Cross-stream oscillations in the granular flow through a vertical channel

The gravity flow of a granular material between two vertical walls separated by a width 2W is simulated using the discrete element method (DEM). Periodic boundary conditions are applied in the flow (vertical) and the other horizontal directions. The mass flow rate is controlled by specifying the average solids fraction (phi)over bar, the ratio of the volume of the particles to the volume of the channel. A steady fully developed state can be achieved for a narrow range of (phi)over bar, (phi)over bar(max )>= (phi)over bar >= (phi)over bar(cr), and the material is in free fall for (phi)over bar < (phi)over bar(min). For an intermediate range of (phi)over bar ((phi)over bar(cr) > (phi)over bar >= (phi)over bar(min)), there are oscillations in the horizontal coordinate of the centre of mass, velocity components and stress. As (phi)over bar decreases in the range (phi)over bar(cr) > (phi)over bar >= (phi)over bar(min), the amplitude of the oscillations increases proportional to root(phi)over bar(cr )- (phi)over bar and the frequency appears to tend to a non-zero value as (phi)over bar -> (phi)over bar(cr), indicating a supercritical Hopf bifurcation. The relation between the dominant frequency and the higher harmonics of the position, velocity and stress fluctuations are explained using the momentum balance. It is found that dissipation in the inter-particle and particle-wall contacts is critical for the presence of an oscillatory state.