COMPUTATIONAL SIMULATIONS AND APPLICATIONS Edited by Jianping Zhu Computational Simulations and Applications Edited by Jianping Zhu Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2011 InTech All chapters are Open Access articles distributed under the Creative Commons Non Commercial Share Alike Attribution 3.0 license, which permits to copy, distribute, transmit, and adapt the work in any medium, so long as the original work is properly cited. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Ana Nikolic Technical Editor Teodora Smiljanic Cover Designer Jan Hyrat Image Copyright Gunnar Pippel, 2011. Used under license from Shutterstock.com First published September, 2011 Printed in Croatia A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechweb.org Computational Simulations and Applications, Edited by Jianping Zhu p. cm. ISBN 978-953-307-430-6 free online editions of InTech Books and Journals can be found at www.intechopen.com Contents Preface IX Part 1 Research and Numerical Algorithms in Computational Fluid Dynamics Simulations 1 Chapter 1 Reynolds Stress Transport Modelling 3 Sharaf F. Al-Sharif Chapter 2 Study of Some Key Issues for Applying LES to Real Engineering Problems 27 Xiaolong Yang Chapter 3 An Introduction of Central Difference Scheme Stability for High Reynolds Number 61 A. R. da Silva, A. Silveira-Neto and A. M. G. de Lima Chapter 4 A Fourth-Order Compact Finite Difference Scheme for Solving Unsteady Convection-Diffusion Equations 81 Wenyuan Liao and Jianping Zhu Chapter 5 Internal Waves Radiation by a Turbulent Jet Flow in a Stratified Fluid 97 Oleg Druzhinin Chapter 6 Numerical Study on Flow Structures and Heat Transfer Characteristics of Turbulent Bubbly Upflow in a Vertical Channel 119 Mitsuru Tanaka Chapter 7 Mathematical Modelling of the Motion of Dust-Laden Gases in the Freeboard of CFB Using the Two-Fluid Approach 143 Alexander Kartushinsky and Andres Siirde Chapter 8 Computation of Non-Isothermal Reversed Stagnation-Point Flow over a Flat Plate 159 Vai Kuong Sin and Chon Kit Chio VI Contents Part 2 Applications Involving Computational Fluid Dynamics 175 Chapter 9 Numerical Modelling and Optimization of the Mixture Formation Processby Multi-Hole Injectors in a GDI Engine 177 Michela Costa and Luigi Allocca Chapter 10 Turbulent Combustion Simulation by Large Eddy Simulation and Direct Numerical Simulation 209 Fang Wang Chapter 11 Numerical Simulation of Dense Gas-Solid Multiphase Flows Using Eulerian-Eulerian Two-Fluid Model 235 Teklay Weldeabzgi Asegehegn, Matthias Schreiber and Hans Joachim Krautz Chapter 12 Numerical Simulation Techniques for the Prediction of Fluid-Dynamics, Combustion and Performance in IC Engines Fuelled by CNG 259 Mirko Baratta and Ezio Spessa Chapter 13 Development of Two-Phase Flow Correlation for Fluid Mixing Phenomena in Boiling Water Reactor 287 Hiroyuki Yoshida and Kazuyuki Takase Chapter 14 Numerical Simulations of Unsteady Fluid Forces in Heat Exchanger Tube Bundles 319 H. Omar, M. Hassan and A. Gerber Chapter 15 Large-Eddy Simulation of Turbulent Flow and Plume Dispersion in a Spatially-Developing Turbulent Boundary Layer Flow 331 Hiromasa Nakayama Chapter 16 Computations of Flowfield over Reentry Modules at High Speed 347 R. C. Mehta Chapter 17 Numerical Simulation of Dense Phase Pneumatic Conveying in Long-Distance Pipe 373 Zongming Liu, Guangbin Duan and Kun Wang Chapter 18 A Three-Dimensional Numerical Simulation of the Free Surface Flow Around a Ship Hull 395 J. B. V. Wanderley, M. Vitola, S. H. Sphaier and C. Levi Chapter 19 Hydrodynamic Analysis of Electrochemical Cells 409 Cesar Augusto Real-Ramirez and Jesus Isidro Gonzalez-Trejo Contents VII Part 3 Other Applications of Computational Simulations 427 Chapter 20 Upper Burst Error Bound for Atmospheric Correlated Optical Communications Using an Alternative Matrix Decomposition 429 Antonio Jurado-Navas, José María Garrido-Balsells, Miguel Castillo-Vázquez and Antonio Puerta-Notario Chapter 21 Climate System Simulations: An Integrated, Multi-Scale Approach for Research and Decision-Making 449 Ángel G. Muñoz, Alfredo Nuñez and Ramón J. Cova Chapter 22 The Effect of Tomography Imaging Artefacts on Structural Analysis and Numerical Permeability Simulations 469 Viivi Koivu and Tuomas Turpeinen Chapter 23 Nongray EWB and WSGG Radiation Modeling in Oxy-Fuel Environments 493 Osama A. Marzouk and E. David Huckaby