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Feedback control stabilization of the no-motion state of a fluid confined in a horizontal porous layer heated from below

Published online by Cambridge University Press:  26 April 2006

Jie Tang  and
Haim H. Bau
Jie Tang
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315, USA
Haim H. Bau
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315, USA
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Abstract

We consider a horizontal three-dimensional saturated porous layer, confined in an upright cubic box, heated from below and cooled from above. In the absence of a controller, the fluid maintains a no-motion state for subcritical Rayleigh numbers R < Rc, where Rc depends on the box's aspect ratio. Once this critical number is exceeded, fluid motion ensues. We demonstrate that, with the use of feedback control strategies which suppress flow instabilities, one can maintain a stable no-motion state for Rayleigh numbers far exceeding the classical critical one for the onset of convection. To preserve the equilibrium no-motion state of the classical problem, the controller alters the system's dynamics so as to stabilize an otherwise non-stable state.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 257 , December 1993 , pp. 485 - 505
Copyright
© 1993 Cambridge University Press

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