Direct numerical simulation of spheroidal particle settling in viscoplastic fluid using Lattice-Boltzmann method

Abstract

A numerical study of ellipsoidal particle settling in quiescent Newtonian and viscoplastic fluid is presented motivated by theoretical aspects and industrial applications, such as cuttings transport in oil drilling. As particle settling at moderate to high Reynolds numbers takes considerable distance to reach periodical or statistically steady regime, memory limitations in direct numerical simulations (DNS) constrain the maximum domain size for this class of flow. In spectral and finite difference methods, some workarounds that allow simulation in unbounded vertical extents are available, such as domain transferring schemes. Due to the locality in most of its algorithm, the lattice Boltzmann method (LBM) is increasingly popular for DNS studies. In present work, a boundary relocation approach is presented, enabling LBM simulations of particle motion in a virtually infinite domain. The scheme consists basically of the truncation of flow domain with the relocation of boundaries to nodes kept outside simulation confines. The immersed boundary method (IBM) is implemented for the liquid-fluid interaction. A thorough mesh generation for ellipsoidal particles is disclosed, as well as an extension of the internal mass compensation strategy of Suzuki and Inamuro (2011). The Bingham model is implemented with a proper adaptation of the boundary relocation approach. The numerical model is assessed sequentially for each of its features, showing good agreement with analytical solutions and results available in the literature. The possibility of improvement through an increase in resolution is also evidenced. Simulations were then performed for oblate spheroids in quiescent Newtonian fluid, in which a variety of motion patterns was delineated. Then, an investigation of ellipsoidal particles settling in viscoplastic fluid was conducted, analyzing shape influence on the motion of a solid-body. It was also shown that for an inclined ellipsoid, the increase of Bingham number leads to constriction and even an inversion in the direction of particle rotation.