-

i

“1

,

.

<. 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.

—

.

.

*

.

.

●

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.

—

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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;H

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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 . ● ✌

25

20

10

5

/

0,

/

Laminar sublayer +- —

I.0 1.5 2.0 2.5 3

Figure 8.-

Iog +

Universalvelocitytistr~bution.

7

3

● a

4.0