Andrzej Styczek

Optimal rotary control of the cylinder wake in the laminar regime

In this paper we develop the Optimal Control Approach to the rotary control of the cylinder wake. We minimize the functional which represents the sum of the work needed to resist the drag force and the work needed to control the flow, where the rotation rate φ(t) is the control variable. Sensitivity of the functional to control is determined using the adjoint equations. We solve them in the “vorticity” form, which is a novel approach and leads to computational advantages. Simulations performed at Re=75 and Re=150 reveal systematic decrease of the total power and drag achieved using a very small amount of control effort. We investigate the effect of the optimization horizon on the performance of the algorithm and the correlation of the optimal controls with the changes of the flow pattern. The algorithm was also applied to the control of the subcritical flow at Re=40, however, no drag reduction was achieved in this case. Based on this, limits of the performance of the algorithm are discussed.

Theoretical and Computational Study of the Wake Control Problem

In the present paper we are concerned with the problem of active drag minimization in the incompressible wake flow generated by a circular cylinder with turbulent Reynolds number. The objectives of the work are twofold: first, we show evidence coming from numerical simulations that a properly designed open-loop algorithm is indeed capable of performing effective flow control resulting in significant drag reduction, and then, with this motivation, we outline a rigorous feedback algorithm based on Optimal Control Theory. In both cases control is performed by rotary motion of the circular cylinder whose boundary we denote Γ0. The flow domain Ω extends to infinity. By an open-loop algorithm we mean a scheme in which the control is determined a priori, without any reference to the instantaneous flow field information and/or its history. Because of computational limitations, throughout the paper we will study two-dimensional (2D) flows only.