Precise evaluation of mass discharge rate (MDR) in hoppers is an important topic in many industries. Facilitated by an Eulerian-formulation finite element method (FEM), this paper uses an elastoplastic model to investigate the MDR in conical hoppers and evaluates its applicability in various cases of hopper geometries and material properties. The obtained flow field complies with the scaling of outlet velocity Vy~gD0 and that of the discharge rate MDR~gD0 5/2 universally. The MDR is basically independent of the fill height and silo width, but a strong height dependency may emerge for very small internal friction angle of granular material, similar to the fluid-like discharging observed in previous DEM simulation. As for the material properties, the MDR is mainly controlled by the plastic parameters such as internal friction angle and dilation but is insensitive to the elastic modulus. The quantitative accuracy of the model is verified by comparing experimental measurements and discrete simulation over a wide range of hopper half angles. The existing correlations are often conditionally applicable in describing MDR – some for steep hoppers while others mainly suitable for shallow ones. An empirical correlation is formulated based on the FEM results to achieve a general applicability, which may help to improve the hopper design in practical applications. The needs for future research are also discussed.
- Elastoplastic theory
- Eulerian finite element method
- Granular material
- Hopper flow
- Mass discharge rate