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

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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.

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