“1i nationaladvisorycommittee foraeronautics/67531/metadc57092/m2/1/high... · “1i,
TRANSCRIPT
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<. NATIONALADVISORYCOMMITTEE
FORAERONAUTICS
TECHNICAL NOTE 4183
INVESTIGATION OF EFFECTS OF DI13TRD3UTEDSURFACEROUGHNESS
ON A TURBULENTBOUNDARYLAYER OVERA BODY
OF REVOLUTIONAT A MACHNUMBEROF 2.01
By JohnR. Sevier, Jr., andK. R. Czarnecki
LangleyAeronauticalLaboratoryLmgley Field, Va.
Washington
February 1958
TECHLIBRARYKAF8,NM
lH NATIONALADVISORYcomIITrEE
. TECHNICALNOTE4183
. INVESTIGATIONOFEFTI!XX!SOFDISTRIBUTEDSURFACEROUGHNEW
ONAERBUUWT BOUNDMYLAYEROVERABODY
OFREVOLUTIONATA MACHNUMHEROF2.01
Hy John
An investigation
R. Sevier,Jr.,andK. R. Czarnecki
SUMM4RY
hasbeenmadeoftheeffectsofdistributedsur-faceroughness,consistingof lathe-toolmarks,ontheskinfrictionof a turbulentboundarylayerovera bodyof revolutionat a Machnum-berof2.01. Theinvestigationwasmadeonthreeogive-cylindersatzeroangleof attackover a surface-roughnessrangefrom23to480microinchesrootmeans uareandfora Reynoldsnumberrangebasedon
%bodylenghhfrom4 x 10 to 30x 106.. Theresultsindicatethattheeffectsofdistributedsurfacerough-
nessona turbulentboundarylayerat a Machnumberof 2.01aregenera~y4 similartothosefoundata Machnumberof1.61andat subsonicspeeds.
Thatis,fora givenroughnessheight,somecriticalReynoldsnumberexistsatwhichtheskinfrictionbeginsto departfromtheclassicalturbulentskin-frictionlawbecauseoftheformdragoftheindividualroughnessparticles.Theresultsfurtherindicatethat(intheReyaoldsnumberrangeofthesetests)increasingtheMachnumberfrom1.61to 2.01increasesthea310wableroughnessfora turbulentboundarylayerby about40percent.Thisincreaseis ingoodagreementwiththatpredictedonthebasisofa constsntratioof allowableroughuessheightto laminar-sublayerthicknessortoa constantvalueoftheReynoldsnumberbasedon allowableroughnessheight,shearing-stressvelocity,andlocalcon-ditionsatthesurface.
INTRODUCTION
As maximumairplsmesndmissilespeedsincreasefromsubsonictosupersonicandhypersonicregimes,theeffectsof surfaceroughnessonboundary-layerskinfrictionandheattransferbecomeof greaterimpor-tance.Consequently,an investigation(ref.1)wasmadeintheLangley4-by 4-footsupersonicpressuretunnelto studytheeffects.
.
2 NACATN 4183
ofuniformlydistributtiroughnessontheskinfrictionofa turbulent .boundarylayerovera bodyofrevolutionat a Machnmber of1.61.Theresultsofreference1 indicatedthattheeffectsof surfaceroughness(fora turbulentboundarylayer)at supersonicspeedsweregenerally .thesaneas thosepredictedby subsonic-speedtheory.Themostexten-siveexperimentaldataavailableonthissubjectwereNikuradse’sincompressible-flowdata(ref.2 or3). A comparisonwasmadeoftheresultsofreference1 withthoseofreference3,eventhoughitwasrecognizedthatthecomparisonmightnotbevalidbecauseof certainbasicdifferencesbetweenthetwotests.In spiteofthedifferences,thecomparisonindicatedthattherewaslittleornoeffectofMachnumberonthecriticalroughnessheight(wheretheeffectsof rough-nessfirstappearina turbulentboundarylayer).Thisindicationwasnotinagreementwiththeexpectationthatthethickerlaminarsub-layersathigherMachnumberswouldincreasethisheight.TheabsenceofthisfavorableMachnumbereffectwasascribedtodifferencesinthetypesofroughnessesinvestigatedandtothedifferentmethodsofmeasuringtheaverageroughnessheightsofthetwotests.An exten-sionofthetestsinthe4-by 4-footsupersonicpressuretunneltohigherMachnumbersonthesamemodelsthusappeareddesirable.Thepurposeofthisinvestigationwastoeffectthisextension.
