Outer scaling of rough and smooth wall boundary layers under adverse pressure gradient conditions

Abstract

Experiments were conducted in adverse pressure gradient (APG) boundary layers over rough and smooth walls. Cases were considered with various pressure gradient strengths and upstream conditions. Profiles of mean velocity and turbulence quantities were measured at multiple streamwise stations to document the response of the flow to the APG. The data suggest that an APG causes attached turbulent eddies to become detached, and motivates the proposal of a new scaling to collapse the data in the outer part of the boundary layer. The distance from the wall is normalized as y*=(y − δ*)/(δ-δ*), where δ and δ* are the boundary layer thickness and displacement thickness, respectively. Velocity is scaled using the friction velocity at the start of the APG region. Data from all cases in which an APG is imposed on a canonical zero pressure gradient (ZPG) boundary layer show good collapse of the mean velocity and Reynolds stress profiles with the new scaling. For cases in which an APG followed directly after a favorable pressure gradient (FPG), the initial development of the boundary layer was changed, but after some distance the new scaling again collapsed the profiles.