Direct numerical simulation of flow over riblets with the yaw angle

Direct numerical simulations of turbulent channel flow with riblets with various yaw angles ($\alpha )$ are performed to investigate the effect of the yaw angle on the flow and drag characteristics. The results show that the performance of drag reduction by the riblets is degraded with increasing yaw angle, but drag reduction is still achieved up to the yaw angle of about 20°, which is consistent with previous experimental results. As the yaw angle increases, stronger near-wall vortical structures are generated above riblet surfaces, and the form drag rapidly increases. To estimate the critical yaw angle at which drag reduction no longer occurs, we investigate the relationship between the drag and yaw angle. A scaling analysis is conducted to find the relationship between the form drag and yaw angle, and FIK identity is used to analyze the skin friction drag. We show that the variation of the drag force on riblets is proportional to the square of sin $\alpha $.