Thepresenttestsweremadeon thethreeogive-cylindermodelsofreference1 whichhadnominaldistributedsurfaceroughness,generatedby lathetools,of 23, 24o,and480microinchesrootmeansquare.Themodelswereidenticalin shapeandhadanogivenose3 calibersinlengthandanoverallfinenessratioof 12.2. Testsweremadeatzeroangleofattackwithnaturaltransitionandwithtransitionfixednearthemodelnoseovera Reynoldsnumberrangefromabout4 X 106toabout30x 106,basedonbodylength.Theresultingskin-frictiondataarecomparedwiththeresultsobtainedata Machnumberof1.61andwith
CD,T
CD,b
cD,p
Nil&rsdse’slow-speed-flowdata.
SYMBOLS
total-dragcoefficient,~qsf
Pb - Pmbasedragcoefficient,—%qsf
forebodypressure-dragcoefficient,
.
.
Forebodypressuredragqsf
d
.
NK!ATN4183 3
. cf,f
s
cf,w
‘f
D
d
k
k’
‘b
R
%
r
%
‘f
Sw
skin-friction
!O,T+ !D,b
skin-friction
dragcoefficientbasedon Sf>
- %,pSf
dragcoefficientbasedon Sw, Cf,f~
incrementalskin-frictioncoefficient@th tyrbulentboundarylayer,(4Cf2 roughnmdel- (Cf,w)smoothmodel
localskin-frictiondragcoefficient
total
model
roughnessheight,
drag
dismeter
roughnessheight,
root-mean-square
absolutevalues,
values
lk0.707
admissibleorallowableroughnessheight,absolutevalues
modellength
Machnumber
basepressure
Qbasedonbodylength, ~
free-streamstaticpressure
free-streamdynamicpressure
free-stresmReynoldsnumber,
Reynoldsnumberperfoot
radiusof curvature
baseareaofmdel, ~ = Sf
maximumfrontalareaofmdel
totalwettedsurfaceareaofmodel
.
NACATN41834
T
u
u
v*
Y
Y
\
P
v
P
T
Subscripts:
o
t
w
temperature
velocityoffreestream
localvelocity
shearing-stressvelocity
distancefrommodelsurface
ratioof specificheats
laminar-sublayerthickness
temperature-recoveryfactor
coefficientofviscosity
coefficientofkinematicviscosity
density
shearingstress
propertiesevaluatedjustoutsideboundarylayer
stagnation
propertiesevaluatedatwall
APPARATUSANDMETHODS
WindTunnelandModels
TheinvestigationwasmadeintheLangley4-by h-footsupersonicpressuretunnel.Calibrationofthetest-sectionflowat M = 2.01indicatesa Machnumbervariationofabout+0.01andno significantflowirregularitiesinthestresmflowdirection.
Thealuminummodelswerebodiesofrevolutioncomposedofa3-caliberogivenosewitha $1.2-calibercylindricalafterbody.(Seefig.1.) Approximatelyconstant,uniformlydistributedroughnesswas
NACATN4183 5
. producedby lathe-toolmarksontheentiresurfaceof eachmodel(fig.2),exceptat thesurfacenearthenose(approximatelythefirst2 inches)wherecontroloftheroughnesswasimpossible.Theaverageroughness,
. dimensions,andareasofthemodelsaregiveninthefollowingtable:
L, in. d, in. k, Sf, Sqftpin.m ~, Sqft
p.o 4.03 23+ 5 0.0885 4.05
X.1 4.06 240*60 .0899 k.08
49.9 4.08 440*50” ●m 4.09
Themannerinwhichtheroughnesswasproducedandthesubsequentroundingoffofthepeaksresultedina roughnessprofilewhichwasapproximatelya sinewave. Surfaceroughnessofthemodelswasmeasuredinmi.croinches,rootmeansquare,bymeansofa PhysicistsResearchCo.Profilometer,ModelNo.IL.*
Themodelswerestingmounted.Total-dragmeasurementsweremade. titha single-componentstrain-gagebalance.Easepressuresweredeter-
minedby takinganaverageofthevaluesgivenby fourtubesspacedat90°intervalsalongthestingintheplaneofthebase. A h-inch-longcylindricalwoodenblockhavingapproximatelythesamediameterasthatofthemodelswaspositionedakmut1/8inchbehindthemodelbasefortestsofthemodelstoreducethebasedrag(byincreasingthebasepressure)andtherebyreducetheloadon thebalanceathighstagna-tionpressures.
