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 NavierStokes 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 NavierStokes Equation 31

3.2 Turbulent Kinetic Energy Equation 33

3.3 𝜖 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 𝜖 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 KármánHowarth 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 a...