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端部旋转的圆柱形容器内的Stokes流

王尕平 刘竟慧

王尕平,刘竟慧. 端部旋转的圆柱形容器内的Stokes流 [J]. 应用数学和力学,2023,44(1):52-60 doi: 10.21656/1000-0887.430197
引用本文: 王尕平,刘竟慧. 端部旋转的圆柱形容器内的Stokes流 [J]. 应用数学和力学,2023,44(1):52-60 doi: 10.21656/1000-0887.430197
WANG Gaping, LIU Jinghui. Stokes Flow in Cylindrical Containers With Rotating Ends[J]. Applied Mathematics and Mechanics, 2023, 44(1): 52-60. doi: 10.21656/1000-0887.430197
Citation: WANG Gaping, LIU Jinghui. Stokes Flow in Cylindrical Containers With Rotating Ends[J]. Applied Mathematics and Mechanics, 2023, 44(1): 52-60. doi: 10.21656/1000-0887.430197

端部旋转的圆柱形容器内的Stokes流

doi: 10.21656/1000-0887.430197
基金项目: 国家自然科学基金(11202043)
详细信息
    作者简介:

    王尕平(1972—),女,副教授,博士,硕士生导师(通讯作者. E-mail:gaping99@sina.com

  • 中图分类号: O357.1

Stokes Flow in Cylindrical Containers With Rotating Ends

  • 摘要:

    该文以端部旋转的圆柱形容器内的Stokes流为研究对象,根据流动的特点,将轴向坐标模拟为时间,则问题归结为Hamilton对偶方程的本征值和本征解问题。利用本征解空间的完备性和本征解之间的共轭辛正交关系,给出了问题解的展开形式,并建立了展开系数的数值求解方法。采用该方法研究了单端旋转、两端以相同或相反角速度旋转时不同外形比(容器的高度与半径之比)时圆柱形容器内流动速度和应力的分布情况,展示了不同边界条件下流场的一些特点。

  • 图  1  圆柱形容器的几何示意图

    Figure  1.  The geometry of the cylindrical container

    图  2  无限长容器内的流动:(a) 速度${U_\theta }$等高线;(b) 应力$ {\bar \tau _{z\theta }} $等高线

    Figure  2.  The flow in the semi-infinite cylindrical container: (a) the contours of velocity ${U_\theta }$; (b) the contours of stress $ {\bar \tau _{z\theta }} $

    图  3  两端部以角速度$\varOmega = 1$同向旋转时,不同外形比的容器内流动速度${U_\theta }$的等高线:(a) A=1;(b) A=2;(c) A=6

    Figure  3.  The contours of velocity ${U_\theta }$ in cylindrical containers with two ends rotating at the same angular velocity $\varOmega = 1$ and different geometric aspect ratios: (a) A =1; (b) A=2; (c) A=6

    图  4  两端部以角速度$\varOmega = 1$反向旋转时,不同外形比的容器内流动速度${U_\theta }$的等高线: (a) A=1;(b) A=2;(c) A=6

    Figure  4.  The contours of velocity ${U_\theta }$ in cylindrical containers with two ends counter rotating at angular velocity $\varOmega = 1$ and different geometric aspect ratios: (a) A=1; (b) A=2; (c) A=6

    图  5  端部应力条件时,外形比为$ A = 6 $的容器内的流动:(a) 速度${U_\theta }$等高线;(b) 应力$ {\bar \tau _{z\theta }} $等高线

    Figure  5.  With stress condition at the end, the flow in the cylindrical container for $ A = 6 $: (a) the contours of velocity${U_\theta }$; (b) the contours of stress $ {\bar \tau _{z\theta }} $

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出版历程
  • 收稿日期:  2022-06-09
  • 修回日期:  2022-06-24
  • 网络出版日期:  2022-07-19
  • 刊出日期:  2023-01-15

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