Analytical and numerical study of Soret mixed convection in two sided lid-driven horizontal cavity: Optimal species separation

Abstract

The coupling between shear-driven convection and thermo-diffusion is a complex phenomenon due to the interactions between the different forces inside the fluid mixture. This paper studies the species separation that may appear in a parallelepipedic cell filled by a binary mixture. Dirichlet boundary conditions are imposed with differentially heated horizontal walls. Each wall can be animated with a uniform velocity. More precisely, two velocities UPex→,andfUPex→ are applied at the upper and the lower horizontal walls respectively. An analytical solution, based on the parallel flow approximation in the core region of the cavity of large aspect ratio, is obtained as a function of the dimensionless parameters of the problem. The species separation is optimized according to the multiple control parameters of the problem. The velocity field obtained is the superposition of the flow generated by the velocity of the walls under weightless conditions and thermoconvective flow under gravity only. The combination of these two flows leads to a mixed convection flow with a single convective cell for f∈-1,0 and two superposed cells for f∈0,1. Only unicellular flow leads to a notable species separation. This study shows that the effective species separation admits a partial optimum as a function of f and Up. As in the case of thermogravitational columns, there is no optimum species separation with respect to parameters ΔT and H but, for a fixed temperature difference ΔT, there is a thickness H that optimizes the separation and vice versa. 2D and 3D direct numerical simulations are performed using a finite element method in order to corroborate the analytical results. The influence of mass Péclet number on the diffusive relaxation time is determined numerically. Taking into account the confinement of the medium in the third dimension, perpendicular to a vertical plane, we show that the aspect ratio in the y-direction has an influence on the species separation.