Skip to main content
SpringerLink
Log in

Uniform shear flow past a circular cylinder

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

This paper solves the two-dimensional problem of the unsteady shear flow of a viscous incompressible fluid past a circular cylinder. The flow is calculated using two methods. The first takes the form of a double series solution where an expansion is carried out in powers of the time, t, and in powers of the parameter where R is the Reynolds number. This approximate analytical solution is valid for small times following the start of the motion and for large Reynolds numbers. The second method involves a spectral-finite difference procedure for numerically integrating the full Navier-Stokes equations expressed in terms of a stream function and vorticity. Our results demonstrate that for small times and moderately large R the two methods of solution are in good agreement. Results are presented for a wide range of Reynolds numbers. Comparisons with previous studies are also carried out and discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Zdravkovich, M. M.: Flow around circular cylinders, vol 1. Fundamentals. Oxford University Press 1997.

  2. Zdravkovich, M. M.: Flow around circular cylinders, vol. 2. Applications. Oxford University Press 2003.

  3. G. K. Batchelor J. T. Green (1972) ArticleTitleThe hydrodynamic interaction of two small freely-moving spheres in a linear flow field J. Fluid Mech. 56 375–400

    Google Scholar 

  4. H. Brenner M. E. O’Neill (1972) ArticleTitleOn the Stokes resistance of multiparticle systems in a linear shear flow Chem. Eng. Sci. 27 1421–1439 Occurrence Handle10.1016/0009-2509(72)85029-2

    Article  Google Scholar 

  5. F. P. Bretherton (1962) ArticleTitleSlow viscous motion round a cylinder in a simple shear J. Fluid Mech. 12 591–613

    Google Scholar 

  6. C. R. Robertson A. Acrivos (1970) ArticleTitleLow Reynolds number shear flow past a rotating circular cylinder. Part 1. Momentum transfer J. Fluid Mech. 40 685–704

    Google Scholar 

  7. S. K. Jordan J. E. Fromm (1972) ArticleTitleLaminar flow past a circle in a shear flow Phys. Fluids 15 972–976 Occurrence Handle10.1063/1.1694058

    Article  Google Scholar 

  8. H. Tamura M. Kiya M. Arie (1980) ArticleTitleNumerical study on viscous shear flow past a circular cylinder Bull. JSME 23 1952–1958

    Google Scholar 

  9. F. Yoshino T. Hayashi (1984) ArticleTitleA numerical solution of flow around a rotating circular cylinder in uniform shear flow Bull. JSME 27 1850–1857

    Google Scholar 

  10. Y. T. Chew S. C. Luo M. Cheng (1997) ArticleTitleNumerical study of a linear shear flow past a rotating cylinder J. Wind Eng. Ind. Aerodyn. 66 107–125 Occurrence Handle10.1016/S0167-6105(97)00016-0

    Article  Google Scholar 

  11. A. Mukhopadhyay P. Venugopal S. P. Vanka (1999) ArticleTitleNumerical study of vortex shedding from a circular cylinder in linear shear flow Trans. ASME J. Fluids. Eng 121 460–468

    Google Scholar 

  12. C. Lei L. Cheng K. Kavanagh (2000) ArticleTitleA finite difference solution of the shear flow over a circular cylinder Ocean. Eng. 27 271–290 Occurrence Handle10.1016/S0029-8018(98)00050-X

    Article  Google Scholar 

  13. A. Mukhopadhyay P. Venugopal S. P. Vanka (2002) ArticleTitleOblique vortex shedding from a circular cylinder in linear shear flow Comp. Fluids 31 1–24 Occurrence Handle10.1016/S0045-7930(01)00017-2

    Article  Google Scholar 

  14. T. Wu C. F. Chen (2000) ArticleTitleLaminar boundary-layer separation over a circular cylinder in uniform shear flow Acta Mech. 144 71–82 Occurrence Handle10.1007/BF01181829