Tests
Alltestsweremadewiththemodelsat zeroangleofattackthrougha stagnation-pressurerangefrom3 to about30lb/sqin.abs,corre-spondingtoReynoldsnumbersbasedonmdel lengthof about4 x 106
to 30x 106. Tunnelstagnationtemperatures,dependingonthestag-nationpressure,variedfromabout90°F to 1300F. Thetunneldew-pointwassufficientlylowtopreventsignificantcondensationeffects.
Dragandbase-pressuredataweretakenthroughtheReynoldsnwberrangeonan themodelswithfixedtransitionandonthe23-and
6 Nl+CATN4183
480-microinch-roughnessmodelswithnaturaltransition.Transitionwasfixedabout1/2inchbehindthenoseofthemodelwithNo.60
.
Carborundumgrainscementedto themodelsurface.Considerablediffi-cultywasencounteredinobtainingbody-dragmeasurementswithnaturaltransitionathighReynoldsnumbersfreeofthe“sandblasting”effects
.
ofparticlesinthetunnelairstream.Thepitsandpeaksproducedbytheseparticlesonthesoftsurfacewereremovedascompletelyaspossible,andrunswererepeatedwitheachmodelinanattemptto obtaindatafreeof sandblastingeffects.
Inordertoobtainforebodypressuredrag,pressuredistributionswereobtainedonan8~-microinch-rou@nessbodythroughtheReynoldsnumberrange.Forthe480-microinch-roughnessnmdel,schlierenobserva- —
tionswerealsomadeovera Reynoldsnumberrangefromabout6 x 106tO 29x 106.
DataReduction
Thevaluesof skin-frictiondragcoefficientwereobtainedby sub-tractingtheforebodypressure-dragcoefficientfromthetotal-dragcoefficient(determinedbymeansofthebalance)andadjustingthetias- -uredbasepressureto correspondwithfree-streamstaticpressure.Theforebodypressuredragwasdeterminedfrommeasuredpressuredistri-
.
butionsoverthenosefora Reynoldsnumberrangefromabout6 x 106. ●
toabout24x 105. Sincethevariationofthevalueof ~,p with
Reynoldsnumberwasofaboutthesameorderasthescatterinthedata,a constantvalueof CD,P= 0.085 wasusedthroughouttheReynolds
numberrangeforallthemodels.
CorrectionsandAccuracy
No correctionsweremadeforbuoyancysincethiseffectwasfoundtobenegligible.Previouscalibrationshaveshowna slightdecreaseintest-sectionMachnumberatstagnationpressuresbelow4 lb/sqin.abs.However,estimatesindicatethatno correctionstothedataarerequired.
Themaximumerrorinskin-frictiondragcoefficientatthehigherReynoldsnumbersfrom25x 106to 30x 106isestimatedtobe about+0.0001(basedonwettedarea);intheReynoldsmmberrangefrOIII
10x 106to 1.2x106themaximumerrorisaboutto.0002;andatthe
.
.
NACATN4183 7
. lowestReynoldsnumbers(about4 x 106),theerrormaybe as greatas*0.0005. However,basedontherepeatabilityofthedataovertwoorthreeruns,itisbelievedthat,forthedatapresentedherein,the
. valuesof skinfriction(especiallyinthelowerReynoldsnumberrange)arenotas inaccurateasareindicatedby themaximumerrors.
RESULTSANDDISCUSSION
GeneralRemarks
As intheinvestigationat M = 1.61 (ref.1),considerabledifficultywasexperiencedinobtainingreliableskin-frictiondataforthenatural-transitioncasebecauseof sandblastingeffectsontherelativelysoftaluminummodels.However,sincetheprimaryobjectiveofthepresentinvestigationwastodetetinetheeffectsofdistributedsurfaceroughnessona turbulentboundarylayerata givenMachnumber,mostofthetestsweremadewithtransitionfixednearthenose.Alimitedanmuntofnatural-transitiondataarepresentedforthe23-andk80-microinch-rou@nessmodelsandrepresentthebestdataobtainedfromtwoorthreerunsoneachmodel.Forfixedtransition,theeffectsof sandblastingdonotinfluencethemeasurements.-ch modelwastestedatleasttwicewiththererunscheckingverycloselywiththeoriginalruns.
h figure3 arepresented$ypicaldata,incoefficientform,showingthevariationwithReynoldsnmnberof totaldrag(asmeasuredby theinternalbalance),basedrag,andtheresultingskin-frictiondrag. Asmentionedpreviously,thepressure-dragcoefficientwasmeasuredandfoundtobe 0.085andwasconstantovertheReynoldsnum-berrange.Thedatapresentedinfigure3 aretheresultoftwoormorerunsofa givenmodel;thedifferentlevelsofbasedragcoefficient(and,therefore,tatal-dragcoefficient)area resultofthefactthatthegapbetweenthemodelbaseandthewooden-baseplugwasnotkeptabsolutelyconstantfromoneruntothenext.
