Feedback control of vortex shedding from an inclined flat plate

Open- and closed-loop control of vortex shedding in two-dimensional flow over a flat plate at high angle of attack is numerically investigated at a Reynolds number of 300. Unsteady actuation is modeled as a body force near the leading or trailing edge and is directed either upstream or downstream. For moderate angles of attack, sinusoidal forcing at the natural shedding frequency results in phase locking, with a periodic variation of lift at the same frequency, leading to higher unsteady lift than the natural shedding. However, at sufficiently high angles of attack, a subharmonic of the forcing frequency is also excited and the average lift over the forcing period varies from cycle-to-cycle in a complex manner. It is observed that the periods with the highest averaged lift are associated with particular phase differences between the forcing and the lift, but that this highest-lift shedding cycle is not always stably maintained with open-loop forcing. We design a feedback algorithm to lock the forcing with the phase shift associated with the highest period-averaged lift. It is shown that the compensator results in a stable phase-locked limit cycle for a broader range of forcing frequencies than the open-loop control, and that it is able to stabilize otherwise unstable high-lift limit cycles that cannot be obtained with open-loop control. For example, at an angle of attack of 40°, the feedback controller can increase the averaged magnitude of force on the plate by 76% and increase the averaged lift coefficient from 1.33 to 2.43.