Frequency Scaling Laws for Active Separation Control on Flat-Plate Wings

Dimensionless frequency scaling laws for active separation control on flat-plate wings, using dielectric barrier discharge plasma actuators, were examined on the basis of maximum increases in the lift coefficient and compared with hovering insect wing-flapping frequencies. Data for a range of angles of attack (15–35°), Reynolds numbers ([Formula: see text]), and semispan wing aspect ratios ([Formula: see text]) collapsed best when scaled with the streamwise-projected chord height. The “forcing Strouhal number” that produced the largest lift coefficient increments ([Formula: see text]) was linked to the conventional bluff-body Strouhal number by recognizing that drag and lift on flat-plate wings are directly proportional at a fixed angle of attack. Flowfield measurements used to determine the time-averaged separation bubble height and local velocity at separation showed that the universal Strouhal number ([Formula: see text])—developed for bluff-body and separation-bubble vortex shedding—can be further generalized to active separation control. Insect wing-flapping frequencies in hover were examined on the basis of Strouhal number scaling and corresponded to the optimum forcing range, although angle-of-attack estimates were a source of uncertainty. For flapping wings, the universal Strouhal number scaling can only be validated with accurate separation bubble height and separation velocity measurements.