Angular momentum integral equation on turbulent boundary layers with pressure gradient

Turbulent boundary layers (TBL) encountering pressure gradients have been the subject of several works because of their engineering application. A fundamental understanding of their physics is essential for modeling and prediction of engineering quantities such as skin friction coefficient. In this study, we apply the angular momentum integral (AMI) equation and re-formulate it to determine the contribution of different flow phenomena such as pressure gradient and Reynolds shear stress to skin friction. These flow phenomena are represented as torques about a length scale, l, that is obtained from zero-pressure-gradient (ZPG) Blasius laminar solution. Such a choice isolates the skin friction of a ZPG laminar flow at the same Reynolds number and evaluates the other flow phenomena relative to the laminar friction. The AMI equation is applied to a set of DNS and LES TBL simulations undergoing various adverse pressure gradients. Although the contribution of the edge pressure gradient and mean fluxes to skin friction respond substantially according to the strength of the pressure gradient, the explicit turbulent contribution is less sensitive to the edge pressure gradient. The study of the TBL history on the statistics using the AMI budget yields a Clauser parameter based on l, β_l. We observe a more robust collapse of the mean velocity and Reynolds stress profiles at matching β_l and Reynolds numbers for the TBL dataset compared with the previous studies.