Spalart-Allmaras Detached Eddy Simulation (DES)

Note
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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

Outlet

Walls

  • wall functions

Further information

Source code:

References:

  • Principle reference: Spalart et al. [73]
  • Low Reynolds number correction: Spalart et al. [74]

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