Turbulence: A Fundamental Approach for Scientists and Engineers

Description

This textbook explains turbulent flows using an introductory but fundamental approach to teaching the core principles, striking a balance between theoretical and practical aspects of the topic without overwhelming the reader with mathematical detail. It is aimed at students in various engineering disciplines―mechanical, civil, environmental―and the geosciences. It is divided in five parts. Part 1 provides the fundamentals of turbulence, main hypotheses, and analysis tools; Part 2 illustrates various measurement techniques used to study turbulent flows; Part 3 explains the modelling and simulation frameworks to study turbulent flows; Part 4 describes brief applications of turbulence in engineering and sciences; and Part 5 presents basic statistical, mathematical, and numerical tools.  Elucidates the theory behind turbulence in a concise yet rigorous manner Combines theoretical, computational, experimental, and applied aspects of the topic Reinforces concepts with practice problems at the end of each chapter Provides brief chapters on statistics, mathematics, and numerical techniques   Preface Acknowledgments Contents Part I Fundamentals 1 Introduction 1.1 Overview References 2 Equations of Fluid Motion 2.1 The Continuity Equation 2.2 The Momentum Equation 2.3 Conserved Passive Scalars 2.4 The Vorticity Equation 2.5 Fluid Element Deformation 2.6 Similitude and Non-Dimensional Transport Equations References 3 Statistical Description of Turbulent Flows 3.1 Preliminaries 3.2 Mean and Moments 3.3 Standardization 3.4 Joint Random Variables 3.5 Normal and Joint-Normal Distributions 3.6 Random Processes 3.7 Random Fields 3.8 Statistically Stationary, Homogeneous, and Axisymmetric Turbulent Flows 3.9 Isotropic and Anisotropic Turbulence 3.10 Two-Point Correlation 3.11 Wavenumber Spectra 3.12 Types of Averaging References 4 Mean Flow Equations 4.1 Overview 4.2 Tensor Properties 4.3 Anisotropy 4.4 Mean Scalar Equation 4.5 Gradient-Diffusion and Turbulent-Viscosity Hypotheses References 5 Wall Flows 5.1 Overview 5.2 Transport Equations and the Balance of Mean Forces 5.3 The Shear Stress Near Wall 5.4 Viscous, Buffer, and Log-Law Sublayers 5.5 Law of the Wall for Temperature References 6 Free Shear Flows 6.1 Overview 6.2 Round Jet 6.3 Axial Velocity 6.4 Self-similarity 6.5 Axial Variation of Scales 6.6 Self-similarity of a Round Jet 6.7 Reynolds Stresses 6.8 Mean Continuity and Momentum Equations for a Jet References 7 Compressible Flows 7.1 Overview 7.2 Continuity Equation for Compressible Flows 7.3 Energy Equation for Compressible Flows 7.4 Momentum Equation for Compressible Flows 7.5 Similitude and Non-dimensional Transport Equations for Compressible Flows 7.6 Boundary Layer Equations for Compressible Flows 7.7 Mach Number References 8 Scales of Turbulent Motion 8.1 Preliminaries 8.2 The Energy Cascade and Kolmogorov Hypotheses 8.3 The Energy Spectrum 8.4 Two-Point Correlation 8.5 Structure Functions 8.6 Taylor Hypothesis References 9 Time and Frequency Domains 9.1 Overview 9.2 Discrete Fourier Transform 9.3 Nyquist Frequency 9.4 Discrete Energy Spectrum 9.5 Discrete Energy Density Spectrum 9.6 Spectra of Two Variables References Part II Measurement Techniques 10 Fundamentals of Measurements 10.1 Overview 10.2 Significant Digits 10.3 Calibration 10.4 Uncertainty 10.5 Statistical Analysis of Random Uncertainties 10.6 