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EFFECT OF DIFFERENT SHAPED TRANSVERSE GROOVES ON A ZERO PRESSURE GRADIE NT
TURBULENT BOUNDARY LAYER
By
"Suta rdi
Athesis submitted tothe Schoo l ofGraduate Studiesin partial fulfillmentof the
requir ementsfor the degree of Doctor ofPhilosoph y
FacultyofEng ineeringandApplied Science Memo rialUnivers ity of Newfoundland
Decemb er,2002
St.John's Newfoundland Canada
Abstract
Anexperimentalstudyhas been performed to investigatethe responseof a turbulent boundarylayerto different shaped transverse grooves. Square,semicircularand triangular grooveswithwidths of 5,10 and20nunanddepthto width(dlw)ratio ofunity were investigated.Theratiosof the groove depthtotheoncomingboundary layer thickness(dllirJ)are0.067,0.133and0.267, respectively,ford»5,10and 20mm.The experimentswere performed at two frcestream velocities(Uo)of 2.0and 5.5m1s, correspondingtoReynolds number(RII)based on themomentum thickness just upstream of the groove of1000 and 3000,respectively.The turbulence parameters were measured usinghot-wireanemometry,andmeasurementswereperformedat severallocations downstream of the groove.The developmentofthewallshearstress and the internal layerdownstream of the groove was alsoinvestigated.The ejectionand sweep events and the bursting frequencywere estimatedbased on the quadrant decompositionmethod.
The development of the turbulentboundarylayer downstream of the grooveswas comparedwith resultsfromthe corresponding smooth-wallcascoFor all groove shapes, the 20mm groovehas the mostpronouncedeffect on all turbulence parameters.In general,the effect of the square groove onthe turbulentcharacteristicsis more pronouncedthan the effectsofthe semicircularandtriangulargrooves. The wall shear stress(T...)was estimated fromthe slope of mean velocityat the wall. An increasein r...
justdownstream of the groovefor allgrooveshapes and sizes was observed.Theincrease inT...is followedby a smalldecreasein r...below the smooth-wallvalue before it relaxes hack to the correspondingsmooth-wallvalue at approximatelyxllirJ'"3.The increase in Twis morepronouncedatRII =3000thanthat atR()=1000.AtRII=1000, the spectrumof
wall-normalturbulenceintensity (v') downstream of the groove showsasignificant increaseat the higherwave number(kl),whiletheincrease inthe spectrum of streamwise turbulence intensity (u? isnot discernible at the same klrange.There is an increaseinthe bursting frequency(f~')on the grooved-wallcomparedtothesmooth-wallcase.The variationoff~'downstream of the grooveis somewhatsimilar to the variation ofCw.
iii
Acknow ledg ements
My deep gratitudegoesto my supervisorDr.Chan Chingforhisguidancewith thisthesis.The frequent discussionswith Dr.Chinghave helped me with my experimental workand completing the thesiswriting.His helpful hand and honesty have been invaluableand unforgettable.
I would also like tothank mysupervisory committeemembers, Dr. NeilA.
Hookey andDr. BruceL.Parsons, fortheir timeandvaluablesuggestions,whichwere very useful in myresearch.
I wouldliketo thank the Indonesian Governmentforsupporting my graduate study at MemorialUniversity of Newfoundland.The financialsupport from May1998 to April2002 is gratefullyacknowledged.The financialsupportfrom the Mechanical Engineering Department,ITS,Surabaya,Indonesia,and fromtheNaturalScience and Engineering ResearchCouncil(NSERC) Canada for the completionofmyresearch are alsogratefully acknowledged.
Mythanks toAungN.00for providingenthusiastic helpwiththe windtunnel work.Furthennore,Iwouldlike to express mythanksto DarrellSparkesandTomPike fortheir help and kind assistance with thepreparation of thetestplatein the wind tunnel testsection.
Finally,Iamindebted to mywife Henyand my son Farhan for theircontinuous support,encouragement, patienceand understanding.
Table of Contents
Abstract Acknowledgements Table of Contents List ofFigures
List ofTab les List of Symbols List of Appcndiccs Cha pter J Introduction
1.1 BackgroundofStudy 1.2 Purpose and Significanceof Study 1.3 Outline of Thesis Chapter2 Literature Review
2.1 Coherent Structuresina Turbulent Boundary Layer 2.2 TurbulentBoundary Layers on Smoolh-Walls 2.3 TurbulentBoundaryLayers on Non-Smooth-Walls 2.4 Simulationsand Experimental Techniques Chapte r3 Experfmenta lFacility,DataRedu ctionProcedu res, and
Experimental Uncerta inties 3.1 Experimenta lFacility
3.1.1 Wind Tunnel andHot-wire Anemometry 3.1.2 PrestonTube
viii
xxiii xxviii
12 13 J7
20 30
39
40 40 42
3.1.3 Data Acquis ition 3.2 Data ReductionProcedures
3.2.1Hot-Wire Calibratio ns
3.2.2 Wall Shear Stress(r...),FrictionVelocity(u,)andSkin Frictio n Cocfficicnt(Cp
3.2.3 InternalLayer Growth(d;)
3.2.4 SweepandEjectionEvents andBurst Detection 3.3 ExperimentalUncertainties
Chapter4 Smooth-WallTurbulentBuundaryLaYl'rResults
4.1 WallShear Stress (r...) 4.2 Mean VelocityProfiles
«(I)
4.3 Turbulence Measurements 4.3.1 StreamwiscTurbulenceIntensity(u) 4.3.2 watt-norma!TurbulenceIntensity (v) 4.3.3 Rey nolds Stress(.uv»
4.3.4 Turbulence Energy Spectra(E( kl » 4.4 Sweep andEjectionEventsand BurstingFrequency
4.5 Summary
Chapter5 ResultsandDiscussion :EffectofGrooveSb:e 5.1 MeanMeasurements
5.1.1 SkinFriction Coefficient(eft 5.1.2 Streamwise Mean Velocity(U) 5.1.3 IntemaILayer (d,)
43 43 43
44 50 52 57 68 69
7.
78 78 78 79 80 81 83 100
101 101 104 107
5.2 TurbulenceMeasurements 5.2.1 Streamwise Turbulence Intensity(u~
5.2.2 Wall-Normal TurbulenceIntensity(v~
10 8 108 112
5.2.3 ReynoldsStress(-uv») 113
5.2.4 Turbulence Energy Spectra (£(kl) ) 114
5.3 Sweepand EjectionEvents andBursting Frequency 116
5.4 Discussionand Summary II8
Cha pter6 Results andDiscussion:Effect ofDiffer ent Shapesof Grooves 176
6.1 Mean Measurements 177
6.2 Turbulence Measurements 180
6.3 Discussionand Summary 185
Chap ter7 Concludi ng Remar ks 210
Refer ences
AppendixA Appendix B AppendixC
215 2J3 249 256
vii
List of Figures
Figure 1.1 Outer manipulator using large-eddy break-up (LEBU).
Figure1.2 Surface with longitudinal riblets.
Figure 1.3 Groove shapes on the test surface.
Figure 2.1 Development of a boundary layer ona flat plate.
Figure 2.2 Model of counter rotatingstreamwisevorticestogetherwith the resulting low-speedstreaks.
Figure 2.3 Low-and high-speedstreaksin the viscoussublayer.
Figure 2.4 Conceptual model of a cycle of the bursting process in the near-wall region.
Figure 2.5 Quadrants of the instantaneousev-plane. Figure 2.6 Atypical plot of mean velocity distributionin a turbulent
boundary layer
10 11 33
34 34
35 35
36
Figure2.7 k-typeroughness. 36
Figure 2.8 d-typeroughness. 37
Figure2.9 Atime sequence of fluid ejection from a square groove. 37 Figure 2.10 Skin friction distribution ora turbulent boundary layer on the flat
plate with a single transverse square groove.
Figure 2.11 Schematic diagram of wall shear stress distribution forslw=40 and 10.
Figure 3.1.1aWind tunnel withits components.
Figure 3.1.lb Detailed test section.
38
38 58 58
Figure 3.t.lcA schematic diagram of the test plate showinga single transverse groove.
Figure 3.1.2 Preston tube arrangement.
Figure3.1.3 Data acquisitionsystem.
Figure 3.2.1 Velocity correctioncoefficient(C~)due to wall conduction in the hot-wire measurements at variousR().
