The dynamic behavior of convective motion in a confined porous medium saturated by a pure fluid under the action of mechanical vibration is studied. A redefinition of vibrational Rayleigh number is proposed from which we distinguish the domain of validity of the mean flow. The weakly nonlinear stability analysis performed demonstrates, contrary to published results, that the bifurcation is of supercritical nature and the subcritical branch does not exist. It is emphasized that, in order to find the thermal behavior of the system for the onset of convection, we should separate the vibrational effect from the thermal effect involving the temperature difference.

The generation of two-dimensional thermal convection induced simultaneously by gravity and high-frequency vibration in a bounded rectangular enclosure or in a layer is investigated theoretically and numerically. The horizontal walls of the container are maintained at constant temperatures while the vertical boundaries are thermally insulated, impermeable and adiabatic. General equations for the description of the time-averaged convective flow and, within this framework, the generalized Boussinesq approximation are formulated. These equations are solved using a spectral collocation method to study the influence of vibrations (angle and intensity). Hence, a theoretical study shows that mechanical quasi-equilibrium (i.e., state in which the averaged velocity is zero but the oscillatory component is in general non-zero) is impossible when the direction of vibration is not parallel to the temperature gradient. In the other case, it is proved that the mechanical equilibrium is linearly stable up to a critical value of the unique stability parameter, which depends on the vibrational field. In this paper, it is shown that high-frequency vertical oscillations can delay convective instabilities and, in this way, reduce the convective flow. The isotherms are oriented perpendicular to the axis of vibration. In the case where the direction of vibration is perpendicular to the temperature gradient, small values of the Grashof number, the stability parameter, induce the generation of an average convective flow. When the aspect ratio is large enough, the character of the bifurcation is practically the same as in the limiting case of an infinitely long layer.

We present a numerical and analytical study of doubly diffusive convection driven by horizontal thermal and solutal gradients in square and rectangular enclosures with no-slip walls subjected to high-frequency vibration. The two vertical walls of the enclosure are maintained at different but uniform temperatures and concentrations while the horizontal walls are assumed to be impermeable and insulating. The resulting system is described by time-averaged Boussinesq equations. These equations possess a doubly diffusive quasi-equilibrium solution provided the thermal and solutal buoyancy forces are equal and opposite. This solution is linearly stable up to a critical value of the stability parameter independently of the strength and orientation of the vibration. The solutions in the neighborhood of the bifurcation point are described analytically as a function of the strength and orientation of the vibration, and the larger amplitude states are computed numerically using a spectral collocation method. For vertical oscillation increasing the vibration amplitude decreases the subcriticality of the solutions and may even reverse it; the opposite occurs with horizontal vibration.

Analytical techniques are used to study the onset of convection in three-dimensional bores of fluid saturated porous material heated from below and subjected to vertical high-frequency vibration. Increasing the vibration amplitude delays the onset of convection and may even create subcritical solutions so as generate different structures of flows. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

Double diffusive convection in a two-dimensional rectangular cavity with imposed vertical differences in temperature and concentration is considered in the presence of high-frequency vertical vibrations. Linear stability analysis permits the domains of oscillatory and stationary convection thresholds to be delimited. Depending on the governing parameters, vibrations are found to delay or speed up the onset of convection. The effect of vibration on the flow structure near the bifurcation is also analyzed, showing different possible behaviors. The stationary bifurcation is then studied by means of a weakly nonlinear analysis. In agreement with the symmetries present in the problem, this bifurcation is found to be pitchfork. The parametric ranges where it can be subcritical or supercritical are precisely delimited. Finally, direct numerical simulations have been performed to confirm and illustrate these findings.

Convective oscillations in porous and fluid media are studied numerically. A two-dimensional, square, differentially heated cavity, filled with a porous medium saturated by a binary fluid or simply by a binary fluid, is considered. This cavity is subjected to linear harmonic oscillations in the vertical direction. The formulation is based on the Darcy-Brinkman-Forchheimer-Boussinesq model. The time dependent Darcy-Brinkman-Forchheimer-Boussinesq equations are solved using a pseudo-spectral Legendre collocation method. The instantaneous and mean characteristics of the flows are studied and discussed. An intensification of the heat and mass transfers is observed at low frequency for sufficiently high vibration intensity. A comparison between the response to the imposed vibrations is made for Darcy numbers varying from Da = 10(-7) to Da = 10.

We present a numerical and analytical study of diffusive convection in a rectangular saturated porous cell heated from below and subjected to high frequency vibration. The configuration of the Horton–Rogers–Lapwood problem is adopted. The classical Darcy model is shown to be insufficient to describe the vibrational flow correctly. The relevant system is described by time-averaged Darcy–Boussinesq equations. These equations possess a pure diffusive steady equilibrium solution provided the vibrations are vertical. This solution is linearly stable up to a critical value of the stability parameter depending on the strength of the vibration. The solutions in the neighborhood of the bifurcation point are described analytically as a function of the strength of vibration, and the larger amplitude states are computed numerically using a spectral collocation method. Increasing the vibration amplitude delays the onset of convection and may even create subcritical solutions. The majority of primary bifurcations are of a special type of symmetry-breaking bifurcation even if the system is subjected to vertical vibration.

Il s'agit d'étudier la convection thermo-solutale en microgravité dans une cavité bi-dimensionnelle carrée. Le but est de déterminer l'influence d'un champ mécanique vibratoire sur le transfert de chaleur et de masse dans cette cavité. Nous étudierons le système d'équations régissant les champs moyens de vitesse, pression, température et concentration. Ce système est résolu numériquement par une méthode spectrale de collocation basée sur les polynomes de Legendre. Nous mentrerons qu'un régime convectif quadricellulaire bifurque vers des solutions tricellulaires en brisant certaines symétries lorsque l'intensité du champ vibratoire augmente. Lorsque l'intensité des vibrations croit, l'écoulement moyen devient instationnaire. Une attention particulière sera portée à l'influence du nombre Lewis sur le transport de chaleur et de masse lorsque le régime convectif est tricellulaire.

Two-dimensional thermo-solutal convection in a square enclosure under weightlessness condition is studied. The main purpose is to investigate the heat and mass transfer induced by means of vibration in microgravity. The problem is based on the system of equations of the mean fields of velocity, pressure, temperature and concentration. The numerical simulations an made using a spectral Legendre collocation method, A 4-cells convective solution undergoes a bifurcation to a 3-cells flow with symmetry-breaking while the intensity of the vibrationnal field increases. As the vibration's intensity keeps increasing, a Hopf bifurcation occurs. A particular attention is paid on the heat and mass transfer for different Lewis number on the branch of 3-cells solutions.

Bifurcation phenomena in a square enclosure, submitted to horizontal temperature and concentration gradients, is studied when the opposing buoyancy forces due to horizontal thermal and concentration gradients are equal. We perform the linear weakly non-linear and finite amplitude stability analysis of the equilibrium solution. We verify that the onset of double diffusive convection corresponds to a transcritical bifurcation point. The subcritical solutions are strong attractors beyond a particular value of the thermal Rayleigh number which corresponds to the location of turning point. The structure of subcritical and transcritical steady solutions has been studied. (C) Academie des Sciences/Elsevier, Paris.