Predictive modeling of boundary-layer flows with pressure gradients

This study has two objectives. Firstly, we investigate how well existing RANS models predict the skin friction coefficient and incipient flow separation for a boundary layer subjected to pressure gradients. Secondly, we develop a new physics-based model by leveraging a recently established universal mean velocity transformation. Four existing models are considered: the local equilibrium wall model with and without Kay’s correction, the one-equation transport Spalart-Allmaras model, and the two-equation transport Wilcox k-omega model, and data in previous studies by Volino, Marusic, Vinuesa, Yang and coauthors are used. While the existing models prove to be quite accurate under mild and moderate pressure gradients, they fall short when facing strong pressure gradients. In contrast, the new model performs reasonably well across all conditions investigated. In addition to presenting the results, we will also attempt to provide a physical explanation for observed behaviors. In particular, the local models predict instant response of the Reynolds stresses to pressure gradients, and the wall treatments in the two transport models are based on the equilibrium law of the wall, both of which are not physical.