Large-scale GPU based DEM modeling of mixing using irregularly shaped particles

Mixing of particulate systems is an important process to achieve uniformity, in particular pharmaceutical processes that requires the same amount of active ingredient per tablet. Several mixing processes exist, this study is concerned with mechanical mixing of crystalline particles using a four-blade mixer. Although numerical investigations of mixing using four-blades have been conducted, the simplification of particle shape to spherical or rounded superquadric particle systems is universal across these studies. Consequently, we quantify the effect of particle shape, that include round shapes and sharp edged polyhedral shapes, on the mixing kinematics (Lacey Mixing Index bounded by 0 and 1) that include radial and axial mixing as well as the inter-particle force chain network in a numerical study. We consider six 100 000 particles systems that include spheres, cubes, scaled hexagonal prism, bilunabirotunda, truncated tetrahedra, and a mixed particle system. This is in addition to two six million particle systems consisting of sphere and truncated tetrahedra particles that we can simulate within a realistic time frame due to GPU computing. We found that spherical particles mixed the fastest with Lacey mixing indices of up to 0.9, while polyhedral shaped particle systems mixing indexes varied between 0.65 and 0.87, for the same mixing times. In general, to obtain a similar mixing index (of 0.7), polyhedral shaped particle systems needed to be mixed for 50% longer than a spherical particle system which is concerning given the predominant use of spherical particles in mixing studies.     

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.     

Discrete element simulation for mixing performances and power consumption in a twin-blade planetary mixer with non-cohesive particles

The present study aims to characterize the mixing performances and power consumption of a twin-blade planetary mixer with non-cohesive particles through the discrete element method (DEM). A DEM model used for simulating the particle flow and mixing kinetics of the mixer was experimentally verified. The particle velocity and mixing mechanism are elaborated quantitatively, indicating that particle mixing is realized under the combined actions of radial, circumferential and vertical circulations, and some local collisions and mergers. Increasing the absolute speed N and the speed ratio i promotes the radial circulation, while the tangential and vertical circulations are strengthened with the increase of N and the decrease of i. The mixing time required for the homogeneous state decreases, and the power consumption increases as N increases and i decreases. Thus, increasing N and decreasing i can improve the mixing performance but require more energy to reach the homogeneous state. Also, the mixing performance shows a strong correlation with the swept volume of blades, which proves that the dominant mixing mechanism of the mixer is convection.     

Influence of particle shape on mixing rate in rotating drums based on super-quadric DEM simulations

Fundamental research on the flow and mixing of non-spherical particles is critical for industrial production and design. In this paper, the Discrete Element Method (DEM) is used to study the flow and mixing of granular materials in the horizontal rotating drum, and the periodic boundary condition is employed to eliminate end wall effect. Super-quadric elements are adopted to describe spherical and non-spherical particles. The influences of rotating speed, blockiness, and aspect ratio on the mixing rate are investigated by the Lacey mixing index. The results show that the rotating speed has a primary effect on the mixing rate, whereas the effect of the particle shape on the mixing rate is a secondary factor for non-spherical granular systems. Moreover, the mixing rate of spherical and non-spherical particle systems is significantly different. The mixing rate of spheres is the lowest, and the cubes have a higher mixing rate than the cylinders. As the blockiness decreases or aspect ratio deviates from 1.0, the mixing rate decreases. Ordered face-to-face contacts and dense packing structures result in a higher mixing rate. The analysis of kinetic energy shows that particle shape affects the transfer efficiency of external energy to the granular systems. The translational kinetic energy of non-spherical particles is higher than that of spherical particles, and their rotational kinetic energy is lower than that of spheres. Meanwhile, the blockiness enhances the transfer efficiency of external energy to the non-spherical systems; in contrast, the aspect ratio reduces the energy conversion efficiency.     

Mixing assessment of non-cohesive particles in a paddle mixer through experiments and discrete element method (DEM)

In this study the mixing kinetics and flow patterns of non-cohesive, monodisperse, spherical particles in a horizontal paddle blender were investigated using experiments, statistical analysis and discrete element method (DEM). EDEM 2.7 commercial software was used as the DEM solver. The experiment and simulation results were found to be in a good agreement. The calibrated DEM model was then utilized to examine the effects of the impeller rotational speed, vessel fill level and particle loading arrangement on the overall mixing quality quantified by the relative standard deviation (RSD) mixing index. The simulation results revealed as the impeller rotational speed was increased from 10?RPM to 40?RPM, generally a better degree of mixing was reached for all particle loading arrangements and vessel fill levels. As the impeller rotational speed was increased further from 40?RPM to 70?RPM the mixing quality was affected, for a vessel fill level of 60% and irrespective of the particle loading arrangement. Increasing the vessel fill level from 40% to 60% enhanced the mixing performance when impeller rotational speed of 40?RPM and 70?RPM were used. However, the mixing quality was independent of vessel fill level for almost all simulation cases when 10?RPM was applied, regardless of the particle loading arrangement. Furthermore, it was concluded that the particle loading arrangement did not have a considerable effect on the mixing index. ANOVA showed that impeller rotational speed had the strongest influence on the mixing quality, followed by the quadratic effect of impeller rotational speed, and lastly the vessel fill level. The granular temperature data indicated that increasing the impeller rotational speed from 10?RPM to 70?RPM resulted in higher granular temperature values. By evaluating the diffusivity coefficient and Peclet number, it was concluded that the dominant mixing mechanism in the current mixing system was diffusion.     

