Feedback control of subsonic cavity flows using reduced-order models

Abstract

Development, experimental implementation, and the results of reduced-order model based feedback control of subsonic shallow cavity flows are presented and discussed. Particle image velocimetry (PIV) data and the proper orthogonal decomposition (POD) technique are used to extract the most energetic flow features or POD eigenmodes. The Galerkin projection of the Navier-Stokes equations onto these modes is used to derive a set of nonlinear ordinary differential equations, which govern the time evolution of the eigenmodes, for the controller design. Stochastic estimation is used to correlate surface pressure data with flow-field data and dynamic surface pressure measurements are used to estimate the state of the flow. Five sets of PIV snapshots of a Mach 0.3 cavity flow with a Reynolds number of 105 based on the cavity depth are used to derive five different reduced-order models for the controller design. One model uses only the snapshots from the baseline (unforced) flow while the other four models each use snapshots from the baseline flow combined with snapshots from an open-loop sinusoidal forcing case. Linear-quadratic optimal controllers based on these models are designed to reduce cavity flow resonance and are evaluated experimentally. The results obtained with feedback control show a significant attenuation of the resonant tone and a redistribution of the energy into other modes with smaller energy levels in both the flow and surface pressure spectra. This constitutes a significant improvement in comparison with the results obtained using open-loop forcing. These results affirm that reduced-order model based feedback control represents a formidable alternative to open-loop strategies in cavity flow control problems even in its current state of infancy. © Cambridge University Press 2007.