Model Experiment and Numerical Simulation on Czochralski Method

对恰克拉尔斯基对流模型中的临界过渡流进行了实验和数值模拟。转动雷诺数Re、普朗特数Pr和瑞利数Ra出现在无量纲控制方程中。分别研究了圆柱形容器（单晶铸锭的直切法模型）和圆柱形容器（坩埚模型）的旋转对圆柱形容器内流动特性的影响。对大范围的混合对流参数Ra/PrRe^2和三种不同的普朗特数进行了研究。研究了加速晶体旋转技术（ACRT）的作用。注意通过改变旋转速率来抑制温度振荡，OMEGA = OMEGA_0 (1+A sin (2pitt /tp))，其中OMEGA_0表示在不应用ACRT的情况下圆柱形棒的恒定旋转速率。对抑制温度振荡的最优值进行了评价。结果表明：浮力对流和强迫对流的主导流动模式和从一种模式到另一种模式的转变是由参数Ra/PrRe^2表征的。当Pr = 4.45 × 10^3和Ra = 4.83 × 10^6时，跃迁的临界值（Ra/PrRe^2） _c为120。在Ra/ prere ^2区域，即浮力效应占主导地位，随着Ra/ prere ^2的减小，温度振荡周期逐渐增大。普朗特数对临界值（Ra/PrRe^2） _c的影响不大。将ACRT的A近似等于0.3，f近似等于0.9，可明显抑制温度振荡。然而，在浮力优势区，温度振荡并未受到抑制。目前的实验结果与数值结果定性一致。

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.