59 59 60
61 Figure3.2.2 Uncorrected mean velocity on the smooth-wall flat plate. 61 Figure 3.2.3 Uncorrected near-wallmean velocity profiles. 62 Figure 3.2.4 Corrected near-wall mean velocityprofiles. 62 Figure 3.2.5 Mean velocityprofiles plotted as a function ofy'l2. 63 Figure3.2.6 Typicalstreamwise and wall-normal velocity fluctuations and the
instantaneous Reynolds stress productof a wall-bounded turbulentflow.
Figure 3.2.7 Contributions of the first, second, third and fourthquadrant signals to theReynolds stress.
Figure3.2.8 Detectionfunctionof the fluctuating signal after the thresholdlevel was applied.
64
65
66 Figure 3.2.9 Histogram of the distribution of time between ejection,T._ 66 Figure3.2.10Probability distributionofT.compared to the exponential
distribution forT.<:TG •
Figure 3.2.11Contribution of the stress producing motionsacross a smooth-wall 67
turbulentboundary layer tothe total Reynolds stress
«-uv».
67Figure 4.1 Static pressure distribution alongthe centerline ofthetest section. 85
ix
Figure4.1.1 Comparisonof Cfbased onPatel's andBechert's calibration equations.
Figure 4.1.2 Mean velocity profiles in the overlap region of a turbulent boundary layer.
Figure 4.1.3 Skin frictioncoefficient distribution obtainedfromDechert's calibration equation.
Figure 4.1.4 Skin friction coefficientdistributionobtained from Patel's calibrationequation.
Figure 4.1.5 PrescntPreston tubecalibration equation.
Figure4.1.6 Skinfriction coefficienr distributionobtained frompresent calibration.
Figure 4.1.7 Mean velocityprofilesnormalizedusing e.obteined from prcsent calibration equation.
86
87
88
88 89
90
90 Figure 4.1.8 Skin frictioncoefficient on the smooth-wall atR, =1000 -1900. 91 Figure 4.1.9 Skin friction coefficienton the smooth-wallatR,=2800-4200. 91 Figure 4.2.1 Mean velocity profiles over a smooth-wall. 92 Figure4.2.2 Comparisonbetweenmean velocity profiles atlower R,wilh the
power-lawlines andtheDNS data. 92
Figure4.2.3 Meanvelocityprofiles in terms of outervariables. 93
Figure 4.2.4 Velocitydefectplots. 93
Figure 4.3.1 Strcamwise turbulence intensityprofiles over a smooth-wall. 94 Figure 4.3.2 Wall-normalturbulenceintensity profiles over a smooth-wall 94 Figure4.3.3 Reynolds stress distribution on thesmooth-wall. 95
Figure 4.3.4 Energyspectraofthestreamwise velocityfluctuati onatRf} ~1000 . 96 Figure4.3.5 Energy spectra of the streamwise velocityfluctuationatRe'"3000. 96 Figure 4.3.6 Energy spectra of the wall-normalvelocityfluctuation
atRf}=1000.
Figure 4.4.laDistribution of the first andsecondquadrants on the smooth-wa ll turbulentboundarylayer.
Figure 4.4.1bDistribution of the thirdandfourth quadrants on the smooth-wall turbulent boundarylayer.
Figure 4.4.2 Distribution oft...,TJT.",andf~'on thesmooth-wallturbulent boundarylayeratRf}'" 1000 .
Figure S.I.laSkinfrictioncoefficient distributiondownstrea mof the different sizedtransverse SQ-groovesatRf} ~1000.
Figure S.I.lbSkinfrictioncoefficient distribution downstream of the different sizedtransverse SQ-groovesatRf}'" 3000.
FigureS.I.lcSkin frictioncoefficient distributiondownstreamofthe different sized transverseSC-groovesatRIJ=1000 .
Figure 5.1.ldSkinfrictioncoefficientdistributiondownstreamof thedifferent sizedtransverse SC-groovesatRIJ""3000.
Figure 5.1.le Skin frictioncoefficientdistributiondownstreamof the different sized transverseT'R-grooves atRIJ'"1000 .
FigureS.I .I f Skin friction coefficient distributiondownstreamof the different sized transverseTR-grooves atRIJ=3000.
97
98
98
99
123
123
124
124
125
125
Figure5.1.2aStreamw ise mean velocityprofiles downstreamof the SQ-grooves aIR, =WOO.
Figure 5.1.2bStrearnwisemean velocity profilesdownstream of the SQ-grooves at R,-3000.
Figure 5.1.2cStreamwise mean velocityprofilesdownstre am ofthe SC-grooves atRo=1000.
Figure 5.1.2dStreamwise meanvelocityprofilesdownstream ofthe SC-grooves atR,=3000.
Figure5.1.2eStreamwise meanvelocity profiles downstreamof the TR-grooves at R,-IOOO.
Figure 5.1.2fStreamwise meanvelocity profiles downstreamof the TR-grooves atRIJ=3000.
Figure5.lo3aStreamwisemean velocityprofiles downstream of the SQ-grooves atRIJ=1000in terms of innervariables.
Figure5.1.3b Streamwise mean velocityprofilesdownstream of the SQ-grooves atRIJ=3000in termsof inner variables.
Figure5.lo3cSrreamwise mean velocityprofiles downstreamof theSC-grooves atRg=1000intermsof inner variables.
Figure5.1.3d Streamwise mean velocity profiles downstreamof theSC.grooves atRIJ=3000 in terms of inner variables.
Figure5.103eStreamwisemean velocityprofilesdownstreamof theTR-grooves atRf1=1000 interms ofinner variables.
126
127
128
129
130
131
132
I3J
134
135
136
Figure s.L3f Streamwisemean velocity profiles downstream of the Tk-grooves atRo=3000 in termsof inner variables.
Figure s.IAa Internal layer growth downstream of three different sizedtransverse So-groovesatRo""1000.
Figure s.l.4bInternallayer growth downstreamofthrce different sized transverse SQ-grooves atRo""3000.
Figure s.l.4c Intcm allaycr growthdownstreamof three different sized transverse SC-groovesat Ro""1000.
Figure s.l.4d Intem al layer growth downstreamof three different sized transverse SC-groovesatRe »3000.
Figures.I.4eInternal layer growthdownstream of three different sized transverse Tk-groovesR(J""1000.
Figure s.IAfInternallayergrowthdownstreamof three different sized transverse TR-groovesR(J-3000.
Figure5.2.laStreamwtse turbulenceintensity profiles downstreamof the different sized transverse SQ-grooves atR(J"1000.
Figu re s.2.lbStreamwiseturbulenceintensityprofiles downstream ofthe different sized transverse SQ-grooves at Ro=3000.
Figures.2.leStreamwise turbulence intensityprofiles downstreamof the different sized transverse SC-grooves atRo""1000.
Figure 5.2.1d Streamwise turbulence intensity profiles downstream of the different sized transverse SC-grooves atRo=3000.
137
138
138
139
IJ9
140
140
14 1
142
143
144
xiii
figure5.2.le Streamw ise turbulence intensity profilesdowns treamof the different sized transverse TR-groovesatRe=1000 .
Figure 5.2.1f Streamwiseturbulenceintensityprofiles downstreamof the different sized transverseTR-grooves atRe=3000.
Figu re 5.2.2a Distributionof(u)...j(u)"""'....as a functionof xf& forthe different sizedSQ-grooveatR(J=1000.
Figure5.2.2bDistributionof(u)...j(u)ma;<~wasafunction ofx/&forthe different sized SQ-grooveatRe""3000.
Figure 5.2.2eDistribution of(u)...j(u)"""....as a functionofx/&forthedifferent sized SC-grooveatRe=1000 .
Figure 5.2.2dDistributionof(u)...jCu)"""'...as a functionofx/&for the different sizedSC·grooveat Re=3000
Figure 5.2.2e Distributionof(u)""",/(u)""",-,...as a functionof xl&for the different sizedTR.groo ve atRe=1000.
Figure 5.2.2f Distributionof(u)...j(u)"""'...as a functio nofx/&for the diffe rent sizedTR-groo ve atRe~3000.
Figu re 5.2.3aStreamwiseturbulenceintensity profilesdownstream of the SQ-groovesatRe=1000 interms of inner variables Figure5.2.3bStream wise turbulence intensity profilesdownstreamof the
SQ-groovesatRe=3000in terms ofinner variables Figu re 5.2.3cStreamwis eturbulenceintensity profi les downstreamof the
SC-groovesatRe=1000 interms of innervariables.
145
146
147
147
148
148
149
149
/50
151
152
155
157 153
154
156 Figure 5.2.3d Streamwiseturbulence intensity profilesdownstream of the
So-groovesatRu""3000in terms of inner variables.
