Turbulent boundary layer over a divergent convergent superhydrophobic surface

Abstract

A direct numerical simulation of a spatially developing turbulent boundary layer over a divergent and convergent superhydrophobic surface (SHS) was performed over the range 800 < Reθ < 1200. The surface patterns were aligned along the streamwise direction. The SHS was modeled as a pattern of free-slip and no-slip surfaces. The gas fraction of the divergent and convergent SHS was the same as that for the straight SHS for a given slip area. The divergent and convergent SHS gave 21% more drag reduction than the straight SHS. Although the maximum value of the streamwise slip velocity was larger over the divergent and convergent SHS, the average slip velocity (Uslip/U∞) was larger over the straight SHS. The greater drag reduction was attributed to the manipulation of the secondary flow in the y–z plane and the changes in the turbulence structure. The streamwise vortices generated by the secondary flow over the divergent and convergent SHS were diminished which reduced drag relative to the flow over the straight SHS. The ejection and sweep motions were weak, and the vortical structure was attenuated near the wall over the divergent and convergent SHS. The skin friction contributions were explored using the velocity–vorticity correlation. The vortex stretching contribution dominated the skin friction budget. The reduced skin friction over the divergent and convergent SHS resulted mainly from reduced vortex stretching.