Closed-Loop Control of Vortex Shedding on a Two-Dimensional Flat-Plate Airfoil at a Low Reynolds Number ∗

Open- and closed-loop control of vortex shedding in two-dimensional flow over a flat plate at high angles 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. However, at sufficiently high angles of attack, subharmonics of the forcing frequency are 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 difference between the forcing and the lift. 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 phaselocked limit cycle for a larger 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 lift coefficient from 1.35 to 2.43, an increase of 80%.