Computational Fluid Dynamics with Moving Boundaries

by Shyy, Wei; Udaykumar, H. S.; Rao, Madhukar M.; Smith, Richard W.

• ISBN13: 9780486458908
• ISBN10: 0486458903
• Format: Paperback
• Copyright: 2007-02-27
• Publisher: Dover Publications

Summary

This advanced-level text describes several computational techniques that can be applied to a variety of problems in thermo-fluid physics, multi-phase flow, and applied mechanics involving moving flow boundaries. Step-by-step discussions of numerical procedures include numerous examples that employ algorithms to solve problems. 1990 edition.

Table of Contents

Preface	p. xv
Numerical Techniques for Fluid Flows with Moving Boundaries	p. 1
Introduction	p. 1
Motivation	p. 1
Overview of the Present Work	p. 3
Numerical Methods Applied to General Moving Boundary Problems	p. 6
Choice of Method-Lagrangian or Eulerian?	p. 8
Review of Available Methods for Moving Boundary Problems	p. 8
Transformation Methods with Body-Fitted Coordinates	p. 9
Boundary Element Methods (BEM)	p. 9
Volume Tracking Methods	p. 9
The Level-Set Method	p. 10
Moving Unstructured Boundary Conforming Grid Methods	p. 12
Phase Field Models	p. 14
Summary	p. 19
Governing Equations and Solution Procedure	p. 21
Formulation	p. 22
Governing Equations	p. 22
Governing Equations in a Body-Fitted Coordinate System	p. 23
Discretization of the Conservation Laws	p. 24
Pressure-Based Algorithm	p. 24
Consistent Estimation of the Metric Terms	p. 32
Illustrative Test Cases	p. 33
Rotated Channel Flow	p. 33
Uniform Flow Using a Moving Grid	p. 35
Formulation and Solution of Flows with Free Surfaces	p. 36
Introduction	p. 36
Prediction of Meniscus Shapes	p. 39
Methodology	p. 39
Effect of Convection on Meniscus Shape	p. 42
Sources of Convection	p. 43
Natural Convection	p. 43
Marangoni Convection	p. 43
Nondimensionalization and Scaling Procedure	p. 44
Heat Conduction Scales	p. 45
Natural Convection Scales	p. 45
The Marangoni Number	p. 45
Formulation and Computational Algorithm for Transport Processes	p. 46
Results and Discussion	p. 48
Prediction of Meniscus Shapes	p. 48
Heat Transfer Calculations	p. 51
Numerical Procedure	p. 52
Heat Conduction Only	p. 52
Natural Convection	p. 53
Interaction of Natural and Thermocapillary Convection	p. 54
Effect of Convection on Meniscus Shape	p. 57
Conclusions	p. 58
Moving Grid Techniques: Fluid Membrane Interaction	p. 61
Description of the Physical Problem	p. 61
Potential Flow-Based Membrane Wing Models	p. 63
Membrane Equilibrium	p. 65
Nondimensionalization of the Governing Equations	p. 67
The Moving Grid Computational Procedure	p. 70
A Potential Flow Model for Thin Wings	p. 72
Membrane Wings in Steady Flow	p. 74
Effect of Outer Boundary Location	p. 74
Classification of Flexible Membrane Wings	p. 76
Elastic Membrane Case	p. 76
Inextensible Membrane Case	p. 77
Membrane Wings in Unsteady Flow	p. 80
Constant Tension Membrane Case	p. 82
Elastic Membrane Case	p. 82
Inextensible Membrane Case	p. 86
Summary and Conclusion	p. 93
Moving Grid Techniques: Modeling Solidification Processes	p. 95
Introduction	p. 95
Morphological Instabilities During Solidification	p. 95
Physics of Morphological Instabilities in Solidification	p. 98
Implications of Morphological Instabilities	p. 103
Need for Numerical Techniques	p. 105
Requirements of the Numerical Method	p. 107
Application of the Boundary-Fitted Approach	p. 108