Normal and Student's t Distributions 10.7 Rejection of Data 10.8 Least-Squares Fitting 10.9 Chi-Squared Test for a Distribution 10.10 Two Sample Statistical Estimation 10.11 Reporting Uncertainties 10.12 Propagation of Uncertainties References 11 In Situ Techniques 11.1 Overview 11.2 U-Tube Manometer 11.3 Strain Gauge Pressure Transducers 11.4 Electrical Resistance Thermometry 11.5 Thermoelectric Temperature Measurement 11.6 Hot Wire Anemometry (HWA) 11.7 Pitot Tube 11.8 Rotameters 11.9 Balloons References 12 Sonic and Ultrasonic Techniques 12.1 Preliminaries 12.2 Sonic and Ultrasonic Anemometers 12.3 SOnic Detection And Ranging (SODAR) References 13 Electro-magnetic Techniques 13.1 Overview 13.2 Shadowgraphy 13.3 Particle Tracking Velocimetry (PTV) 13.4 Particle Image Velocimetry (PIV) 13.5 Schlieren Imaging 13.6 Laser Doppler Velocimetry (LDV) 13.7 Radiometry and Pyrometry 13.8 Light Detection And Ranging (LiDAR) References Part III Turbulence Modelling and Simulation 14 Introduction to Modelling and Simulation 14.1 Preliminaries 14.2 Summary of Approaches 14.3 Model or Simulation Completeness 14.4 Turbulence Model or Simulation Closure Problem 14.5 Digital Computation References 15 Turbulent-Viscosity Models 15.1 Preliminaries 15.2 Algebraic Models 15.3 Spalart–Allmaras Model 15.4 Turbulence Kinetic Energy Models 15.5 The k-ε Model 15.6 The k-ω Model 15.7 Turbulent-Viscosity Models for the Atmospheric Boundary Layer References 16 Large-Eddy Simulation Models 16.1 Preliminaries 16.2 Filtering 16.3 Filtered Conservation Equations 16.4 The Smagorinsky Model 16.5 One-equation Turbulence Kinetic Energy Model 16.6 The Problem of Inlet Condition 16.7 A Synthetic Inlet Turbulence Generator for Atmospheric Boundary Layers References 17 Direct Numerical Simulation 17.1 Overview References 18 Wall Models 18.1 Preliminaries 18.2 Point-Wise Standard Wall Function 18.3 Integrated Werner–Wengle Wall Function 18.4 van Driest Near-Wall Treatment 18.5 Wall Models for the Atmospheric Boundary Layer 18.6 Wall Function Summary References 19 Model Evaluation 19.1 Overview 19.2 Verification and Validation 19.3 Time and Space Discretization Error Estimation 19.4 Order of Convergence 19.5 Grid Independence Test (GIT) 19.6 Grid Convergence Index (GCI) 19.7 Reference and Model Error Quantification References Part IV Applications 20 Engineering 20.1 Overview 20.2 Liquid–Liquid Extraction Industries 20.3 Coalescer 20.4 Waste Water Treatment 20.5 Desalination 20.6 Combustion Devices 20.7 Indoor Ventilation 20.8 Aeronautics 20.9 Renewable Energy 20.10 River Engineering References 21 Sciences 21.1 Overview 21.2 Meteorology 21.3 Oceanography 21.4 Space References Part V Fundamental Analysis Tools and Principles 22 Statistics 22.1 Random Variables 22.2 Event 22.3 Probability 22.4 Cumulative Distribution Function 22.5 Probability Density Function 22.6 Mean and Moments 22.7 Probability Distributions References 23 Mathematics 23.1 Einstein's Notation 23.2 Kronecker Delta 23.3 Alternating Symbol 23.4 Position Vector 23.5 Divergence 23.6 Gradient 23.7 Curl 23.8 Laplacian 23.9 Dot Product of Two Vectors 23.10 Cross Product of Two Vectors 23.11 Material or Substantial Derivative 23.12 Tensors References 24 Numerical Methods 24.1 Taylor Series Expansion 24.2 The Finite Difference Method 24.3 Newton's Method for Solving Non-linear Systemof Equations 24.4 Explicit and Implicit Euler Methods 24.5 Under Relaxation References Index