Sensor Placement Based on Proper Orthogonal Decomposition Modeling of a Cylinder Wake

Abstract

The effectiveness of a sensor configuration for feedback flow control on the wake of a circular cylinder is investigated in both direct numerical simulation as well as in a water tunnel experiment. The research program is aimed at suppressing the von Karman vortex street in the wake of a cylinder at a Reynolds number of 100. The design of sensor number and placement was based on data from a laminar direct numerical simulation of the Navier Stokes equations for the unforced condition. A low-dimensional Proper Orthogonal Decomposition (POD) was applied to the vorticity calculated from the flow field and sensor placement was based on the intensity of the resulting spatial eigenfunctions. The numerically generated data was comprised of 70 snapshots taken from the steady state regime. A Linear Stochastic Estimator (LSE) was employed to map the velocity data to the temporal coefficients of the reduced order model. The capability of the sensor configuration to provide accurate estimates of the four low-dimensional states was validated experimentally in a water tunnel at a Reynolds number of 108. For the experimental wake, a sample of 200 Particle Image Velocimetry (PIV) measurements was used. Results show that for experimental data, the root mean square estimation error of the estimates of the first two modes was within 6% of the desired values and for the next 2 modes was within 20% of the desired values. This level of error is acceptable for a moderately robust controller.