Toward a Universal Roughness Correlation

Abstract

The effects of several surface parameters on equivalent sand roughness (ks) in fully rough regime are investigated by means of direct numerical simulation (DNS) of flow in channels with different wall geometries at Reτ≅500. The roughness geometry is generated by randomly distributing roughness elements of random size and prescribed shape on a flat surface. The roughness generation approach allows systematic variation of moments of surface height probability density function (PDF), size distribution of roughness peaks, and surface slope. A total number of 38 cases are solved. It is understood that a correlation based on surface height skewness and effective slope (ES) can satisfactorily predict ks normalized with maximum peak-to-valley roughness height within a major part of the studied parameter space. Such a correlation is developed based on the present data points and a number of complementary data points from the literature. It is also shown that the peak size distribution can independently influence the skin friction; at fixed values of rms surface height, skewness, kurtosis, and ES, a surface with uniform size peaks causes higher skin friction compared to one with nonuniform peak sizes. Additionally, it is understood that a roughness generated by regular arrangement of roughness elements may lead to a significantly different skin friction compared to a random arrangement. A staggered and an aligned regular arrangement are examined in this paper and it is observed that the former produces significantly closer results to the corresponding random arrangement.