Lattice Boltzmann Simulations of Skin-Friction Drag Reduction in Turbulent Channel Flow with Slip/No Slip Wall Ridges

To gain a better understanding of the mechanisms at work in skin friction drag reduction with superhydrophobic surfaces, Lattice Boltzmann simulations were performed in turbulent channels with alternating slip/no slip ridges on the walls. Simulations were performed in turbulent channels of size $5h \times 2.5 \times 2h$ and $10h \times 5h \times 2h$ at a base Reynolds number of $Re_\tau \sim 230$. Alternating slip/no slip ridges of width $4 \le w+ \le 140$, aligned in the streamwise direction, all with the same fractional area of slip boundary, were studied. Drag reductions of 4\%, 8\%, 21\%, 33\% and 47\%, corresponding to slip velocities of $U_{slip}/U_{bulk}=$ 0.05, 0.1, 0.26, 0.31 and 0.36 were observed for $w+=g+=$ 4, 8, 40, 70 and 140, respectively. The mean velocity profiles display the characteristics of combined slip described by Min and Kim [Min et al. 2004]. The streamwise and spanwise turbulence intensities show large slips at the wall, the magnitude of which increases with increasing drag reduction. Examination of the anisotropy invariant maps shows a shift of turbulence structure towards the one-dimensional turbulence limit near the wall with increasing drag reduction. For $z^+ > 25$, the turbulence structure returns to the isotropic limit.