Manipulation of turbulent flow for drag reduction and heat transfer enhancement 1

Meanwhile, the turbulent term of drag coefficient for thecorrugated surface was not obviously reduced.The heat transfer and flow in a channel with asymmetric dimples or protrusions on singl

MANIPULATION OF TURBULENT FLOW FOR DRAG REDUCTION AND HEAT TRANSFER

ENHANCEMENT

CHEN YU

(B Sci., Peking University, China)

A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE

2013

I hereby declare that this thesis is my original work and it has beenwritten by me in its entirety I have duly acknowledged all the sources of

information which have been used in the thesis

This thesis has also not been submitted for any degree in any university

previously

CHEN YUMay 28, 2013

i

First of all, I am deeply grateful to my supervisors, Professor YongTian Chew and Professor Boo Cheong Khoo, for their continuous guidance,supervision and enjoyable discussions during this work I also owe a debt

of gratitude to Professor K.S Yeo, Professor J.M Floyran, Dr K.C Ng,

Mr Junhong Wang, Mr C.M.J Tay for their instructions and discussions

In addition, the National University of Singapore has provided mevarious supports, including the research scholarship, the abundant libraryresources, and the advanced computing facilities as well as a conduciveenvironment, which are essential to the completion of this work

Finally I would like to thank, from the bottom of my heart, my parentsand wife for their endless love, understanding and encouragement

Chen Yu

ii

To my parents

To my wife Weiwei and son Xiaohan

iii

iv

1.2.2 Protrusions 26

1.3 Background on turbulence 28

1.3.1 Coherent structures 30

1.3.2 Techniques to educe the coherent structures 35

1.4 Objectives and scope 41

1.4.1 Drag reduction 42

1.4.2 Heat transfer 43

1.4.3 Scope of present work 45

Chapter 2 Methodology 46 2.1 Governing equations 46

2.2 Calculation of the thermo-aerodynamic performance 50

2.3 Numerical simulation methods 54

2.3.1 On Direct Numerical Simulation 54

2.3.2 On Detached Eddy Simulation 55

2.4 Verification of numerical methods 58

2.4.1 Grid independence test 59

2.4.2 Other parameters and flow structure 63

Chapter 3 Corrugated surface 70 3.1 Geometry of corrugated channel 71

3.1.1 Sinusoidal grooves 72

3.1.2 Other groove shapes 72

3.2 Laminar channel flow 74

3.2.1 Simplified governing equations 74

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3.2.2 Theoretical solution 75

3.2.3 Global performance of drag difference 77

3.2.4 Velocity profile 87

3.2.5 Skin friction drag profile 90

3.2.6 Analysis of interaction between bulk flow rearrangement and skin friction distribution 93

3.2.7 Summary 98

3.3 Turbulent channel flow 98

3.3.1 Drag difference 100

3.3.2 Mean velocity profile 105

3.3.3 Skin friction drag profile 112

3.3.4 Turbulence quantities 115

3.3.5 Decomposition of drag coefficient 124

3.3.6 Theoretical prediction at small wave number 128

3.3.7 Additional cases with phase shift 131

3.3.8 Summary 136

3.4 Concluding remarks 137

Chapter 4 Heat transfer over asymmetric dimples 142 4.1 Configuration of asymmetric dimples 143

4.2 Configuration of studied cases 146

4.3 Global thermo-aerodynamic performance 150

4.3.1 Symmetric dimple 150

4.3.2 Asymmetric dimple 151

4.3.3 Effect of asymmetry versus effect of depth 158

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4.4 On mean characteristics 158

4.4.1 Mean flow field patterns 160

4.4.2 Mean characteristics of drag and heat transfer 166

4.5 Instantaneous characteristics of flow 173

4.5.1 Flow field 175

4.5.2 Vortex structures 175

4.6 Turbulent advective heat flux 177

4.7 Turbulent kinetic energy 180

4.8 Spectral analysis of velocity 181

4.9 Concluding remarks 182

Chapter 5 Heat transfer over protrusions 186 5.1 Configuration of protrusions 186

