Predictions of the effective slip length and drag reduction with a lubricated micro-groove surface in a turbulent channel flow

We perform direct numerical simulations of a turbulent channel flow with a lubricated micro-grooved surface to investigate the effects of this surface on the slip characteristics at the interface and the friction drag. The interface between water and lubricant is assumed to be flat, i.e. the surface-tension effect is neglected. The solid substrate, where a lubricant is infused, is composed of straight longitudinal grooves. The flow rate of water inside the channel is maintained constant, and a lubricant layer under the interface is shear driven by the turbulent water flow above. A turbulent channel flow with a superhydrophobic (i.e. air-lubricated) surface having the same solid substrate configuration is also simulated for comparison. The results show that the drag reduction with the liquid-infused surface highly depends on the lubricant viscosity as well as the groove width and aspect ratio. The amounts of drag reduction with the liquid-infused surfaces are not as good as those with superhydrophobic surfaces, but are still meaningfully large. For instance, the maximum drag reduction by the heptane-infused surface is approximately 13 % for a rectangular groove whose spanwise width and depth in wall units are 12 and 14.4, respectively, whereas a superhydrophobic surface with the same geometry results in a drag reduction of 21 %. The mean slip length normalized by the viscosity ratio and groove depth depends on the groove aspect ratio. The ratio of fluctuating spanwise slip length to the streamwise one is between 0.25 (ideal surface without groove structures) and 1 (i.e. isotropic slip), indicating that the slip is anisotropic. Using the Stokes flow assumption, the effective streamwise and spanwise slip lengths are expressed as a function of groove geometric parameters and lubricant viscosity. We also suggest a predictive model for drag reduction with the heptane-lubricated surface by combining the predicted effective slip lengths with the drag reduction formula used for riblets (Luchini et al., J. Fluid Mech., vol. 228, 1991, pp. 87-109). The predicted drag reductions are in good agreements with those from the present and previous direct numerical simulations.