The production term, , is modeled as

(4–19)

where

(4–20)

and

(4–21)

and are constants, is the distance from the wall, and is a scalar measure of the deformation tensor. By default in Ansys Fluent, as in the original model proposed by Spalart and Allmaras, is based on the magnitude of the vorticity:

(4–22)

where is the mean rate-of-rotation tensor and is defined by

(4–23)

The justification for the default expression for is that, for shear flows, vorticity and strain rate are identical. Vorticity has the advantage of being zero in inviscid flow regions like stagnation lines, where turbulence production due to strain rate can be unphysical. However, an alternative formulation has been proposed  [129] and incorporated into Ansys Fluent.

This modification combines the measures of both vorticity and the strain tensors in the definition of :

(4–24)

where

with the mean strain rate, , defined as

(4–25)

Including both the rotation and strain tensors reduces the production of eddy viscosity and consequently reduces the eddy viscosity itself in regions where the measure of vorticity exceeds that of strain rate. One such example can be found in vortical flows, that is, flow near the core of a vortex subjected to a pure rotation where turbulence is known to be suppressed. Including both the rotation and strain tensors more accurately accounts for the effects of rotation on turbulence. The default option (including the rotation tensor only) tends to overpredict the production of eddy viscosity and hence over-predicts the eddy viscosity itself inside vortices.

You can select the modified form for calculating production in the Viscous Model Dialog Box.