Soret-driven convection and separation of binary mixtures in a horizontal porous cavity submitted to cross heat fluxes

摘要

An analytical and numerical study of Soret-driven convection in a horizontal porous layer saturated by audbinary fluid and subjected to uniform cross heat fluxes is presented. The flow is driven by the combinedudbuoyancy effect due to temperature and induced mass fraction variations through a binary water ethanoludmixture. In the first part of the study, a closed-form analytical solution in the limit of a large aspect ratioudof the cell (A 1) is developed. We are mainly concerned with the determination of the mass fractionudgradient of the component of interest along the horizontal direction, which determines the speciesudseparation. In the second part, numerous numerical simulations are carried out in order to validate theudanalytical results and extend heat and mass transfer to an area not covered by the analytical study. Goodudagreement is found between analytical and numerical results concerning the species separation obtainedudfor a unicellular flow. In this configuration, the Soret separation process is improved by two controludparameters: the heat flux density imposed on the horizontal walls of the cell and the ratio, a, of heat fluxuddensity imposed on vertical walls to that on horizontal walls. The influence of the heat flux density ratio,uda, on the transient regime (relaxation time) is also investigated numerically. We observe that an increaseudin the parameter a leads to a decrease in the relaxation time. Thus, for a cell heated from below withoutudlateral heating, the onset of convection from the mechanical equilibrium state is analyzed. The linearudstability analysis shows that the equilibrium solution loses its stability via a stationary bifurcation or audHopf bifurcation depending on the separation ratio and the normalized porosity of the medium. Theudlinear stability results are widely corroborated by direct 2D numerical simulations. The thresholds ofudvarious multicellular solutions are determined in terms of the governing parameters of the problemudusing nonlinear direct numerical simulations