Skip to main content
SpringerLink
Log in

Vortex ring formation for low Re numbers

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The dynamics of formation and evolution of vortex rings with low Reynolds numbers created in a piston-cylinder arrangement are studied. The ratio of the piston displacement L m to the nozzle diameter D 0 determines the vortex size and evolution. Experiments with different conditions are presented: translation velocity of the piston and stroke ratio L m /D 0 for 150 < Re < 260. Measurements of the 2D velocity field were obtained with a PIV technique. The vortex circulation was computed considering a vortex identification scheme (Q criterion). The results show that there is a critical value of L m /D 0 above which the circulation inside the vortex cannot increase and remains constant. For the Reynolds numbers studied, we found that the limit stroke ratio is 4 ≤ L m /D 0 ≤ 6. As Re decreases, the vortices become “thicker”; therefore, they are able to accumulate more vorticity and increase their circulation.

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. Shariff K., Leonard A.: Vortex rings. Ann. Rev. Fluid Mech. 24, 235–279 (1992)

    Article  MathSciNet  Google Scholar 

  2. Lim, T.T., Nickels, T.B.: Vortex rings. In: Green S.I. (ed.) Fluid Vortices, Kluwer Academic Publishers, Berlin, pp. 95–153. (1995)

  3. Anderson E.J., Demont M.E.: Jet flow in steadily swimming adult squid. J. Exp. Biol. 208, 1125–1146 (2005)

    Article  Google Scholar 

  4. Bartol I.K., Krueger P.S., Stewart W.J., Thompson J.T.: Pulsed jet dynamics of squid hatchlings at intermediate Reynolds numbers. J. Exp. Biol. 212, 1506–1518 (2009)

    Article  Google Scholar 

  5. Bartol I.K., Krueger P.S., Thompson J.T.: Hydrodynamics of pulsed jetting in juvenile and adult brief squid Lolliguncula brevis: evidence of multiple jet modes and their implications for propulsive efficiency. J. Exp. Biol. 212, 1889–1903 (2009)

    Article  Google Scholar 

  6. Dabiri J.O., Colin S.P., Costello J.H.: Fast-swimming hydromedusae exploit velar kinematics to form an optimal vortex wake. J. Exp. Biol. 209, 2025–2033 (2006)

    Article  Google Scholar 

  7. Gharib M., Rambod E., Kheradvar A., Sahn D.J.: Optimal vortex formation as an index of cardiac health. Proc. Natl. Adad. Sci. USA 103, 6305–6308 (2006)

    Article  Google Scholar 

  8. Querzoli G., Falchi M., Romano G.P.: On the flow field generated by a gradually varying flow through an orifice. Eur. J. Mech. B Fluid. 29, 259–268 (2010)

    Article  MATH  Google Scholar 

  9. Maxworthy T.: Some experimental studies of vortex rings. J. Fluid Mech. 81, 465–495 (1977)

    Article  Google Scholar 

  10. Didden N.: On the formation of vortex rings: rolling-up and production of circulation. Z. Angew. Mech. Phys. 30, 101–116 (1979)

    Article  Google Scholar 

  11. Glezer A., Coles D.: An experimental study of a turbulent vortex ring. J. Fluid Mech. 211, 243–283 (1990)

    Article  Google Scholar 

  12. Weigand A., Gharib M.: On the evolution of laminar vortex rings. Exp. Fluids 22, 447–457 (1997)

    Article  Google Scholar 

  13. Gharib M., Rambod E., Shariff K.: A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  14. Mohseni K., Ran H., Colonius T.: Numerical experiments on vortex ring formation. J. Fluid Mech. 430, 267–282 (2001)

    Article  MATH  Google Scholar 

  15. Rosenfeld M., Rambod E., Gharib M.: Circulation and formation number of laminar vortex rings. J. Fluid Mech. 376, 297–318 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  16. Dabiri J.O., Gharib M.: Delay of vortex ring pinch-off by an imposed bulk counter-flow. Phys. Fluids 16, L28–30 (2004)

    Article  Google Scholar 

  17. Krueger P.S., Dabiri J.O., Gharib M.: The formation number of vortex rings formed in uniform background coflow. J. Fluid Mech. 556, 147–166 (2006)

