhasthehighestdra-g-divergenceWch number
DATAANDSCOPE“
Thedatausedinthisstudywereobtainedfromreferences475,6, I’, and8. Theairfoilsectionsconsideredarebothcaziberedanduncaniberedandareofthe.NACAfour-digitseries,five-digitseries,* 6 series.NO dataon airfoilsectionswithdeflectedflaPs$amoflsectionsharlngreflexedcsmiberlines,orairfoil.sectionsdesignedforsupersonicapplicationarestudied.Thethiclmess-chOrdratioof theairfoilsectionsconsideredrangesfrom0.06to0.18.
Thedatapresentedinreferences5 and8 are tromtwo-dimensionaltestsmadeintheAmes1-by 3-1/2-foothigh-speedwindtunnelandhavebeencorrectedfortheeffectsof thetunnelwallsby themethodspre-sentedinreference9. FortheMachnwherstobe considered,theReynoldsntier ofthesetestswasabout2 million.Thedataofrefer-ences4,6, and7 wereobtainedfromtestsoffinite-spanmddelsintheD’VL(2.7meterdiameter)high-speedwindtunnel.However,thesemodelswereequippedwithendplatesandtheanglesofattackwerecorrectedto correspondto infinitespan. Correctionswerealsoappliedto converttheexperimentalvaluesto free-airconditions.TheReynoldsn-r forthesetestswasabout6 millionfortheMachnunibersstudiedin thisreport.
Thequestionarisesas to theaccuracyof thetunnelcorrectionswhichwereappliedto thesewind-tunnelmeasurementsmadeathighspeeds,especiallywhentherewashighdrag,flowsep-tion~md a .largewake. AtMachnumberslowerthanthoseatwhichtheabruptsupercriticaldragrisebegan(dragdivergence),onlytiesolidblock%eofthemdels wasimportantandthesmallsizeofthemodelsrelativeto thewind-tunnelcross-sectionareasinsuredthatthetunnel-walJ-correctionsweresmallandpredictablefromtheory.However,athigherMachnumbers,withtherapidincreaseindragcoefficient,thecorrec-tionfortheeffectsofthemodelwakebecamelarge.Theeffectsofcompressibilityonthewake-blockagecorrectionweredeterminedbymeansof thePrandtlrulewhichmaynotbe applicable.Infact,an
.— _—— —.—
— ———.
L
IfflCAm 2825 5\
ew?erimentaJ-studybyFeldman(reference10)showsthatwhenthereisa relativelylargedragcoefficientdqetopressuredragtheconven-tionaltunnel-wallcorrectionssretoosmall.1The.Machnumbersshowninthefiguresofthepresentreportmaybe inerrorby seyeralpercentwhichimposesa limitationontheusefulnessofthesedataforquantita-tiveanalyses.
T!ransonicS3ndlarity”Rule
Thetransonicsixuilari@rules(e.g.,references2 and3) relatithetransonic’potential’flowfieldsaboutthinbodieshayingsimilaraerc@namicshapesbutdifferentthickness-chordratios.Theconditionnecessaryfora seriesofbodiestohave
Y& = f(x/c)t/c
Theflowsabouttwobodieshavingshapessatisfiedaresimilar(i.e.,representedpotential-flowequation)when,according
ismet.(forthe
.
similaraerodynamicshapesis
suchthatequation(1)isbyto
k
Moreover,theSsalevalueof
(1)
thesamenondimensionalreference3, thecondition
= ‘K (2)
pressure+3ragcoefficientsofthetwobodiesK) arethenrelatedby
(t/c)5@. . NM2/gcap .
=(t/c)-
1 2
‘ThetheoreticalblockagecorrectionsappliedbyFeldmanarebasedontheworkofThem(referencen). Lateranalysishasledto somerevisionsofthesetheoreticalcorrections.However,theserevisionsdonotaffectsignificantlytheresultsyresentedbyFeldman.
——-——. —. —.
. . .
