Direct numerical simulation of random rough surfaces in turbulent channel flow

Direct numerical simulation (DNS) is performed to study the effects of random rough surfaces on the flow field in a turbulent channel flow at Re_τ = 400. The rough surface tiles generated synthetically from a prescribed energy spectrum using a power-law are provided by Flack and Schultz (personal communication). The rough surface is applied on the bottom wall only. The skin friction coefficient of the rough wall shows good agreement with the experimental results from Flack and Schultz. The turbulent statistics are compared to DNS results of the turbulent smooth channel flow. A velocity deficit is observed in the log-law region, indicating an increased drag due to roughness. Streamwise (x) and spanwise (z) velocity fluctuations are enhanced in the near-wall region. The pressure fluctuations are larger in the roughness sublayer when compared to a smooth channel flow. The mean momentum balance (MMB) is examined using the ratio of the viscous stress gradient to the Reynolds stress gradient. The results demonstrate that the qualitative features of the MMB layer of the smooth wall are maintained for the rough wall. The peak Reynolds stress location y_p shifts closer to the wall and is less than y⁺ = 40 (y_p of a smooth channel case). DNS of a rod-roughened channel flow is also performed for comparison. The probability density function (PDF) distribution of the streamwise and spanwise wall shear-stress components τ_yx and τ_yz for the rod-roughened and the random rough surface exhibits higher kurtosis than the smooth case. This implies that the probability of extreme events is higher for rough walls. For the rod-roughened case, the joint PDF distribution indicates the dominance of recirculation zones between adjacent rods. For the random rough surface, the presence of valleys leads to reverse flows near the roughness elements, however, they are not as strong as the recirculation zones in the rod-roughened case.