Volume 8, Issue 4
Numerical Simulations of Two Coaxial Vortex Rings Head-on Collision

Hui Guan, Zhi-Jun Wei, Elizabeth Rumenova Rasolkova & Chui-Jie Wu

Adv. Appl. Math. Mech., 8 (2016), pp. 616-647.

Published online: 2018-05

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  • Abstract

Vortex rings have been a subject of interest in vortex dynamics due to a plethora of physical phenomena revealed by their motions and interactions within a boundary. The present paper is devoted to physics of a head-on collision of two vortex rings in three dimensional space, simulated with a second order finite volume scheme and compressible. The scheme combines non-iterative approximate Riemannsolver and piecewise-parabolic reconstruction used in inviscid flux evaluation procedure. The computational results of vortex ring collisions capture several distinctive phenomena. In the early stages of the simulation, the rings propagate under their own self-induced motion. As the rings approach each other, their radii increase, followed by stretching and merging during the collision. Later, the two rings have merged into a single doughnut-shaped structure. This structure continues to extend in the radial direction, leaving a web of particles around the centers. At a later time, the formation of ringlets propagate radially away from the center of collision, and then the effects of instability involved leads to a reconnection in which small-scale ringlets are generated. In addition, it is shown that the scheme captures several experimentally observed features of the ring collisions, including a turbulent breakdown into small-scale structures and the generation of small-scale radially propagating vortex rings, due to the modification of the vorticity distribution, as a result of the entrainment of background vorticity and helicity by the vortex core, and their subsequent interaction.

  • Keywords

Three dimensional numerical simulation, vortex ring, collision, large eddysimulation.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-8-616, author = {}, title = {Numerical Simulations of Two Coaxial Vortex Rings Head-on Collision}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {4}, pages = {616--647}, abstract = {

Vortex rings have been a subject of interest in vortex dynamics due to a plethora of physical phenomena revealed by their motions and interactions within a boundary. The present paper is devoted to physics of a head-on collision of two vortex rings in three dimensional space, simulated with a second order finite volume scheme and compressible. The scheme combines non-iterative approximate Riemannsolver and piecewise-parabolic reconstruction used in inviscid flux evaluation procedure. The computational results of vortex ring collisions capture several distinctive phenomena. In the early stages of the simulation, the rings propagate under their own self-induced motion. As the rings approach each other, their radii increase, followed by stretching and merging during the collision. Later, the two rings have merged into a single doughnut-shaped structure. This structure continues to extend in the radial direction, leaving a web of particles around the centers. At a later time, the formation of ringlets propagate radially away from the center of collision, and then the effects of instability involved leads to a reconnection in which small-scale ringlets are generated. In addition, it is shown that the scheme captures several experimentally observed features of the ring collisions, including a turbulent breakdown into small-scale structures and the generation of small-scale radially propagating vortex rings, due to the modification of the vorticity distribution, as a result of the entrainment of background vorticity and helicity by the vortex core, and their subsequent interaction.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m829}, url = {http://global-sci.org/intro/article_detail/aamm/12107.html} }
TY - JOUR T1 - Numerical Simulations of Two Coaxial Vortex Rings Head-on Collision JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 616 EP - 647 PY - 2018 DA - 2018/05 SN - 8 DO - http://dor.org/10.4208/aamm.2014.m829 UR - https://global-sci.org/intro/aamm/12107.html KW - Three dimensional numerical simulation, vortex ring, collision, large eddysimulation. AB -

Vortex rings have been a subject of interest in vortex dynamics due to a plethora of physical phenomena revealed by their motions and interactions within a boundary. The present paper is devoted to physics of a head-on collision of two vortex rings in three dimensional space, simulated with a second order finite volume scheme and compressible. The scheme combines non-iterative approximate Riemannsolver and piecewise-parabolic reconstruction used in inviscid flux evaluation procedure. The computational results of vortex ring collisions capture several distinctive phenomena. In the early stages of the simulation, the rings propagate under their own self-induced motion. As the rings approach each other, their radii increase, followed by stretching and merging during the collision. Later, the two rings have merged into a single doughnut-shaped structure. This structure continues to extend in the radial direction, leaving a web of particles around the centers. At a later time, the formation of ringlets propagate radially away from the center of collision, and then the effects of instability involved leads to a reconnection in which small-scale ringlets are generated. In addition, it is shown that the scheme captures several experimentally observed features of the ring collisions, including a turbulent breakdown into small-scale structures and the generation of small-scale radially propagating vortex rings, due to the modification of the vorticity distribution, as a result of the entrainment of background vorticity and helicity by the vortex core, and their subsequent interaction.

Hui Guan, Zhi-Jun Wei, Elizabeth Rumenova Rasolkova & Chui-Jie Wu. (2020). Numerical Simulations of Two Coaxial Vortex Rings Head-on Collision. Advances in Applied Mathematics and Mechanics. 8 (4). 616-647. doi:10.4208/aamm.2014.m829
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