6
Fora familyofsimilarlyshapedisthusglvenbytherelation
M2i3cdp
(t/c)=@
NACA!lN2825
bodiesthepressure4ragcoefficient
= F(K) (3)
Thebasicassumptionsmadeinthederivationofthetransonicsimilarityrulesarethattheflowisinviscidandthatthevelocityat eachpetitinthefluidisnotfardifferentfromthelocalveloci~of sound.Theflowstobe consideredinthisreport(woundairfoilsat supercriticsl,mibsonicspeeds)arenotentirelyinaccordwiththeseassumptions.Theflowaboutairfoilsectionsat supercriticalspeedsisinfluencedby thepresenceof shock-waveboundary-layerinteraction.Buttheapplicabilityofthesimilarityruleismoredrasticallycurtailedbythefactthatthedragriseofairfoilsofmoderatethichess-chordratioorofthinairfoilsatmoderateanQesof attackstartsatfree-streamMachnumberssubstantiallylessthanunity.Moreover,airfoilsectionsdesignedforsubsonicspeedapplica-tionshavelargedisturbances-atthebluntleadingexs whichproducestagnationpoints.Ontheotherhand,theflowfieldisapproximatelypotentialfortheinitis2portionofthesupercriticsd.drag-risecueforwhichtheviscouslossesaregenerallysmallandessentiallyinde-pendentofMachnuuiber.Theinitialsupercriticaldragriseisprimarilyan increaseofpressuredragduetothechangeofpressuredistributionintheregionwheretheflowkelocityisapproximatelysonic;therefore,itcannotbe concludeda priorithatthepresenceofa stagnationregionandof shock-waveboundary-layerinteractionobviatestheusefulnessofthesimZLsri@rules.
OneformofthetransonicsimilsrityrulesW nowbe testedhymeansof someexperimentaldragdatafora familyof symmetricalairfoilsectionsat zeromgle ofattack.
[email protected] Similari~Rules
Ingeneral>airfoil-sectiondragcoefficientsaredeterminerifrumwake-surveyorbalancemeasurementsand,conseqyenkly,includeboth \skinfrictionandpressuredrag.Sincethetransonicshilarityrulesapplytothepressuredragonly,itisnecessaryto subtracttheskin-frictiondragfromthemeasureddrag. Thedragof commonlyusedairfoilsectionsat smsllanglesof attackandat subcriticalMachznmbersisessentiallyindependentofMachnuniberandduealmosteiltirelyto skinfriction.At supercriticalspeeds,theskin-frictiondragmaybe somewhatlowerthanat subcriticalMachnumbersbecau$e“of theincreasedchordwiseextentofthefavorablepressuregradient
—— ..—— —.
mcA m 2825 7
overtheforwsrdportionoftheairfoilandtheincreasedstabilityofthelsadnarboundarylayer(reference12),whichmaycausethetransi-tionpointtomoverearward. However,becauseofthedifficultyinestimatingthevalue(probablysmQl)of‘thedecreaseinskin-frictioncoefficient,itisassumedinthefollowingcorrelationthattheskin-frictiondragcoefficientatallsupercriticalMachnmibersisequalto theexperimentallydeterminedtotalairfoil-sectiondragcoefficientat thecriticalMachnuniber.Theremainingportionofthedragcoeffi-cientat supercriticalMachnumbersisconsideredtobe thepressure-dragcoefficient,thatis,
High-speeddragdataforsymmetricalNACAfour-digit-seriesairfoilsectionsof 6-}9-Y~-z 15-S~ 18-m=nt-chora thic~essj eachat 0°angleofattack,arepresentedinreferenceh. Valuesofthe
M2%Cdparameter— calculatedusingtheexperimentaldataof
(t/c)@N-1encek areplotted(fig.1)againsttheparameter
(M%/c)2is
refer-
as
suggestedby oneformofthetransonicshilari~rule. (Seeequa-tion(3).) Thismethodofplottingthedataprovidesgoodcorrelationexceptforthe6-percent-thicksection,andthemaximumdifferencebetweenthecurveforthissectionandthatfortheg-percent-thicksectioncorrespondstoa possibleerrorin+fachnu?iberofonlyabout2 percentat&pressuredragcoefficientofabout0.02.
Theexcellenceofthiscorrelationmustbe regsrdedas somewhatfortuitousbeca~etheformof the’similarityparameterusedhappensto correlatethecriticalMachnumbersofthisfamilyofairfoilsec-tions. ThisformoftheparameterdoesnotcorrelatethecriticalMachnumbersofellipsesorlow-dragairfoils.Fromtheoreticalcon-siderationsitcanbe arguedthattherearetwo%aturallfformsof thes~larityparameter,thatpresentedinequation(2)withthe M-4/3factoreitherincludedordeleted.ThesetwoformsarisebecauseM2eithercanbe retainedorsetequalto1 inthedifferentialequationfortransonicflow,thebasicparameterbeing(M2- 1). Forthedatapresentedihfigure1,retainingthefactor’M-4@ isessentialtothecorrelationof criticalMachnuuiber;theothernaturalformof thesimilaritypsxameterdoesnotprovidegoodcorrelationof thissuper-critic&Ldragdata.In general,neithernaturalformofthesimil=i~parameterprovidesgoodcorrelationofthecriticallfachnumbersoffamiliesofairfofis.Although-thecriticallfachnmiberisnotthe ‘
. Machnuniberatwhichforcebreaksoccur,it isthelowerlimitofthetrdhsonicrsmge.Thedegreeofcorrelationof criticalMachnwiberisa measureoftheaccuracyofthesimil=ity?mlefora givenfamilyofairfoilsat Machnumbersmilwtantiallybelow1.