5.2 Results and Discussion 189

5.2.1 Hydrodynamic and thermal performance 189

5.2.2 Distribution of local drag and heat transfer rate 191

5.2.3 Flow structure 200

5.2.4 Turbulent kinetic energy 213

5.2.5 Spectral analysis of velocity 213

5.3 Concluding remarks 215

Chapter 6 Overall conclusions and recommendations 217 6.1 Conclusions 217

6.1.1 Corrugated surface 218

6.1.2 Heat transfer over asymmetric dimples 218

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6.1.3 Heat transfer over protrusions 219

6.2 Recommendations 220

Bibliography 222 Appendix A Analytical solutions of channel with both corru-gated walls 238 A.1 Governing equations 238

A.2 Solution 241

A.2.1 Velocity field 241

A.2.2 Flow rate 242

Appendix B Analytical solutions of channel with single cor-rugated wall 244 B.1 Governing equation 244

B.2 Solution 246

B.2.1 Velocity field 246

B.2.2 Flow rate 247

Appendix C Wetted area of corrugated channel 249 Appendix D Theoretical prediction at small wave number 251 D.1 Preparation—local friction velocity, friction Reynolds num-ber, wall length 251

D.2 Skin friction profile in the spanwise direction 256

D.3 Velocity, flux and friction coefficient 257

D.3.1 Flat channel 257

D.3.2 Arbitrary X-Y plane in the corrugated channel 258

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D.3.3 Flux—integration of bulk velocity 260

D.3.4 Mean bulk velocity 261

D.3.5 Skin friction coefficient 261

D.4 Re τ = 180 264

D.4.1 S=0.5 264

D.4.2 S=1 265

D.4.3 Validation of results 266

D.5 Re τ → ∞ 267

D.5.1 S=0.5 267

D.5.2 S=1 268

Appendix E Configuration of asymmetric dimple 269

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With recent advancement and globalization of economy, the demand forenergy continues to increase rapidly, resulting in severe energy crisis inthe world To reduce the demand side of the energy equation, energy-efficiency process/device with reduced energy wastage is essential Inorder to achieve these goals, flow manipulation technologies especially forturbulent flow are needed to reduce drag (i.e corrugated surface) and toenhance thermal efficiency in heat exchangers and others (i.e asymmetricdimple and protrusion)

In this thesis, the drag reduction capabilities of corrugated surface werefirstly investigated using perturbation method and numerical simulations(Direct Numerical Simulation and Detach Eddy Simulation) Additionally,flow patterns, vortex structures, turbulent kinetic energy were examined toreveal possible mechanisms of drag reduction It was shown that corrugatedsurface can create comparable drag reduction to (or even possibly higherthan) riblets and other traditional drag reduction devices for turbulentchannel flow It was also found that lower wave number and higheramplitude create more drag reduction The corrugated surface increasesflow rate through rearranging the bulk velocity distribution or reducing

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bulk term of drag coefficient Study of turbulent kinetic energy (TKE)and Reynolds stress showed that the corrugated surface rearranges therespective distribution while keeping the volume-averaged intensity largelyunchanged Meanwhile, the turbulent term of drag coefficient for thecorrugated surface was not obviously reduced.

The heat transfer and flow in a channel with asymmetric dimples

or protrusions on single wall were then examined by DES method Thethermal-hydrodynamic performance of asymmetric dimple was investigated

in terms of Nussselt number, friction and performance factors more, the distribution of friction factor and Nusselt number together withthe flow/vortex patterns over dimples/protrusions were discussed

Further-For the asymmetric dimple, the results showed that the skewing of thedeepest point of dimple to the downstream side while still maintaining thecircular shaped print diameter is a feasible way to enhance heat transferwith fairly similar pressure loss Furthermore, skewing the deepest point

of shallow dimple (h/D < 20%) in the downstream direction provides a

more efficient way to enhance heat transfer efficiency than only increasing

its depth ratio (h/D ≥ 20%) The better performance of the asymmetric

dimple is broadly attributed to its stronger flow ejection, weaker lation zone, stronger vortices and eddies, and higher turbulent advectiveheat flux

recircu-For protrusions, it was found that larger protrusion’s height induceshigher friction factor and Nusselt number, which may be due to theasymmetric flow features However, when the height ratio increases, the

