Rheology of high speed granular flows in presence and absence of air

¹ R&D Tata Steel limited, Jamshedpur, Jharkhand, India
² Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India
³ Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

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Published online: 1 December 2025

Abstract

The rheology of granular materials at large inertial numbers (I ≥ 1) exhibits a non-monotonic variation of the effective friction coefficient μ(I), as shown by Patro et al. (2021, 2023). These studies highlight the need to account for the non-monotonic behavior of μ(I), the dilatancy law linking solids fraction (ϕ) to I, and stress anisotropy via a normal stress difference law to accurately predict flow properties in rapid granular flows. While this inertial number-based rheology successfully describes both dense and dilute flow regimes, most simulations neglect the presence of air, despite its non-negligible drag in high-speed flows. This raises questions about the applicability of simulation findings to real-world scenarios. We conducted CFD-DEM simulations of 1mm, slightly polydisperse, inelastic, frictional spheres flowing over a bumpy chute at a high inclination (θ = 38◦), using LIGGGHTS for DEM (no air) and CFDEM coupled with OpenFOAM (with air). Air is modeled as an incompressible Newtonian fluid with drag based on the Di Felice model. Results show that air reduces grain velocity v_x, slightly increases ϕ, and lowers the steady-state inertial number I. We analyze how air alters μ(I), ϕ(I), and normal stress differences, emphasizing its role in high-speed granular flows.