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We have investigated the effects of rib surface curvature of a superhydrophobic wall in both laminar and turbulent channel flows. Direct numerical simulation is performed for laminar flows and large eddy simulation is performed for turbulent flows. The parametric study shows that a convex rib surface leads to a lower flow ratethan a flat rib for all Reynolds numbers. A concave rib surface firstly increases and then decreases the flow rate as the curvature angle becomes larger, where an optimal curvature angle exists to maximise flow rate. The value of the optimal curvature angle varies with the Reynolds number. A curved rib surface can modify the distribution of the mean velocity and turbulent statistics near the SH wall. Analysis shows that the overall effect of a curved rib surface on the flow rate is the combination of the wetted area augmentation and the change to the spanwise flow interaction, which depends on the curvature angle and the Reynolds number. The SH wall does not change the fundamental structures of near-wall vortices in turbulent flows. The ridge-groove pattern formed by the curved rib surface can provide additional drag reduction similar to that arising from the surface riblets.

Drag reduction by a superhydrophobic surface with longitudinal grooves: the effects of the rib surface curvature