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Shih quadratic k-ε

Properties​

  • Incompressible only

Model equations​

The turbulence kinetic energy equation is given by:

DDt(k)=∇ ∙ (Dk∇k)+G−ϵ \Ddt{k} = \div \left(D_k \grad k \right) + G - \epsilon

and the dissipation rate by:

DDt(ϵ)=∇ ∙ (Dϵ∇ϵ)+C1Gϵk−C2ϵ2k \Ddt{\epsilon} = \div \left( D_{\epsilon} \grad \epsilon \right) + C_1 G \frac{\epsilon}{k} - C_2 \frac{\epsilon^2}{k}

The turbulence generation, GG is given by:

G=[νt(∇u+(∇u)T)−τnl] ⁣:∇u G = \left[\nu_t \left( \grad \u + \left(\grad \u\right)^T \right) - \tensor{\tau}_{nl}\right] \colon \grad \u

where τnl\tensor{\tau}_{nl} is the non-linear stress.

Default model coefficients​

Usage​

The model is specified using:

RAS
{
    turbulence      on;
    RASModel        ShihQuadraticKE;
}

Further information​

Source code:

Reference:

  • Shih et al. 63