Coaxial and non-coaxial collisions between vortex rings and stationary spheres

Abstract

A large-eddy simulation-based study has been carried out focusing on the coaxial and non-coaxial collisions between a R e Γ 0 = 3000 vortex ring and stationary spheres. The effect of sphere size on vortex dynamics was investigated by varying the sphere-to-vortex ring diameter ratio, D / d , from 1 to 4 (where D and d are the sphere and vortex ring diameters, respectively). Four offset distances ranging from δ / D = 1 / 8 to 1 / 2 were used for non-coaxial collisions. Coaxial configurations produce vortex ring collision outcomes that are increasingly restricted to the upper part of the sphere as the diameter ratio increases. In contrast, non-coaxial configurations lead to progressively more asymmetric vortex ring collisions that feature nonuniform formations and entrainment of secondary and tertiary vortex rings. This in turn produces circumferential flows from the end closer to the sphere (near-end) to the end further away from the sphere (far-end), where they become stronger as the offset distance increases. As such, near-end primary vortex ring segments experience vortex stretching, while their far-end counterparts undergo compression. Temporal variations in circulation and vortex-stretching levels as the collisions unfold are presented to quantify these flow differences. Additionally, secondary vortex ring behavior underpins the key collision phenomena observed in non-coaxial collisions across the different spheres, reinforcing their important role in the collision mechanism. Finally, present results demonstrate that the relative sphere size matters less beyond a critical diameter ratio, while the offset distance becomes increasingly important in non-coaxial collisions.