Influence of skewed three-dimensional sinusoidal surface roughness on turbulent boundary layers

Abstract

The impact of roughness skewness ( k s k ) on turbulent boundary layer (TBL) flow with a zero pressure gradient over three-dimensional (3D) sinusoidal rough surfaces was experimentally investigated using a single hotwire anemometer. Nine 3D sinusoidal profiles were manufactured with positive, negative, and zero roughness skewness values. Measurements were taken at three different freestream velocities for each surface and compared with smooth wall TBL results. This study covered a range of friction Reynolds numbers ( R e τ ) from approximately 1000 to 4000, with δ / k ≈ 20 ± 2 , where δ represents the local boundary layer thickness, and k is the maximum height of the roughness, measured from the valley to peak. The results indicate that the wall-unit normalized streamwise mean velocity profiles for all rough surfaces exhibit a downward shift compared to the smooth wall profiles. Surfaces with positive roughness skewness produced the highest drag, leading to the largest downward shift. The friction coefficient ( C f ) decreased as k s k decreased. The percentage increase in C f and Δ U + (the roughness function) was much larger when moving from negative to zero roughness skewness than when moving from zero to positive roughness skewness. The small differences in turbulence intensity profiles and higher-order turbulence statistics in the outer region of the TBL support the outer layer similarity hypothesis for the roughness considered in this study. The autocorrelation study revealed that surfaces with positive roughness skewness tend to shorten the average length of turbulence structures in the near-wall region.