Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Study on Stokes Flow Past Circular Cylinder in Two-Dimensional Channel

2차원 채널 내의 원형실린더를 지나는 스톡스 유동에 대한 연구

  • Received : 2013.02.15
  • Accepted : 2013.07.24
  • Published : 2013.10.01
Download PDF
⟨ Previous Next ⟩

Abstract

A two-dimensional Stokes flow past a circular cylinder in a channel is analyzed. The circular cylinder is located at the center of the channel, and a plane Poiseuille flow exists upstream and downstream far from the circular cylinder. The Stokes approximation is used, and the flow is investigated analytically by using the eigenfunction expansion and the least square methods. From the analysis, the stream function and pressure distribution are obtained, and the pressure and shear stress distributions on the circular cylinder and channel wall are calculated. The additional pressure drop induced by the circular cylinder and the force exerted on it are calculated as functions of the length of the radius of the circular cylinder. For a typical length of the radius of the circular cylinder, the streamline pattern and pressure distribution are shown.

2차원 채널 내의 원형실린더를 지나는 유동에 대한 이론적 연구를 수행하였다. 원형 실린더는 채널의 상하 중앙부에 위치하며, 원형실린더에서 멀리 떨어진 채널 내에는 포아제 유동이 존재한다. 스톡스 근사를 적용하고 유동의 고유함수 전개와 오차의 최소제곱법을 사용하여 유동장을 해석하였다. 해석의 결과로 유동함수와 압력분포 식을 구하였으며, 채널의 벽면과 원형실린더에 작용하는 압력 및 전단응력 분포를 계산하였다. 원형실린더로 인해 부가적으로 발생하는 압력 강하와 원형실린더가 받는 힘을 원형실린더의 반지름 길이의 함수로 계산하였으며, 대표적인 실린더 반지름 길이에 대하여 유선과 압력분포를 도시하였다.

Keywords

References

  1. Petropoulos, A., Kaltsas, G., Randjelovic, D. and Gogolides, E., 2010, "Study of Flow and Pressure Field in Micro-channels with Various Cross-section Areas," Microelectronic Engineering 87, pp.827-829. https://doi.org/10.1016/j.mee.2009.10.025
  2. Dalabaev, U., 2011, "Numerical Investigation of the Character of the Lift on a Cylindrical Particle in Poiseuille Flow of a Plane Channel," Journal of Engineering Physics and Thermophysics, Vol. 84, No. 6, pp.1388-1392. https://doi.org/10.1007/s10891-011-0609-2
  3. Singha, S. and Sinhamahapatra, K. P., 2010, "Flow Past a Circular Cylinder Between Parallel Walls at Low Reynolds Numbers," Ocean Engineering, Vol. 37, pp.757-769. https://doi.org/10.1016/j.oceaneng.2010.02.012
  4. Ozgoren, M., 2006, "Flow Structure in the Downstream of Square and Circular cylinders," Flow Measurement and Instrument, Vol. 17, pp.225-235. https://doi.org/10.1016/j.flowmeasinst.2005.11.005
  5. Buyruk, E., Johnson, M. W. and Owen, I., 1998, "Numerical and Experimental Study of Flow and Heat Transfer Around a Tube in Cross Flow at Low Reynolds Number," International Journal of Heat and Fluid Flow, Vol. 19, pp.223-232. https://doi.org/10.1016/S0142-727X(97)10027-3
  6. Wang, C. Y., 2002, "Stokes Flow Through a Channel Obstructed by Horizontal Cylinders," Acta Mechanica, Vol. 157, pp.213-221. https://doi.org/10.1007/BF01182165
  7. Yoon, S. H. and Jeong, J. T., 2011, "Study of Stokes Flow Past a Vertical Plate in a Two Dimensional Channel," Trans. Korean Soc. Mech. Eng. B, pp.609-615. https://doi.org/10.3795/KSME-B.2011.35.6.609
  8. Dvinsky, A. S. and Popel, A. S., 1987, "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
  9. Dvinsky, A. S. and Popel, A. S., 1987, "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
  10. Kalita, J. C. and Gupta, M. M., 2010, "A Stream function-Velocity Approach for 2D Transient Incompressible Viscous Flows," International Journal for Numerical Methods in Fluids, Vol. 62, pp.237-266.
  11. Park, G. S. and Kwak, Y. K., 2004, "Flow Survey Around Two-Dimensional Circular Cylinder Using PIV Technique," The Korean Society of Ocean Engineers, Vol. 18, pp.1-7.
  12. White, F. M., 1991, Viscous Fluid Flow, McGraw-Hill, New York, pp.91-95.