### 2.3.2. Omega-Based Reynolds Stress Models

CFX provides two Reynolds Stress- models: the Omega Reynolds Stress and Baseline (BSL) Reynolds stress models. The two models relate to each other in the same way as the two equation and BSL models. For details, see The Baseline (BSL) k-omega Model.

The Reynolds Stress- turbulence model, or SMC- model, is a Reynolds stress model based on the -equation. The advantage of the -equation is that it allows for a more accurate near wall treatment with an automatic switch from a wall function to a low-Reynolds number formulation based on the mesh spacing.

The modeled equations for the Reynolds stresses can be written as follows:

| (2–110)

The production due to buoyancy is modeled in the same way as given in the Equation 2–93 and Equation 2–94. The default value of is 0.9 for the Boussinesq buoyancy model and 1.0 in the full buoyancy model based on density differences.

#### 2.3.2.1. The Omega Reynolds Stress Model

The Omega Reynolds Stress Model uses the following equation for :

| (2–111)

The following coefficients apply:

| (2–112)

#### 2.3.2.2. The BSL Reynolds Stress Model

The coefficients and of the -equation, as well as both the turbulent Prandtl numbers and , are blended between values from the two sets of constants, corresponding to the -based model constants and the -based model constants transformed to an -formulation:

| (2–113)

- Set 1 (SMC- zone):

  | (2–114)

  The value of here corresponds to the model. For details, see The Wilcox k-omega Model. The von Karman constant has a commonly used value of 0.41.

- Set 2 (SMC- zone):

  | (2–115)

The blending of coefficients is done by smooth linear interpolation with the same weight function F1 as the one used in a cross-diffusion term of the -equation (Equation 2–113):

| (2–116)

where with:

| (2–117)

and

| (2–118)

#### 2.3.2.3. Pressure-Strain Correlation

The constitutive relation for the pressure-strain correlation is given by:

| (2–119)

The production tensor of Reynolds stresses is given by:

| (2–120)

The tensor D ij, participating in the pressure-strain model Equation 2–119, differs from the production tensor in the dot-product indices:

| (2–121)

The turbulent viscosity in the diffusion terms of the balance equations (Equation 2–110 and Equation 2–111) is calculated in the same way as in the Wilcox model. For details, see The Wilcox k-omega Model.

| (2–122)

The coefficients for the model are:

#### 2.3.2.4. Wall Boundary Condition

The model is used in combination with the automatic wall treatment developed for the based models (, BSL and SST). The formulation has been recalibrated to ensure a constant wall shear stress and heat transfer coefficient under variable near wall resolution.

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