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Journal of Porous Media
Facteur d'impact: 1.752 Facteur d'impact sur 5 ans: 1.487 SJR: 0.43 SNIP: 0.762 CiteScore™: 2.3

ISSN Imprimer: 1091-028X
ISSN En ligne: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v1.i1.80
pages 107-121

Onset of a Double-Diffusive Convective Regime in a Rectangular Porous Cavity

Marie-Catherine Charrier-Mojtabi
Laboratoire PHASE E.A. 3028, Université Paul Sabatier, France
Mohammad Karimi-Fard
Mejdi Azaiez
IMFT, UMR CNRS/INP/UPS N°5502, UFR MIG, Université Paul Sabatier, 118r oute de Narbonne, 31062, Toulouse Cedex, France
Abdelkader Mojtabi
Institut de Mecanique des Fluides, UMR CNRS-INP-UPS №5502 Universite Paul Sabatier, 118 route de Narbonne, F 31062 Toulouse, Cedex France.

RÉSUMÉ

The onset of a double-diffusive convective regime in a rectangular cavity filled with a porous medium saturated by a binary fluid is studied. The two vertical walls are kept at different but uniform temperatures and concentrations, while the horizontal walls are impermeable and adiabatic. When the ratio of the resulting solutal and thermal buoyancy forces is equal to (−1), an equilibrium solution corresponding to a purely diffusive regime is obtained. We demonstrate that this regime is linearly stable until a critical thermal Rayleigh number, Rac, depending on the cell aspect ratio, A, and the Lewis number, Le. For a square cavity we obtained Rac|Le − 1| = 184.06, and for an infinite vertical layer the critical parameters are found to follow Rac|Le − 1| = 105.33 and kc = 2.51. These analytical results are in good agreement with numerical direct simulations. It is thus found that the bifurcation that corresponds to the onset of convection is a transcritical type for A = 1. The structures of the subcritical and supercritical steady solutions, at several values of the Lewis number and for a square cavity, have been studied numerically. The double-diffusive convective regime taking place when the equilibrium regime loses its stability is also described.


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