Drag reduction in Turbulent Channel Flow with Longitudinal Arrays of Slip/no-slip Stripes on the Walls

Drag reduction in channels covered with longitudinal arrays of slip/no-slip stripes on the walls has been investigated using DNS with the lattice Boltzmann method. Computations were performed in channels of size $5h \times 2.5h \times 2h$ at a $Re_{b}=3600$ ($Re_{\tau 0} \approx 230$) with stripes of size $0.02 \le g/h=w/h \le 0.56$ corresponding to $4 \le g^{+0}=w^{+0} \le 128$ where $g=w$ denotes the widths of the slip/no-slip stripes and $h$ is the channel half-width. Unlike in laminar flow, where the magnitude of DR is controlled by geometrical parameters $g/h$ and $w/h$, in turbulent flow the magnitude of DR is found to scale with $g^{+0}=w^{+0}$, independent of Reynolds number. DRs of $5\%,11\%,18\%,23\%,38\%,47\%$, and slip velocities of $U_{s}/U_{b}=0.06, 0.10, 0.15, 0.23, 0.32, 0.37$ were observed for $g^{+0}=w^{+0}= 4, 8, 16, 32, 64, 128$, respectively. Analysis of the mechanism of DR reveals that in the LDR regime ($DR<25\%$, $g^{+0} \le 32$, $U_s/U_b<0.25$), DR is due to a combination of wall-slip and change in the anisotropy structure of turbulence near the wall, while in the HDR regime ($DR> 30\%$, $g^{+0} \ge 64$, $U_s/U_b>0.3$), DR is primarily due to cessation of turbulence production over the slip stripes due to the large slip velocities over these regions.