On predictive models for the equivalent sand grain roughness for wall-bounded turbulent flows

One of the long-standing goals of rough wall fluid dynamics research is to determine the drag penalty of surfaces based solely on their topographical parameters. The most important length scale or roughness parameter that best describes a surface in relation to friction drag has not been agreed upon yet, despite the many studies that, over the years, have attempted to identify the most appropriate surface parameter. The concept of an equivalent sand-grain roughness (ks) was introduced to standardize different types of roughness in wall-bounded turbulence, serving as an input parameter for predicting the roughness function ΔU+. To anticipate ΔU+ generated by a rough surface under turbulent flow conditions, experts use roughness correlations that establish a correspondence between the topographical characteristics of the surface and ks. Therefore, a chronological compilation of roughness correlations is presented, detailing the parameter ranges and types of roughness used in their development. This study evaluates the effectiveness of predictive correlation functions and aims to formulate a universal function by exploring a comprehensive assortment of three-dimensional (3D) surface textures available in the literature. The results suggest that a correlation based on surface height skewness (ksk) and streamwise effective slope (ESx) can predict the ratio (ks/kq), where kq is the root mean square roughness height for 3D roughness in the fully rough regime. Despite the fact that the correlation is restricted to 3D surface roughness, which is a more realistic representation, the model demonstrated a high level of accuracy in predicting ks for over 120 distinct rough surfaces.