Mach number effect on drag control via spanwise wall oscillation in wall-bounded turbulent flows

The spanwise wall oscillation (SWO) is known to substantially reduce the skin-friction drag in wall-bounded turbulent flows. To understand the scope and limitations of this flow control for compressible flows, direct numerical simulations of isothermal channel flow with SWO are performed. At a fixed bulk Reynolds number Re_b of 3000, we investigate subsonic and supersonic flows at bulk Mach numbers Ma_b of 0.8 and 1.5, respectively. The drag reduction DR as a function of the control parameters (namely, maximum wall velocity A⁺ and oscillation period T⁺; + denotes wall units scaling) has similar trend as the incompressible case: DR increases monotonically with A⁺, but varies non-monotonically with T⁺. For a given maximum wall velocity A⁺(=12), similar maximum DR is achieved as in the incompressible cases at the same Re_τ. However, the optimal oscillation period T⁺ is found to slightly increase with Ma. The flow statistics and physics are examined to explain the mechanism for drag reduction. Similar to the incompressible case, the coherent structures are highly suppressed by SWO. These results suggest that significant DR can still be achieved via SWO even when the compressibility effect is considered. The effectiveness of SWO at higher Re’s and Ma’s is being explored.