Nicolin Govender

Understanding the dynamical behavior of Granular Media (GM) is extremely important to many industrial processes. Thus simulating the dynamics of GM is critical in the design and optimization of such processes. However, the dynamics of GM is complex in nature and cannot be described by a closed form solution for more than a few particles. A popular and successful approach in simulating the underlying dynamics of GM is by using the Discrete Element Method (DEM). Computational viable simulations are typically restricted to a few particles with realistic complex interactions or a larger number of particles with simplified interactions. This paper introduces a novel DEM based particle simulation code (BLAZE-DEM) that is capable of simulating millions of particles on a desktop computer utilizing a NVIDIA Kepler Graphical Processor Unit (GPU) via the CUDA programming model. The GPU framework of BLAZE-DEM is limited to applications that require large numbers of particles with simplified interactions such as hopper flow which exhibits task level parallelism that can be exploited on the GPU. BLAZE-DEM also performs real-time visualization with interactive capabilities. In this paper we discuss our GPU framework and validate our code by comparison between experimental and numerical hopper flow.

Blaze-DEMGPU is a modular GPU based discrete element method (DEM) framework that supports polyhedral shaped particles. The high level performance is attributed to the light weight and Single Instruction Multiple Data (SIMD) that the GPU architecture offers. Blaze-DEMGPU offers suitable algorithms to conduct DEM simulations on the GPU and these algorithms can be extended and modified. Since a large number of scientific simulations are particle based, many of the algorithms and strategies for GPU implementation present in Blaze-DEMGPU can be applied to other fields. Blaze-DEMGPU will make it easier for new researchers to use high performance GPU computing as well as stimulate wider GPU research efforts by the DEM community.

The importance of shape non-uniformity and the polydispersed nature of granular media in industrial hopper discharge applications has been well established experimentally. Although numerous hopper discharge simulations have been conducted over the last thirty years, the investigations into the non-uniformity of particle shape and the polydisperse nature of particle systems remains limited. These studies are usually limited to a single hopper configuration, while the number of polyhedral particles considered are usually limited to a maximum of 5000 particles. In this study we consider the polydispersed particle systems for hoppers at various angles, particle systems with non-uniform shape for hoppers at various angles and polyhedral particle systems up to 1 million particles. This is made possible by extensively utilizing the graphical processing unit (GPU) computing platform via the BlazeDEM3D-GPU code. We first perform an experimental validation of the code for mono-sized spherical and convex polyhedral shaped particles for lab-scale hoppers at three half angles using 3D printed polylactic acid material (PLA) particles. We found good agreement between the experimental, Meyrs and Sellers empirical relation and simulation discrete element method (DEM) discharge rates. We then simulate three larger square hoppers with varying half-angles to study the effect polydispersity and non-uniformity of particle shape have on the mass discharge rate. Again, good agreement between the DEM simulated mono-dispersed spherical particle systems and the Meyrs and Sellers empirical relation is obtained to verify the simulations. Finally we simulate an industrial sized silo for which we compare mono-dispersed spheres against mono-dispersed polyhedra using over a million polyhedral shaped particles. Finally, we briefly comment on the effect that the polydisperse nature of particle systems has on the loading of the supporting structure.

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.

The Discrete Element Method (DEM) simulation of charge motion in ball, semi-autogenous (SAG) and autogenous mills has advanced to a stage where the effects of lifter design, power draft and product size can be evaluated with sufficient accuracy using either two-dimensional (2D) or three-dimensional (3D) codes. While 2D codes may provide a reasonable profile of charge distribution in the mill there is a difference in power estimations as the anisotropic nature within the mill cannot be neglected. Thus 3D codes are preferred as they can provide a more accurate estimation of power draw and charge distribution. While 2D codes complete a typical industrial simulation in the order of hours, 3D codes require computing times in the order of days to weeks on a typical multi-threaded desktop computer. A newly developed and recently introduced 3D DEM simulation environment is BLAZE-DEM that utilizes the Graphical Processor Unit (GPU) via the NVIDIA CUDA programming model. Utilizing the parallelism of the GPU a 3D simulation of an industrial mill with four million particles takes 1 h to simulate one second (20 FPS) on a GTX 880 laptop GPU. This new performance level may allow 3D simulations to become a routine task for mill designers and researchers. This paper makes two notable extensions to the BLAZE-DEM environment. Firstly, the sphere-face contact is extended to include a GPU efficient sphere-edge contact strategy. Secondly, the world representation is extended by an efficient representation of convex geometrical primitives that can be combined to form non-convex world boundaries that drastically enhances the efficiency of particle world contact. In addition to these extensions this paper verifies and validates our GPU code by comparing charge profiles and power draw obtained using the CPU based code Millsoft and pilot scale experiments. Finally, we conclude with plant scale mill simulations.

