Aspect ratio and capillary ratio dependence of thermal-solutal capillary-buoyancy flow of a binary mixture in an annular pool

Abstract

In order to understand the aspect ratio and capillary ratio dependence of the coupled thermal-solutal capillary-buoyancy flow in an annular pool subjected to radial temperature and solute concentration gradients, a series of three-dimensional numerical simulations are conducted by applying the finite volume method. The annular pool was filled with the silicon-germanium melt with the silicon mass fraction of 1.99% (Pr = 6.37 × 10−3 and Le = 2197.8). Results show that axisymmetric stable flow always occurs in an annular pool when the thermal capillary Reynolds number is relatively small. The evolution of the flow pattern undergoes two and three stages with the increase of the aspect ratio and the capillary ratio, respectively. Besides the special case of Rσ = −1, the critical thermal Reynolds number at which the flow bifurcates into a three-dimensional flow rises with the increase of the capillary ratio and the decrease of the aspect ratio. Various three-dimensional flow patterns, including the lotus-like pattern, spoke pattern, hydrosolutal waves, ear-like pattern, growth-ring-like pattern and petal-like pattern, appear in the annular pool. The transitions and characteristic parameters of these flow patterns are strongly related to the capillary ratio, aspect ratio and thermal capillary Reynolds number.