. .— ._. ___ —-—— —_—_ ____
-.. —. .. —--- -—.- ——— —— _—-— .——
8 mcA m 2825
Inreference8 thesupercriticaldragdatafor16 camberedairfoilsat zeroangleofattackwerecorrelatedbothempiricallymd accordingtoa modifiedformofthetransonicsimilarityniles.Theairfoilsconsideredhaddifferentthickness-chordratiosbutallhadthessmecamberlineandhencewerenotsimilar.In anattempttoadjustforthedisshilan“@ inshape,thevariableK wasreplacedby K - K&.Sucha substitutionwouldbeconsistentwiththe,transonictheoryifKCr wereconstant;however,asw pointedoutintheprecedingpara-=aph~~r actuallymaynotbe constantforsimilarairfoils.Thismodificationofthesimilari~parameter,Whichledto satisfactory~orrelationofthedataconsidered,wassomewhatarbitrsrybecausetheParsmeter&r (notconstantfortheseairfoils)wasadjustedtotheactualcriticalMachnuubers.Thisapplicationofthesimilarityrulesindicatesthatformsofthesimilari~parameterswhichprovideanaccuratecorrelationof criticalMachnuniber,eveniftheseformsaresynthetic,smeusefulforcorrelatingthesupercriticaldragcharacter-isticsofairfoilsections.
Thecritical~ch nunbercanbecalculatedtithreasonableaccuracyby meansofpotentialtheoryplustheK&rm&n-Tsiencompressibilitycorrection.Thusitis-possibleto calculatecriticalMachnumbersandthenselectparticularformsofthesi.milari~parameterwhichareusefulfora givenfsmilyofairfoils.In derivingtransonlcsimihxrityrulestheassumptionismadethatvelocityperturbationsaresmall,whichmeansthattheJ@chnuuibersthroughouttheflowfielddifferonlyslightlyfromunity.Hencefactorssuchas M orM2 are,totheaccuracyofthetheory,equalto1 andcanbe insertedor deletedatwill. Itisthusappsmentthatthereareanunlimitednunherofformsofthesimilarityparametersfromwhichto chooseonewhichcorrelatescriticalMachnuibersofa givenfamilyofairfoils.
SemiempiricalCorrelationofExperimentalDragData
An alternativemethodforcorrelatingdragdatais suggestedbytheanalysisofreference1. In reference1 theinitialsupercriticaldragriseofanairfoilwasrelatedtotwopressure-distributionchanges:
1. Atpointsaheadoftheairfoilcrest(thepointontheairfoilatwhichthesurfaceis~ent tothefree-streamdirection)forfree-streamMachnumbersgreaterthanthedrag-divergenceMachnumber,thelocalMachnuniberwasessentiallyconstantforincreasingfree-stresmMachnuniber.TheseconstantlocalMachnumbersresultinincreasinglypositivelocal.pressurecoefficientsontheforwsxdportionoftheairfoil,andconsequentlyan increaseindragcoefficient,asthefree-streamMachnumberisincreasedbeyondthatfordragdivergence.
.— . .——.—
I ,
ZF IwcAm 2825 9
2. Themipersonicregionbehindtheairfoilcrestincreasesinchordwiseextenta.sthefree-streamMachnumberisincreasedbeyondthatfordragdivergence.Thisresultsina decreaseinpress&ecoef-ficientovertherearportionof theairfoilandhencean increaseindragcoefficient.