Formulation	p. 109
Assessment of the Quasi-stationary Approximation	p. 112
A General Procedure for Interface Tracking	p. 113
Results and Discussion	p. 115
Case 1. Calculations with Temperature Field Active in One Phase Only	p. 115
Case 2. Calculations with Temperature Field Active in Both Phases	p. 116
Motion of Curved Fronts	p. 117
Interfacial Conditions	p. 117
Scales for the Morphological Instability Simulations	p. 120
Features of the Computational Method	p. 122
Results and Discussion	p. 123
Issues of Scaling and Computational Efficiency	p. 128
Choice of Reference Scales and Resulting Equations	p. 129
Conclusions	p. 130
Fixed Grid Techniques: Enthalpy Formulation	p. 135
Governing Equations	p. 135
Scaling Issues	p. 136
The Macroscopic Scales	p. 139
Velocity Scales	p. 141
Thermal Scales	p. 143
Low Prandtl Number (Metallic Melts)	p. 143
High Prandtl Number (Organic Melts)	p. 144
The Morphological Scales	p. 146
Pure Conduction	p. 147
Morphological Scales in the Presence of Convection	p. 149
Low Prandtl Number Melts	p. 149
High Prandtl Number Melts	p. 150
Enthalpy Formulation	p. 151
Heat Conduction	p. 152
Implementation	p. 155
Implementation of the T-Based Method	p. 155
Implementation of the H-Based Method	p. 156
Results and Discussion	p. 156
Accuracy Assessment	p. 156
Performance Assessment	p. 158
Summary	p. 163
Convective Effects	p. 163
Governing Equations	p. 163
Source Terms in the Momentum Equations	p. 164
Sources of Convection	p. 165
Computational Procedure	p. 166
Bridgman Growth of CdTe	p. 166
Multi-Zone Simulation of Bridgman Growth Process	p. 171
Governing Equations	p. 173
Two-Level Modeling Strategy	p. 177
The Global Furnace Simulation	p. 177
The Refined Ampoule Simulation	p. 178
Float Zone Growth of NiAl	p. 184
Calculation Procedure	p. 185
Results and Discussion	p. 187
Heat Conduction	p. 187
Thermocapillary Convection	p. 188
Summary	p. 192
Fixed Grid Techniques: ELAFINT-Eulerian-Lagrangian Algorithm For INterface Tracking	p. 195
Introduction	p. 195
Interface Tracking Procedure	p. 197
Basic Methodology	p. 198
Procedures for Mergers/Breakups	p. 202
Solution of the Field Equations	p. 211
Control Volume Formulation with Moving Interface with Moving Interface	p. 211
The Control Volume Formulation for a Transport Variable	p. 213
Discretization	p. 213
Treatment of Variables on the Staggered Grid	p. 216
Computation of Convective Fluxes	p. 216
Evaluation of the Diffusion and the Full Discretized Form	p. 217
Evaluation of the Source Term	p. 220
Computation of Interfacial Fluxes	p. 221
Computation of the Pressure Field	p. 227
Computing the Velocities of the Interfacial Markers	p. 228
Dealing with Cut Cells	p. 228
Conservation and Consistency at Cell Faces	p. 229
Anomalous Cases	p. 229
Distinction Between Liquid and Solid Cells	p. 231
Moving Boundary Problems-Treatment of Cells That Change Phase	p. 232
Results for Pure Conduction	p. 232
Grid Addition/Deletion	p. 233
Planar Interface Propagation	p. 234
Non-planar Interfaces	p. 235
Zero Surface Tension	p. 236
Low Surface Tension	p. 238
Stable Fingers for Significant Surface Tension	p. 241
Summary	p. 244
Assessment of Fixed Grid Techniques	p. 249
Introduction	p. 249
Results for Stationary Boundaries	p. 249
Melting from a Vertical Wall	p. 250
Summary	p. 259
Concluding Remarks	p. 260
References	p. 261
Index	p. 281
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