Self-similar velocity and solid fraction profiles in silos with eccentrically located outlets

Abstract

We examine the gravity-induced flow of dry and cohesionless granular media through an outlet placed eccentrically in a planar silo, employing computations based on a soft-sphere discrete element method. The vertical velocity profiles, measured at the outlet, are self-similar when the eccentric position of an outlet is given in terms of the smallest gap ( s) between its corners and the lateral walls. On the other hand, the self-similarity of vertical velocity does not always hold for all eccentricities ( e) given by the distance between the centers of an outlet and the silo base, which is a typical metric of eccentricity. For the former measure of the eccentric location, the flow conditions are observed to be similar for different outlet sizes. In contrast, we observe, the latter leads to differing flow patterns for the highest eccentricity wherein the largest outlet touches the sidewall and the rest are located at a distance. The effect of using s on the self-similarity of solid fraction profiles is observed to be minor in comparison to e. This study establishes the importance of s compared to e from the viewpoint of the self-similarity of the vertical velocity profiles at the outlet and generalizes the notion of the scaling of velocity and solid fraction reported by Janda et al. [“Flow rate of particles through apertures obtained from self-similar density and velocity profiles,” Phys. Rev. Lett. 108, 248001 (2012)] in a silo with a centric exit to the one with eccentric granular discharge. Finally, we propose expressions for the scaled vertical velocity and solid fraction in terms of s.