Realizable k-epsilon

Table of Contents

• Properties
• Model equations
• Default model coefficients
• Initialisation
• Usage
• Boundary conditions
• Further information

Note

Under construction - please check again later

Properties

Model equations

The turbulence kinetic energy equation is given by:

\[ \Ddt{\rho k} = \div \left(\rho D_k \grad k\right) + \rho G - \frac{2}{3}\rho \left(\div \u\right) k - \rho \epsilon + S_k \]

and the dissipation rate by:

\[ \Ddt{\rho \epsilon} = \div \left(\rho D_\epsilon \grad \epsilon \right) + C_1 \rho \mag{\tensor{S}} \epsilon - C_2 \rho \frac{\epsilon^2}{k + \left(\nu \epsilon\right)^{0.5}} + S_\epsilon \]

The turbulence viscosity is calculated using:

\[ \nu_t = C_{\mu} \frac{k^2}{\epsilon} \]

where the \( C_{\mu} \) is given by:

\[ C_{\mu} = \frac{1}{A_0 + A_s U^{*} \frac{k}{\epsilon}} \]

Default model coefficients

Initialisation

Usage

The model is specified using:

RAS
{
    turbulence      on;
    RASModel        realizableKE;
}

Boundary conditions

Walls

Further information

Source code:

• Foam::RASModels::realizableKE

References:

• Shih et al. [67]

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