Feedback flow control on a plunging circular cylinder

Abstract

In this study, closed-loop flow control is implemented in order to attenuate the lift fluctuation of a circular cylinder oscillating harmonically in a uniform stream. Through the numerical simulation of the incompressible flow around the oscillating cylinder, a time-invariant base flow is obtained by averaging the flow over time to linearize the incompressible Navier–Stokes equations in the cylinder-fixed frame. A resolvent-analysis-based model derived from the linearized equations is used to design two linear feedback control schemes. First, the loop-shaping method is adopted to design a robust controller that maximizes the stability margin and rejects the disturbance imposed by the periodic boundary condition. The simulation shows this control scheme can reduce the lift fluctuation by 3.3%. Furthermore, the model reference adaptive control is introduced to deal with the time-varying linear plant due to the addition of the controller. A direct approach of this control is adopted to directly update the time-varying adaptive control gains. The results show that the adaptive controller successfully reduces lift fluctuation by 19.7%.