DEM study of the effect of impeller design on mixing performance in a U-shape ribbon mixer

The mixing of powders in a U-shape mixer is significantly influenced by the mixer design, especially impellers, but the studies on the mixing processes are still insufficient. In this study, the effect of impeller designs on mixing performance in an industrial-scale U-shaped ribbon mixer is studied using DEM simulations. Three impeller designs are studied: 2-bladed impeller spiralling in the same direction (i.e., Design I) and the opposite direction (i.e., Design II), and 4-bladed impeller (i.e., Design III). Different particle mixing behaviours in three different impeller designs are studied in aspects of mixing status, particle path line, velocity distribution, and forces. The radial direction has the highest dispersion coefficient while the axial direction has the lowest dispersion coefficient. Most particles in the mixers are imposed a weak force. Design III shows the best mixing performance among the three with the front-by-back and top-by-bottom loading used. Design II shows a better mixing performance used than Design I and III with the side-by-side loading but takes a longer time to reach the stable status. This work evaluates the effect of different impeller designs on the mixing performance in an industrial-scale U-shaped ribbon mixer and provides an effective way to assist industrial design in an economical and safe manner.     

A novel mixing method for levitated particles using electrostatic fields

A continuous particle mixing system using electrostatic forces and vibrations was developed. The system consists of two symmetrically arranged devices. The same or different types of charged particles were continuously fed from each device in a dispersed state and mixed instantaneously in the space between devices. When charged particles with opposite polarities were fed from each device by changing the direction of the electric field, the particles were homogeneously mixed. The electric field and particle trajectories were numerically calculated to elucidate the particle-mixing mechanism. Furthermore, the mixing state of the particles was evaluated quantitatively using Shannon entropy.     

DEM simulation for optimal design of powder mixing in a ribbon mixer

A ribbon mixer is often employed in powder mixing in a wide range of engineering fields. The structure of the ribbon mixer is extremely complicated. This structure makes it difficult to understand the mixing mechanism by experimental approaches due to problems related to accurate sampling. At present, the mixing mechanism in the ribbon mixer is empirically identified as convection, despite a lack of precise assessment. Additionally, experimental investigations to find the optimal design of the ribbon mixer have not been sufficiently conducted because of its prohibitive cost. As such, there is a lack of sufficient discussion concerning the design for better mixing in the ribbon mixer. Numerical technologies represent a promising approach for solving the aforementioned problems. Significant improvements in computer hardware have enabled numerical models such as the discrete element method (DEM) to be positively employed in powder mixing. In the current study, an identification approach is developed for convective mixing, and besides, the study explores an effective parameter for better mixing in the ribbon mixer using the DEM. A swept volume measurement approach due to paddle movement is newly developed to identify the main mixing mechanism as convection. Sensitivity analyses are performed to find an effective parameter for better mixing. Through the sensitive analyses, the blade width is indicated as an important factor for achieving better mixing. Moreover, this study shows that the relationship between the swept volume and mixing index remains, even if the paddle width changes. Thus, the swept volume measurement method is revealed as useful for identifying the mechanism as convection in the ribbon mixer. Thus, not only novel finding regarding the blade width for better mixing but also the development of an approach for identifying convective mixing in the ribbon mixer is presented herein. Incidentally, convection being the dominant mechanism is consistent with the novel finding regarding blade width achieving better mixing.     