The coating of tablets to prevent product degradation or control dissolution is a typical process in its production. Coating uniformity is critical for the quality of final product and batch acceptance. Therefore, the coating process needs to be optimized in order to achieve the desired uniformity and reduce manufacturing costs. Thus, understanding how process parameters such as spray properties, equipment geometry and tablet shape influence the coating process is critical for process optimization and approval by regulatory bodies. However this is a non-trivial task as obtaining information about the detailed processes in a tablet coater via experimental means is limited. Thus, computational modeling is the most feasible option to obtain information about the physical processes affecting the performance of tablet coaters. The most widely used computational method for such numerical modelling is the Discrete Element Method (DEM) where individual particles (tablets) are simulated. However, the computational cost of representing the typical shape of tablets is high for industrially relevant simulations. Thus tablet shape is typically approximated by simpler shapes such as spheres or multi spheres. Even with such simplifications, typical simulations take months to complete making it unfeasible for process optimization and design. In the last decade, the Graphical Processor Unit (GPU) has enabled large-scale simulations of tens of millions of spheres and millions of shaped particles using the XPS code. In this paper, we present an algorithm for modeling accurate bi-convex tablets that is tailored to the GPU. We firstly validate the algorithm and implementation against a number of experiments. Finally we perform a simulation of 20 million tablets in a drum coater to illustrate the usefulness of GPU computing for industrial coating applications. We found that the proposed method yields a good match against the lab scale experiments. For the industrial simulation the proposed method gave a more accurate result compared to the multi sphere approach while being significantly faster.

Twin screw granulation (TSG) is increasingly used to produce granules in various industries, such as food, pharmaceutical, and fine chemicals. However, there is a large parametric space in terms of screw designs, formulation properties and operating conditions, so how to maximise the production throughput while maintaining consistent product quality is not a trivial task and still needs further investigation. In this study, the TSG process was systematically analysed using a discrete element method (DEM) based on the graphics processor unit (GPU) architectures that can provide not only macroscopic information but also microscopic insights into the complicated TSG process. In particular, the particle flow profiles and residence time distributions were obtained from the simulations and analysed in details. The effects of particle size and screw speed on flow behaviour of particles in TSG were also explored. It was shown that the mean residence time and its variance in the granulator decreased with increasing particle size and screw speed. The E-curves of the residence time with larger particle size at higher screw speed had a narrower spread, implying that particles with a larger size had similar residence time in the twin screw granulator. In addition, the cumulative distribution function, the F-curves, showed a higher increasing rate for larger particles and higher screw speeds, indicating a faster conveying efficiency.

During twin screw granulation (TSG), small particles, which generally have irregular shapes, agglomerate together to form larger granules with improved properties. However, how particle shape impacts the conveying characteristics during TSG is not explored nor well understood. In this study, a graphic processor units (GPUs) enhanced discrete element method (DEM) is adopted to examine the effect of particle shape on the conveying characteristics in a full scale twin screw granulator for the first time. It is found that TSG with spherical particles has the smallest particle retention number, mean residence time, and power consumption; while for TSG with hexagonal prism (Hexp) shaped particles the largest particle retention number is obtained, and TSG with cubic particles requires the highest power consumption. Furthermore, spherical particles exhibit a flow pattern closer to an ideal plug flow, while cubic particles present a flow pattern approaching a perfect mixing. It is demonstrated that the GPU-enhanced DEM is capable of simulating the complex TSG process in a full-scale twin screw granulator with non-spherical particles.

Convex polyhedra represent granular media well. This geometric representation may be critical in obtaining realistic simulations of many industrial processes using the discrete element method (DEM). However detecting collisions between the polyhedra and surfaces that make up the environment and the polyhedra themselves is computationally expensive. This paper demonstrates the significant computational benefits that the graphical processor unit (GPU) offers DEM. As we show, this requires careful consideration due to the architectural differences between CPU and GPU platforms. This paper describes the DEM algorithms and heuristics that are optimized for the parallel NVIDIA Kepler GPU architecture in detail. This includes a GPU optimized collision detection algorithm for convex polyhedra based on the separating plane (SP) method. In addition, we present heuristics optimized for the parallel NVIDIA Kepler GPU architecture. Our algorithms have minimalistic memory requirements, which enables us to store data in the limited but high bandwidth constant memory on the GPU. We systematically verify the DEM implementation, where after we demonstrate the computational scaling on two large-scale simulations. We are able achieve a new performance level in DEM by simulating 34 million polyhedra on a single NVIDIA K6000 GPU. We show that by using the GPU with algorithms tailored for the architecture, large scale industrial simulations are possible on a single graphics card.

Numerous practical applications of the Discrete Element Method (DEM) require a flexible description of particles that can account for irregular and non-convex particle shape features. Capturing the particle non-convexity is important since it allows to model the physical interlocking when the particles are in contact. To that end, the most flexible approach to capture the particle shape is via a polyhedron, which provides a faceted representation of any shape, albeit at a significant computational cost. In this study we present a decomposition approach to modeling non-convex polyhedral particles as an extension of an existing open source convex polyhedral discrete element code, BlazeDEM-GPU, which computes using general purpose graphical processing units (GPGPUs). Although the principle of decomposition of non-convex particles into convex particles is not new, its application by the discrete element modeling community has been rather limited. The non-convex extension of BlazeDEM-GPU was validated using a hopper flow experiment with identical convex and identical non-convex 3D printed particles. The experiment was designed around two sensitive flow points, with the convex particles following the intermittent flow and the non-convex particles forming stable arches. It was demonstrated that the DEM simulations can be applied to reproduce both the convex and the non-convex flow behavior using the same parameter set. This study is a significant step towards general computing of non-convex particles for industrial-scale applications using the GPGPUs.

