Computational Fluid Dynamics with Moving Boundaries

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

Overview

This 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 multiple examples that employ algorithms in problem-solving.
In addition to its survey of contemporary numerical techniques, this volume discusses formulation and computation strategies as well as applications in many fields. Researchers and professionals in aerospace, chemical, mechanical, and materials engineering will find it a valuable resource. It is also an appropriate textbook for advanced courses in fluid dynamics, computation fluid dynamics, heat transfer, and numerical methods.

Product Details

ISBN-13:	9780486458908
Publisher:	Dover Publications
Publication date:	02/27/2007
Series:	Dover Books on Engineering Series
Pages:	304
Product dimensions:	6.14(w) x 9.21(h) x (d)

Table of Contents

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

Editorial Reviews

Reviews recent advances and develops computational algorithms pertaining to moving boundary problems in fluid dynamics, and demonstrates their application to the numerical solutions of problems within the framework of the finite-volume approach. Draws detailed examples from high-temperature materials processing and fluid-flexible structure interactions. Summarizes the pressure-based algorithm for fluid flow equations to allow readers to follow the detailed numerical development. Does not address any of the generic aspects of computational fluid dynamics. Of interest to aerospace, chemical, mechanical, and materials engineers. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews