Multiphase flow of dense granular material in a partially filled rotating drum

Abstract

The two-dimensional granular flow within a partially filled rotating drum is investigated, using a stabilized Finite Element algorithm, coupled with a phase field method for capturing the interface between the granular medium and ambient air. The granular material rheology is modelled using the $\mu \left(I\right)$ constitutive equation within a continuum framework. A mesh-dependent instability associated with the original $\mu \left(I\right)$ rheology is identified, which is observed for the first time in the rotating drum configuration. This instability is removed by employing the partially regularized $\mu \left(I\right)$-model proposed by Barker and Gray (2017), leading to stable simulations. We successfully reproduce the characteristic flow dynamics, reported in experimental studies, including the formation of the active and passive layers, and we compute the thickness of the active layer at mid-chord. We visualize the yielded/unyielded regions using the Drucker-Prager criterion, showing a strong resemblance to the active/passive layers. Through extensive parametric analysis, we explore the effects of angular velocity, filling degree, static friction coefficient and grain diameter on the flow. Our results provide insights into the relationship between these parameters and key flow characteristics, such as the kinetic energy, the dynamic angle of repose, the active layer thickness, and the yielded region dynamics.