Properties

Two equation model for the turbulence kinetic energy, \( k \), and turbulence specific dissipation rate, \( \omega \).
Based on the k-omega SST model

Model equations

The turbulence specific dissipation rate equation is given by:

\[ \Ddt{\rho \omega} = \div \left( \rho D_\omega \grad \omega \right) + \rho \gamma \frac{G}{\nu} - \frac{2}{3} \rho \gamma \omega \left( \div \u \right) - \rho \beta \omega^2 - \rho \left( F_1 - 1 \right) CD_{k \omega} + S_\omega, \]

and the turbulence kinetic energy by:

\[ \Ddt{\rho k} = \div \left( \rho D_k \grad k \right) + \min\left( \rho G, \left(c_1 \beta^{*}\right) \rho k \omega \right) - \frac{2}{3} \rho k \left( \div \u \right) - \rho \frac{k^{1.5}}{\tilde{d}} + S_k. \]

The length scale, \( \tilde{d} \), is given by:

\[ \min \left(C_{DES} \Delta, \frac{\sqrt{k}}{\beta^{*} \omega}\right) \]

The turbulence viscosity is obtained using:

\[ \nu_t = a_1 \frac{k}{\max (a_1 \omega_, b_1 F_{23} \tensor{S})} \]

Default model coefficients

Base model coefficients:

\(\alpha_{k1}\) | \(\alpha_{k2}\) | \(\alpha_{\omega 1}\) | \(\alpha_{\omega 2}\) | \(\beta_1\) | \(\beta_2\) | \(\gamma_1\) | \(\gamma_2\) ----------—|--------—|--------—|--------------—|-------------—|-----------—|--—|---------— 0.85 | 1.0 | 0.5 | 0.856 | 0.075 | 0.0828 | 5/9 | 0.44

\(\beta^{*}\) | \(a_1\) | \(b_1\) | \(c_1\) -------------—|--------—|--------—|-------— 0.09 | 0.31 | 1.0 | 10.0

DES model coefficients:

\(CDESkom\)	\(CDESkeps\)
0.82	0.6

Initialisation

Usage

The model is specified using:

LES
{
    turbulence      on;
    LESModel        kOmegaSSTDES;
}

Boundary conditions

Inlet

Fixed value

Outlet

Constrained outlet

Walls

wall functions

Further information

Source code:

Foam::LESModels::kOmegaSSTDES

References:

Strelets [79]

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