Effect of an Exit-Wedge Angle on Pinch-off and Mass Entrainment of Vortex Rings in Air

Article

Abstract

The effects of exit-wedge angle on evolution, formation, pinch-off, propagation and diffusive mass entrainment of vortex rings in air were studied using digital particle image velocimetry. Vortex rings were generated by passing a solenoid-valve-controlled air jet through a cylindrical nozzle. Experiments were performed over a wide range of exit-wedge angles (10° ≤ α ≤ 90°) of the cylindrical nozzle, initial Reynolds numbers (450 ≤ Re ≤ 4,580) and length-to-diameter ratios (0.9 ≤ L/D ≤ 11) of the air jet. For sharp edges (α ≤ 10°), a secondary ring may emerge at high Reynolds numbers, which tended to distort the vortex ring if ingested into it. For blunt edges (α ≥ 45°), by contrast, stable vortex rings were produced. The formation phase of a vortex ring was found to be closely related to its evolution pattern. An exit-wedge angle of 45° was found to be optimal for rapid pinch-off and faster propagation and better stability of a vortex ring. Diffusive mass entrainment was found to be between 35% and 40% in the early stages of a vortex ring propagation and it gradually increased throughout the course of vortex ring propagation. Entrainment fraction was found to be sensitive to the L/D ratio of the initial jet and decreases when the L/D ratio is increased.

Keywords

Vortex ring Evolution Pinch-off Mass entrainment 

References

  1. 1.
    Shariff, K., Leonard, A.: Vortex rings. Annu. Rev. Fluid Mech. 24, 235–279 (1992). doi:10.1146/annurev.fl.24.010192.001315 CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    Lim, T.T., Nickels, T.B.: Vortex Rings. Fluid Vortices. Kluwer Academic, Norwell, pp. 95–153 (1995)Google Scholar
  3. 3.
    Maxworthy, T.: Some experimental studies of vortex ring. J. Fluid Mech. 81, 465–495 (1977) doi:10.1017/S0022112077002171 CrossRefADSGoogle Scholar
  4. 4.
    Didden, N.: On the formation of vortex rings: rolling-up and production of circulation. J. App. Math. Phys. 30, 101–115 (1979). ZAMP doi:10.1007/BF01597484 CrossRefGoogle Scholar
  5. 5.
    Gharib, M., Rambod, E., Shariff, K.: A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140 (1998). doi:10.1017/S0022112097008410 MATHCrossRefADSMathSciNetGoogle Scholar
  6. 6.
    Mohseni, K., Gharib, M.: A model for universal time scale of vortex ring formation. Phys. Fluids 10, 2436–2438 (1998). doi:10.1063/1.869785 CrossRefADSGoogle Scholar
  7. 7.
    Rosenfeld, M., Rambod, E., Gharib, M.: Circulation and formation number of laminar vortex rings. J. Fluid Mech. 376, 297–318 (1998). doi:10.1017/S0022112098003115 MATHCrossRefADSMathSciNetGoogle Scholar
  8. 8.
    Shusser, M., Gharib, M.: Energy and velocity of a forming vortex ring. Phys. Fluids 12, 618–621 (2000). doi:10.1063/1.870268 MATHCrossRefADSMathSciNetGoogle Scholar
  9. 9.
    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). doi:10.1017/S0022112000002263 MATHCrossRefADSGoogle Scholar
  10. 10.
    Mohseni, K., Ran, H., Colonius, T.: Numerical experiments on vortex ring formation. J. Fluid Mech. 430, 267–282 (2001). doi:10.1017/S0022112000003025 MATHCrossRefADSGoogle Scholar
  11. 11.
    Baird, M.H.I., Wairegi, T., Loo, H.J.: Velocity and momentum of vortex rings in relation to formation parameters. Can. J. Chem. Eng. 55, 19–26 (1977)CrossRefGoogle Scholar
  12. 12.
    Muller, E.A., Didden, N.: Zur erzeugung der zirkulation bei der bildung eines ringwirbels an einer dusenmundung. Stroj. Casop. 31, 363–372 (1980)Google Scholar
  13. 13.
    Auerbach, D.: Stirring properties of vortex rings. Phys. Fluids A. 5, 1351–1355 (1991). doi:10.1063/1.858064 CrossRefADSGoogle Scholar
  14. 14.
    Maxworthy, T.: The structure and stability of vortex rings. J. Fluid Mech. 51, 15–32 (1972). doi:10.1017/S0022112072001041 CrossRefADSGoogle Scholar
  15. 15.
    Dabiri, J.O., Gharib, M.: Fluid entrainment by isolated vortex rings. J. Fluid Mech. 511, 311–331 (2004). doi:10.1017/S0022112004009784 MATHCrossRefADSGoogle Scholar
  16. 16.
    Allen, J.J., Auvity, B.: Interaction of a vortex ring with a piston vortex. J. Fluid Mech. 465, 353–378 (2002). doi:10.1017/S0022112002001118 MATHCrossRefADSMathSciNetGoogle Scholar
  17. 17.
    Cater, J.E., Soria, J., Lim, T.T.: The interaction of the piston vortex with a piston-generated vortex ring. J. Fluid Mech. 499, 327–343 (2004). doi:10.1017/S0022112003006980 MATHCrossRefADSGoogle Scholar
  18. 18.
    Widnall, S.E., Sullivan, J.P.: On the stability of vortex rings. Proc. R. Soc. Lond. 332, 335–353 (1973)MATHCrossRefADSGoogle Scholar
  19. 19.
    Sallet, D.W.: Impulsive motion of a circular disk which causes a vortex ring. Phys. Fluids 18, 109–110 (1975). doi:10.1063/1.860982 CrossRefADSGoogle Scholar
  20. 20.
    Dziedic, M., Leutheusser, H.J.: An experimental study of viscous vortex rings. Exp. Fluids 21, 315–324 (1996)Google Scholar
  21. 21.
    Arakeri, J.H., Das, D., Krothapalli, A., Lourenco, L.: Vortex ring formation at the open end of a shock tube—a particle image velocimetry study. Phys. Fluids 16, 1008–1019 (2004). doi:10.1063/1.1649339 CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringKAISTDaejeonSouth Korea

Personalised recommendations