Effects of Actuation Frequency on Flow Control Applied to a Wall-Mounted Hump

Active flow control, and particularly unsteady mass injection (synthetic jets), promotes reattachment of naturally separated flows and can increase lift and decrease drag on airfoils at high angles of attack. Synthetic-jet actuators are typically characterized by the unsteady momentum coefficient =(ρ_sh_s)/(0.5ρ_(∞)U^2_(∞)c) and the actuation frequency F^(+)= fX_sep/U_∞, where ρ_s and u_s are the density and velocity of the injected fluid, respectively; h_s is the slot velocity; f is the actuation frequency; and X_sep is the separation distance or chord length, depending on the author or application. Actuation frequencies are often chosen to be on the order of the natural large-scale shedding frequency, or F^(+) ~ O(1). At this frequency, large-scale vortex shedding is induced, which increases the entrainment rate and promotes deflection of the separated shear layer toward the surface. Recent investigations have looked at a second regime of actuation frequencies, which are typically an order of magnitude higher than the most dominant natural frequency in the separated flow and are designed to excite Kelvin–Helmholtz instabilities in the boundary layer. In the airfoil experiments of Amitay and Glezer and Glezer et al., high-frequency excitation was found to be more effective in improving the aerodynamic performance than actuation at lower frequencies by increasing the suction force immediately after the leading edge actuation location. Simulations performed by Visbal and Visbal et al. have shown that plasma-based actuation pulsed at frequencies in the range of F^(+) = 4–8 are effective in promoting laminar-turbulent transition and suppressing separation. However, when applied to a fully turbulent boundary layer, the plasma actuation required significantly more power to achieve a reduction in separation bubble size. Other airfoil simulations at low or transitional Reynolds number have found that actuation close to the fundamental shear-layer frequency is ineffective, and forcing closest to the natural shedding frequency is more optimal; however, such two-dimensional simulations may not be accurately capturing the three-dimensional flow physics. Similar results are seen in the numerical experiments by Dandois et al. on a backward-facing step, in which the separation bubble length increased with high-frequency forcing. Here, we briefly report results for a compressible, large-eddy simulation (LES) of flow past a wall-mounted hump at high Reynolds number where oscillatory control is applied at F^(+) ~ O(10). The LES with F^(+) ~ O(1) was previously validated and found to compare favorably with extensive experimental results of this geometry. Many other computational results in the low-frequency regime were reported in the NASA Langley Computational Fluid Dynamics Validation workshop. We simulate the flow at Re_c = 500,000 and Mach numbers of 0.25 and 0.6, the latter of which is significantly higher than previous simulations of high-frequency actuation