\BoththesefactorsdependontheMachnuniberdistributionoverthe
airfoilsection.Thissuggestsrelatingthedragrisetothetotal-pressureof thefreestreamratherthanthedynamicpressure,thatis,A(cd~Po) = (cdq/Po)M- (cdq/Po)%rDAccordingly$thedatapresen~d
infigure1 were~lottedon curvesof A(cdq/p) versusM. Itwas8observedthatthecurvesfortheseveralalrfo s weresWar. h
ordertoillustratethesimilarity,thecurvesweresuperposedbyarbitrarilyshiftingtheMachnumberscalesothattheincrementinMachnumberislueasuredfromthatMachnumberMk atwhichA(cd!l/po).equals0.008(fig.2). Asidefromthesomewhatmorerapidinitial@ag riseofthethickestairfoilsection(possiblydueto sep=ationeffects)thesimilarityismmked. Thecurveswerematched.ata pointcorrespondingtoa relativelylargedragriseinordertominimizeerrorsintroducedby theassumptionthatabovethecriticalMachnmibertheskin-frictioncoefficientis independentofMachnuniber.
FortheEl@ 0015airfoilsection,anothersetofmeasurements(mfemnce’~ iSalsoplottedonfigures1 and2. Thesetitswereobtainedata Reynoldsnumberofabout2 millionas comparedwitha&ynoldsnuniberofabout6 millionforthedatafromreference4. ~differencesinthesetwosetsofdataareprobablyprimarilyduetoMachnumbererrors-(seesectionDataandScope) [email protected] methodofcorrelationusedinfigure2 absorbsMachnumbererrorsinthequantity~.
Dataforotherseriesofsymmetricalairfoilsectionsof similarshapebutclifferentthickness-chordratioswerenotavailable.Inreference8 axepresenteddragdataforlUICA63-2xxP64-2xx,65-2xxPand66+XXairfoilsectionsatvariousanglesofattack.Foreachgrouptherearedataforfourthickness-chordratios(0.06,0.08,0.10,and0.12).Eachoftheairfoilsectionsoftheabovegrowswascamberedwithan a = 1.0 typemeanlinefora designliftcoefficientof0.2. At 0°singleofattackthetheoreticalvaluesforvelocitiesovertheuppersurfaceofan airfoilwithan a = 1.0 typeme= l~eareuniformly~eaterthsmthevelocitiesoverthelowersm’face.It
, isthereforeapparentthatat this-angleofattackthesupercritical-dragriseduetoflowovertheuppersurfacewiJlbeginata lowerMachnunberthanthedragrisecausedby theflowoverthelowersurface.Theangleofattackforwhichthedragrisedueto theflowovereaasurfacebeginsat thesameMachnumber(a= 0°forsymmetricalairfoils)is obviouslythatsingleofattack~ forwhichtheinitialdragrise
.. ——- _______ __ ..—. —— —.——_
——.— .—— .—-_L_ ——. —
10 NACATN 2825
startsatthehighestMachnumber.Fortheafore-mentionedNACA64-65-, and66-seriesairfoilsectionsthisangleofattackisabout+8 ●
(ThedatafortheNACA63 seriesindicatea valueof ~ closerto0°thanto -2°soforthesakeof simplicitythesesectionswillnotbeincludedinthecorrelations.)Itmightbe expectedthatthedatafortheseairfoilsat -2°angleofattackwouldbe comparabletothoseforthesymmetrical~CA OOXXseriesat0°angleofattack.Theresultsof theanalysisarepresentedinfigure3. No significantdifferencebetweenthethreeairfoilgroupsisapparent.Furthermore,thefairedcurvedrawnthroughthesedataisthesameas thatdrawnthroughthedatapresentedinfigure2.
Someadditionaldata(reference6)forcmiberedairfoilsattheangleofattack(forwtously~ . -2°again)formssdmumdrag-divergenceMachnumberarepresentedinfigurek. EachsectionhadanNACA230meanlineandthesamethicknessdistributionasanNACAfour-digit-seriesairfoil,ofequalthickness-chordratio.Forthesecamberedairfoilsat theangleof incidence~ thepressuredistribu-tionontheupperandlowersurfacesdifferedmarkedlyfromeachother;nevertheless,thesedataareinreasonableageementwiththefairedcurveobtainedfortheuncamberedMCA fou-digit-seriesairfoilsat0°angleofattack.
Inreference1, itwasshownthattheMachnumberatwhichtheabruptsupercriticddragrisebeginsisassociatedwiththatMachnumberMP forwhichsonicvelocityisreachedattheairfoilcrest.Valuesof MB calculatedby appl@ngthePrandtl-Glauertruletothetheoreticalpressuredistributionsobtainedframreference13arecom-paredwithvaluesof Mk inthefollowingtable.Ifa systematicvariationof l& -Mp withairfoilshapeorthickness-chordratiocouldbe establisheditwouldbe possibletopredictthesupercriticaldragriseofotherrelatedairfoils.ThetabulatedvaluessuggestthatthisMachnumberincrementvarieswiththickness-chordratioandairfoilfslnily.However,sincethisvariationisof theexperimentaluncertain~inthedeterminationofnumberinthesetests,itisnotpossibletousea basisforpredicting~.
samemagnitude asthe IthecorrelationMachthesedataindevising
I?ACA‘%
MP% - ‘~ ReferenceF=,airfoilsection(deg) calculated
00060009oo12001500150018
0.888 0.845 0.043 4 2.863 ;7“; .065.820 .055..805 .742 .063.795 .742 .053
‘1.774 .702 .072 ;
—_—— —-——.
