k-omega Shear Stress Transport (SST)

- 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 [53]

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:

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

\(\alpha_{k1}\) | \(\alpha_{k2}\) | \(\alpha_{\omega 1}\) | \(\alpha_{\omega 2}\) | \(\beta_1\) | \(\beta_2\) | \(\gamma_1\) | \(\gamma_2\) |
---|---|---|---|---|---|---|---|

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 |

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.

The model is specified using:

RAS { turbulence on; RASModel kOmegaSST; }

Inlet

Outlet

Walls

- wall functions

Source code:

References:

- Base model:
*Menter and Esch*[51] - Updated model:
*Menter et al.*[53] - Corrections: consistent production terms from the 2001 paper as form in the 2003 paper is a typo, see [56]
- F3 term for rough walls:
*Hellsten*[26]

See also:

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