Properties🔗
- Two equation model for the turbulence kinetic energy, \(k\), and turbulence specific dissipation rate, \(\omega\).
- Aims to overcome the defficiencies of the standard k-omega model wrt dependency on the freestream values of k and omega
- Able to capture flow separation
- OpenFOAM variant is based on the 2003 model [49]
Model equations🔗
The turbulence specific dissipation rate equation is given by:
\[\Ddt{\rho \omega} = \div \left( \rho D_\omega \grad \omega \right) + \frac{\rho \gamma G}{\nu} - \frac{2}{3} \rho \gamma \omega \left( \div \u \right) - \rho \beta \omega^2 - \rho \left(F_1 - 1\right) CD_{k\omega} + S_\omega,\]and the turbulence kinetic energy by:
\[\Ddt{\rho k} = \div \left( \rho D_k \grad k \right) + \rho G - \frac{2}{3} \rho k \left( \div \u \right) - \rho \beta^{*} \omega k + S_k.\]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🔗
\(\alpha_{k1}\) | \(\alpha_{k2}\) | \(\alpha_{\omega 1}\) | \(\alpha_{\omega 2}\) | \(\beta_1\) | \(\beta_2\) | \(\gamma_1\) | \(\gamma_2\) |
---|---|---|---|---|---|---|---|
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 |
Initialisation🔗
For isotropic turbulence, the turbulence kinetic energy can be estimated by:
\[k = \frac{3}{2} \left(I |\u_{\ref}|\right)^{2}\]where \(I\) is the intensity, and \(\u_{\ref}\) a reference velocity. The turbulence specific dissipation rate follows as:
\[\omega = \frac{k^{0.5}}{C_{\mu}^{0.25} L}\]where \(C_{\mu}\) is a constant equal to 0.09, and \(L\) a reference length scale.
Usage🔗
The model is specified using:
RAS
{
turbulence on;
RASModel kOmegaSST;
}
Boundary conditions🔗
Inlet
Outlet
Walls
- wall functions
Further information🔗
Source code:
References:
- Base model: Menter and Esch [48]
- Updated model: Menter et al. [49]
- Corrections: consistent production terms from the 2001 paper as form in the 2003 paper is a typo, see [52]
- F3 term for rough walls: Hellsten [24]
See also: