Fluid Dynamics with a Computational Perspective

✍ Scribed by Paul A. Durbin, Gorazd Medic

• Publisher: Cambridge University Press
• Year: 2007
• Tongue: English
• Leaves: 363
• Edition: 1
• Category: Library

✦ Synopsis

In recent decades, numerical algorithms and computer power have advanced to the point where computer simulations of the equations fluid flow have become routine. How does that affect the way we teach fluid dynamics? This book seizes on that question. One of its objectives is to integrate computer solutions into fluid dynamics education; another is to review important concepts of fluid dynamics that a computationalist needs in order to understand computed flows. This book provides a development of fluid flow theory in concert with a perspective on how computations are formulated and effected.

✦ Table of Contents

Cover
Half-title
Title
Copyright
Dedication
Contents
Preface
1 Introduction to Viscous Flow
1.1 Why Study Fluid Dynamics?
1.2 Viscosity
1.3 Navier–Stokes Equations
1.4 Reynolds Number
1.5 Parallel Flow Approximation
1.5.1 Couette–Poiseuille Flow
1.5.2 Oscillatory Boundary Layer
1.6 Some Basics
1.6.1 One-Dimensional Conservation Laws
1.6.2 Bernoulli's Equation
1.6.3 Unsteady Flow
1.7 Swirl
1.7.1 Computation of Swirling Flow in an Expansion
1.8 Vorticity and Its Dynamics
1.8.1 Vortex Kinematics and Dynamics
1.8.2 Stretching and Rotation
1.8.3 Origin of Vorticity
1.8.4 Circulation and Lift
1.8.5 Diffusion of Vorticity
1.8.6 Visualization of Vortices
1.9 Turbulence
2 Elements of Computational Analysis
2.1 Geometry and Grid Generation
2.1.1 Computational Domain
2.1.2 Discrete Representation of the Geometry
2.1.3 Structured Grids
2.1.4 Unstructured Meshes
2.1.5 Mesh Quality
2.2 Computation of Fluid Flow
2.2.1 Discrete Equations
2.2.2 Centered and Upwind Differencing
2.2.3 Solvers
2.2.4 Boundary Conditions
2.3 Solution (In-)Accuracy
2.3.1 Residuals and Convergence
2.3.2 Grid Independence
2.4 Postprocessing and Visualization
2.4.1 Streamlines
2.4.2 Vectors and Contours
2.4.3 Quantitative Data
2.5 Packages and Codes
3 Creeping Flow
3.1 The Low Reynolds Number Limit
3.1.1 Stokes Flow around a Sphere
3.1.2 Resistance Matrix
3.1.3 Resistance Due to Relative Motion
3.1.4 Computation of Resistance Coefficients
3.1.5 Eddies in Stokes Flow
3.2 Hydrodynamic Lubrication
4 Intermediate Reynolds Numbers
4.1 Separation, Vorticity, and Vortex Shedding
4.1.1 Five Examples
4.1.2 Secondary Circulation
4.2 Wakes, Jets, and Mixing Layers
4.2.1 Scaling Shear Layer Evolution
4.2.2 Entrainment
4.2.3 Free and Impinging Round Jets
5 High Reynolds Number Flow and Boundary Layers
5.1 Formal Definition of the Boundary Layer
5.1.1 Growth of the Boundary Layer
5.1.2 Pressure Gradients and Separation
5.1.3 Gridding
5.2 Approximate Equations
5.3 Three-Dimensional Boundary Layers
5.4 Separation in Three Dimensions and Critical Points
5.5 High Reynolds Number Flow over a Spheroid
5.6 Potential Flow
5.6.1 Point Sources
5.6.2 Images
5.6.3 Point Vortices and Circulation
5.6.4 Stream Function
5.6.5 Added Mass
6 Turbulent Flow
6.1 Computational Approaches
6.2 Statistically Averaged Method
6.2.1 Eddy Viscosity Model
6.2.2 Computed Example
6.2.3 Limitations of Scalar Eddy Viscosity Models
6.3 Turbulent Shear Flows
6.3.1 Boundary Layers
6.3.2 Wall Functions
6.3.3 Free Shear Layers
6.3.4 Computed Axisymmetric Jets
6.4 Eddy Simulation
6.4.1 Spectrum of Turbulence
6.4.2 Direct Numerical Simulation
6.4.3 DNS of Isotropic Turbulence
6.4.4 Approximate Simulation of Large Eddies
6.5 Instability Theory
6.5.1 Inflection Point Theorem
6.5.2 Instability in Boundary Layers
7 Compressible Flow
7.1 Thermodynamics
7.1.1 First Law
7.1.2 Equation of State
7.1.3 Entropy and Irreversibility
7.1.4 First Law with Flow
7.1.5 Isentropic Relations
7.2 Mach Waves
7.2.1 Speed of Sound
7.2.2 Occurrence of Shock Waves
7.3 One-Dimensional Gas Dynamics
7.3.1 Normal Shock
7.3.2 Supersonic Flow over a Hemisphere
7.3.3 Expansion Fan
7.3.4 Supersonic Flow over a Wedge
7.4 Quasi-One-Dimensional Gas Dynamics
7.4.1 Shock Patterns and Shock-Induced Separation
7.5 Computation of Compressible Flows
8 Interfaces
8.1 Interface Conditions
8.2 Surface Tension
8.2.1 Capillarity and Contact Angle
8.2.2 Disintegration by Capillarity
8.2.3 Simulation of Capillary Breakup
8.3 Inviscid Free Surface
8.3.1 Group Velocity and Its Connection to Surface Excrescence
8.3.2 Sloshing
8.3.3 Numerical Simulation of Sloshing
8.4 Volume of Fluid Method
8.4.1 Pouring a Viscous Liquid
Bibliography
Index