Computational fluid dynamics with moving boundaries

Title:

Publication Information:

Philadelphia, PA : Taylor & Francis , 1996

ISBN:

9781560324584

Subject Term:

Fluid dynamics -- Technique

Computer algorithms

Numerical grid generation (Numerical analysis)

Added Author:

Wei Shyy...[et al]

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ KL	30000005171834	QC151 C66 1996	Open Access Book	Book	Searching... Unknown

Presents developments in computational techniques pertaining to moving boundary problems in fluid dynamics. It describes several computational techniques which can be applied to a variety of problems in thermo-fluid physics, multi-phase flow, and applied mechanics which involve moving flow boundaries. The book demonstrates the application of a variety of techniques for the numerical solution of moving boundary problems within the framework of the finite-volume approach, with appropriate examples.

Preface	p. xv
1 Numerical Techniques for Fluid Flows with Moving Boundaries	p. 1
1.1 Introduction	p. 1
1.1.1 Motivation	p. 1
1.1.2 Overview of the Present Work	p. 3
1.2 Numerical Methods Applied to General Moving Boundary Problems	p. 6
1.2.1 Choice of Method-Lagrangian or Eulerian?	p. 8
1.2.2 Review of Available Methods for Moving Boundary Problems	p. 8
1.2.2.1 Transformation Methods with Body-Fitted Coordinates	p. 9
1.2.2.2 Boundary Element Methods (BEM)	p. 9
1.2.2.3 Volume Tracking Methods	p. 9
1.2.2.4 The Level-Set Method	p. 10
1.2.2.5 Moving Unstructured Boundary Conforming Grid Methods	p. 12
1.2.2.6 Phase Field Models	p. 14
1.2.3 Summary	p. 19
2 Governing Equations and Solution Procedure	p. 21
2.1 Formulation	p. 22
2.1.1 Governing Equations	p. 22
2.1.2 Governing Equations in a Body-Fitted Coordinate System	p. 23
2.2 Discretization of the Conservation Laws	p. 24
2.2.1 Pressure-Based Algorithm	p. 24
2.2.2 Consistent Estimation of the Metric Terms	p. 32
2.2.3 Illustrative Test Cases	p. 33
2.2.3.1 Rotated Channel Flow	p. 33
2.2.3.2 Uniform Flow Using a Moving Grid	p. 35
2.3 Formulation and Solution of Flows with Free Surfaces	p. 36
2.3.1 Introduction	p. 36
2.3.2 Prediction of Meniscus Shapes	p. 39
2.3.2.1 Methodology	p. 39
2.3.2.2 Effect of Convection on Meniscus Shape	p. 42
2.3.3 Sources of Convection	p. 43
2.3.3.1 Natural Convection	p. 43
2.3.3.2 Marangoni Convection	p. 43
2.3.4 Nondimensionalization and Scaling Procedure	p. 44
2.3.4.1 Heat Conduction Scales	p. 45
2.3.4.2 Natural Convection Scales	p. 45
2.3.4.3 The Marangoni Number	p. 45
2.3.5 Formulation and Computational Algorithm for Transport Processes	p. 46
2.3.6 Results and Discussion	p. 48
2.3.6.1 Prediction of Meniscus Shapes	p. 48
2.3.6.2 Heat Transfer Calculations	p. 51
2.3.6.3 Numerical Procedure	p. 52
2.3.6.4 Heat Conduction Only	p. 52
2.3.6.5 Natural Convection	p. 53
2.3.6.6 Interaction of Natural and Thermocapillary Convection	p. 54
2.3.7 Effect of Convection on Meniscus Shape	p. 57
2.4 Conclusions	p. 58
3 Moving Grid Techniques: Fluid Membrane Interaction	p. 61
3.1 Description of the Physical Problem	p. 61
3.1.1 Potential Flow-Based Membrane Wing Models	p. 63
3.1.2 Membrane Equilibrium	p. 65
3.1.3 Nondimensionalization of the Governing Equations	p. 67
3.1.4 The Moving Grid Computational Procedure	p. 70
3.1.5 A Potential Flow Model for Thin Wings	p. 72
3.2 Membrane Wings in Steady Flow	p. 74
3.2.1 Effect of Outer Boundary Location	p. 74
3.2.2 Classification of Flexible Membrane Wings	p. 76
3.2.3 Elastic Membrane Case	p. 76
3.2.4 Inextensible Membrane Case	p. 77
3.3 Membrane Wings in Unsteady Flow	p. 80
3.3.1 Constant Tension Membrane Case	p. 82
3.3.2 Elastic Membrane Case	p. 82
3.3.3 Inextensible Membrane Case	p. 86
3.4 Summary and Conclusion	p. 93
4 Moving Grid Techniques: Modeling Solidification Processes	p. 95
4.1 Introduction	p. 95
4.1.1 Morphological Instabilities During Solidification	p. 95
4.1.2 Physics of Morphological Instabilities in Solidification	p. 98
4.1.3 Implications of Morphological Instabilities	p. 103
4.1.4 Need for Numerical Techniques	p. 105
