Proportional closed-loop feedback control of flow separation

The aim of this experimental study is the implementation of a practical and efficient closed-loop feedback control of the turbulent flow over a NACA-4412 airfoil equipped with leading-edge zero-net-mass-flux actuators. By using prior computation of correlations between particle image velocimetry data and multiple surface pressure measurements, real-time instantaneous low-dimensional estimates of the velocity field over the wing are then computed from the unsteady surface pressure. From such estimates, a direct knowledge of the state of the flow above the airfoil is obtained (i.e., attached, incipient separation, or fully separated flow). We first show the effectiveness of the low-dimensional modeling approach in extracting and estimating the underlying large-scale structures in a turbulent flow, using the proper orthogonal decomposition and the modified linear/quadratic stochastic measurements. We then show how such an approach is used successfully in a simple, but practical, proportional feedback loop to delay the separation of the flow over the wing at high angles of attack. The benefits of closed-loop vs open-loop control are then discussed. These fundamental results validate the use of low-dimensional modeling techniques for further, more sophisticated, closed-loop feedback control algorithms.