Turbulent Fluid Flow

A guide to the essential information needed to model and compute turbulent flows and interpret experiments and numerical simulations

Turbulent Fluid Flow offers an authoritative resource to the theories and models encountered in the field of turbulent flow. In this book, the author - a noted expert on the subject - creates a complete picture of the essential information needed for engineers and scientists to carry out turbulent flow studies. This important guide puts the focus on the essential aspects of the subject - including modeling, simulation and the interpretation of experimental data - that fit into the basic needs of engineers that work with turbulent flows in technological design and innovation.

Turbulent Fluid Flow offers the basic information that underpins the most recent models and techniques that are currently used to solve turbulent flow challenges. The book provides careful explanations, many supporting figures and detailed mathematical calculations that enable the reader to derive a clear understanding of turbulent fluid flow. This vital resource:

• Offers a clear explanation to the models and techniques currently used to solve turbulent flow problems

• Provides an up-to-date account of recent experimental and numerical studies probing the physics of canonical turbulent flows

• Gives a self-contained treatment of the essential topics in the field of turbulence

• Puts the focus on the connection between the subject matter and the goals of fluids engineering

• Comes with a detailed syllabus and a solutions manual containing MATLAB codes, available on a password-protected companion website

Written for fluids engineers, physicists, applied mathematicians and graduate students in mechanical, aerospace and civil engineering, Turbulent Fluid Flow contains an authoritative resource to the information needed to interpret experiments and carry out turbulent flow studies.

Autorentext

PETER S. BERNARD is a Professor in the Department of Mechanical Engineering at the University of Maryland. He has been a Professor since 1994. He is a fellow of the APS and Associate Fellow of AIAA. Professor Bernard has an extensive background in the theory, physics and computation of turbulent flows.

