Numerical Study Of Two Vortex Rings’ Head-on Collision

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 article is devoted to a head-on collision of two vortex rings in three dimensional space, simulated in the Second Order Explicit Scheme. Therefore the application of the3D Cartesian-grid Finite Volume Scheme on compressible LES is investigated. The scheme combines non-iterative approximate Riemann-solver (based on linearized differ-ential relations along characteristics of one dimensional hyperbolic conservation law) and piecewise-parabolic reconstruction used in inviscid flux evaluation procedure.The computations 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 stretch-ing 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 clumping of particles is observed as distinct reconnected vortical structures have been formed, and the for-mation of ringlets propagate radially away from the center of collision. The following deformation, growth of the instability and cancellation, leads to a reconnection in which small-scale ringlets are generated.The experimental data shows that, the non-iterative approximate Riemann-solver combined with a piecewise-parabolic reconstruction, result in a robust scheme that can be extended into the late stages of the evolution of flow. In addition, it is shown that the scheme captures several experimentally observed features of the ring collisions, includ-ing a turbulent breakdown into small-scale structures and the generation of small-scale radially propagating vortex rings, due to the modifiation of the vorticity distribution, as a result of the entrainment of background vorticity and helicity by the vortex core, and their subsequent interaction. The turbulent eddy viscosity indicates that the vortex rings colliding experience a degree of turbulence during their collision, which steadily dies off.