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7. TURBULENCE MODELLING IN CFD SPRING 2005
7.1 Turbulence models for general-purpose CFD
7.2 Linear eddy-viscosity models
7.3 Non-linear eddy-viscosity models
7.4 Differential stress models
7.5 Implementation of turbulence models in CFD
7.1 Turbulence Models For General-Purpose CFD
Turbulence models for general-purpose CFD must be f rame-invariant – i.e. independent of
any particular coordinate system – and hence must be expressed in tensor form. This rules out
simpler models of boundary-layer type (e.g. mixing-length models).
Turbulent flows are computed either by solving the Reynolds-averaged Navier-Stokes
equations with suitable models for turbulent fluxes or by computing the fluctuating quantities
directly. The main approaches are summarised below.
Rey nolds-Averaged Navier-Stokes (RANS) Models
• Linear eddy-viscosity models (EVM)
– assume that (deviatoric) turbulent stress is proportional to mean strain;
– an eddy viscosity is based on turbulent scales (usually k + one other), determined by
solving transport equations.
• Non-linear eddy-viscosity models (NLEVM)
– assume that the turbulent stress is a non-linear function of mean strain and vorticity;
– coefficients depend on turbulence scales (usually k + one other), determined by
solving transport equations;
– mimic response of turbulence to certain important types of strain.
• Differential stress models (DSM)
– aka Reynolds-stress transport models (RSTM) or second-order closure (SOC);
– solve transport equations for all turbulent stresses.
Comp utation of f luctuating quantities
• Large-eddy simulation (LES)
– compute time-varying flow, but model sub-grid-scale motions.
• Direct numerical simulation (DNS)
– no modelling; resolve the smallest scales of the flow.
CFD
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