Effectsof SurfaceRoughnessonSkinFriction
Infigure4 axepresentedtheresultsoftheskin-frictiondragcoefficient(basedonwettedsurfacearea)asa functionofReynoldsnumber(basedontidylength)forthethreeroughnessheightstested.Thetheoreticalcurveswereobtainedby theextendedl?mnkl-Voishelmethod(ref.4)fortheturbulentboundarylayerandby theChapman-Rubesinmethod(ref.5)forthelaminarboundarylayer.Mangler’s
8
transformation(ref.suregradientonthevaluesapplicableto
NACATN4183
6), withtheadditionalassumptionof zeropres- .model,wasusedtonmdifytheseresultsandobtaintheogive-cylinderbodyinvestigated.
v
Examinationoffiguresh(a)and4(c)forthe23-and480-microinch-roughnessmodels,respectively,indicatesthattheexperimentalskinfriction(forthenatural-transitioncase)neverquitereachesthetheoreticallsminarlevelevenatthelowestReynoldsnumber.Itisof interesttonotethatthedragdataareleastreliableinthislowReynoldsnumberrangebecausetheforcesmeasuredby thestrain-gagebalanceareonlya smallpercentageoffull-scaledeflection.
Onthebasisofexperiencegainedinreference1,it isbelievedthattheabruptjumpsin skin-frictiondragcoefficientinthetransi-tionalregion(figs.4(a)and4(c))area resultofthemodelsbecomingsandblasted.
Theagreementofthefixed-transitiondatawiththeturbulent-boundary-layertheoryisconsideredtobe good,particularlyforthe23-and240-microinch-roughnessmodels.A possibleexplanationforthefactthattheskin-frictiondataforthe480-microtnch-rou@nessmodelis somewhathigherthantheorymaybethatthisroughnessis suffi-cientlygreatto causeadditionalwavedrag,atleastovertheforwardpartofthemodelwheretheboundarylayerisrelativelythin.As .mentionedpreviously,theforebodypresstiedragusedinthereductionofallthedatawasthatmeasuredona smoothermodel(85microinchesrootmeansquare). ●
Examinationoffigure4(c)forthe480-microinch-roughnessmodelshowstheexpectedtrendin Cf,w withReynoldsnumberfortheturbu-lentboundarylayer.InthelowerReynoldsnumberrange(4x 106to 10x 106),theskin-frictioncurvedecreaseswithincreasingReynolds-numberandextendsparalleltothetheoreticalcurveuntil,at somepoint,itbeginstodivergefromthetheoreticalcurveandfinallybecomesconstant(intherangeofthesetests)astheReynoldsnumbercontinuesto increase.Thisbehaviorwasfirstnotedby Niku.radseinlow-speedtestsof sand-roughenedpipes(ref.2),andthesue effectwasfoundat supersonicspeedsinreference1. Inthepresenttests,thediver-genceReynoldsnumberwasfoundtobe 11x 106forthe480-microinch-
6roughnessmodeland24x 10 forthe240-microinch-roughnessmodel.ThedivergenceReynoldsnumberforthe23-microinch-roughnessmodelwas,as expected,abovetheReynoldsnumberrangeofthepresenttests.
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NACATN4183 9
ComparisonWithResultsat M = 1.61
Inreference1,a comparisonwasmadebetweenthedatafortheallow-ableroughnessheightoftheogive-cylindersat M = 1.61 andthemostextensivedataavailable(ref.3) whichwerelow-speeddataon sand-roughenedflatplates(whichSchlichtinghadconvertedfromNikuradsetsoriginalexperimentsinref.2 on sand-roughenedpipes).Thevaluesofallowableroughnessforthelow-speeddataweretakendirectlyfromthelcurvesshowninreference3 ratherthanby applyingthelessrepresenta-tiveformulaindicatedby Schlichting.Thecomparisonindicatedthattheallowableroughnessheightsforthetwotestswereincloseagreement;however,itwasrecognizedthattheagreementmayhavebeenfortuitousbecauseofpossibleerrorsiameasuringtheabsoluteroughnessheightontheogive-cylindermodel,thedifferenttypeofroughnessusedintheinvestigations(circumferentialridgesandsandgrains),andthefactthatthree-dimensionalboundary-layerflowoccursontheogive-cylinderandtwo-dimensionalboundary-layerflowoccursontheflatplate.Thisagreementbetweenreferences1 and3 isdiscussedinmaredetaillaterinlightof theresultsofthepresenttests.
