Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-20T06:54:34.182Z Has data issue: false hasContentIssue false
  • English
  • Français

Head-on collision of two coaxial vortex rings: experiment and computation

Published online by Cambridge University Press:  26 April 2006

Chin-Chou Chu ,
Chi-Tzung Wang ,
Chien-Cheng Chang ,
Ray-Yu Chang  and
Wen-Tyzh Chang
Chin-Chou Chu
Affiliation:
Institute of Applied Mechanics, College of Engineering, National Taiwan University, Taipei 106, Taiwan, Republic of China
Chi-Tzung Wang
Affiliation:
Institute of Applied Mechanics, College of Engineering, National Taiwan University, Taipei 106, Taiwan, Republic of China
Chien-Cheng Chang
Affiliation:
Institute of Applied Mechanics, College of Engineering, National Taiwan University, Taipei 106, Taiwan, Republic of China
Ray-Yu Chang
Affiliation:
Institute of Applied Mechanics, College of Engineering, National Taiwan University, Taipei 106, Taiwan, Republic of China
Wen-Tyzh Chang
Affiliation:
Institute of Applied Mechanics, College of Engineering, National Taiwan University, Taipei 106, Taiwan, Republic of China
Get access Rights & Permissions [Opens in a new window]

Abstract

Head-on collision of two coaxial vortex rings has been studied by joint experimental and numerical investigation. The Reynolds number, ReΓ, based on the initial circulation of the vortex rings, ranged from 400 to 2700. Besides numerical data, the vorticity field was also resolved by a non-intrusive visualization technique, LIPA, which enabled simultaneous measurement of velocities at multiple locations on a plane area. It was found that the enstrophy, rather than circulation, revealed three stages of evolution of the vortex rings prior to their breakdown. These include the free-travelling stage, stage of vortex stretching and the stage of viscous dissipation dominance. The results indicate that it would be incorrect to neglect the viscous effect, in particular, for the latter two stages of flow development. In fact, the rebound behaviour of the vortex rings for lower ReΓ is essentially a viscous phenomenon and is found to be closely related to the dissipation of enstrophy when the vortex rings are brought to interact actively with each other and is also related to the increase of the vorticity core diameter in the stage of dominance of viscous dissipation. Furthermore, an instant dimensionless group, Nt/ReΓ, based on the local vorticity distribution and the radius of a vortex ring, is found to be appropriate to characterize the onset of instability. Our investigation indicates that, in the range of observation, bulging instability will be observed during collision when Nt/ReΓ exceeds a critical value, (Nt/ReΓ)cr, which is a function of the initial core-size of the vortex ring. Comparisons showed that the numerical, measured, and visualization results were in consistent agreement; this not only enables us to assess the range of validity of the axisymmetry assumed for the numerical simulation, but also provides us with a rational basis for further analysis of azimuthal instability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 296 , 10 August 1995 , pp. 39 - 71
Copyright
© 1995 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chu, C. C. & Liao, Y. Y. 1992 A quantitative study of the flow around an impulsively started circular cylinder. Exps Fluids 13, 137–146.Google Scholar
Chu, C. C., Wang, C. T. & Hsieh, C. S. 1993 An experimental investigation of vortex motions near surfaces. Phys. Fluids A 5, 662–676.Google Scholar
Crow, S. C. 1970 Stability theory for a pair of trailing vortices. AIAA J. 8, 2172–2179.Google Scholar
Kambe, T. & Minota, T. 1983 Acoustic wave radiated by head-on collision of two vortex rings. Proc. R. Soc. Lond. A 386, 277–308.Google Scholar
Kambe, T. & Mya Oo, U. 1984 An axisymmetric viscous vortex motion and its acoustic emission. J. Phys. Soc. Japan 53, 2263–2273.Google Scholar
Khorrami, M. R. 1991 On the viscous modes of instability of a trailing line vortex. J. Fluid Mech. 225, 197–212.Google Scholar
Leonard, A. 1985 Three dimensional vortex flows. Ann. Rev. Fluid Mech. 17, 523–559.Google Scholar
Lim, T. T. & Nickels, T. B. 1992 Instability and reconnection in the head-on collision of two vortex rings. Nature 357, 225–227.Google Scholar
Maxworthy, T. 1972 The structure and stability of vortex rings. J. Fluid Mech. 51, 15–32.Google Scholar
Maxworthy, T. 1977 Some experimental studies of vortex rings. J. Fluid Mech. 81, 465–495.Google Scholar
Oshima, Y. 1978 Head-on collision of two vortex rings. J. Phys. Soc. Japan 44, 328–331.Google Scholar
Peace, A. J. & Riley, N. 1983 A viscous vortex pair in ground effect. J. Fluid Mech. 129, 409–426.Google Scholar
Shariff, K., Leonard, A., Zabusky, N. J. & Ferziger, J. H. 1988 Acoustics and dynamics of coaxial interacting vortex rings. In Vortex Motion (ed. H. Hasimoto & T. Kambe), pp. 337–343. North-Holland.
Shariff, K. & Leonard, A. 1992 Vortex rings. Ann. Rev. Fluid Mech. 24, 235–279.Google Scholar
Spall, R. E., Gatski, T. B. & Grosch, C. E. 1987 A criterion for vortex breakdown. Phys. Fluids 30, 3434–3440.Google Scholar
Stanaway, S., Shariff, K. & Hussain, F. 1988 Head-on collision of viscous vortex rings. Proceedings of the Summer Program, Center for Turbulence Research, pp. 287–309.
Widnall, S. E., Bliss, D. B. & Tsai, C.-Y. 1974 The instability of short waves on a vortex ring. J. Fluid Mech. 66, 35–47.Google Scholar