k-ω Shear Stress Transport (SST)

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

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

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