Figure 5.2.3eStreamwiseturbulence intensity profiles downstream of the TR-groo ves atRu=1000 in termsof inner variables. Figure 5.2.3f Streamwiseturbulence intensity profiles downstream of the
Tg-groo ves atRu= 3000 in terms ofinner variables.
Figure 5.2.4aWall-nonnal turbulence intensity profiles downstream ofthe different sized transverse SQ-grooves atRu=1000.
Figure 5.2.4b Wall-nonnal turbulence intensity profiles downstream of the
different sized transverse SC-groovesatRe=WOO.
Figure 5.2.4c Wall-nonnal turbulence intensityprofiles downstream of the different sized transverseTR-groo ves atR(J~1000. 158
160 159
16 1 Figure 5.2.5aRey nolds stress profilesdownstream of the different sized
transverse SO-groovesatRu=WOO.
Figure 5.2.5bReynolds stress profiles downstreamof the differentsized transverse SC-grooves atR(J ~1000.
Figure 5.2.5cReynolds stress profiles downstream of the different sized transverse TR-groovesatRu=1000.
Figure 5.2.6a Spectra ofu' at a location whereu'IU Qismaximum and at xl&;=0.013 for three differentsized SQ-grooves atR(J=1000. 162 Figure 5.2.6bSpectra ofu'at a locationwhereu'IUf/is maximum and at
xl&;-0.013for three different sizedSQ-grooves atRu~3000. 162
Figure5.2. 6c Spec traofu' al alocation whereu'IUoismaximu mandat xl80'"0.0 13forthree differen t sizedSC-groo ves atRo"1000. 163 Figure 5.2.6d Spectra ofu ' at a locat ionwhereu'lUQis maximumand at
x/80'" 0.0 13for threedifferentsizedSC-groovesatRo= 3000. 163 Figure 5.2.6e Spectra ofu'atalocationwhereu'lUIIismaximum andat
xl80'"0.013 forthree different sizedTR-groo ves atRo-1000 . 164 Figure 5.2.6f Spectraofu'at a locationwhereu'IUIIismaximum and at
xl80-0.013for threedifferent sized Tk- groo vesatRo'"3000. 164 Figure 5.2.7aSpectraof v'atalocationwhereu'lUois maximumandat
xl80'"0.QI3 for three differentsizedSrj-groo ves atRo-1000. 165 Figure5.2.7bSpectra of v'at alocation whereu'lUois maxi mumandat
xl80-0.0 13forthree differentsized SC·groovesatRo=1000. 165 Figure 5.2.7eSpectra ofv'at a location whereu'IUoismaximum and at
xll50'"0.0 13 forthreedifferentsizedTR-groo vesatRo'"1000. 166 Figure 5.3.laCont ribution of the secondquadrant(q;)tothe Reynoldsstress
downstre am ofthe different sizedSQ-grooveatRo=1000. 167 Figure 5.3. lb Contribution of the fourthquadrant(q;)to theReynolds stress
downstreamofthe differentsized SQ-grooveatRo'"1000. 167 Figure 5.3.le Contributionof the secondquadrant(q;) to theReynolds stress
downstrea mofthediffe rentsized SC-grooveatRo-1000 . 168 Figu re 5.3.JdContrib utionof thefourth quadrant(q;)tothe Reynoldsstress
downstream ofthe different sizedSC-groove atRo=1000 . 168
Figure 5.3.le Contribution of the second quadrant(q;)to the Reynoldsstress downstream ofthe different sizedTR-groo ve atRo=1000. 169 Figu re 5.3.lfContribution of the fourthquadrant(q;)tothe Reynolds stress
downstream of thediffere nt sized TR-grooveatRo=1000. 169 Figure5.3.2a Contribution of the first quadrant(q;)to the Reynolds stress
downstream of the different sized SQ-grooveatRo=1000. 170 Figure 5.3.2b Contributionof the third quadran t(q;)to theReynolds stress
downstream of the differentsized SQ-groove atRo=1000. 170 Figure5.3.2cContributionof the firstquadrant(qt)to theReynolds stress
downstream of the different sized SC-grooveatRo=1000 171 Figure 5.3.2dContributionof thethird quadran t(q;)to theReynolds stress
downstream of the different sized SC-groove atRo~1000. 171 Figure5.3.2e Contributionof thefirst quadrant(qt)10the Reynoldsstress
downstream of thedifferent sized TR-groove atRo=1000. 172 Figure 5.3.2f Contributionof the thirdquadrant(q;)to theReynolds stress
downstream of the different sizedTR-groo ve at Ro=1000. 172 Figure 5.3.3aDistributionofthe bursting frequency /;downstream of the
different sized transverse SQ-groove atRo=1000.
Figure5.3.3bDistribution of the bursting frequency
t;
downstreamcf the different sized transverse SC-groove atRo= 1000.173
173
xvii
174 175 Figu re 5.3.3c Distribution of theburstingfrequency
f;
downs tream of thedifferentsized transverse TR-grooveatRo'"1000.
Figu re 5.4.1 Schematicdiagramoffluid ejection from thegroove.
Figu re 6.1.laSkinfriction coefficientdistributiondownstreamof thethree different shaped transverse groovesford'"20mm atRo=1000. 190 Figu re 6.1.l bSkinfriction coefficientdistributiondownstream ofthe three
different shapedtransversegrooves ford=20m matRo'"3000. 190 Figu re6.1.2a Strearnwisemean velocity profilesdownstreamof thethree
differentshapedtransverse grooves ford=20nun atRo=1000. 19 1 Figu re 6.1.2bStreamwise mean velocityprofilesdownstrea mof the three
differentshapedtransversegrooves ford=20mmatRo""3000. 192 Figu re 6.1.3aStreamwise meanvelocityprofiles downs trea mofthe three
different shaped transverse grooves ford=20mm atRo=1000 in termsof innervariables.
Figure6.1.3bStreamwisemeanveloc ity profiles downstreamof thethree differentshaped transversegrOOVl;:Sford=20mmatRo=3000 in termsofinner variables.
193
194
195 Figure 6.1.4 Internal layergrowthdownstream of three differentshaped
transverse groovesford..2Omm.
Figure 6.2.laStreamwiseturbulence intensity profilesdown streamofthethree differentshaped transverse groovesford=20nun at Ro=1000 . 196 Figure 6.2.lbStrearnwiseturbulenceintensity profiles downstreamofthethree
differentshaped transverse grooves ford""20rrunatRo=3000. 197
Figure6.2.2 Inner and outerboundarieswhereu'lUI)is affectedby the 20mm threedifferent shaped transverse groovesatRI)=3000. 198 Figure 6.2.3a Streamwise turbulenceintensityprofilesdownstreamofthethree
different shapedtransversegroovesford=20mm atRo=1000 in termsof innervariables.
Figure 6.2.3bStreamwise turbulence intensityprofilesdownstream of the three differentshapedtransverse grooves ford=20mrnatRo=3000 intcnnsofirmcrvariables.
199
200 Figure 6.2.4 Wall-nonnalturbulenceintensityprofiles downstream of the three
differentshapedtransverse groovesford=20mmatRo=1000. 201 Figure6.2.5 Reynolds stressprofiles downstreamof thethree differentshaped
transverse grooves ford=20mm atRI)=1000.
Figure6.2.00 Spectra ofu'ata locationwhereu'lUoismaximumandat xl&,=0.013forthree differentshapedtransverse grooves ford-20rrunat Ro-1000.
Figure6.2.6b Spectraofu' ata locationwhereu'lUois maximumand at xl&,=0.013 forthree differentshaped transverse grooves ford-2Ommat Ro=3000.
Figure 6.2.6cSpectraof v'ata locationwhereu'IUoismaximumand at xl&,=0.013forthree differentshapedtransversegrooves ford=20mmatR (I=1000.
202
20J
20J
204
xix
Figure6.2.711.Contributionofthe second quadrant(q;)tothe Reynoldsstress downstream of the three different shapedtransverse grooves ford=20mmatRo""1000.
Figure 6.2.7bContributionof thefourth quadrant(q;)to the Reynoldsstress downstream of the three different shaped transverse grooves ford=20mmatRo=1000.
Figure 6.2.7cContributionof the first quadrant(q,+)to the Reynoldsstress downstreamof the threedifferentshapedtransverse grooves
ford=20mmat Ro=1000.
Figure 6.2.7dContribution ofthe third quadrant(q;)to the Reynoldsstress downstream ofthe threedifferent shaped transverse grooves
forJ=20mmatRo""1000.
