Drag force in the open-loop control of the cylinder wake in the laminar regime

In this paper we are interested in identifying the physical mechanisms that accompany mean drag modifications in the cylinder wake flow subject to rotary control. We consider simple control laws where the obstacle rotates harmonically with frequencies varying from half to more than five natural frequencies. In our investigation we analyze the results of the numerical simulations at Re=150. All the simulations were performed using the vortex method, which in the paper is outlined and benchmarked. We confirm the earlier findings concerning mean drag reduction at higher forcing frequencies and show that for the considered values of Re this control technique is energetically inefficient. The main result is that changes of the mean drag are achieved by modifying the Reynolds stresses and the related mean flow correction. The controlled flows are carefully characterized in terms of these fields. Drag reduction is related to elongation of the recirculation bubble. It is argued that mean drag reduction is associated with control driving the mean flow toward the unstable symmetric state (the basic flow).