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

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.