kOmegaSSTCCM model
The kOmegaSSTCC is a two-equation RANS turbulence model based on the Shear Stress Transport (SST) k-ω model developed by Menter (Menter, Kuntz, and Langtry 2003) as included in standard OpenFOAM distribution. It incorporates a curvature correction (CCM) to account for the effects of streamline curvature and system rotation on turbulence production, following the approach proposed by Zhang and Yang (Zhang and Yang 2013).
Model Equations
The transport equations for the kOmegaSSTCCM model are given by:
\[ \begin{aligned} \frac{\partial (\rho k)}{\partial t} + \frac{\partial (\rho k u_j)}{\partial x_j} &= P_k f_{r1} - \beta^* \rho k \omega + \frac{\partial}{\partial x_j} \left[ (\mu + \sigma_k \mu_t) \frac{\partial k}{\partial x_j} \right], \\ \frac{\partial (\rho \omega)}{\partial t} + \frac{\partial (\rho \omega u_j)}{\partial x_j} &= P_\omega f_{r1}- \beta \rho \omega^2 + \frac{\partial}{\partial x_j} \left[ (\mu + \sigma_\omega \mu_t) \frac{\partial \omega}{\partial x_j} \right] + C_D, \end{aligned} \] where: \[ \begin{aligned} P_k &= \tau_{ij} \frac{\partial u_i}{\partial x_j}, \\ \tau_{ij} &= \mu_t \left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i} \right) - \frac{2}{3} \rho k \delta_{ij}, \\ S_{ij} &= \frac{1}{2} \left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i} \right), \\ P_\omega &= \frac{\gamma \rho}{\mu_t} P_k, \\ C_D &= 2(1 - F_1)\frac{\rho \sigma_{\omega 2}}{\omega} \frac{\partial k}{\partial x_j} \frac{\partial \omega}{\partial x_j}. \end{aligned} \]
Turbulent viscosity is computed as: \[ \mu_t = \frac{a_1 \rho k}{\max(a_1 \omega, S F_2)} \] with \(S = \sqrt{2 S_{ij} S_{ij}}\).
The curvature correction function \(f_{r1}\) is defined as: \[ f_{r1} = \max\left[\min\left(f_{r}, 1.25\right), 0\right] \] where \[ f_{r} = (1 + c_{r1})\frac{2r^*}{1+r^*}\left[1 - c_{r3} \arctan\left( c_{r2} \tilde{r} \right)\right] - c_{r1} \] with \[ \begin{aligned} r^* &= \frac{S}{\Omega}, \\ \tilde{r} &= \frac{\Omega}{S}\left(\frac{\Omega}{S} - 1\right). \end{aligned} \]
Model Coefficients
For the standars kOmegaSST model coefficients see (Menter, Kuntz, and Langtry 2003) or the OpenFOAM manual. The curvature correction coefficients are set to:
- \(c_{r1} = 1.0\)
- \(c_{r2} = 2.0\)
- \(c_{r3} = 1.0\)
Notes on OpenFOAM implementation
See the OpenFOAM manual for details on basic kOmegaSST model implementation.