v2-f

Table of Contents

• Properties
• Model equations
• Default model coefficients
• Usage
• Further information

Note

Under construction - please check again later

Properties

Model equations

Dissipation equation

\[ \Ddt{\rho \epsilon} = - \div \left(\rho \u \epsilon \right) + \div \left( \rho D_{\epsilon} \grad \epsilon \right) + C_{\epsilon1} \rho \frac{G}{T_s} - \frac{2}{3} C_{\epsilon 1} + C_{\epsilon 3} \rho \left(\div \u \right) \epsilon - C_{\epsilon 2} \frac{\rho}{T_s} \epsilon + S_\epsilon \]

Turbulent kinetic energy equation

\[ \Ddt{\rho k} = \div \left(\rho D_k \grad k\right) + \rho G - \frac{2}{3}\rho \left(\div \u\right) k - \rho \epsilon + S_k \]

Relaxation function equation

\[ - \div^2 f = - \frac{f}{L^2} - \frac{1}{L^2 k} \left(\alpha - C_2 G \right) \]

Turbulence stress normal to streamlines equation

\[ \Ddt{\rho \nu^2} = \div \left( \rho D_k \grad \nu^2 \right) + \rho \min \left(k f, C_2 G - \alpha \right) - N \rho \frac{\epsilon}{k} \nu^2 + S_{\nu^2} \]

Where

\[ \alpha = \frac{1}{T_s} \left(\left(C_1 - N\right) \nu^2 - \frac{2}{3} k \left(C_1 - 1\right) \right) \]

Default model coefficients

Usage

The model is specified using:

RAS
{
    turbulence      on;
    RASModel        v2f;
}

Further information

Source code:

• Foam::RASModels::v2f

References:

• Base model: Lien and Kalitzin [45]
• Modifications: Davidson et al. [14]

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