Examinationoffigure5 indicatesa considerableincreaseinallow-ableroughnessheightbetweenM = 1.61 and M = 2.01$atleastintheReynoldsnumberrangeofthesetests.SinceonlytwodatapointsexistforeachMachnumberandthesepointsaresubjectto inaccuraciesindeterminingdivergenceReynoldsnumber,it isdifficulttodeterminepreciselythemagnitudeofthisincrease.However,foranyreasonablestraight-linefairing(aslow-speedresultswouldindicate),thereisabouta 40-percentincreaseinallowableroughnessfrom M = 1.61 toM= 2.01. IfthisstrongMachnumbereffecto-nallowableroughnesscanbe expectedtoholdtohigherMachnumbers,thenthefavorableeffectof increasingMachnumberat a givenaltitudeovershadowstheunfavor-ableeffectof increasir?zReynoldsnumberonthea~owableroughness(becauseincreasea resultteststo
Thebetween
ofthinningthe–ba&darylayer)andresultsinan overallinallowableroughnessat thehigherlhchnumber.Beforesuchcanbe verified,itwillbe necessaryto extendthepresenthigherMachnumbersandhigherReynoldsnunbers.
reasonforthelargeincreasein allowableroughnessheightM=l.61 ~d M= 2.01 canbe explainedonthebasisofthe
followingdiscussion.Intheclassicalpipeflowwork(ref.2),itwasdeterminedthatthecharacteristicparameterinvolvedwastheratioofroughnessheightto laminar-sublayerthickness.Iftheroughnessheightis sufficientlysma~ incomparisontothelamina~sublsyerthickness,theeffectofroughnesson turbulentskinfrictionisnegli-gibleandtheskinfrictionisdependentonlyuponReynoldsnumber.Ontheotherhand,iftheroughnessheightissufficientlylargesuchthatsU theroughnessparticlesprojectoutofthelsminarsublayer,thefrictiondragbecomespredominantlytheformdragof theindividual
10 NACATN4183
roughnessparticles.k thisrange,thefrictiondragis independent .ofReynoldsnumberanddependsonlyuponth,erelativeroughness.Anintermediateregionexistsbetweenthesetwoextremesinwhichthefric-tiondragdependsonboththeReynoldsnumberandtherelativeroughness. ‘Thus,onthebasisoftheseearlypipe experiments,itwouldbe expectedthatwhateverMachnumbereffectexistedbetweenthepresenttestsandthoseofreference1 wouldbe a resultoftheincreaseinlaminar-sublayerthicknessand,moreover,thatthemagnitudeoftheincreaseinallowableroughnessheightwouldbe ofthesameorderastheincreasein laminar-sublayerthiclmessata givenReynoldsnumber.Thisrea-soningappearstobe ingoodagreementwiththeresultssincetheincreaseinlaminar-sublayerthicknessbetweenM = 1.61 and M = 2.01wascalculatedtobe about30percent(seetheappendix),whereasthemeasuredincreaseinallowableroughnessheightwasabout40percent.Therefore,withintheaccuracyofthedata:itmaybe concludedthat
v*k‘adtheReynoldsnunibery , basedonallowableroughnessheight,
shearing-stressvelocity,andlocalconditionsat thesurface,isinde-pendentofMachnumber,at leastintheMachnumberrangefrom1.6to 2.0.Thisisequivalentto statingthattheratioofallowableroughnessheightto lamlnar-sublayerthicknessisindependentofMachnumber.
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An itemof interestisthechangewhichoccursinthelaminar-sublayerthickness(and,therefore,intheallowableroughness)becauseofthecombinedeffectof increasingMachnumberandReynoldsnumber.Sucha calculationwouldbe ofmorepracticalinterestthanonebasedonchangingMachnumberandcowrbntReynoldsnumber,becausea changeinMachnumberwouldusuallyresultina changeinReynoldsnumber.Forexample,ifthepresentconfigurationwereoperatingata constantaltitudeandtheMachnumberwereincreasedfrom1.61to 2.01(seefig.5),thefavorablel@chnumbereffectincombinationwiththeunfa-vorableReynoldsnumbereffectwouldresultina netfavorableeffectofincreasingtheallowableroughnessby 10to15percent,as comparedwithabouta 40-percentincreasefortheconstantReynoldsnumbercase.Onthebasisoftheanalysispresentedintheappendix,iftheMachnum-berhadincreasedfrom1.61to 5.0(atconstantaltitude),theallowableroughnesswouldbe increasedby a factorof3.5as comparedwithafactorof10fortheconstantReynoldsnumbercase.
