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

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 Declaration I hereby declare that this thesis is my original work and it has been written 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 YU May 28, 2013 i Acknowledgments First of all, I am deeply grateful to my supervisors, Professor Yong Tian 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 me various supports, including the research scholarship, the abundant library resources, and the advanced computing facilities as well as a conducive environment, which are essential to the completion of this work. Finally I would like to thank, from the bottom of my heart, my parents and wife for their endless love, understanding and encouragement. Chen Yu ii To my parents To my wife Weiwei and son Xiaohan iii Contents Declaration i Acknowledgments ii Contents iv Summary x List of Tables xiii List of Figures xv Nomenclature xxii Chapter Introduction 1.1 1.2 Review of drag reduction methods . . . . . . . . . . . . . . . 1.1.1 Passive methods . . . . . . . . . . . . . . . . . . . . 1.1.2 Active methods . . . . . . . . . . . . . . . . . . . . . 15 1.1.3 Summary of different drag reduction methods . . . . 18 Review of heat transfer enhancement methods . . . . . . . . 18 1.2.1 Dimples . . . . . . . . . . . . . . . . . . . . . . . . . 20 iv 1.2.2 1.3 1.4 Protrusions . . . . . . . . . . . . . . . . . . . . . . . 26 Background on turbulence . . . . . . . . . . . . . . . . . . . 28 1.3.1 Coherent structures . . . . . . . . . . . . . . . . . . . 30 1.3.2 Techniques to educe the coherent structures . . . . . 35 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 Methodology 46 2.1 Governing equations . . . . . . . . . . . . . . . . . . . . . . 46 2.2 Calculation of the thermo-aerodynamic performance . . . . . 50 2.3 Numerical simulation methods . . . . . . . . . . . . . . . . . 54 2.4 2.3.1 On Direct Numerical Simulation . . . . . . . . . . . . 54 2.3.2 On Detached Eddy Simulation . . . . . . . . . . . . . 55 Verification of numerical methods . . . . . . . . . . . . . . . 58 2.4.1 Grid independence test . . . . . . . . . . . . . . . . . 59 2.4.2 Other parameters and flow structure . . . . . . . . . 63 Chapter Corrugated surface 3.1 3.2 70 Geometry of corrugated channel . . . . . . . . . . . . . . . . 71 3.1.1 Sinusoidal grooves . . . . . . . . . . . . . . . . . . . 72 3.1.2 Other groove shapes . . . . . . . . . . . . . . . . . . 72 Laminar channel flow . . . . . . . . . . . . . . . . . . . . . . 74 3.2.1 Simplified governing equations . . . . . . . . . . . . . 74 v 3.3 3.4 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 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 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . 137 Chapter 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 vi 4.4 4.5 On mean characteristics . . . . . . . . . . . . . . . . . . . . 158 4.4.1 Mean flow field patterns . . . . . . . . . . . . . . . . 160 4.4.2 Mean characteristics of drag and heat transfer . . . . 166 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 Heat transfer over protrusions 186 5.1 Configuration of protrusions . . . . . . . . . . . . . . . . . . 186 5.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . 189 5.3 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 5.2.4 Turbulent kinetic energy . . . . . . . . . . . . . . . . 213 5.2.5 Spectral analysis of velocity . . . . . . . . . . . . . . 213 . . . . . . . . . . . . . . . . . . . . . 200 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . 215 Chapter Overall conclusions and recommendations 6.1 217 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 6.1.1 Corrugated surface . . . . . . . . . . . . . . . . . . . 218 6.1.2 Heat transfer over asymmetric dimples . . . . . . . . 218 vii 6.1.3 6.2 Heat transfer over protrusions . . . . . . . . . . . . . 219 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . 220 Bibliography 222 Appendix A Analytical solutions of channel with both corrugated 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 corrugated 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 number, 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 viii 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 Reτ = 180 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 D.4.1 S=0.5 . . . . . . . . . . . . . . . . . . . . . . . . . . 264 D.4.2 S=1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 D.4.3 Validation of results . . . . . . . . . . . . . . . . . . 