Thermofluid Dynamics of Turbulent Flows: Fundamentals and Modelling

Description

The book provides the theoretical fundamentals on turbulence and a complete overview of turbulence models, from the simplest to the most advanced ones including Direct and Large Eddy Simulation. It mainly focuses on problems of modeling and computation, and provides information regarding the theory of dynamical systems and their bifurcations. It also examines turbulence aspects which are not treated in most existing books on this subject, such as turbulence in free and mixed convection, transient turbulence and transition to turbulence. The book adopts the tensor notation, which is the most appropriate to deal with intrinsically tensor quantities such as stresses and strain rates, and for those who are not familiar with it an Appendix on tensor algebra and tensor notation are provided. Preface References Acknowledgements Contents About the Author Symbols and Abbreviations Greek Symbols Superscripts Subscripts Averages and Statistics Abbreviations and Acronyms 1 Introduction and Governing Equations 1.1 Eulerian and Lagrangian Approaches 1.1.1 Continuity 1.1.2 Momentum 1.1.3 Scalar Transport 1.1.4 Governing Equations for Constant-Property Fluids 1.1.5 Boussinesq Approximation for Buoyancy 2 Properties of Turbulence 2.1 Direct Simulation and Turbulence Modelling 2.2 Decomposition and Fluctuations 2.3 The Kolmogorov Energy Cascade 2.4 Turbulence Spectra 2.5 Scalar Transport in Turbulence 2.6 Coherent Structures 2.7 Three-Dimensional Versus Two-Dimensional Turbulence 2.8 Turbulence and Strange Attractors 2.9 A Heuristic Approach to Turbulence Modelling References 3 Direct Numerical Simulation (DNS) 3.1 Direct Numerical Simulation and Spatio-Temporal Resolution 3.2 Resolution Requirements for Turbulent Plane Poiseuille Flow 3.3 DNS and Computing Performances 3.4 An Example of Very High-Resolution DNS References 4 Large Eddy Simulation 4.1 Spatial Filtering 4.2 Terms Arising from the Spatial Filtering of the Governing Equations 4.3 The Smagorinsky Sub-Grid Model 4.4 The “Dynamic” Sub-Grid Model 4.5 Other Sub-Grid Models 4.6 Boundary and Initial Conditions for LES References 5 Rans Models 5.1 Reynolds Averaging 5.2 Eddy Viscosity Models 5.3 The k–ε Model and Its Variants 5.4 Boundary Conditions and Wall Functions 5.5 Low Reynolds Number k–ε Models 5.6 The k–ω Model and Its Variants 5.7 Algebraic Reynolds Stress/Flux Models 5.8 Differential Reynolds Stress/Flux Models References 6 Turbulence in Natural and Mixed Convection 6.1 Buoyancy and Turbulence 6.2 Direct Contribution of Buoyancy to the Balance of Reynolds Stresses and k 6.3 Direct Contribution of Buoyancy to the Balance of Dissipation 6.4 Examples of Turbulent Natural Convection 6.5 Turbulence in the Atmospheric Boundary Layer (ABL) References 7 Transient Turbulence 7.1 Unsteadiness and Turbulence 7.2 Laminar Oscillatory Flow 7.3 Turbulent Oscillatory Flow 7.4 Turbulence and Temporal Acceleration 7.5 Turbulence and Spanwise Oscillations 7.6 Conclusive Remarks on Transient Turbulence References 8 Transition to Turbulence 8.1 Attractors, Transitions and Bifurcations 8.2 Transition in Toroidal Pipes 8.3 Transition in Serpentine Ducts 8.4 Transition in Spacer-Filled Plane Channels References Conclusions Appendix Elements of Tensor Algebra A.1 Vector and Tensor Notation A.2 Invariants of a Second-Order Tensor A.3 Kinematic Tensors A.4 Stresses and Constitutive Equations A.4.1 Stress Tensor A.4.2 Constitutive Equations