NACAT$J2825
NACA % QM~ Mk -l@ R_—-
airfoilsection(deg) calculated ceFigure——&l-206641-208641-210641-2X2
6~-208651-2106y2r2
6~-206661-208661-210
230092301223015
0.885.861.841.830
.867
.853
.828
.888
.867
.855
0.790.770● 7%.730
.769● 755.730
.8X
.785
.768
0.095.091●091.100
.098. .098
.098
.076
.082
.087
.868 .796 .072
h
4.839 ● 757 .082.804 .727 .077
Thesupercriticaldragriseofan airfoilsectionat anyangleofattackdifferingsignificantlyfrom.% mightbe ~ected to%e lessrapidthanthatat ~ sincethesupersonicregionson theupperand
, lowersurfacesdonotdevelopsimultaneous~.Dataforthepreviouslyconsideredgroupsofairfoilsectionsat anglesof attackgreaterthanq arepresentedinfigures5, 6~ 7,and8. In eachfigurethedataforthevariousthickness-chordratiosappeartodefinea singlecurveForallmoderateanglesofattackthecurvesfortheNACA00XXatifoilsectionsares=lar tothosefortheNilCA230series.In ordertoillustratethissimilari@thesamecurve(differingslightlyfromthecurvein fig.5)hasbeenplottedInfigures6 and8. ThedatafortheNACA6-seriesairfoilsforthetwomoderatesinglesof attackdefineonecurvewhichdiffersfromthatfortheNACA00XXandNACA2+30-seriesairfoilsections.
Valuesof Mk chosenonthebasisof thee~erimentsldataare~resentedinthefollowingtable:
0006 2 0.860 0.763 0.097 - 4 60009
!
.853 ‘ J:: .120oo12 .804 .098 IC015 .804 .685 .llg0015 ●777 .685 .092
‘1”5
0018 .773 .66Q .113 k
———.— —-. —. —— .— —
—. —— -.. ——. .—.-. . ..— ————.—.-
12 NACATN2825
WA % %MB ~ -Mp ~~ F=.
afioilsection(deg) calculated——00090012001500150018
2300923032?230152300923(X.223015230092301.223015230092301223015
6kl-2066~-2086~-21064~-2126~-2086~-ao6 -m261-206
661-20864-210
641-206641-208641-ao64&126~-2066~-2086~-ao6 -=%6 -206
661-208661-210661-2X2
0.769.754.767.727.744
.836
.8u
.783●775.762.737.718.703.676
:%.615
.885
.859
.832
.814
.859
.835
.813
.895
.869
.854
.817
.&)3
.779
.762
.829
.8I2
.789
.789
.884
.826
.807
.800
0.665.648.632.632.616
.7h2.n5.700.677.655.650.615.598● %5.560.560.540
.794
.770
.-m.
.727
.769
.752
.7P
.ti8-.786.766
.75Q
.736
.73-5
.698●755.735.725.710.776.755●735.720
0.104.106.135.095.128
.094
.096
.083
.098
.107
.087
.103
.105
.091
.082
.084
.075
.091
.089
.081
.087
.090
.083
.081
.087
.083
.087
.067
.067,064.064.074.077.064.079.068.oil.072.080
4
J54
6
v
8
.
.
—
——
13
NACAa~oil section
6kI-20864@lo641-2X26~-2086~-2Lo6 -u361-210661-212
Mp% - ‘P Reference~~(:g) % c~cutea.— — — —
4 0.746
I
0.690 0.056 , 8 7.723 .680 ‘ .045973.7 .670 .047.760 .695 .065.747 .690 .057.736 .670 .066 “.764 .700 .064.753 .688 -.065 . 1]
In thistable,as intheprecedingone,possiblesystematictrends~% - MB aremaskedby theexperimental.n’certaintginthedeter-minationofthewind-tunnelMachnumberat @. Inparticular,notethatthedifferencein l& -M~ forthel?ACA0015airfoil.as deter-minedintwowindtunnelsisas greatas thevariationin ~ -M~fortheNACAOOXX-seriesaixfojlsasdeterminedinoneofth&e &dtunnels.
