Computation of Viscous Incompressible Flows (eBook)

Foreword 8
Acknowledgements 10
Contents 11
1 Introduction 15
1.1 Flow Physics 15
1.2 History of Computational Approaches 16
1.3 Scope of this Monograph 18
2 Methods for Solving Viscous Incompressible Flow Problems 20
2.1 Overview 20
2.2 Mathematical Models 21
2.3 Formulation for General Geometry 22
2.4 Overview of Solution Approaches 25
2.4.1 Pressure-Based Method 26
2.4.1.1 MAC Method 26
2.4.1.2 Pressure Field Solution for MAC-Type Method 28
2.4.1.3 Simplified Pressure Iteration (SIMPLE-Type) Method 31
2.4.2 Artificial Compressibility Method 33
2.4.3 Methods Based on Derived Variables 34
2.4.3.1 Stream Function-Vorticity 35
2.4.3.2 Vorticity-Velocity Method 35
3 Pressure Projection Method in Generalized Coordinates 37
3.1 Overview 37
3.2 Formulation in Integral Form 38
3.3 Discretization 39
3.3.1 Geometric Quantities 39
3.3.2 Mass Conservation Equation 42
3.3.3 Momentum Conservation Equation 43
3.4 Solution Procedure 46
3.4.1 Fractional-Step Procedure 46
3.4.2 Solution of Momentum Equations Using an Upwind Scheme 47
3.4.3 Pressure Poisson Solver 49
3.5 Validation of the Solution Procedure 50
4 Artificial Compressibility Method 53
4.1 Artificial Compressibility Formulation and Physical Characteristics 53
4.1.1 Characteristics of Pseudo Waves 55
4.1.2 Wave-Vorticity Interaction 56
4.1.3 Rate of Convergence 58
4.1.4 Limit of Incompressibility 59
4.2 Steady-State Formulation 60
4.3 Steady-State Algorithm 61
4.3.1 Difference Equations 61
4.3.2 Approximate Factorization Scheme 63
4.3.2.1 Diagonal Algorithm 65
4.3.3 LU-SGS Scheme 66
4.3.4 Line Relaxation Scheme 67
4.3.5 Numerical Dissipation or Smoothing 68
4.3.6 Boundary Conditions 71
4.3.6.1 Solid Surface 71
4.3.6.2 Inflow, Outflow and Far-Field Conditions 72
4.4 Time-Accurate Procedure 73
4.5 Time-Accurate Algorithm Using Upwind Differencing 75
4.5.1 Upwind Differencing Scheme 75
4.5.2 Implicit Scheme 78
4.5.3 Boundary Conditions for Upwind Scheme 79
4.6 Validation of Solution Procedure 81
4.6.1 Two-Dimensional (2-D) Channel Flow 81
4.6.2 Flow over a Backward-Facing Step 83
4.7 Unified Formulation 85
4.7.1 Time-Derivative Preconditioning Method 86
4.7.2 Numerical Results 87
4.7.2.1 Liquid Flow over a NACA 0015 Hydrofoil 87
5 Flow Solvers and Validation 90
5.1 Scope of Validation 91
5.1.1 Artificial Compressibility Codes 91
5.1.1.1 INS3D 91
5.1.1.2 INS3D-UP 91
5.1.2 Pressure Projection Code 92
5.1.2.1 INS3D-FS 92
5.2 Selection of Codes for Engineering Applications 92
5.3 Steady Internal Flow: Curved Duct with Square Cross Section 93
5.4 Time-Dependent Flow 99
5.4.1 Flow Over a Circular Cylinder 100
5.4.2 Impulsively Started Flat Plate at 90. 103
5.4.3 Pulsatile Flow Through A Constricted 2-D Channel 106
5.4.3.1 Oscillating Wall 106
5.4.3.2 Oscillating Inflow 109
5.4.4 Flapping Foil in a Duct 112
5.4.4.1 Experimental and Computational Models 114
5.4.4.2 Computed Results 117
5.5 External and Juncture Flow 127
5.5.1 Cylinder on a Flat Plate 127
5.5.2 Wing-Body Junction 129
5.5.2.1 Wing-Body Juncture Flow 130
5.5.3 Wingtip Vortex Flow 131
5.5.3.1 Experimental-Computational Validation Approach 132
5.5.3.2 Geometry 134
5.5.3.3 Grid 135
5.5.3.4 Turbulence Modeling 136