DEM simulation of the shear behaviour of breakable granular materials with various angularities

Particle shape is an important factor that affects particle breakage and the mechanical behaviour of granular materials. This report explored the effect of angularity on the mechanical behaviour of breakable granular materials under triaxial tests. Various angular particles are generated using the quasi-spherical polyhedron method. The angularity α is defined as the mean exterior angle of touching faces in a particle model. A breakable particle is constructed as an aggregate composed of coplanar and glued Voronoi polyhedra. After being prepared under the densest conditions, all assemblies were subjected to triaxial compression until a critical state was reached. The macroscopic characteristics, including the shear strength and dilatancy response, were investigated. Then, particle breakage characteristics, including the extent of particle breakage, breakage pattern and correlation between the particle breakage and energy input, were evaluated. Furthermore, the microscopic characteristics, including the contact force and fabric anisotropy, were examined to probe the microscopic origins of the shear strength. As α increases, the peak shear strength increases first and then remains constant, while the critical shear strength generally increases. Assemblies with larger angularity tend to cause more serious particle breakage. The relative breakage is linearly correlated with α under shear loading. Compared with unbreakable particles, the peak shear strength and the critical volumetric strain decline, and the degree of decline linearly increases with increasing α.     

DEM study on identification of mixing mechanisms in a pot blender

A pot blender with both blending and storage capabilities offers an advantage over a conventional rotating drum. However, the mixing mechanism of the pot blender is extremely complicated because the pot blender rotates and swings simultaneously. Owing to the lack of systematic investigations, the mixing mechanism of the pot blender has not been fully elucidated. In this study, we clarify the mixing mechanism of the pot blender by using the discrete element method. Simulation results reveal that the main mixing mechanism is convective mixing in the rotational direction and shear mixing in the axial direction. Moreover, the mixing performance is unaffected by particle density, whereas the velocity gradient in the axial direction, which mainly determines the axial mixing performance, is affected by the particle filling ratio. Considering the relationship between the variance of axial particle velocity and granular temperature, the filling ratio is shown to significantly influence the mixing efficiency in the pot blender. In addition, the dependency of shear and diffusive mixing on Lacey’s mixing index in the pot blender is newly clarified. Consequently, this study demonstrates essential insights into the mixing mechanism of the pot blender and the pot blender as an effective industrial mixer.     

Numerical study of particle mixing in a tilted three-dimensional tumbler and a new particle-size mixing index

A new mixing index is proposed, which is an improved Lacey index based on coordination number fraction. The differences and similarities among many mixing indices are compared, including the new mixing index, the information entropy based on coordination number fraction, the Lacey index based on local concentration, and the information entropy based on local concentration. The first two indices are microscopic since the coordination number fraction is on particle-scale, whereas the latter two are mesoscopic as the local concentration is mesoscopic scale. The newly proposed mixing evaluation indices does not include inauthentic temporal oscillations. Moreover, using mixing index, the mixing characteristics of particles in a tilted tumbler are studied by discrete element method (DEM). The tumbler’s angle of tilt α = 0°, 10°, 20°, 30°, 40°, 50°, 60° and 70°, at five rotating velocities ω = 0.175, 0.35, 0.5, 0.6, 0.7 and 1.4 rad/s corresponding to Froude number F_r = 0.0025, 0.001, 0.002, 0.003, 0.004, 0.016 respectively are simulated. It is found that both increasing the tilt angle and the rotating speed have negative effects on the particle mixing within the scope of this study.     

Effects of mixing ratio and order of admixed particles with two diameters on improvement of compacted packing fraction

To improve particle flowability, a technique is used in which fine particles are admixed with the main particles. However, the effects of coating structure on the improvement in flowability are not yet fully understood. Thus, predicting the improvement resulting from this technique is difficult. In this study, we focused on the effects of the particle diameter distribution of the admixed particles on coating structures and improvement of flowability in terms of the compacted packing fraction in a particle bed. Main particles of size 397 nm with admixed particles of sizes 8 and 104 nm were used. Bimodal particle diameter distributions were adjusted by changing the mixing ratios of the two admixed particles. Furthermore, the main and admixed particles were mixed in various orders. We examined the compacted packing fractions for these different mixing ratios and orders. Scanning electron microscopy images were obtained in order to analyze the coating structures on the main particle surfaces. The results show that the main particle packing fraction was most greatly improved by pre-mixing the two admixed particles. This can be explained by a linked rigid-3-bodies model with leverage based on increasing the apparent diameter of the main particles.     

Application of a new method for experimental validation of polydispersed DEM simulation of silo discharge

There are numerous experimentally validated simulations for mono-dispersed systems in the literature based on discrete element method (DEM). In practice, however, most of granular systems consist of polydispersed assemblies of particles. Few studies have considered the effect of polydispersity, and yet fewer have experimentally validated the results. In this study, application of a new experimental method for granular flow analysis is presented, capable of validating the results of an in-house developed GPU-based DEM solver in both monodispersed and polydispersed assemblies. Silo discharge is chosen as the case study in which discharge time, flow pattern and more importantly, the outlet composition variation with time (for polydispersed configurations) have been experimentally evaluated and validated with numerical results. The outlet composition, which is the ratio of fine to coarse particles in the outlet stream, is an essential measure of segregation in polydispersed silos, and its numerical prediction can be correct only if the interactions between fine and coarse particles within the silo are modelled precisely. Measuring this parameter is not possible using conventional experimental methods established in silo discharge studies such as high speed photographing or high-frequency weight measurement of the bed. A new apparatus has been developed which can measure this parameter. The device is a compartmented wheel rotating with a motor which gathers the outlet stream of the silo into different compartments. Due to practical limitations, design and function of the apparatus are not ideal. Forward mixing, distribution of particles with the same resident time in different compartments, is the most critical problem. Non-idealities must be compensated by means of post-processing codes so that comparable results are obtained from experiment and simulation.     