In blast furnaces, burden topography and packing density affect the stability of the burden, permeability of gas flow as well as the heat transfer efficiency. A fundamental understanding of the influence and interaction of coke and ore particles on the burden topography and packing density is therefore essential, in particular, the influence of particle shape polydispersity and particle size polydispersity. In this paper we analyze the effect of particle shape and size polydispersity on the coke and ore charge distribution inside a bell-less blast furnace using the discrete element method (DEM). We first validate experimentally the polyhedral particle model with a simplified lab-scale charging experiment. A comparative study between spheres, with rolling friction to account for shape, and polyhedra is conducted for shape and size polydisperse particle systems. It was found that shape polydispersity mainly influenced the topography of the burden, whereas the size polydispersity mainly influenced the inter-layer percolation, i.e. localized particle diffusion, hence the local spatial packing density. The differences between the spherical particle models and polyhedral particle models on the burden topography are also quantitatively and qualitatively presented, especially on the role of particle shape on the push-up of coke in the centre. This study demonstrates that modelling particle shape effects using spheres with rolling friction is insufficient to fully describe the complex behaviour of shaped particles in a blast furnace, as the particle shape has a noteworthy influence on the burden characteristics.

Breakage of particles will have greatly influence on mechanical behavior of granular material (GM) under external loads, such as ballast, rockfill and sand. The discrete element method (DEM) is one of the most popular methods for simulating GM as each particle is represented on its own. To study breakage mechanism of particle breakage, a cohesive contact mode is developed based on the GPU accelerated DEM code - Blaze-DEM. A database of the 3D geometry model of rock blocks is established based on the 3D scanning method. And an agglomerate describing the rock block with a series of non-overlapping spherical particles is used to build the DEM numerical model of a railway ballast sample, which is used to the DEM oedometric test to study the particles’ breakage characteristics of the sample under external load. Furthermore, to obtain the meso-mechanical parameters used in DEM, a black-analysis method is used based on the laboratory tests of the rock sample. Based on the DEM numerical tests, the particle breakage process and mechanisms of the railway ballast are studied. All results show that the developed code can better used for large scale simulation of the particle breakage analysis of granular material.

Granular material (GM) is the second most manipulated substance in the world and is present in most industries either as raw materials or finished products. Often the temperature of the granular material needs to be manipulated for example in the case of heating iron ore to induce a phase change or to be kept within a certain temperature range in the case of pharmaceutical powders and food products. Thus a detailed understanding of how heat is transferred in granular materials is essential. The most feasible numerical approach to study heat transfer in granular materials is using the discrete element method (DEM), where each particle is explicitly modeled. In terms of conductive heat transfer particle shape can be expected to have a significant effect on the heating of granular materials, due to the nature of the grain to grain contacts and packing topology which control the heat flow paths and the rate that heat is conducted along these. This paper considers the effect of particle shape on heat conduction in thermally simple or low Biot number granular materials using a polyhedral particle representation. The volume based contact model for granular heat conduction is firstly verified against the analytical solution for solid heat conduction as well as experiment with cubic particles. The resulting model is then used to study the effect of particle shape on the effective thermal conductivity (ETC) and heat distribution within packed stationary beds. It was found that for irregularly shaped (polyhedral) particles the ETC does not have a linear relationship with the packing density as found in previous studies with spherical and ellipsoidal shaped particles. Rather that there is an exponential dependence on the micro-structural quantities of contact area and isotropy, with non-homogeneity in the packing density resulting in complex conduction paths and dead zones affecting conduction thru the bed.

Numerous industrial processes require the blending of granular materials that differ in morphology for which the resulting mixing cannot be predicted from bulk tests. Discrete element method simulations are an attractive approach to understanding mixing at the particle level within processing equipment. However, due to computational cost, particle shape is typically approximated as spherical despite most materials being non-spherical. In this paper, the combined effect of cohesion and particle shape using polyhedral particles is studied in a rotating drum. It was found that repose angle calibrated spheres were unable to reproduce the same percolation behaviour as polyhedra, leading to significantly different results with a better match in the case of highly cohesive paste like materials that diminish the particle scale effects. Symmetric polyhedral shapes exhibited the best mixing, while irregular shapes had the worst mixing. Mixing improves with increasing cohesive particle size due to the ability to percolate the finer non-cohesive material. Finally, equipment geometry and rotation speed had a significant effect on mixing, such that making conclusions on the general mixing of materials without the actual mechanical actions it is subjected to should be done with caution.

Failure processes are common in geomaterials under external loads. In this study, a cohesive fracture model (CFM) and its implementation in a graphical processing unit (GPU)-based discrete element method (DEM) solver is presented within the context of simulating the failure of rock and other geomaterials. The CFM and its GPU implementation advances the simulation of the processes of meso-fracture initiation, propagation, and interaction. The CFM discretizes a domain into a series of pre-defined rigid polyhedral blocks. These blocks are bonded along the contact faces by a cohesive criterion with normal and shear strengths. This poses a computational challenge as few DEM codes can simulate polyhedrons, and amongst those the limited number of particles and required computational run-time make it intractable to do simulations of more than a few thousand polyhedral elements. This makes it computationally infeasible to combine CFM with such DEM models for practical applications. However, the GPU based code Blaze-DEM does allow for simulations of tens of millions of polyhedrons within practical runtimes. In this study we implement the CFM in Blaze-DEM and show the efficiency and usefulness of the model using GPU compute. Two typical examples, including a block sliding along a slope and the fracture process of an arch structure, are used to verify the provided CFM. This is followed by the simulation of Brazilian tests and uniaxial tests of limestone using the CFM that are validated against laboratory experiments. These tests demonstrate that the provided CFM can simulate not only the fracture process well, but also mechanical behaviors at the meso and macro scale of the geomaterials. Furthermore, based on the failure mechanisms of the Brazilian test and uniaxial test, an inversion method is proposed to obtain the mechanical parameters in CFM.

