Assessment of reynolds stress predictions by two-equation turbulence models

In this paper, we evaluate the k - ε and k - ω turbulence models in terms of their accuracy in predicting the Reynolds shear stress in equilibrium boundary layers under arbitrary streamwise pressure gradients. The models are tested against the theoretical formulation of Perry et al. (1994) which is based on the law of the wall and law of the wake formulation of the mean velocity profile. Using this formulation, we study the effect Reynolds number and pressure gradient has on the eddy viscosity distribution in the boundary layers flows. In the viscous sub-layer and the buffer layer of zero-pressure gradient boundary layers, the normalized eddy-viscosity, v⁺_T, is found to be independent of the Reynolds number. A damping function is derived for the k - c model from the theoretical value of v⁺_T in the sub-layer and buffer layer, and is used to evaluate several low Reynolds number versions of the k - ε model. In the the defect layer, log layer and beyond, the ratio of v⁺_T to the Reynolds number based on the friction velocity is found to be self-similar, which is consistent with the theoretical formulation. Also, there is a strong influence of the pressure gradient on the distribution of V⁺_T in this region. The k - ε model prediction is found to be close to the theoretical values of V⁺_T for favorable and mild adverse gradient flows, whereas the k - ω model works better for strong adverse pressure gradient cases.