Study of Effects of Friction Coefficients to Granular Flow Dynamics by Discrete Element Simulation
Date Issued
2016
Date
2016
Author(s)
Lo, Wei-Lin
Abstract
The relation between the interactions of microscopic particles and phenomena of macroscopic granular flow have attracted great interests recently. As the numerical simulation techniques improve, many quantities of microscopic particles that are difficult to be observed or measured by experiments can be ready to computed. For example, the contact forces and relative velocities between particles can be calculated by simulation schemes. Thus, the relations between microscopic behaviors and macroscopic phenomena can be found. For granular flows, one of the most popular numerical simulation schemes is the discrete element method (DEM), because it can process large-scale particle simulations and produce numerical results in a good agreement with experimental measurements. The inertial number, I, is a non-dimensional parameter to quantify the flowing regime of granular flows. Recently, constitutive laws of granular flows have been derived by using the relations between I and the macroscopic effective friction coefficient, μ. Through DEM simulation, some studies suggested that the macroscopic effective friction coefficient was independent of the microscopic friction coefficient, f. However, there were studies claimed that μ was linearly dependent on f when f≤0.4. In order to improve the understanding of the relation between μ and f, shear cell simulations are performed in this research. The macroscopic effective friction coefficients of the granular flows in the shear cell are found to monotonically grow with microscopic friction coefficients under similar values of I, because the influence of f on normal forces is much less than tangential forces on the cell wall. At the same time, the increasing f raises the criterion of Coulomb friction and allows larger tangential forces between particles and cell wall, thus resulting in the increasing of μ. Besides, because the pendulum effect occurs on the particles on the cell wall, the directions of tangential forces between particles and cell wall are not identical, thus resulting in the values of μ from steady state granular flows much less than f. On the other hand, when the rotating speeds of the shear cell are fast enough, all tangential forces between the particles and cell wall of transient granular flows reach the criterion of Coulomb friction. At this moment, all particles on the cell are driven by the friction forces with the same direction, named complete synchronization herein. The granular flows under the complete synchronization state have the same values of μ and f. The relation between the microscopic friction coefficients and velocity profiles of particle systems in rotating drums is the other research issue in this thesis. When the particle systems, half-filled the drum, reach a steady state, the ones with higher f will form higher dynamic repose angles, thus resulting in higher potential energies. However, the velocity profiles of the particle systems in the rotating drum are not obviously influenced by f. These similar velocity profiles suggest that the particle systems with different f have similar kinetic energy. Although the particle systems with higher f have higher potential energies, the kinetic energies are almost identical, which indicates f has significant effects on the work of internal forces between particles. In this research, through the application of principle of work and energy and the calculation of microscopic energy using the DEM simulation, the potential energies of steady state particle systems with different f are found determined by the work, Π*, done by contact forces during the first kinetic peak period. In other words, the difference of potential energies of particle systems with different f comes from the difference of their Π*. Furthermore, to analyze the components of Π* with different f, the particle systems with higher f are found not dissipating more energy, but obtaining more energy from tangential contact force.
Subjects
granular flow
friction coefficient
velocity profile
granular energy
shear cell
rotating drum
discrete element method
Type
thesis
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