Flow dynamics of spherical grains through conical cardboard hoppers

Abstract

The gravity-driven flow of monodisperse spherical grains of different nature and diameter d, through conical cardboard hoppers, has been studied as function of the orifice diameter D for different values of the aperture angle α (~ 3° ÷ 15°) at large grains conditions (D ≤ 10d). The mass flow rate trend function has displayed, at the lowest angles, a series of linear tracts, with increasing slope, delimited by approximately odd integers of the grains diameter. The linear tracts have been associated to different flow rate regimes, governed by the formation, at the bottom of the granular column, of short-lived arches of “quantized” size (~ 5d, ~ 7d, ~ 9d, …), acting as brakes to flow, by their detachment and ejection from the hopper. This mechanism of events should give rise to a modulation of the flow whose frequency was effectively measured, for the arches of ~ 5d size, by analyzing the signal produced by the falling grains on a microphone. The data of mass flow rate W, as function of the orifice diameter D, have shown, on average, a growth following the 5/2 power-law function, as foreseen by the well-known Beverloo law. Here we analyze the simplified expression of the mass flow rate with the dimension of the square root of the acceleration of gravity, which shows only a slight dependence on the aperture angle of the hopper. The jamming of grains at the outlet opening has been also investigated throughout the transition region at D ~ 3d ÷ 4d, which characterizes the passage from the blocked to the continuous flow for few tens thousand grains, by an optical method and by measuring the frequency of the clogging events.