We were pleasantly surprised by the ready acceptance of the first edition of our book by the CFD community and by the amount of positive feedback received over a period of 10 years. To us this has provided justification of our original plan, which was to provide an accessible introduction to this fast-growing topic to support teaching at senior undergraduate level, post- graduate research and new industrial users of commercial CFD codes. Our second edition seeks to enhance and update. The structure and didactic approach of the first edition have been retained without change, but aug- mented by a selection of the most important developments in CFD.In our treatment of the physics of fluid flows we have added a summary of the basic ideas underpinning large-eddy simulation （LES） and direct numerical simulation （DNS）. These resource-intensive turbulence predic- tion techniques are likely to have a major impact in the medium term on CFD due to the increased availability of high-end computing capability.Over the last decade a number of new discretisation techniques and solution approaches have come to the fore in commercial CFD codes. To reflect these developments we have included summaries of TVD techniques, which give stable, higher-order accurate solutions of convection-diffusion problems, and of iterative techniques and multi-grid accelerators that are now commonly used for the solution of systems of discretised equations. We have also added examples of the SIMPLE algorithm for pressure-velocity coupling to illustrate its workings.At the rime of writing our first edition, CFD was firmly established in the aerospace, automotive and power generation sectors. Subsequently, it has spread throughout engineering industry. This has gone hand in hand with major improvements in the treatment of complex geometries. We have devoted a new chapter to describing key aspects of unstructured meshing techniques that have made this possible.Application of CFD results in industrial research and design crucially hinges on confidence in its outcomes. We have included a new chapter on uncertainty in CFD results. Given the rapid growth in CFD applications it is difficult to cover, within the space of a single introductory volume, even a small part of the submodelling methodology that is now included in many general-purpose CFD codes. Our selection of advanced application material covers combustion and radiation algorithms, which reflects our local perspec- tive as mechanical engineers with interest in internal flow and combustion.
Preface Acknowledgements 1 Introduction 1.1 What is CFD? 1.2 How does a CFD code work? 1.3 Problem solving with CFD 1.4 Scope of this book 2 Conservation laws of fluid motion and boundary conditions 2.1 Governing equations of fluid flow and heat transfer 2.2 Equations of state 2.3 Navier-Stokes equations for a Newtonian fluid 2.4 Conservative form of the governing equations of fluid flow 2.5 Differential and integral forms of the general transport equations 2.6 Classification of physical behaviours 2.7 The role of characteristics in hyperbolic equations 2.8 Classification method for simple PDEs 2.9 Classification of fluid flow equations 2.10 Auxiliary conditions for viscous fluid flow equations 2.11 Problems in transonic and supersonic compressible flows 2.12 Summary 3 Turbulence and its modelling 3.1 What is turbulence? 3.2 Transition from laminar to turbulent }low 3.3 Descriptors of turbulent flow 3.4 Characteristics of simple turbulent flows 3.5 The effect of turbulent fluctuations on properties of the mean flow 3.6 Turbulent flow calculations 3.7 Reynolds-averaged Navier-Stokes equations and classical turbulence models 3.8 Large eddy simulation 3.9 Direct numerical simulation 3.10 Summary 4 The finite volume method for diffusion problems 4.1 Introduction 4.2 Finite volume method for one-dimensional steady state diffusion 4.3 Worked examples: one-dimensional steady state diffusion 4.4 Finite volume method for two-dimensional diffusion problems 4.5 Finite volume method for three-dimensional diffusion problems 4.6 Summary 5 The finite volume method for convection-diffusion problems 5.1 Introduction 5.2 Steady one-dimensional convection and diffusion 5.3 The central differencing scheme 5.4 Properties of discretisation schemes 5.5 