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Closed-loop control of an open cavity flow using reduced-order models

Published online by Cambridge University Press:  30 November 2009

ALEXANDRE BARBAGALLO ,
DENIS SIPP  and
PETER J. SCHMID
ALEXANDRE BARBAGALLO
Affiliation:
ONERA-DAFE, 8 rue des Vertugadins, 92190 Meudon, France Laboratoire d'Hydrodynamique (LadHyX), CNRS-Ecole Polytechnique, 91128 Palaiseau, France
DENIS SIPP
Affiliation:
ONERA-DAFE, 8 rue des Vertugadins, 92190 Meudon, France
PETER J. SCHMID*
Affiliation:
Laboratoire d'Hydrodynamique (LadHyX), CNRS-Ecole Polytechnique, 91128 Palaiseau, France
*
†Email address for correspondence: [email protected]
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Abstract

The control of separated fluid flow by reduced-order models is studied using the two-dimensional incompressible flow over an open square cavity at Reynolds numbers where instabilities are present. Actuation and measurement locations are taken on the upstream and downstream edge of the cavity. A bi-orthogonal projection is introduced to arrive at reduced-order models for the compensated problem. Global modes, proper orthogonal decomposition (POD) modes and balanced modes are used as expansion bases for the model reduction. The open-loop behaviour of the full and the reduced systems is analysed by comparing the respective transfer functions. This analysis shows that global modes are inadequate to sufficiently represent the input–output behaviour whereas POD and balanced modes are capable of properly approximating the exact transfer function. Balanced modes are far more efficient in this process, but POD modes show superior robustness. The performance of the closed-loop system corroborates this finding: while reduced-order models based on POD are able to render the compensated system stable, balanced modes accomplish the same with far fewer degrees of freedom.

JFM classification

Flow Control: Flow Control Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 641 , 25 December 2009 , pp. 1 - 50
Copyright
Copyright © Cambridge University Press 2009

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References

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Barbagallo et al. supplementary movie

Movie 1. Linearized Direct Numerical Simulation of the cavity at Re=7500 without control. The initial condition is the most unstable mode. The perturbations, displayed by contour of streamwise velocity, are exponentially amplified.

Download Barbagallo et al. supplementary movie(Video)
Video 8.1 MB

Barbagallo et al. supplementary movie

Movie 2. Linearized Direct Numerical Simulation of the cavity at Re=7500 using the "best-control strategy". The initial condition is the most unstable mode. The perturbations, displayed by contour of streamwise velocity, are amplified for T<2. For T>2, the estimator provides a sufficiently accurate estimated state for the control to be effective.

Download Barbagallo et al. supplementary movie(Video)
Video 9.8 MB