Influence of Buoyancy Force on Thermocapillary Convection Instability in the Differentially Heated Annular Pools of Silicon Melt
Influence of Buoyancy Force on Thermocapillary Convection Instability in the Differentially Heated Annular Pools of Silicon Melt
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DOI：
10.1007/s12217-009-9118-8
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发表时间：
2009-05
影响因子：
1.8
通讯作者：
W. Shi;M. K. Ermakov;You-Rong Li;L. Peng;N. Imaishi
中科院分区：
文献类型：
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作者：
W. Shi;M. K. Ermakov;You-Rong Li;L. Peng;N. Imaishi
本文用数值方法研究了浮力对硅熔体（Pr= 0.011）外壁温差加热内壁温差冷却环形熔池（Ri= 20 mm，Ro= 40 mm，深度1 ~ 10 mm）中热毛细对流不稳定性的影响。在微重力和正常重力条件下，通过线性稳定性分析（LSA）确定了振荡流起始的临界Marangoni数（Mac）。结果表明，在3 ~ 10 mm的不同液层深度下，浮力使热毛细对流不稳定。随着地层深度的增加，临界波数、临界方位波数和临界相速度均减小。部分三维仿真结果与LSA的结果进行了比较。除了D = 0.05的情况外，三维模拟结果与LSA结果一致，其中三维模拟给出了大Ma下的稳态三维流动。
The influence of buoyancy force on the thermocapillary convection instability in the annular pools (Ri= 20 mm,Ro= 40 mm, and depthdranging from 1 to 10 mm) of silicon melt (Pr= 0.011), differentially heated at the outer wall and cooled at the inner wall, is investigated numerically. The critical Marangoni numbers (Mac) for the incipience of oscillatory flow are determined by linear stability analysis (LSA) under both microgravity and normal gravity conditions. The results indicate that the buoyancy force destabilizes the thermocapillary convection under different liquid layer depths from 3 to 10 mm. With increasing the layer depth, the criticalManumber, critical azimuthal wave number and critical phase velocity decrease. Some of 3-D simulation results are compared with those of LSA. 3-D results are found consistent with the LSA results except for a case ofD= 0.05 where 3-D simulation gives a stationary 3-D flow under a largeMa.