Drag reduction effect by sinusoidal superhydrophobic surface in turbulent channel flow

The drag reduction e ff ect of sinusoidal superhydrophobic surfaces (SHSs) in turbulent channel flow is investigated by means of direct numerical simulations. The microgrooves and micro-ridges in SHS are represented by free-slip and no-slip conditions, respectively. The simulations are performed under constant pressure gradient condition at two friction Reynolds numbers of 180 and 395. A parametric study shows that the drag reduction rate increases and gradually decreases as increasing the wavelength in sinusoidal SHSs. The sinusoidal SHSs, except in the short wavelength case, increase the drag reduction rate more than conventional straight SHSs with streamwise uniform microgrooves. We analyzed the contribution of the skin-friction drag by the FIK identity equation. The contributions from the slip velocity and the coherent RSS are significantly smaller than that of the laminar flow and random RSS. For the shorter wavelength cases, the contribution of the slip velocity depends on the Reynolds number. On the other hand, the contribution of the random RSS is scaled by the wavelength in the wall unit and the Reynolds number dependency is small.