The Discrete Element Method (DEM) is increasingly used to study the failure behavior of rock. Despite DEM's intrinsic capability to capture the mechanical behavior of discontinua, there remains several open questions that include the numerical modelling of the meso-fracture evolution and behavior of brittle rock bodies. A Cohesive Fracture Model (CFM) designed explicitly for polyhedral shaped DEM particles is proposed for the simulation of the fracture and behavior of brittle rock bodies. A rock body is discretized into a series of rigid polyhedral blocks which are bonded along the boundary faces along the normal and shear directions. A cohesive criterion dictates the normal and shear break strengths of the bonds for the CFM. The computational efficiency of the CFM for polyhedral shaped DEM simulations is enhanced by parallelization over multiple graphical processing units (GPUs) in the Blaze-DEM framework. A series of numerical and laboratory tests are conducted. For marble, these include three-point bending and uniaxial tests to investigate the relationship between the meso-mechanical parameters and macro-mechanical behavior. Following a sensitivity analysis of the meso-mechanical parameters, an inversion procedure is established to estimate the numerical meso-mechanical parameters of the CFM model. Two different failure modes for different rocks are proposed.

The reduction in particle size of raw materials using grinding mills is an energy and cost intensive task. Optimization of grinding processes is not trivial as obtaining experimental information is extremely difficult due to the harsh environment. Thus, computational modeling is the most feasible option for obtaining information on the dynamics of the media. However, the computational cost of modeling each particle is high, resulting in the shape of the media being approximated by simple shapes, and in most cases, a reduction in the size of the mill. Even with these simplifications typical simulations take many weeks to months to complete making it infeasible for design prototyping and process optimization. In the last decade, the Graphical Processor Unit (GPU) has enabled large scale simulations of tens of millions of spheres in ball mills using the Blaze-DEM GPU code. Recently, this code was expanded to provide detailed contact detection for polyhedra using the volume-overlap method which is the most accurate approach amongst commercial and academic codes. In this study we first validated the code against experimental results for spherical and cube particle systems in a lab-scale ball mill. Thereafter, we performed a number of ball mill simulations with four additional polyhedral particle systems (truncated tetrahedra, Biluna, elongated hexagonal prisms and a mixed polyhedral particle systems) to study the effect of particle shape. This allows for a first investigation into the roles of particle angularity and aspect ratio on power draw, normal and shear power dissipation between particles, particles and lifters and, particles and the shell. We also show qualitative differences in charge profiles and force chain networks between the various particle systems.

A number of industrial applications require the control of granular material temperature across individual grains. Particle level simulations using the DEM is thus critical for optimization. However due to computational cost, particle shape in DEM is often omitted. In this paper advances in GPU computing via the Blaze-DEM code is used to study the effect of particle shape on heat transfer in a rotating drum. Shape irregularity was found to have the greatest effect with non-symmetric shapes having a better heat conduction of at-least 30%. A linear trend of system temperature as function of both RPM and fill level was found. In all cases temperature increased sub-linearly over time. All shapes where found to be sensitive to particle size increases larger than 1.5x. Finally significant diffusion of particles in the axial direction demonstrated the importance of considering the full domain rather than a slice to limit computational cost.

The capability of solving a geotechnical discrete element method (DEM) applications is determined by the complexity of the simulation and its computational requirements. Collision detection algorithms are fundamental to resolve the mechanical collisions between millions of particles efficiently. These algorithms are a bottleneck for many DEM applications resulting in excessive memory usage or poor computational performance. In particular, for GPU based DEM, there are many factors for a user to consider when deciding on an algorithm. This study discusses a set of diverse classes of geotechnical problems and the impact of algorithm choice. Four factors were considered: i) the world domain size, number of particles and particle density, ii) polydispersity in size, iii) the time evolution and iv) the particle shape. This study shows that for spherical particles, the choice of broad-phase collision detection algorithm has the most impact on computational performance. The computational cost for convex polyhedral particles is dominated by the selection of the particles' bounding volumes and their intersection tests over the selection of the broad-phase collision detection algorithm. On average for convex polyhedral particles, the broad-phase occupies at most 1.3% of the total runtime, while the narrow-phase collision detection and collision response require more than 87% of the runtime. A combination of bounding spheres and axis-aligned bounding boxes for use as bounding volumes of particles showed the best performance reducing the computational cost by 20%. This study serves as a guide for further research in the field of GPU based DEM collision detection and the application in geotechnics.

Screw conveyors are widely used in several industries to transport various granular materials needed to manufacture products or components in a product chain. Degradation of the material and variable packing in the screw pitches are some of the significant operational concerns. This paper explores the effect that particle shape has on the material's behaviour in screw conveyors. Specifically, faceted polyhedral particles are considered and computed on GPUs using the DEM code, Blaze-DEM. Particle shape significantly influences bulk discharge characteristics, in particular, for higher rotation speeds of the screw. Although spheres yield similar bulk discharge rates to symmetric and equiaxed polyhedra at lower rotational speeds, the packing structure and collision dynamics within the screw are shown to be significantly different between the particle shapes. In general polyhedra have a larger fraction of normal impacts between particles and increased abrasion with the screw and enclosing case. On the other hand, spheres have the highest fraction of energy dissipated as shear between particles.

The majority of publications in DEM use simplified particle shapes, in this study we use polyhedral shapes to determine the effect of particle shape on shear strength via a direct-shear test. Grain aspect ratio was found to be the primary determinant of shear strength with elongated polyhedra having a lower shear resistance. Grain irregularity also had a significant effect, shapes with isotropic contacts angles had the highest shear strength. The variability of granular material behavior due to shape was demonstrated by non-convex shapes re-orientating to jam in certain cases. Shapes with multi-stable packed orientations were found to offer the highest resistance to reordering under localized vibration.

