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Model Experiment and Numerical Simulation on Czochralski Method

直拉法模型实验与数值模拟

基本信息

批准号：
08650224
负责人：
KOYAMA Hideharu
金额：
$ 0.77万
依托单位：
Tokyo Denki University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1997
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08650224/
关键词：
Czochralski method Temperature oscillation Flow visualization Numerical simulation

项目摘要

Experiment and numerical simulation of critical transition flow modes in Czochralski convection model were performed. Rotational Reynolds number Re, Prandtl number Pr and Rayleigh number Ra emerge in the non-dimensional governing equations. Effects of the rotations of a cylindrical red (a model for a single crystal ingot of Czochralski method) and a cylindrical container (a model for a crucible) on flow regime in a cylindrical container were investigated separately. Studies were carried out in a broad range of mixed convection parameter Ra/PrRe^2 and for the three different Prandtl numbers.Effect of the accelerated crystal rotation technique (ACRT) was also investigated. The attention is directed to the suppression of temperature oscillation by changing the rotation rates, OMEGA = OMEGA_0 (1+A sin (2pift/tp)), where OMEGA_0 represents the constant rotation rate of cylindrical rod without the application of ACRT.An assessment is made of the optimal values to suppress the temperature oscillations.From the results the following conclusions are obtained :Buoyancy-and forced-convection dominant flow modes and transition from one mode to another were found to be characterized by the parameter Ra/PrRe^2. The critical value (Ra/PrRe^2) _c for the transition was 120 for the case of Pr = 4.45x10^3 and Ra = 4.83 x 10^6. In the region of Ra/PrRe^2>120, i.e.the buoyancy effect is dominant, as Ra/PrRe^2 decreases the time period of temperature oscillation gradually increases. Effect of the Prandtl number on the critical value (Ra/PrRe^2) _c was not substantial.Temperature oscillation was suppressed considerably by adjusting A nearly equal to 0.3 and f nearly equal to 0.9 of ACRT in the rotation-dominant region. However, the temperature oscillation was not suppressed in the buoyancy dominant region. Present experimental results agree qualitatively with the numerical results.

对切克劳斯基对流模型中的临界转捩流动模式进行了实验和数值模拟。无量纲控制方程中出现了旋转雷诺数Re、普朗特数Pr和瑞利数Ra。分别研究了直拉法单晶锭的模型--圆柱体和坩埚的模型--圆柱体的旋转对圆柱体内流态的影响。研究在混合对流参数Ra/PrRe ^[2]和三种不同普朗特数的宽范围内进行，同时还研究了加速晶体旋转技术（ACRT）的影响。注意力集中在通过改变旋转速率来抑制温度振荡，Ω = Ω_0（1+A sin（2 pift/tp）），其中Ω_0表示圆柱形杆在不应用ACRT的情况下的恒定转速，对抑制温度振荡的最佳值进行了评估，从结果中得出以下结论：研究发现，参数Ra/PrRe ^[2]表征了浮力和强制对流占主导地位的流动模式以及从一种模式向另一种模式的转变。在Pr = 4.45 × 10 ^3和Ra = 4.83 × 10 ^6的情况下，跃迁的临界值（Ra/PrRe^2）_c为120。在Ra/PrRe ^2>120的区域，即浮力效应占主导地位，随着Ra/PrRe ^2的减小，温度振荡的时间周期逐渐增大。普朗特数对临界值（Ra/PrRe^2）_c的影响不大，在旋转占优区，通过调整ACRT的A接近于0.3，f接近于0.9，可以显著抑制温度振荡。然而，温度振荡没有被抑制在浮力占主导地位的区域。目前的实验结果与数值计算结果定性一致。