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Developing A Rheological Relation for Transient Dense Granular Flows Via Discrete Element Simulation in A Rotating Drum

Published online by Cambridge University Press:  25 August 2020

C.-C. Lin ,
M.-Z. Jiang  and
F.-L. Yang Open the ORCID record for F.-L. Yang [Opens in a new window]
C.-C. Lin
Affiliation:
Department of Mechanical Engineering National Taiwan UniversityTaipei, Taiwan
M.-Z. Jiang
Affiliation:
Department of Mechanical Engineering National Taiwan UniversityTaipei, Taiwan
F.-L. Yang*
Affiliation:
Department of Mechanical Engineering National Taiwan UniversityTaipei, Taiwan
*
*Corresponding author (fulingyang@ntu.edu.tw)
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Abstract

This work examines the μ(I) relation that describes the effective friction coefficient μ of a dense granular flow as a function of flow inertial number I, at the center of a rotating drum from its flow onset to steady state using DEM. We want to see how the internal friction coefficient of an accelerating flow may be predicted so that the associated tangential stress can be estimated with the proper knowledge of the normal stress. Under the three investigated drum speeds (3, 4.5 and 6 rpm), the bulk normal stress, σn(y), is found to be a consistent linear depth profile throughout the flow development with a slope degraded from the hydrostatic value, Ph(y), due to lateral wall friction. With the discovery of a non-constant depth-decaying effective wall friction coefficient, we derive analytically a wall-degradation factor K(h) to give σn(y)= K(h)Ph(y). The depth profile of tangential stress, however, varies in time from a concave shape upon acceleration, τa(y), to a more linear trend at the steady state, τss(y). Hence, the μa-Ia profile (with μa=τ/σn) upon flow acceleration offsets from the steady μss(Iss) relation. A pseudo-steady acceleration modification number, ΔI, is proposed to shift the inertial number in the acceleration phase to I* = Ia+ΔI so that the μa-I* data converge to μss(Iss). This finding shall allow us to predict a transient tangential stress by τa(y) = μss(I*)K(y)Ph(y) using the well-accepted knowledge of steady flow rheology, hydrostatic pressure, and the currently developed wall-degradation factor.

Keywords

Transient granular flowdense flow μ(I) rheologydiscrete element simulationwall friction
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 5 , October 2020 , pp. 707 - 719
Copyright
Copyright © 2020 The Society of Theoretical and Applied Mechanics

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