Fully resolved fluid–solid coupling is explored with the gradient corrected weakly compressible SPH methodology being used to simulate an incompressible Newtonian fluid as well as being used to obtain the coupling force information required to accurately represent these interactions. Gradient correction allows for the application of the Neumann boundary condition required to describe the pressure fields at solid interfaces, as well as symmetry boundary conditions for velocity (where applicable) without the use of ghost or mirrored particles. A scaling study is performed by investigating the drag on an infinitely long cylinder at different smoothed particle hydrodynamics (SPH) resolutions, with finer resolution scales showing good correlation to other studies. The drag characteristics of several particle shapes and topologies are also investigated making use of both convex and non-convex particle shapes. Clear distinction for both the fluid and solid particle responses for the various solid particle shapes are observed. Boundary effects are also explored with results showing a strong responses to changing domain geometry aspect ratios. A many particle system with two different particle shapes are simulated to investigate bulk behaviour of the different solids falling under gravity in a fluid. All results presented in this paper are obtained from full 3D simulations.

Hybrid fluid–particle systems are prevalent in nature and engineering practices, but accurately simulating the dynamic behaviour is challenging due to their inherent strong non-linearity. This study proposes a three-dimensional resolved numerical framework for analysing complex shape polyhedron–fluid interaction. The weakly compressible smoothed particle hydrodynamics (SPH) is employed to describe the complex hydrodynamic behaviour, and the discrete element method (DEM) is applied to solve the motion of irregular polyhedral granular materials. An accurate contact collision algorithm is implemented in the coupling model to address the dynamic response of polyhedral particles. The high-fidelity modelling of the complex morphology of granular materials is realised. Hence, the coupling code is developed based on two high-performance open-source platforms, and an efficient two-way coupling scheme is designed to manage the fluid–particle interaction under a unified time framework. The reliability and the applicability of the SPH-DEM solver are demonstrated through extensive validations based on existing experimental and numerical data involving violent free-surface flow impacting multiple rigid bodies and cube deposition. Furthermore, a more complex case of wave-flow impact on rock piles is conducted, exhibiting great potential to employ this model in real-life engineering problems.

Die filling is a critical stage during powder compaction, which can significantly affect the product quality and efficiency. In this paper, a forced feeder is introduced attempting to improve the filling performance of a lab-scale die filling system. The die filling process is analysed with a graphics processing units (GPU) enhanced discrete element method (DEM). Various stirrer designs are assessed for a wide range of process settings (i.e., stirrer speed, filling speed) to explore their influence on the die filling performance of free-flowing powder. Numerical results show that die filing with the novel helical-ribbon (i.e., type D) stirrer design exhibits the highest filling ratio, implying that it is the most robust stirrer design for the feeder configuration considered. Furthermore, die filling performance with the type D stirrer design is a function of the stirrer speed and the filling speed. A positive variation of filling ratio (ηf>0%) can be ensured over the whole range of filling speed by adjusting the stirrer speed (i.e., increasing the stirrer speed). The approach used in this study can not only help understand how the stirrer design affects the die filling performance but also guide the optimization of feeder system and process settings.

The effect of the size and shape of the insert (inverted cone, sphere) when placed axially above an orifice on the mass discharge rate (MDR) of monodisperse spherical particles from a cylindrical silo has been investigated through experiments and DEM simulations. MDR characteristics have been measured for various distances between the insert and the orifice. An important practical finding is that, within a specific range of placement distances, the MDR increases by approximately 10% when a conical insert is used, whereas no such effect was observed when a spherical insert was employed. It was observed that, in some cases, a slight increase in friction coefficient leads to an increase in MDR as result of alterations in the initial grain structure, facilitating faster discharge. In a quasi-2D configuration, significant changes in flow rate occur when the thickness exceeds the natural multiple of dp, allowing the next layer of particles to flow.

Multiple software frameworks based on the Discrete Element Method (DEM) are available for simulating granular materials. All of them employ the same principles of explicit time integration, with each time step consisting of three main steps: contact detection, calculation of interactions, and integration of the equations of motion. However, there exist significant algorithmic differences, such as the choice of contact models, particle and wall shapes, and data analysis methods. Further differences can be observed in the practical implementation, including data structures, architecture, parallelization and domain decomposition techniques, user interaction, and the documentation of resources. This study compares, verifies, and benchmarks nine widely-used software frameworks. Only open-source packages were considered, as these are freely available and their underlying algorithms can be reviewed, edited, and tested. The benchmark consists of three common bulk processes: silo emptying, drum mixing, and particle impact. To keep it simple and comparable, only standard features were used, such as spherical particles and the Hertz-Mindlin model for dry contacts. Scripts for running the benchmarks in each software are provided as a dataset.

This paper introduces a novel smoothed particle hydrodynamics (SPH) - discrete element method (DEM) to enhance our understanding of the impact of free-surface flow on breakwater structures. SPH is employed to simulate incompressible fluids, while DEM is utilized to track the trajectories of solid particles. Advanced strategies including polyhedral particle modeling and contact model are adopted to enhance the model's capability in solving the dynamic behavior of irregular particle. Several cases are analyzed to validate the accuracy of coupling model, showing a high level of agreement. Additionally, the impact of wave flow on coastal breakwaters composed of irregular rocks is simulated. This work reveals that the coupling model effectively provides extensive information about the flow field and dynamic response of multi-particle systems, such as velocity, fluid force and force chain distribution. This model exhibits significant potential for analyzing the dynamic response of severe free surface flow on the multi-block structures.