266 D.5 Reτ → ∞ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 D.5.1 S=0.5 . . . . . . . . . . . . . . . . . . . . . . . . . . 267 D.5.2 S=1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 Appendix E Configuration of asymmetric dimple 269 Vita 274 ix small scales (l < lDI ) where eddy motion is statistically isotropic, the energy is dissipated by molecular viscosity. 1.3.1 Coherent structures From the 1960s, with the advancement of experimental methodologies and capabilities of computers, increasing amount of information/database have been gathered in the study of turbulent flow. The study of such large amounts of data enable the delineation of coherent structures (CS) of the flow from the background incoherent flow characteristics. There are several different definitions of CS due to the different mathematical definitions, but a good introduction concept is provided by Robinson (1991): “ .region of the flow field in which flow variables exhibit significant correlation with themselves or other variables over space/time intervals that is remarkably higher with respect to the smallest scales of the flow .”. Though the detailed/exact definitions of CS are different from one another, it is generally accepted that CS has these properties: (i) it has typical structure (e.g. line vortex, hairpin vortex), whose length scale is similar to that of characteristic length scale of flow; (ii) it is regular and repeatable in geometry and dynamics; (iii) it survives over a distance much longer than its own length scale as it travels downstream; (iv) it affects significantly the various turbulence quantities (i.e. turbulent energy, Reynolds stress and mixing of fluid); (v) its structure is similar to that encountered in the transition from laminar to turbulence; (vi) it can regenerate by itself after (initial) destruction. It has been shown that coherent structure contains about 10–20% of total kinetic energy of turbulent flow, and is the main 30 source of flow noise. The development of turbulence is closely related to the reaction, pairing and entrainment of coherent structure. Thus coherent structure affects flow mixing, combustion, chemical reaction and heat transfer. It, therefore, provides the motivation for researchers interested in drag reduction or heat transfer enhancement to consider controlling and manipulating the coherent structure. Generally, coherent structure differs much from each other in the published literature because of the different detection technology (Robinson, 1991): • Low speed streaks in viscous sub-layer • Ejection of slow fluid in near wall region outward, including lift-up of low speed streaks • Sweep of fast fluid toward wall, including entrainment of fluid from outer region • Various kinds of vortical structures • Motions of big scale 3D bulges in the outer layer which are discussed in the following sections. 1.3.1.1 Streaks, ejection, sweep and bursting Hydrogen bubbles visualization of turbulent flow (see Kline et al., 1967) showed alternating streaks of high- and low-speed fluid very near to the wall (y + = 2.7), which is called ‘low speed streaks’. It is found that 31 the streaky structures are persistent, quiescent, and randomly distributed. The spanwise spacing and streamwise size of streaks are found as about z + = 100 and x+ = 1000, respectively. Strictly, low speed and high speed region are respectively related to ejection and sweep events near the wall (5 < y + < 15), which were found by Corino and Brodkey (1969) in a fully turbulent pipe flow (see Figure 1.7). And these two events can be identified through the quadrant analysis, depending on the sign of velocity fluctuations u and v : Q1 u > and v > 0, high-speed fluid moves toward the center of the flow field; Q2 u < and v > 0, low-speed fluid moves toward the center of the flow field, away from the wall (ejection); Q3 u < and v < 0, low-speed fluid moves toward the wall; Q4 u > and v < 0, high-speed fluid moves toward the wall (sweep) Figure 1.7: Instantaneous velocity field view in end view in the cross-flow plane, adapted from Smith and Walker (1994) Ejection and sweep which are mostly related to production of Reynolds stress and turbulence, actually demonstrate the dynamic processes of 32 evolution of turbulent structures in the boundary layer. The streaky structure interacts with the flow in outer region through an intermediate cyclic (not periodic) turbulent events — gradual outflow, lift-up, sudden oscillation and break up, which are called bursting phenomena. The so-called bursting phenomena are believed to play an important role in turbulent kinetic energy production and transport between inner and outer regions. Blackwelder and Kaplan (1976) showed that burst is an important ingredient of the regeneration of turbulence and production of Reynolds stress. Kim et al. (1971) suggested that almost all the net production of turbulent energy occurs in the near-wall region (0 < y + < 100), and associates with a sequence of turbulent events. 