Large eddy simulations of roughened channel flows: Estimation of the energy losses using the slope of the roughness

Several efforts have been made in the last decades to find a direct correlation between a geometric parameter of the wall roughness and the induced energy loss. The roughness, in fact, increasing the overall resistance of the current, causes the downward shift of the streamwise mean velocity profile, in the logarithmic region. This reduction is well known in literature as roughness function and it is indicated with the symbol ΔU+. This shift has been deeply investigated and related to several geometric parameters, both for regular or irregular roughness geometries. It is generally accepted that the equivalent sand grain ks can be used to estimate the roughness function, throughout a logarithmic law. Even though the fundamental importance of the equivalent sand grain roughness cannot be questioned, some researches pointed out that ks itself is not a physical length of the roughness and its value can be estimated once the mean velocity profile is achieved. Different parameters have been thus tested. Here, a new logarithmic law is proposed to determine the roughness function, once the wall geometry is know. Specifically, using Large Eddy Simulations (LES) to investigate on the effects of regular, as well as irregular, rough surfaces on the mean velocity profiles, it has been observed a logarithmic dependence between the Effective Slope (ES), which take into account both the height and the texture of the roughness elements, and the roughness function ΔU+. The proposed law has been supported by several literature findings.