Structure and Dynamics of Turbulence in Super-Hydrophobic Channel Flow

Abstract

The structure and dynamics of turbulence in turbulent channel flow with super-hydrophobic (SH) walls has been investigated using DNS with Lattice Boltzmann methods. The channel walls consisted of longitudinal arrays of SH microgrooves of width g, separated by distances of w. The liquid/gas interfaces in the SH walls were modeled as idealized, flat, shear-free surfaces. Simulations were performed at a bulk Reynolds number of \(Re_b = U_{bulk} h/\nu = 3600\), corresponding to \(Re_{\tau _0} = u_{\tau _0} h / \nu \approx 223\). Drag reductions (DR) of 5–47 % and 51–83 % were obtained with \(g/w=1\), and \(g/w = 7\) and \(g/w = 15\), respectively. DR was found to be primarily due to surface slip. Mathematical analysis shows that the magnitude of DR in both laminar and turbulent flow is given by \(DR = U_{slip}/U_{bulk} + O(\varepsilon )\). In laminar flow, where DR is purely due to surface slip, \(\varepsilon \) is zero. In turbulent flow, \(\varepsilon \) attains a small nonzero value at high DR, reflecting additional DR effects resulting from modification of the turbulence dynamics in the interior of the flow due to the presence of the SH surface. Analysis of the turbulence statistics and kinetic energy budgets in the drag-reduced flow reveals that the influence of the SH surface remains confined to a surface layer of thickness on the order of the SH microgrooves width, g. Outside of this layer, the ‘normalized’ turbulence dynamics proceeds as in regular turbulent channel flow. Within the surface layer, the presence of the pattern of longitudinal microgrooves on the SH surfaces gives rise to spanwise variations in all Reynolds-averaged turbulence quantities, leading to development of a mean secondary flow and additional turbulence production and Reynolds shear stresses within the surface layer of the SH channel.