5.5.3.5 Near Wake Computation Using the Artificial Compressibility Method 137
5.5.3.6 Near Wake Computation Using the Pressure Projection Method 138
5.5.3.7 Initial Rollup of Round Wingtip Vortex 140
6 Simulation of a Liquid-Propellant Rocket Engine Subsystem 150
6.1 Historical Background 151
6.2 Flow Analysis in the Space Shuttle Main Engine (SSME) 152
6.3 Flow Analysis Task and Computational Model for the SSME Powerhead 153
6.3.1 Computational Model Description 154
6.3.2 Multiple-Zone Computation 157
6.3.3 Grid and Geometry Effects 159
6.4 Turbulence Modeling Issues 161
6.4.1 Selection of Turbulence Model for Internal Flow 162
6.4.1.1 An Extended Prandtl-Karman Mixing Length Model for Internal Flow 163
6.4.1.2 Application to Pipe and Channel Flow 165
6.4.2 Turbulence Modeling Issues Involving Strong Streamwise Curvature 167
6.4.2.1 Two-Dimensional U-Duct Study 168
6.4.2.2 Axisymmetric U-Duct 174
6.5 Analysis of the Original Three-Circular-Duct HGM Configuration 179
6.6 Development of New Two Elliptic-Duct HGM Configuration 184
6.6.1 From Redesign to Flight 190
7 Turbopumps 191
7.1 Historical Background 191
7.2 Turbopumps in Liquid-Propellant Rocket Engines 192
7.3 Mathematical Formulation for a Steady Rotating Frame of Reference 194
7.4 Validation of Simulation Procedures Using a Steadily Rotating Inducer 196
7.5 Application to Impeller Simulation 201
7.5.1 SSME Impeller 201
7.5.2 Advanced Impeller 203
7.6 Simulation of a Complete Pump Geometry 205
7.6.1 Geometry and Computational Grid 205
7.6.2 Issues Related to Large-Scale Computations 207
7.6.3 Issues Related to Flange-to-Flange Simulation 210
7.7 High-Fidelity Unsteady Flow Application to SSME Flowliners 211
7.7.1 Description of the Flow Simulation Task 212
7.7.2 Computational Model and Grid System 213
7.7.3 Computed Results 216
7.8 Some Aspects of a Parallel Implementation 221
8 Hemodynamics 225
8.1 Issues in Computational Hemodynamics for Humans 226
8.1.1 Geometry of the Human Vascular System 227
8.1.2 Modeling Non-Newtonian or Stress-Supporting Flow 228
8.1.3 Turbulence Model 228
8.1.4 Geometry and Morphology 228
8.1.5 Arterial Wall Model 228
8.1.6 Boundary Conditions 229
8.1.7 Cardiovascular Model 230
8.1.8 Brain Model 230
8.2 Model Equations for Blood Flow Simulation 231
8.2.1 Blood Flow Model 232
8.2.2 Deformable Wall Model 233
8.2.3 Vascular Bed Model 234
8.2.4 Arteriolar Auto-Regulation Model 236
8.3 Validation of the Simulation Procedure 237
8.3.1 Carotid Bifurcation 237
8.3.2 Circular Tube with 90 Bend 239
8.3.3 Effect of Arterial Wall Distensibility 239
8.3.4 Effects of Altered Gravity on Blood Circulation 243
8.4 Blood Circulation in the Human Brain 244
8.4.1 Collateral Circulation Under Auto-Regulation 245
8.4.2 Extraction of Geometry Data from Anatomical Picture 247
8.4.3 Effects of Gravitational Variations 249
8.5 Simulations of Blood Flow in Mechanical Devices 251
8.5.1 Artificial Heart Valves 251
8.5.2 Ventricular Assist Devices 255
8.5.2.1 Pulsatile Devices 256
8.5.2.2 Axial Flow Pump 261
Closing Remarks 270
Future Possibilities and Challenges 271
Solution Procedures 271
Prediction of Physics 271
Computational Hemodynamics 272
Human Resources and CFD Validation 272
For Further Reading 273
References 274
Index 288