Granular discharge and clogging for tilted hoppers
Original entry by Sagar Bhandari, APPHY 225 Fall 2010
Granular discharge and clogging for tilted hoppers, Hannah G. Sheldon and D. J. Durian, Granular Matter,Volume 12, Number 6, 579-585
tilted hoppers, glass beads, granular discharge, clogging
In this paper, the authors study the behavior of spherical glass beads when passed through a small hole and the diameter and tilt angle - dependence of the flow rate. They also study the condition for zero flux /clogging in terms of hole diameter and tilt angle.
The authors use granular medium consisting of spherical glass beads, with two different diameters: d = 0.30 ± 0.05 mm and d = 0.9 ± 0.1 mm. Both have bulk density of 1.53±0.01 g/cubic cm. and draining angle of repose of 24 degrees. As a medium to pass the bead through, two different containers are used - steel can and aluminum square tube. Holes are drilled in three different locations: in the bottom at center, in the bottom at 2 cm from the side, and in the side at 2 cm above the bottom. In their experiments, the containers are grounded to prevent electrostatic charging, while the tilt angle of the plane of the hole away from horizontal is measured with a plumb bob and protractor. Figure 1 shows the sketch of four different tilt angles.
The discharge rate is measured by weighing the material collected during a timed interval. Initially, the hole is covered with a piece of paper and the granular medium is poured into the container. After filling the container,the covering is removed and flow allowed to proceed for a several seconds or more. Next a beaker is used to collect the discharge stream while simultaneously starting a timer which is then removed while simultaneously stopping the timer. As shown in Figure 2, the observed discharge rates increase with hole size. The discharge rates are faster for small holes and approaches power law as the hole size is increased. It also can be noticed in Figure 2 (a) and (b) that the discharge rates fits well with Beverloo relation.
The authors also point out that the tilt angle dependence can be considered empirically without using the Beverloo relation. For a given hole size, the authors examine how tilting causes the flux to decrease from a maximum at zero-angle. They plot discharge rates for various hole diameters vs cosine of tilt angle as shown in Fig. 4 for d = 0.3 mm diameter grains.
They also mention that for large holes, the it follows a common linear dependence on cosine of tilt angle. They also obtain the condition for the hole diameter for crossover from clogged to flowing as D = Ad/[1−(tilt angle/156◦)^1/�alpha].