Evaluation of the momentum integral method to determine the wall skin friction in separated flows

The momentum integral-based method developed by Mehdi and White (Exp Fluids 50(1):43–51. https://​doi.​org/​10.​1007/​s00348-010-0893-1, 2011) for determining wall skin friction in turbulent wall-bounded flow is evaluated in separated flows in which independent estimates of wall skin friction are known. Owing to flow complexities, a direct measurement of the wall skin friction in separated flow is experimentally challenging. In this pursuit, the momentum integral-based method is particularly attractive as the method is mathematically exact and determination of the wall skin friction only requires measurement of the wall-normal profile of mean velocity and Reynolds shear stress. The present analysis uses existing experimental particle image velocimetry and direct numerical simulation data of flow over a backward-facing step as well as DNS over a smooth hump to demonstrate that the method is viable. The method is also shown to be viable in estimating the wall skin friction in flows over non-flat geometries.