Feedback control of resonator flows using linear tools : towards experiments

The wake of a cylinder or the shear-layer over an open cavity are archetypes of resonator flows oscillating in a self-sustained fashion. The latter configuration is particularly relevant to military applications, but it is also an ideal test-bench to validate flow control methods in the lab. The aim is to suppress oscillations using a feedback loop between an actuator located at the leading-edge of the cavity and a sensor located further downstream. Self-sustained oscillations are the signature of strongly nonlinear autonomous dynamics, yet it is found numerically that full stabilization is achievable from the oscillating state, using linear tools only, without prior knowledge of the target base flow. After reviewing the heuristic method initially used in simulation, we will discuss some progress made towards its practical implementation and theoretical justification. In particular, we will present a fully data-driven version of the initial method based on the « mean transfer function » (MTF) rather than impractical linearization about a mean flow. The method is assessed numerically on the case of cylinder flow (see figure 1a). We study key properties of the MTF, in particular its close connection to linearization about a mean flow. We then investigate the MTF system identification problem on two distinct cavity flow experiments performed at ONERA and LISN (see figures 1b and 1c).