K-Omega Models Reference

• Space: Axisymmetric, Two Dimensional, or Three Dimensional
• Time: Steady, Implicit Unsteady, PISO Unsteady, or Harmonic Balance
• Material: Gas, Liquid, Multiphase, Multi-Component Gas, or Multi-Component Liquid
• Viscous Regime: Turbulent
• Turbulence: Reynolds-Averaged Navier-Stokes
• Reynolds-Averaged Turbulence: K-Omega Turbulence

• Wall Distance: Wall Distance*

• K-Omega Wall Treatment: All y+ Wall Treatment, High y+ Wall Treatment, and Low y+ Wall Treatment

• Optional Models: Turbulent Viscosity User Scaling

• Compressibility Parameters (optional, see Compressibility Correction)
• Realizability Coefficient, Vorticity Coefficient (optional, see Realizability Option)
• Curvature Correction Parameters (optional, see Curvature Correction Option)
• Low Re Damping Parameters (optional, see Low Re Damping Modification)

• K-Omega Turbulence
• K-Omega Turbulent Viscosity

• Sdr (specific dissipation rate)
• Tke (turbulent kinetic energy)

• Effective Viscosity
• Kolmogorov Length Scale
• Kolmogorov Time Scale
• Specific Dissipation Rate
• Strain Rate Tensor Modulus
• Taylor Micro Scale
• Turbulent Kinetic Energy
• Turbulent Viscosity
• Turbulent Viscosity Ratio
• Turbulent Dissipation Rate

a1

The coefficient ${\text{a}}_1$ in Eqn. (1211) and Eqn. (1212).

Alpha

The coefficient $\alpha$ in Eqn. (1220).

Beta

The coefficient $\beta$ in Eqn. (1216).

Beta1

The coefficient ${\beta }_1$ in Eqn. (1224) and Eqn. (1226).

Beta2

The coefficient ${\beta }_2$ in Eqn. (1224) and Eqn. (1227).

BetaStar

The coefficient ${\beta }^{\text{*}}$ in Eqn. (1214) and Eqn. (1215).

Compressibility Correction

Controls whether to apply a compressibility correction to account for dilatation dissipation.

This correction is irrelevant for incompressible flows.

Compressibility Parameters

Child node that provides the parameter Zeta_Star to modify the model coefficients in Eqn. (1262) and Eqn. (1263).

For guidelines when to apply a compressibility correction, see Accounting for Compressibility Effects.

Constitutive Option

Controls the type of constitutive relation used. Consider applying a non-linear relation in the presence of anistropic turbulence. See Accounting for Anisotropy of Turbulence.

• Linear: Selects the linear constitutive relation as implied by the Boussinesq approximation (see Eqn. (1147).
• QCR: Selects the quadratic constitutive relation (Eqn. (1241)).
• Cubic: Selects the cubic constitutive relation (see Eqn. (1242)).

Convection

Controls the convection scheme.

• 1st-order: Selects the first-order upwind convection scheme.
• 2nd-order: Selects the second-order upwind convection scheme.

Curvature Correction Option

Controls whether to apply a curvature correction, that supplies the effects of strong (streamline) curvature and frame-rotation.

When On, a curvature correction factor $f_c$ is applied, that alters the turbulent kinetic energy production term according to local rotation and vorticity rates (see Eqn. (1217)). Only use this option when you have a stable solution, to improve the results.

Curvature Correction Parameters

Child node that provides the parameters Cr1, Cr2, Cct and Upper Limit ( $C_{\max }$ ) to calculate $f_c$ using Eqn. (1287).

For guidelines when to apply a curvature correction, see Accounting for Strong Streamline Curvature and Frame-Rotation.

Free-Shear Modification

Controls the method to use for the free-shear modification.

• None: The modification is not included.
• Dissipation Limiter: The modifications detailed in Eqn. (1231).
• Cross-diffusion Limiter: The modification detailed in Eqn. (1232).

For guidelines when to apply a free-shear modification, see Improving Predictions for Free-Shear Flows.

Kappa

The coefficient $\kappa$ , see Eqn. (1226) and Eqn. (1227).

Low Re Damping Modification

When On, the low Reynolds number modification is incorporated.

LowRe Damping Parameters

Child node that provides the parameters RBeta (${\mathrm{Re}}_{\beta }$), Rk (${\mathrm{Re}}_k$), and Rw (${\mathrm{Re}}_{\omega }$) to modify the model coefficients in Eqn. (1235) to Eqn. (1240).

