Hydrodynamical instabilities of thermocapillary flow in a half-zone
Hydrodynamical instabilities of thermocapillary flow in a half-zone
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DOI：
10.1017/s0022112095003132
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发表时间：
1995-08
影响因子：
3.7
通讯作者：
M. Levenstam;G. Amberg
中科院分区：
文献类型：
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作者：
M. Levenstam;G. Amberg
借助直接数值模拟，分析了半区结构中流动的稳定性。这项工作集中在典型的半导体熔体的小普朗特数有关。轴对称热毛细流动被发现是不稳定的一个稳定的非轴对称状态的方位波数为2，与纵横比为1的区域。该分叉的临界雷诺数为1960。该三维定常解在雷诺数为6250时失去稳定性而变为振荡状态。对于小的普朗特数，这两个分叉被认为是相当不敏感的普朗特数的变化，因此流体动力学的性质。薄涡环的不稳定性的类比。这个类比提出了不稳定性背后的物理机制，也给出了如何选择分叉解的方位波数的解释。这对浮区晶体生长过程的影响进行了讨论。
The stability of the flow in a half-zone configuration is analysed with the aid of direct numerical simulation. The work is concentrated on the small Prandtl numbers relevant for typical semiconductor melts. The axisymmetric thermocapillary flow is found to be unstable to a steady non-axisymmetric state with azimuthal wavenumber 2, for a zone with aspect ratio 1. The critical Reynolds number for this bifurcation is 1960. This three dimensional steady solution loses stability to an oscillatory state at a Reynolds number of 6250. For small Prandtl numbers, both bifurcations are seen to be quite insensitive to changes in the Prandtl number, and are thus hydrodynamic in nature. An analogy to the instability of thin vortex rings is made. This analogy suggests a physical mechanism behind the instability and also gives an explanation of how the azimuthal wavenumber of the bifurcated solution is selected. The implications of this for the floating-zone crystal growth process are discussed.