Linear stability analysis of thermocapillary flow in a slowly rotating shallow annular pool using spectral element method
Linear stability analysis of thermocapillary flow in a slowly rotating shallow annular pool using spectral element method
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慢速旋转浅环池热毛细管流动的谱元法线性稳定性分析
DOI：
10.1016/j.ijheatmasstransfer.2016.02.031
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发表时间：
2016-06
影响因子：
5.2
通讯作者：
Zhang Yongxiang
中科院分区：
文献类型：
--
作者：
Yin Linmao;Zeng Zhong;Qiu Zhouhua;Mei Huan;Zhang Liangqi;Zhang Yongxiang
采用勒让德谱元方法研究了低速旋转浅环形池中热毛细流动的稳定性。硅熔体（Pr = 0.011）填充在具有绝热自由表面和底部的池中，在外圆柱壁处加热，在内圆柱壁处冷却。通过线性稳定性分析，确定了无因次转速ω从0到2000的临界稳定条件。此外，应用能量分析进一步阐明了流动不稳定性的内在机制。结果表明，当ω< 940和ω> 1185时，系统存在一个Hopf分支.当ω< 940时，热毛细流动是第一不稳定性的主导因素，当ω> 1185时，热毛细流动是第一不稳定性的主导因素。在940 <$ω <$1185区间内观察到三个转折点，对应于二维定常流和三维振荡流之间的三个转变，这是由于两种驱动力在固定ω下随Marangoni数增加而竞争的结果。结果表明，在旋转条件下，流动不稳定性首先发生在冷壁附近区域，并伴随着极大的速度梯度和局部动能的分布。
The stability of thermocapillary flow in a slowly rotating shallow annular pool was investigated by using the Legendre spectral element method. The silicon melt (Pr = 0.011), filling in a pool with adiabatic free surface and bottom, was heated at the outer cylindrical wall and cooled at the inner cylindrical wall. The critical stability conditions for different dimensionless rotation ratesω, ranging from 0 to 2000, were determined by linear stability analysis. Moreover, the energy analysis was applied to further illustrate the underlying mechanism of the flow instability. The results indicate that there is one Hopf bifurcation forω< 940 andω> 1185. Thermocapillary flow is the dominant factor of the instability forω< 940, and the pool rotation becomes the key role for the first instability forω> 1185. Three turning points were observed in the interval 940 ⩽ω⩽ 1185, corresponding to three transitions between two-dimensional steady flow and three-dimensional oscillatory flow, owing to the competition of two driving forces with increasing Marangoni number at a fixedω. With pool rotation, the results exhibit that the flow instability is deduced to occur initially in the zone near the cold wall with the evidence of the extreme velocity gradient and also the distribution of the local kinetic energy.
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影响因子：
1.8
作者：
J. Walker;L. Witkowski;B. Houchens
通讯作者：
J. Walker;L. Witkowski;B. Houchens
DOI：
10.1140/epjst/e2013-01776-4
发表时间：
2013-03
期刊：
The European Physical Journal Special Topics
影响因子：
--
作者：
K. Davis;Yue Huang;B. Houchens
通讯作者：
K. Davis;Yue Huang;B. Houchens
DOI：
10.1007/s100510170352
发表时间：
2001
期刊：
The European Physical Journal B - Condensed Matter and Complex Systems
影响因子：
--
作者：
N. Garnier;A. Chiffaudel
通讯作者：
N. Garnier;A. Chiffaudel
影响因子：
3.7
作者：
D. Schwabe;A. Zebib;Bok-Cheol Sim
通讯作者：
D. Schwabe;A. Zebib;Bok-Cheol Sim
影响因子：
3.7
作者：
SMITH, MK;DAVIS, SH
通讯作者：
DAVIS, SH