205
20'
206
206 Figure 6.2.8 Distribution of the burstingfrequency(1;)downstreamof the three
different shaped transverse grooves forJ-20mm atRo=1000. 207 Figure6.3.1 Schematicdiagramof vorticalmotions(eddies)inside the grooves. 208 Figure 6.3.2 Schematicdiagram of flow streamlinesoversquareand triangular
grooves
FigureA.I Typical calibrationcurveofa S'c-wtreprobe . Figure A.2 Typical calibration curve of an X-wireprohc.
Figure A.3 Wires of an x-wireprobe.
FigureAA Slanted and normal wires withtheiroutputvoltages.
209
234 235 236 237
Figure A.S Yawed anduti-ya wed wires with their outputvoltages . 238 FigureB.l Typ icalClause r-chartplottodetermin eUp 25J FigureB .2 Cla user-charttechniquetodetermineu,presented in
aif -y.plane. 253
Figu reB .3 Plot of thej-intercept(B)versusvonKarman constant(K)from 254
Figu re 8.4 Mean velocitydistrib utioncompared withthepower-lawlines. 254
Figu reB .5 Mean velocity in the near-wall region. 255
Figu re B.6 Normalizedmean velocityin the near-wallregion. 255 FigureC.l Uncertainty inUobtained from hot-wirecalibrated using
the'TSIinstrument'. 258
FigureC.2 v'distributionaty16=0.02 fora smooth-wa llflatplateturbulent
boundary layer. 259
FigureC.3 Histogram ofvdistributio natyl6=0.02 fora smooth-w allflat plate turbul ent boundarylayer.
Figure C.4 Est imation ofu,usinga log-lawtechnique.
260 264
xxi
List ofTables
Tabl e 3.1 Relativecontribution sof{uv)l.(-UV}2.(uv)Jand{-UV}4 to thetotal Reynolds stress (-uv»)at Ro""1000 . 56
Table 3.2 Experimen ta luncert ainties . 57
Table4.1 Experimen tal conditionsandflo wpara meters insmoo th-wall
experi ments. 69
Table 4.2 Averag e diffe re ncein C/obtainedfrom Patel'sandBeche n's
calib rationequations. 73
Table 4.3 Average ofmaximumdifferenceinC/meas uredfromthela rges t
andthe smalles ttubes. 74
Table4.4 Reco rdedsmoo th- wallburs tdata. 83
Table 4.5 Thenormaliz ed average time between bursts
(r;" '"
~u;Iv). 84 Table 5.1 Expe rime ntalcondi tions and flow pa rameters in grooved-wal lexperi men ts. '0 1
Tab le 5.1.1 Effectofd/80andIi'on«C/ ,Cj.o)/Cj.o)""",and((C/ ,Cj.o)/Cj.O)",i.
forthree different shapedandsized grooves. 103 Ta ble6.1 Effectofd/80andIi'on((C/-C/,o)/C/,o)"""and«C/-Cj.o)/C/.O)..in
for three differentshaped grooves withd"2Omm. 178
Table B.1 Various propo sed values of /(and B. 251
Table C.! Experi mental uncertain tie s 272
List of Symbols Gener a l:
y-intercept(Eq.3.4) [non-dimensio nal]
Cf skinfrictioncoefficient,(Cf"2l""J(p(uQl »(non-dimensional}
Cf,a skin frictioncoefflcienr on thesmooth-wall [non-dimensional]
C.. correction factorfor the meanveloc ity(Eq.3.9) [non-dimensional ) groove depth,orthe outside tube diameterin thePrestontube measurements, or detection functionin turbulent burst analysis[m] (for thegroovedepth and the outside tube diameter),[non-dimensional)(for the detectionfunction)
d'" du, /v[non-dimensional)
d; internallayer thickness[m]
D empirical constant (Eq. 3.10)[non-dimensional)
D~ diameterofthe idealized primary eddy insidethegroove[m] (Fig.6.3.1) D~.. diameterof the idealized secondary eddiesinside thegroo ve [m] (Fig.6.3.1) E turbulent energyspectrum, or y-interceptfor the velocitydefect-law (Eq.4.3) [ml/s2)(for the turbulentenergyspectrum), [non-dimensiona l](for they- intercept]
/ frequency[radls]
Is burstingfrequency[burstls]
f~· normalized bursting freq uency(f~·~vfaI(u,)2)[non-dimensional]
f, sampling frequency[sample rs]
channel heightem] (Table 4.5) H thresholdlevel (Eq.3.14)[non-dimensional]
hf heightofidealizedejectedfluid from a groove [m] (Fig.5.4.1)
xxiii
wave number(2ftf lV) [1m]
tunnel span [m]
effecti velength of the wire (forhot-wire)[rn]
length of idealizedejected fluidfrom a groove[m](Fig. 5.4.1) N~ numberofbursts
lip differentialpressurebetweenthetotaland staticpressuresatthe wall[N/m2](Eq.
3.11)
8;1+ nonnalizedAp(Ap+_~/(pY»[non-dimensional](Eq.3 .13)
q/ quadrant decomposi tioncontributingtothetotal Reynoldsstress(-uv).
(qj+ '"(_uv)/(u.)2,i»1, 2. 3,4)[non-dimensional}
R6 Reynoldsnumberbased on0(R6-U06Iv)(non-dimensional]
R~, d Reynoldsnumber based onPreston tubeoutside diame ter,d(R<,d'"UedIv) [non-dimensional] (Eq.4.2)
Reh Reyno ldsnumberbased onh andV ..(Reh .. U.,hIv)[non-dimensional](Table 4.5)
RQ Reynoldsnumber based on 8(RQ""V,{j Iv)[non-dimc nsiona l]
S(I) instan taneousvelocityvector[mis]
grooveor riblctspacing[m]
.5' normalizedr byinnervariables (s+•SUt/v )[non-dimensional]
temperature(C)
~ averagetime betweenbursts lsl
r;+
normalized average timebetween bursts(r;;+
IIT;;U,2tv)[non-dimensional]T. time betweentwoconsecutive detected ejections[s]
T~,.. averageofT~[sl
To averageof the durationofdetected ejections [s]
T. sampling time[s]
time]s]
t+ normalized t byinnervariables(t'_u,lt/V)[non-dimensional](Fig.2.9) V meanvelocit yin the .r-direction [mls]
V< correct local mean velocity [mls]
V.. averagemass velocityinthe channel flow [mls]
V","", measured localmeanvelocity[mls]
Vn freestream velocity[mls]
if normalizedmean velocityin the.r-direction byinner variable(u+'"Ulu,) [non-dimensional]
u(t) instantaneous velocityin thex-directio n(U(l)-=U+II(t»[mls]
u(t) instantaneousfluctuation velocity in ther-direction [mls]
u' rrns of fluctuationofvelocit y in thea-direction(mls]
u" nonnalizedu'byinner variable(u'·.u'!u,)[non-dimensional) friction velocity(u, =(t"/p)o,,)[mls]
(uv) Reynolds stress [m2!s2]
v(t) instantaneousveloc ity in the y-d irection(v(t)=V+v(t)) [mls]
v(tJ instantaneousfluctuation velocityin they-direction [m/s]
v' rms of fluctua tionofvelocityinthe y-d irection [mls) groovewidth in thestreemwisedirection [m]
streamwisc coordinatemeasuredfrom the groovetrailingedge [m]
x· normalizedpressure(Eq.3.12)[non-dimensional]
wall-n ormal coordinate [m]
y" nonnalizedy by inner variables(1.>+..yu,/v)(non-dimensional]
y. normaliz ed wall shear stress(&I,.3.12)[non-dimensional]
Greeksymbols:
constant in the power-law equation(&I,.3.6)[non-dimensional]
instantaneous velocity angle (Eqs.A.2 and A.3), or a constant in the hot-wire calibration(Eq.C.3)[degree] (for the instantaneous velocity angle),[non- dimensional](forthe constantinthe hot-wire calibration)
localboundarylayer thickness[m]
00 boundarylayer thickness just upstreamofthe groove,unless otherwisestated[m]
turbulentkineticenergydissipationrate [m2ls3]
wire diameter [m]
Kolmogoro v lengthscale (Tl..v314/t.114)[m]
von Karm an constant[non-dimensional]
kinematicviscosity[m2/sJ moment umthickness [m]
fluiddensity [kglml] maximumvalue of T.[s]
wall shear stress[N/m2]
t+ nonnalizedwall shearstress (Eq. 3.13) [non-dimensional]
Kolmogorov velocity scale (o..[ve)114)[m/s]
(...)and....are usedinterchangably to denotethe time averaged quantities
Ab breviatio ns:
ND analogtodigital DNS directnumericalsimulation HWA hot-wireanemomctry LDA laser Doppleranemometry LDV laserDoppler velocimetry LEBU largeeddy break-up LES large eddysimulation MEMSmicro-electro-mechanical-system PIV particle image velccimerry PTV particle tracking velocimetry VITA variable-time interval-averaging
xxvii
List ofAppendices
Appendix A HOI-wire calibration and program listings Appendix B Wallshear stress estimation Appendix C Experimentaluncertainties
233 249 256
Chapter 1 Introduction
Despite being studied formanyyears , turbulentboundarylaye rs ,particularlyover rough surfaces.still remain poorlyunderstood.A completepictureoftheint era ctio n of thenear-wall structures in turbulentboundarylayerswith thesurfacehasnot been uncovered.Asignificant effort isstilldevotedtothestudy of the turbulent boundary layerbecause of its importance inmany practicalapplications.Theinteractionof the near-wall structures with the surface is primarilyresponsible forthe highskin frictionon the surface. A turbulentboundary layerrespondsdifferently todifferent surface geometries.For example,it hasbeen shownthatlo ngitud inalriblets(Fig.1.2 ) can reduce the friction drag, whiletransversal riblets tend to increasethe friction drag.
