Correlation for ReTheta_c

The correlation for the critical Reynolds number ${\mathrm{Re}}_{\theta c}$ is defined as follows:

where $C_{\mathrm{TU}1}$, $C_{\mathrm{TU}2}$, and $C_{\mathrm{TU}3}$ are Model Coefficients.

For the Gamma transition model, the quantities $T{u}_L$ and ${\lambda }_{\theta L}$ are approximated locally as:

and

where:

• $k$ is the turbulent kinetic energy.
• $\omega$ is the specific dissipation rate.
• $d$ is the distance to the nearest wall.
• $\nu$ is the kinematic viscosity.
• $n$ is the wall-normal unit vector.
• $\overline{v}$ is the mean velocity vector.

For the SA Gamma transition model, ${\lambda }_{\theta L}$ is given by Eqn. (1560) and $T{u}_L$ is a Model Coefficient.

The function $F_{PG}\left({\lambda }_{\theta L}\right)$ is calculated as: