Flow of particles suspended in a sheared viscous fluid: Effects of finite inertia and inelastic collisions

Abstract

in Wiley Online Library (wileyonlinelibrary.com).We investigate in this article the macroscopic behavior of sheared suspensions of spherical particles. The effects of the fluid inertia, the Brownian diffusion, and the gravity are neglected. We highlight the influence of the solid-phase inertia on the macroscopic behavior of the suspension, considering moderate to high Stokes numbers. Typically, this study is concerned with solid particles O (100 lm) suspended in a gas with a concentration varying from 5% to 30%. A hard-sphere collision model (with elastic or inelasic rebounds) coupled with the particle Lagrangian tracking is used to simulate the suspension dynamics in an unbounded periodic domain. We first consider the behavior of the suspension with perfect elastic collisions. The suspension properties reveal a strong dependence on the particle inertia and concentration. Increasing the Stokes number from 1 to 10 induces an enhancement of the particle agitation by three orders of magnitude and an evolution of the probability density function of the fluctuating velocity from a highly peaked (close to the Dirac function) to a Maxwellian shape. This sharp transition in the velocity distribution function is related to the time scale which controls the overall dynamics of the suspension flow. The particle relaxation (resp. collision) time scale dominates the particulate phase behavior in the weakly (resp. highly) agitated suspensions. The numerical results are compared with the prediction of two statistical models based on the kinetic theory for granular flows adapted to moderately inertial regimes. The suspensions have a Newtonian behavior when they are highly agitated similarly to rapid granular flows. However, the stress tensors are highly anisotropic in weakly agitated suspensions as a difference of normal stresses arises. Finally, we discuss the effect of energy dissipation due to inelastic collisions on the statistical quantities. We also tested the influence of a simple modeling of local hydrodynamic interactions during the collision by using a restitution coefficient which depends on the local impact velocities.

A Lagrangian VOF tensorial penalty method for the DNS of resolved particle-laden flows

“…The DNS of resolved dense particle flows could also be used to simulate the behavior of particles in simple sheared flows under periodic boundary conditions. The simulated results could be compared to the reference works of Sangani et al [106] and Abbas et al [107].…”

A hyperbolic two-fluid model for compressible flows with arbitrary material-density ratios

“…However, one would also need to account for inelastic collisions, particle-phase viscosity, as well as other effects (see, e.g. Abbas et al 2010) in most applications, none of which affect the hyperbolicity.…”

“…Depending on the value of Z 0 , the particle pressure can play a significant role in the momentum balances. In real applications, Θ p (and, hence, p p ) will be much smaller due to inelastic collisions and lubrication effects (Abbas et al 2010). However, this will not affect the hyperbolicity.…”

“…To this end, direct numerical simulations of particle suspensions over a wide range of material-density ratios, Reynolds numbers and volume fractions would be useful (such as is done in Moore & Balachandar 2019;Tavanashad et al 2019;du Cluzeau et al 2020), especially if one can unequivocally relate model variables such as c m and P a fp to the data from such simulations (Zhang 2020). Finally, work along the lines of Gu et al (2019) and Abbas et al (2010) will be required to account for viscous effects in the particle phase.…”

Numerical modelling of finite-size particle collisions in a viscous fluid

“…Direct hydrodynamic interactions and particle-particle or particle-wall collisions are important features which control the overall dynamics of the flow for moderately concentrated suspension. 2 Efficient numerical models are highly desirable to predict the physics of those complex flows 3 and to optimize the design of industrial devices involving dispersed two-phase flows. Recent numerical techniques [4][5][6] provide useful tools to simulate suspension flows seeded with finite size particles.…”