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Concept
Spalart–Allmaras turbulence model
Résumé
In physics, the Spalart–Allmaras model is a one-equation model that solves a modelled transport equation for the kinematic eddy turbulent viscosity. The Spalart–Allmaras model was designed specifically for aerospace applications involving wall-bounded flows and has been shown to give good results for boundary layers subjected to adverse pressure gradients. It is also gaining popularity in turbomachinery applications.
In its original form, the model is effectively a low-Reynolds number model, requiring the viscosity-affected region of the boundary layer to be properly resolved ( y+ ~1 meshes).
The Spalart–Allmaras model was developed for aerodynamic flows. It is not calibrated for general industrial flows, and does produce relatively larger errors for some free shear flows, especially plane and round jet flows. In addition, it cannot be relied on to predict the decay of homogeneous, isotropic turbulence.
It solves a transport equation for a viscosity-like variable . This may be referred to as the Spalart–Allmaras variable.
The turbulent eddy viscosity is given by
The rotation tensor is given by
where d is the distance from the closest surface and is the norm of the difference between the velocity at the trip (usually zero) and that at the field point we are considering.
The constants are
According to Spalart it is safer to use the following values for the last two constants:
Other models related to the S-A model:
DES (1999)
DDES (2006)
There are several approaches to adapting the model for compressible flows.
In all cases, the turbulent dynamic viscosity is computed from
where is the local density.
The first approach applies the original equation for .
In the second approach, the convective terms in the equation for are modified to
where the right hand side (RHS) is the same as in the original model.
The third approach involves inserting the density inside some of the derivatives on the LHS and RHS.
The second and third approaches are not recommended by the original authors, but they are found in several solvers.
Source officielle
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