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Development and Application of a Reduced Order Model for the Control of Self-Sustained Instabilities in Cavity Flows

Published online by Cambridge University Press:  03 June 2015

Kaushik Kumar Nagarajan ,
Laurent Cordier  and
Christophe Airiau
Kaushik Kumar Nagarajan*
Affiliation:
National Aerospace Laboratories, Bengaluru, 560017, India
Laurent Cordier*
Affiliation:
PPRIME Institute CEAT, 43 route de l’aérodrome, 86000 Poitiers, France
Christophe Airiau*
Affiliation:
Université de Toulouse; INPT, UPS; IMFT (Institut de Mécanique des Fluides de Toulouse); Allée Camille Soula, F-31400 Toulouse, France
*
Corresponding author.Email:kaushik@ctfd.cmmacs.ernet.in
Email:laurent.cordier@univ-poitiers.fr
Email:Christophe.Airiau@imft.fr
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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 based on the method of Proper Orthogonal 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 calibration based on the minimization of a linear functional of error, to the sensitivity of the modes, is proposed. The calibrated low order model is used to design 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.

Keywords

93C0593C1076N25Reduced order modellingproper orthogonal decompositioncavity flowsfeedback control
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 1 , July 2013 , pp. 186 - 218
Copyright
Copyright © Global Science Press Limited 2013

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