Development and Application of a Reduced Order Model for the Control of Self-Sustained Instabilities in Cavity Flows (Communications in Computational Physics, 2014)
Flow around a cavity is characterized by a self-sustained mechanism inwhich the shear layer impinges on the downstream edge of the cavity resulting ina feedback mechanism. Direct Numerical Simulations of the flow at low Reynoldsnumber has been carried out to get pressure and velocity fluctuations, for the case ofun-actuated and multi frequency actuation. A Reduced Order Model for the isentropiccompressible equations based on the method of Proper Orthogonal Decomposition hasbeen constructed. The model has been extended to include the effect of control. TheReduced Order dynamical system shows a divergence in time integration. A methodof calibration based on the minimization of a linear functional of error, to the sensitivityof the modes, is proposed. The calibrated low order model is used to design a feedbackcontrol of cavity flows based on an observer design. For the experimental implementation of the controller, a state estimate based on the observed pressure measurementsis obtained through a linear stochastic estimation. Finally the obtained control is introduced into the Direct Numerical Simulation to obtain a decrease in spectra of thecavity acoustic mode.