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Influence of Vertical Vibrations on the Stability of a Binary Mixture in a Horizontal Porous Layer Subjected to a Vertical Heat Flux

Ouadhani, Soumaya and Abdennadher, Ali and Mojtabi, Abdelkader and Bergeon, Alain Influence of Vertical Vibrations on the Stability of a Binary Mixture in a Horizontal Porous Layer Subjected to a Vertical Heat Flux. (2018) Transport in Porous Media, 123 (372). 1-18. ISSN 0169-3913

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Official URL: http://dx.doi.org/10.1007/s11242-018-1059-5

Abstract

We present an analytical and numerical stability analysis of Soret-driven convection in a porous cavity saturated by a binary fluid mixture and subjected to vertical high-frequency and small-amplitude vibrations. Two configurations have been considered and compared: an infinite horizontal layer and a bounded domain with a large aspect ratio. In both cases, the initial temperature gradient is produced by a constant uniform heat flux applied on the horizontal boundaries. A formulation using time-averaged equations is used. The linear stability of the equilibrium solution is carried out for various Soret separation ratios φ, vibrational Rayleigh numbers Rv, Lewis numbers Le and normalized porosity. For an infinite horizontal layer, the critical Rayleigh number Rac is determined analytically.For a steady bifurcation to a one-cell solution (the critical wavenumber is zero), we obtain Rac=12/(φ(Le+1)+1) for all Rv. When the bifurcation is a Hopf bifurcation or when the critical wavenumber is not zero, we use a Galerkin method to compute the critical values. Our study is completed by a nonlinear analysis of the bifurcation to one-cell solutions in an infinite horizontal layer that is compared to numerical simulations in bounded horizontal domains with large aspect ratio.

Item Type:Article
Additional Information:Thanks to Springer editor. The original PDF of the article can be found at : https://link.springer.com/article/10.1007%2Fs11242-018-1059-5#citeas
Audience (journal):International peer-reviewed journal
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Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Ecole Polytechnique de Tunisie - EPT (TUNISIA)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
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CNES
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Deposited On:23 May 2018 07:18

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