AIWX’SISOFlIXPERIMENIMLIJTTDATA
thevariationwithMachnumberofthenormal-forceInfigure9,coefficientforthefamilyof symmetricalairfoilsofreference7 atan angleofattackof4° ispresented.TheMachnuuiberscaleusedinfigwe 9 issuchthata linearmriationwould.meanthat en ispro-portions&to (l-l@-l/% Theseairfo,il.sat thiseagleofattacksxeofparticularinterestlecauseoftheunusualcoincidencethatthedrag-divergenceMachnuikr ofeachisaboutthesame.Thecmesof cdversusM arealsonearlyidentical.However,thereh con-siderabledifferenceinthevariationofliftcoefficientwithMachnumber.Largerlossesinliftoccurat supercriticalspeetiforthethickersections.
Ittightbe expectedthattheinitialsupercriticdlossinlift(shockstall)isa directresultof thepressurechangesbroughtaloutby thedevebpmentota localsupersonicregionontheuppr surface‘oftheairfoil.However,inreference1, it isti~catedthatthelossinliftisdueprimarilyto changesinthepressuredistributionoverthelowersurface.
!In figure10,a%reakdownof theno--force coefficientfortie
. airfoilsectionsoffigure9 intothenormal-forcecoefficientsoftheupperandlowersurfaces’ispresented.TheseMues ofsi@e-surf~enormal-forcecoefficientsweredeterminedfrominte~ationsofthe
. pressuredistributionsofreference7.
-..__—. ..— — — —. .— —.
___ —-—————
14 NACA~ 2825
A numberOf trendsareappsrentfromthedataforthenormal-forcecoefficientsfortheindividualsurfaces.Thedevelopmentofa super-sonicrdgionontheuppersurfaceoftheairfoilsectionsyroduceslittlechangeinthemannerinwhfchtheupper-surfacenormal-forcecoefficientvarieswtthMachnuniberuntila Mch numberwellbeyondthatfordragd.ivergericeisattained.Mom thecurvesforthelowersurfacesinfigue 10,itmaybe seenthatataboutthedrag~ivergenceMachnumberthereisa changeintheslopeofthelower-surfacenormsl-force+oefficientvariationwith(1-1@-1/2.Theslopeofthecurves,after~ hasbeenexceeded,variesconsiderablytiththickness-chordratio.
Thevariationwithfichnumberoftheupper-andlower-surfacenormal-forcecoefficientsforthreeNACAairfoilsectionsat severalanglesofattackispresentedinfi~e D. Theairfoilsectionsme:thelUICA0015,a symnetricsd.conventionalairfoil.;theI?ACA23015,afo~d-camiberedconventionala~dlj andtheNACA672-215,a = 0.5,a car(ibered.low-dragairfoil.Indiscussingthesedata,obtainedfromreference5,itisconvenienttodividethecm?vesintothreegroups:(1)Curvesforwhich ~ %%, in%?hZchcasessupersonicregionsdevelopalmosts@mltaneouslyonbothairfoilsurfaces;(2)curves “fortheuppersurfacewith ~<~ orforthelowersurfacewith~>~, onwhichsurfaces,hereintermed“subsonic,”thevelocitiesremainsubsonicfora considerableMachnumberincrementaftersuper-sonicregionsdevelopontheoppositesurface;and (3) curvesfortbeuppersurfacewith ~>~ orforthelowersurfacewith ~<~ onwhichsurfaces,hereintermed‘supersonic,”anextensivesupersonicregiondevelopsbeforesupersonicvelocitiesarereachedontheopposite(subsonic)surfaceoftheairfoil.
Forthesubsonicsurfaces,thevariationofnormal-forcecoeffi-cientwithMachnumberchangedmarkedlyinthevicinityofthedrag-divergenceMachnwiber.Therateofchangeoftheabsolutevalueof cn with(1-M2)-1!2atMachnumbersgreaterthanthosefordragdivergencewasapproximatelythesameforallthreeairfoils.Fortheexamplestreatedinthisreport,thisvariationofnormsl-forcecoef-ficientwasbroughtaboutby analmostuniformchangeofpressurecoef-ficientoverthestisonicsurface.It ispossiblethatthesesubsonic-surfacepres-e changeswerecausedbyvelocityincrementsinducedbythelargewakewhichistheconcomitantoftherapiddragrise.
