Computational Techniques for Complex Transport Phenomena

by Wei Shyy , S. S. Thakur , H. Ouyang , J. Liu , E. Blosch

• ISBN13: 9780521592680
• ISBN10: 0521592682
• Format: Hardcover
• Copyright: 1997-10-13
• Publisher: Cambridge University Press

Summary

Complex fluid flows are encountered widely in nature, in living beings and in engineering practice. These flows often involve both geometric and dynamic complexity and present problems that are difficult to analyse because of their wide range of length and time scales, as well as their geometric configuration. This book describes some newly developed computational techniques and modelling strategies for analysing and predicting complex transport phenomena. It summarizes advances in the context of a pressure-based algorithm. Among methods discussed are discretization schemes for treating convection and pressure, parallel computing, multigrid methods, and composite, multiblock techniques. With respect to physical modelling, the book addresses issues of turbulence closure and multiscale, multiphase transport from an engineering viewpoint. Both fundamental and practical issues are considered, along with the relative merits of competing approaches. The final chapter is devoted to practical applications that illustrate the advantages of various numerical and physical tools. Numerous examples are given throughout the text. Mechanical, aerospace, chemical and materials engineers can use the techniques presented in this book to tackle important, practical problems more effectively.

Table of Contents

Preface	ix
1. Introduction	1	(23)
1.1 Dynamic and Geometric Complexity	1	(3)
1.1.1 Dynamic Complexity	1	(1)
1.1.2 Geometric Complexity	2	(2)
1.2 Computational Complexity	4	(19)
1.3 Scope of the Present Book	23	(1)
2. Numerical Scheme for Treating Convection and Pressure	24	(36)
2.1 Summary of Pressure-Based Algorithms	24	(5)
2.1.1 Governing Equations and Numerical Algorithm	24	(5)
2.1.2 Solution Procedure	29	(1)
2.2 Treatment of Convection and Pressure Splitting	29	(20)
2.2.1 Estimation of the Fluxes for the CVS and AUSM Schemes	31	(1)
2.2.2 Convective Fluxes	32	(3)
2.2.3 Treatment of the Pressure Flux	35	(3)
2.2.4 Analysis of Eigenvalues	38	(2)
2.2.5 Numerical Dissipation of the Various Schemes	40	(1)
2.2.6 Extension to Second-Order Spatial Accuracy	40	(2)
2.2.7 Results of One-Dimensional Test Cases	42	(7)
2.3 Implementation of the CVS in the Pressure-Based Algorithm	49	(9)
2.3.1 Momentum Equations	49	(2)
2.3.2 Pressure Correction Equation	51	(1)
2.3.3 Additional Issues Due to the Staggered Grid Layout	51	(2)
2.3.4 Results of Two-Dimensional Computations	53	(5)
2.4 Concluding Remarks	58	(2)
3. Computational Acceleration with Parallel Computing and Multigrid Method	60	(62)
3.1 Introduction	60	(1)
3.2 Overview of Parallel Computing	61	(12)
3.2.1 Motivation	61	(1)
3.2.2 Classification of Parallel Machines	61	(3)
3.2.3 Parallel Algorithms: Implementation	64	(6)
3.2.4 Parallel Algorithms: Performance	70	(3)
3.3 Multigrid Method for Convergence Acceleration	73	(22)
3.3.1 Background	73	(9)
3.3.2 Issues Relating to the Multigrid Convergence Rate	82	(13)
3.4 Data-Parallel Pressure-Correction Methods	95	(25)
3.4.1 Single-Grid Computational Issues	96	(15)
3.4.2 Multigrid Computational Issues	111	(9)
3.5 Concluding Remarks	120	(2)
4. Multiblock Methods	122	(41)
4.1 Introduction	122	(1)
4.2 Overview of Multiblock Method	123	(2)
4.3 Analysis of Model Equations on Multiblock Grids	125	(6)
4.3.1 1-D Poisson Equation	125	(3)
4.3.2 2-D Poisson Equation	128	(1)
4.3.3 1-D Convection-Diffusion Equation	128	(2)
4.3.4 Analysis of the Navier-Stokes Equations	130	(1)
4.4 Multiblock Interface Treatments for the Navier-Stokes Equations	131	(9)
4.4.1 Multiblock Grid Arrangement	131	(2)
