Sensor placement for closed-loop flow control of a "D" shaped cylinder wake

The effectiveness of a sensor configuration, based solely on body surface pressure readings, for feedback flow control of the wake of a D shaped cylinder is investigated by DNS. The research is aimed at suppressing unsteady loads resulting from the von Kármán vortex shedding in the wake of bluff bodies at a Reynolds number range of 100-1000. The design of sensor number and placement was based on data from a laminar direct numerical simulation of the Navier Stokes equations for the baseline condition. A low-dimensional Proper Orthogonal Decomposition (POD) procedure was applied to the pressure and stream-wise velocity of the flow field. The sensor placement was based on the intensity of the spatial Eigen-functions obtained by applying POD to 286 surface pressures. The numerically generated data was comprised of 100 snapshots taken from the flow regime that corresponds to steady state vortex shedding. A Linear Stochastic Estimator (LSE) was employed to map the pressure signals from the body mounted sensors to the temporal coefficients of the reduced order model of the wake flow field in order to provide accurate yet compact estimates of the low-dimensional states. For a ten sensor configuration, results show that the root mean square estimation error of the estimates of the first two modes is within 1-3% of the desired values and for the third mode it is 12-20% accurate. This level of error is acceptable for a moderately robust controller required to close the loop, based on previous investigation.