Author : Ijas Hussain 1
Date of Publication :13th April 2017
Abstract: Vortex rings can be easily produced in the laboratory by pushing a definite column of fluid into a tank containing stationary fluid at a certain velocity. The velocity of a single vortex ring is reducing up on its propagation and diameter is increasing due to the conservation of momentum. The Reynolds number has no influence in the ring diameter and it is depending on stroke ratio only but Reynolds number effecting inversely to the core diameter of the vortex ring. Interaction of vortex rings with cylinders shows cut and reconnection of vortex rings for small diameter cylinders. The interaction produces a pair of secondary vortices having opposite vorticity and reduces the diameter of the primary ring. The interaction with higher diameter cylinders causes the ring to become turbulent and no such observations as other are visible.
- Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press
- Saffman, P. G., (1970) “The Velocity of Viscous Vortex Rings”, Studies in Applied Mathematics. 49(4): 371- 380.
- Norbury, J., (1973) “A family of steady vortex rings”, Journal of Fluid Mechanics. 57: 3: 417-431.
- Maxworthy, T., (1972) “The structure and stability of vortex rings”, Journal of Fluid Mechanics. 51: 15-32.
- Widnall, S. E. & Sullivan, J. P., (1973) “On the stability of vortex rings”, Proceedings of the Royal Society of London A. 332: 335-353.
- Didden, N., (1979) “On the Formation of Vortex Rings: Rolling up and Production of Circulation”, Journal of Applied Mathematics and Physics (ZAMP). 30: 101-116.
- Lim, T. T., (1997(a)) “A note on the leapfrogging between two coaxial vortex rings at low Reynolds numbers”, The Physics of Fluids. 9 (1): 239-241.
- Dabiri, J. O., (2005) “Unsteady Fluid Mechanics of Starting-Flow Vortex Generators with Time-Dependent Boundary Conditions”, PhD thesis, California Institute of Technology.
- Gharib, M., Rambod, E. & Shariff, K., (1998) “A universal time scale for vortex ring formation”, Journal of Fluid Mechanics. 360: 121-140.
- Akhmetov, D. G., Lugovtsov, B. A. & Tarasov, V. F., (1980) “Extinguishing gas and oil well fires by means of vortex rings”, Combustion, Explosion & Shock Waves. 16: 490-494