The inner most region of the layerisparticularly interesting,because of the possibilityofmanipulatingtheturbulent structuresin thisregion to obtainsomedesired benefits.The innerregion constitutesapproximately20 percentof the totalboundary layer thickness(8),butthe most dominant turbulent activities take place withinthis
region. For example,approximately 85percent of the total turbulentkinetic energy dissipation takesplacein thisregion (Klebanoff,1955). Experimental and numerical results show that the turbulent quantities,such as turbulence intensities, turbulence energy spectra, and Reynolds stresses,change very rapidly in this region as the solid boundary is approached. Also, turbulentbursts, recognized as one of the mostimportant stress-producingeventsin a turbulent boundary layer, originate in this inner region.A study of thestructure of turbulentboundarylayers, especiallyin theinnermostregion,is important to enhance our understanding of the near-wall characteristicsof thelayer.
Skin friction,whichisdissipative in nature,plays an importantrole in the system performance for both externalandinternal flows.For example, the skin friction drag determinesthe overallefficiency of aircraft,high-speed vehicles,marine vessels,piping, and dueting systems.In transportation applications,overallfuelefficiency can be improved by reducingthetotal drag force.The required thrust is directly proportional to drag force,and fora typicalciviltransport aircraft, skin frictiondrag can contribute up to 50 percent of the total drag at cruisingspeed(Coustol and Savill, 1991).In internal flows, such as inpipelinesandductingsystems, almost 100 percent of the drag is due toskin friction.Alarge numberof investigations of skin frictiondrag reduction have been performed over the last five decades, because of the economicbenefits. For example.for a typical long rangetransport aircraft, a reduction in skin friction drag of less than 5 percent can producea considerable savings on direct operating costs.The drag reduction is directly related to the reductionin fuel consumption,and the fuel consumption contributes up to approximately22percent of the total directoperating cost (Marec, 2000).
1.1Backgr oundofStudy
A tremendousamount ofliterature on methods of manipulating a turbulent boundarylayer to achieve a skin friction drag reduction is alreadyavailable.It is well known thatthe coherent structures suchas quasi-streamwise vortices andlow-speed streaks embedded in the near-wall region of the turbulent boundarylayer can be manipulatedfor possible skinfriction drag reduction.However,a clear understanding of the ncar-wallstructures of a turbulent boundary layerand how they interactwith a surface is necessarytoimplement any drag reduction scheme. Despite being studied for many years,probably sincethe study of Nikuradse(1933), the effect of different surface modifications on a turbulentboundary layer is still not fully understood.
Several drag reductionschemes have been investigated, which can basicallybe classifiedinto two different categories:active and passive control.For active control, externalenergy is required,whileno auxiliaryenergyis necessary for passive control.
Some active controltechniques are:(I)laminar flow control;(2) suction andblowing;(3) micro bubbletechnique;(4) moving surface;(5) electromagnetic forces;and (6) reactive control. With laminar flow control,transition of the boundary layerto turbulence can be delayed. Suctionin a turbulent boundary layercan be used for re-laminarization and attenuationof turbulentactivityin the near-wall region. A reduction in skin friction drag due to suction has been reported (Antonia etal.,1995;Park and Choi. 1999).Inj ection of lightgases or micro-bubbles into a turbulentboundary layer can reduce skin frictiondrag (Latorreand Babcnko,1998; Kodama et al.,2000). Usingthis technique,an overall skin friction drag reduction upto 30 percent hasbeen reported (Latorreand Babenko,1998).
Amoving surfaceeither inthe strearnwisedirection (Modi,1997),or oscillatingmotion in the spanwisedirection(ChoiandClayton, 1998;Choi, 2002) canbeused to reduce drag. ChoiandClayton(1998)andChoi(2002) reportedthat a reductionin skinfriction dragupto45 percentcan beachievedusing anoscillating surfacein the spanwise direction.Electromagnetic forces can be used for controllingturbulentboundarylayers in conductivefluidssuchas seawater(Kim,1998;Lee andKim, 2002).Adrag reduction up to50percentusingthis controlschemewas reported(Kim,1998).Arecentdevelopment of turbulentboundary layer control is through reactive control.Ingeneral,reactive controlismore complexandits construction and implementation are moredifficultthan the previousmethods(Gad-el-Hak,1996).Althoughskin frictiondragreductionofup to 50percent canbe achieved usingactive control.theoverallenergyefficiencyof this control technique is poor(Kim,1998).Through passiveturbulencecontroltechniques, the skin frictiondrag could potentially be reducedwithout anyextraauxiliary energy.
Twoof themost wellknownpassive control techniquesfor turbulentskin friction drag reductionare the useofexternalmanipulatorssuchas largeeddybreak-updevices (LEBUs)embeddedin theouterpart of a turbulentboundarylayer (Fig.1.1),or internal devicesthatinvolve analterationofthe wallgeometry suchaslongitudinalgrooves (riblets)onthesurface(Fig. 1.2).Sowden(1998) notedan averagelocal skin friction dragreductionofapproximately 3 percentdownstreamofLEBUs.The LEBU support drag andthestructuralcomplexitynecessary for their instal1ation,however,tend to negateany benefits of drag reduction.Bechertet al.(1997) showed that whenthe geometryof theriblets isproperly optimized,a drag reductionof approximately 10 percent can be achieved.The maintenanceof longitudinalmicro grooves on a surface has
posedseveral difficulties,however.Whilepassive control techniqueswill not yieldas much drag reductionas activecontrol,they are simplertoimplement.
Perturbing elements can be used onaflatplate to enhance momentumand heat transfer associatedwithboundary layers.Theenhancement ofthe momentum and heat transfer is a resultofan increase in turbulenttransport due tohigher turbulenceintensity levelsinthe near-wall region.Inthestudiesusing a transverse square groove(Choi and Fujisawa,1993;ElavarasanetaI., 1996;Pearson et al., 1997)anda v-shapedgroove (Tantirige et al.,1994),an increase in the turbulenceintensitywas reponed.There have beenseveralstudiesof the response of a turbulentboundary layer to a short perturbation;
see,for example,Andreopoulus andWood (1982),Webster et al.(1995) and Pearsonet al.,(1997,1998).In these studies,it wasshown that skinfrictioncoefficient(Cf)and Reynoldsstresses,includingII',v',and(-/Iv),are significantly shifted from meoriginal smooth-wallvalues.There is a localincrease and decreaseinCfdownstream of the perturbation, and the Reynoldsstresses are increasedconsiderablydownstreamof the perturbingelement. Pearsonet al. (1998) noted that the Cfdistributiondownstreamof the perturbationis anindicator ofthe responseof theturbulentboundary layerto the perturbation. Whilethe responseof turbulentboundary layersto ashort perturbationwith a single sized perturbingelement is wendocumented,there have been relativelyfew studiesof the effect of differentsized and shapedshort perturbations. There is a need for morestudiestoinvestigate theresponse of turbulent boundary layersto differentsized and shapedshort perturbations
1.2 Purpose and Significanceof Study
A study of the responseof a turbulentboundarylayerto shortperturbations will provide a better insight and understandingintotheinteraction between the surface and the boundarylayer.especially in the near-wallregion.Althoughtherehave been several studies on turbulent boundarylayers perturbedbyasingletransversesquare or v-groove, the effectof the sizeof the groovehas notbeen investigated.There have been no systematic studieson the relaxationofa turbulentboundary layer downstreamof different shaped transversegrooves.The possibility of drag reduction using ad-type roughnesshas beenproposed(Choiand Fujisawa,1993).A smalllocalskin friction reduction downstream of a transversesquaregroovewas observed(ChoiandFujisawa, 1993; Elavarasanetal.,1996;Pearsonetal.,1997).The totalskin friction dragdueto the presence ofthe groove. however,is higher than the correspondingsmooth-wallvalue (Elavarasanet al.,1996).ChingandParsons(1999) suggested a possibilityto reducethe total skin friction drag byusing transverse squaregroovesin series in the mainflow direction.