1.3.1.2 Vortical structure The study of vortex is important for turbulence research because: (i) any vortical structure whose direction does not coincide with wall normal direction contribute towards the momentum and mass transfer normal to the wall; (ii) vortex is often associated with that of the coherents structures; (iii) dynamic interactions of vortices help the understanding of turbulence. The key feature of vortical structure, rotational motion, is generally employed to mathematically define it. Much effort has been made to extract appropriately-defined vortical structures from in-coherent background flow. Theodorsen (1952) first introduced the existence of hairpin/horseshoe vortex in turbulent flow. Robinson (1991) confirmed the existence of 33 arch-like vortices and quasi-streamwise vortices (QSVs) (Figure 1.8). The combination of QSV(s) with an arch-like vortex results in a complete (or most frequently one-sided) hairpin/horseshoe vortex, which often depends on the vortex detection technique (Smith et al., 1991). In inner region, low speed streaks generally appear with streamwise counter-rotating vortices, and are regions that lie between streamwise vortices where there is an upwelling of fluid in a secondary motion. One basic hypothesis is that there exists ejection region (upwelling fluid) near the legs of the vortex passing over the wall, resulting in low speed streaks being generated (Acarlar and Smith, 1987; Singer and Joslin, 1994). Figure 1.8: Scheme of the distribution of vortical structures in the different regions of a turbulent boundary layer, adapted from Robinson (1991) After Theodorsen (1952), many interpretative models were proposed for hairpin vortex evolution (Acarlar and Smith, 1987; Smith et al., 1991; Panton, 2001) and for cane-shaped one-sided hairpins evolution (Robinson, 1991; Zhou et al., 1999). The bursting phenomenon in terms of the evolution circles of vortical structures was described by Hinze (1975). In contrast, some researchers (see Schoppa and Hussain, 1998a, 2002; Asai et al., 2007) believed that the growth and breakdown of unstable low-speed 34 streaks generate wall turbulence and vortices. 1.3.2 Techniques to educe the coherent structures An appropriate approach to detect coherent structure in turbulent flow is important for scientific understanding of turbulence. Many researchers have contributed to this research area. The main idea of identification of coherent structure is that the flow’s coherency is associated with a mathematical description of flow variables, like velocity and pressure. 1.3.2.1 Invariants of velocity gradient tensor A vortex structure can be seen as a rotational streamline pattern observed by a nonrotating observer moving with the velocity at that point. As such, it can be classified by the invariants of the velocity gradient tensor at that point. First, chose an arbitrary point ‘O’ in the flow field. Each velocity component ui can then be written in a Taylor series expansion in terms of the spatial coordinates, with the origin in ‘O’: ui = x˙ i = A0i + Aij xj + A1ijk xj xk + . . . and the first-order linear approximation is u = A0 + Ax 35 where the deformation tensor A is defined as Aij = ∂ui = ∇u. ∂xj The characteristic equation and three invariants of A can be written as: λ3 + I λ2 + I λ + I = where I1 =tr (A) = tr (∇u) = ∇ · u I2 = [tr (A)]2 − tr A2 I3 = − det (A) . For incompressible flow, the first invariant I1 of A is zero because of continuity, so the characteristic equation can be rewritten as: λ3 + I2 λ + I3 = 0. (1.1) The relationship between invariants and eigenvalues λ of fluid deformation tensor A can reflect the rotating nature of fluid. There are several methods and approaches to achieve this goal. • Complex eigenvalues of the velocity gradient Chong et al. (1990) proposed the following definition of vortex “. . . the vortex core is a region of space where the vorticity is sufficiently strong to 36 cause the rate-of-strain tensor to be dominated by the rotation tensor, i.e. the rate-of deformation tensor has complex eigenvalues. . . ”. The discriminant of whether eigenvalues