Direct numerical simulation of turbulent channel flow with an idealized superhydrophobic surface having an air layer

Abstract

The slip effect on a superhydrophobic surface in a turbulent boundary layer determines the performance of a skin-friction drag reduction, and it is affected by the superhydrophobic grating parameters. With the assumption that the air-water interface is flat, direct numerical simulations of turbulent channel flow with superhydrophobic surfaces having an air layer are conducted in the present study.

First, an idealized superhydrophobic surface (i.e., without any supporting structures inside the air layer) is considered as a slippery surface for keeping only its useful effects (Busse et al. 2013

Jung et al. 2016). Inside the air layer, both the shear-driven flow and recirculating flow with zero net mass flow rate are considered. With increasing air-layer thickness, the slip length, slip velocity and percentage of drag reduction increase. At a given air-layer thickness, the shear-driven flow in the air layer supplies more slip than the recirculating flow. It is shown that the slip length is independent of the water-flow condition and depends only on the air-layer geometry. The amount of drag reduction obtained is in between those by the empirical formulae from the streamwise slip only and isotropic slip, indicating that the present air-water interface generates an anisotropic slip, and the streamwise slip length ($b_x$) is larger than the spanwise one ($b_z$). From the joint probability density function of the slip velocities and velocity gradients at the interface, we confirm the anisotropy of the slip lengths and obtain their relative magnitude ($b_x/b_z=4$) for the present idealized superhydrophobic surface. It is also shown that the Navier slip model is valid only in the mean sense, and it is generally not applicable to fluctuating quantities.

Second, the superhydrophobic surface with longitudinal grooves is considered. The surface grating parameters are the air-layer thickness, pitch length and gas fraction. A wide range of pitch lengths are simulated from microscale $O(1)$ to macroscale $O(10^2)$ in the viscous wall unit. The minimal channel flow (Jimenez & Moin 1991) is adopted for a microgrooved surface. Since the small pitch length is accompanied by small groove width, the growth of the slip velocity at the air-water interface is inhibited. At a large pitch length, however, the percentage of drag reduction obtained is saturated with the gas fraction as the air-layer thickness increases. In this case, the slip lengths for the instantaneous velocity components ($b_x$ and $b_z$) varies at the air-water interface in the spanwise direction.