Inhalt

Preface xiii About the Companion Website xv 1 Introduction 1 1.1 What is Turbulent Flow? 1 1.2 Examples of Turbulent Flow 2 1.3 The Goals of a Turbulent Flow Study 7 1.4 Overview of the Methodologies Available to Predict Turbulence 9 1.4.1 Direct Numerical Simulation 9 1.4.2 Experimental Methods 10 1.4.3 Turbulence Modeling 11 1.5 The Plan for this Book 12 References 13 2 Describing Turbulence 15 2.1 Navier-Stokes Equation and Reynolds Number 15 2.2 What Needs to be Measured and Computed 16 2.2.1 Averaging 17 2.2.2 One-Point Statistics 19 2.2.3 Two-Point Correlations 21 2.2.4 Spatial Spectra 25 2.2.5 Time Spectra 28 Reference 29 3 Overview of Turbulent Flow Physics and Equations 31 3.1 The Reynolds Averaged Navier-Stokes Equation 31 3.2 Turbulent Kinetic Energy Equation 33 3.3 epsilon Equation 37 3.4 Reynolds Stress Equation 39 3.5 Vorticity Equation 40 3.5.1 Vortex Stretching and Reorientation 42 3.6 Enstrophy Equation 43 References 44 4 Turbulence at Small Scales 47 4.1 Spectral Representation of epsilon 48 4.2 Consequences of Isotropy 50 4.3 The Smallest Scales 54 4.4 Inertial Subrange 58 4.4.1 Relations Between 1D and 3D Spectra 58 4.4.2 1D Spatial and Time Series Spectra 61 4.5 Structure Functions 65 4.6 Chapter Summary 67 References 67 5 Energy Decay in Isotropic Turbulence 71 5.1 Energy Decay 71 5.1.1 Turbulent Reynolds Number 75 5.2 Modes of Isotropic Decay 76 5.3 Self-Similarity 77 5.3.1 Fixed Point Analysis 79 5.3.2 Final Period of Isotropic Decay 80 5.3.3 High Reynolds Number Equilibrium 84 5.4 Implications for Turbulence Modeling 87 5.5 Equation for Two-Point Correlations 88 5.6 Self-Preservation and the Kármán-Howarth Equation 92 5.7 Energy Spectrum Equation 94 5.8 Energy Spectrum Equation via Fourier Analysis of the Velocity Field 96 5.8.1 Fourier Analysis on a Cubic Region 97 5.8.2 Limit of Infinite Space 99 5.8.3 Applications to TurbulenceTheory 101 5.9 Chapter Summary 102 References 103 6 Turbulent Transport and its Modeling 107 6.1 Molecular Momentum Transport 107 6.2 Modeling Turbulent Transport by Analogy to Molecular Transport 110 6.3 Lagrangian Analysis of Turbulent Transport 112 6.4 Transport Producing Motions 115 6.5 Gradient Transport 119 6.6 Homogeneous Shear Flow 122 6.7 Vorticity Transport 128 6.7.1 Vorticity Transport in Channel Flow 130 6.8 Chapter Summary 132 References 133 7 Channel and Pipe Flows 135 7.1 Channel Flow 135 7.1.1 Reynolds Stress and Force Balance 138 7.1.2 Mean Flow Similarity 141 7.1.3 Viscous Sublayer 142 7.1.4 Intermediate Layer 143 7.1.5 Velocity Moments 145 7.1.6 Turbulent Kinetic Energy and Dissipation Rate Budgets 148 7.1.7 Reynolds Stress Budget 150 7.1.8 Enstrophy and its Budget 154 7.2 Pipe Flow 156 7.2.1 Mean Velocity 158 7.2.2 Power Law 160 7.2.3 Streamwise Normal Reynolds Stress 162 References 163 8 Boundary Layers 167 8.1 General Properties 169 8.2 Boundary Layer Growth 171 8.3 Log-Law Behavior of the Velocity Mean and Variance 174 8.4 Outer Layer 175 8.5 The Structure of Bounded Turbulent Flows 177 8.5.1 Development of Vortical Structure in Transition 177 8.5.2 Structure in Transition and in Turbulence 180 8.5.3 Vortical Structures 181 8.5.4 Origin of Structures 186 8.5.5 Fully Turbulent Region 192 8.6 Near-Wall Pressure Field 197 8.7 Chapter Summary 197 References 199 9 Turbulence Modeling 203 9.1 Types of RANS Models 204 9.2 Eddy Viscosity Models 207 9.2.1 Mixing Length Theory and its Generalizations 208 9.2.2 K-epsilon Closure 211 9.2.2.1 K Equation 212 9.2.2.2 The epsilon Equation 212 9.2.2.3 Calibration of the K-epsilon Closure 214 9.2.2.4 Near-Wall K-epsilon Models 215 9.2.3 K-omega Models 218 9.2.4 Menter Shear Stress Transport Closure 219 9.2.5 Spalart-Allmaras Model 221 9.3 Tools forModel Development 222 9.3.1 Invariance Properties of the Reynolds Stress Tensor 222 9.3.2 Realizability 226 9.3.3 Rapid Distortion Theory 226 9.4 Non-Linear Eddy Viscosity Models 227 9.5 Reynolds Stress Equation Models 229 9.5.1 Modeling of the Pressure-Strain Correlation 230 9.5.2 LRR Model 232 9.5.3 SSG Model 234 9.5.4 Transport Correlation 238 9.5.5 Complete Second Moment Closure 239 9.5.6 Near-Wall Reynolds Stress Equation Models 240 9.6 Algebraic Reynolds Stress Models 242 9.7 Urans 243 9.8 Chapter Summary 244 References 245 10 Large Eddy Simulations 251 10.1 Mathematical Basis of LES 252 10.2 Numerical Considerations 257 10.3 Subgrid-Scale Models 258 10.3.1 Smagorinsky Model 261 10.3.2 Wale Model 263 10.3.3 Alternative Eddy Viscosity Subgrid-Scale Models 265 10.3.4 Dynamic Models 266 10.4 Hybrid LES/RANS Models 270 10.4.1 Detached Eddy Simulation 271 10.4.2 A Hybrid LES/RANS Form of the Menter SST Model 272 10.4.3 Flow Simulation Methodology 273 10.4.4 Example of a Zonal LES/RANS Formulation 274 10.4.5 Partially Averaged Navier-Stokes 276 10.4.6 Scale-Adaptive Simulation 277 10.5 Chapter Summary 278 References 278 11 Properties of Turbulent Free Shear Flows 283 11.1 Thin Flow Approximation 283 11.2 Turbulent Wake 285 11.2.1 Self-Preserving FarWake 286 11.2.2 Mean Velocity 290 11.3 Turbulent Jet 292 11.3.1 Self-Preserving Jet 292 11.3.2 Mean Velocity 293 11.3.3 Reynolds Stresses 295 11.4 Turbulent Mixing Layer 298 11.4.1 Structure of Mixing Layers 298 11.4.2 Self-Preserving Mixing Layer 300 11.4.3 Mean Velocity 302 11.4.4 Reynolds Stresses 303 11.5 Chapter Summary 304 References 306 12 Calculation of Ground Vehicle Flows 309 12.1 Ahmed Body 309 12.2 Realistic Automotive Shapes 317 12.3 Truck Flows 324 12.4 Chapter Summary 326 References 327 Author Index 329 Subject Index 335