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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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References

REFERENCES

Forterre, Y. and Pouliquen, O., “Flows of dense granular media,” Annual Review of Fluid Mechanics, 40, pp. 1–24 (2008).CrossRefGoogle Scholar
Midi, GDR, “On dense granular flows,” European Physical Journal E, 14, pp. 341–365 (2004).CrossRefGoogle Scholar
Renouf, M., Bonamy, D., Dubois, F. and Alart, P., “Numerical simulation of 2D steady granular flows in rotating drum: On surface flows rheology,” Physics of Fluids, 17, 103303 (2005).CrossRefGoogle Scholar
Da Cruz, F., Emam, S., Prochnow, M., Roux, J.-N. and Chevoir, F., “Rheophysics of dense granular materials: Discrete simulation of plane shear flows,” Physical Review E, 87, 022202 (2005).Google Scholar
Jop, P., Forterre, Y. and Pouliquen, O., “A constitutive law for dense granular flows,” Nature, 441, pp. 727–730 (2006).CrossRefGoogle ScholarPubMed
Chou, H. T. and Lee, C. F., “Cross-sectional and axial flow characteristics of dry granular material in rotating drums,” Granular Matter, 11, pp. 13–32 (2009).CrossRefGoogle Scholar
Cortet, P. P., Bonamy, D., Daviaud, F., Dubrulie, B. and Renouf, M., “Relevance of visco-plastic theory in a multi-directional inhomogeneous granular flow,” Europhysics Letters, 88, 14001 (2009).CrossRefGoogle Scholar
Fall, A., Ovarlez, G., Hautemayou, D., Meziere, C., Roux, J. N. and Chevoir, F., “Dry granular flows: rheological measurements of the μ(l)-rheology,” Journal of Rheology, 59, 1065 (2015).CrossRefGoogle Scholar
Govender, I., “Granular flows in rotating drums: A rheological perspective,” Minerals Engineering, 92, pp. 168–175 (2016).CrossRefGoogle Scholar
Tapia, F., Pouliquen, O. and Guazzelli, E., “The influence of surface roughness on the rheology of immersed and dry frictional spheres,” Physical Review Fluids, 4, 104302 (2019).CrossRefGoogle Scholar
Pahtz, T., Duran, O., Klerk, D. N., Govender, I. and Trulsson, M., “Local rheology relation with variable yield stress ration across dry, wet, dense, and dilute granular flows,” Physical Review Letters, 123, 048001 (2019).CrossRefGoogle Scholar
Lacaze, L. and Kerswell, R. R., “Axisymmetric granular collapse: a transient 3D flow test of viscoplasticity,” Physical Review Letter, 102, 108305 (2009).CrossRefGoogle ScholarPubMed
Yang, C. T and Hsieh, S. H., “An object-oriented framework for versatile discrete element simulation using design patterns,” Computational Mechanics, 36(2), pp.85–99 (2005).CrossRefGoogle Scholar
Chang, W. T. and Hsieh, S. H., “Parallelization of Discrete Element Simulation,” Journal of the Chinese Institute of Engineers, 32(6), pp. 825–841 (2009).CrossRefGoogle Scholar
Cundall, P. A. and Strack, O. D. L., “A discrete numerical model for granular assemblies,” Geotechnique, 29(1), pp. 47–65 (1979).CrossRefGoogle Scholar
Verlet, L., “Computer “Experiments” on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules,” Physical Review Journal Archive, 159, pp. 98–103 (1967).CrossRefGoogle Scholar
Yang, F.-L., Chang, W. T., Huang, Y. T., Hsieh, S. H. and Chen, C. S., “Dry granular avalanche down a flume: Choice of discrete element simulation parameters,” Physics of Fluids, 25, 123303 (2013).CrossRefGoogle Scholar
Huang, Y., “Investigation of the Dynamics of Steady Granular Flow in a Rotation Drum by Lagrangian Coherent Structure Evolution,” Master Thesis, National Taiwan University (2014).Google Scholar
Onoda, G. Y. and Liniger, E. G., “Random Loose Packings of Uniform Spheres and the Dilatancy Onset,” Physical Review Letter, 64(22), pp. 2727–2730 (1990).Google ScholarPubMed
Ancey, C., “Dry flows down an inclined channel: Experimental investigations on the frictional-collision regimes,” Physical Review E, 65, 011304 (2001).CrossRefGoogle Scholar
Silbert, L. E., Landry, J. W. and Grest, G. S., “Granular flow down a rough inclined plane: Transition between thin and thick piles,” Physics of Fluids, 15, pp. 1–10 (2003).CrossRefGoogle Scholar
Yang, F.-L. and Huang, Y.T., “New aspects for friction coefficients of finite granular avalanche down a flat narrow reservoir,” Granular Matter, 18, pp. 77 (2016).CrossRefGoogle Scholar
Artoni, R. and Richard, P., “Effective wall friction in wall-bounded 3D dense granular flows,” Physical Review Letter, 115, 158001 (2015).CrossRefGoogle ScholarPubMed