Suboptimal feedback control of vortex shedding at low Reynolds numbers

Abstract

The objective of this study is to develop a method of controlling vortex shedding behind a bluff body using control theory. A suboptimal feedback control procedure for local sensing and local actuation is developed and applied to the flow behind a circular cylinder. The location of sensors for feedback is limited to the cylinder surface and the control input from actuators is the blowing and suction on the cylinder surface. Three different cost functionals to be minimized (J₁ and J₂) or maximized (J₃) are investigated: J₁ is proportional to the pressure drag of the cylinder, J₂ is the square of the difference between the target pressure (inviscid flow pressure) and real flow pressure on the cylinder surface, and J₃ is the square of the pressure gradient on the cylinder surface, respectively. Given the cost functionals, the flow variable to be measured by the sensors and the control input from the actuators are determined from the suboptimal feedback control procedure. Several cases for each cost functional have been numerically simulated at Re = 100 and 160 to investigate the performance of the control algorithm. For all actuations, vortex shedding becomes weak or disappears, and the mean drag and drag/lift fluctuations significantly decrease. For a given magnitude of the blowing/suction, reducing J₂ provides the largest drag reduction among the three cost functionals.