Numerical study into the morphology and formation mechanisms of three dimensional particle structures in vibrated cylindrical cavities with various heating conditions

摘要

The present analysis extends the author’s earlier work (Lappa, Phys. Fluids, 26, 093301, 2014) on the properties of patterns formed by the spontaneous accumulation and ordering of solid particles in certain types of flow. It is shown that under certain conditions, when subjected to vibrations to induce natural flow, non-isothermal fluids with dispersed solid particles are characterized by intervals of solid-pattern-forming behaviour due to particle rearrangements preceded by intervals in which no recognizable structures of solid matter can be detected. The dynamics of these systems are highly nonlinear in nature. Because this new family of particle attractors is known to exhibit strong sensitivity to the “symmetry properties” of the considered vibrated system and related geometrical constraints, the present study attempts to clarify the related dynamics in a geometry with curved walls (cylindrical enclosure). In particular, by assuming vibrations always directed perpendicularly to the imposed temperature gradient, we show that the morphology, spatial extension (percentage of physical volume occupied), “separation” (spatial distance) and mechanisms responsible for the formation of the resulting particle structures change significantly according to whether the temperature gradient is parallel or perpendicular to the symmetry axis of the cylinder. This indicates that the “physics” is not invariant with respect to 90 rotations in space of the specific forcing considered (direction of the imposed temperature gradient and associated perpendicular vibrations). Additional insights into the problem are obtained by assessing separately the influence played by the time-averaged (mean) and oscillatory effects. According to the numerical results, the intriguing diversity of particle agglomerates results from the different role/importance played by (curved or straight) boundaries in constraining particles and, from the different structure and topology of the resulting macroscopic (large-scale) thermovibrational flow oscillating in time at the same acceleration frequency of the imposed vibrations.