Scaling properties of vortex ring formation at a circular tube opening

Abstract

A vortex sheet model is applied to study vortex ring formation at the edge of a circular tube, for accelerating piston velocities Up∼tm. We determine properties of the vortex ring as a function of the piston motion and investigate the extent to which similarity theory for planar vortex sheet separation applies. For piston strokes up to half the tube diameter, we find that the ring diameter, core size and circulation are well predicted by the planar similarity theory. The axial ring translation is a superposition of an upstream component predicted by the theory and a downstream component which is linear in the piston stroke. The front of the fluid volume exiting the tube is also linear in the piston stroke and travels with 75% of the piston velocity. The core size decreases and the distribution of fluid near the core becomes more asymmetric as the parameter m increases.