This work presents a two-way coupling strategy combining Smoothed Particle Hydrodynamics (SPH) and Discrete Element Method (DEM), allowing efficient and accurate modeling of the intricate interaction between fluids and granular materials. A high-performance coupling module based on Message Passing Interface (MPI) toolbox is developed based on two open-source platforms, named DualSPHysics and Blaze-DEM. DualSPHysics specializes in nonlinear free-surface flow and violent interaction problems, while Blaze-DEM excels at simulating complex contacts involving irregularly shaped granular materials. A series of validation tests based on several typical benchmarks are performed to verify and analyze the accuracy of the coupled model. Next, the complex surface wave induced by the collapse of the particle column into water is reproduced, and the performance of the coupling solver is emphatically analyzed involving the sensitivity of the solver to different DEM object shapes and SPH resolutions. The findings of this study reveal that the developed coupling solver offers a three-dimensional insight, allowing for a comprehensive understanding of the intricate interactions between fluids and irregularly shaped granular materials.

The discrete element method, implemented in a modular GPU based framework that supports polyhedral shaped particles (Blaze-DEM), was used to investigate effects of particle shape on backfill response behind integral bridge abutments during temperature-induced displacement cycles. The rate and magnitude of horizontal stress build-up were found to be strongly related to particle sphericity. The stress build-up in particles of high sphericity was gradual and related to densification extending relatively far from the abutment. With increasing angularities, densification was localised near the abutment, but larger and more rapid stress build-up occurred, supported by particle reorientation and interlock developing further away.

The use of the Discrete Element Method (DEM) for industrial civil engineering industrial applications is currently limited due to the computational demands when large numbers of particles are considered. The graphics processing unit (GPU) with its highly parallelized hardware architecture shows potential to enable solution of civil engineering problems using discrete granular approaches. We demonstrate in this study the pratical utility of a validated GPU-enabled DEM modeling environment to simulate industrial scale granular problems. As illustration, the flow discharge of storage silos using 8 and 17 million particles is considered. DEM simulations have been performed to investigate the influence of particle size (equivalent size for the 20/40-mesh gravel) and induced shear stress for two hopper shapes. The preliminary results indicate that the shape of the hopper significantly influences the discharge rates for the same material. Specifically, this work shows that GPU-enabled DEM modeling environments can model industrial scale problems on a single portable computer within a day for 30 seconds of process time.

Understanding die filling behaviour of powders is critical in developing optimal formulation and processes in various industries, such as pharmaceuticals and fine chemicals. In this paper, forced die filling is analysed using a graphics processing unit (GPU) based discrete element method (DEM), for which a powder feeder equipped with a wired stirrer is considered. The influences of operating parameters, such as the initial powder bed height, the filling speed, and the stirrer speed, on the die filling performance are systematically explored. It is shown that a larger initial powder bed height leads to a higher filling ratio, which can be attributed to a higher filling intensity; while the deposited particle mass in the die is almost independent of the powder bed height, when the initial fill level is larger than a critical bed height. Additionally, the filling ratio slightly increases with the increase of stirrer speed for cases with a stirrer, while the filling ratios are lower than that without a stirrer, which is attributed to the stirrer occupying some space above the die and reducing the effective discharge area. The obtained results can provide useful information for optimising the feeder system design and the operating condition.

Continuous powder blending is an essential operation during continuous pharmaceutical manufacturing. However, the complex granular dynamics in the blender is still poorly understood. This study employs a graphic processor unit (GPU) enhanced discrete element method (DEM) to analyse the granular dynamics in a continuous blender. Numerical results indicate that only a small fraction of powder distributes in the upper region of the blender, while most of that distributes in the middle and lower regions. Besides, a higher impeller speed leads to a smaller hold-up mass and a shorter mean residence time. Interestingly, the maximum number of blade passes is achieved at an intermediate impeller speed. There are two distinct regimes during continuous blending: i) a shearing regime at low impeller speeds; and ii) a dynamic regime at high impeller speeds. This study demonstrates that the GPU-enhanced DEM can be a robust tool for analysing powder flow during continuous pharmaceutical manufacturing.

Numerical simulation of particulate materials is required in many industrial processes with applications ranging from ball mills in mining to powder mixers in pharmaceuticals. While the discrete element method (DEM) has become the defacto standard for numerical simulation of particulate materials, the large computational cost associated with the method limits the number of particles that can be simulated in a realistic time frame on a typical computer to less than a million. Simulations of millions of particles are only possible on expensive clusters which are typically not accessible to the majority of users. However, the computational architecture plays a significant role on the performance that can be realized. In the last few years the trend of increasing Central Processing Unit (CPU) clock speed resulting in more computations being performed in the same time period has stopped due to the physical limits on the materials used in the manufacturing of computer hardware. While computational power still scales with Moore’s Law, this scaling is now achieved through increasing the number of computing cores on a single chip as opposed to make a single core faster. Leading this evolution from multi core to many core processing chips is the Graphical Processor Unit (GPU) that can perform billions arithmetic operations in parallel. In this paper we present the GPU based code Blaze-DEM that allows for tens of millions of particles to be simulated on a single computer.

