Influence of a variable thermal diffusion coefficient on convection of a binary mixture in rectangular cavities

Abstract

This paper presents the results of numerical simulation of nonlinear convection regimes of a NaCl aqueous solution in square and horizontally elongated rectangular cavities with hard and impermeable boundaries. The vertical boundaries of the cavities are thermally insulated, and the horizontal ones are maintained at different constant temperatures, which corresponds to heating from below. Calculations are carried out within the non-stationary approach using of Boussinesq approximation and taking into account the polynomial temperature dependence of the thermal diffusion coefficient. According to this approximation, at T*≈285.4 K, the thermal diffusion coefficient changes sign, and thus the direction of the concentration gradient also changes. The temperature gradients on the horizontal boundaries are chosen so that the thermal diffusion coefficient changes sign inside the cavity. Other transport coefficients are considered to be constant. Simulations were performed under Earth-gravity and reduced-gravity conditions. Based on the results of simulations, the local and integral characteristics of non-linear regimes were obtained, and the structure of the emerging flow and the distribution of NaCl concentration were determined. It is shown that the temperature dependence of the thermal diffusion coefficient only slightly affect the structure and intensity of the emerging flow but significantly reduces the degree of separation of mixture components. Under the influence of the Earth’s gravitational field, an oscillatory four-vortex flow with reconnection of vortices occurs in the square cavity, and a multi-vortex flow - in the rectangular cavity. The characteristics of the multi-vortex flow vary irregularly. At reduced gravity, a stationary flow is observed in both square and rectangular cavities. Under microgravity conditions, the concentration isolines are “frozen” into the stream function field, i.e., the similarity between the fields is pronounced.