4.4.2 Interface Treatment for the Momentum Equations	133	(2)
4.4.3 Interface Treatment for the Pressure-Correction Equation	135	(3)
4.4.4 Interface Treatment for Mass Flux	138	(2)
4.5 Solution Methods	140	(3)
4.5.1 General Procedure	140	(1)
4.5.2 Solution Strategy for the Navier-Stokes Equations on Multiblock Grids	141	(1)
4.5.3 Convergence Criterion	142	(1)
4.6 Data Structures	143	(9)
4.6.1 General Interface Organization	143	(1)
4.6.2 Interpolation	144	(3)
4.6.3 Interpolation with Local Conservative Correction	147	(5)
4.7 Assessment of the Interface Treatments	152	(10)
4.7.1 Assessments of Conservative Treatments Using the N-N Boundary Condition for the Pressure-Correction Equation	152	(6)
4.7.2 Comparison of Two Different Interface Conditions for the Pressure-Correction Equation	158	(4)
4.8 Concluding Remarks	162	(1)
5. Two-Equation Turbulence Models with Nonequilibrium, Rotation, and Compressibility Effects	163	(68)
5.1 Basic Information	163	(3)
5.2 Turbulent Transport Equations	166	(2)
5.2.1 Reynolds-Stress Transport Equation	166	(1)
5.2.2 K-XXX Transport Equations	166	(2)
5.3 Implementation of the K-XXX Model	168	(7)
5.3.1 Boundary Conditions and Wall Treatment	169	(3)
5.3.2 Implementation of the Wall Shear Stress in Momentum Equations	172	(2)
5.3.3 Implementation of the K-XXX Equations near Wall Boundaries	174	(1)
5.4 Nonequilibrium Effects	175	(2)
5.5 Computational Assessment of Nonequilibrium Modifications	177	(10)
5.5.1 Backward-Facing Step Flow	177	(5)
5.5.2 Hill Flow Inside a Channel	182	(5)
5.5.3 3-D Diffuser Flow	187	(1)
5.6 Rotational Effects	187	(12)
5.6.1 The Turbulent Transport Equations with Rotational Effects	191	(3)
5.6.2 Displaced Particle Analysis	194	(1)
5.6.3 Simplified Reynolds-Stress Analysis	195	(2)
5.6.4 Proposed Rotational Modifications	197	(2)
5.7 Computational Assessment of Rotational Modifications	199	(11)
5.7.1 Rotating Channel Flow	199	(4)
5.7.2 Rotating Backward-Facing Step Flow	203	(7)
5.8 Compressibility Effects	210	(20)
5.8.1 Governing Equations	211	(4)
5.8.2 Modeling of Compressibility Effects	215	(15)
5.9 Concluding Remarks	230	(1)
6. Volume-Averaged Macroscopic Transport Equations	231	(29)
6.1 Microscopic Transport Equations	231	(1)
6.2 Background of Macroscopic Transport Equations	232	(3)
6.2.1 Morphological Complexities and Disparate Scales	232	(2)
6.2.2 Definition of Averaging Volume	234	(1)
6.3 Volume-Averaging Approach	235	(8)
6.3.1 Definitions and Theorems	236	(2)
6.3.2 The Derivation Procedure	238	(1)
6.3.3 The Treatment of Microscopic Deviation and Interfacial Terms	239	(4)
6.4 Macroscopic Transport Equations via the Volume-Averaging Approach	243	(8)
6.4.1 Macroscopic Equation of Mass Conservation	243	(1)
6.4.2 Macroscopic Equation of Energy Conservation	243	(3)
6.4.3 Macroscopic Equation of Species Conservation	246	(1)
6.4.4 Macroscopic Equation of Momentum Conservation	247	(1)
6.4.5 Special Comment on the Formulation of Effective Coefficients	248	(1)
6.4.6 Comments on the Momentum Equation	249	(2)
6.5 Mixture Approach	251	(1)
6.6 Application to the Columnar Solidification of Binary Alloys	252	(6)
6.6.1 The Simplification of Transport Equations	252	(4)
6.6.2 Implementation of the Numerical Procedure	256	(2)
6.7 Concluding Remarks	258	(2)
7. Practical Applications	260	(37)
7.1 Flow in a Hydraulic Turbine	260	(7)
7.1.1 Distributor Flow Computations	260	(5)
7.1.2 Flow in the Draft Tube	265	(2)
7.2 Thermohaline Stratification	267	(16)
7.2.1 Introduction	267	(4)
7.2.2 Grid Refinement Strategy	271	(2)
7.2.3 Numerical Simulation Results	273	(10)
7.3 Vertical Bridgman Crystal Growth	283	(13)
7.3.1 Background	284	(1)
7.3.2 Experimental Procedure	285	(3)
7.3.3 Comparison with Numerical Results	288	(5)
7.3.4 Analysis of Processing Conditions	293	(3)
7.4 Concluding Remarks	296	(1)
References	297	(17)
Index	314