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friction factor increases more rapidly than the Nusselt number does, suchthat the thermal performance factor initially increases and then reachesits asymptotic limit or even decreases It is also shown that the highestfriction factor and Nusselt number are co-located at the upstream portion

of protrusions due to the strong convection and impingement of fluid onthe upstream portion of protrusions Additionally, the distributions offriction factor and Nusselt number were symmetric and asymmetric onthe protrusion surface according to the height ratio being low and high,respectively This can be attributed to the symmetric and asymmetric flowpattern and vortex structures for low and high protrusions, respectively

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List of Tables

1.1 Advantages and disadvantages of the various types of active

and passive methods for drag reduction 19

2.1 Grid independence test for the DNS code 60

2.2 Domain independence test for DNS 60

2.3 Grid independence test for the DES code 61

2.4 Domain independence test for DES 62

3.1 Comparison of numerical and theoretically predicted ΔD for channel with both corrugated walls at α = 2 84

3.2 Configuration of different grooves for study of wave number and amplitude effects: ‘Y’ means it is invested by DES, ‘†’ means that triangular and trapezoidal grooves are also investigated at such parameter, ‘∗’ means that it is also examined by DNS 99

3.3 Comparison of drag difference of the original shape and the first mode in Fourier space at α = 0.25 and S = 1 102

3.4 Comparison of drag coefficient difference ΔD computed by DES and DNS 102

3.5 Ratio of each term of drag coefficient to the total drag coefficient on flat plate 126

3.6 Ratio of each term of drag coefficient on corrugated surface to that on flat plate 127

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4.1 Different configurations of dimples for Case 2 at h/D = 10%:

‘C’ stands for the case where dimple’s deepest point is

skewed in streamwise centerline (Dz = 0%), ‘S’ stands for

the case where dimple’s deepest point is on offset side of

centerline (Dz = 15%); * stands for symmetric dimple, cases

without * are asymmetric dimples 148

4.2 Different configurations of dimples for Case 3 at h/D = 15%.

The meanings of ‘C’, ‘S’ and * are the same as in Table 4.1 149

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List of Figures

1.1 Top view of traditional riblets and ‘wavy riblets’ 6

1.2 Different arrangements of ‘V’ protrusions 6

1.3 Staggered sailfish skin, adapted from Sagong et al (2008) 8

1.4 Different arrangement of dimples in Veldhuis and Vervoort (2009) 11

1.5 Asymmetric dimple used by Isaev et al (2000b) 12

1.6 Mean velocity in turbulent channel flow 29

1.7 Instantaneous velocity field view in end view in the cross-flow plane, adapted from Smith and Walker (1994) 32

1.8 Scheme of the distribution of vortical structures in the different regions of a turbulent boundary layer, adapted from Robinson (1991) 34

1.9 The local streamline pattern with the eigenvectors of the velocity gradient tensor in the neighborhood of a vortex core, adapted from Zhou et al (1999) 40

2.1 Computational domain for a flat channel 47

2.2 Effects of Reynolds number on C f and Nu 63

2.3 Mean velocity in turbulent channel flow 64

2.4 Mean temperature in turbulent channel flow 65

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2.5 Time-averaged turbulent kinetic energy components

normal-ized by u2

τ 66

2.6 Reynolds stress u  v  normalized by u2

τ 662.7 Streamwise velocity contours (low speed streaks) in differ-ence X-Z plane slices given by DES and DNS 67

2.8 Resolved Reynolds stress −u  v  and modeled Reynolds stress

2.9 Eddy viscosity ν t 69

3.1 Channel with (a) two corrugated walls (b) single corrugatedwall Sinusoidal groove is taken as an example here 733.2 Sketches of the grooves used in the analysis: sinusoidal,triangular and trapezoidal 73

3.3 Theoretical prediction of ΔD on channel where (a) both

walls are corrugated and (b) single wall is corrugated.Dashed lines refer to drag reduction and solid lines refer to

drag increase Results herein is valid for α → 0 corresponds

to a corrugated channel with a very long wavelength, but

not valid for α = 0 81 3.4 Theoretical prediction of ΔD on channel where (a) both

walls are corrugated (b) single wall is corrugated Results

herein is valid for α → 0 corresponds to a corrugated channel with a very long wavelength, but not valid for α = 0 82 3.5 Ratio of theoretical ΔD for channel with both corrugated

walls versus channel with single corrugated wall Results

herein is valid for α → 0 corresponds to a corrugated channel with a very long wavelength, but not valid for α = 0 83

3.6 Comparison of theoretical prediction and numerical results

at α = 0.5 85

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3.7 Normalized wetted area difference ΔA w and theoretical total

drag difference ΔD for channel with both corrugated walls

at different S and α Results herein is still valid for α → 0

corresponds to a corrugated channel with a very long

wave-length, but not valid for α = 0 86

3.8 Normalized theoretical drag difference per unit wetted area

for channel with both corrugated walls at different S and

α Results herein is still valid for α → 0 corresponds to

a corrugated channel with a very long wavelength, but not

valid for α = 0 87 3.9 Streamwise velocity u on Z-Y plane: (a) α = 0.5, S = 0.5 (b) α = 0.5, S = 1 (c) α = 2, S = 0.5 (d) α = 2, S = 1 (e) flat 88

3.10 Normalized shear drag on corrugated surface 91

3.11 Velocity contour for α = 2 and S = 1 in physical domain 92

3.12 Force analysis in control volumes 93

3.13 Drag coefficient difference (a) effects of α (b) effects of S 103 3.14 Normalized wetted area difference ΔA w and total drag dif-

ference ΔD at different S and α 104

3.15 Normalized drag difference per unit wetted area at different

S and α 105 3.16 Streamwise velocity u on Z-Y plane (a) α = 0.25, S = 0.5 (b) α = 0.25, S = 1 (c) α = 0.5, S = 0.5 (d) α = 0.5, S = 1 (e) α = 2, S = 0.5 (f) α = 2, S = 1 107 3.17 Streamwise velocity u on Z-Y plane for flat plate 107 3.18 Streamwise velocity u on unscaled Z-Y plane (a) α = 0.5,

S = 0.5 (b) α = 2, S = 0.5 109 3.19 Streamwise velocity u on Z-Y plane (a) three planes position; mean velocity on three planes for (b),(d) α = 0.5, S = 0.5, (c), (e) α = 2, S = 0.5 110 3.20 Normalized shear drag on corrugated surface for S = 0.5 113

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3.21 Normalized shear drag on corrugated surface for α = 0.5 113

3.22 Turbulent kinetic energy (TKE) in corrugated and flat chan-nel Three components u 2 , v 2 and w 2 for (a)(c) α = 0.5, S = 0.5 (b)(d) α = 2, S = 0.5; total amount k for (e) α = 0.5, S = 0.5 (f) α = 2, S = 0.5 116

3.23 Reynolds stress (u  v  ) in corrugated and flat channel (a) α = 0.5, S = 0.5 (b) α = 2, S = 0.5 118

3.24 u  w  and v  w  in corrugated channel for (a)(c) α = 0.5, S = 0.5 (b)(d) α = 2, S = 0.5 119

3.25 Volume averaged (a) turbulent kinetic energy (TKE) k (b) u  v  (c) u  w  and v  w  121

3.26 Turbulence structures for (a) α = 0.5, S = 0.5 (b) α = 2, S = 0.5 (c) α = 0.5, S = 0 (d) α = 2, S = 0 122

3.27 Body fitted orthogonal coordinate (ξ, η) established in corru-gated channel, solid lines stand for ξ and dashed lines stand for η 125

3.28 The drag difference ΔD at different Re τ and S when α → 0 130 3.29 Effects of phase shift ϕ on drag coefficient difference ΔD 132

3.30 Streamwise velocity u on Z-Y plane for different phase shift (a) ϕ = 0, (b) ϕ = π/2 and (c) ϕ = π 135

3.31 Shear drag stress on Z-Y plane for different phase shift ϕ at α = 0.5 and S = 1 136

4.1 Sectional drawing of a single dimple 144

4.2 Dimple’s surface along the streamwise centerline of dimple, the displacement of the deepest point is ΔX = dp(−h), the fluid flows from left to right 146

4.3 Computational domain and dimpled plate 147

4.4 Arrangement of dimples on bottom channel wall 148

4.5 Deepest point of dimple for different configurations 149

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4.6 Depth ratio effects for symmetric dimple 1524.7 Comparison with experimental results in Burgess and Ligrani(2005) 153