Foranglesofattackdifferingfrom ~ by 2°ormore,thenormal-forcecoefficientsforthesupersonicsurfacevariedapproxim-ately inaccordancewiththePrandtl-GlauertruleforMachnunibersUP tothosefordragdivergence.AtMachnumbersgreaterthanthosefordragdivergencetherewasconsiderablechange,withbothairfoilsectionandangleofattack,inthecharacterofthe-Zation withMachnumberofthenormal-force-coefficientcomponentforthesupersonicsurface.
.—.— -— —
.
.
NACA~ 2825 ‘ 15
.An examinationofthesedataindicatesthattherearefundamental
differencesbetweenthevariationwith(1-@)-1’2oftheliftcontribu-tionsofthesubsonicandsupersonicsurfacesofmoderatelythickati-foilsat supercriticalMachnumbers.Toa firstapproximation,theliftcontributionofthesubsonicsurfaceappearstobeprimarilya functionofthickness-chordratio;whereasthecontributionofthesupersonicsurfacedependsonairfoilshapeandangleofattack.Thus,ina theo-reticalanalysisofthesupercriticalliftcharacteristicsofmoderatelythickairfoilsitmightbe advantageousto treatthesubsonicandsuper-sonicsuxfacesseparately.ForthefiveNACA00XXairfoil.sections,atequalangleofattackandwithessentiallyidenticalvariationsofdragcoefficientwithMachnumber,themagnitude”oftheadverseeffectoftheliftvariationonthesubsonicsurfacedecreaseswithdecreasingthickness-chordratio.Hence,forsufficientlythinsectionstheinfluenceoftheairfoilsubsonicsurfaceonsupercriticalliftcharacteristicsmaybecameof onlysecondaryimportancesothattransonicsimilarityrulescouldbeexpectedto apply.
CONCLUDINGREMARKS
By theuseofa formofthetransonicsimilarityparameterwhichcorrelatedthecriticalMachnumbersoflJACA00XXairfoilsectionsatzeroangle,itwaspossibleto correlatethesupercriticaldragdataforthisfamilytowithintheexpertientalaccuracy.TheexcellenceofthiscorrelationofthedragdatawasattributedtothefactthatthecriticalMachnumberswerecorrelated;however,foramarbitrgfamilyofairfoils,thikwouldnotgenerallybe thecaseunlesssyntheticformsofthesimilarityparameterswereused. Theothertypeof correla-tionexaminedinthisreportis,inessence,drag(ratherthandragcoef-ficient)riseasa functionofsupercriticalMachnumberincrement.Themajorexperimentaluncertaintyin suchdataobtainedina windtunnelisintheMachnumberincrementintroducedby thepresenceofthewakewhich,fora fixedratioofairfoilchordtowind-tunneldepth,2s dependentondrag. (Seereference9.) Thusinsofarasthepresentcorrelationcom-paresequalvaluesofdrag,,itmaycircumventa majorsourceof errorinthesewind-tunneldata.Fortheairfoilsconsidered,thereisan essen-.,tiallyuniqueshapeofthedrag-risecurvewhentheangleofattackisthatformaximumdrag-divergenceMachnumber.Theprimaryeffectofchangingtheairfoilshapeapparentlyisto changetheMachnumberatwhichthedragrisebegins.
Theportionofthestudydevotedtolift-coefficientvariationwithMachnumberwaslimitedtoa considerationofseveralairfoilsectionsforwhichhigh-speed-pressuredistributionswereavailable.Oneofthemostsignificantobservationstobemaderegsrdimgthesedataisthat,atmoderateanglesofattackandintherangeofMachnumbersforwhichsupersonicflowoccurredoveronlyonesurfaceoftheairfoil,there
-—. . . . . ... —.___ —___ ._ —. — —
.—. . _____ —.——.._—..- —.-—
16 mcA m 2825
appearaia markedchangeintherateofvariationwith(1-~)‘1’2ofnormal-forcecoefficientoftheoppositesurfacesoonafterthetiag-tivergenceMachnumberwasexceeded.T’MSchangewasmostabruptforthethickerairfoilsectionsstudiedandwastheprimsrycauseoflossinliftat supercriticalspeeds.Insofarasthistrendisrelatedtopressurechangesinducedby thewake,applicationto airfoilliftchar-acteristicsofa transonictheorywhichneglectsviscositywouldbeexpectedtobe successfulonlyforrelativelytltlnairfoilsections.
AmesAeronauticalLaboratoryl@tionalAdvisoryCommittee
Moffett’Field,Cal-if.,forAeronauticsApril10,1952
.
