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A dynamic observer to capture and control perturbation energy in noise amplifiers

Published online by Cambridge University Press:  13 October 2014

Juan Guzmán Iñigo ,
Denis Sipp  and
Peter J. Schmid
Juan Guzmán Iñigo*
Affiliation:
Département d’Aérodynamique Fondamentale et Expérimentale, ONERA, 8 Rue des Vertugadins, 92190 Meudon, France
Denis Sipp
Affiliation:
Département d’Aérodynamique Fondamentale et Expérimentale, ONERA, 8 Rue des Vertugadins, 92190 Meudon, France
Peter J. Schmid
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

In this article, we introduce techniques to build a reduced-order model of a fluid system that accurately predicts the dynamics of a flow from local wall measurements. This is particularly difficult in the case of noise amplifiers where the upstream noise environment, triggering the flow via a receptivity process, is not known. A system identification approach, rather than a classical Galerkin technique, is used to extract the model from time-synchronous velocity snapshots and wall shear-stress measurements. The technique will be illustrated for the case of a transitional flat-plate boundary layer, where the snapshots of the flow are obtained from direct numerical simulations. Particular attention is directed to limiting the processed data to data that would be readily available in experiments, thus making the technique applicable to an experimental set-up. The proposed approach combines a reduction of the degrees of freedom of the system by a projection of the velocity snapshots onto a proper orthogonal decomposition basis combined with a system identification technique to obtain a state-space model. This model is then used in a feedforward control set-up to significantly reduce the kinetic energy of the perturbation field and thus successfully delay transition.

JFM classification

Boundary Layers: Boundary layer control Flow Control: Control theory Flow Control: Instability control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 758 , 10 November 2014 , pp. 728 - 753
Copyright
© 2014 Cambridge University Press 

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Guzmán Iñigo et al. supplementary movie

Video of the streamwise disturbance component obtained from the DNS and the recover from signal s via the model.

Download Guzmán Iñigo et al. supplementary movie(Video)
Video 8.8 MB

Guzmán Iñigo et al. supplementary movie

Simulation of the LQR-control design based on the dynamic observer. The streamwise component of the disturbance velocity is showed together with the temporal evolution of the kinetic energy E(t), the control signal u(t) and the friction-sensor signal s(t).

Download Guzmán Iñigo et al. supplementary movie(Video)
Video 3.2 MB