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).
In our previous paper (part I), an experimental result was presented on the normal impact of a vortex ring on the granular layer (glass beads of diameter 0.10 mm), which was placed at a specified distance from the outlet of the vortex ring generator. The Reynolds number of the vortex ring ranged from 1000 to 6000, whereas the traveling distance ranged from 2 to 13 times of the diameter of the vortex ring generator nozzle. In part I, the deformation of the vortex ring impacting on the granular layer and the development of the secondary vortex ring were focused. In this paper (part II), the erosion of the granular surface by the vortex ring is described. Various patterns were found depending on the Reynolds number of the vortex ring and the traveling distance. Two patterns, one (grooves) which has radial striations from the central depressed region to the outer edge of the rim and the other (dimples) which is characterized by isolated small depressions around the outer edge of the rim, are examined in detail. The formation processes of these patterns are elucidated in terms of the deformation of the vortex ring.
Vibro-acoustic coupling between plate vibrations and the sound field inside a cylindrical structure is investigated. Each end plate of the cylindrical structure is excited by a point force. When the excitation position, which directly affects the vibration characteristics of the plates, is examined by shifting the point of application radially along the plate, the sound field is estimated based on the contribution defined as the ratio of acoustic energy stored in each acoustic mode to the total acoustic energy in the entire sound field. Coupling is intensified by the coincidence of a circumferential order with respect to the modes of plate vibration and of the sound field. Therefore, if the vibration modes at the two end plates have different orders due to the influence of the excitation position, then the sound field is composed of a number of acoustic modes. In particular, excitation at a position near the greatest flexural displacement causes the vibration energy to increase, and the contribution of the corresponding acoustic mode also increases. However, approaching the nodal circle of plate vibration, the excitation position develops coupling solely with the other plate vibration, because the occurrence of the vibration mode is restrained.
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