Oscillatory Thermal Convection and its Three-Dimensional Structure in a Cylindrical Cavity Filled with Liquid Metal.

本文对圆柱腔内的热对流作为坩埚生长过程的模型进行了数值和实验研究。腔体的侧壁和底部保持在均匀的高温下。熔体表面作为生长的单晶与棒接触，固体/熔体界面保持在均匀的低温下。在低普朗特数（Pr）流体中出现的对流振荡，会导致生长中的晶体的不良结构，称为“条纹”。本研究的目的在于阐明对流结构。在a)熔体表面无热损失（绝热）且无棒体旋转、b)无热损失且有棒体旋转、c)有热损失且有棒体旋转等条件下，对型腔长径比、Ar=2、半径比、Rr=0.3和0.5、Pr=0.025以及各种Grashof数进行了数值计算。结果如下：1。当自然对流占主导地位时，与杆的旋转引起的强迫对流相比，流动结构为单环面滚流，中心轴附近的流动下降，沿腔壁的流动上升。环形滚转是旋转对称的，方位角波数为3或4.3。随着转速的增加，出现了相速为3的旋转流，其方位波数为3。在Ar=2, Rr=0.5的条件下，用镓进行了实验，结果如下：当自然对流占主导地位时，发生振荡的临界格拉什夫数随杆的旋转增加而减小。当强迫对流占主导地位时，杆的旋转一般表现出抑制振荡的趋势。

Thermal convection in a cylindrical cavity, as a model of a crucible in Czochralski crystal growth process, has been studied numerically and experimentally. The sidewall and bottom of the cavity are maintained at a uniform high temperature. The melt surface is in contact with a rod as a growing single crystal, and the solid/melt interface is maintained at a uniform low temperature.Convective oscillations, which appear in low Prandtl number (Pr) fluids, cause undesirable structure of growing crystals called as 'striations.' It is the aim of this study to clarify the convective structure.Numerical calculations are carried out for the aspect ratio of the cavity, Ar=2, the radius ratio, Rr=0.3 and 0.5, Pr=0.025, and various Grashof numbers under the conditions, a) without heat loss on the melt surface (adiabatic) and without rotation of the rod, b) without heat loss and with rotation of the rod, and c) with heat loss and with rotation of the rod. The results are as follows.1. When the natural convection dominates in comparison with the forced convection due to rotation of the rod, the flow structure consists of a single toroidal roll with descending flow in the vicinity of the central axis and ascending flow along the cavity wall.2. The toroidal roll is rotationally symmetric with an azimuthal wavenumber of 3 or 4.3. As the rotation rate is increased, a rotating flow appears with phase speed of azimuthal wavenumber of 3.The experiments conducted using Gallium for Ar=2 and Rr=0.5 shows the following results.1. When the natural convection dominates, critical Grashof number, at which oscillation occurs, decreases with increasing rotation of the rod.2. When the forced convection dominates, the rotation of the rod generally shows a tendency to suppress oscillations.