Assessment of the central differencing scheme for convectiondiffusion problems 5.6 The upwind differencing scheme 5.7 The hybrid differencing scheme 5.8 The power-law scheme 5.9 Higher-order differencing schemes for convection-diffusion problems 5.10 TVD schemes 5.11 Summary 6 Solution algorithms for pressure-velocity 6.1 Introduction 6.2 The staggered grid 6.3 The momentum equations 6.4 The SIMPLE algorithm 6.5 Assembly ora complete method 6.6 The SIMPLER algorithm 6.7 The SIMPLEC algorithm 6.8 The PISO algorithm 6.9 General comments on SIMPLE, SIMPLER, SIMPLEC and PISO 6.10 Worked examples of the SIMPLE algorithm 6.11 Summary 7 Solution of discretised equations 7.1 Introduction 7.2 The TDMA 7.3 Application of the TDMA to two-dimensional problems 7.4 Application of the TDMA to three-dimensional problems 7.5 Examples 7.6 Point4terative methods 7.7 Multigrid techniques 7.8 Summary 8 the finite volume method for unsteady flows 8.1 Introduction 8.2 One-dimensional unsteady heat conduction 8.3 Illustrative examples 8.4 Implicit method for two- and three-dimensional problems 8.5 Discretisation of transient convection-diffusion equation 8.6 Worked example of transient convection-diffusion using QUICK differencing 8.7 Solution procedures for unsteady flow calculations 8.8 Steady state calculations using the pseudo-transient approach 8.9 A brief note on other transient schemes 8.10 Summary 9 Implementation of boomfary confftions 9.1 Introduction 9.2 Inlet boundary conditions 9.3 Outlet boundary conditions 9.4 Wall boundary conditions 9.5 The constant pressure boundary condition 9.6 Symmetry boundary condition 9.7 Periodic or cyclic boundary condition 9.8 Potential pitfalls and final remarks 10 Errors and uncertainty in CFD modelling 10.1 Errors and uncertainty in CFD 10.2 Numerical errors 10.3 Input uncertainty 10.4 Physical model uncertainty 10.5 Verification and validation 10,6 Guidelines for best practice in CFD 10.7 Reporting/documentation of CFD simulation inputs and results 10.8 Summary 11 Methods for dealing with complex geometries 11.1 Introduction 11.2 Body-fitted co.ordinate grids for complex geometries 11.3 Catesian vs. curvilinear grids - an example 11.4 Curvilinear grids - difficulties 11.5 Block-structured grids 11.6 Unstructured grids 11.7 Discretisation in unstructured grids 11.8 Discretisafion of the diffusion term 11.9 Discretisafion of the convective term 11.10 Treatment of source terms 11.11 Assembly of discretised equations 11.12 Example calculations with unstructured grids 11.13 Pressure-velocity coupling in unstructured meshes 11.14 Staggered vs. co-located grid arrangements 11.15 Extension of the face velocity interpolation method to unstructured meshes 11.16 Summary 12 CFD modelling of combustion 12.1 Introduction 12.2 Application of the first law of thermodynamics to a combustion system 12.3 Enthalpy of formation 12.4 Some important relationships and properties of gaseous mixtures 12.5 Stoichiometry 12.6 Equivalence ratio 12.7 Adiabatic flame temperature 12.8 Equilibrium and dissociation 12.9 Mechanisms of combustion and chemical kinetics 12.10 Overall reactions and intermediate reactions 12.11 Reaction rate 12.12 Detailed mechanisms 12.13 Reduced mechanisms 12.14 Governing equations for combusting flows 12.15 The simple chemical reacting system (SCRS) 12.16 Modelling of a laminar diffusion flame - an example 12.17 CFD calculation of turbulent non-premixed combustion 12.18 SCRS model for turbulent combustion 12.19 Probability density function approach 12.20 Beta pdf 12.21 The chemical equilibrium model 12.22 Eddy break-up model of combustion 12.23 Eddy dissipation concept 12.24 Laminar flamelet model 12.25 Generation oflaminar, flamelet libraries 12.26 Statistics of the non-equilibrium parameter 12.27 Pollutant formation in combustion 12.28 Modelling of thermal NO formation in combustion 12.29 Flamelet-based NO modelling 12.30 An example to illustrate laminar flamelet modelling and NO modelling of a turbulent flame 12.31 Other models for non-premixed combustion 12.32 Modelling ofpremixed combustion 12.33 Summary 13 Numedcal calculation of radiative heat transfer 13.1 Introduction 13.2 Governing equations of radiative heat transfer 13.3 Solution methods 13.4 Four popular radiation calculation techniques suitable for CFD 13.5 Illustrative examples 13.6 Calculation of radiative properties in gaseous mixtures 13.7 Summary Appendix A Accuracy of a flow simulation Appendix B Non-uniform grids Appendix C Calculation of source terms Appendix D Limiter functions used in Chapter 5 Appendix E Derivation of one-dimensional governing equations for steady, incompressible flow through a planar nozzle Appendix F Alternative derivation for the term (n . grad Ai) in Chapter 11 Appendix G Some examples Bibliography Index
