k-ω-SST Detached Eddy Simulation (DES)

Properties

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

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})}

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

The model is specified using:

LES
{
    turbulence      on;
    LESModel        kOmegaSSTDES;
}

Inlet

Outlet

Walls

Source code:

References: