A wall stress model to predict high-Reynolds number flow over rough walls

Abstract

Wall-modeled large eddy simulation of turbulent channel flow with rough walls was performed for Reynolds numbers of Reτr=615–2080. The eddy viscosity parameter in a wall stress model was modified to include the effects of wall roughness. Symmetric and asymmetric channel flows were studied for transitionally and fully rough states with ks+=62 and 112, respectively. The wall shear stress was estimated based on the velocity field within the wall layer using the total shear stress term. For the wall layer, the matching point was located well above the height of the virtual roughness elements. The numerical predictions for the mean velocity profile and Reynolds stresses compared well with the experimental data. The prediction for the mean velocity shift due to roughness agreed with the experimental measurements and empirical correlations. For the asymmetric channel flows with roughness on only one wall, the numerical simulations correctly reproduced the displacement of the mean flow away from the rough wall. Overall, the proposed wall-model allows for the prediction of the effects of wall roughness without resolving the geometry of the roughness elements on the wall. This is consistent with the goal of performing large eddy simulations of wall-bounded flows at high-Reynolds numbers with minimal resolution of the wall region, which results in a much reduced computational cost.