A new method to implement comminution functions into DEM simulation of a size reduction system due to particle-wall collisions

The ability to design a size reduction system prior to full scale experiments and to optimize existing systems has long been a goal of designers. Such a design and optimization could be achieved by correctly simulating any system under any operating condition. In this paper we present a new and innovative procedure to implement empirical comminution functions into DEM–CFD simulations. The paper is focused on the implementation procedures and not the DEM/CFD simulations, which deserve full attention. Therefore, this paper is not aimed to study any specific mill. The comminution functions include: initial strength distribution, selection function, breakage function and fatigue function. First, the traditional comminution functions (strength distribution, selection and breakage functions) and the recently investigated fatigue function are briefly described and modified. Then a procedure for implementing the functions into a DEM–CFD model or any other source to provide impact velocities and number of impacts, is described in detail. The implementation involves converting the probability comminution functions into individual particle properties by a random method and then converting the velocity dependent comminution functions into strength dependent ones. In this way, and mainly owing to the use of the fatigue function (which defines the weakening of those particles that are not breaking), a real size reduction system, in which each particle is subjected to multiple impacts at various velocities can be simulated. Three case studies for multiple impact conditions at the same average velocity (several impacts at the same velocity, various velocities at each impact and randomly selected velocities) are presented and analyzed in order to confirm qualitatively the procedure, although the comminution functions need to be further quantitatively modified. It should be emphasized that although the new procedure presents a step towards the final goal, some limitations do exist and some questions remain open.     

A large deformation breakage model of granular materials including porosity and inelastic distortional deformation rate

A general constitutive model of crushable granular materials is developed within the context of large deformations. The time evolution equations for breakage, inelastic porous compaction and dilation, and distortional deformations are coupled by a yield surface and restrictions are imposed to ensure that these inelastic processes are dissipative. Some of the most salient mechanisms of such materials are described, including: (1) stiffness dependent on the breakage (a variable index of grading), porosity, and pressure; (2) critical comminution pressure and isotropic hardening, also dependent on the breakage and porosity; (3) jamming transition between solid and gaseous states; (4) a dilation law that embodies competition between porous compaction (due to the rate of breakage) and bulking (porous dilation at positive pressure due to the rate of inelastic distortional deformation); and finally, (5) the non-unique critical state relation between stress and porosity, in terms of the loading history and grading changes.     

Micromechanical behaviour of Si-based particulate assemblies: A comparative study using DEM and atomistic simulations

In this paper, we investigate the micromechanical behaviour of Si-based particulate systems subjected to tri-axial compression loading. The investigations are based on three-dimensional discrete element modelling (DEM) and simulations. At first, we compare the variation of mean compressive stress for a silicon assembly subjected to tri-axial compression, predicted at two different scales: at the particulate scale, using the DEM simulation (mono-dispersed particulates) and at the atomistic scale using the molecular dynamics (MD) simulation results for silicon mono-crystal reported by Mylvaganam and Zhang (2003) [K. Mylvaganam, L. Zhang, Key Eng. Mater. 233–236 (2003) 615–620]. Both the simulation methods considered the silicon assembly subjected to an identical (tri-axial) loading condition. We observed a good qualitative agreement between the DEM and MD simulation results for the mean compressive stress when the assembly was subjected to small volumetric strain. However, at large volumetric strain, the mean stress of the silicon assembly predicted from MD simulation did not scale-up with the DEM results. This discrepancy could be due to that MD simulation is only valid for particle contacts, which are independent of one another and does not consider the inherent ‘discrete’ nature of particulates and the induced anisotropy prevailing at particulate scale. The micromechanical behaviour of particulate assemblies strongly depends on the inherent discrete nature of the particles, their single-particle properties and the induced anisotropy during mechanical loading. At the second stage, using DEM, we present the evolution of macroscopic compressive stress and several micromechanical features for four cases of the commonly used Si based poly-dispersed particulate assemblies (Si, SiC,Si₃N₄ and SiO₂) under tri-axial compression loading. We also present the evolution of several other phenomena occurring at particulate scale, such as the energy dissipation characteristics due to sliding contacts and the features of fabric structures developed during mechanical loading. The study shows that the single-particle properties of the Si based assemblies considered here significantly affect the micromechanical behaviour of the assemblies and DEM is a powerful tool to get insights on the internal behaviour of discrete particulates under mechanical loading.     

Regimes of segregation and mixing in combined size and density granular systems: an experimental study

Granular segregation in a rotating tumbler occurs due to differences in either particle size or density, which are often varied individually while the other is held constant. Both cases present theoretical challenges; even more challenging, however, is the case where density and size segregation may compete or reinforce each other. The number of studies addressing this situation is small. Here we present an experimental study of how the combination of size and density of the granular material affects mixing and segregation. Digital images are obtained of experiments performed in a half-filled quasi-2D circular tumbler using a bi-disperse mixture of equal volumes of different sizes of steel and glass beads. For particle size and density combinations where percolation and buoyancy both contribute to segregation, either radial streaks or a “classical” core can occur, depending on the particle size ratio. For particle combinations where percolation and buoyancy oppose one another, there is a transition between a core composed of denser beads to a core composed of smaller beads. Mixing can be achieved instead of segregation if the denser beads are also bigger and if the ratio of particle size is greater than the ratio of particle density. Temporal evolution of these segregated patterns is quantified in terms of a “segregation index” (based on the area of the segregated pattern) and a “shape index” (based on the area and perimeter of the segregated pattern).     

