Turbulent skin friction drag reduction over dynamically rough superhydrophobic surfaces

The presence of dynamic wetting conditions on superhydrophic (SH) surfaces can lead to dynamically rough superhydrophobic surfaces. The dynamics of turbulence in the presence of such rough SH surfaces is investigated by direct numerical simulation (DNS) using free-energy lattice Boltzmann (FELB) methods in turbulent channel flows with arrays of SH longitudinal microgrooes on both walls. Simulations were performed in channel flows at a bulk Reynolds number of Re_b = 7200 (Re_τ0 ≈222), with SH longitudinal micrgrooves of groove width 15 ≤ g⁺⁰ ≤ 64 in base-flow wall-units, at nominal solid fractions of φ_s,n = 1/2 and 1/16, and groove aspect ratios of d/g = 1, with a viscosity ratio of N = μ_liq/μ_vap≈55, Weber number of We_τ0 = ρ_liq u_τ0 ν_liq/σ ≈ 3:65x10^-3, and advancing and receding contact angles of θ_adv = 112^o & θ_rec = 106^o. It is observed that dynamic surface roughness can result in drops of ~ 3 - 17% and ~ 11 - 35% in the magnitude of drag reduction (DR) at φ_s,n=1/2 and φ_s,n=1/16, respectively, compared to the drag reductions obtained with smooth, shear-free, superhydrophobic interfaces. These drops in DR arise primarily from dynamic contact line motion, through (i) an increase in the effective solid fraction, from the nominal solid fraction, φ_s,n, to a wetted solid fraction, φ_s,w > φ_s,n, which the fluid is exposed to, and (ii) the formation of streamwise corner vortices due to the motion of the interface and the contact line, which can act as surface roughness. The former leads to drops of 10% - 35% in the effective streamwise slip velocity, whereas the latter leads to enhancements of up to 200% in the effective spanwise slip. The scaling laws for DR, streamwise slip and spanwise slip, as well as the detailed turbulence statistics in the presence of dynamic rough SH surfaces will be discussed.