Two-equation turbulence modeling of an oscillatory boundary layer under steep pressure gradient

A total of seven versions of two-equation turbulence models (four versions of low Reynolds number k-ε model, one k-ω model and two versions of k-ε I k-ω blended models) are tested against the direct numerical simulation (DNS) data of a one-dimensional oscillatory boundary layer with flat crested free-stream velocity that results from a steep pressure gradient. A detailed comparison has been made for cross-stream velocity, turbulent kinetic energy (TKE), Reynolds stress, and ratio of Reynolds stress and turbulent kinetic energy. It is observed that the newer versions of k-ε model perform very well in predicting the velocity, turbulent kinetic energy, and Reynolds stress. The k-ω model and blended models underestimate the peak value of turbulent kinetic energy that may be explained by the Reynolds stress to TKE ratio in the logarithmic zone. The maximum bottom shear stress is well predicted by the k-ε model proposed by Sana et al. and the original k-ω model.