环形浅池内硅熔体中的热流体波

Hydrothermal wave in shallow annular silicon melt pool

为了了解工业Czochralski炉内硅熔体表面轮型的基本特征,对环形浅池内硅熔体的热毛细-浮力对流进行了三维数值模拟,硅熔池内径为15 mm,外径为50 mm,深度为3 mm,熔池外壁被加热,内壁被冷却,底部固壁和顶部自由表面均绝热或者允许一个垂直方向的传热。模拟结果表明,当径向温差较小时,熔池内会产生稳定的单胞热毛细-浮力流动,随着温差的增大,流动将转变为三维振荡流动,在熔体自由表面会出现沿周向运动的轮型,小的垂直方向的热流密度(3W/cm2)对这种振荡流动没有大的影响。同时,讨论了流动和温度波动的特征,并确定了振荡流动的临界条件。

In order to understand the nature of surface spoke patterns on the silicon melt in industrial Czochralski furnaces, a series of unsteady three-dimensional numerical simulations were conducted for thermocapillary-buoyancy flow of silicon melt in an annular pool （inner radius ri = 15 mm, outer radius ro= 50 mm, depth d= 3 mm）. The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces either are adiabatic or allow heat transfer in the vertical direction. Results show that a small temperature difference in the radial direction generates steady roll-cell thermocapillary- buoyancy flow. With large temperature difference, the simulation can predict three-dimensional oscillatory flow, which is characterized by spoke patterns traveling in the azimuthal direction. The small vertical heat flux （3W/cm^2） does not have significant effects on the characteristics of this oscillatory flow. Details of the flow and temperature disturbances are discussed and the critical conditions for the onset of the oscillatory flow are determined.