We recently introduced Blaze-DEMGPU, a GPUGraphical processing unit(GPU) based computing framework for convex polyhedral shaped particles (Govender et al. Appl. Math. Comp. 267, 810–829, 2015). The computing framework was validated against numerous industrial applications that include particulate discharge and estimating power draw for a ball mill in comminution applications. In this study we extend the computing capabilities of the convex polyhedral Blaze-DEMGPU computing platform to include non-convexNon-convex polyhedralPolyhedral particles. We follow a similar philosophy to the well known clumping, clustering or fusing of spheres (Chong et al. Gran. Mat. 17, 377–387, 2015), but instead we fuse convex polyhedral particles. This allows for fused or super polyhedral particles that constitute effective physical properties for the fused particle e.g. the inertia tensor. The major benefit of fused polyhedral particles as opposed to clustered spherical particles is that the number of particles required to fuse fairly complex particle shapes is small. In addition, numerous decompositions exist to exactly decompose a non-convex particle in a number of convex particles. The main complexity of non-convex polyhedral particles is to resolve contact effectively and efficiently on the GPU. In this paper we outline our approach.

This work describes a comparative study on the milling process modelled by Discrete Element Method and lab-scale experiments. In particular, analogical complex granular media with spherical and polyhedral shaped particles have been used to support the development of Blaze-DEM GPU, which is graphical processor unit (GPU) based computing framework for convex polyhedral particle shapes. DEM simulations and experiments were performed for several filling rate, rotational speed and shaped particles. The experimental and DEM surface profiles are in good agreement that include avalanching, rolling, cascading and cataracting, The various flow regimes have been validated. The GPU allows for the computational efficient simulation of large numbers of particles or more complex polyhedral shaped particles. We consider the dodecahedron in this study. Therefore, GPU based DEM simulation conducted appropriately allows for large-scale industrial investigations to be conducted.

The packing density and flat bottomed hopper discharge of non-convex polyhedral particles are investigated in a systematic experimental study. The motivation for this study is two-fold. Firstly, to establish an approach to deliver quality experimental particle packing data for non-convex polyhedral particles that can be used for characterization and validation purposes of discrete element codes. Secondly, to make the reproducibility of experimental setups as convenient and readily available as possible using affordable and accessible technology. The primary technology for this study is fused deposition modeling used to 3D print polylactic acid (PLA) particles using readily available 3D printer technology. A total of 8000 biodegradable particles were printed, 1000 white particles and 1000 black particles for each of the four particle types considered in this study. Reproducibility is one benefit of using fused deposition modeling to print particles, but an extremely important additional benefit is that specific particle properties can be explicitly controlled. As an example in this study the volume fraction of each particle can be controlled i.e. the effective particle density can be adjusted. In this study the particle volumes reduces drastically as the non-convexity is increased, however all printed white particles in this study have the same mass within 2% of each other.

Accurately predicting the dynamics of particulate materials is of importance to numerous scientific and industrial areas with applications ranging across particle scales from powder flow to ore crushing. Computational discrete element simulations is a viable option to aid in the understanding of particulate dynamics and design of devices such as mixers, silos and ball mills, as laboratory scale tests comes at a significant cost. However, the computational time required to simulate an industrial scale simulation which consists of tens of millions of particles can take months to complete on large CPU clusters, making the Discrete Element Method (DEM) unfeasible for industrial applications. Simulations are therefore typically restricted to tens of thousands of particles with highly detailed particle shapes or a few million of particles with often oversimplified particle shapes. However, a number of applications require accurate representation of the particle shape to capture the macroscopic behaviour of the particulate system. In this paper we give an overview of the recent extensions to the open source GPU based DEM code, BlazeDEM3D-GPU, that can simulate millions of polyhedra and tens of millions of spheres on a desktop computer with a single or multiple GPUs.

The use of the Discrete Element Method to model engineering structures implementing granular materials has proven to be an efficient method to response under various behaviour conditions. However, the computational cost of the simulations increases rapidly, as the number of particles and particle shape complexity increases. An affordable solution to render problems computationally tractable is to use graphical processing units (GPU) for computing. Modern GPUs offer up 10496 compute cores, which allows for a greater parallelisation relative to 32-cores offered by high-end Central Processing Unit (CPU) compute. This study outlines the application of BlazeDEM-GPU, using an RTX 2080Ti GPU (4352 cores), to investigate the influence of the modelling of particle shape on the lateral pull behaviour of granular ballast systems used in railway applications. The idea is to validate the model and show the benefits of simulating non-spherical shapes in future large-scale tests. The algorithm, created to generate the shape of the ballast based on real grain scans, and using polyhedral shape approximations of varying degrees of complexity is shown. The particle size is modelled to scale. A preliminary investigation of the effect of the grain shape is conducted, where a sleeper lateral pull test is carried out in a spherical grains sample, and a cubic grains sample. Preliminary results show that elementary polyhedral shape representations (cubic) recreate some of the characteristic responses in the lateral pull test, such as stick/slip phenomena and force chain distributions, which looks promising for future works on railway simulations. These responses that cannot be recreated with simple spherical grains, unless heuristics are added, which requires additional calibration and approximations. The significant reduction in time when using non-spherical grains also implies that larger granular systems can be investigated.

The Discrete Element Method (DEM) has been successfully used to further understand GM behaviour where experimental means are not possible or limited. However, the vast majority of DEM publications use simplified spheres with rolling friction to account for particle shape, with a few using clumped spheres and super quadratics to better capture grain geometric detail. In this study, we compare the shear strength of packed polyhedral assemblies to spheres with rolling resistance to account for shape. Spheres were found to have the highest shear resistance as the limited rolling friction model could not capture the geometric of rotation grains which caused reordering and dilation. This geometric arrangement causes polyhedra to align faces in the shear direction, reducing the resistance to motion. Conversely, geometric interlocking can cause jamming resulting in a dramatic increase in shear resistance. Particle aspect ratio (elongation and fatness) was found to significantly lower shear resistance, while more uniform aspect ratio’s increased shear resistance with shape non-convexity showing extremes of massive slip or jamming. Thus, while spheres with rolling friction may yield bulk shear strength similar to some polyhedra with a mild aspect ratio, the grain scale effect that leads to compaction and jamming from rotation and interlocking is missed. These results shed light on the complex impact that individual grain shape has on bulk behaviour and its importance.

