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Nonlinear global modes in inhomogeneous mixed convection flows in porous media

Published online by Cambridge University Press:  08 January 2008

M. N. OUARZAZI ,
F. MEJNI ,
A. DELACHE  and
G. LABROSSE
M. N. OUARZAZI
Affiliation:
Laboratoire de Mécanique de Lille, UMR CNRS 8107, USTL, bd. Paul Langevin 59655 Villeneuve d'Ascq cedex, France
F. MEJNI
Affiliation:
Laboratoire de Mécanique de Lille, UMR CNRS 8107, USTL, bd. Paul Langevin 59655 Villeneuve d'Ascq cedex, France
A. DELACHE
Affiliation:
Laboratoire de Mécanique de Lille, UMR CNRS 8107, USTL, bd. Paul Langevin 59655 Villeneuve d'Ascq cedex, France
G. LABROSSE
Affiliation:
Université Paris Sud, Limsi-CNRS, Bâtiments 508 et 502, 91403 Orsay, France
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Abstract

The aim of this work is to investigate the fully nonlinear dynamics of mixed convection in porous media heated non-uniformly from below and through which an axial flow is maintained. Depending on the choice of the imposed inhomogeneous temperature profile, two cases prove to be of interest: the base flow displays an absolute instability region either detached from the inlet or attached to it. Results from a combined direct numerical simulations and linear stability approach have revealed that in the first case, the nonlinear solution is a steep nonlinear global mode, with a sharp stationary front located at a marginally absolutely unstable station. In the second configuration, the scaling laws for the establishment of a nonlinear global mode quenched by the inlet are found to agree perfectly with the theory. It is also found that in both configurations, the global frequency of synchronized oscillations corresponds to the local absolute frequency determined by linear criterion, even far from the threshold of global instability.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 595 , 25 January 2008 , pp. 367 - 377
Copyright
Copyright © Cambridge University Press 2008

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