A.J. Matchett

Validation tests on a distinct element model of vibrating cohesive particle systems

Abstract The discrete element method (DEM) is becoming widely used to simulate granular flows. This method simulates the individual dynamics of all particles in an assembly by numerically integrating their acceleration resulting from all the contact forces. It is generally recognised that such a complex model must be validated by comparison with experimental results. Indeed the authors have addressed this in earlier publications given in the references. However, one important aspect is often given little attention, and that is testing the code to ensure that the computer program executes the model specification correctly. This paper describes in detail a DEM program for cohesive particle vibration and shows some simple simulations that have helped to verify the code. It is concluded that these ‘mathematical tests’ on artificial situations can uncover bugs in programs that appear to be running correctly, even if they appear to simulate real experiments reasonably well. These tests are published with the aim of helping others validate their programs in similar applications. The paper also discusses the widely used simplification of particle–particle interactions by Hookes law and suggests that its validity depends upon the application. The main limitation of the DEM technique is the computational (CPU) time required. Techniques to minimise this are described, in particular in relation to particle referencing and array sizes. The runtimes shown illustrate the importance of optimising array sizes for the neighbourhood lists.

Damping and elastic properties of binary powder mixtures

Damping and elastic properties of binary powder mixtures were investigated by a dynamic measurement method using vibration. Experiments were performed on a range of binary powder mixtures comprised of glass sphere, sand, polyethylene and rubber powders. Loss factor and Youngs modulus of binary mixtures were calculated from the experimental data. The calculated loss factors were dependent upon the mixing fraction, but almost independent of compressive stress and packing conditions. In order to describe the properties of binary mixtures, a simple two-phase model has been developed and compared with experimental data. Reasonable agreement between the model and the experimental data was obtained.

Energy monitoring in distinct element models of particle systems

Abstract This paper describes techniques for monitoring energy in discrete element method (DEM) simulations of granular flow. They have been applied to DMX a three-dimensional model of polydisperse cohesive spheres flowing into a cylindrical vessel, settling and then subject to vibration. The model takes account of gravitational potential energy, linear and tangential ‘particle spring’ potential energies and net work done by the particles, normal and angular kinetic energies, dissipated energies due to linear and tangential damping and friction, and the work done by the vibrating vessel on the particle system. Energy monitoring enhances understanding of the physics and further validates the program code. It was found that the numerical technique inherently introduces artificial energy components, but that these can be explicitly monitored. Energy conservation was thus verified and the artificial components explained. Simulations of various particle types and sizes were performed monitoring all the energy components with time. The results show that explicit dissipated energy calculation is required and cannot be simplified as the remainder term of total minus potential and kinetic energies, and that energy is dissipated mainly in normal damping and gross sliding. Total energy dissipation is not sensitive to particle stiffness, but moderately sensitive to damping and friction. However, the maximum rate of energy dissipation is significantly affected by the damping coefficient and the particle stiffness, and only negligibly by the friction coefficient. Initial studies showed that in some low energy vibration the artificial energy component is not negligible and its effect must be considered in some DEM applications.

Effective mass of powder beds subjected to low magnitude vibration and its application to binary systems: Part 1—experimental methodology

Abstract Spring and damper models of the mechanical properties of powder beds rely on treating the distributed mass of the powder bed as a point mass, or effective mass, which differs from the real bed mass. This paper presents an experimental methodology to determine the effective mass of powder beds at low applied vibration ( g ) where the bed remains a coherent entity, using a vibrating bed of powder surmounted by a top-cap mass. Two types of transfer functions, apparent mass Tfa, defined as a ratio of base force to base acceleration, and acceleration transmissibility Taa, defined as a ratio of top-cap acceleration to base acceleration, were used for the determination. Theoretical analysis demonstrates that it is possible to estimate experimentally the effective mass from only the slope dTfa/dTaa below half of the resonant frequency, without any arbitrary fitting parameters. Powders were enclosed in a vertical, open, cylindrical vessel, surmounted by a top-cap mass plus accelerometer, and subject to vibration at the base, through an impedance head consisting of an accelerometer and force transducer. Experiments were performed on a range of sample powders, including glass spheres, sands, polyethylene and rubber powders. The experimental transfer function data conformed to the theoretical trends, and the slope corresponding to the effective mass was dependent upon sample powders, top-cap and the bed masses. Furthermore, a comparison of the experimental effective mass data and theoretical values based upon Rayleighs energy method was made. Results showed a reasonable agreement between the experimental data and the Rayleighs approximation.

Effective mass of powder beds subjected to low magnitude vibration and its application to binary systems: Part 2—comparison of segregated and well-mixed binary powder mixtures

Abstract This paper presents an investigation of segregated and well-mixed binary powder mixtures in terms of the effective mass of the powder beds, when subject to low magnitude vibration ( g ) . An experimental system, developed in Part 1 of the present series of papers, was used to measure the effective mass of powder beds. Segregated systems were produced from materials of different densities, by layering materials. Tests were performed with both segregated and well-mixed systems with changing the mixing ratio. There was a significant difference in the effective mass between segregated and well-mixed systems, indicating that the effective mass of binary powder mixtures is dependent upon the dispersion of composition and the quality of mixing. The effective mass of well-mixed systems was in agreement with Rayleighs theory, whilst the segregated systems showed significant deviations from the theory. A simplified model based upon Rayleighs energy method was proposed to predict effective mass for segregated systems, and compared to experimental data. Results showed a reasonable agreement between the model and experimental data. The application of this technology to mixing has been examined, and the effective mass has been measured as a function of mixing time in a number of mixing situations. The effective mass indicates not only the deviation from an ideal mix, but also the direction of segregation.

Distinct element model of energy dissipation in vibrated binary particulate mixtures

Distinct element model (DEM) simulations of energy dissipation in vibrated particle beds are compared with experimental results. DMX, a 3-D DEM of polydisperse spheres in an open-top vibrating cylinder, was used. Simulations were conducted for vibrating mono and binary particle systems. Energy dissipation rate per vibration cycle at different frequencies and maximum accelerations was examined. Experimental data from previous publications were compared with the simulations. Reasonable qualitative agreement was achieved on scaled-up (by number of particles) simulation results. These show that DEM can capture the harmonic phenomena, showing resonance in dissipation at several frequencies at low accelerations (<1 g). At high acceleration levels (>1 g) no harmonics are observed. At low frequency levels where the vibration amplitudes are higher, the DEM reproduces experimental energy dissipation levels better than a continuum viscoelastic model. For a larger diameter vessel (fewer layers and decreased wall effects) the resonant dissipation frequency increases. Quantitative agreement between DMX predictions and the experiments is reasonable given the scatter in the experimental results; at high frequency there is at least an order of magnitude difference in the rate of dissipation, which was also observed in viscoelastic model predictions. Results show that even with using only 100 particles the agreement between DMX predictions and the experiments is qualitatively reasonable. This will enable the examination of many more situations and combinations as it can be carried out relatively “fast.”

Dynamic response of well-mixed binary particulate systems subjected to low magnitude vibration

The dynamic response of well-mixed binary mixtures subjected to low magnitude vibration was investigated using a newly developed non-invasive method. An apparent mass, defined as a ratio of the base force to base acceleration, was measured when applying a sweep vibration that ranged from 10 to 2000 Hz. The method could operate more rapidly, conveniently and non-destructively for a wider range of particle packing states, including a natural packed bed, compared to previous methods. The apparent mass data exhibited several significant peaks due to the bed harmonic resonance. The first peak frequency gave the longitudinal elastic modulus of the bed via the velocity of longitudinal stress wave propagation. For loosely packed mixture beds, the mixing fraction dependence upon the elastic modulus was found to be describable by the two-phase series model. In addition, the particle packing dependence upon the elastic modulus agreed reasonably well with the fourth power scaling law in spite of the wide size distribution. Comparison of the two-phase series model and experimental data for a range of particle packing fractions was made in terms of the coefficient of the scaling law.

Dynamic response of segregated two-phase systems subjected to low magnitude vibration and its application to non-invasive monitoring of a powder mixing transition process

The effect of the mixing quality upon the dynamic response of binary mixtures subjected to low magnitude vibration was investigated. The non-invasive method developed in a previous paper was used to measure the apparent mass as a function of frequency. Horizontally segregated two-phase systems were made by layering the materials. Comparison with well-mixed data showed qualitatively a significant dependence of the apparent mass data upon the quality of mixing, although the quantitative mixing index has not been discussed in this study. The mixing dependence was considered to be attributable to the resonant characteristics of two phases and their interaction effects. Furthermore, the principle was found to be applicable for the monitoring of mixing situations of mixture beds non-destructively and non-invasively. The apparent mass data indicated not only the deviation from an ideal mix, but also the direction of segregation.

Modeling particle settling behavior using the discrete element method

Abstract The discrete element model DMX was used to simulate the settling behavior of a unique particle in an assembly of other particles in a hopper filling process. No fluid effects or cohesive forces were modeled so the results are applicable for non-cohesive particles with diameters greater than about 1 mm where air effects can be neglected. No vibration or other such external load was included. The settling behavior of the unique particle was investigated in terms of the density ratio and the diameter ratio, and of varying conditions of chronological entry position, initial assembly velocity and system friction. The model showed satisfactory agreement with several observations reported regarding this behavior. The model demonstrated that at a high density ratio ‘sinking’ is dominant irrespective of the size of the particle, initial position or initial velocity, whereas a balance between particle size and density determine whether a particle sinks or rises at other densities. Based on this, a preliminary phase diagram was derived showing when a particle will sink or rise or do neither (termed ‘neutral’) as a function of particle size and diameter ratios. The model also showed that the initial position has only a qualifying effect on the behavior of the unique particle and the initial velocity is only significant at low-density ratios where with higher velocities the lighter particle will rise more. At lower friction these effects are enhanced. Repeating some simulation runs on larger binary systems showed that these effects could cause some segregation during settling.