Analysis of the factors contributing to the skin friction coefficient in adverse pressure gradient turbulent boundary layers and their variation with the pressure gradient

This paper reports on a study of the various factors contributing to the skin friction in incompressible adverse pressure gradient turbulent boundary layer (APG-TBL) flows. Specifically, it deals with the contributions to the skin friction coefficient from the Reynolds stresses and the viscous effects and the role of the pressure gradient. The skin friction coefficient is calculated based on the theoretical decomposition for mean skin friction generation introduced by Renard and Deck (2016). This decomposition is compatible with spatially developing flows as it is applicable to every local streamwise position. The turbulent flows are generated through the direct numerical simulation of a TBL on a smooth flat plate with the desired farfield pressure gradient. It is observed that the Reynolds shear stress provides the dominant positive contribution to the skin friction coefficient for all the pressure gradient cases. However, with increasing adverse pressure gradient, the skin friction coefficient continues to decrease and approaches zero as the positive contribution from the Reynolds shear stress is diminished by the negative contribution of the pressure gradient. When the flow reaches the verge of separation, the predominant Reynolds shear stress contribution to the skin friction coefficient is from a spatially localized outer peak at an approximate height of the displacement thickness (y= δ₁) which coincides with the inflection point of the mean streamwise velocity. Even though, the decompositions in Renard and Deck (2016) and Fukagata et al. (2002) give a different distribution for the skin friction coefficient in the zero pressure gradient (ZPG) and the mild APG cases, both of the identities capture the dominant outer peak of the Reynolds shear stress contribution when the flow reaches the verge of separation. This emphasizes the growing importance of the outer layer dynamics with increasing pressure gradient as it pertains to skin friction generation.