Feedback control of von Kármán vortex shedding behind a circular cylinder at low Reynolds numbers

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Abstract
A computational study of the feedback control of von Kármán vortex shedding behind a circular cylinder at low Reynolds numbers is reported. The two‐dimensional Navier–Stokes equations with feedback are solved numerically. The control actuators are a pair of blowing/suction slots located at ±110° from the leading stagnation point. A single feedback sensor is used and the actuators are 180° out of phase with each other. Complete suppression of vortex shedding is achieved for the simulation at Reynolds number Re=60. The suppression window in the feedback sensor location xs is narrow. With the feedback sensor location fixed at the optimum location, vortex shedding becomes suppressed with increasing feedback gain α. However, further increase of the feedback gain destabilizes the flow again. At Reynolds number Re=80, and above, the feedback control stabilizes the primary vortex shedding mode, but a secondary mode which may be lower or higher in frequency than the primary depending upon the phase of the feedback (feedback sensor location xs) and the feedback gain α arises.