A systematic numerical investigation of turbulent channel flow over hydrophobic bottom wall: an analogue of rough wall turbulent boundary layer

Hydrophobic surfaces (HSs) can reduce the surface drag because air bubbles trapped inside their micro-grooves form shear-reduced or shear-free regions when water passes over. The corresponding drag reduction mechanism is affected by turbulence, slippery effects, and the so-called “roughness” effects because of the heterogeneity due to the existence of the hydrophobic region. To systematically study the roles of those effects, we carry out direct numerical simulations (DNSs) on turbulent channel flows over various micro-ridge structured HSs at the bottom wall. We explore slippery effects in both the streamwise and spanwise directions by comparing the results with those where only streamwise slip exists on bubble surfaces. To discover the roles of turbulence, spatial heterogeneity, and slippery effects on drag reduction, an equation relating the modified roughness function to Reynolds, dispersive, and wall shear stresses is derived and analyzed based on DNSs at different ridge-groove widths of HSs and Reynolds numbers. Although we neglect three-dimensional effects such as curvature of air-water interface, results reveal that it is proper to treat turbulent boundary layers over HSs as strip-type rough wall turbulent boundary layers where the drag reduction is quantified via a modified roughness function,