Dynamics of Granular Flow through a Vertical Pipe: Effect of Medium Flow

Density waves of granular particles (rough sand) in a vertical pipe are experimentally investigated under the condition where the medium (air) flow is well controlled. When a cock attached to the bottom-end of the pipe is open, air is dragged by falling granular particles and flows together with sand. No density waves are observed for this situation. As the cock is gradually closed, however, the pressure gradient of air inside the pipe becomes larger and, as a result, density waves of granular particles emerge. Power spectrum P ( f ) of time series signals of density waves shows a clear power-law form P ( f ) ∼ f -α and the precise measurements indicate that the exponent α is close to 4/3. The value of α is robust even under the medium flow as far as density waves can be seen.