    Article  MATH  Google Scholar 

  18. Linden P.F., Turner J.S.: The formation of optimal vortex rings, and the efficiency of propulsion devices. J. Fluid Mech. 427, 61–72 (2001)

    Article  MATH  Google Scholar 

  19. Dabiri J.O., Gharib M.: Starting flow through nozzles with temporally variable exit diameter. J. Fluid Mech. 538, 111–136 (2005)

    Article  MATH  Google Scholar 

  20. Jeong J., Hussain F.: On the identification of a vortex. J. Fluid Mech. 285, 69–94 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  21. Haller G.: An objective definition of a vortex. J. Fluid Mech. 525, 1–26 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  22. Chakraborty P., Balachandar S., Adrian R.J.: On the relation between local vortex identification schemes. J. Fluid Mech. 535, 189–214 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  23. Hunt, J.C.R., Wray, A., Moin, P.: Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Report CTR-S88 (1988)

  24. Chong M.S., Perry A.E., Cantwell B.J.: A general classification of three-dimensional flow fields. Phys. Fluids A 2, 765–777 (1990)

    Article  MathSciNet  Google Scholar 

  25. Okubo A.: Horizontal dispersion of floatable trajectories in the vicinity of velocity singularities such as convergences. Deep Sea. Res. 17, 445–454 (1970)

    Google Scholar 

  26. Weiss J.: The dynamics of entrophy transfer in 2-dimensional hydrodynamics. Phys. D 48, 273–294 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  27. Oullette N.T., Gollub J.P.: Curvature fields, topology, and the dynamics of spatiotemporal chaos. Phys. Rev. Lett. 99, 194502 (2007)

    Article  Google Scholar 

  28. Braun W., Lillo F.de , Eckhardt B.: Geometry of particle paths in turbulent flows. J. Turbul. 7, 62 (2006)

    Article  MathSciNet  Google Scholar 

  29. Willert C., Gharib M.: Digital particle image velocimetry. Exp. Fluids 10, 181–193 (1991)

    Article  Google Scholar 

  30. Raffel M., Willert C., Kompenhans J.: Particle Image Velocimetry. A practical guide. Springer, Berlin (1998)

    Google Scholar 

  31. Ozcan O., Meyer K.E., Larsen P.S.: Measurement of mean rotation and strain rate tensors by using stereoscopic PIV. Exp. Fluids 39, 771–783 (2005)

    Article  Google Scholar 

  32. Holman J.P.: Experimental Methods for Engineers, 6th edn. McGraw-Hill, New York (1994)

    Google Scholar 

  33. Lourenco L., Krothapalli A.: On the accuracy of velocity and vorticity measurements with PIV. Exp. Fluids 18, 421–428 (1995)

    Article  Google Scholar 

  34. Dabiri J.: Optimal vortex formation as a unifying principle in biological propulsion. Ann. Rev. Fluid Mech. 41, 17–33 (2009)

    Article  MathSciNet  Google Scholar 

  35. Michalke A., Timme A.: On the inviscid instability of certain two-dimensional vortex-type flows. J. Fluid Mech. 29, 647–666 (1967)

    Article  MATH  Google Scholar 

  36. Shetty S., Assay-Davis X., Marcus P.: On the interaction of Jupiter’s great red spot and zonal jet streams. J. Atmos. Sci. 64, 4432–4444 (2007)

    Article  Google Scholar 

  37. Mohseni K., Gharib M.: A model for universal time scale of vortex ring formation. Phys. Fluids 10, 2436–2438 (1998)

    Article  Google Scholar 

  38. Fraenkel L.E.: Examples of steady vortex rings of small cross-section in an ideal fluid. J. Fluid Mech. 51, 119–135 (1972)

    Article  MATH  Google Scholar 

  39. Norbury J.: A family of steady vortex rings. J. Fluid Mech. 57, 417–431 (1973)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, 04510, Mexico, DF, Mexico

    C. Palacios-Morales & R. Zenit

Authors
  1. C. Palacios-Morales
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Zenit
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Zenit.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Palacios-Morales, C., Zenit, R. Vortex ring formation for low Re numbers. Acta Mech 224, 383–397 (2013). https://doi.org/10.1007/s00707-012-0755-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-012-0755-4

Keywords

Search

Navigation