For guidelines when to apply a low Reynolds number modification, see Accounting for Low Reynolds Number Effects.

Normal Stress Term

This property is an explicit term that directly incorporates divergence and turbulent kinetic energy, $-\frac{2}{3}\mathrm{\rho k}\mathbf{\text{I}}$ , according to the full Boussinesq approximation.

When On, the stress tensor is modeled as

${\mathbf{\text{T}}}_{\mathrm{RANS}}=2{\mu }_t\mathbf{\text{S}}-\frac{2}{3}({\mu }_t\nabla \cdot \mathbf{\text{v}}+\rho k)\mathbf{\text{I}}$

and the turbulent production is modeled using

$G_k={\mu }_t{S}^2-\frac{2}{3}\rho k\nabla \cdot \overline{v}-\frac{2}{3}{\mu }_t{(\nabla \cdot \overline{v})}^2$

When Off, the stress tensor is modeled as

${\mathbf{\text{T}}}_{\mathrm{RANS}}=2{\mu }_t\mathbf{\text{S}}-\frac{2}{3}\left({\mu }_t\nabla \cdot \mathbf{\text{v}}\right)\mathbf{\text{I}}$

and the turbulent production is assumed to be

$G_k={\mu }_t{S}^2-\frac{2}{3}{\mu }_t{(\nabla \cdot \overline{v})}^2$

This property is off by default, in which case the quantity $-\frac{2}{3}\rho k\mathbf{\text{I}}$ is absorbed into the pressure, and causes the pressure to be slightly different. However, the results are the same even if this term is not explicitly included.

In incompressible flow only the gradients of pressure matter, so this setting has no effect on the results. In compressible flow, however, the absolute value of pressure is used in the Ideal Gas Law (Eqn. (671)). Activating this option may affect the solution convergence if $k$ happens to be poorly initialized.

Realizability Option

Selects whether a limiter is applied to the turbulent time scale. The following options are available:

• None—no limiter is applied.

• Durbin Scale Limiter—activates the Durbin's realizability minimum constraint on the turbulent time scale. This is the default.
• Vorticity Limiter—activates the vorticity limiter for the turbulent time scale in Eqn. (1210) and [eqnlink]. When activated, provides the Vorticity Coefficient node. Available only when the VOF Waves model is selected as part of a Volume of Fluid (VOF) multiphase simulation.

Realizability Coefficient

Specifies the realizability coefficient $C_T$ to calculate the turbulent time scale $T$ using Eqn. (1209) (ST W KO) and Eqn. (1212) (SST M KO).

For guidelines on when to activate Durbin's realizability constraint, see Overcoming an Unexpectedly Large Growth of K.

Vorticity Coefficient

Specifies the vorticity coefficient for calculating the turbulent time scale. This is the term ${\lambda }_2\frac{\beta }{{\beta }^{\text{*}}\alpha }$ in Eqn. (1210) (ST W KO) and [eqnlink] (SST M KO).

For guidelines on when to activate the vorticity limiter, see Turbulence Damping for Free-Surface Waves.

Secondary Gradients

Neglect or include the boundary secondary gradients for diffusion and/or the interior secondary gradients at mesh faces.

• On: Include both secondary gradients.
• Off: Exclude both secondary gradients.
• Interior Only: Include the interior secondary gradients only.
• Boundaries Only: Include the boundary secondary gradients only.

Sdr Minimum

The minimum value that the transported variable $\omega$ is permitted to have. An appropriate value is a small number that is greater than the floating point minimum of the computer.

Sigma_k

The coefficient ${\sigma }_k$ in Eqn. (1215).

Sigma_k1

The coefficient ${\sigma }_{k1}$ in Eqn. (1228).

Sigma_k2

The coefficient ${\sigma }_{k2}$ in Eqn. (1228).

Sigma_w

The coefficient ${\sigma }_{\omega }$ in Eqn. (1216).

Sigma_w1

The coefficient ${\sigma }_{\omega 1}$ in Eqn. (1229).

Sigma_w2

The coefficient ${\sigma }_{\omega 2}$ in Eqn. (1229) and Eqn. (1222).

TkeMinimum

The minimum value that the transported variable $k$ is permitted to have. An appropriate value is a small number that is greater than the floating point minimum of the computer.

Vortex Stretching Modification

When On, the vortex modification as detailed in Eqn. (1233) through Eqn. (1234) is incorporated.

For guidelines when to activate the vortex modification, see Overcoming the Round/Plane-Jet Anomaly.