K-Epsilon Models Reference

• Theory Guide—K-Epsilon Model (RKE, RKE 2L, SKE, SKE LRe, SKE 2L)
• Theory Guide—Elliptic Blending Model (EB KE, EBL KE)

• Space: Axisymmetric, Two Dimensional, or Three Dimensional
• Time: Steady, Implicit Unsteady, PISO Unsteady, or Harmonic Balance (all except EB KE and EBL KE)
• Material: Gas, Liquid, Multiphase, Multi-Component Gas, or Multi-Component Liquid
• Viscous Regime: Turbulent
• Turbulence: Reynolds-Averaged Navier-Stokes
• Reynolds-Averaged Turbulence: K-Epsilon Turbulence

• Wall Distance: Wall Distance*

• Wall Treatment: All y+ Wall Treatment and Low y+ Wall Treatment (SKE LRe, EB KE, EBL KE), High y+ Wall Treatment (RKE, SKE), or Two-Layer All y+ Wall Treatment (RKE 2L, SKE 2L)

• Optional Models: Turbulent Viscosity User Scaling and Temperature Flux Model (SKE LRe)

• C3e (optional, see Buoyancy Production of Dissipation)
• Curvature Correction Parameters (optional, see Curvature Correction Option)
• Non-Linear Cmu Coefficients (optional, see Constitutive Relation)
• Non-Linear Cubic Coefficients (optional, see Constitutive Relation)
• Non-Linear Quadratic Coefficients (optional, see Constitutive Relation)
• Realizability Coefficient, Vorticity Coefficient (optional, see Realizability Option)

• K-Epsilon Turbulence (all except EB KE, and EBL KE)
• EB K-Epsilon Turbulence (EB KE)
• Lag K-Epsilon Turbulence (EBL KE)
• K-Epsilon Turbulent Viscosity

• Tdr (turbulent dissipation rate)
• Tke (turbulent kinetic energy)
• Alpha (elliptic blending function, EB KE and EBL KE)
• Phi (reduced stress function, EB KE and EBL KE)

• Effective Viscosity
• Elliptic Blending Function (EB KE, EBL KE)
• Kolmogorov Length Scale
• Kolmogorov Time Scale
• Reduced Stress Function (EB KE, EBL KE)
• Strain Rate Tensor Modulus
• Taylor Micro Scale
• Turb Wall Distance Re (RKE 2L, SKE LRe, SKE 2L)
• Turbulent Dissipation Rate
• Turbulent Kinetic Energy
• Turbulent Viscosity
• Turbulent Viscosity Ratio

See K-Epsilon Field Functions Reference.

Alpha Minimum

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

Buoyancy Production of Dissipation

Determines how the coefficient $C_{\epsilon 3}$ in the production term $P_{\epsilon }$ is calculated (see Eqn. (1169) and Eqn. (1268) (EB KE, EBL KE)).

• None: Sets $C_{\epsilon 3}$ to zero.
• Boundary Layer Orientation: Computes $C_{\epsilon 3}$ according to Eqn. (1191).
• Thermal Stratification: Computes $C_{\epsilon 3}$ according to Eqn. (1192).
• Constant Coefficient: Computes $C_{\epsilon 3}$ as a constant coefficient. This option requires the specification of $C_{\epsilon 3}$ in the corresponding child node C3e .

C coefficient

The coefficients $C$ in Eqn. (1187).

C_T

The coefficient $C_T$ in Eqn. (1265).

C1

The coefficient $C_1$ in Eqn. (1275) (EB KE) and Eqn. (1276) (EBL KE).

C1e

The coefficient $C_{\epsilon 1}$ in the basic transport equations.

C1s

The coefficient $C_1^{*}$ in Eqn. (1276).

C2

The coefficient $C_2$ in Eqn. (1275) (EB KE).

C2e

The coefficient $C_{\epsilon 2}$ in the basic transport equations.

C3

The coefficient $C_3$ in Eqn. (1283).

C3e

The coefficient $C_{\epsilon 3}$ in Eqn. (1274).

C3s

The coefficient $C_3^{*}$ in Eqn. (1276).

C4

The coefficient $C_4$ in Eqn. (1276).

C5

The coefficient $C_5$ in Eqn. (1276).

Cd0 coefficient

The coefficient $C_{d0}$ in Eqn. (1188).

Cd1 coefficient

The coefficient $C_{d1}$ in Eqn. (1188).

Cd2 coefficient

The coefficient $C_{d2}$ in Eqn. (1188).

Ceta

The coefficient $C_{\eta }$ used in the calculation of the turbulent length scale $L$ .

Ck

The coefficient $C_k$ in Eqn. (1280).

Cl

The coefficient $C_L$ used in the calculation of the turbulent length scale $L$ .

