Scaling laws for velocity profile of granular flow in rotating drums

TL;DR

This paper combines theoretical, numerical, and analytical approaches to derive and validate scaling laws for the velocity profile of granular flow in rotating drums, revealing how flow characteristics depend on system size and rotation speed.

Contribution

It introduces new scaling laws for granular flow velocity profiles in rotating drums, supported by both simulations and analytical dimensional analysis.

Findings

Velocity profiles are in quantitative agreement between discrete element method and continuum model.

Surface flow layer thickness scales with drum diameter and weakly with angular velocity.

Derived scaling laws are validated through numerical simulations.

Abstract

We theoretically and numerically investigate the steady flow of two-dimensional granular materials in a rotating drum using the discrete element method and a continuum model with the $\mu(I)$-rheology. The velocity fields obtained from both methods are in quantitative agreement. The granular flow exhibits two distinct regions: a surface flow layer and a static flow regime corresponding to rigid rotation near the drum bottom. The thickness of the surface flow layer increases with the drum diameter and shows a weak dependence on the angular velocity of the drum. Using dimensional analysis of the continuum equations, we analytically identify nondimensional parameters for the velocity profile and the surface flow layer thickness, which lead to scaling laws characterising the flow in rotating drums with low Froude number and large system size. The validity of the scaling laws is confirmed by numerical simulations.