Spalart–Allmaras turbulence model

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Overview[edit]

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). In ANSYS FLUENT, the Spalart–Allmaras model has been extended with a y+ -insensitive wall treatment (Enhanced Wall Treatment), which allows the application of the model independent of the near wall y+ resolution.

The formulation blends automatically from a viscous sublayer formulation to a logarithmic formulation based on y+. On intermediate grids, (1< y+ <30), the formulation maintains its integrity and provides consistent wall shear stress and heat transfer coefficients. While the y+ sensitivity is removed, it still should be ensured that the boundary layer is resolved with a minimum resolution of 10–15 cells.

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.

Original model[edit]

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

Modifications to original model[edit]

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) [1]

DDES (2006)

Model for compressible flows[edit]

There are two approaches to adapting the model for compressible flows. In the first approach, the turbulent dynamic viscosity is computed from

where is the local density. The convective terms in the equation for are modified to

where the right hand side (RHS) is the same as in the original model.

Boundary conditions[edit]

Walls:

Freestream:

Ideally , but some solvers can have problems with a zero value, in which case can be used.

This is if the trip term is used to "start up" the model. A convenient option is to set in the freestream. The model then provides "Fully Turbulent" behavior, i.e., it becomes turbulent in any region that contains shear.

Outlet: convective outlet.

References[edit]

  • Spalart, P. R. and Allmaras, S. R., 1992, "A One-Equation Turbulence Model for Aerodynamic Flows" AIAA Paper 92-0439

External links[edit]