A critical assessment of turbulent flow over textured superhydrophobic surfaces

Abstract

Over the past century, a sustained effort has been expended on the research and development of surfaces that reduce the amount of drag experienced by a fluid as it passes by, motivated by both environmental and economic savings. Superhydrophobic surfaces have recently emerged as an attractive means to reduce the levels of skin-friction drag under both laminar and turbulent flow conditions. A superhydrophobic state is attained naturally or synthetically through a combination of surface topology and surface chemistry and can, in some cases, support a free-stress gas-liquid interface. In the presence of bulk fluid motion, the interfaces permit a finite slip velocity which has been credited to the reduction of the average wall shear stress. The fundamental drag reduction mechanism, however, remains unclear. In order to accurately resolve the full spectrum of turbulent scales, direct numerical simulations of fully turbulent channel flow over superhydrophobic textures at a friction Reynolds number of Reτ ≈ 180 were conducted. The instantaneous flow fields were subject to triple decomposition which permits statistical quantities to be accumulated in a phase-averaged form. From these phase-averaged statistics the mean, periodic and stochastic fluid motions can be considered independently. Following a detailed statistical analysis, the contributions of the mean, periodic and stochastic fluid motions towards the local levels of wall shear stress were determined by the derivation and evaluation of an appropriate skin-friction identity. In addition, a new modification to superhydrophobic surfaces is investigated by means of meandering the surface topology in the streamwise direction. Relative to a streamwise-aligned topology, it was anticipated that superior drag reduction would be achieved due to the addition of an oscillatory spanwise motion to the mean flow.