Cmu

The coefficient $C_{\mu }$ in the calculation of the turbulent viscosity ${\mu }_t$ and in the basic transport equations.

Constitutive Relation

Controls the type of constitutive relation used.

• Linear: Selects the linear constitutive relation as implied by the Boussinesq approximation (see Eqn. (1147). Use this selection for most simulations.
• Quadratic: Selects the quadratic constitutive relation (see Eqn. (1203)). This relation requires the coefficients $C_{\mu }$ , $C_1$ , $C_2$ , and $C_3$ .

  Non-Linear Cmu Coefficients

  Child node that provides the parameters Ca0, Ca1, Ca2, and Ca3 to calculate $C_{\mu }$ .

  Non-Linear Quadratic Coefficients

  Child node that provides the parameters Cnl1, Cnl2, Cnl3, Cnl6, and Cnl7 to calculate $C_1$ , $C_2$ , and $C_3$ .

• Cubic: Selects the cubic constitutive relation (see Eqn. (1204)). This relation requires the coefficients $C_{\mu }$ , $C_1$ , $C_2$ , $C_3$ , $C_4$ , and $C_5$ .

  Non-Linear Cmu Coefficients

  As for Quadratic.

  Non-Linear Quadratic Coefficients

  As for Quadratic.

  Non-Linear Cubic Coefficients

  Child node that provides the parameters Cnl4, Cnl5 to calculate $C_4$ and $C_5$ .

For guidelines when to use non-linear constitutive relations see Accounting for Anisotropy of Turbulence.

Convection

Controls the convection scheme.

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

Ct

The coefficient $C_t$ used in the calculation of the turbulent time scale $T$ .

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. (1177) to Eqn. (1180)). 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.

D coefficient

The coefficient $D$ in Eqn. (1184).

E coefficient

The coefficient $E$ in Eqn. (1184).

Free-stream Option

Controls the definition of $C_{\epsilon 2}^{*}$ in the transport equation for $\epsilon$ (see Eqn. (1268)):

• Variable C2e Option: Uses a variable $C_{\epsilon 2}^{*}$ value (see Eqn. (1281)). Set by default.
• Off: Uses a constant $C_{\epsilon 2}^{*}$ value (see Eqn. (1282)).

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)). If $k$ is poorly initialized, activating this option affects the solution convergence.

Phi Minimum

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

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 $T$ in Eqn. (1165).
• Vorticity Limiter—activates the vorticity limiter for the turbulent time scale in Eqn. (1166) and Eqn. (1167). When activated, provides the Vorticity Coefficient node. Available only if the VOF Waves model is selected.

Realizability Coefficient

Specifies the realizability coefficient $C_T$ in Eqn. (1165).

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 $T$ . This is the term ${\lambda }_2\frac{C_{ϵ2}}{C_{ϵ1}}$ in Eqn. (1166) (SK) and Eqn. (1167) (RKE).

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

Sarkar

The coefficient $C_M$ in the compressibility modification ${\Upsilon }_M$ (see Eqn. (1185)). For EB KE and EBL KE, see Eqn. (1279).

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.

Sigma_e

The coefficient ${\sigma }_e$ in the basic transport equations.

Sigma_k

The coefficient ${\sigma }_k$ in the basic transport equations.

Sigma_phi

The coefficient ${\sigma }_{\phi }$ in Eqn. (1269).

Tdr Minimum

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

Tke Minimum

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.

Two-Layer Delta ReY

The value of $\Delta {\text{Re}}_y$ in Eqn. (1195).

Two-Layer ReY*

The value of ${{\text{Re}}_y}^{*}$ in Eqn. (1194).

Two-Layer Type

Controls the type of two-layer formulation

• Shear Driven (Wolfstein): Selects the two-layer formulation of Wolfstein [317]. Use this selection for flows where buoyancy forces do not dominate. See Eqn. (1197) and Eqn. (1198).
• Buoyancy Driven (Xu): Selects the two-layer formulation of Xu [318]. Use this selection for flows where buoyancy forces dominate. See Eqn. (1201) and Eqn. (1202).
• Shear Driven (Norris-Reynolds) : Selects the two-layer formulation of Norris and Reynolds [312]. Use this selection for flows where buoyancy forces do not dominate. See Eqn. (1199) and Eqn. (1200).

Yap Correction

When On, includes the Yap correction ${\Upsilon }_y$ in the transport equation for $\epsilon$ , see Eqn. (1174)(SKE 2L) and Eqn. (1176) (SKE LRe). The default setting is Off.

Yap Cl

The coefficient $C_l$ in the Yap correction (see Eqn. (1186)).

Yap Cw

The coefficient $C_w$ in the Yap correction (see Eqn. (1186)).