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首页> 外文期刊>International Journal of Heat and Mass Transfer >Linear stability analysis of thermocapillary flow in a slowly rotating shallow annular pool using spectral element method
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Linear stability analysis of thermocapillary flow in a slowly rotating shallow annular pool using spectral element method

机译：用谱元法分析缓慢旋转浅环形池中毛细血管流动的线性稳定性

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摘要

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 rates ω, 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 for ω ＜ 940 and ω ＞ 1185. Thermocapillary flow is the dominant factor of the instability for ω ＜ 940, and the pool rotation becomes the key role for the first instability for ω ＞ 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 fixed ω. 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.
机译：使用Legendre谱元方法研究了缓慢旋转的浅环形池中毛细血管流动的稳定性。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，并在内圆柱壁处冷却。通过线性稳定性分析确定了不同的无量纲旋转速度ω（从0到2000）的临界稳定性条件。此外，应用了能量分析以进一步说明流动不稳定性的潜在机理。结果表明，对于ω＜940和ω＞ 1185，存在一个Hopf分叉。热毛细流是ω＜940的不稳定性的主导因素，池旋转成为ω＞ 1185的第一不稳定的关键。在940≤ω≤1185的区间内观察到转折点，这对应于二维稳定流和三维振荡流之间的三个过渡，这是由于两个驱动力在固定ω时随着马兰戈尼数的增加而竞争。在池旋转的情况下，结果表明，可以推断出流动不稳定性最初是在冷壁附近的区域中发生的，这证明了极速梯度以及局部动能的分布。

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  • 来源
  • 作者

    Linmao Yin; Zhong Zeng; Zhouhua Qiu; Huan Mei; Liangqi Zhang; Yongxiang Zhang;

  • 作者单位

    Department of Engineering Mechanics, College of Aerospace Engineering, Chongqing University, Chongqing 400044, China,State Key Laboratory of Coal Mine Disaster Dynamics and Control (Chongqing University), China;

    Department of Engineering Mechanics, College of Aerospace Engineering, Chongqing University, Chongqing 400044, China,State Key Laboratory of Crystal Material (Shandong University), China,Chongqing Key Laboratory of Heterogeneous Material Mechanics (Chongqing University), China;

    Department of Engineering Mechanics, College of Aerospace Engineering, Chongqing University, Chongqing 400044, China;

    Department of Engineering Mechanics, College of Aerospace Engineering, Chongqing University, Chongqing 400044, China;

    Department of Engineering Mechanics, College of Aerospace Engineering, Chongqing University, Chongqing 400044, China;

    Department of Engineering Mechanics, College of Aerospace Engineering, Chongqing University, Chongqing 400044, China,Chongqing Key Laboratory of Heterogeneous Material Mechanics (Chongqing University), China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Thermocapillary flow; Spectral element method; Linear stability analysis; Energy analysis;

    机译：热毛细流;光谱元素法线性稳定性分析;能量分析;

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