Exploration into the thermal inhomogeneities dependent particle self-organization in fluid-flow under reduced gravity conditions

Particle laden flows are omnipresent on Earth and beyond. This research aligns with a line of inquiry where the existence of solid particle attractors in laminar thermo-vibrational flow has been investigated under reduced gravity conditions to explore new mechanisms for the control of multiphase systems. In particular, the present work delves deeper into the effect of inhomogeneous thermal boundary conditions on the particle structures that are formed in the fluid due to the interplay of particle inertial and (convective) thermo-vibrational effects. The problem is addressed in the frame of numerical simulations relying on a hybrid Eulerian-Lagrangian approach. First conditions are examined where, for simplicity, a two-dimensional (2D) square cavity is considered, with the thermal inhomogeneities being introduced in the form of temperature spots located in the center of otherwise uniformly heated walls; then the more computationally expensive fully three-dimensional (3D) cubic cavity is analyzed. The Prandtl number, vibrational Rayleigh number and angular frequency are fixed to 6.11 (water at ambient temperature), Ra_ω=10⁴ and Ω=10³ respectively, with a particle stoke number value of St=5x10^-6 and a particle-fluid density ratio of ξ=2. For these representative conditions, two important degrees of freedom are explored, namely, the size of the localized thermal spots (l) and the magnitude (γ) of the acceleration resulting from the application of vibrations. It is shown that a zoo of particle aggregations is enabled accordingly. In 2D, an increase in the multiplicity N of the attracting loci from 2 to 4 is possible for certain combinations of l and γ. Another key finding concerns the identification of a new type of particle structure or aggregation. Its distinguishing mark with respect to earlier observations is the absence of a particle-dense boundary separating the particle-rich region from the clear fluid located outside; moreover, these formations can show up in conjunction with the classical boundary-dense structures or exist in isolation. When the fully 3D problem is considered, these alternate formations are taken over by fascinating quadrupolar patterns, which coexist with the classical boundary-dense cylindrical structures, thereby increasing the multiplicity of the attractors to a value as high as N=8. Moreover, if the plane of vibrations is rotated by 45° with respect to the walls of the cubic enclosure, some of these apparently independent structures can coalesce, thereby leading to very complex patterns, which however still display well-defined and recognizable geometric properties. The provision of these results is intended as a further step towards the collection of a critical mass of data that may lead in the future to train an algorithm of Artificial Intelligence for a kind of “reverse engineering” (able to provide as an “output” the set of required thermal boundary conditions and vibrations characteristics corresponding to a given “input” shape of the particle structure).