Granular flows down inclined channels with a strain-rate dependent friction coefficient. Part I: Non-cohesive materials

The flow of a granular material down an incline of finite width with a strain-rate dependent coefficient of friction and a conical yield criterion is semi-analytically obtained using a characteristic method for flows on a deep layer of grains. This analysis leads to a flow field with three distinct zones: a Bagnold-flow zone below the free surface, a dead-zone and a matching zone between the two, linked to slippage at the wall. A good agreement between the computed flow field and experimental data is obtained.     

Measuring the velocity fields of granular flows – Employment of a multi-pass two-dimensional particle image velocimetry (2D-PIV) approach

Measuring velocity fields plays a crucial role in investigating the dynamics of granular flows, which can improve the modeling of hazardous geophysical flows (e.g. avalanches and debris flows) and the control of powder flows in industrial applications. Non-invasive optical methods are invaluable tools for estimating this physical quantity at the laboratory scale. Despite the recent improvements of particle image velocimetry (PIV) algorithms, the employment of PIV to granular flows is still a non-trivial application, where there are several specific aspects to be carefully addressed. Here, we address the main challenges of granular PIV applications and systematically test the open-source window deformation multi-pass code, PIVlab [Thielicke and Stamhuis, J. Open Res. Soft., 2014], for dry granular flows in rotating drum and chute flow experiments. Three granular media (glass spheres, Ottawa sand and acetalic resin beads) with different optical properties are used as a broad test bench for validating the PIV approach. As well, comparisons between the estimations by PIVlab and those obtained by the commercial code, IDT ProVision-XS, are reported, where the advantages of the multi-pass approach are highlighted. This extensive experimental investigation allowed the evaluation of the accuracy of PIVlab in granular flow applications and also helped to assess the reliability of measurements of second-order statistics, such as the granular temperature. Finally, a guideline for setting a reliable PIV arrangement is suggested.     

Granular flows down inclined channels with a strain-rate dependent friction coefficient. Part II: cohesive materials

A strain-rate dependent rheology for granular materials with a constant cohesion, is proposed and applied in the case of a flow down an inclined channel. The results obtained show that a plug flow zone appears below the free surface and show that low cohesion may affect drastically the flow behaviour when the inclination of the channel is close to the repose angle. These results give also a basic understanding of h _stop, the depth of the remaining granular layer on an inclined channel, treating dilatancy like a cohesion-like behaviour.     

Numerical study of the mixing process of binary-density particles in a bladed mixer

Discrete element method (DEM) simulations of binary mixing of particles with different densities were conducted to study the influence of density ratio, blade speed, and filling level on the particle dynamics and mixing performance in a bladed mixer. Four particles with different densities at different locations were tagged to discuss the influence of three factors on the particle trajectory and velocity field in the mixer. A method based on cubic polynomial fitting of relative standard deviation was used to determine the critical revolution during the mixing process. It was found that the non-dimensional tangential velocity decreases with the increase of the blade speed and filling level, the fluctuation of vertical velocity increases with the radial location, blade speed, and filling level, and it is more pronounced than the fluctuation of tangential and radial velocity during the mixing process. Results obtained indicate that the mixing performance of particles with different density increases with the decrease of density ratio and filling level, while it increases with the increase of blade speed.     

A study of early-time response in dynamically loaded visco-elastic composites

Spalling is an important failure mode which triggers delamination, thus affects through-thickness integrity of a laminate and hinders the later integral plate action.The aim of the present study is to model the propagation of one-dimensional waves caused by a short-duration dynamic load through a visco-elastic medium. Two types of viscous effects are considered and described by means of partial differential equations. Four pulse load shapes are considered and four cases analysed. A higher order Lagrangian finite element is used to model the wave propagation and the weak-form Galerkin method is adopted to solve the differential equations. Numerical solutions are compared to analytical ones (where they exist) and excellent temporal and spatial correlation is achieved.It is found that damping leads to a decrease in peak stresses and strains by up to 11% for 5% of critical damping, even during the direct loading phase. It is shown that the inclusion of strain-rate did not have an effect on strains but led to an increase in stresses by almost 100%. The inclusion of damping and strain-rate effects increased stress values by up to 70% compared to the non-viscous cases, rendering strain-rate effects more pronounced than damping effects.     

A method to evaluate the overall breakage degree of pre-weakening processing and its applications

The product fineness indicator t₁₀ and the pre-weakening degree indicator percentage change of A * b value (C_Ab) were used to described the two aspects of the breakage result of processing with pre-weakening effect. However, there lacks a method to evaluate the ‘overall’ breakage degree with a single index. It was observed that when the high voltage pulse breakage (HVP breakage or HVPB) induced cracks inside pre-weakened particles were consumed during impact breakage, the breakage characteristics of the progeny particles are the same to raw ore particles. Based on this phenomenon, the concepts of equivalent size S_ie and equivalent size reduction t_10e are proposed. Raw ore particles of size S_ie is ‘equivalent’ to pre-weakened particles of size S_i in terms of their impact breakage product size distribution. Therefore the value of S_i and the consequently derived t_10e can be used to evaluate the overall breakage degree of pre-weakened particles. The calculation procedure of S_ie and t_10e is demonstrated in the context of HVP breakage. It is found that the impact breakage product of pre-weakened particles can be well predicted from S_ie. In addition to the evaluation of overall breakage degree of pre-weakening processing, this method also has potential to apply in the simulation of comminution circuits with pre-weakening processing and the development of breakage model for processing with pre-weakening effect.     

Three-dimensional distinct element simulation of spherocylinder crystallization

We present a three-dimensional distinct element model (DEM) able to handle populations of spherocylinders. We report on granular crystallization occurring when vibrating mono-disperse assemblies of spherocylinders that faithfully reproduce the corresponding results of physical experiments from the literature.