Physica A: Statistical Mechanics and its Applications
Rolling friction in the dynamic simulation of sandpile formation
Introduction
The formation of a heap of particles is important in all industries dealing with particulate materials ranging from agricultural products such as flour and grains to minerals such as coal and metal ores. It is related to almost all typical phenomena associated with granular materials, and many aspects of heaping, including particle segregation [1], packing [2], and stress distribution [3], [4], have been studied in the past. In recent years, many efforts have been made to understand the governing mechanisms involved, which are linked to important phenomena such as self-organisation [5], [6] and stratification [7], [8] that have stimulated the interest in particulate science and technology significantly [9], [10], [11].
The bulk behaviour of a particle system depends on the collective interactions of individual particles. Therefore, it is very useful to study the heaping process on the particle scale. In the past, various computer simulation techniques have been developed for this purpose, including Monte Carlo [12], [13], [14], [15], cellular automation [16], and granular dynamic simulations [17], [18]. The latter is probably most realistic, because it explicitly takes into account not only the geometrical factors but also the forces involved. In recent years, it has been used by various investigators to study the formation of two-dimensional sandpiles [19], [20], [21], [22]. However, to form a stable heap of particles with a finite angle of repose, special treatments or assumptions have to be employed in a simulation. For example, Lee and Herrmann [19] and Luding [20] ignored the rotation of particles or tangential forces, Elperin and Golshtein [21] set the velocities of all particles to zero after every 5000–15 000 iterations and Baxter et al. [22] started their simulation with a static substrate consisting of a row of equally spaced particles. Theoretically, such treatments are arbitrary and may distort reality, leading to inaccurate information.
The purpose of this paper is to propose a simulation method that can simulate the formation of a stable heap of spheres under three-dimensional conditions. The method is essentially that originally proposed by Cundall and Strack [17], but modified by introducing a rolling friction torque based on the experimental and theoretical analysis of Beer and Johnson [23] or Brilliantov and Poschel [24]. The effect of the rolling friction coefficient on the formation of a sandpile is studied in detail. The validity of the proposed modification is confirmed by the good agreement between the simulated and measured results under comparable conditions.
Section snippets
Simulation method
A particle can undergo translational and rotational motion, depending on the forces and torques acting on it, which may come from its interactions with neighbouring particles, with confining walls or substrates and with surrounding fluids. Strictly speaking, this movement is affected not only by the forces and torques originated from its neighbouring particles and vicinal fluid but also the particles and fluids far away through the propagation of disturbance waves. The complexity of such a
Motion of a sphere on a flat plate
It is known that a sphere moving on a horizontal plate with an initial translational velocity will gradually loss its kinetic energy and finally stop after travelling a certain distance because of the resistance from its interaction with the plate. This simple fact has been used here as the first case to test the proposed approach. In particular, it is assumed that initially the sphere just touches the plate with an initial translational velocity of 1 m/s but no angular velocity; and the
Conclusions
Rolling friction, due to elastic hysteresis losses or viscous dissipation, has been incorporated in the dynamic simulation model developed by Cundall and Strack [17]. A numerical study of the formation of a heap of particles under different conditions indicates that the rolling friction plays a critical role in achieving physically or numerically stable results, and the angle of repose increases with rolling friction coefficient and decreases with particle size. While not clear from a
Acknowledgements
The authors would like to thank ARC and BHP for financial support, Dr. P. Zulli and Mr. S.J. Chew of BHP research and Prof. U. Tüzün of University of Surrey (UK) for helpful discussions, and Prof. P. Meakin of University of Oslo for helpful comments to enhance the quality of the paper.
References (43)
- et al.
Powder Technol.
(1991) - et al.
Powder Technol.
(1994) - et al.
Physica A
(1992) - et al.
Adv. Powder Technol.
(1992) Physica A
(1992)- et al.
Physica A
(1997) - et al.
Powder Technol.
(1991) - et al.
Wear
(1995) - et al.
Powder Technol.
(1976) - et al.
Chem. Eng. Sci.
(1982)
Phys. Rev. E
Phys. Rev. Lett.
Nature
Nature
Nature
Science
Nature
J. de Physique IV
Cited by (643)
Unchannelized granular flows: Effect of initial granular column geometry on fluid dynamics
2024, Chemical Engineering ScienceNumerical investigations of traction behaviors of a pneumatic tire on wet granular terrains: DE/FE simulations
2024, Journal of TerramechanicsLocal scour around the monopile: A microscopic perspective using CFD-DEM
2024, Ocean EngineeringNumerical simulation analysis of debris filtration in the bottom nozzle
2024, Annals of Nuclear Energy