A mattertonotefst~t surfacecoo~ng,ata givenMachnum-berandReynoldsnumber,willservetoreducethelmlnar-sublayerthicknessandtherebyreducetheallowableroughnessheight.Onthebasisofthisanalysis,then,theagreementbetweentheallowableroughnessheightsofthelow-speedexperimentsofreference3 andthoseoftheinvestigationofreference1 at M-=1.61 appearstobemerelyfortuitous(aswassuggestedinref.1) sincea roughcalculationindicatesa 100-percentchangeinlaminar-sublayerthicknessbetween
NACATN4183 11
thetwoinvestigationsatthesameReynoldsnumber.Apparently,thes previouslymentioneddifferencesbetweentheinvestigationsofrefer-
ences1 and2 invalidate~ sortofdirectcomparisonof allowableroughnessheights.
.Thevariationof incrementalskin-frictiondragcoefficientdue
toaddingroughness~f,w withReynoldsnumberandReynoldsnumber
perfootis showninfigure6 forthe480-microinch-roughnessmodel‘5). Resultsof the240-(k’ = 0.00068inch and k’/L= 1.4x 10
microinch-roughnessmodelarenotincludedinfigure6 sincethedivergenceReynoldsnumberissocloseto themaximumtestReynoldsnumberthatonlya smallrangeofdataareavailable.As mntionedpreviously,f!Cf,wforlowspeedsconsistsmainlyoftheformdragoftheindividualroughnessparticleswhichprojectfromthelsminarsub-layer.Inaddition,at supersonicspeeds,theseroughnessparticleswouldbe expectedtogiverisetowavedrag. Thiscondttionis sub-stantiatedbytheschlierenphotographof figure7 inwhichweakshockwavescanbe seenemanatingfromtheroughnessparticles,particularlyovertheforwardpartof thebodywherethelaminarsublayeristhinnest.Therefore>~fjw wouldbe expectedto increasemorerapidlywithReynoldsnumb& at M = 2.01 thanat lowspeeds.Infact,withanextremelysensitivebalance,detectionof anincreasein N!f,w betweenM= 1.61 and M = 2.01 shouldbepossible,protidedthebasedragismeasuredwithsufficientaccuracy.However,a comparisonofthepresentdatatiththelow-speeddata(ref.3)andwiththedataat M = 1.61(ref.1)doesnotindicateanyeffectsconsistentwiththepretiousdiscussion.Twopossibleexplanationsforthisresultmightbe that(1)thecomparisonwithlow-speedresultsisnotvalidbecauseof thepreviouslydiscusseddifferencesbetweenthelow-speedandsupersonictests,and(2)thebalanceemployedinthepresenttestswasnotsensi-tiveenoughtomeasuretherelativelysmallwavedragoftheroughnessparticles.
CONCLUDINGRIMARKS
An investigationhasbeenmadeoftheeffectssurfaceroughness,consistingof lathe-toolmarks,
ofdistributedontheskinfriction
of a turbulentboundarylayerovera bodyofrevolutionat a Machnum-berof 2.01. Thetestsweremadeonthreeogive-cylindersat zeroangleofattackovera surface-roughnessrangefrom23to 480micro-inchesrootmeansquareandfora Reynoldsnumberrangebasedonbodylengthfrom4 x 106 to SO x 106.
12 NACATN4183
Theeffectsofdistributedsurfaceroughnessona turbulentboundarylayerata Machnumb-e~-of-2.01arefoundtobe generallysimilartothose -at a Machnumberof’1.61andat subsonicspeeds.Thatis,foragivenroughnessheight,somecriticalReynoldsnumberexistsatwhichtheskinfrictionbeginstodepartfromtheclassicalturbulentskin-
.
frictionlawbecauseoftheformdragoftheindividualroughnesspar-ticles.IntheReynoldsnumberrmge ofthesetests,increasingtheMachnumberfrom1.61to 2.01increasesthe--allowableroughnessforaturbulentboundarylayerby about40percent.Thisincreaseis in good
agreementwiththatpredictedonthebasisofa constantratioofallowableroughnessheighttolaminar-sublayerthicknessorto a constantvalueoftheReynoldsnumberbasedonallowableroughnessheight,shearing-stressvelocity,andlocalconditionsatthesurface.
