Viscous diffusion effects on the self-induced distortions of rectangular vortex rings

Abstract

Large eddy simulation, stereoscopic particle image velocimetry, and hot-wire anemometry are conducted to study the viscous diffusion effects on the self-induced deformations of the aspect ratio 2 rectangular vortex rings at Reynolds numbers Ri = UDh/ν = 355, 877.5, 1775, 8775, 17 750 (i = 1, …, 5). The differences between the axis-switching of isolated vortex rings and rectangular jets are explained. At increased viscous effects, the rotational content of the vortices diffuses and grows in size. The high curvature corners of the rectangular vortex rings induce additional velocities which distort the topology until it appears to be rotated for 90°, the so-called axis-switching phenomenon. Strong viscous effects (R1) diffuse the ring before the switching is completed, while reduced viscous effects allow for the first (R2, R3) and second (R4, R5) switching. For R2 and R3, the rotated rectangular rings bifurcate into a pair of semi-circular topologies. Space-time mapping of the instantaneous streamwise velocity at the vortex ring axis reveals strong correlation spots for the occurrence of each axis-switching. Vortex rings are found to decelerate more quickly with increased viscous effects and hence exhibit reduced penetration rates. The temporal variation of the advection velocity of the vortex ring demonstrates major peaks in accordance with the number of axis-switchings. Trajectories of the vortex cores in two orthogonal planes demonstrate contractions/expansions conforming to the sine/cosine waves associated with the varicose instability modes. A pair of orthogonal varicose modes interacts with the phase lagging/leading equal to the quarter of a full cycle which is interestingly equal to the axis-switching frequency.