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k-omega 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 [53]

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 [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]