# Shear Stress Transport (SST) Model with Rotation/Curvature Correction

Since the SST model relies on the Boussineq approximation, it also has poor performance for the prediction of flows with streamline curvature and system rotation because the Reynolds stress tensor is aligned to the mean strain rate tensor.

In order to remedy this problem, the rotation curvature correction for the SST 2003 model modifies the production terms in both the kinetic energy equation and eddy frequency equation (Smirnov and Menter, 2009). The corrected model yields better performance over the SST base model when predicting flows with strong streamline curvature and rotating flows caused by strong swirl or geometric constraints.

## Production Modeling

- ${f}_{r1}$ = $max\left(min\left[{f}_{rotation},1.25\right],0.0\right)$
- ${f}_{rotation}$ = $\left(1+{C}_{r1}\right)\frac{2{r}^{*}}{1+{r}^{*}}\left(1-{C}_{r3}ta{n}^{-1}\left[{C}_{r2}\widehat{r}\right]\right)-{C}_{r1}$
- $\widehat{r}=\frac{2{\text{\Omega}}_{ij}{\text{S}}_{ij}}{\sqrt{{\text{\Omega}}_{ij}{\text{\Omega}}_{ij}}D}\left(\frac{D{\text{S}}_{ij}}{Dt}+\left[{\epsilon}_{imn}{\text{S}}_{jn}+{\epsilon}_{jmn}{\text{S}}_{in}\right]{\text{\Omega}}_{m}^{rot}\right)$
- ${\text{\Omega}}_{ij}=\frac{1}{2}\left[\left(\frac{\partial \overline{{u}_{i}}}{\partial {x}_{j}}-\frac{\partial \overline{{u}_{j}}}{\partial {x}_{i}}\right)+2{\epsilon}_{mji}{\text{\Omega}}_{m}^{rot}\right]$
- ${\text{S}}_{ij}=\frac{1}{2}\left(\frac{\partial \overline{{u}_{i}}}{\partial {x}_{j}}+\frac{\partial \overline{{u}_{j}}}{\partial {x}_{i}}\right)$
- $D=\sqrt{max\left({S}^{2},0.09{\omega}^{2}\right)}$
- ${r}^{*}=\frac{S}{W}$
- $S=\sqrt{2{S}_{ij}{S}_{ij}}$
- $W=\sqrt{2{W}_{ij}{W}_{ij}}$

## Model Coefficients

${\beta}^{*}$ = 0.09, ${C}_{r1}$ = 1.0, ${C}_{r2}$ = 2.0, ${C}_{r3}$ = 1.0.