Volume 14, Issue 1
Development and Application of a Reduced Order Model for the Control of Self-Sustained Instabilities in Cavity Flows

Kaushik Kumar Nagarajan ,  Laurent Cordier and Christophe Airiau

10.4208/cicp.300112.100812a

Commun. Comput. Phys., 14 (2013), pp. 186-218.

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  • Abstract

Flow around a cavity is characterized by a self-sustained mechanism in which the shear layer impinges on the downstream edge of the cavity resulting in a feedback mechanism. Direct Numerical Simulations of the flow at low Reynolds number has been carried out to get pressure and velocity fluctuations, for the case of un-actuated and multi frequency actuation. A Reduced Order Model for the isentropic compressible equations basedonthe method of ProperOrthogonal Decomposition has been constructed. The model has been extended to include the effect of control. The Reduced Order dynamical system shows a divergence in time integration. A method of calibrationbasedontheminimization ofalinearfunctional oferror,tothe sensitivity of the modes, is proposed. The calibratedlow ordermodel is used todesign a feedback control of cavity flows based on an observer design. For the experimental implementation of the controller, a state estimate based on the observed pressure measurements is obtained through a linear stochastic estimation. Finally the obtained control is introduced into the Direct Numerical Simulation to obtain a decrease in spectra of the cavity acoustic mode. 

  • History

Published online: 2014-07

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