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

TL;DR

This study investigates how eccentric outlet placement affects flow profiles in silos, revealing that the gap between the outlet and wall ($s$) is crucial for self-similarity, extending previous findings on central outlets.

Contribution

It demonstrates the significance of the gap measure ($s$) over the center-to-base eccentricity ($e$) in determining flow self-similarity in silos with eccentric outlets.

Findings

Vertical velocity profiles are self-similar when measured by gap $s$.

Flow patterns vary significantly with high eccentricity when measured by $e$.

Flow conditions are similar across different outlet sizes when using $s$ as a measure.

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 eccentricity is given in terms of the gap ($s$) between the wall and the corner of the outlet nearest to the wall. 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. Similar observations are noted for the profiles of solid fraction. For the former measure of eccentricity, 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. This study establishes the importance of $s$ compared to $e$ from the viewpoint of the self-similarity of the vertical velocity and solid fraction profiles at the outlet, and generalizes the notion of the scaling of velocity and solid fraction reported by Janda et al. [Phys. Rev. Lett. 108, 248001 (2012)] in a silo with a centric exit to the one with eccentric granular discharge.