Transition, Turbulence and Combustion Modelling

1 Introduction.- 1.1 Equations for compressible flows.- 1.2 Laminar boundary layers.- 1.3 Combustion.- References.- 2 Stability of Boundary Layer Flows.- 2.1 Introduction.- 2.2 Introduction to stability of incompressible parallel flows.- 2.3 Stability of compressible parallel flows.- 2.4 Stability of non-parallel compressible flows.- 2.5 Applications.- References.- 3 Transition Prediction in Industrial Applications.- 3.1 Introduction.- 3.2 Qualitative description of some transition mechanisms.- 3.3 Some theoretical elements for “natural” transition.- 3.4 The eN method.- 3.5 Application to transonic flows : laminar flow control.- 3.6 Application to high speed flows.- 3.7 Conclusion.- References.- 4 An Introduction to Turbulence Modelling.- 4.1 Introduction.- 4.2 Basic properties of turbulence and the mean flow equation.- 4.3 Transport equations for single-point moments.- 4.4 The hierarchy and history of single-point closures.- 4.5 What should a closure fulfill?.- 4.6 Purely algebraic models.- 4.7 Eddy-viscosity based two-equation models.- 4.8 Differential Reynolds stress models for incompressible flow.- 4.9 Algebraic Reynolds stress models.- References.- 5 Modelling of Turbulence in Compressible Flows.- 5.1 Introduction.- 5.2 Averaged equations.- 5.3 Compressibility effects due to turbulent fluctuations and modelling of explicit compressibility terms.- 5.4 Transport equation models.- References.- 6 Large-Eddy Simulations of Incompressible and Compressible Turbulence.- 6.1 Introduction.- 6.2 Large-eddy simulation (LES) formalism.- 6.3 Smagorinsky’s model.- 6.4 Spectral Eddy-viscosity and eddy-diffusivity models.- 6.5 Return to physical space.- 6.6 Vortex control in a round jet.- 6.7 Rotating flows.- 6.8 Compressible LES formalism.- 6.9 Compressible mixing layer.-6.10 Compressible boundary layers on a flat plate.- 6.11 Conclusion.- References.- 7 Direct Numerical Simulations of Compressible Turbulent Flows: Fundamentals and Applications.- 7.1 Introduction.- 7.2 Physical nature of compressible turbulent flows.- 7.3 Governing equations.- 7.4 Numerical methods.- 7.5 DNS of compressible free-shear flows.- 7.6 DNS of shock-turbulence interaction.- 7.7 DNS of aerodynamically-generated sound.- 7.8 Concluding remarks.- References.- 8 Turbulent Combustion Modelling.- 8.1 Introduction.- 8.2 Mixture fraction based theories.- 8.3 Large-eddy simulations.- References.