Nonlinear effect of grain elongation on the flow rate in silo discharge

Abstract

By means of two-dimensional numerical simulations based on contact dynamics, we present a systematic analysis of the joint effects of grain shape (i.e., grain elongation) and system size on silo discharge for increasing orifice sizes D. Grains are rounded-cap rectangles whose aspect ratio are varied from 1 (disks) to 7. In order to clearly isolate the effect of grain shape, the mass of the grains is keeping constant as well as the condition of the discharge by reintroducing the exiting grains at the top of the silo. In order to quantify the possible size effects, the thickness W of the silos is varied from 7 to 70 grains diameter, while keeping the silos aspect ratio always equal to 2. We find that, as long as size effects are negligible, the flow rate Q increases as a Beverloo-like function with D, also for the most elongated grains. In contrast, the effects of grain elongation on the flow rate depend on orifice size. For small normalized orifice sizes, the flow rate is nearly independent with grain elongation. For intermediate normalized orifice sizes the flow rate first increases with grain elongation up to a maximum value that depends on the normalized size of the orifice and saturates as the grains become more elongated. For larger normalized orifice size, the flow rate is an increasing function of grains' aspect ratio. Velocity profiles and packing fraction profiles close to the orifice turn out to be self-similar for all grain shapes and for the whole range of orifice and system sizes studied. Following the methodology introduced by Janda et al. [Phys. Rev. Lett. 108, 248001 (2012)], we explain the nonlinear variation of Q with grain elongation, and for all orifice sizes, from compensation mechanisms between the velocity and packing fraction measured at the center of the orifice. Finally, an equation to predict the evolution of Q as a function of the aspect ratio of the grains is deduced.

Dynamical behaviour of non-spherical grains in granular rapid flows

“…CHAPTER 2. QUASI 2D MONO-LAYER SILO 2.10(a) and (b) suggests that the larger the aspect ratio of the particle, the smaller the discharge rate of the particles will be, which is consistent with the study of Bignon et al [64]. Although the analysis introduced by Janda et (2.12), with the parameters obtained from the fits to the vertical velocity and solid fraction profiles [Eqs.…”

“…Many studies have confirmed the scaling of both velocity and solid fraction profiles and its relationship with the discharge rate [22,[130][131][132][133]for spherical particles. Although this idea has also been tested for poly-disperse systems [152,153], only a recent numerical work validates its applicability to non-spherical particles performing the 2D numerical simulations of elongated particles having the same mass and same cross-sectional area [64]. In this paper, we present the results of a similar experiment done in the quasi 2D mono-layer silo setup for the spheres and two types of elliptical particles with different aspect ratios.…”

“…They showed that it is connected to the high spatial variation in the volume fraction, contact pressure, and velocity field inside the silo. More recently Bignon et al [64] also investigated the effect of the aspect ratio of elongated particles and silo width by using 2D contact dynamics simulations. All their particle shapes have the same mass and same cross-sectional area.…”

“…The findings of all of the above studies show that the particle shape does influence the flow dynamics in the silo. Only Bignon [64] kept the mass and cross-sectional area constant for all particles in their simulations to maximally control the influence of particle shape. Untill now, nobody has changed the particle shape systematically in experiments in order the check the true effect of particle shape.…”

“…Even the smooth flow of the particles from the silo is governed by local dynamics around the orifice. However, there have been few studies which connected the discharge process with local dynamics of micro-mechanical variables around the orifice [18,21,22,64,[130][131][132][133]. Most of these studies carried out only with spherical particles.…”