Skin-friction Drag Reduction in Turbulent Channel Flow with Idealized Superhydrophobic Walls

Skin-friction drag reduction by super-hydrophobic (SH) surfaces was investigated using Lattice Boltzmann DNS in turbulent channel flow with SH longitudinal microgrooves on both walls. The liquid/gas interfaces in the SH microgrooves were modeled as flat, shear-free surfaces. Drag reductions (DR) ranging from $5\%$ to $47\%$ were observed for microgrooves of size $4 \le g^{+0} = w^{+0} \le 128$ in channels of bulk Reynolds number $Re_b= U_b h/\nu = 3600$ ($Re_{\tau_0} = u_{\tau_0}h/\nu \approx 230$), where $g^{+0}$ and $w^{+0}$ denote the widths of the slip and no-slip surfaces in base flow wall units. It is shown that in both laminar and turbulent flow, DR scales as $DR = U_s/U_b + \varepsilon$. In laminar flow, where DR is purely due to surface slip, $\varepsilon=0$. In turbulent flow, $\varepsilon$ remains negligible when the slip length is smaller than the thickness of the viscous sublayer. For $DR>40\%$, where the effect of surface slip can be felt in the buffer layer, $\varepsilon$ attains a small non-zero value. Analysis of turbulence statistics and turbulence kinetic energy budgets confirms that outside of a layer of size approximately one slip length from the walls, the turbulence dynamics proceeds as in regular channel flow with no-slip walls.