Super-Hydrophobic Drag Reduction in Turbulent Channel and Pipe Flows

Abstract

In the present study, direct numerical simulations (DNS) of turbulent pipe and channel flows with superhydrophobic surface (SHS) are performed to investigate the influence of the turbulence dynamics and the resultant drag reduction of the flows under similar conditions. SHSs at the wall are modeled in spanwisealternating longitudinal regions with a boundary with no-slip and shear-free conditions, and the two parameters of the spanwise periodicity (P/δ) and SHS fraction (GF) within a pitch are considered. The skin friction drag for the pipe and channel flows over SHSs is continuously decreased with increases in P/δ and GF. However, the drag reduction (DR) rate in the pipe flows is greater than that in the channel flows with an accompanying reduction of the Reynolds stress. The enhanced performance of the DR for the pipe flow is attributed to the increased streamwise slip and weakened Reynolds shear stress contributions. In addition, a mathematical analysis of the spanwise mean vorticity equation suggests that the presence of a strong spanwise slip for the pipe flows makes a greater negative contribution of advective vorticity transport than the channel flows, resulting in a higher DR value.