in Eq. 1.1 are complex can be defined as D= I3 I2 + and two cases are possible: 1. D > 0, one real eigenvalue and two conjugate complex eigenvalues (flow pattern is focus topology) 2. D < 0, three real eigenvalues (flow pattern is node-saddle-saddle topology). So the iso-surfaces of a positive small value of the discriminant D can be used to identify vortices. A more detailed classification of the topology of a three-dimensional flow field based on the analysis of two dimensional I2 -I3 plane was introduced by Soria et al. (1994). • Projection of motion on the rotational and irrotational subspace The deformation tensor can be split into symmetric and anti-symmetric components: Aij = ∂ui ∂uj + ∂xj ∂xi =Sij + Ωij , 37 + ∂uj ∂ui − ∂xj ∂xi where S is the rate-of-strain tensor and Ω is the rate-of-rotation tensor: A + AT A − AT Ω= . S= Zhong et al. (1998) suggested that projection of motion on the rotational subspace subspace S Ω minus projection of motion on the irrotational can reflect the strength of rotational motion. That is, Ω 2− S 2 = (Ωij Ωij − Sij Sij ) . Q= This criteria of vortex is coordinate transform invariant; it can be drawn from the second invariant of deformation tensor. 1. Q > 0, rotational motion dominates strain motion; 2. Q < 0, strain motion dominates rotational motion. If Q > 0, the absolute value defines strength of vortex. • Imaginary part of eigenvalues in deformation tensor If matrix A has two conjugate complex eigenvalues λcr ± iλci and one real eigenvalue λr , the relationship between them can be drawn as: ⎧ ⎛ ⎪ ⎪ ⎪ Avr = λr vr ⎜ Avr = λr vr ⎪ ⎪ ⎜ ⎪ ⎨ ⎜ ⇒⎜ A (v + iv ) = (λ + iλ ) (v + iv ) ⎜ Avcr = λcr vcr − λci vci cr ci cr ci cr ci ⎪ ⎜ ⎪ ⎪ ⎪ ⎝ ⎪ ⎪ ⎩ A (vcr − ivci ) = (λcr − iλci ) (vcr − ivci ) Avci = λci vcr + λcr vci 38 where vcr ± ivci , and vr are the normalized eigenvectors of tensor A respectively for eigenvalues of λcr ± iλci and λr . Zhou et al. (1999) suggested that for such case, matrix A can be transformed into diagonal matrix: ⎡ ⎤ ⎡ A⎣ v r vcr vci ⎡ ⎦=⎣ vr vcr vci ⎤ ⎢ ⎢ λr ⎤⎢ ⎢ ⎢ ⎦⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎡ ⇒ A = [Aij ] = ⎣ v r vcr vci ⎢ ⎢ λr ⎤⎢ ⎢ ⎢ ⎦⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ λcr λci −λci ⎤ λcr λcr λci −λci λcr ⎥ ⎥ ⎥⎡ ⎥ ⎥ ⎥⎣ ⎥ vr ⎥ ⎥ ⎥ ⎥ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤−1 vcr The local streamline (Figure 1.9) can be expressed as y1 (t) = Cr exp [λr t] y2 (t) = Cc exp [λcr t] sin [λci t + φ] y3 (t) = Cc exp [λcr t] cos [λci t + φ] . Strength of the local swirling motion can be quantified by λci , the imaginary part of the complex eigenvalue of deformation tensor A. 39 vci ⎦ Figure 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) 1.3.2.2 Hessian matrix of pressure It is assumed that a vortical structure in a turbulent flow is always accompanied by a local minimum pressure in a plane perpendicular to the vortex axis. The symmetric part of gradient of Navier-Stokes equation can be written as DSij + ν∂k ∂k Sij + Bij = − ∂i ∂j p Dt ρ where Bij = Sik Skj + Ωik Ωkj . By neglecting the first two parts, Jeong and Hussain (1995) pointed that a local low pressure region (vortex core) in a plane (not necessarily 3-D minimum pressure) is connected with at least two negative eigenvalues of B. This implies the second largest eigenvalue λ2 is negative (λ1 ≥ λ2 ≥ λ3 are eigenvalues of B). 40 1.3.2.3 Summary From the literature review above, iso-surface of discriminants: D, Q, λci (imaginary part of complex eigenvalues of A) or negative λ2 of B can be used to characterize CS of turbulence, such as hairpin/horseshoe vortex. These techniques are also applied to study mechanisms of turbulent structure regeneration. Proper eduction technology helps to achieve better understanding of turbulence and may inspire different methods of manipulating turbulent flow. The four criteria of vortical structures (D, Q, λci and λ2 ) have been studied by the author, and the performance of them are basically similar. Considering the fact that λ2 is commonly used in investigation of drag reduction and heat transfer enhancemeent (Lienhart et al., 2008; Doo et al., 2010), only the results of λ2 are presented in this dissertation. 1.4 Objectives and scope From the above literature review of flow manipulation methods, it can be seen that numerous works have been done. However, several problems are still left unsolved: the disadvantages of some methods limit their application in engineering, and the effectiveness of some methods are still controversial. All theses together with the importance and relevance of this research area to the industry motivate us to undertake investigations on drag reduction and heat transfer enhancement methods. 