Journal of computational fluids engineering (한국전산유체공학회지)

Korean Society of Computational Fluids Engineering (한국전산유체공학회)
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AXISYMMETRIC STOKES FLOW PAST A DISK IN A CIRCULAR TUBE

원관 내의 디스크를 지나는 축대칭 스톡스 유동

  • Received : 2016.08.22
  • Accepted : 2016.10.28
  • Published : 2016.12.31
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Abstract

A two-dimensional Stokes flow past a circular disk in a circular tube is analyzed. The circular disk is located coaxially with the circular tube and the Hagen-Poiseuille flow exists at upstream and downstream far from the circular disk. The Stokes approximation is used and the flow is investigated analytically by using the method of eigenfunction expansion and the method of least square. From the analysis, the stream function and the pressure of the flow field are obtained, and the streamlines and pressure distribution are shown. Also, the pressure and shear stress distributions on the circular disk and circular tube wall are calculated, and shown for some typical radii of the circular disk. The additional pressure drop induced by the disk and the drag force exerted on the disk are compared as functions of the radius of the circular disk, and it is shown that the shear force on the wall of the tube increases due to the disk.

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References

  1. 1965, Happel, J. and Brenner, H., Low Reynolds Number Hydrodynamics, Prentice-Hall, New Jersey.
  2. 2005, Karniadakis, G., Beskok, A. and Aluru, N., Microflows and Nanoflows Fundamentals and Simulation, Springer, New York.
  3. 2010, Berthier, J. and Silberzan, P., Microfluidics for Biotechnology, Artech House, Boston.
  4. 1969, Wang, H. and Skalak, R., "Viscous Flow in a Cylindrical Tube Containing a Line of Spherical Particles," J. Fluid Mech., Vol.38, pp.75-96. https://doi.org/10.1017/S002211206900005X
  5. 1996, Wang, C.Y., "Settling of Discs Inside a Vertical Fluid-Filled Tube," Appl. Sci. Res., Vol.56, pp.43-51. https://doi.org/10.1007/BF02282921
  6. 1969, Shail, R. and Norton, D.J., "On the Slow Broadside Motion of a Thin Disc along the Axis of a Fluid-Filled Circular Duct," Proc. Camb. Phil. Soc., Vol.65, pp.793-802. https://doi.org/10.1017/S0305004100003625
  7. 1984, Ui, T.J., Hussey, R.G. and Roger, R.P., "Stokes Drag on a Cylinder in Axial Motion," Phys. Fluids, Vol.27, pp.787-795. https://doi.org/10.1063/1.864706
  8. 1996, Pulley, J.W., Hussey, R.G. and Davis, A.M.J., "Low Nonzero Reynolds Number Drag of a Thin Disk Settling Axisymmetrically within a Cylindrical Outer Boundary," Phys. Fluids, Vol.8, pp.2275-2283. https://doi.org/10.1063/1.869014
  9. 2005, Nitin, S. and Chhabra, R.P., "Wall Effects in Two-dimensional Axisymmetric Flow over a Circular Disk Oriented Normal to Flow in Cylindrical Tube," Can. J. Chem. Eng., Vol.83, pp.450-457.
  10. 2011, Yoon, S.-H. and Jeong, J.-T., "Study of Stokes Flow Past a Vertical Plate in a Two Dimensional Channel," Trans. of the KSME(B), Vol.35, pp.609-615.
  11. 2013, Jeong, J.-T. and Yoon, S.-H., "Study on Stokes Flow Past a Circular Cylinder in a Two Dimensional Channel," Trans. of the KSME(B), Vol.37, pp.895-900.
  12. 1987, Dvinsky, A.S. and Popel, A.S., "Motion of a Rigid Cylinder between Parallel Plates in Stokes Flow, Part 1 : Motion in a Quiescent Fluid and Sedimentation," Computers & Fluids, Vol.15, No.4, pp.391-404. https://doi.org/10.1016/0045-7930(87)90031-4
  13. 1987, Dvinsky, A.S. and Popel, A.S., "Motion of a Rigid Cylinder between Parallel Plates in Stokes Flow, Part 2 : Poiseuille and Couette Flow," Computers & Fluids, Vol.15, No.4, pp.405-419. https://doi.org/10.1016/0045-7930(87)90032-6
  14. 2000, Selvadurai, A.P.S., Partial Differential Equations in Mechanics 2, Springer, New York, pp.409-411.
  15. 2005, Jeong, J.-T. and Choi, S.-R., "Axisymmetric Stokes Flow through a Circular Orifice in a Tube," Phys. Fluids, Vol.17, 053602. https://doi.org/10.1063/1.1921867
  16. 1976, Hildebrand, F.B., Advanced Calculus for Applications, 2nd ed., Prentice-Hall, New Jersey, pp.141-153.