The open source CFD toolbox
k-omega-SST Delayed Eddy Simulation (DES)

Note
Under construction - please check again later

# Properties

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

# Model equations

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:

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

# Default model coefficients

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

# Usage

The model is specified using:

LES
{
turbulence      on;
LESModel        kOmegaSSTDES;
}


# Boundary conditions

Inlet

Outlet

Walls

• wall functions

Source code:

References: