The formation of turbulent vortex rings by synthetic jets

An investigation is made into the mechanism of pinch-off for turbulent vortex rings formed by a synthetic jet using time resolved particle image velocimetry measurements in air. During formation, measurements of the material acceleration field show a trailing pressure maximum (TPM) forms behind the vortex core. The adverse pressure gradient behind this TPM inhibits vorticity transport into the ring and the TPM is spatially coincident with the termination of vorticity flux into a control volume moving with the ring. A Lagrangian Coherent Structures (LCS) analysis is shown to be in agreement with the role of the TPM in pinch-off and in identifying the vortex ring before separation. The LCS analysis provides physical insights which form the basis of a revised model of pinch-off, based on kinematics, which predicts the time of formation (formation number) well for the present dataset. The delivery of impulse to the vortex ring is also considered. Two equally important mechanisms are shown to play a role: a material flux and a vortex force. In the case of long maximum stroke ratio, it is demonstrated that a vortex force continues to deliver impulse to the ring after the material flux is terminated at pinch-off and that this contribution may be substantial. This shows that the pinch-off and separation process cannot be considered impulse invariant, which has important implications for unsteady propulsion, present models of vortex ring formation, and existing explanations for vortex ring pinch-off. (C) 2013 AIP Publishing LLC.