On the estimation of the roughness function using a logarithmic scaling of the effective slope

Abstract

LESs are carried out in turbulent channel flows to investigate on the effects of irregular rough surfaces on the mean velocity profiles. In rough walls, due to increase of resistance induced by the wall irregularities, the mean velocity is reduced despite the same pressure gradient drives the current. In literature the downward shift of the streamwise mean velocity profile, in the logarithmic region, is called Roughness Function ΔU+. This shift has been deeply investigated and related to several geometrical parameters, both for regular and irregular roughness geometries. In the fully rough regime it was observed that the roughness function is related to the equivalent sand grain ks through a logarithmic law. Following this theory here a novel logarithmic approach is proposed to determine the roughness function. The results showed that, among the geometrical parameters that characterise the wall geometries, the Effective Slope (ES), which take into account both the height and the texture of the roughness elements, correlates well with the roughness function ΔU+.