    Article  Google Scholar 

  15. Y. Xu C. Dalton (2001) ArticleTitleComputation of force on a cylinder in a simple shear flow J. Fluids Struct. 15 941–954 Occurrence Handle10.1006/jfls.2001.0390

    Article  Google Scholar 

  16. C. A. Kossack A. Acrivos (1974) ArticleTitleSteady simple shear flow past a circular cylinder at moderate Reynolds numbers: a numerical solution J. Fluid Mech. 66 353–376

    Google Scholar 

  17. C. F. Chen B. J. Mangione (1969) ArticleTitleVortex shedding from circular cylinders in sheared flow AIAA J. 7 1211–1212

    Google Scholar 

  18. M. Kiya H. Tamura M. Arie (1980) ArticleTitleVortex shedding from a circular cylinder in moderate-Reynolds number shear flow J. Fluid Mech. 101 721–735

    Google Scholar 

  19. T. S. Kwon H. J. Sung J. M. Hyun (1992) ArticleTitleExperimental investigation of uniform-shear flow past a circular cylinder Trans. ASME J. Fluids Eng. 114 457–460

    Google Scholar 

  20. H. J. Sung C. K. Chun J. M. Hyun (1995) ArticleTitleExperimental study of uniform-shear flow past a rotating cylinder Trans. ASME J. Fluids Eng. 117 62–67

    Google Scholar 

  21. C. M. Zettner M. Yoda (2001) ArticleTitleThe circular cylinder in simple shear at moderate Reynolds numbers: An experimental study Exp. Fluids 30 346–353 Occurrence Handle10.1007/s003480000206

    Article  Google Scholar 

  22. C. H. K. Williamson (1988) ArticleTitleThe existence of two stages in the transition to three-dimensionality of a circular wake Phys. Fluids 31 3165–3168 Occurrence Handle10.1063/1.866925

    Article  Google Scholar 

  23. H.-Q. Zhang U. Fey B. R. Noack M. Konig H. Eckelmann (1995) ArticleTitleOn the transition of the cylinder wake Phys. Fluids 7 779–794 Occurrence Handle10.1063/1.868601

    Article  Google Scholar 

  24. R. L. Panton (1984) Incompressible flow Wiley New York

    Google Scholar 

  25. S. Szepessy P. W. Bearman (1992) ArticleTitleAspect ratio and end plate effects on vortex shedding from a circular cylinder J. Fluid Mech. 234 191–218

    Google Scholar 

  26. Graham J. M. R.: Comparing computation of flow past circular cylinders with experimental data. In: Bluff body wakes, dynamics and instabilities, pp. 317–324. New York: Springer 1993.

  27. H. M. Blackburn R. D. Henderson (1999) ArticleTitleA study of two-dimensional flow past an oscillating cylinder J. Fluid Mech. 385 255–286 Occurrence Handle10.1017/S0022112099004309

    Article  Google Scholar 

  28. H. M. Badr S. C. R. Dennis (1985) ArticleTitleTime-dependent viscous flow past an impulsively started rotating and translating circular cylinder J. Fluid Mech. 158 447–488

    Google Scholar 

  29. W. M. Collins S. C. R. Dennis (1973) ArticleTitleFlow past an impulsively started circular cylinder J. Fluid Mech. 60 105–127

    Google Scholar 

  30. Dennis, S.C.R., Chang, G.-Z.: Numerical integration of the Navier-Stokes equations in two, dimensions. Technical Summary Report No. 859, p. 89. Mathematics Research Center, University of Wisconsin 1969.

Download references

Author information

Authors and Affiliations

  1. Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario, M5S 3H6, Canada

    K. Rohlf

  2. Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    S. J. D. D’Alessio

Authors
  1. K. Rohlf
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. J. D. D’Alessio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. J. D. D’Alessio.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rohlf, K., D’Alessio, S. Uniform shear flow past a circular cylinder. Acta Mechanica 178, 199–222 (2005). https://doi.org/10.1007/s00707-004-0197-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-004-0197-8

Keywords

Search

Navigation