4.8 Friction and Nusselt number ratios for Case 2 at h/D = 10% 154

4.9 Area and volume goodness factor ratios 155

4.10 Friction and Nusselt number ratios for Case 3 at h/D = 15% 157

4.11 Depth ratio effects on asymmetric dimple’s performance 159

4.12 Flow patterns for Case 2 (h/D = 0.1), the fluid flows from

left to right (red dots refer to the deepest point of dimple,the same hereinafter) 161

4.13 Flow patterns for Case 3 (h/D = 0.15), the fluid flows from

left to right 1634.14 Mean streamlines patterns on X-Y plane (Z=5), the fluidflows from left to right 165

4.15 Contours of mean vertical velocity v on X-Y plane (Z=5),

the fluid flows from left to right 165

4.16 Contour of longitudinal velocity U in the vicinity of the

dimpled wall, the fluid flows from left to right 167

4.17 Contour of transverse velocity W in the vicinity of the

dimpled wall, the fluid flows from left to right 167

4.18 Shear stress Sm/Sm0 for Case 3 (h/D = 0.15), the fluid

flows from left to right 169

4.19 Form drag F m/F m0for Case 3 (h/D = 0.15), the fluid flows

from left to right 171

4.20 Nusselt number distribution for Case 3 (h/D = 0.15), the

fluid flows from left to right 1744.21 Instantaneous streamlines patterns on X-Y plane (Z=5), thefluid flows from left to right 175

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4.22 Contours of instantaneous vertical velocity v on X-Y plane

(Z=5), the fluid flows from left to right 1764.23 Vortex structures 177

4.24 Turbulent advective heat flux v  T  on X-Y planes 179

4.25 Iso-surfaces of high w 2 = 7, red dots refer to the location ofsampling point over dimples 1804.26 Power spectral density at different angular frequency ofvelocity fluctuations 1815.1 Channel with protrusions 1875.2 Sectional drawing of a single protrusion 188

5.3 Effect of h/D on Nusselt number, friction coefficient and formance factors: h/D stands for height ratio for protrusion,

per-while it stands for depth ratio for dimple 191

5.4 Normalized friction Sm/Sm0 at different height ratios h/D 193 5.5 Normalized friction F m/Sm0 at different height ratios h/D 195 5.6 Normalized Nusselt number Nu/Nu0 at different height

ratios h/D 196 5.7 Normalized skin friction Sm/Sm0, form drag F m/F m0 and

Nusselt number Nu/Nu0 at h/D = 20% 199 5.8 Streamlines on y+ = 1.5 at different height ratios h/D 201 5.9 3-D streamlines at different height ratios h/D, the dashed

line refers to the streamline tracing markers, the fluid flowsfrom left bottom corner to right top corner 203

5.10 Streamlines on X-Y planes for different height ratios h/D 204 5.11 Velocity contours in vicinity of protrusion (y+ = 8) withdifferent height ratios 2055.12 Slices position over protrusions 206

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5.13 Streamwise vorticity (ω x) and streamlines on different Z-Yplane slices, red dashed lines refer to boundary of protrusions 209

5.14 Vortex structure identified by iso-surface of λ2 213

5.15 Iso-surfaces of high turbulent kinetic energy k = 3, red dots

refer to the location of sampling point over high protrusion 2145.16 Power spectral density at different angular frequency ofvelocity fluctuations 214

D.1 Mean velocity v.s wall distance: lines are different palnes

in the corrugated channel at α = 0.25 and S = 0.5, symbols

are flat channel with different channel opening 254D.2 TKE v.s wall distance: lines are different palnes in the

corrugated channel at α = 0.25 and S = 0.5, symbols are

flat channel with different channel opening 255D.3 mean velocity and TKE v.s wall distance: lines are different

palnes in the corrugated channel at α = 0.5 and S = 0.5,

symbols are flat channel with different channel opening 255

D.4 Skin friction force ratio at S = 0.5 and Re τ = 180 256E.1 Coordinate system in 3D rendition of the dimple 270

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A w wetted surface area of channel

