Model for density waves in gravity-driven granular flow in narrow pipes

Abstract

A gravity-driven flow of grains through a narrow pipe in vacuum is studied by means of a onedimensional model with two coefficients of restitution. Numerical simulations show clearly how density waves form when a strikingly simple criterion is fulfilled: that dissipation due to collisions between the grains and the walls of the pipe is greater per collision than that which stems from collisions between particles. Counterintuitively, the highest flow rate is observed when the number of grains per density wave grows large. We find strong indication that the number of grains per density wave always approaches a constant as the particle number tends to infinity, and that collapse to a single wave, which was often observed also in previous simulations, occurs because the number of grains is insufficient for multiple wave formation.

Length scale of density waves in the gravitational flow of fine grains in pipes

“…Constant b in Eqs. (11) and (12) was considered ∼ Ŵ/D, where Ŵ is the surface tension of water. The rest of the model constants were fixed to the values used in Raafat et al [9], Aider et al [7], and Bertho et al [8], i.e., d = 0.125 mm, D = 10 mm, W = 5 g/s, ρ s = 2,500 kg/m 3 , c = 0.6, κ = 0.5, P atm = 10 5 Pa, and the gas properties were that of air.…”

“…Ellingsen et al (2010) [12] studied the gravitational flow of grains in a narrow pipe under vacuum conditions. They performed numerical simulations based on a one-dimensional model for the granular flow where the collisions were modeled by two coefficients of restitution, one among grains and the other between the grains and the pipe walls.…”

Helical inner-wall texture prevents jamming in granular pipe flows

“…3,4 These waves induce potentially destructive pressure transients on the inner-wall of the pipe and provide the mechanism responsible for the intermittent behavior of the flow. Although the dynamics of density waves in granular pipe flows have been studied extensively in the past both experimentally [5][6][7][8][9][10] and through different types of models, 3,4,[11][12][13][14][15][16][17][18][19] it is still a challenging problem to control the mass flux of the granular material flowing through a pipe. For example, Zuriguel et al 20 showed how insertion of an obstacle just above the outlet of a silo can significantly reduce the probability that the granular flow is arrested due to the formation of an arch blocking the silo's outlet.…”

Intermittent gravity-driven flow of grains through narrow pipes

“…The author found that the kinetic energy of the falling grains increases up to a characteristic threshold, from which density waves of no definite wavelength appear. Ellingsen et al [15] studied the gravitational flow of grains through a narrow pipe under vacuum conditions. Their numerical results showed that granular waves could form in the absence of air if the dissipation caused by the collisions among the grains was smaller than that between the grains and the walls.…”

“…Numerical studies on intermittent granular flows in pipes have been carried out in recent years. Ellingsen et al [15] studied the gravitational flow of grains through a narrow pipe under vacuum conditions. They performed numerical simulations based on a one-dimensional model for the granular flow where the collisions were modeled using two coefficients of restitution, one among grains and the other between the grains and the pipe walls.…”