Spalart-Allmaras Detached Eddy Simulation (DES)

Properties

• One equation model based on a modified turbulence viscosity, $\tilde{\nu}$

Model equations

The $\tilde{\nu}$ transport equation is given by:

\Ddt{\rho \tilde{\nu}} = \div \left( \rho D_\tilde{\nu} \tilde{\nu} \right) + \frac{C_{b2}}{\sigma_{\nu_t}} \rho \mag{\grad \tilde{\nu}}^2 + C_{b1} \rho \tilde{S} \tilde{\nu} \left(1 - f_{t2}\right) - \left(C_{w1} f_w - \frac{C_{b1}}{\kappa^2} f_{t2}\right) \rho \frac{\tilde{\nu}^2}{\tilde{d}^2} + S_\tilde{\nu}

where the length scale $\tilde{d}$ is defined by:

$$\tilde{d} = \min \left( \Psi C_{DES} \Delta, y \right)$$

and $\Psi$ is the low Reynolds number correction function:

$$\Psi^2 = \min \left[ 10^2, \frac{1 - \frac{1 - C_{b1}}{C_{w1} \kappa^2 f_w^{*}} \left[ f_{t2} + \left(1 - f_{t2}\right) f_{v2} \right]}{f_{v1} \max \left(10^{-10}, 1-f_{t2} \right)} \right]$$

Default model coefficients

$\sigma_{\nu_t}$	$C_{b1}$	$C_{b2}$	$C_{w1}$	$C_{w2}$	$C_{w3}$
2/3	0.1355	0.622	$\frac{C_{b1}}{\kappa^2} + \frac{1 + C_{b2}}{\sigma_{\nu_t}}$	0.3	2

$C_{v1}$	$C_{s}$	$C_{\mathit{DES}}$	$C_{k}$	$C_{t3}$	$C_{t4}$	$f_w^{*}$

7.1 |           0.3 |                      0.65 |    0.07      |   1.2          | 0.5 | 0.424

Initialisation

Usage

The model is specified using:

LES
{
    turbulence      on;
    LESModel        SpalartAllmarasDES;

    // Optional entries
    SpalartAllmarasDESCoeffs
    {
        // Apply low-Reynolds number correction; default = yes
        lowReCorrection     yes;
    }
}

Boundary conditions

Inlet

• fixedValue

Outlet

• Constrained outlet

Walls

• wall functions

Further information

Source code:

• Foam::LESModels::SpalartAllmarasDES

References:

• Principle reference: Spalart et al. 67
• Low Reynolds number correction: Spalart et al. 68