Volume 44 Issue 1
Jan.  2023
Turn off MathJax
Article Contents
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

Stokes Flow in Cylindrical Containers With Rotating Ends

doi: 10.21656/1000-0887.430197
  • Received Date: 2022-06-09
  • Rev Recd Date: 2022-06-24
  • Available Online: 2022-07-19
  • Publish Date: 2023-01-15
  • The Stokes flow in cylindrical containers with rotating ends was studied. Based on the characteristics of the flow, the problem was reduced to the eigenvalue and eigensolution problem of Hamiltonian dual equations with the axial coordinate simulated as the time scale. By means of the completeness of the symplectic eigensolution space and the adjoint symplectic orthogonality relationship between the eigensolutions, the expansion of the solution to the problem was obtained, and the numerical method for calculating the expansion coefficients was given. In the cases of one-end rotating, two-end rotating at the same or opposite angular velocity, the velocity and stress distributions of the flow in the cylindrical containers with different aspect ratios (of the length to the radius), were investigated. The velocity and stress distributions, and the characteristics of the flows under different boundary conditions were revealed.

  • loading
  • [1]
    PAO H P. Numerical solution of the Navier-Stokes equations for flows in the disk-cylinder system[J]. Physics of Fluids, 1972, 15(1): 4-11. doi: 10.1063/1.1693752
    [2]
    BERTELÀ M, GORI F. Laminar flow in a cylindrical container with a rotating cover[J]. Journal of Fluids Engineering-Transactions of the ASME, 1982, 104(1): 31-39. doi: 10.1115/1.3240849
    [3]
    DUCK P W. On the flow between two rotating shrouded discs[J]. Computers & Fluids, 1986, 14(3): 183-196.
    [4]
    DIJKSTRA D, VAN HEIJST G J F. The flow between two finite rotating disks enclosed by a cylinder[J]. Journal of Fluid Mechanics, 1983, 128: 123-154. doi: 10.1017/S0022112083000415
    [5]
    VOGEL H U. Experimentelle ergebnisse über die laminare strömung in einem zylindrischen gehäuse mit darin rotierender scheibe[D]. PhD Thesis. Göttingen: Max-Planck-Inst für Strömungsforschung, 1968.
    [6]
    ESCUDIER M P. Observation of the flow produced in a cylindrical container by a rotating endwall[J]. Experiments in Fluids, 1984, 2: 189-196. doi: 10.1007/BF00571864
    [7]
    VALENTINE D T, JAHNKE C C. Flows induced in a cylinder with both end walls rotating[J]. Physics of Fluids, 1994, 6(8): 2702-2710. doi: 10.1063/1.868159
    [8]
    GELFGAT A Y, BAR-YOSEPH P Z, SOLAN A. Stability of combined swirling flow with and without vortex breakdown[J]. Journal of Fluid Mechanics, 1996, 311(1): 1-36.
    [9]
    KAHOUADJI L, WITKOWSKI L M. Free surface due to a flow driven by a rotating disk inside a vertical cylindrical tank: axisymmetric configuration[J]. Physics of Fluids, 2014, 26: 072105. doi: 10.1063/1.4890209
    [10]
    MUKHERJEE A, STEINBERG V. Von Kármán swirling flow between a rotating and a stationary smooth disk: experiment[J]. Physical Review Fluids, 2018, 3: 014102. doi: 10.1103/PhysRevFluids.3.014102
    [11]
    LIM C W, XU X S. Symplectic elasticity: theory and applications[J]. Applied Mechanics Reviews, 2010, 63(5): 050802. doi: 10.1115/1.4003700
    [12]
    钟万勰. 弹性力学求解新体系[M]. 大连: 大连理工大学出版社, 1995.

    ZHONG Wanxie. A New Systematic Methodology for Theory of Elasticity[M]. Dalian: Dalian University of Technology Press, 1995. (in Chinese)
    [13]
    ZHONG W X. Duality System in Applied Mechanics and Optimal Control[M]. New York: Kluwer Academic Publishers, 2004.
    [14]
    胡启平, 陈哲, 周娟. Hamilton力学下框筒结构剪滞翘曲位移模式研究[J]. 应用数学和力学, 2022, 43(4): 374-381

    HU Qiping, CHEN Zhe, ZHOU Juan. Research on shear lag warping displacement modes of frame-tube structures based on the Hamiltonian mechanics[J]. Applied Mathematics and Mechanics, 2022, 43(4): 374-381.(in Chinese)
    [15]
    满淑敏, 高强, 钟万勰. 非完整约束Hamilton动力系统保结构算法[J]. 应用数学和力学, 2020, 41(6): 581-590

    MAN Shumin, GAO Qiang, ZHONG Wanxie. A structure-preserving algorithm for Hamiltonian systems with nonholonomic constraints[J]. Applied Mathematics and Mechanics, 2020, 41(6): 581-590.(in Chinese)
    [16]
    张俊霖, 倪一文, 李庆东, 等. 吸湿老化影响下天然纤维增强复合圆柱壳屈曲分析的辛方法[J]. 应用数学和力学, 2021, 42(12): 1238-1247

    ZHANG Junlin, NI Yiwen, LI Qingdong, et al. A symplectic approach for buckling analysis of natural fiber reinforced composite shells under hygrothermal aging[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1238-1247.(in Chinese)
    [17]
    张鸿庆, 阿拉坦仓, 钟万勰. Hamilton体系与辛正交系的完备性[J]. 应用数学和力学, 1997, 18(3): 217-221

    ZHANG Hongqing, ALATANCANG, ZHONG Wanxie. The Hamiltonian system and completeness of symglectic orthogonal system[J]. Applied Mathematics and Mechanics, 1997, 18(3): 217-221.(in Chinese)
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(5)

    Article Metrics

    Article views (129) PDF downloads(45) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return