AΣ cross section area of channel

A pro projected area of channel wall in the X-Z plane

C fb bulk term of drag coefficient

C ft turbulent term of drag coefficient

C p heat capacity at constant pressure

C DES Detached Eddy Simulation constant

d nominal diameter of dimpe/protrusion

D

discriminant of vortex or print diameter of ple/protrusion

dim-D x , D z skewness of asymmetric dimple in X and Z directions

D h hydraulic diameter of channel

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d w distance from the wall

D p  total form drag

D f  total skin friction drag

h depth/height of dimple/protrusion

k thermal conductivity or turbulent kinetic energy

Nu surface Nusselt number

q constant heat flux on channel walls

Q criteria of vortex or flow rate

S amplitude of corrugated surface

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St Stanton number

Sm skin friction drag per unit projected area

F m form drag per unit projected area

u1, u2, u3 velocity components in x, y and z directions

Δx, Δy, Δz grid sizes

y+ distance to the wall in wall units

xxiv

A, A ij velocity gradient tensor

S, S ij rate of strain tensor

Ω, Ωij rate of rotation tensor

B, B ij tensor determined by S and Ω

τ ij sub-grid-scale Reynolds stress

Superscripts

time-averaged or volume-averaged quantity

 time and space filtered quantity in DES model

0 results for smooth channel obtained by empirical formula

Greek symbols

α wave number of corrugated surface

δ local height of corrugated channel

λ wave length of corrugated surface

λ2 the sencond largest eigenvalue of B

Ω cross section region of channel

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Chapter 1 Introduction

In recent decades, the increasing energy costs have led to insufficientnonrenewable energy supply for mankind, hence extensive research effortshave been focused on increasing energy-efficiency and curtailing wastage

In order to increase energy-efficiency, drag needs to be reduced and thermalefficiency needs to be enhanced by say flow manipulation methods Addi-tionally, flow speed is generally high in most real-life applications (like airover vehicles, water/oil in piping system and so on), resulting in the flowoperating in the turbulent regime Hence, turbulent flow manipulatingstrategies to reduce drag and enhance heat transfer continue to attract alot of attention

1.1 Review of drag reduction methods

As most of the supplied power is dissipated by skin friction on moving body,reducing drag on body surface is an important consideration in engineering

1

For a commercial airplane, improvement of the lift-to-drag ratio implies afuel saving For underwater vehicles, for which 90% of the total drag isdue to skin friction, drag reduction would mean an increase in speed orlonger operational range For piping systems (e.g petroleum), significantpressure losses occur due to the viscous drag inside the pipelines, hencedrag reduction is also desirable Engineers and scientists have perennialinterests in devising methods to reduce drag on surface In turbulent flow,

it is clear that if the near-wall low-speed streaks are stabilized, the burstingphenomena will be suppressed, hence resulting in less cross-flow mixing andhence skin friction reduction (Iuso et al., 2002) As such, researchers arealways on the lookout for optimal devices to control coherent structuresand suppress turbulent energy production/dissipation in order to reducedrag The following are different approaches to drag reduction, which are

broadly classified into passive and active means.

1.1.1 Passive methods

Since the early days, people have always believed that the drag onsmooth surface is always lower than that on rough ones In recentyears, researchers found that some special geometric structure of surfacecan reduce drag Such structures include shark skin, riblets, dimples,

‘V’ protrusions, cylindrical elements, superhydrophobic surface, polymeradditive and corrugated surface

2

1.1.1.1 Shark skin and riblets

Shark (superorder Selachimorpha) is one kind of the fastest swimming fish,whose speed can exceed 40–50km/h (the ‘shortfin mako shark’ and the

‘great white shark’) during feeding or attacking Microscopic tion of shark skin showed that shark skin consists of small jagged andoverlapping scales with valley/ridge structure (denticle) aligned in flowdirection The scales are believed to disrupt turbulent flow structures overthe skin, considerably reducing the drag on the shark as it swims (Bechert

examina-et al., 2000; Dean and Bhushan, 2010) Han examina-et al (2008) directly copiedthe surface of shark’s skin by hot-embossing method and experimentallystudied flow over it in water tunnel In their experiment, drag on surfacewas measured directly by force sensors The results showed that the dragreduction of copied shark skin is about 8.25% compared to flat plate, butthis result is not compared with those of classical riblets and real sharkskin under the same flow condition More recently, in order to study thehydrodynamics of shark skin under dynamic conditions, Oeffner and Lauder(2012) measured the swimming speed of flapping flexible foil covered by

real shark skin membrane in water tunnel (13, 000 < Re < 27, 000) They

found that the swimming speed of foils with shark skin is 12.3% higherthan the counterpart of foils after removing denticles It was believed thatshark skin denticles may enhance thrust, as well as reduce drag However,the denticles on shark skin could not be removed completely Thus, theremaining small stubs may cause the difference between it and smoothunderlying collagen surface of shark skin, leading to measurement error ofdenticle’s hydrodynamic effect

