A new kinematic criterion for vortex ring pinch-off

Abstract

This study lays out a methodology whereby conditions necessary for a vortex ring to separate from the shear flow can be identified by a relationship between characteristic velocities of the jet and the vortex ring along the axis of symmetry. This criterion identifies pinch-off to take place when the velocity induced at the origin of the forming vortex ring surpasses the maximum feeding velocity along the centerline, defined to be twice the piston velocity. A strategy for determining these characteristic velocities purely from the jet driving programs (i.e., without direct knowledge of the state of the leading vortex ring) is presented. A variety of jet driving conditions, including different nozzle geometries (converging radial velocity) and different jet velocity programs, are examined to validate the relationship between pinch-off and the characteristic velocities. These parameters are examined and adjusted independently of each other so that the effect of each jetting parameter can be observed independently. Nozzles which induce a converging radial velocity decrease the jet formation number to approximately two (for nearly constant velocity programs), due to the large increase in vorticity flux without increasing volume flux. Accelerating the jet velocity to compensate for the growing vortex ring substantially increases the formation number of both parallel and converging jet flows. The new centerline velocity criterion coincided very closely with vortex ring pinch-off for all cases tested, validating this criterion as a predictive tool.