DEM study of monodisperse granular flow in a pipe

Flow of granular material through a pipe has several industrial applications but maintaining a uniform mass flux is quite challenging. In this work, monodisperse granular flow (non-turbulent and non-dense phase particle transport) through a vertical pipe was simulated using discrete element method (DEM). Effects of different geometric and granular parameters on mass flux of cohesive and non-cohesive solids were analyzed and evaluated. Several important parameters and their effects on mass flux were studied like: L/D ratio, pipe diameter to particle diameter ratio (D/D_p), Poisson ratio, and pipe inclination angle. Furthermore, effects of moisture content and Bond number on mass flux were also investigated. These parameters influenced mass flux except Poisson ratio which showed no significant improvement in mass flux upon increasing the value of this ratio.     

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.     

Investigating the upper limit for applying the coarse grain model in a discrete element method examining mixing processes in a rolling drum

Mixing is an essential manufacturing process in various industries. The processing procedure and final product quality depend on the homogeneity of mixing. Because it is difficult to evaluate mixing systems experimentally, the discrete element method is commonly employed. However, as the number of particles increases, this approach incurs huge computational costs. The coarse grain model offers a potential solution, but its applicability has not been widely demonstrated; this study aimed to elucidate the upper limit for applying the coarse grain model. To determine the appropriate simulation parameters, calibrations were performed by comparing the powder bed in experiments versus simulations. Various mixing processes were numerically evaluated, and the mixing characteristics were qualitatively consistent among all coarse-grained ratios. These mixing systems were also evaluated quantitatively based on Lacey’s mixing index, which indicated that the upper limit of the coarse-grained ratio was five times. It is therefore important to secure a sufficient number of particles in each cell and to use an appropriate number of cells. This study clarified the upper application limit and criteria for the coarse grain model and verified the maximum coarse-grained ratio (five times). This approach can be used to determine the coarse-grained ratio and reduce computational costs.     

Determining a lower boundary of elasticity modulus used in the discrete element method (DEM) in simulation of tumbling mills

Discrete Element Method (DEM) simulations of industrial tumbling mills could involve millions of particles. Even with the considerable increase in the computational power, the simulations still require a large amount of time. Reducing the computational load by selecting a small value for the particle elasticity modulus to increase the time step has become a common approach. As the elasticity modulus decreases, the overlap required to provide the rebound force increases. The appropriate value of overlap is application-dependent and requires a detailed study to ascertain that the accuracy of the results do not adversely affected. In this study, a relationship incorporating particle density and mill diameter was proposed between the elasticity modulus and the interparticle overlap for tumbling mills. The effect of interparticle overlap on the accuracy of the simulated charge shape (i.e. toe and shoulder positions) by DEM was then investigated. A model tumbling mill (100 cm by 21 cm) with a transparent end wall was used to measure the actual charge trajectory by photography. A comparison of the DEM simulations with the model mill charge shape showed that when the overlap was assumed to be lower than the particle radius, the error was negligible. When the interparticle overlap became equal to the particle radius, the lower boundary of elasticity modulus and the maximum simulation speed was achieved. The speed was 102 times of the speed of simulation when an overlap equal to 0.01 of the particle radius was chosen.     

Analysis of powder behaviour in bin blending processes at different scales using DEM

Obtaining a desired content uniformity with satisfactory flowability is one of the main challenges during blending process of the pre-mixture with lubricants. In this study, Discrete Element Method (DEM) simulations were implemented to examine blending time and mixing behaviour during the blending process on the lab and industrial scales. The main goal was to investigate the possible influence of operational conditions on the blending behaviour and the change in powder cohesivity during the scale-up process. The effects of rotational speed and filling mass on the particles' travelled distance, velocity, shear stress and blending time were studied in the simulations. Based on the simulations, blending time and particle exposure to shear during the blending process were calculated for different scales. It was observed that the system's mass significantly influences them, and the effect of rotational speed could be neglected. The novelty of this paper is connecting particle exposure to shear from DEM to the flow function coefficient (ffc) of powder from experiments. It was done to define a critical range of exposure to shear that changes the powder flowability in different scales.