Partially-averaged Navier-Stokes method for turbulent flows: k-w model implementation

Kolmogorov's k-ω model lacked a production term in the equation for ω making the model flawed. Also the model lacked a molecular diffusion term making the model strictly applicable to high Reynolds number flows and unable to be integrated through the viscous sub-layer. Wilcox 2 proposed the k-ω model with the production term included in the ω equation. This two equation model has proven to be numerically more stable that the standard k-e model primarily in the viscous sub-layer near the wall. The model does not require explicit wall-damping functions compared to the k-e model as the specific dissipation rate, ω is large in the wall region. In a numerical computation, specifying the wall boundary condition requires only the specification of the distance from the wall to the first point off the wall without any viscous corrections. In the logarithmic region, the model gives good agreement with experimental results for adverse pressure gradient flows due to the lack of a cross diffusion term in the ω equation. The model predicts the turbulent kinetic energy behavior close to the solid boundary with good accuracy and even describes the boundary-layer transition reasonably well. However, the lack of a cross diffusion term causes the model to be sensitive to small freestream values of ω, adversely affecting the performance of the model in free shear flows. Even though, the sensitivity of the model is reduced for complex flows 3 such as flow past a circular cylinder, the presence of small freestream ω in the wake imparts ambiguity in the predicted results. In the present work, we consider the revised k-ω model 4