Discharge of non-spherical particles from a Hopper using fast x-ray imaging.

Abstract

Three-dimensional (3D), axisymmetric hoppers are widely used in industries for generating smooth outflow of granular materials from storage bins and it is well known that their discharge behavior is governed by the local dynamics at the orifice. Measuring the details of the outflow from a 3D hopper is challenging due to the fact that the flow is dense and the granular material is opaque. In this paper, x-ray tomography is used to image the cross section near the orifice opening. We investigate the vertical velocity, volume fraction, and particle orientations of spherical, oblate (lentil-shaped), and prolate (rice-shaped) particles for various hopper angles. We create a three-dimensional respresentation by time stacking the cross sections. We process these 3D images using standard image filtration techniques and propose simple experimental models to extract the velocity, volume fraction, and orientation angles of the particles based on their shape. We found that the hopper inclination influences both the velocity and volume fraction profiles in such a way that the magnitude of both profiles increases with increasing hopper inclination. Moreover, lentil-shaped particles achieve the highest velocity and pack more densely than the other two particles. In addition, the latter packed more orderly than the prolate (rice-shaped) particles. Finally, it is found that the independently measured experimental discharge rate has a good agreement with the discharge rate obtained from the velocity and volume fraction profiles for sphere and lentil-shaped particles.