The mainpurpose ofthepresentstudy isto investigatethe responseof a turbulent boundarylayer to differentshaped transversegrooves.Three differentgroove shapes:
square(SQ),semicircularbase(SC) and triangular(TR) were investigated.For each shape,three differentsized grooveswere usedinthis study: 5,10 and20mm(Fig.1.3).
Thedepthto widthratio(Jlw)of eachgroovewas set tounity.The response of the turbulentboundarylayer to the groove is investigatedfromx/So=0up tox/SQ'"2.0.
Experimentswere performedattwo Reynoldsnumbers,Ro=1000 and 3000.Hot-wire
ancmomctry using single-normaland X-wireswas usedtomeasure theturbulence characteristicsdownstream ofthe groove.
Thepresent study attemptsto clarify the differencesoftheturbulentboundary layer characteristicsover differenttransverse groovesfrom the correspondingsmooth- wall case.First,differenttechniques ofwall shear stress (t,..)measurements forsmooth- wallturbulentboundarylayers are evaluated. Themost appropriatee,measurement techniques using indirect methodsapplied toaboundary layer developingdownstreamof a shortperturbation are then examined. Next, the ...distribution inturbulentboundary layers downstreamofthe different sizedandshaped groovesis studied.Thisprovides some insight intothepossibility of drag reductioninturbulent boundarylayers using different sized andshapedgrooves.The changes in turbulentcharacteristics (u',v',(-uv),
E(kj ) ,sweep andejectionevents, and the burstingfrequency)and their relaxation
downstream of the groovesarestudied. Also, theeffects of the oncoming boundarylayer thickness(00)on the turbulentcharacteristics are evaluated.
1.3 OutlineofThesis
Aliterature review relevanttothis research ispresented in chapter2, which consists of foursections.In the first section, coherent structuresin a turbulentboundary layer are reviewed, while the structure ofaturbulent boundarylayerunder zeropressure gradientonsmoothandnon-smooth walls is reviewed in the secondand third sections, respectively.Simulationsand experimentaltechniques used to studyturbulentboundary layers are reviewed in the fourth section.
In chapter3, descriptionsof the experimentalfacility, instrumentationanddata reduction procedures are presented. Firstly, the wind tunnelis described with detailsof thetunnel geometry,dimensions,capabilitiesand limitations.A briefdescription of hot- wire anemometryis presentednext, followedby a description ofthePrestontube arrangement anddataacquisitionsystem.The data reductionprocedures for theReynolds stress, wall shear stress, internallayer growth, sweep and ejection events, andbursting frequencyarepresented inthischapter.Thelast pan of this chapter presents the experimentaluncenainties.
In chapter4, theexperimentalresults forthe baselinesmooth-wallturbulent boundarylayer arepresented and discussed. The resultsanddiscussionincludewall shear stress(1...),mean velocity CU),Reynoldsstresses and turbulent energy spectra.Sweepand ejection events and bursting frequency are also discussed.Wallshear stress measurementsusing a Preston tubeare also presented in this chapter.
In chapter5, the experimental results of the grooved-wallexperimentsare presented and discussed,which includesthe experimentalresultsfromthe square (SQ ), semicircularbase (SC) and triangular(TR)grooves. Themain emphasisof thediscussion inthis chapteris to examinethe effectof the groove size on flow parameters closetothe groove suchas wall shear stress (1,.,),meanvelocity (U) andmternal Iayer(d;)growth downstream ofthe groove. The turbulencemeasurements, sweep and eject ionevents, and burstingfrequencyarepresented and discussed in separate sub-sections.
Inchapler6, theeffects of the differentshapes of the grooves on the turbulent boundarylayer are discussed. Conclusionsand recommendationsare given in chapter7, andthe contributiunsof thepresent study tothe literature are also highlighted.
o,
--- .--- --- ----_.
X
Fig.1.10 utermanipulatorusinglarge-edd. ybreak-up (LEBU)
U
o
y x
• I _______
.~z
Fig.1.2 Surfacewithlongitudinal riblets
(b) (x) w= 5, 10,and 20mm d=w
u,
q
y- U"' "; ,, ,---'C- -
d- - - - - - -I--.'C.j---'-
~ - d---
I--.'C.j
U, y
t
xC d
(e)
Fig.1.3Groove shapesonthetestsurface: (a)Square(SQ);(b)semicircular base (SC);
(c)triangular(TR).
11
Chapter 2 Literature Review
Boun darylayersplay an importan t rolein themomentumandhea t transferat the wall. Typically,boundary layerscanbeclassifi ed into three differen t regimes:lam inar, transitional,and turbulen t(Fig. 2.1).Inlaminar boundarylayers.themom entumtransfer is essentiallybymoleculardiffusion,whereas inturbulent boundary layersthe mom entu mtransferbythefluctuatingveloci ty playsa significa nt role.Intransitional boundary layers,momentumtransfer duetovelocity fluctuationscantakeplace, however, the momentum transfer isnot asintense as in turbulentbounda ry layers.There hasbeen alargeamount ofresea rch on turbulentboundarylayers,bothexperimentally and numeric ally,becauseorits impo rtance inmanypractical applications.Although the transport mechanisms in turbulentboundarylayershave beenstudiedfor manydecade s, the dynamicsofturbulent boundarylayersare still notfullyunderstood.With advan cesin modeminstrumentation along with therece nt advances indirectnumerical simulation (DNS),howeve r,someofthekeydynamic sin turbulentboundarylayershavebeen
uncovered, especiallythe role of the quasi-coherent structures,or coherent motions.In thischapter,previous studiesonturbulentboundarylayers arereviewed briefly.The reviewconsistsof foursections:(i)coherentstructures inturbulent boundarylayers;(ii) turbulent boundary layersonsmooth-walls; (iii)turbulentboundarylayers onnon- smooth-walls;and (iv) simulationsand experimental techniques in turbulentboundary layer studies.This short reviewshould provide a betterundemanding of the effect of different surface geometriesonthe structureandcharacteristicsof a turbulentboundary layer.
2.1Coherent Stru ctu res inaTurbul entBound ary Laye r
In the last decade or so,asignificant amount of effort has beendevoted to the study of quasi-coherentstructures,orcoherentmotions,ina turbulent boundary layer. A substantial amount of informationhas been collectedon thesestructures throughdetailed probe measurements,flow visualization,whole flowfield measurements, particle image velocimetry (PIV),and from directnumericalsimulation(DNS) (e.g.Head and Bandyopadhyay,1981;Robinson,1991;Main and Mahesh,1998;Na etaI.,2(01). While there is no precisedefinitionfor quasi-coherentstructures,Robinson (1991) providesa definitionfor acoherent structureas"a three-dimensionalregion of theflow over which atleast onefundamentalflowvariable (velocity component. density,temperature,erc.}
exhibits significantcorrelationwith itself,or with another variable,over arangeofspace and/ortime thatissignificantlyforger thanthe smallestlocaf scales of the flow".The coherentstructures in a turbulentflowfield occurrandomly in time andspace, andthey are characterized by a verywide range of length andtimescales (Carpenter,1997).The
13
most dynamicallydominant coherentstructuresin thenear-wall regionof aturbulent boundarylayerare the quasi-streamwise vortices(Headand Bandyopadhyay,1981;
Cantwell,1981;SmithandSchwartz, 1983). Jeong etal.(1997)showedthat the coherent structuresinthe near-wall region aremostly highly elongated quasl-streamwisevortices, andthesevorticesare well organized.Low-speedstreaks areformed between two adjacentquasi-strcamwisevortices.Figure 2.2depictsa schematic diagram of a low- speedstreaksurrounded by quasi-streamwisevortices (reproducedfrom Blackwelder and Ecke1mann, 1979), andFig. 2.3 showsthe near-wallstreak structureaty.=2.7 (reproducedfrom Kline etal.,1967). As the vortices develop,they becomelonger, reduce in diameter, and liftupawayfromthewall.When the 'head'of the vortex liftsup,the leading edge of thelow-speed streak.moves togetherwith the vortex awayfrom the wall (Smith andWalker,1997).Inthe finalstepof their cycle, theybreakup('bursting' ).
