Collision of a vortex ring on granular material. Part I. Interaction of the vortex ring with the granular layer

Abstract

An experimental study was carried out on the normal impact of the vortex ring on the granular layer. The Reynolds number of the vortex ring ranged from 1000 to 6000, whereas the distance to the granular layer (glass beads of diameter 0.10 mm) varied between 2 and 13 times of the diameter of the vortex ring generator nozzle. The velocity field was visualized by the sodium fluorescein and was measured by particle image velocimetry or particle tracking velocimetry. The flow field in the vicinity of the granular surface was also visualized by an almost mono-layer of fine particles deposited on the main granular layer, which elucidated the development of the secondary and tertiary vortex rings. Generally speaking, the characteristics of the granular layer are found to be similar to a liquid plane for the impact of a vortex ring of a smaller impulse, whereas it is closer to a solid plane for a vortex ring of a larger impulse. For the vortex ring with a much larger impulse, the granular layer is engraved, whose patterns reflect the deformation of the primary and/or secondary vortex ring due to the interaction with the granular layer (as will be described in part II).

Behavior of Vortex Rings

“…Collision of a vortex ring with a granular surface, which has both fluid and solid properties, leaves rather compli-cated erosion patterns. Depending on the strength of the vortex ring, "hardness" of the granular layer and the distance to the granular plane, several types of erosion patterns are reported (Munro et al, 2009;Bethke and Dalziel, 2012;Masuda et al, 2012;Yoshida et al, 2012;Yoshida and Sano, 2015). A weaker vortex ring, but above a certain critical strength, will create a shallow circular depression on the granular surface, which reflects the shape of the axisymmetric vortex ring.…”

Fingering induced by a solid sphere impact to viscous fluid

“…Furthermore, some recent studies have concerned granular target impacts as well as fluid target impacts. Examples include a solid sphere's impact to a granular bed [7][8][9][10][11][12], a liquid droplet impact to a granular bed [13,14], and a vortex ring impact to a granular bed [15].…”

Vortex rings impinging on permeable boundaries

“…This value lies within the laminar regime and is comparable to the lower circulation Reynolds number cases of the experiments performed by other authors (i.e., Refs. [17][18][19], and is within the larger scenarios performed by other research articles (i.e., Refs. 11-13).…”