Open-loop active flow control of a periodically moving body based on resolvent analysis

We design an open-loop active flow control for separated flows around a rigid body undergoing a periodic motion based on resolvent analysis. A linear time-periodic system for control is obtained by linearizing the non-inertial incompressible vorticity equation in the body-fixed frame about a time-averaged base flow. Using the Lyapunouv–Floquet transformation, the linear time-periodic system is transformed into a similar linear time-invariant system, whose resolvent is analyzed to obtain optimal locations and Strouhal number to excite the transformed linear system. A plunging circular cylinder is selected as a demonstration of the developed method. The cylinder is plunging at a Strouhal number of 0.36 and a Reynolds number of 500. The current Floquet-resolvent analysis reveals that the transformed linear system can be excited with actuations near the separation points on the cylinder surface at an optimal Strouhal number of 0.1464. Simulations show that the active control with tangential actuations is capable of reducing the lift fluctuation by up to 25.7% when the flow is actuated near the predicted harmonic and subharmonic frequencies of the optimal Strouhal number.