Outer-Layer Similarity in the Presence of Highly-Irregular Surface Roughness

Abstract

High-resolution particle image velocimetry measurements are made in the streamwise{ wall-normal plane of a zero-pressure-gradient turbulent boundary layer over smooth and rough walls at Reµ … 13000. The roughness considered herein is replicated from a surface scan of a turbine blade damaged by deposition of foreign materials and its topology is highly irregular and contains a broad range of topological scales. Two physical scalings of the same roughness topology are considered, yielding two difierent rough surfaces with ‐=k = 28 and ‐=k = 50 (where ‐ is the boundary-layer thickness and k is the characteristic height of the roughness). However, both surfaces yield ‐=ks > 40, where ks is the equivalent sand-grain height. The mean velocity deflcits along with the Reynolds normal and shear stress proflles for both roughness conditions collapse on the smooth-wall baseline in the outer layer when appropriately scaled by the friction velocity, u?. Probability density functions and quadrant analysis of the instantaneous events contributing to the mean Reynolds shear shtress show similar consistency between the smooth and rough cases when scaled on u?. The observed collapse of the smooth- and rough-wall statistics in the outer layer supports Townsend’s wall similarity hypothesis for ∞ow over the highly-irregular roughness considered herein.