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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

# 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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