Thermal-solutal capillary-buoyancy flow of a low Prandtl number binary mixture with various capillary ratios in an annular pool

Abstract

In order to understand the influence of the capillary ratio on the coupled thermal-solutal capillary-buoyancy flow in an annular pool subjected to simultaneous radial temperature and solute concentration gradients, a series of three-dimensional numerical simulations are carried out by using the finite volume method. The annular pool was filled with the silicon-germanium melt with an initial silicon mass fraction of 1.99%. The Prandtl number and the Lewis number of the silicon-germanium melt are 6.37×10−3 and 2197.8, respectively. Results indicate that the coupled thermal-solutal capillary-buoyancy flow is steady and axisymmetric when the thermal capillary Reynolds number is relatively small. With the decrease of the capillary ratio, the stable flow pattern experiences three stages, including the single counter-clockwise vortex, the combination of clockwise and counter-clockwise vortexes, and the single clockwise vortex. Besides the special case of the capillary ratio Rσ=−1, the critical thermal capillary Reynolds number for the incipience of the three-dimensional flow decreases with the decrease of the capillary ratio. Seven kinds of three-dimensional flow patterns are observed in the annular pool, which are the petal-like pattern, spoke pattern, rosebud-like pattern, hydrosolutal waves, ear-like pattern, target-like pattern and copper coin-like pattern. Actual flow pattern is strongly dependent on the capillary ratio, thermal capillary Reynolds number and the aspect ratio.