Effect of pressure evolution on the formation enhancement in dual interacting vortex rings

In the biological locomotion, the ambit pressure is of particular importance to use as a means of propulsion. The multiple vortex rings have been proved to generate additional thrust by interaction, but the mechanism of this thrust enhancement is still unknown. This study examines the effect of ambit pressure on formation enhancement in interacting dual vortex rings. The vortex rings, which have the same formation time, are successively generated in a piston-cylinder apparatus. The finite-time Lyapunov exponent (FTLE) visualizes the flow fields as an indication of Lagrangian coherent structures (LCSs), and the pressure field is calculated based on the digital particle image velocity (DPIV). We extract the back pressure of the rear vortex in dual vortices and the back pressure circulation \varGamma_\rm b, which is defined as a form of overpressure circulation \varGamma_\rm p. The \varGamma_\rm b has a positive linear relationship with \varGamma_\rm p. A critical interval distance d_\rm cr^* in a range of 0.32-0.42 is found where \varGamma_\rm b and \varGamma_\rm p reach the maximum synchronously, leading to a full-interaction mode. Moreover, an over-interaction mode and an under-interaction mode are proposed when the dimensionless interval distance d^* is smaller or larger than d_\rm cr^*. To conclude, the high back pressure caused by vortex interaction can enhance the formation of vortex rings and lead to high thrust.