Low Dimensional Modeling, Estimation and Control of a Cylinder Wake

The effect of feedback flow control on the wake of a circular cylinder at a Reynolds number of 100 is investigated in direct numerical simulation. Actuation is implemented as displacement of the cylinder normal to the flow. This control approach uses a low dimensional model based on a 15 mode double proper orthogonal decomposition (DPOD). A state estimator was designed to enable full state control by estimating all 15 modes. However, a single input control law that applies linear proportional and differential feedback to the estimate of the first DPOD mode alone is effective. The control law is then modified to allow for multiple inputs which include feedback based on the estimate of the mean flow shift mode. The shift mode provides corrections for spatial variations in the POD eigenfunctions which result from transient excitations of the cylinder. Results show that while both controller laws stabilize all 15 modes, the multi-input approach appears to be more effective. In the next step, the developed controllers will be validated in a high resolution simulation and in experiments