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
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