Flow Pattern Transitions of Silicon Melt Thermocapillary Flow in a Slowly Rotating Annular Pool

摘要

In order to understand the mechanism of the flow pattern transitions on silicon melt in Czochralski furnaces, we conducted a series of unsteady three-dimensional numerical simulations of silicon melt flow in a rotating shallow annular pool in the counter-clockwise direction under micro-gravity. The pool is heated from the outer cylinder and cooled at the inner cylinder. The temperature differences between the vertical outer and inner cylinders ranged from 5 K to 28 K and annular pool rotation rate from 0 and 2 rpm. Bottom and top surfaces of the melt pool are adiabatic. The simulation results indicate that two flow transitions occur when increasing the radial temperature difference along the free surface. At first, the steady two-dimensional flow becomes the hydrothermal wave and then oscillatory three-dimensional flow. The critical conditions for the onset of the instability and the transition zone between the hydrothermal wave and oscillatory three-dimensional flow were determined at various rotation rates. Characteristics of the steady and the three-dimensional flows were discussed.