插圖︰The discussion of the k-e turbulence model, to which we return later, the material in Chapters 2 and 3 is largely self-contained. This allows the use of this book by those wishing tO concentrate principally on the numerical algorithms, but requiring an overview of the fluid dynamics and the math- ematics behind it for occasional reference in the same text.The second part of the book is devoted to the numerical algorithms of the finite volume method and covers Chapters 4 to 9. Discretisation schemes and solution procedures for steady flows are discussed in Chapters 4 to 7. Chapter 4 describes the basic approach and derives the central difference scheme for diffusion phenomena. In Chapter 5 we emphasise the key prop- erties of discretisation schemes, conservativeness, boundedness and trans- portiveness, which are used as a basis for the further development of the upwind, hybrid, QUICK and TVD schemes for the discretisation of con- vective.terms. The non-linear nature of the underlying flow phenomena and the linkage between pressure and velocity in variable density fluid flows requires special treatment, which is the subject of Chapter 6. We introduce the SIMPLE algorithm and some of its more recent derivatives and also discuss the PISO algorithm. In Chapter 7 we describe algorithms for the solution of the systems of algebraic equations that appear after the discret- isation stage. We focus our attention on the well-known TDMA algorithm, which was the basis of early CFD codes, and point iterative methods with multigrid accelerators, which are the current solvers of choice.The theory behind all the numerical methods is developed around a set of worked examples which can be easily programmed on a PC. This pres- entation gives the opportunity for a detailed examination of all aspects of the discretisation schemes, which form the basic building blocks of practical CFD codes, including the characteristics of their solutions.In Chapter 8 we assess the advantages and limitations of various schemes to deal with unsteady flows, and Chapter 9 completes the development of the numerical algorithms by considering the practical implementation of the most common boundary conditions in the finite volume method.The book is primarily aimed to support those who have access to a CFD package, so that the issues raised in the text can be explored in greater depth. The solution procedures are nevertheless sufficiently well documented for the interested reader to be able to start developing a CFD code from scratch.The third part of the book consists of a selection of topics relating to the application of the finite volume method to complex industrial problems. In Chapter 10 we review aspects of accuracy and uncertainty in CFD. It is not possible to predict the error in a CFD result from first principles, which creates some problems for the industrial user who wishes to evolve equip- ment design on the basis of insights gleaned from CFD. In order to address this issue a systematic process has been developed to assist in the quantifica- tion of the uncertainty of CFD output. We discuss methods, the concepts of verification and validation, and give a summary of rules for best practice that have been developed by the CFD community to assist users. In Chapter 11 we discuss techniques to cope with complex geometry. We review various approaches based on structured meshes: Cartesian co-ordinate systems, gen- eralised co-ordinate systems based on transformations, and block-structured grids, which enable design of specific meshes tailored to the needs of dif- ferent parts of geometry. We give details of the implementation of the finite volume method on unstructured meshes. These are not based on a grid of lines to define nodal.
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