41 1.4.1 Drag reduction On drag reduction aspect, there are many methods proposed (e.g. riblets, dimples, ’V’ protrusions, corrugated surface, wall-oscillation, counterrotating vortex and others). However, employing active methods needs additional power input to drive these active devices. Furthermore, sealing problem restricts the application of spanwise wall oscillation method in engineering. It behaves us to focus our attentions on passive devices to reduce drag, which is usually mechanically far simpler. Yet, despite the volume of work, it remains unclear whether the ’V’ protrusions and dimples can effectively reduce drag, whereas surface with riblets, though effective, is difficult to manufacture and maintain. Our initial attention is on the much less researched macro-scale passive drag reduction device, corrugated surface (longitudinal grooves), which can surprisingly reduce drag for laminar flow in spite of increase in wetted area (see Floryan, 2011). In addition, it satisfies several desirable characteristics of drag reduction devices: passive (no need for extra energy supply), macro-scale (easy to manufacture and maintain), and potential of high drag reduction (similar to or higher than riblets). However, the amplitude of grooves investigated in Floryan (see 2011) is very small thus the potential of drag reduction has not been tapped completely. Furthermore, according to the author’s best knowledge there is no study about its performance in turbulent channel flow. Thus the first objective of this study is to determine and ascertain the drag reduction capabilities of corrugated surface with large amplitude in 42 laminar and tubulent channel flow. Flow patterns, vortex structures, and turbulent kinetic energy will be investigated to reveal possible mechanisms of drag reduction. The results of investigation may reveal whether the corrugated surface can reduce drag in turbulent flow and demonstrate the possible mechanisms of the drag reduction. 1.4.2 Heat transfer 1.4.2.1 Asymmetric dimple On heat transfer over dimples, our interest is on a systematic study on the mechanics leading to enhancement of the thermal performance of an array of staggered (symmetric/spherical) dimple as opposed to only increasing its depth ratio often seen in the published literature. One may also note that existing study on modified dimples may encounter some complexity in manufacturing (Chyu et al., 1997; Doo et al., 2010) and/or the drawback of smaller coverage area of dimple surface (Isaev et al., 2000b,a, 2001, 2002, 2003, 2007; Isaev and Leontiev, 2010; Isaev et al., 2010b; Kornev et al., 2010; Turnow et al., 2011). Furthermore, most of these works (Isaev et al., 2000b,a, 2001, 2002, 2003, 2007; Isaev and Leontiev, 2010; Isaev et al., 2010b; Kornev et al., 2010; Turnow et al., 2011) are mainly restricted to the studies of flow over an isolated dimple where the mechanism of enhanced heat transfer due to the interaction of flows over adjacent dimples is absent. As such, the second objective of this study is to propose a novel asymmetric dimple, which can intensify secondary flow and vortex inside the 43 dimple while retaining a high coverage area of dimpled surface, to enhance the overall thermal-hydraulic performance. By skewing the deepest point of a circular dimple to generate asymmetric flow, the circular print diameter and hence the area coverage ratio remains unchanged. This obviates the area coverage ratio as an additional parameter to consider in the present study. It will focus on numerical investigation of the relation between the flow and heat transfer enhancement of a single wall with densely populated asymmetric dimples in channel flow. Asymmetric dimples with different depth ratio and skewing direction are investigated systematically to evaluate the effects of these factors. It shall be noted that higher coverage ratio of dimples has larger effect on heat transfer augmentation. To obtain heat transfer augmentation as high as enough, dimples and protrusions in this study are arranged densely to reach the highest coverage ratio. 