On the convective instability of a horizontal binary mixture layer with Soret effect under transversal high frequency vibration

Gershuni, G. Z.; Kolesnikov, A. K.; Legros, Jean Claude; Myznikova, B. I.

doi:10.1016/s0017-9310(98)00154-9

Cited by 41 publications

(19 citation statements)

References 6 publications

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“…The thermovibrational convection in a fluid received more attention than the thermovibrational convection in a porous medium. A good summary of this work was achieved by Gershuni et al [4,5].…”

Section: Introductionmentioning

confidence: 94%

Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer: The effect of vertical vibrations

2017

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This is an author-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID: 17918Open Archive Toulouse Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Abstract. The authors studied the effect of vertical high-frequency and small-amplitude vibrations on the separation of a binary mixture saturating a porous cavity. The horizontal bottom plate was submitted to constant uniform heat flux and the top one was maintained at constant temperature while no mass flux was imposed. The influence of vertical vibrations on the onset of convection and on the stability of the unicellular flow was investigated for positive separation ratio ψ. The case of high-frequency and small-amplitude vibrations was considered so that a formulation using time averaged equations could be used. For an infinite horizontal porous layer, the equilibrium solution was found to lose its stability via a stationary bifurcation leading to unicellular flow or multicellular one depending on the value of ψ. The analytical solution of the unicellular flow was obtained and separation was expressed in terms of Lewis number, separation ratio and thermal Rayleigh number. The direct numerical simulations using the averaged governing equations and analytical stability analysis showed that the unicellular flow loses its stability via oscillatory bifurcation. The vibrations decrease the value of ψ uni, which allows species separation for a wide variety of binary mixtures. The vibrations can be used to maintain the unicellular flow and allow species separation over a wider range of Rayleigh numbers. The results of direct numerical simulations and analytical model are in good agreement. To cite this version:

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Section: Introductionmentioning

confidence: 94%

Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer: The effect of vertical vibrations

2017

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“…average flow in the form of the four vortexes located in pairs near the sidewalls of the cavity is generated and in the central part of the cavity the flow is nearly absent, the flow intensity is rather weak and the deformation of the solute concentration fields by the convective flow is not visible. When the vibrational Rayleigh number approaches 4 …”

Section: Soret-induced Convection In Gravity Field In the Absence Of mentioning

confidence: 99%

“…For example, the longitudinal high-frequency vibrations make destabilizing effect on the horizontal layer of binary mixtures with positive separation ratios and stabilizing effect on binary mixtures with negative separation ratios [3]. Vibrations applied in the direction perpendicular to the layer play stabilizing role independently of the separation ratio sign [4]. In square cavity at side heating in conditions of low gravity the residual flow can be damped by applying an appropriate vibration intensity in the appropriate direction [5].…”

Section: Introductionmentioning

confidence: 99%

Vibration effect on the Soret-induced convection of ternary mixture in a rectangular cavity heated from below

Lyubimova

Zubova

2017

IOP Conf. Ser.: Mater. Sci. Eng.

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“…Many instability modes such as stationary multi-cellular, mono-cellular, and oscillatory multi-cellular may be observed too. This problem in the context of the high-frequency vibration in a binary mixture was pioneered by Gershuni et al (1997) for horizontal vibration and Gershuni et al (1999) for vertical vibration. Razi et al (2004a) completed this study for arbitrary directions of vibration.…”

Section: Influence Of High-frequency Mechanical Vibration On a Porousmentioning

confidence: 99%

A Summary of New Predictive High Frequency Thermo-Vibrational Models in Porous Media

2009

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In this paper, we consider the effect of mechanical vibration on the onset of convection in porous media. The porous medium is saturated either by a pure fluid or by a binary mixture. The importance of a transport model on stability diagrams is presented and discussed. The stability threshold for the Darcy-Brinkman case in the Ra T c -R and k c -R diagrams is presented (where Ra T c , k c and R are the critical Rayleigh number, the critical wave number and the vibration parameters, respectively). It is shown that there is a significant deviation from the Darcy model. In the thermo-solutal case with the Soret effect, the influence of vibration on the reduction of multi-cellular convection is emphasized. A new analytical relation for obtaining the threshold of mono-cellular convection is derived. This relation shows how the separation factor is related to the controlling parameters of the problem, = f (R, ε * , Le), when the wave number k → 0. The importance of vibrational parameter definition is highlighted and it is shown how, by using a proper definition for vibrational parameter, we may obtain compact relationship. It is also shown how this result may be used to increase component separation.

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On the convective instability of a horizontal binary mixture layer with Soret effect under transversal high frequency vibration

Cited by 41 publications

References 6 publications

Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer: The effect of vertical vibrations

Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer: The effect of vertical vibrations

Vibration effect on the Soret-induced convection of ternary mixture in a rectangular cavity heated from below

A Summary of New Predictive High Frequency Thermo-Vibrational Models in Porous Media

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