Turbulent Fluid Flow

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.

• Preface xiiiAbout the Companion Website xv1 Introduction 11.1 What is Turbulent Flow? 11.2 Examples of Turbulent Flow 21.3 The Goals of a Turbulent Flow Study 71.4 Overview of the Methodologies Available to Predict Turbulence 91.4.1 Direct Numerical Simulation 91.4.2 Experimental Methods 101.4.3 Turbulence Modeling 111.5 The Plan for this Book 12References 132 Describing Turbulence 152.1 Navier–Stokes Equation and Reynolds Number 152.2 What Needs to be Measured and Computed 162.2.1 Averaging 172.2.2 One-Point Statistics 192.2.3 Two-Point Correlations 212.2.4 Spatial Spectra 252.2.5 Time Spectra 28Reference 293 Overview of Turbulent Flow Physics and Equations 313.1 The Reynolds Averaged Navier–Stokes Equation 313.2 Turbulent Kinetic Energy Equation 333.3 𝜖 Equation 373.4 Reynolds Stress Equation 393.5 Vorticity Equation 403.5.1 Vortex Stretching and Reorientation 423.6 Enstrophy Equation 43References 444 Turbulence at Small Scales 474.1 Spectral Representation of 𝜖 484.2 Consequences of Isotropy 504.3 The Smallest Scales 544.4 Inertial Subrange 584.4.1 Relations Between 1D and 3D Spectra 584.4.2 1D Spatial and Time Series Spectra 614.5 Structure Functions 654.6 Chapter Summary 67References 675 Energy Decay in Isotropic Turbulence 715.1 Energy Decay 715.1.1 Turbulent Reynolds Number 755.2 Modes of Isotropic Decay 765.3 Self-Similarity 775.3.1 Fixed Point Analysis 795.3.2 Final Period of Isotropic Decay 805.3.3 High Reynolds Number Equilibrium 845.4 Implications for Turbulence Modeling 875.5 Equation for Two-Point Correlations 885.6 Self-Preservation and the Kármán–Howarth Equation 925.7 Energy Spectrum Equation 945.8 Energy Spectrum Equation via Fourier Analysis of the Velocity Field 965.8.1 Fourier Analysis on a Cubic Region 975.8.2 Limit of Infinite Space 995.8.3 Applications to TurbulenceTheory 1015.9 Chapter Summary 102References 1036 Turbulent Transport and its Modeling 1076.1 Molecular Momentum Transport 1076.2 Modeling Turbulent Transport by Analogy to Molecular Transport 1106.3 Lagrangian Analysis of Turbulent Transport 1126.4 Transport Producing Motions 1156.5 Gradient Transport 1196.6 Homogeneous Shear Flow 1226.7 Vorticity Transport 1286.7.1 Vorticity Transport in Channel Flow 1306.8 Chapter Summary 132References 1337 Channel and Pipe Flows 1357.1 Channel Flow 1357.1.1 Reynolds Stress and Force Balance 1387.1.2 Mean Flow Similarity 1417.1.3 Viscous Sublayer 1427.1.4 Intermediate Layer 1437.1.5 Velocity Moments 1457.1.6 Turbulent Kinetic Energy and Dissipation Rate Budgets 1487.1.7 Reynolds Stress Budget 1507.1.8 Enstrophy and its Budget 1547.2 Pipe Flow 1567.2.1 Mean Velocity 1587.2.2 Power Law 1607.2.3 Streamwise Normal Reynolds Stress 162References 1638 Boundary Layers 1678.1 General Properties 1698.2 Boundary Layer Growth 1718.3 Log-Law Behavior of the Velocity Mean and Variance 1748.4 Outer Layer 1758.5 The Structure of Bounded Turbulent Flows 1778.5.1 Development of Vortical Structure in Transition 1778.5.2 Structure in Transition and in Turbulence 1808.5.3 Vortical Structures 1818.5.4 Origin of Structures 1868.5.5 Fully Turbulent Region 1928.6 Near-Wall Pressure Field 1978.7 Chapter Summary 197References 1999 Turbulence Modeling 2039.1 Types of RANS Models 2049.2 Eddy Viscosity Models 2079.2.1 Mixing Length Theory and its Generalizations 2089.2.2 K–𝜖 Closure 2119.2.2.1 K Equation 2129.2.2.2 The 𝜖 Equation 2129.2.2.3 Calibration of the K–𝜖 Closure 2149.2.2.4 Near-Wall K–𝜖 Models 2159.2.3 K–𝜔 Models 2189.2.4 Menter Shear Stress Transport Closure 2199.2.5 Spalart–Allmaras Model 2219.3 Tools forModel Development 2229.3.1 Invariance Properties of the Reynolds Stress Tensor 2229.3.2 Realizability 2269.3.3 Rapid Distortion Theory 2269.4 Non-Linear Eddy Viscosity Models 2279.5 Reynolds Stress Equation Models 2299.5.1 Modeling of the Pressure-Strain Correlation 2309.5.2 LRR Model 2329.5.3 SSG Model 2349.5.4 Transport Correlation 2389.5.5 Complete Second Moment Closure 2399.5.6 Near-Wall Reynolds Stress Equation Models 2409.6 Algebraic Reynolds Stress Models 2429.7 Urans 2439.8 Chapter Summary 244References 24510 Large Eddy Simulations 25110.1 Mathematical Basis of LES 25210.2 Numerical Considerations 25710.3 Subgrid-Scale Models 25810.3.1 Smagorinsky Model 26110.3.2 Wale Model 26310.3.3 Alternative Eddy Viscosity Subgrid-Scale Models 26510.3.4 Dynamic Models 26610.4 Hybrid LES/RANS Models 27010.4.1 Detached Eddy Simulation 27110.4.2 A Hybrid LES/RANS Form of the Menter SST Model 27210.4.3 Flow Simulation Methodology 27310.4.4 Example of a Zonal LES/RANS Formulation 27410.4.5 Partially Averaged Navier–Stokes 27610.4.6 Scale-Adaptive Simulation 27710.5 Chapter Summary 278References 27811 Properties of Turbulent Free Shear Flows 28311.1 Thin Flow Approximation 28311.2 Turbulent Wake 28511.2.1 Self-Preserving FarWake 28611.2.2 Mean Velocity 29011.3 Turbulent Jet 29211.3.1 Self-Preserving Jet 29211.3.2 Mean Velocity 29311.3.3 Reynolds Stresses 29511.4 Turbulent Mixing Layer 29811.4.1 Structure of Mixing Layers 29811.4.2 Self-Preserving Mixing Layer 30011.4.3 Mean Velocity 30211.4.4 Reynolds Stresses 30311.5 Chapter Summary 304References 30612 Calculation of Ground Vehicle Flows 30912.1 Ahmed Body 30912.2 Realistic Automotive Shapes 31712.3 Truck Flows 32412.4 Chapter Summary 326References 327Author Index 329Subject Index 335