Czochralski晶体生长中非定常热对流过程的数值模拟

NUMERICAL SIMULATION OF UNSTEADY THERMAL CONVE-CTIVE PROCESS IN CZOCHRALSK1 CRYSTAL GROWTH

本文应用有限控制体算法,采用中心差分格式处理具有Boussinesq近似的N-S方程的对流和扩散通量项,计算了无坩埚和籽晶旋转情况下CZ晶体生长中熔体的非定常自然对流。数值计算的结果得到了某些典型时刻的流场结构和温度分布情况。结合计算得到的CZ熔体总动能和总热能随时间变化的规律,分析了流场和温度场的不稳定变化过程。此外,计算结果还给出了在非稳定热对流影响下的晶-液界面热通量的变化。非定常计算的结果对于研究自然对流和CZ单晶生长,具有理论和实际意义。

A numerical study for representing time-dependent natural convection of Czochralski melts, while the growing crystal and crucible do not rotate, is presented in this paper. Using a finite control volume algorithm with central-diference discretization of advective and diffusive fluxes, the Czochralski flow which is governed by the rwo-dimensional N-S equations based on Bous-sinesq approximation is computed. The calculations present some interesting streamlines and isotherms with typical time, total kinetic and thermal energy as function of time. The time-de-pendent transport phenomena in Czochralski melt extend into oscillatory for Gr = 1.6×106 in Pr = 0.015. This results obviously influence the thermal fluxes at the crystal-liquid interface. The unsteady simulation in this paper is much helpful for the recognition of natural convection and actural crystal growth in Czochralski melts. The program are also available to other models of Czochralski crvstal growth.