Vortex ring velocity and minimum separation in an infinite train of vortex rings generated by a fully pulsed jet

A pulsed jet with a period of no flow between pulses (i.e., a fully pulsed jet) produces a multiplicity of vortex rings whose characteristics are determined by the jet pulsing parameters. The present study analyzes the case of impulsively initiated and terminated jet pulses in the limit of equal pulse duration and period to determine the minimum possible vortex ring separation obtainable from a fully pulsed jet. The downstream character of the flow is modeled as an infinite train of thin, coaxial vortex rings. Assuming inviscid flow and matching the circulation, impulse, kinetic energy, and frequency of the jet and vortex ring train allow the properties of the vortex ring train to be determined in terms of the ratio of jet slug length-to-diameter ratio (L/D) used for each pulse. The results show the minimum ring separation may be made arbitrarily small as L/D is decreased and the corresponding total ring velocity remains close to half the jet velocity for L/D < 4, but the thin-ring assumption is violated for L/D > 1.5. The results are discussed in the context of models of pulsed-jet propulsion.