Statistical discussions on skin frictional drag of turbulence over randomly distributed semi-spheres

Abstract

The influence of dynamical effects of rough wall turbulence, namely velocity dispersion, drag force and turbulence, on rough wall skin friction coefficient is statistically discussed by performing direct numerical simulation of rough-walled open channel flows and analyzing spatial and Reynolds (double) averaged equations. Numerical calculations are conducted by the D3Q27 multiple-relaxation-time lattice Boltzmann method (MRT-LBM). For the rough surfaces, randomly distributed semi-spheres are considered. Analyzing an integrated double averaged momentum equation, a main contributor to the skin friction coefficient is found to be the turbulence contribution and a second contributor is the drag contribution, and the drag contribution particularly increases with increasing the equivalent roughness. Although the streamwise mean velocity dispersion is significantly induced by the acceleration/deceleration of the streamwise velocity due to the roughness elements, the wall-normal mean velocity dispersion is not significant. Consequently, the off-diagonal component of the dispersive covariant term is far smaller than the Reynolds shear stress and the velocity dispersion thus hardly contributes to an increase in the skin friction coefficient.