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Linear Stability Analysis of Thermocapillary Flow in Rotating Shallow Pools Heated from Inner Wall

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Abstract

Thermocapillary flow of silicon melt (Pr=0.011) in shallow annular pool heated from inner wall was simulated at the dimensionless rotation rate ω ranging from 0~7000. The effect of pool rotation on the stability of the thermocapillary flow was investigated. The steady axisymmetric basic state was solved by using the spectral element method; the critical stability parameters were determined by linear stability analysis; the mechanism of the flow instability was explored by the analysis of energy balance. A stability diagram, exhibiting the variation of the critical Marangoni number versus the dimensionless rotation rate ω was presented. The results reveal that only one Hopf bifurcation point appeared in the intervals of ω<3020 and ω>3965, and the corresponding instability was caused by the shear energy, which was provided by the thermocapillary force and pool rotation, respectively. In addition, the competition between thermocapillary force and pool rotation leads to three Hopf bifurcation points in the range of 3020<ω<3965 with the increase of Marangoni number.

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Acknowledgements

This work is supported by the National Natural Science Foundation of P. R. China (No. 11572062), and Program for Changjiang Scholars and Innovative Research Team in University (No. IRT_17R112).

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Authors and Affiliations

  1. State Key Laboratory of Coal Mine Disaster Dynamics and Control (Chongqing University), Chongqing, 400044, China

    Zu-an Tian & Zhong Zeng

  2. Department of Engineering Mechanics, College of Aerospace Engineering, Chongqing University, Chongqing, 400044, China

    Zu-an Tian, Zhong Zeng, Hao Liu, Linmao Yin, Liangqi Zhang & Long Qiao

  3. Department of Engineering Mechanics, College of Mathematics and Physics, Chongqing University of Science and Technology, Chongqing, 401331, China

    Zu-an Tian

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  1. Zu-an Tian
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  2. Zhong Zeng
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Correspondence to Zhong Zeng.

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Tian, Za., Zeng, Z., Liu, H. et al. Linear Stability Analysis of Thermocapillary Flow in Rotating Shallow Pools Heated from Inner Wall. J. Therm. Sci. 29, 251–259 (2020). https://doi.org/10.1007/s11630-019-1156-y

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  • DOI: https://doi.org/10.1007/s11630-019-1156-y

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