Supercritical convective flows of melt water in an open horizontal rectangular cavity with a prescribed vertical heat flux

Abstract

The influence of the intensity of heating, expressed by the Grashof number, on supercritical regimes of thermal convection of melt water in a horizontal rectangular cavity with an aspect ratio of two is investigated. On the lateral solid boundaries, the thermal insulation conditions are satisfied, and a constant vertical heat flux is set on the lower solid and upper free horizontal and non-deformable edges. Under conditions when the cavity-average temperature is close to the temperature of water density inversion in the cavity, a state of mechanical equilibrium is possible, when a stably stratified layer is located on top of an unstable stratified layer. For two cases of the position of the horizontal boundary between these layers, the structure of stationary planar supercritical thermal convection is investigated. The calculations were carried out by the finite-difference method on a square grid with 128 nodes along the horizontal coordinate and 64 along the vertical one. Calculations have shown that, with an equal thickness of unstable and stably stratified layers, supercritical convection in the region up to about six supercriticalities has a two-cell structure in the horizontal direction with two (large at the bottom and weaker at the top) vortices in each of the cells. With an increase in supercriticality, this two-cell structure turns into a four-cell structure in a hysteresis manner. For the case when the thickness of the stably stratified layer is three times less than the thickness of the unstable stratified layer, the supercritical convective flow has the general form of a single-vortex cell elongated horizontally. With an increase in the Grashof number up to about a hundredfold supercriticality, it remains generally single-vortex and does not experience bifurcations.