Model Experiment and Numerical Simulation on Czochralski Method

对Czochralski对流模型中的临界过渡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、Prandtl数Pr和Rayleigh数Ra。分别研究了圆柱形红色(直拉法单晶锭模型)和圆柱形容器(坩埚模型)的旋转对圆柱形容器内流动状态的影响。在较宽的混合对流参数Ra/PrRe^2范围内，对三种不同的Prandtl数进行了研究，并考察了加速晶体旋转技术(ACRT)的影响。注意通过改变转速omega=omega_0(1Asin(2pift/tp))来抑制温度振荡，计算结果表明：在Ra/PrRe^2&GT范围内，以浮力和强迫对流为主的流动模式以及从一种模式向另一种模式的转变具有参数Ra/PrRe^2的特征。在Pr=4.45×10^3和Ra=4.83×10^6的情况下，转变的临界值(Ra/PrRe^2)_c为120；120，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。Prandtl数对(Ra/PrRe^2)_c临界值的影响不大，在旋转占优势区域，通过调整A接近等于ACRT的0.3和f接近等于ACRT的0.9，温度振荡得到了显著的抑制。但是，在浮力占优势的区域，温度振荡并未被抑制。目前的实验结果与数值结果定性地吻合。

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.