3

Riblet as inspired by shark skin, which also consist of microgrooves on

the surface aligned with mean flow direction, is one of the popular passive

methods for controlling turbulent flow Still, riblet structure is differentfrom shark skin, for the former is one continuous geometry and the later isdiscrete in the streamwise direction Riblets generally have two main crosssection configurations: wedge-like and blade-like (see Sudo et al., 2002)

The height and spacing (h+ and s+, superscript + means wall units) ofriblets’ ‘wedge’ or ‘blade’, are commonly set at about 10–30 It is accepted

by most researchers that the highest drag reduction of riblets in turbulentchannel flow is around 7%–9% (see Bechert et al., 1997; Itoh et al., 2006).The results of flow over riblets obtained by Choi et al (1993) based onDirect Numerical Simulation showed that the drag reduction over riblets areinduced by depression of velocity, vorticity fluctuations and the Reynoldsstress Similar drag reduction‘mechanism’, that the riblets obstruct thenear wall lateral flow, has also been proposed by Bechert and Bartenwerfer(1989); Choi (1989)

Riblet has been flight-tested by Airbus and other companies throughthe use of special 3M adhesive riblet films on aircrafts (Viswanath, 2002;Thiede, 2001; Houghton and Carpenter, 2003) Airbus collaborated withLufthansa/Cathy Pacific Airlines to study an Airbus A340-300 coated withriblets to approximately 60% of the surface, and the results showed a totaldrag reduction about 2%–3% However, riblets with micro structure arevulnerable, as such the coating shall be replaced frequently Consideringthe cost of installing and maintaining, the performance benefits of ribletcoating are marginal Riblets have also been used in Olympics Games and

4

other sports competitions (i.e rowing, swimming).

Besides traditional straight riblets, researchers also proposed modifiedriblets-like geometry to obtain higher total drag reduction Itoh et al.(2006) conducted experiments on seal fur surface in turbulent channel

flow (Re 2H is about 2,000 to 40,000), and found that it can reduce dragcoefficient by 10% while riblets can only reduce by 8% compared to flatplate Peet et al (2008); Peet and Sagaut (2009) tried to obtain moredrag reduction by adjustable riblets called ‘wavy riblets’ (see Figure 1.1)which can induce lateral velocity oscillation Peet and Sagaut (2009)found that ‘wavy riblets’ can produce about 2% more reduction of skinfriction than traditional riblets do with numerical simulation of channel

(Re τ = 180) However, the amount of form drag created by ‘wavy riblets’was not reported in their work Hence, it is unclear whether the totaldrag of ‘wavy riblets’ is lower or higher than that of traditional riblets As

a follow up, Kramer et al (2010) studied the hydrodynamic performance

of ‘wavy riblets’ in channel (5, 700 < Re < 5, 900) both numerically and

experimentally They found that the effect of ‘wavy riblets’ with small

amplitude (see a in Figure 1.1) is very weak, and cannot be detected outside

the uncertainty range On the other hand, the increasing form drag lessenthe total drag reduction when amplitude is large Thus, whether ‘wavyriblets’ can achieve higher drag reduction than the traditional one is verydoubtable

1.1.1.2 ‘V’ shape protrusions and Sailfish skin

5

(a) Straight traditional riblets (b) ‘Wavy riblets’

Figure 1.1: Top view of traditional riblets and ‘wavy riblets’

Sirovich et al (1990) found that plane waves in turbulence appear to be

“essential to the local production of turbulence via bursting or sweepingevents in turbulent boundary layer” Thus in order to control turbulenceand reduce drag, the coherency has to be destroyed or disrupted Later, thesame team Handler et al (1993) numerically showed that the randomization

of selected Fourier modes of plane waves brings 58% drag reduction and 30%increase of mass flux in channel The authors claimed that drag reduction

by this method is due to the destruction of the coherency in producing structures near the wall Then Sirovich and Karlsson (1997)

turbulence-Figure 1.2: Different arrangements of ‘V’ protrusions

employed randomly pattern ‘V’ protrusions (see Figure 1.2) and

exper-6

imentally detected 10% drag reduction by pressure sensors in turbulent

channel flow (15, 000 < Re 2H < 40, 000) compared to flat smooth plate.

