Limitations of achievable performance in control of cavity flow oscillations

Clancy Rowley, Mechanical and Aerospace Engineering, Princeton University

The flow past a rectangular cavity produces large-amplitude pressure oscillations that are undesirable in many engineering applications, such as aircraft wheel wells and weapons bays. These oscillations are usually described as "self-sustained": even without excitation by external disturbances, finite-amplitude oscillations persist. The usual dynamical-systems view of the flow is that there is an unstable equilibrium point, with a nearby stable limit cycle. However, recent experimental results suggest that in some cases, this equilibrium point may actually be stable (but lightly damped), and the finite-amplitude oscillations are caused not by the presence of a limit cycle, but by amplification of external disturbances.

We present the results of some recent experiments using feedback to attenuate the oscillations. The experiments reveal a "peak-splitting" phenomenon, where the main oscillation frequency splits into two nearby frequencies when feedback is introduced. The same phenomenon has been observed in experiments on control of combustion instabilities. We present a linear model which explains this phenomenon, using the disturbance-amplification viewpoint described above, and which suggests some fundamental limitations of achievable performance of feedback controllers.