By default in Ansys Fluent, the pressure-strain term, , in Equation 4–226 is modeled according to the proposals by Gibson and Launder [203], Fu et al.  [194], and Launder  [337],  [338].

The classical approach to modeling uses the following decomposition:

(4–230)

where is the slow pressure-strain term, also known as the return-to-isotropy term, is called the rapid pressure-strain term, and is the wall-reflection term.

The slow pressure-strain term, , is modeled as

(4–231)

with = 1.8.

The rapid pressure-strain term, , is modeled as

(4–232)

where = 0.60, , , , and are defined as in Equation 4–226, , , and .

The wall-reflection term, , is responsible for the redistribution of normal stresses near the wall. It tends to damp the normal stress perpendicular to the wall, while enhancing the stresses parallel to the wall. This term is modeled as

(4–233)

where , , is the component of the unit normal to the wall, is the normal distance to the wall, and , where and is the von Kármán constant (= 0.4187).

is included by default in the Reynolds stress model.

When the RSM is applied to near-wall flows using the enhanced wall treatment described in Two-Layer Model for Enhanced Wall Treatment, the pressure-strain model must be modified. The modification used in Ansys Fluent specifies the values of , , , and as functions of the Reynolds stress invariants and the turbulent Reynolds number, according to the suggestion of Launder and Shima  [341]:

(4–234)

(4–235)

(4–236)

(4–237)

with the turbulent Reynolds number defined as . The flatness parameter and tensor invariants, and , are defined as

(4–238)

(4–239)

(4–240)

is the Reynolds-stress anisotropy tensor, defined as

(4–241)

The modifications detailed above are employed only when the enhanced wall treatment is selected in the Viscous Model Dialog Box.

An optional pressure-strain model proposed by Speziale, Sarkar, and Gatski  [625] is provided in Ansys Fluent. This model has been demonstrated to give superior performance in a range of basic shear flows, including plane strain, rotating plane shear, and axisymmetric expansion/contraction. This improved accuracy should be beneficial for a wider class of complex engineering flows, particularly those with streamline curvature. The quadratic pressure-strain model can be selected as an option in the Viscous Model Dialog Box.

This model is written as follows:

(4–242)

where is the Reynolds-stress anisotropy tensor defined as

(4–243)

The mean strain rate, , is defined as

(4–244)

The mean rate-of-rotation tensor, , is defined by

(4–245)

The constants are

The quadratic pressure-strain model does not require a correction to account for the wall-reflection effect in order to obtain a satisfactory solution in the logarithmic region of a turbulent boundary layer. It should be noted, however, that the quadratic pressure-strain model is not available when the enhanced wall treatment is selected in the Viscous Model Dialog Box.

The stress-omega model is a stress-transport model that is based on the omega equations and LRR model [708]. This model is ideal for modeling flows over curved surfaces and swirling flows. The stress-omega model can be selected in the Viscous Model Dialog Box and requires no treatments of wall reflections. The closure coefficients are identical to the - model (Model Constants), however, there are additional closure coefficients, and , noted below.

The stress-omega model resembles the - model due to its excellent predictions for a wide range of turbulent flows. Furthermore, low Reynolds number modifications and surface boundary conditions for rough surfaces are similar to the - model.

Equation 4–230 can be re-written for the stress-omega model such that wall reflections are excluded:

(4–246)

Therefore,

(4–247)

where is defined as

(4–248)

The mean strain rate is defined in Equation 4–244 and is defined by

(4–249)

where and are defined in the same way as for the standard , using Equation 4–85 and Equation 4–91, respectively. The only difference here is that the equation for uses a value of 640 instead of 680, as in Equation 4–85.

The constants are

The above formulation does not require viscous damping functions to resolve the near-wall sublayer. However, inclusion of the viscous damping function [708] could improve model predictions for certain flows. This results in the following changes:

where , , and would replace , , and in Equation 4–247. The constants are

Inclusion of the low-Re viscous damping is controlled by enabling Low-Re Corrections under k-omega Options in the Viscous Model Dialog Box.

The stress-BSL model solves the scale equation from the baseline (BSL) - model, and thus removes the free-stream sensitivity observed with the stress-omega model. It uses the same relation (Equation 4–247) for the pressure-strain correlation in the Reynolds stress equations as the stress-omega model, but without low-Reynolds number corrections. The coefficient is equal to .

There is also an option GEKO which allows the combination of the EARSM with the Generalized (GEKO) Model (see Generalized k-ω  (GEKO) Model for more information on the GEKO model).