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
Author(s): Amir A. Aliabadi
Series: Mechanical Engineering Series
Publisher: Springer
Year: 2022
Language: English
Pages: 295
City: Cham
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