However, drag increase would extend to 20% if the ‘V’ protrusions werealigned compared to flat smooth plate Monti et al (2001) experimentallymeasure the skin friction over ‘V’ shape protrusion in turbulent boundarylayer flow by studying the velocity profile They obtained a significant skinfriction reduction up to 30% on random pattern ‘V’ protrusions in a narrow

Reynolds number range (Re θ = 2, 500–4,500) However, the form drag was

not reported, which may cancel out the reduction in skin friction

Since the sailfish skin is very similar to the ‘V’ shape protrusion1,Sagong et al (2008) conducted experiments and simulations on differentpatterns (aligned, random and staggered) of sailfish skin and ‘V’ pro-trusions2 The staggered sailfish skin protrusions and those presented

by Sirovich and Karlsson (1997) are similar in shape, but opposite inflow directions The experiment was conducted in wind tunnel with

momentum thickness Reynolds number Re θ ranging from 4,400–8,300,while the immersed boundary method was implemented in the numerical

simulation of turbulent channel flow (Re τ = 180, Re 2H = 4, 200) Both

the experimental and numerical results obtained by Sagong et al (2008)showed no overall drag reduction can be produced by sailfish skin and ‘V’shape protrusions Conversely, the total drag on plates with sailfish skin or

‘V’ shape would increase by 0%–15% Furthermore, the numerical resultsdemonstrated that shear drag would decrease, but the net drag differences

1Sailfish skin is very similar to ‘V’ protrusion in size and shape, but opposite in flow

direction (see Figure 1.3)

2These protrusions are the same as those investigated by Sirovich and Karlsson (1997)

in shape and size

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became positive because of the larger increase in form drag They alsofound that in most situations, staggered and random pattern protrusionstend to produce similar amount of drag increase, which is almost one half

of that produced by aligned pattern

Figure 1.3: Staggered sailfish skin, adapted from Sagong et al (2008)

The opinions of researchers on whether ‘V’ protrusion induces dragreduction are diverse, hence the author (Chen et al., 2010) conductedexperiment on random and aligned ‘V’ shape protrusions in air channel

with a wide Reynolds number range (10, 000 < Re 2H < 40, 000) The

air channel used by the author is 8m long, where the contraction ratio

is 17:1; and the test section of the channel is 800mm long, 400mm wideand 20mm high The pressure sensor (Setra model 239) was connected totubes installed on the upstream and downstream sides of the test section

to avoid interference with the flow in the test section The drag differencebetween the test plate and flat plate was determined by interpolating theupstream and downstream pressure distributions (see details in Chen et al.,2010) The relative errors of drag difference measurement were less than2.5% for our experiment However, the error becomes larger when Reynoldsnumber is low because of uncertainty in low pressure measurement Theresults showed that both the random and aligned ‘V’ protrusions lead to

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drag increase about 0%–15%, which becomes higher with larger Reynoldsnumber However, we cannot rule out the possibility that random pattern

‘V’ protrusion reduces drag at low Reynolds number (Re 2H < 5, 000),

because of the uncertainty induced by the relative low pressure gradientand the unstable transitional flow in our air channel at such low Reynoldsnumbers In addition, the drag induced by the aligned ‘V’ protrusions

is higher than that induced by random ‘V’ protrusions Furthermore,such difference between drag of the aligned and random ‘V’ protrusionbecomes smaller when Reynolds number increases Thus, it was concludedthat neither random and aligned ‘V’ protrusion can reduce drag of fullydeveloped turbulent channel flow

1.1.1.3 Dimples

Dimples on golf balls have been found to delay boundary layer separationand subsequently reduce the drag compared to a smooth ball (see Bearmanand Harvey, 1993) While studying dimpled surface in turbulent channelflow, Russian scientists Alekseev et al (1998) found that dimples might

be useful for friction drag reduction instead of delaying flow separation onbluff bodies Their experimental results showed that the skin-friction drag

on shallow dimples was decreased up to 20% (not the “golf ball” effect)However, no clear mechanism has been provided to explain this effect sofar There appears to be no follow up work by the same group to capitalise

on the large percentage of drag reduction (purportedly) found

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