LangleyAeronauticalLaboratory,NationalAdvisoryCommitteeforAeronautics,
LangleyField,Vs.,September24,1957.
.
NAC!ATN4183 13
.
.ESTIU&lTIONOFCHAIWE
FROM M=
APPENDIX
INLAMINKR-SUEIAYER
1.61 TO M= 2.01
TKtCKNEss
Onthebasisoftheuniversalvelocitydistribution(fig.8),it‘%LV*is assumedthatthequantity~ is independentofMachnumber.
Thatis,if
5LV*— = Constsnt= Cv
then,
(1)
wherethepropertiessublayer.Sincetheat theouteredgeof
areevaluatedattheouteredgeofthel.aminartemperatureatthewallisaboutthesaJ&asthatthe@minarsublayer,thepropertiesin equa-
tion(1)canbe takentoke thewallvalueswithlittlelossinaccuracy.
Ifthefollowingexpressionsaresubstitutedintoeqmtion(l):
i“Twv*=—
“w
then,
.
.
NACATN4183
wherethesubscripto denotesthatthepropertiesareevaluatedjustoutsidetheturbulentboundarylayer.
Since‘w
cf=—* pouo2
andR Pouoft,o= ~
then,
Theratioof()% ()
‘0 %*1.61 atthesamefree-stremM=2.01
Reynoldsnumberis
;:;”=’=o’=(*F-M=l.61 ~ .
P. PwM=I.61
Ifitacrossthe
isassumedthatthereisnovariationin staticpressureboundarylayer,theperfect-gaslawgives
ForsimpliCitY~assumed.Thu8,
a linearvariationofviscositywithtemperateis
15
%/ ‘w—= —
FortheVoishel
P. To
localskin-frictiondragexpressionisusedwhich
coefficient,theextendedltmnkl-gives
At thesamefree-streamReynoldsnumber R(()0 M=l.61= (R+J=2.01)‘
Then,
Since
Vr= ‘w - ‘o
El+-To
and
~=1+7-1 M2To 2
16 NACATN4183
,-
then,
%—=l+qrTo
(*$)
Fora recoveryfactorqr of 0.90with y = 1.4:
(%) 2 3/2*2.01 = 1 + 0.18 %.01 )
r)L M=l.61[ )
z 3/21+ o.181q61 ()l-t 0.2 ~*o~2 0.2335
1 + o.2~,612
Substitutingtheindicatedvaluesof M intotheprecedingequationgives
()bL ()= 1.331 ~
M=2.01 M=I.61 .
Ifthemoreexactvariationofviscositywithtemperatureasgivenby ~Sutherland’sformulahadbeenused,theresultwouldhavebeen(inthetemperaturerangeofthesetests)
(y ()= 1.313 5LM161M=2.01 =.
ThisestimateforthechangeinI-aminar-subwerthicknesswithMachnumberhasbeenmadeonly’fora flatplatesndshouldbemodifiedsomewhattoapplyovertheforwardpartoftheogive-cylinderwhereapressuregradientexists.An esthatewasmadeforthechangeinlaminar-sublayerthickness(fromM = 1.61 to M =2.01)overtheogive-cylinderofthepresentinvestigation,anda differenceoflessthsm5 percentfromtheflat-plateresultwasfoundto exist.
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NACATN4183
REFERENCES
1. Czarnecki,K.R.,Robinson,RossB.,andHilton,JohnH.,Jr.:InvestigationofDistributedSurfaceRoughnessona BodyofRevolutionata MachNuniberof1.61. NAC!ATN 3230,1954.
17
2.Nikuradse,J.: LawsofFlowinRoughPipes.NACATM12g2,1950.
3. Schlichting,H.: LectureSeries“BoundaryLayerTheory.”PartII -TurbulentFlows.mm ~ 1=8, 1949.
4.Rubesin,MorrisW.,Maydew,RsndaXlC!.,andVarga,StevenA.:AnAnalyticalandE@erimentalInvestigationoftheSkinFrictionoftheTurbulentI!mndaryLayerona FlatPlateatSupersonicSpeeds.NACATN2305,1951.
5. Chapman,DeanR.,andRubesin,MorrisW.: TemperateandVelocityProfilesintheCompressibleLamfnarEcmndaryLayerWithArbitraryDistributionof SurfaceTemperature.JOU. Aero.Sci.,VO1. 16,
no.9, Sept. 1949,pp. 547-565.