4.2 Requirements of the Numerical Method	p. 107
4.3 Application of the Boundary-Fitted Approach	p. 108
4.3.1 Formulation	p. 109
4.3.2 Assessment of the Quasi-stationary Approximation	p. 112
4.4 A General Procedure for Interface Tracking	p. 113
4.4.1 Results and Discussion	p. 115
4.4.1.1 Case 1. Calculations with Temperature Field Active in One Phase Only	p. 115
4.4.1.2 Case 2. Calculations with Temperature Field Active in Both Phases	p. 116
4.4.2 Motion of Curved Fronts	p. 117
4.4.2.1 Interfacial Conditions	p. 117
4.4.2.2 Scales for the Morphological Instability Simulations	p. 120
4.4.2.3 Features of the Computational Method	p. 122
4.4.3 Results and Discussion	p. 123
4.5 Issues of Scaling and Computational Efficiency	p. 128
4.5.1 Choice of Reference Scales and Resulting Equations	p. 129
4.6 Conclusions	p. 130
5 Fixed Grid Techniques: Enthalpy Formulation	p. 135
5.1 Governing Equations	p. 135
5.2 Scaling Issues	p. 136
5.2.1 The Macroscopic Scales	p. 139
5.2.2 Velocity Scales	p. 141
5.2.3 Thermal Scales	p. 143
5.2.3.1 Low Prandtl Number (Metallic Melts)	p. 143
5.2.3.2 High Prandtl Number (Organic Melts)	p. 144
5.2.4 The Morphological Scales	p. 146
5.2.5 Pure Conduction	p. 147
5.2.6 Morphological Scales in the Presence of Convection	p. 149
5.2.6.1 Low Prandtl Number Melts	p. 149
5.2.6.2 High Prandtl Number Melts	p. 150
5.3 Enthalpy Formulation	p. 151
5.3.1 Heat Conduction	p. 152
5.3.2 Implementation	p. 155
5.3.2.1 Implementation of the T-Based Method	p. 155
5.3.2.2 Implementation of the H-Based Method	p. 156
5.3.3 Results and Discussion	p. 156
5.3.3.1 Accuracy Assessment	p. 156
5.3.3.2 Performance Assessment	p. 158
5.3.4 Summary	p. 163
5.4 Convective Effects	p. 163
5.4.1 Governing Equations	p. 163
5.4.2 Source Terms in the Momentum Equations	p. 164
5.4.3 Sources of Convection	p. 165
5.4.4 Computational Procedure	p. 166
5.5 Bridgman Growth of CdTe	p. 166
5.6 Multi-Zone Simulation of Bridgman Growth Process	p. 171
5.6.1 Governing Equations	p. 173
5.6.2 Two-Level Modeling Strategy	p. 177
5.6.2.1 The Global Furnace Simulation	p. 177
5.6.2.2 The Refined Ampoule Simulation	p. 178
5.7 Float Zone Growth of NiAl	p. 184
5.7.1 Calculation Procedure	p. 185
5.7.2 Results and Discussion	p. 187
5.7.2.1 Heat Conduction	p. 187
5.7.2.2 Thermocapillary Convection	p. 188
5.8 Summary	p. 192
6 Fixed Grid Techniques: ELAFINT-Eulerian-Lagrangian Algorithm For INterface Tracking	p. 195
6.1 Introduction	p. 195
6.2 Interface Tracking Procedure	p. 197
6.2.1 Basic Methodology	p. 198
6.2.2 Procedures for Mergers/Breakups	p. 202
6.3 Solution of the Field Equations	p. 211
6.3.1 Control Volume Formulation with Moving Interface with Moving Interface	p. 211
6.3.2 The Control Volume Formulation for a Transport Variable	p. 213
6.3.2.1 Discretization	p. 213
6.3.2.2 Treatment of Variables on the Staggered Grid	p. 216
6.3.2.3 Computation of Convective Fluxes	p. 216
6.3.2.4 Evaluation of the Diffusion and the Full Discretized Form	p. 217
6.3.2.5 Evaluation of the Source Term	p. 220
6.3.2.6 Computation of Interfacial Fluxes	p. 221
6.3.2.7 Computation of the Pressure Field	p. 227
6.3.2.8 Computing the Velocities of the Interfacial Markers	p. 228
6.3.2.9 Dealing with Cut Cells	p. 228
6.3.2.10 Conservation and Consistency at Cell Faces	p. 229
6.3.2.11 Anomalous Cases	p. 229
6.3.2.12 Distinction Between Liquid and Solid Cells	p. 231
6.3.2.13 Moving Boundary Problems-Treatment of Cells That Change Phase	p. 232
6.4 Results for Pure Conduction	p. 232
6.4.1 Grid Addition/Deletion	p. 233
6.4.2 Planar Interface Propagation	p. 234
6.4.3 Non-planar Interfaces	p. 235
6.4.4 Zero Surface Tension	p. 236
6.4.5 Low Surface Tension	p. 238
6.4.6 Stable Fingers for Significant Surface Tension	p. 241
6.5 Summary	p. 244
7 Assessment of Fixed Grid Techniques	p. 249
7.1 Introduction	p. 249
7.2 Results for Stationary Boundaries	p. 249
7.3 Melting from a Vertical Wall	p. 250
7.4 Summary	p. 259
7.5 Concluding Remarks	p. 260
References	p. 261
Index	p. 281

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