Supersonic turbulent boundary layer drag control using spanwise wall oscillation

Spanwise wall oscillation has been extensively studied to explore possible drag control methods, mechanisms and efficacy - particularly for incompressible flows. We performed direct numerical simulation for fully developed turbulent channel flow to establish how effective spanwise wall oscillation is when the flow is compressible and also to document its drag reduction (DR) trend with Mach number. Drag reduction DR is first investigated for three different bulk Mach numbers M_b D0:3, 0:8 and 1:5 at a fixed bulk Reynolds number Re_b D3000. At a given velocity amplitude AC (D12), DR at M_bD0:3 agrees with the strictly incompressible case; at M_bD0:8, DR exhibits a similar trend to that at M_b D 0:3: DR increases with the oscillation period TC to a maximum and then decreases gradually. However, at M_b D 1:5, DR monotonically increases with TC. In addition, the maximum DR is found to increase with M_b. For M_b D 1:5, similar to the incompressible case, DR increases with AC, but the rate of increase decreases at larger AC. Unlike the flow behaviour when incompressible, the flow surprisingly relaminarizes when it is supersonic (at AC D 18 and TC D 300) - this enigmatic behaviour requires further detailed studies for different domain sizes, Re_b and M_b. The Reynolds number effect on DR is also investigated. Although DR generally decreases with Re_b, it is less affected at small TC, but drops rapidly at large TC. We introduce a simple scaling for the oscillation period as T∗ DTC C lC I =lC C , with lC I and lC C denoting the mean streak spacing for incompressible and compressible cases, respectively. At the same semi-local Reynolds number Re∗τ c = Reτ √pc=√w=.μc=μw/(subscripts c and w denote quantities at the channel centre and wall, respectively), DR as a function of T∗ exhibits good agreement between the supersonic and strictly incompressible cases, with the optimal oscillation period becoming M_b-invariant as T∗ opt ≈100.