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Drag reduction by super-hydrophobic surfaces is investigated using Lattice Boltzmann simulations in turbulent channel flow. The super-hydrophobic surface is modeled as longitudinal arrays of slip/no-slip stripes of size 4 ≤ g+0 = w+0 ≤ 128, covering both channel walls, where g+0 and w+0 denote the widths of the slip and no-slip stripes, respectively, normalized with respect to the friction- velocity of the base flow and viscosity. An additional case was also run with g+0 = 28, w+0 = 4. All simulations were performed in channels of size 5h × 2.5h × 2h at a bulk Reynolds number of Reb = Ubh/ν = 3600 (Reτ0 ≈ 230), where h denotes the channel half height. Drag reductions of 5%, 11%, 18%, 23%, 38%, 47% and 51% were observed for g+0 = w+0 = 4, 8, 16, 32, 64, 128 and g+0 = 28, w+0 = 4, respectively. Mathematical analysis shows that the magnitude of drag reduction can be expressed as DR = Us/Ub +ε, where ε is zero in laminar flow, but attains a small non-zero value in turbulent flow proportional to the magnitude of DR. Results from both the present DNS studies as well as prior experiments [1] were found to fit this scaling. The one-point turbulence statistics show characteristics of combined slip described by [3]. When normalized in wall units, the turbulence statistics and structure remains nearly unchanged outside of a layer of thickness on the order of one slip-length from the walls. Drag reduction is found to be due to a weakening of the turbulence structures accompanied by a drop in turbulence production throughout the channel, but especially over the slip surfaces.
Author(s):
Amirreza Rastegari
University of Michigan, Ann Arbor
United States
Rayhaneh Akhavan
University of Michigan, Ann Arbor
United States