Numerical study of a vortex ring impacting a flat wall

We numerically study a vortex ring impacting a flat wall with an angle of incidence theta >= 0 degrees in three dimensions by using the lattice Boltzmann equation. The hydrodynamic behaviour of the ring-wall interacting flow is investigated by systematically varying the angle of incidence theta in the range of 0 degrees <= theta <= 40 degrees and the Reynolds number in the range of 100 <= Re <= 1000, where the Reynolds number Re is based on the translational speed and initial diameter of the vortex ring. We quantify the effects of theta and Re on the evolution of the vortex structure in three dimensions and other flow fields in two dimensions. We observe three distinctive flow regions in the theta-Re parameter space. First, in the low-Reynolds-number region, the ring-wall interaction dissipates the ring without generating any secondary rings. Second, with a moderate Reynolds number Re and a small angle of incidence theta, the ring-wall interaction generates a complete secondary vortex ring, and even a tertiary ring at higher Reynolds numbers. The secondary vortex ring is convected to the centre region of the primary ring and develops azimuthal instabilities, which eventually lead to the development of hairpin-like small vortices through ring-ring interaction. And finally, with a moderate Reynolds number and a sufficiently large angle of incidence theta, only a secondary vortex ring is generated. The secondary vortex wraps around the primary ring and propagates from the near end of the primary ring, which touches the wall first, to the far end, which touches the wall last. The rings develop a helical structure. Our results from the present study confirm some existing experimental observations made in the previous studies.