Chapter 24 Numerical Modeling of Solidification Process 513 Bohdan Mochnacki Chapter 25 Performance Evaluation of Adaptive Algorithms for Wave Field Analysis/Synthesis Using Sound Field Simulations 543 Paolo Peretti, Stefania Cecchi, Laura Romoli and Francesco Piazza Preface Over the last half a century, the rapid integration of mathematical modeling, computing technology, and real-life applications has made computational simulation a powerful tool for researchers to study complex phenomena in the nature and the society around us. Along with theory and experiment, computational simulation has now become the third pillar for the foundation of scientific exploration. In many circumstances, computational simulations enable researchers to study complex problems in greater detail with better understanding than theory or experiments, such as in the study of protein dynamics. In other circumstances, computational simulations allow researchers to explore numerous different scenarios much more quickly and cost-effectively than experiments, such as in optimal design of modern aircrafts or screening of potential drug molecules. One of the main challenges facing researchers in the field of computational simulations is the highly interdisciplinary nature of the field, which typically involves complex real-world application problems, mathematical models describing those problems, appropriate numerical solution algorithms for solving those model equations, and necessary computer hardware and software to carry out simulations. Successful computational simulation projects often require team-efforts and knowledge in mathematical modeling, computer programming, and specific application problems being studied. The purpose of this book is to highlight the interdisciplinary nature of computational simulations and to introduce researchers and graduate students who are interested in computational simulations to a broad range of applications, with a particular emphasis on those involving computational fluid dynamics (CFD) simulations. The book is divided into three parts: Part I covers some basic research topics and development in numerical solution algorithms for computational fluid dynamics, including Reynolds stress transport modeling and central difference schemes for convection-diffusion equations (chapter 1 – 4), and flow simulations involving simple geometries such as a flat plate or a vertical channel (chapter 5 – 8). Part II covers a variety of important applications in which CFD simulations play a crucial role, including combustion process and automobile engine design (chapter X Preface 9 – 12), fluid heat exchange (chapter 13 – 14), airborne contaminant dispersion over buildings and atmospheric flow around a re-entry capsule (chapter 15 – 16), gas-solid two phase flow in long pipes (chapter 17), free surface flow around a ship hull (chapter 18), and hydrodynamic analysis of electrochemical cells (chapter 19). Part III covers applications of non-CFD based computational simulations, including atmospheric optical communications (chapter 20), environmental studies involving climate system simulations, porous media flow, and combustion (chapter 21 – 23), solidification (chapter 24), and sound field simulations for optimal acoustic effects (chapter 25). I am grateful to InTech for the opportunity to serve as the editor for this book, and I wish to sincerely thank all contributing authors around the world for their diligence in following editorial guidelines, their willingness to support open access publications, and their valuable technical contributions that made this book possible. Special thanks are due to Ms. Ana Nikolic, Mr. Zeljko Spalj, and the technical staff at InTech for their editorial efforts, detailed reviews, and professional assistance. I also would like to thank the University of Texas at Arlington for supporting my participation in this book project. Without the support from the authors, InTech staff, and the University, this book could not have become a reality. Jianping Zhu, Ph.D. Professor and Chair Department of Mathematics The University of Texas at Arlington Arlington, Texas, USA [...]