1.4.2.2 Protrusion For heat transfer over protrusions, it has been shown that protrusions can lead to higher heat transfer and friction than dimples. However, there is also a lack of deep and systematic research on this topic. For example, it is difficult to distinguish respective influences of dimples and protrusions in the studies of Ligrani et al. (2001b); Mahmood et al. (2001); Elyyan et al. (2008). Furthermore, the effect of depth/height ratio (h/D) on heat transfer and flow structures has not been studied in Hwang et al. (2008). All these motivate us to undertake an in-depth study of flow and heat 44 transfer in a channel with protrusion on single wall. In summary, such stand-alone asymmetric dimple and protrusions may have better thermal-hydrodynamic performance than the more familiar symmetric dimples found in the published literature. 1.4.3 Scope of present work In this study, the drag reduction capabilities of corrugated surface and dimples in turbulent channel flow are examined by using Direct Numerical Simulation (DNS) and Detach Eddy Simulation (DES) methods based on Reynolds number (Re 2H , see the definition Eq. 2.27) ranging from 4,000 to 6,000. Overall, this work on flow manipulation to reduce drag and enhance thermal efficiency is organized as follows. Chapter will introduce the analytical and numerical methods used in this study, including perturbation method, Direct Numerical Simulation (DNS) and Detach Eddy Simulation (DES) methods. Chapter will examine the drag reduction capabilities of corrugated surface. Chapter will present the thermal performance of asymmetric dimples, while Chapter will present the thermal performance of protrusions. Finally, conclusions and recommendations are presented in Chapter 6. 45 [...]... ratio being low and high, respectively This can be attributed to the symmetric and asymmetric flow pattern and vortex structures for low and high protrusions, respectively xii 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 ... 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 10 2 3.4 Comparison of drag coefficient difference ΔD computed by DES and DNS 10 2 3.5 Ratio of each term of drag coefficient to the total drag coefficient on flat plate 12 6 3.6 Ratio of each term of drag coefficient on corrugated surface... Case 3 at h/D = 15 % The meanings of ‘C’, ‘S’ and * are the same as in Table 4 .1 14 9 xiv 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... stand for ξ and dashed lines stand for η 12 5 3.28 The drag difference ΔD at different Reτ and S when α → 0 13 0 3.29 Effects of phase shift ϕ on drag coefficient difference ΔD 13 2 3.30 Streamwise velocity u on Z-Y plane for different phase shift (a) ϕ = 0, (b) ϕ = π/2 and (c) ϕ = π 13 5 3. 31 Shear drag stress on Z-Y plane for different phase shift ϕ at α = 0.5 and. .. 18 1 5 .1 Channel with protrusions 18 7 5.2 Sectional drawing of a single protrusion 18 8 5.3 Effect of h/D on Nusselt number, friction coefficient and performance factors: h/D stands for height ratio for protrusion, while it stands for depth ratio for dimple 19 1 5.4 Normalized friction Sm/Sm0 at different height ratios h/D 19 3 5.5 Normalized friction... for Case 3 at h/D = 15 % 15 7 4 .11 Depth ratio effects on asymmetric dimple’s performance 15 9 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) 16 1 4 .13 Flow patterns for Case 3 (h/D = 0 .15 ), the fluid flows from left to right 16 3 4 .14 Mean streamlines patterns... dimple for different configurations 14 9 xviii 4.6 Depth ratio effects for symmetric dimple 15 2 4.7 Comparison with experimental results in Burgess and Ligrani (2005) 15 3 4.8 Friction and Nusselt number ratios for Case 2 at h/D = 10 % 15 4 4.9 Area and volume goodness factor ratios 15 5 4 .10 Friction and Nusselt number ratios for Case 3 at h/D = 15 % 15 7... 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... effects of S 10 3 3 .14 Normalized wetted area difference ΔAw and total drag difference ΔD at different S and α 10 4 3 .15 Normalized drag difference per unit wetted area at different S and α 10 5 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 10 7... 12 7 xiii 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 14 8 4.2 Different configurations of dimples for . x List of Tables xiii List of Figures xv Nomenclature xxii Chapter 1 Introduction 1 1 .1 Reviewofdragreductionmethods 1 1 .1. 1 Passive methods 2 1. 1.2 Active methods 15 1. 1.3 Summary of different drag. Configurationofprotrusions 18 6 5.2 ResultsandDiscussion 18 9 5.2 .1 Hydrodynamicandthermalperformance 18 9 5.2.2 Distribution of local drag and heat transfer rate . . . 19 1 5.2.3 Flowstructure 200 5.2.4 Turbulent. depth 15 8 vi 4.4 Onmeancharacteristics 15 8 4.4 .1 Meanflowfieldpatterns 16 0 4.4.2 Mean characteristics of drag and heat transfer . . . . 16 6 4.5 Instantaneouscharacteristicsofflow 17 3 4.5 .1 Flow eld 17 5 4.5.2