Figure 2.4shows a schematicdiagramof burstformation in thenear-wallregion (reproducedfrom Hinze,1975).It is believedthat thebursting proceess initiates anew generationof vorticalstructures, and then the cycleis repeated (Carpenter, 1997).In additiontothesee amwtscvortices,transverse (lateral)and wall-normalvortices maybe present, withthelatterones occurring lessfrequently.These vortices,exceptthewall- normalvortices,could'pump-out'mass andmomentum fromthewall(Robinson,1991).
Itis conjectured that there is a strong correlation between skinfriction and the quasi- streamwise vortices inthe near-wallregion.If these vorticescan bemoved awayfromthe ncar-wallregion,a reductioninskin frictionmay be possible (Pollard, 1996). Also,ifthe coherentstructures can be stabilized,then theskin frictiondrag wouldbe reduced (Sirovich andKarlsson,1997).
Flow visualization wasusedextensivelyin manyearlystudies(e.g.Klineetal., 1967;Kimet al., 1971;Falco, 1980a. b.1991;Head andBandyopadhyay,198 1) to educe thestructureof turbulentboundarylayers.Kline et at. showedthat there were well organizedmotions in theinnerregion of the layer. Streak patterns inthelayer were shownat severaldifferentdistance sfrom thewall, fromveryclose to the wall(y+=-2.7) up to the wake region(y+=507). The streak patterns across thelayer were shown to be differentfrom onelocation to another asthestreak moves awayfromthe wall.Inthe innennost region.the orientationofthestreaksiswell defined and isinthe streamwise direction.Fartheraway from the wall,the orientationofthestreaks islessdefined .Fa lco (1980a) showedthat large-scalethree-dimensionalbulgesare present in theouter region of theturbulentboundarylayer.
The near-wallturbulentdynamicsarecontinuousand self-regenerating activities (Choi.1996).Ejectionsandsweepsplayan important role inthedynamicsof turbulent Reynolds stresses,turbulence production,andturbulentkineticenergydissipat ion (Coustolsand Savill,1991). The ejectionsare associatedwithnegative streamwise(-u) and positivewall-normal(+v)velocityfluctuations,whilethe sweepsare associatedwith positivestreamwise(+u)and negativewall-normal(-v)velocity fluctuations(Wallaceet al.,1972).In the uvquadrant-splittingdescription(Wallace et al.,1972;Willmarthand Lu,1972), ejections and sweeps are definedas(UV)2and (UV)4,respectively,where subscripts2 and 4 represent the second and fourth quadrant,respectively(Fig.2.5).
Wallace et aJ.(1972)identified that the majorturbulent events in the wallregionare ejectionsof low-speedfluid outwardfrom the wallandsweeps of high-speedfluid inwardtoward the wall. The ejectionsandsweeps are believedto playakey role in
IS
maintaining the turbulence activitiesin the near-wall region, and these two activities produce the majorpartof the Reynolds stresses (Scherz. 1993).
In the outer region ofa turbulentboundary layer,large scale eddiesseem to be more dominant. Robinson (1991) found eddies onthe scale of the boundary layer
thickness(0)in this region.Falco (l980a, b) observed a clear demarcation line between the turbulent andnon-turbulent region.It is believed that there is a strong interaction between the outer large-scale structures andthe quasi-streamwise coherent structuresin the innerregion. Several studies have shown that breakingthe outer large-scale structures,usingLEBUs or micro-electro-mechanical-systems (MEMS)forexample. can result in a skin friction reduction(Mainand Bewley,1994; Ho andTai,1998; Sowdon, 1998). The definite relationshipbetween the outer large-scale structures and inner region coherentstructures,however,has not been clearly resolved.Despite the vast amount of information available on thesecoherentmotions, the interactionof these motions with different surface geometries has notbeen resolved.For example. there is still no consensus on how differentsurface roughnessesinteract with the near-walllow-speed streaks and quasi-srrearnwisevortices.Additionally,although several mechanismsfor reductioninskin friction drag by manipulating the near-wallcoherent structureshave beenproposed,the exactmechanism of this is not clearly understood.So far, there has been no systematic study of the influenceofwall-roughness onthe turbulentbursting frequency.Although flow visualizationshowed the structure of the turbulentboundary layer on non-smoothsurfaces does not differ significantlyfrom that on a smooth surface (Grass,1971;Ching etal.,1995h), theroughness geometry can affect the bursting frequency.In thefollowingsection,previous studieson the effects of different surface
geometriesonthenear-wallturbulent structures and turbulentparametersaredescribed briefly.
2.2 TurbulentBoundaryLayerson Smooth-W alls
Asignificant numberof experimental andnumerical studiesof turbulentboundary layers overboth smooth- and non-smooth-wallshavebeenperformed.The characteristics of smooth-wallturbulentboundary layersare brieflyreviewedfirstto providea better understanding of how the characteristicsof turbulentboundary layers over non-smooth- wallsdiffer. There are two main regionsin a turbulentboundarylayer designated as tbe innerand theouterregions(Fig.2.6).Theinner region occupiesapproximately20 percentof the boundarylayer thickness(t5)and consistsof threesub-regions:the laminar sub-layer(uptov"~5),bufferregion (5!':y'!':40).andan overlapregion.Inthe laminar sub-layerthe viscous shear dominates,whilein the overlapregionboth viscousand turbulentshear stresses are non-negligible.The innerlimitof theoverlapregionis approximatelyaty+:<40,but the outerlimitoftbisregiondependsonthe flow Reynolds number. For example, at aReynolds numberabout1000 (basedon the momentum thicknessand freestreamvelocity), thisouterlimitisapproximatelyy+:<200,butthis limitincreases upto approximatelyatj-">750 atRII:<13000.In thefigure, theouter limit oftbe overlapregion refers to the data atthe lowerRj).The outerregion consists of two sub-regions:the overlapregionand a wake region.The outerregionismuchlarger than theinner region,and occupiesuptoapproximately80 percent oftheboundarylayer thickness. Unlikein the innerregion,theturbulentshearstressis muchmore important than the viscousshearstress inthe outer region.
17
Uptodate,there has been a vast amount ofreviewsandstudieson smooth-wall turbulentboundarylayers. Several issues,suchas the effect ofReynolds number (e.g.
Gad-el-HakandBandycpadhyay,1994;Ching et al.,1995a; Mochizukiand Nieuwstadt, 19% ), scaling laws(Clauser,1956;George andCastillo,1997;DeGraff and Eaton, 2(00), and universal log-law inthe overlap region (Osterlundet al., 2(00) havebeen investigated.
The structures ofturbulentboundary layersdepend stronglyon Reynolds numbers.Itis well known that athighcr Reynoldsnumbers,there exists an overlap region ofmean velocitywhennonna hzedusingwall variables(u cand \I). The extentof the overlap regionwidensas theReynolds numbcrincreases. Atlow Rcynolds numbers, however, the overlapregionisvery narrow, anditsexistence is questionable(Ching et al.,1995a).The latter authors also showedthatthe locationsof peakvalues of Reynold"
stresses[v",w" ,and <-u+v'» increasewithRlJ,althoughthelocation of thepeak valueof u..is nearly unchanged.In the studyof Antonia and Kim (1994),it was shownthat the low Reynoldsnumber effect can beidentified using two importantcharacteristics.First, thereisan intensificationof the quasi-streamwisevortices, buttheaverage locationand diameterof the vortices,in terms ofUrandv,were approximately unchanged. Second, theuse ofu,andvas the nonnalizingparametersformostturbulencequantit iesinthe ncar-wallregion wereless appropriatethan theuse ofKolmogorov velocity(u)and length<TJ) scales.The Reynolds number effects are found to penetratedeeper into the boundarylayer in the case of streamwise turbulence intensity(u? thanthatof the mean velocity(ll)(Gad-el-HakandBandyopadhyay,1994).A strongdependence ofu'on the Reynolds numberis also evident from thestudies of Fernholz and Finley(1996).
