Modification of the Eddy Viscosity Based on the Wall Law at Adverse Pressure Gradient

This paper presents an attempt to enhance the predictive accuracy of the [Formula: see text]-type Reynolds-averaged Navier–Stokes turbulence model for adverse pressure gradient (APG) flows. The approach is grounded in refining the wall law governing the mean velocity profile within the inner layer of the turbulent boundary layer (TBL) under APG conditions. Drawing insights from direct numerical simulations (DNS), the wall law has been modified to maintain good consistency with the mean velocity profile provided by DNS data in flows with strong nonequilibrium effects. Further theoretical analysis shows that the analytical solutions of turbulent quantities satisfying the wall law under APG cannot satisfy the turbulent kinetic energy transport equation ([Formula: see text]-equation). Based on the analysis, an approximate solution for the eddy viscosity coefficient ([Formula: see text]) that complies with the [Formula: see text]-equation in flows with slight APG to correct [Formula: see text] in APG flows is proposed. Leveraging this approximate solution, the eddy viscosity in the shear stress transport model has been modified. The resultant modification induces an elevation of the mean velocity profile within the inner layer of the TBL at APG, leading to augmentation of the skin-friction coefficient.