Circulation of a Vortex Ring Generated by Pulsating Jet Flow

Abstract

In order to use vortex rings for mass and momentum transport, the relationship between the circulation of vortex rings generated continuously by a pulsating jet flow, which are referred to herein as ‘cyclic vortex rings’, and the conditions of jet flow are investigated experimentally. The results indicate that the formation time at which the cyclic vortex rings reach maximum circulation, i.e., become optimal vortex rings, can be estimated using the concept proposed by Gharib et al. Based on their concept, the optimal vortex rings are formed when the translation velocity of the vortex core becomes equal to the convection velocity of the shear layer of the jet. The translation velocity of vortex rings and the convection velocity of shear layers can be estimated by empirical equations under pulsating jet conditions. Therefore, the formation time of the optimal vortex rings can be estimated from the pulsating jet conditions, when the circulation of vortex rings stop growing and the vortex rings start to become disconnected from the shear layers. The circulation of vortex rings estimated using this method is in good agreement with the measurement data within the measurement error. There exists a specific Strouhal number at which the circulation of the vortex rings reaches the maximum value. This Strouhal number is expected to be the optimal generating condition of cyclic vortex rings for using transportation.