Three dimensional simulations of a feedback controlled circular cylinder wake

Three dimensional open loop and closed loop feedback control simulations of the wake behind a circular cylinder are analyzed to explore the effect of spanwise phase variations. For feedback control, a low dimensional model based on Proper Orthogonal Decomposition (POD) in conjunction with a Least-Squares Estimation is used to estimate the flow state in the center plane behind the cylinder. In two dimensional simulations, we observed that at low Reynolds numbers (100 or less), the von Karman Vortex Street can be strengthened or weakened depending on the phase shift applied in the controller. At higher Reynolds numbers, if the vortex shedding is weakened, spanwise phase variations eventually lead to loss of control. The current computations show that the sensor plane can be successfully controlled for all cases. However, the vortices in other spanwise planes are out of phase and are amplified. Clearly, spanwise observability is necessary to stabilize the wake in three dimensions.

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