Dynamics of a free rectangular vortex ring generated by an impulsively driven piston

Large-eddy simulations were conducted on the formation and behaviour of an aspect ratio of 2 rectangular vortex ring (RVR) modelled after an impulsively driven piston for a ‘cylindrical-slug’-based approach, instead of assuming idealised conditions for its initialisation. Results show the occurrence of over-pressure effects where the orifice exit velocity profile varies with time, evolving from a ‘saddleback’ to a ‘top-hat’ profile as the RVR is being generated. A robust axis-switching behaviour is observed with localised effects conferred by the four corners, leading to intriguing changes to the RVR shape during a full cycle and agrees well with earlier results from Ghasemi et al. (2018 Phys. Fluids , vol. 30, no. 12). However, comparisons with the earlier study reveal that the present RVR penetration is significantly deeper and faster with higher advection velocities, as well as the presence of an additional advection velocity peak caused by the impulsively started piston. Vortex-core trajectories predicted using a previously proposed sinusoidal model show significant discrepancies with the present results and hence, a dual-wavelength damped-oscillation-based prediction model is proposed to better account for both the oscillating axis-switching behaviour and localised trajectory variations. Finally, circulation, vortex stretching and helicity density results are presented to showcase their transient behaviours for the present RVR and how they relate to the key axis-switching stages. In particular, the continuously evolving and complex circumferential flows along the RVR filament due to its unique geometry and axis-switching behaviour are demonstrated based on circumferential flows determined along the RVR filament.