An openfoam numerical investigation of leapfrogging of vortex rings

In this report, coaxial circular and elliptical vortex rings at AR=3 were simulated with OpenFOAM 2.4.0 by solving the incompressible Navier-Stokes equations. A modified pimpleFoam solver and Large Eddy Simulation (LES) were used in order to reduce the effects of numerical dissipation and capture the large-scale eddy structures. The study aims to investigate if leapfrogging is possible for elliptical vortex rings and whether bifurcation and axis-switching will affect the occurrence. Leapfrogging of two coaxial circular vortex rings at Re=3000, axis-switching of single elliptical vortex ring at Re=2200 were first simulated and validated with existing literature. The results obtained satisfactory comparability at the specified mesh size of R0=30Δx. Two coaxial elliptical vortex rings were then simulated next at Re=2200 and Re=4400. One through pass was observed for both cases even though the dynamics were very convoluted. Bifurcation of Ring 2 (trailing) into 2 side rings and 1 centre ring, and leapfrogging occurred in tandem at the early stages of the simulation. The side rings impinged on Ring 1 (leading) and vortex reconnections were observed. Consequently, only the bifurcated centre ring went through a complete pass. It was observed that Ring 2 axis switched with a higher frequency than Ring 1 for both Re cases after the first full pass. Based on the current initial core size, separation distance and aspect ratio, it was concluded that a second pass is not plausible due to the increasing stream-wise distance between the two rings after the first pass.Bachelor of Engineering (Aerospace Engineering