1. ~itzberg,”GeraldE.,and
REFERENCES
Crandall,Stewaxt:A StudyofF1OWChangesAssociatedwithAirfofl-SectionDragRiseatS@er-criticalSpeeds.ItACATM1813,1949.
.2. vonK&m&n,Theodore:TheSimilari@Lawof ‘l@msonicFlow.
Jour.Math.andPhysics,vol.26,no.3,Ott.1947,PP.182-19o.
3. Busemann,Adolf:ApplicationofTransonicSimilarity.NACA~ 2687,1952.
4. G6thert,B.: ProfilmessungenW DVLHochgeschwindigkeits+indkanol(2.7M) Zentralefi WissenschtitlichesBerichtswesenderLuft-fahrtforschung,(Berlin-Adlershof)FB 1490. (AvailableasHat.Res.Iab.Tech.ham. ‘IT-Xl,Ottim,Cmati,Sept.6?1947.)
5. Graham,DonaldJ.,Nitzberg,GeraldE.,andOlson,Robert~.:A ~tewtic InvestigationofPressureDistributionsatHighSpeedsOverFiveRepresentativeNACALow-DragandConventionalAirfoilSections.ltACARep.832,1945. (FormerlyllACARM A7B04andMRA~Oa)
.
6. G6thert,B.: HochgeschwindigkeitsmessWenanl?rofilenderReiheNACA230mitverschiedenenDickenverhdtnissen,~n~~e ~WissenschaftlichesBerichtswesenderLuftfahrtforschung,UM 1259/1-3.(Berlin-Adlershof),194-4.(AvailableasBritishtrans.,~istry ofAircraftProduction.Volkenroti.Repts.~dTrans.40>, 409b,and409C.High-SpeedMeasurementsonSectionsofSeriesIVACA230withDifferentThi@knessRatios.May,1946.)
—— —
I
mcA m 2625
7. G6thert,B.: Druckverteilungs- und
17
hmmlsverlustschatiilderfidasfiofilEACAOCRX-l.lO-beihohen&terschallgeschwindigkeiten7Zentralef%rWissenschsftlichesBerichtswesenderLuftfahrt-forschung,FBNr.1505/1-5.(I!.erl.in-Adlershof)~ 1941. (Availableas Canadianta?ans.,Nat.Res.Labs.,Div.ofMech.Eng.,Tech.b-. TII-252Tr-26, IJ?r-27,m-28, mi !rr-29. PressureDistribu-tionandMomentumLossDiagramsfortheNACAProfileO M XX [email protected], 194’7.)
,8. VanDyke$lUton D.: High-SpeedSUbsonicChara&eristicsof16
NACA6-Seriesldrfoils.NACATN 2670,1951..
9. Allen,H. Julian?andVincenti,WalterG.: WallInterferenceina Two-Dimensional-FlowWindTunnel,withConsiderationoftheEffectof Compressibility.NACARep.782,194-4.(FormerlyNACAARRkK03)
10. Feldman,F.: UntersuchungvonSynm&rischenTragflugelprofilenheihohenUnterschallgeschwindigkeitenineimm GealhlossenenWindkanal. Mitteilungenausd.emInstitutfi.irAerodynamic,HeftNr.14,Zurich1948.
u. Thorn,A.: BlockageCorrectionsR&MNo.2033British,A.R.C.,
12. Allen,H. Julianjandl?itzberg,CompressibilityontheGrowthonIow-DragWbgs andBodies.
ina ClosedHigh-SpeedTunnel.1943.
GeraldE.: TheEffectofof theLaminarBoundaryLayerNACA‘TN3.255,1947.
13. Abbott,IraH.,vonDoenhoff,AlbertE.,andStivers}IouisS.yJr.:summaryofAirfomllata.NACARep.824,1945. (FormerlyNACAACRL5C05)
— ..-. ——. . . .—..——. — — . —
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.— —..—..—— .. .—. — ~ .— —. — . ..—
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Figure8.- Gorrelotionof pressure-dragcoefficientfor severulA!ALU230- seriesoirfoil sectionsot vorlousunglesof ottock.
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26 NACAm 2825
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.
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for severalIVACAOOXX40 angleof attock.
—
.. —.——. -—-– .——.. - — .——— ——— ——- —————
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Variation with free -etreom Mach number of upper- and Iower-surfoce normaf - uforce coefficients for several 16-percent - thick NAGA airfoil 8ections at sov;ral mangle8 of attack.
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Upper surface
(d Airfoil section,
Rgure Il. - Conclu&d.
*
