A Unified Energy Feature of Vortex Rings for Identifying the Pinch-Off Mechanism

Abstract

Owing to the limiting effect of energy, vortex rings cannot grow indefinitely and thus pinch off. In this paper, experiments on the vortex rings generated using a piston-cylinder apparatus are conducted so as to investigate the pinch-off mechanisms and identify the limiting effect of energy. Both theoretical and experimental results show that the generated vortex rings share a unified energy feature, regardless of whether they are pinched-off or not. Moreover, the unified energy feature is quantitatively described by a dimensionless energy number γ, defined as γ=(E/I2Γωmax) and exhibiting a critical value γring = 0.14 ± 0.01 for the generated vortex rings. This unified energy feature reflects the limiting effect of energy and specifies the target of vortex ring formation. Furthermore, based on the tendency of γ during vortex ring formation, criteria for determining the two timescales, i.e., pinch-off time and separation time, which correspond to the onset and end of pinch-off process, respectively, are suggested.

Flow characteristics and formation optimization of vortex ring air supply

“…The pinch‐off mechanism of the vortex ring makes it impossible to grow indefinitely. In follow‐up studies, 14–19 it was found that the formation of the vortex ring was also related to the non‐pulse velocity program. When the piston is started in different velocity programs, there are obvious differences in the velocity distribution at the open interface of the generator, affecting the environmental circulation and the evolution of the vortex ring, which further affects the formation number of the vortex ring.…”

“…The pinchoff mechanism of the vortex ring makes it impossible to grow indefinitely. In follow-up studies, [14][15][16][17][18][19] it was found that the formation of the vortex ring was also related to the non-pulse velocity program.…”