Reynolds-number effect on vortex ring evolution

F. Kaplanski, Yasuhide Fukumoto, Y. Rudi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

An analytical model describing a vortex ring for low Reynolds numbers (Re) proposed previously by Kaplanski and Rudi [Phys. Fluids,17, 087101 (2005)], is extended to a vortex rings for higher Reynolds numbers. The experimental results show that the vortex ring core takes the oblate ellipsoidal shape with increasing Re. In order to model this feature, we suggest an expression for the vorticity distribution, which corrects the linearized solution of the Navier-Stokes equation, with two disposable nondimensional parameters λ and β governing the shape of the vortex core, and derive the new expressions for the streamfuction, circulation, energy and translation velocity on the basis of it. The appropriate values of λ and β are calculated by equating the nondimensional energy Ed and circulation Γd of the theoretical vortex to the corresponding values obtained from the experimental or numerical vortex ring. To validate the model, the data adapted from the numerical study of a vortex ring at Re=1400 performed by Danaila and Helie [Phys. Fluids, 20, 073602 (2008)], is applied. It is shown that the predicted temporal evolution of the translation velocity at high Reynolds numbers matches very well with the experiments and numerical simulations.

Original languageEnglish
Title of host publicationRecent Progresses in Fluid Dynamics Research - Proceedings of the Sixth International Conference on Fluid Mechanics, ICFM VI
Pages57-60
Number of pages4
DOIs
Publication statusPublished - Nov 8 2011
EventProceedings of the 6th International Conference on Fluid Mechanics: Recent Progresses in Fluid Dynamics Research, ICFM VI - Guangzhou, China
Duration: Jun 30 2011Jul 3 2011

Publication series

NameAIP Conference Proceedings
Volume1376
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

OtherProceedings of the 6th International Conference on Fluid Mechanics: Recent Progresses in Fluid Dynamics Research, ICFM VI
CountryChina
CityGuangzhou
Period6/30/117/3/11

Fingerprint

vortex rings
Reynolds number
high Reynolds number
vortices
fluids
low Reynolds number
Navier-Stokes equation
vorticity
energy
simulation

All Science Journal Classification (ASJC) codes

  • Ecology, Evolution, Behavior and Systematics
  • Ecology
  • Plant Science
  • Physics and Astronomy(all)
  • Nature and Landscape Conservation

Cite this

Kaplanski, F., Fukumoto, Y., & Rudi, Y. (2011). Reynolds-number effect on vortex ring evolution. In Recent Progresses in Fluid Dynamics Research - Proceedings of the Sixth International Conference on Fluid Mechanics, ICFM VI (pp. 57-60). (AIP Conference Proceedings; Vol. 1376). https://doi.org/10.1063/1.3651834

Reynolds-number effect on vortex ring evolution. / Kaplanski, F.; Fukumoto, Yasuhide; Rudi, Y.

Recent Progresses in Fluid Dynamics Research - Proceedings of the Sixth International Conference on Fluid Mechanics, ICFM VI. 2011. p. 57-60 (AIP Conference Proceedings; Vol. 1376).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kaplanski, F, Fukumoto, Y & Rudi, Y 2011, Reynolds-number effect on vortex ring evolution. in Recent Progresses in Fluid Dynamics Research - Proceedings of the Sixth International Conference on Fluid Mechanics, ICFM VI. AIP Conference Proceedings, vol. 1376, pp. 57-60, Proceedings of the 6th International Conference on Fluid Mechanics: Recent Progresses in Fluid Dynamics Research, ICFM VI, Guangzhou, China, 6/30/11. https://doi.org/10.1063/1.3651834
Kaplanski F, Fukumoto Y, Rudi Y. Reynolds-number effect on vortex ring evolution. In Recent Progresses in Fluid Dynamics Research - Proceedings of the Sixth International Conference on Fluid Mechanics, ICFM VI. 2011. p. 57-60. (AIP Conference Proceedings). https://doi.org/10.1063/1.3651834
Kaplanski, F. ; Fukumoto, Yasuhide ; Rudi, Y. / Reynolds-number effect on vortex ring evolution. Recent Progresses in Fluid Dynamics Research - Proceedings of the Sixth International Conference on Fluid Mechanics, ICFM VI. 2011. pp. 57-60 (AIP Conference Proceedings).
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