Turbulence and skin friction modification in channel flow with streamwise-aligned superhydrophobic surface texture

Direct numerical simulations of turbulent flow in a channel with superhydrophobic surfaces (SHS) were performed, and the effects of the surface texture on the turbulence and skin-friction coefficient were examined. The SHS is modeled as a planar boundary comprised of spanwise-alternating regions of no-slip and free-slip boundary conditions. Relative to the reference no-slip channel flow at the same bulk Reynolds number, the overall mean skin-friction coefficient is reduced by 21.6%. A detailed analysis of the turbulence kinetic energy budget demonstrates a reduction in production over the no-slip phases, which is explained by aid of quadrant analysis of the Reynolds shear stresses and statistical analysis of the turbulence structures. The results demonstrate a significant reduction in the strength of streamwise vortical structures in the presence of the SHS texture and a decrease in the Reynolds shear-stress component ⟨R12⟩ which has a favorable influence on drag over the no-slip phases. A secondary flow which is set up at the edges of the texture also effects a beneficial change in drag. Nonetheless, the skin-friction coefficient on the no-slip features is higher than the reference levels in a simple no-slip channel flow. The increase in the skin-friction coefficient is attributed to two factors. First, spanwise diffusion of the mean momentum from free-slip to no-slip regions increases the local skin-friction coefficient on the edges of the no-slip features. Second, the drag-reducing capacity of the SHS is further reduced due to additional Reynolds stresses, ⟨R13⟩.