... ∂ ∂xi k1.5 ε (58d) ∂ ∂xi k1.5 ε (58e) 16 14 Computational Simulations and Applications Numerical Simulations 3.8 The Speziale–Sarkar–Gatski model Speziale et al (1991) developed a pressure-strain rate model that is quadratic in aij by first considering the most general form for φij (slow and rapid) that is linear in the mean strain and rotation tensors and quadratic in aij Then they obtained their... models, such as the exact form of the stress production terms, and the abandoning of the incorrectly assumed direct link between stress and strain that characterises eddy–viscosity formulations The presentation also serves to illustrate some inherent weaknesses of present RST models, 24 22 Computational Simulations and Applications Numerical Simulations which might also be thought of as areas for potential... , (84) (85) Ω∗ = Ωk/ε, (86) Ω = (2Ωij Ω ji )1/2 , (87) √ 2 2Sij S jk Ski (Slm Sml )3/2 , (88) and Sij = 1 2 ∂Uj ∂Ui + ∂x j ∂xi , Ωij = 1 2 ∂Uj ∂Ui − ∂x j ∂xi (89) 20 18 Computational Simulations and Applications Numerical Simulations The inhomogeneous corrections are independent of the wall-normal vector, and are given by ε inh,s A = f w1 (ul uk dlA δij − 3 ui uk d jA − 3 u j uk diA )dk φij 2 2 k +... length-scale correction based on the proposal of Iacovides & Raisee (1997), and is given by ˜ ε2 YE = Cεl max[ F ( F + 1)2 , 0], (102) k and F in turn is given by F= ∂l ∂l ∂x j ∂x j − Cl {[1 − exp(− Bε Ret )] + Bε Cl Ret exp(− Bε Ret )} , l = k3/2 /ε, Bε = 0.1069, Cl = 2.55 (103) (104) 22 20 Computational Simulations and Applications Numerical Simulations The remaining coefficients are given by 1.92 √ , 1 + 0.7Ad... Because of limited computational capability at the time, successful computations were not carried out until several decades later (Speziale, 1991) Another important development came when the continuum mechanics community speculated on the potential similarity between turbulent flow and the flow of non-Newtonian fluids (Gatski, 4 2 Computational Simulations and Applications Numerical Simulations 2004) This... modelled using the GGDH, and the standard high-Re version of the ε equation (50) is used, but the coefficient Cε2 is assigned the slightly lower value of 1.83 ´ ´ 3.9 The Hanjalic–Jakirlic low-Re model Jakirli´ & Hanjali´ (1995) developed a low-Re RSTM that is based on the LRR-IP model, and c c the Gibson & Launder (1978) wall corrections (27) and (28), making modifications to handle Low-Re and near-wall effects... where l = k3/2 /ε, and Cl = 2.5 The anisotropic stress dissipation rate tensor is modelled as: 2 ε ij = f s ε∗ + (1 − f s ) δij ε, ij 3 (75) where ε∗ is given by: ij ε∗ = ij ε ui u j + ( ui u k n j n k + u j u k ni n k + u k u l n k n l ni n j ) f d , u u k 1 + 3 n p nq p q f fs = 1 − √ 2 AE2 , k (76) d f d = (1 + 0.1Ret )−1 (77) 18 16 Computational Simulations and Applications Numerical Simulations 3.10... condition, and by inviscid effect through the impermeability condition DNS results show that 10 8 Computational Simulations and Applications Numerical Simulations the viscous effect is confined to a region within y+ ≈ 15 from the wall (Mansour et al., 1988) The inviscid wall-blocking effect on the other hand is significant where the distance from the wall is of the same order as the turbulent length scale... experimental accuracy Thus dependence of the coefficients Cε1 , Cε2 , Cε on the turbulence Reynolds number is often (not always) abandoned Finally the viscous diffusion term, neglected in high-Re models, is retained in its exact form 14 12 Computational Simulations and Applications Numerical Simulations 3.7 The Launder–Reece–Rodi models In their seminal 1975 paper, Launder, Reece & Rodi laid out a hierarchy of... equation and satisfies appropriate boundary conditions that ensure the superposition of the three parts, p, satisfies its own boundary conditions (Pope, 2000) This final term is only significant close to a wall or a free surface, and, since the emphasis here is on modelling regions away from walls, it will be neglected Wall effects on φij are considered in Section 3.3 8 6 Computational Simulations and Applications . COMPUTATIONAL SIMULATIONS AND APPLICATIONS Edited by Jianping Zhu Computational Simulations and Applications Edited by Jianping. orders@intechweb.org Computational Simulations and Applications, Edited by Jianping Zhu p. cm. ISBN 978-953-307-430-6 free online editions of InTech Books and Journals can be found. Alexander Kartushinsky and Andres Siirde Chapter 8 Computation of Non-Isothermal Reversed Stagnation-Point Flow over a Flat Plate 159 Vai Kuong Sin and Chon Kit Chio VI Contents Part 2 Applications