6. _er, w.: BoundaryLayersWithSymmetricalAirflowAboutI?&iesofRevolution.Rep.No.R-30-18,pt.20,GoodyearAircraftCorp.,Mar.6, 1946.
Pco
\
mr =37.09
—— .— ——
1--.””
d— - 2
12.29—+
‘“” 0’ “:.~
Mgure .1.- Sketch of model. All dimensionsare in inches except roughnesswhich is in microlnchesroot mesn squsre.
height k,
. .
“1’, ,
.1
. . 1 * ● ✌
Fz
(a) 25-mic.oinchmodel. (b) @3-microinch model. L-8258L
Figure2.-&tailsofsurfacesof23-andJt80-microhmh-roughnessmodels.
20 NACATN4183
CD,T
.(M*
3c ,
D,b .02 “ ‘) ~ (5 ,c d3
r 90 0
0 ‘
.
.
.
d Fixed transitionI Io Naturaltransition I
.16
3.14
.12 ($
Cf,f
.100
0.08
0 3 co 0>
.060 4 8 12 16 20 24 28 32xDe
R
(a) 23-ticroinch-ro~hessmdel.
Figure3.-Representativevariationof CD,T,CD,b,and Cf,f withReynoldsnumberfornaturalandfixedtransition.
.
.
.
NACATN4183 ZL
cD,b
o
–.02dFixed transition
–.04 ()
–.06 d
d d$ ~ d~ ~d–.08
d d&&jf&~
–.10
Cf,f
R
(b) 240-microin&-ro~ess
Figure3.- Continued.
model.
x 106
CD,T
cD,b
%f
.32
I.30 ~
.28
.26
.24~
.22 Q
.20 b
.18
.16, ;
.14‘ Ijd ($d{ $ dddCt ~
.12o’ Fixed transition~ Naturaltransition
.10 c
0( >0 0 Oo
.080 0 00 0
0.06 ‘>
0 4 8 12 16 20 24 28 32 x 106
R
(c) ~0-microinch-roughness
Figure3.-Concluded.
model.
.
.
“
—
NACATN 4183 23
Cf,
I I I I I
J=?v
-2
8
R
(a) 23-microinch-roughnessmodel.
Figure4.-Variationof skin-frictiondragcoefficientbasedon ~withReynoldsmmiberforseveralvaluesof surfaceroughness.
24
.
.
10-2
8
6
4
3
2
Cf,w
163
8
6
4
3
2
164106 2 3468 107 2
R
(b) 240-microinch-roughness
Figure4.-Continued.
346 8 108
model.
.
“
.
.
m NACATN4183 25
I
4 . I I
— , . _3 I I I II
Ill
Cf,w
1[
.
●
1 I I I I I 1
.I06 2346 8 10’ 2
R
(c) ~0-microinch-roughness
Figure4.-Concluded.
346 8 10=
model.
.
.
NACATN 4183
.
I I I I i I I II
#u
106 2 34 681072 346810.*2S4 6 8 109R
(a) k’d L asa functionofReynoldsnuniber.
*
.
b
—
Figure5.- Cqarison ofallowableroughnessresultsforogive-cylinderat M = 1.61 ad M = 2.01 andcomparisonwithlow-speeddataforsand-roughenedflatplate.
.
.
27
.
k;d,
pin,
[0486
43
2
10386
43
2I
[0286
43
2
10105234 66 [062 3468 [072 34 68108
(b) k’d as a functionofReynoldsnuniberperfoot.
Figure5.-Concluded.
.
.
..
L4xI0~s
I .2
1.0 -
.8
4,W
.6
.4
.2
006 2 3
—— Referme 3
— Presenf results
-— --- R
4
E- = l.4xlo-5-
5 6789K17 2 34
R
(a) M!f,w asa TunctionofReynoldsnumber.
~iguxe 6.- Variationof ACf,wwithReynoldsnm?berforvariousvalues
,
.
56789108
of k’ W k’/L.
., m
● ✌,.
I — F?esent results I----- Refer6nce I
.6
Acf,w
.4
.2
/“
/./
0--”’ ~ /---”
o~I 15 2 2.53 4 5 678
Rft
. ,
9 K)XD6
!2.!=P
8
(b) Mf ,W as a functionofReynolaBnumberper root.
Figure6.-Co@tia.
-. .- .
Figure 7.-Representativesclillerenphotographof~-microlnch-roughnessmodel. L-57-2758~ = 6.9x IOG.
● a . ● ✌