Cross-stream oscillation in gravity flow through a vertical channel*

The gravity flow of cohesionless granular material between two vertical walls separated by width 2W has been simulated using the discrete element method. Periodic boundary conditions are applied in the flow (vertical) and other horizontal directions. The mass flow rate is controlled by specifying the average solids fraction Φ^a, the ratio of volume of the particles to volume of the channel. There is no flow for Φ^a>Φ^a_max=0.62. As Φ^a reduces, the flow becomes dilute and material flows faster. A steady fully developed state can be achieved only for a narrow range Φ^a_max≥Φ^a≥Φ^a_c. When Φ^a is decreased below Φ^a_c, the flow is unstable and oscillates between the side walls for Φ^a_c>Φ^a≥Φ^a_min. For Φ^a<Φ^a_min, the material is in free fall under gravity. In oscillatory regime, the horizontal coordinate of centre of mass of the flowing material oscillates with a non-zero amplitude and frequency in the cross-stream direction, analogous to a spring-mass system resulting in higher fluctuations in wall stresses. The phenomenon resembles the ‘clustering instability’ in granular flows. If the normal component of interparticle contact force depends only on a elastic spring, the cross-stream oscillation is absent; it is independent of nature of wall-particle interactions, except for frictionless walls.