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Mechanisms of non-modal energy amplification in channel flow between compliant walls

Published online by Cambridge University Press:  23 December 2009

JÉRÔME HŒPFFNER ,
ALESSANDRO BOTTARO  and
JULIEN FAVIER
JÉRÔME HŒPFFNER*
Affiliation:
Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Yokohama 223-8522, Japan
ALESSANDRO BOTTARO
Affiliation:
DICAT, Università di Genova, Via Montallegro 1, 16145 Genova, Italy
JULIEN FAVIER
Affiliation:
DICAT, Università di Genova, Via Montallegro 1, 16145 Genova, Italy
*
†Present address: Institut Jean le Rond D'Alembert, UMR 7190, Université Pierre et Marie Curie, Paris, France. Email address for correspondence: jerome.hoepffner@upmc.fr
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Abstract

The mechanisms leading to large transient growth of disturbances for the flow in a channel with compliant walls are investigated. The walls are modelled as thin spring-backed plates, and the flow dynamics is modelled using the Navier–Stokes equations linearized round the Poiseuille profile. Analysis for streamwise invariant perturbations show that this fluid-structure system can sustain oscillatory energy evolution of large amplitude, in the form of spanwise standing waves. Such waves are related to the travelling waves which a free wall can support, modified to account for an ‘added mass’ effect. Simple scaling arguments are found to provide results in excellent agreement with computations of optimal disturbances, for low-to-moderate values of the stiffness parameter characterizing the compliant surface.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 642 , 10 January 2010 , pp. 489 - 507
Copyright
Copyright © Cambridge University Press 2010

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References

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Hoepffner et al. supplementary movie

Movie 1. Time evolution of the optimal initial conditions, for Re=1000, wavelength 2 π, and four different spring stifnesses K. The streamwise velocity perturbation is represented by the color map, whereas the inplane velocity is made visible using particles tracers. The arbitrary wall deformation and particle movement amplitudes are scaled such as to give a clear visual impression of the flow motion.

Download Hoepffner et al. supplementary movie(Video)
Video 10.3 MB

Hoepffner et al. supplementary movie

Movie 2. Animation of the model flow deformations for sinuous and varicose symmetries. The Poiseuille base flow is displaced up and down by the sinuous wall standing wave, or streched/contracted by the varicose deformation.

Download Hoepffner et al. supplementary movie(Video)
Video 3.2 MB