Mochizukiand Nieuwstadt (1996) showed the peak valueof u' is nearly independentof the Reynoldsnumber,whileMetzgerandKlewicki(200 1) foundthatthe peak value ofu' is dependenton ROoThe Reynolds number effect on wall-normal turbulenceintensity(VI and Reynolds stress«-uv»havealso been reported(Fernholz andFinley,1996; Ching et al.,1995a).Ingeneral, selfsimilaritiesin v"and(-u"v+)are confinedtothe region very close to the wall(say
»' :;
10).Scaling issuesin turbulentboundarylayers are stillbeing investigated. For instance, while the scaling parameter for mean velocityis well established.scaling parameters for normalstresses are stillin debate.For example,Purtell etal.(1981) argued that streamwiseturbulenceintensity scales favorably with outer parameters(Ua andb),whereasDeGraff and Eaton (2000)proposed that mixed-parameters are more appropriate.Moreover, the correct scalingparameters for the turbulent burstare stillnot clearly understood.For example,BlackwelderandHaruomdis (1983), Kim and Spalart (1987),and Luchik andTiedenn an (1987)arguedthatthe inner variables (urand l1 are the best scalingparameters for the average burstingperiod.On the contrary,Raoetat.
(1971)and Kimetal. (1971) foundthat outervariables (SandUo)weremore appropriate.
While the inner scaling parameters may bethe most appropriatefor the turbulent burst periodatlowReynolds numbers,scaling using mixed variables (outer and inner variables) seems to be more appropriateathigherReynolds numbers(RII~6000) (Shah and Antonia,1989).
The studies ofKlebanoff and Diehl(1952) andKlebanoff(19 55) were the earliest comprehensiveexperimentalstudieson smooth-wall turbulent boundarylayers.They found that the turbulentenergy production and dissipation reach a maximumvalue in the
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region closeto the wall(y+<30). Theyalsosuggested thatthe concept of localisotropy wasnotappropriateto estimatetherateof turbulent energydissipation.The flow visualizationstudies of Kline et al. (1967) andHead and Bandyopadhyay(1981) provided some insight intothe near-wallturbulent structures,includinglow-and high- speedstreaks. Morerecently,directnumericalsimulations (DNS) (see, forexample, Spalart, 1988)have provided considerable insight into turbulent boundarylayersand provided a benchmark databaseforlaboratory experimentaldata.
2.3TurbulentBoundaryLayersonNon-Smooth-Walls
The discovery of coherent structures,including quasi-streamwisevorticesand streakstructuresin wall-boundedturbulentflows, led tothepossibilityof developing flow controlschemes forturbulentboundarylayers.The controlschemescan be classifiedas activemethodsorpassive methodsusing surfacemodifications.Onlythe passivemethodsusing surface modificationsare discussedin thisthesis.The surface modificationsincludesurface roughnessor theuseofshortperturbations
Usingflowvisualization, Grass(1971)and Grass etal.(199 1)showed thatthe basic characteristics oftheinner-regionofturbulentboundary layersovera wall roughenedwith sandgrainswere notsignificantly different from that on the smooth-wall.
Low-speed streaksand turbulentbursteventsincluding thesweep and ejectionevents werealso found in therough-wall turbulentboundarylayer, similarto those inthe smooth-wallturbulentboundary layers.Similarto thefinding of Grass (1971),Chinget al. (1995b)and Djenid iet al.(1999)showed that the low-speed streak structure over ad- typerough-wallisnot toodifferentfrom thaton the smooth-wall. Theappearance and the
break-upof thestreakpatternswere similarto the low-speedstreaks observedbyKline et al. (1967).
Although flow visualizationtechniqueshave shown that the basic structuresof the near-wall low-speed streaksoverthesmooth- and rough-wallturbulent boundarylayers aresimilar,theinherentturbulentquantitiesare different.Thisismostsignificantin the near-wall region,say withiny' ::;100 (Antonia, 1994;Mochizuki andOsaka,1998). Also, the wallshearstress(r..) onrough-wallsis differentfromthat onsmooth-walls (AndreopoulusandWood,1982;E1avarasan et al., 1996;Pearson etal.,1998).Antonia andLuxton(197Ia ) introducedtheconcept of aninternal layer(0;)inaturbulent boundarylayer fora suddenchangein wall boundarycondition.The internal layer is defined as the regionwithintheturbulent boundary layer where the effects of the change inboundary conditionare felt.Several types of rough-wallshavebeen studied,including turbulentboundarylayers over sand-grainroughness(Andreopoulusand Bradshaw, 1981),riblet surfaces (Choiet al.,1993; BechertetaI.,1997;LeeandLee,2001),k-and d-typerough-walls (Perryet al.,1969;Bandyopadhyay andWatson, 1988; Antoniaand Djenidi,1997), andtransverseV-grooves (Tantirige etal.,1994). The effect of simple perturbations(short-roughness,2D bump,andsingletransverse squaregroove) on turbulent boundarylayershavealsobeen studiedbymany researchers(Andreopoulusand Wood, 1982;ChoiandFujisawa,1993;Webster et al.,1996;Pearson etal.,1997,1998).
2.3,1k-type RoughWall
The k-typc rough-wall (Fig. 2.7)is defined as containing transverse2D rectangular grooves withwlk>LTheusefulness of thistype of roughness is its abilityto
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enhance the turbulenceintensitiesinthe near-wallregion(Bandyopadhyay andWatson, 1988). Many studies onturbulent boundarylayers over this type of roughnesshave been performed (e.g.Perryetal.,1969; Anton iaandLuxton,1971b; Bandyopadhyayand Watson, 1988). Theflow is stronglyaffectedbythe roughness height(k),which is also believed to be themost appropriatescalingparam eter forthe length scale inthewall- region.Bandyo padhyayand Watson (1988)showed that the second and third moments were increased byup to13and 50 percent,respect ively,overak-type rough-wa ll. The increase in the second momen t over this type of rough-wallwas alsoobserved by Antonia and Luxton(197Ib).The skinfrictionover ak-type rough-wall was found to be highe r than thatonthe smooth-wall(Bandyopadh yay and Watson,1988) .
1.3.1d-typeRough Wall
A d-type rough-wa ll(Fig. 2.8) is characterized by regularlyspaced two- dimensionalsquare grooves placednormal to the flow,one element width apart (II'=d)in the streamwisedirection(Antonia,1994;Elavarasanet aI.,1996).Bandyopadhyay(1986) and Bandyopadhyayand Watson (1988)alsoused the d-type rough-w all tenn forwid-cI.
The d-typerough wallispart icularly interest ingbecauseofthe possibility thatthe boundarylayer over this roughness type may be exactly self-preserving[Djenidietal., 1994). Also, it has beensuggested thatthe drag overthis rough-wallshouldnot be mueh differentfrom that over a smooth-wall,and could even be smaller (Tani etal.,1987;
Osaka andMochizuki,1988). The d-type rough-wall has also been studiedas a meansof surface drag reductionby combining thissurfacewithother potentia l drag reducing devicessuch as LERUs (Bandyopadhyay,1986).
Using flow visualization,Townesand Sabersky(1966) showedthatthere was a significant interaction betweentheflowinthe grooves ofthed-type rough-wa llandthe outerflow.They identifiedseveralphasesofactivities : ejectionsof fluid out of the groove,inflows intothe groove,and periodsof relative calmwherethe outerlayer skims overthe groove.Djenidi et al.(1994) speculatedthatthe near-wallquasi-stre arnwise vorticesareresponsible forthe ejections of fluid outofthe groove,and also responsible forthe increase in theReynolds stress(-uv».The observationsofTownesand Sabersky werecorroboratedby Chingetal.(1995b), who showedthat passage of near-wallquasi- streamwisevorticesoverthe groovestriggeredthc ejectionsof fluidoutof the groove.
They alsoshowed that the streakstructureon the d-type rough-wallis somewhatsimilar to that on the smooth-wall.Figure2.9showsa time sequenceoffluidejectionfromthe grooveto the overlyinglayer (Elavarasanetal.,19%).
There weresignificantdifferencesin themeanvelocity (U),turbulent intensities (u'andv'),andReynolds stress(-uv»over thed-typeroughnesswhen comparedwiththe smooth-wall case (Antonia,1994;Mochizukiand Osaka, 1998;Djenidi etaI.,1999).
Antoniafounda decreaseinifin theregiony+:;;100 andincreasesinu",v"and(-u'v+) overthe d-type rough-wallcomparedto thatover thesmooth-wall.Antoniaarguedthat theincreases inu",v'",and(-u'v+)must beassociatedwith theincreaseinthewall shear stress, althoughthe latter was notexplicitly described. Mochizuki and Osaka(1998), using a d-type rough-wallwithinsertion oflongitudinal ribs insidethe grooves,found a reductioninu'compared to that observed in the smooth-walt.Djenidi etal.(1999) showed that r..exhibitsaperiodic behaviorwith a wavelength that resemblesthe periodicity ofthe surfacegeometry.Ther",attainsamaximum at alocationjust
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