The $\mu(I)$ model and extensions applied to granular material in silo with inserts

TL;DR

This study uses the $$ rheology within Navier-Stokes equations to analyze how insert shape and size influence flow rate and static zones in granular silos, with extensions for pseudo-dilatancy and nonlocal effects.

Contribution

It extends the $$ model to include pseudo-dilatancy and nonlocal fluidity, providing new insights into silo flow dynamics with inserts.

Findings

Insert shape significantly affects flow rate and static zones.

Extensions have limited impact on flow rate but influence static material.

Flow rate varies with insert size; static zones are less affected.

Abstract

Granular material is often handled using silos with inserts in industrial processes to prevent "rat-holing" and similar behaviour, optimise mixing behaviour, and prevent segregation. We study the mass flow rate and the static zones of granular silos using the $\mu(I)$ rheology in the incompressible Navier-Stokes equations. We also extend the $\mu(I)$ model to incorporate pseudo-dilatancy and nonlocal fluidity. We find that insert shape has a significant effect on flow rate and static material. We also find that the effect of inserts on flow rate is not strongly affected by the extensions, while the amount of static material is highly dependent on the interactions between insert shape and extensions. Finally, we find that the effect on flow rate varies with insert size, while the amount of static material is not significantly affected by increasing insert size. These results could provide important insights for optimising silo design.