Numerical modelling of dynamic pressure and flow in hopper discharge using the Arbitrary Lagrangian–Eulerian formulation

Abstract

Silos and hoppers are commonly used for the storage and handling of bulk solids in industry. Although the pressures acting on the silo walls during filling are well understood, an accurate prediction of pressures during discharge remains an important open problem for silo design. This paper describes a finite element analysis of the granular flow in a conical hopper to investigate the dynamic pressure and flow during discharge. The behaviour of the stored solid is modelled using a continuum mechanics approach formulated in an Arbitrary Lagrangian–Eulerian (ALE) frame of reference. With the aid of the ALE approach, in principle almost a complete silo discharge process may be simulated satisfactorily without mesh distortion problems, which are often encountered in modelling silo discharge using a continuum approach. Temporally averaged discharge pressure distribution is evaluated from the FE simulation and found to be in good agreement with the commonly quoted theoretical solution.Significant pressure fluctuations are predicted during the initial discharge period, which are comparable to the fluctuating pressure patterns reported in some silo discharge experiments. Spectral analysis of the predicted pressure fluctuation reveals two dominant frequencies. The causes for these frequency events have been investigated thoroughly in the paper, which lead to the conclusion that compression wave propagation and intermittent shear zones within the granular solid are responsible for the higher and lower frequency event respectively. These dynamic events provide a plausible explanation for silo quaking and vibration that are associated with silo discharge. Further parametric study has also been performed to investigate the effect of discharge velocity and wall roughness on these dynamic events.