The Unsteady Wake of a Circular Cylinder near a Free Surface

  • Paul Reichl
  • Kerry Hourigan
  • Mark Thompson
Article

Abstract

The behaviour of the wake Strouhal number for flow past a cylinder close to a free surface at both low and moderate Froude numbers is investigated numerically. For the low Froude number case (i.e., gravity-dominated), the results obtained are similar to those for flow past a cylinder close to an adjacent no-slip boundary. As the distance between the wall and the cylinder is reduced, the Strouhal number, as measured from the time varying lift, increases to a maximum at a gap ratio of 0.70. Further gap reduction leads to a rapid decrease in the Strouhal number, with shedding finally ceasing altogether at gap ratios below 0.16. The agreement between the results for a free surface and a no-slip boundary suggests that the mechanism behind the suppression of vortex shedding is common. For flow at a fixed gap ratio and a moderate Froude number, two distinctly different wake states are observed with the flow passing over the cylinder tending to switch from a state of attachment to the free surface, to one of separation from it, and then back again in a pseudo-periodic fashion. Even though there is a significant difference in Reynolds number, the predicted numerical two-dimensional behaviour is found to compare favourably with the experimental observations at higher Reynolds number.

bluff-body flows free surface metastability unsteady wake 

References

  1. 1.
    Angrilli, F., Bergamschi, S. and Cossalter, V., Investigation of wall induced modifications to vortex shedding from a circular cylinder. ASME J. Fluids Engrg. 104 (1982) 518–522.CrossRefGoogle Scholar
  2. 2.
    Barkley, D. and Henderson, R.D., Three-dimensional Floquet stability of the wake of a circular cylinder. J. Fluid Mech. 322 (1996) 215–241.MATHCrossRefADSGoogle Scholar
  3. 3.
    Bearman, P.W., On vortex shedding from a circular cylinder in the critical Reynolds number regime. J. Fluid Mech. 37 (1969) 577–585.CrossRefADSGoogle Scholar
  4. 4.
    Bearman, P.W. and Zdravkovich, M.M., Flow around a circular cylinder near a plane boundary. J. Fluid Mech. 89 (1978) 33–47.CrossRefADSGoogle Scholar
  5. 5.
    Grass, A.J., Raven, P.W.J., Stuart, R.J. and Bray, J.A., The influence of boundary layer velocity gradients and bed proximity on vortex shedding from free spanning pipelines. ASME J Fluids Engrg. 106 (1984) 70–78.Google Scholar
  6. 6.
    Hirt, C.W. and Nichols, B.D., Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1981) 201–225.MATHCrossRefADSGoogle Scholar
  7. 7.
    Hoyt, J.W. and Sellin, R.H.J., A comparison of the tracer and PIV results in visualizing water flow around a cylinder close to the free surface. Exp. Fluids 28 (2000) 261–265.CrossRefGoogle Scholar
  8. 8.
    Huerre, P. and Monkewitz, P.A., Local and global instabilities in spatially developing flows. Annual Rev. Fluid Mech. 22 (1990) 473–537.MATHCrossRefADSMathSciNetGoogle Scholar
  9. 9.
    Karniadakis, G.Em. and Triantafyllou, G.S., Frequency selection and asymptotic states in laminar wakes. J. Fluid Mech. 199 (1989) 441–469.MATHCrossRefADSGoogle Scholar
  10. 10.
    Koch, W., Local instability characteristics and frequency determination of self-excited wake flows. J. Sound Vibration 99(1) (1985) 53–83.CrossRefADSGoogle Scholar
  11. 11.
    Lei, C., Cheng, L. and Kavanagh, K., Re-examination of the effect of a plane boundary on force and vortex shedding of a circular cylinder. J. Wind Engrg. Ind. Aerodynam. 80 (1999) 263–286.CrossRefGoogle Scholar
  12. 12.
    Martin, J.C. and Moyce, W.J., Part IV: An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philos. Trans. Roy. Soc. London 244 (1952) 312–334.ADSMathSciNetGoogle Scholar
  13. 13.
    Miyata, H., Shikazono, N. and Kani, M., Forces on a circular cylinder advancing steadily beneath the free-surface. Ocean Engrg. 17 (1990) 81–104.CrossRefGoogle Scholar
  14. 14.
    Ohring, S. and Lugt, H.J., Interaction of a viscous vortex pair with a free surface. J. FluidMech. 227 (1991) 47–70.ADSGoogle Scholar
  15. 15.
    Reichl, P.J., Flow past a cylinder close to a free surface. Ph.D. Thesis, Monash University (2002).Google Scholar
  16. 16.
    Sarpkaya, T., Vorticity, free-surface and surfactants. Annual Rev. Fluid Mech. 28 (1996) 83–128.CrossRefADSMathSciNetGoogle Scholar
  17. 17.
    Sheridan, J., Lin, J.-C. and Rockwell, D., Metastable states of a cylinder wake adjacent to a free surface. Phys. Fluids 7 (1995) 2099–2101.MATHCrossRefADSGoogle Scholar
  18. 18.
    Sheridan, J., Lin, J.-C. and Rockwell, D., Flow past a cylinder close to a free surface. J. Fluid Mech. 330 (1997) 1–30.CrossRefADSGoogle Scholar
  19. 19.
    Taneda, S., Experimental investigation of vortex streets. J. Phys. Soc. Japan 20 (1965) 1714–1721.CrossRefADSGoogle Scholar
  20. 20.
    Triantafyllou, G.S. and Dimas, A.A., Interaction of two-dimensional separated flows with a free surface at low Froude numbers. Phys. Fluids A 1(11) (1989) 1813–1821.CrossRefADSGoogle Scholar
  21. 21.
    Williamson, C.H.K., The existence of two stages in the transition to three-dimensionality of a cylinder wake. Phys. Fluids 31 (1988) 3165–3168.CrossRefADSGoogle Scholar
  22. 22.
    Yu, D. and Tryggvason, G., The free-surface signature of unsteady two-dimensional vortex flows. J. Fluid Mech. 218 (1990) 547–572.CrossRefADSGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Paul Reichl
    • 1
  • Kerry Hourigan
    • 1
  • Mark Thompson
    • 1
  1. 1.Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical EngineeringMonash UniversityClaytonAustralia

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