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流向磁场下球形气泡绕流的线性稳定性分析

郑晓琳 潘君华 倪明玖

郑晓琳, 潘君华, 倪明玖. 流向磁场下球形气泡绕流的线性稳定性分析. 力学学报, 2023, 55(7): 1-10 doi: 10.6052/0459-1879-23-101
引用本文: 郑晓琳, 潘君华, 倪明玖. 流向磁场下球形气泡绕流的线性稳定性分析. 力学学报, 2023, 55(7): 1-10 doi: 10.6052/0459-1879-23-101
Zheng Xiaolin, Pan Junhua, Ni Mingjiu. The linear stability analysis of flow past a spherical bubble under the effect of streamwise magnetic field. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(7): 1-10 doi: 10.6052/0459-1879-23-101
Citation: Zheng Xiaolin, Pan Junhua, Ni Mingjiu. The linear stability analysis of flow past a spherical bubble under the effect of streamwise magnetic field. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(7): 1-10 doi: 10.6052/0459-1879-23-101

流向磁场下球形气泡绕流的线性稳定性分析

doi: 10.6052/0459-1879-23-101
基金项目: 国家自然科学基金(52006212), 中国科学院基础前沿科学研究计划(ZDBS-LY-JSC033)和中国科协青年人才托举工程 (2022QNRC001)资助项目
详细信息
    通讯作者:

    潘君华, 助理研究员, 主要研究方向为磁流体动力学、计算流体力学和颗粒两相流. E-mail: panjunhua@ucas.ac.cn

  • 中图分类号: O35

THE LINEAR STABILITY ANALYSIS OF FLOW PAST A SPHERICAL BUBBLE UNDER THE EFFECT OF STREAMWISE MAGNETIC FIELD

  • 摘要: 电磁冶金中氩气通常作为动力和载体将脱硫剂、脱氧剂吹入到液态金属中, 因此存在磁场环境下气泡在液态金属中自由运动的问题, 而绕流作为自由运动的特殊形态, 是研究自由运动问题的第一步. 本文通过有限元方法研究流向磁场作用下球形气泡绕流的全局线性稳定性, 讨论$\mathit{Re}\leqslant 1000,N\leqslant 60$参数范围内稳态轴对称基本流对时间−方位角模态小扰动的响应, 发现了8个不稳定的驻定模态, 并绘制它们在$ \mathit{Re}-N $参数平面与$ \mathit{Re}-Ha $参数平面的中性曲线. 结果显示方位角波数$ m = 1 $的驻定模态首先导致第一次常规分岔, 该模态已被广泛证实为轴对称绕流中最不稳定的模态, 使轴对称尾迹转变为由一对反向旋转涡组成的单平面对称尾迹. 同时第一次分岔的中性曲线展示磁场对球形气泡绕流先失稳后致稳的作用. 后续分岔依次由$m = 2, 3, \cdots, 8$的不稳定模态导致. 这些分岔为认识磁场环境下气泡绕流的尾迹结构提供重要的参考价值.

     

  • 图  1  计算域示意图

    Figure  1.  Sketch of the computational domain

    图  2  无磁场环境下不同纵横比$ \chi $的气泡第一次常规分岔和第二次Hopf分岔对应的临界$ Re $与文献结果的对比

    Figure  2.  The comparison of the critical Reynolds number at the first regular bifurcation and the second Hopf bifurcations with results from literatures at different aspect ratios $ \chi $ without magnetic fields

    图  3  定常轴对称基本流的流线和涡量分布

    Figure  3.  Streamlines and vorticity of steady axisymmetric base flow

    图  4  $ \mathit{Re} = 600 $时回流区长度和分离角随相互作用数$ N $的变化

    Figure  4.  The variations of recirculation length and separation angle with $ N $ at $ \mathit{Re} = 600 $

    图  5  Re=600时最大涡量随相互作用数$ N $的变化

    Figure  5.  The variations of the maximum vorticity with $ N $ at $ \mathit{Re} = 600 $

    图  6  $ \mathit{Re} = 600,N = 20 $时特征值谱在$m = 0, 1,2, \cdots,7$的分布

    Figure  6.  The eigenvalue spectra for $m = 0, 1,2, \cdots,7$ at $ \mathit{Re} = 600,N = 20 $

    图  7  不稳定模态的流向扰动速度$ {u}_{x} $的空间分布

    Figure  7.  The spatial distributions of streamwise perturbation velocity $ {u}_{x} $ for unstable modes

    图  8  $Re = 600$$m = 0, 1, 2,\cdots , 8 $的驻定模态的增长率随$ N $的连续性变化

    Figure  8.  The variations of growth rate with $ N $ for $m = 0, 1, 2,\cdots , 8$ stationary modes at $ Re = 600 $

    图  9  $m = 1, 2, \cdots, 8$的定常不稳定模态的中性曲线, $ \mathit{Re} = 600 $不同颜色的实线表示不同模态占优对应的$ N $$ Ha $的范围

    Figure  9.  The neutral curves of $m = 1, 2, \cdots, 8$ stationary unstable modes, solid lines of different colors indicate the range of $ N $ and $ Ha $ corresponding to different dominant modes at $ \mathit{Re} = 600 $

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出版历程
  • 收稿日期:  2023-03-20
  • 录用日期:  2023-05-05
  • 网络出版日期:  2023-05-06

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