This paper introduces a boundary condition scheme for weakly compressible (WC) renormalised first-order accurate meshless Lagrangian methods (MLM) by considering both solid and free surface conditions. A hybrid meshless Lagrangian method-finite difference (MLM-FD) scheme on prescribed boundary nodes is proposed to enforce Neumann boundary conditions. This is used to enforce symmetry boundary conditions and the implied Neumann pressure boundary conditions on solid boundaries in a manner consistent with the Navier-Stokes equation leading to the accurate recovery of surface pressures. The free surface boundary conditions allow all differential operators to be approximated by the same renormalised scheme while also efficiently determining free surface particles. The boundary conditions schemes are implemented for two renormalised MLMs. A WC smoothed particle hydrodynamics (SPH) solver is compared to a WC generalised finite difference (GFD) solver. Applications in both 2D and 3D are explored. A substantial performance benefit was found when comparing the WCGFD solver to the WCSPH solver with the WCGFD solver realising a maximum speedup in the range of three times over WCSPH in both 2D and 3D configurations. The solvers were implemented in C++ and used the NVIDIA CUDA 10.1 toolkit for the parallelisation of the solvers.

An under-resolved coupling strategy for the discrete element method (DEM) and the weakly compressible (WC) generalised finite difference method (GFD) is proposed. A novel filtering technique is proposed that allows for the recovery of a continuum porosity field in an arbitrary domain from DEM information. This allows fine spherical DEM particles to be treated in an under-resolved fashion using well-established drag relations for dynamic porous media to determine the fluid forces acting on them. To handle the momentum balance between phases, an inter-phase momentum transfer scheme is proposed as well. Verification and validation of the coupling strategy is performed. This includes comparisons to a fully-resolved WCGFD scheme when the associated computational cost allows for it. This strategy's benefits are seen when simulating a fluidised bed with an evolving fluid domain. It is shown that both under-resolved and fully-resolved dynamic information can seamlessly be treated with this scheme.

IV International Conference on Particle-Based Methods – PARTICLES 2015, Barcelona, Spain, 28 – 30 September, 2015. Due to copyright restrictions, the attached PDF file only contains the abstract of the full text item. For access to the full text item, please consult the publisher's website

Mill power models have been used in a variety of ways in industrial practice since power directly equates to throughput and fineness of ground product. We first start with Hogg-Fuerstenau Power Model and show how this model successfully predicted the power draw of many grinding mills in several mining operations. Then, we show how this model was on the verge of being able to predict the influence of lifter design on power draw. Next, we describe the discrete element model and how it overcame the issues faced by the previous power model. Using a DEM software known as Millsoft, we show the influence of lifter design geometry on power draw and analyze the power draw of rubber lifters versus the steel lifters via several case studies. As years passed, the two-dimensional discrete element model imbedded in Millsoft is superseded by three-dimensional discrete element method. Due to the gigantic computational power of graphic processing units, new computational codes that can do the tumbling motion along the entire length of the mill has come about. Here, we show the predictive capability of Blaze-DEM for ball and SAG mills.

FEMTEC 2013: 4th International Congress on Computational Engineering and Sciences, Stratosphere, Las Vegas, 19-24 May 2013

6th International Conference on Discrete Element Methods and Related Techniques, Colorado School of Mines in Golden, Colorado, USA, 5-6 August 2013

The simulation of grinding mills with the discrete element method (DEM) has been advancing. First, it emerged as a method for studying charge motion with spherical balls and predicting the power draw of the mill. Subsequently, studies on liner wear, charge motion with ellipsoidal and polyhedral shaped particles simulated with three dimensional DEM followed. Further, the impact energy spectra computed in the DEM algorithm is leading to the development of models for the breakage of brittle particles in mills. The core elements in such simulations are the shape of particles in the mill charge and the power draw of the mill due to operating variables. To advance the field, we present a set of experimental data and the corresponding DEM validation results for a 90 × 13 cm mill. The DEM algorithm uses the volume-overlap method which is more realistic for multifaceted irregular particle collisions. Further, we use the scanned shape of the rock media and multifaceted spherical shape for the grinding media to represent as close as possible the actual charge in the mill. First, we present DEM validation for spherical grinding media-only experiments, rock-only experiments, and a mixture of spherical grinding media and rocks, as well as aluminum cubes only to represent the theme of particle shape. Finally, a discussion of the contact mechanics parameters in the four modes of experiments is given. Since the feed ore to plant scale mills can vary in shape, mill simulations with scanned shape of typical particles are the future for more accurate results.

In blast furnaces, burden topography and packing density affect the stability of the burden, permeability of gas flow as well as the heat transfer efficiency. A fundamental understanding of the influence and interaction of coke and ore particles on the burden topography and packing density is therefore essential, in particular the influence of particle shape polydispersity and particle size polydispersity. In this paper we analyze the effect of particle shape and size polydispersity on the coke and ore charge distribution inside a bell-less blast furnace using the discrete element method (DEM). We first validate experimentally the polyhedral particle model with a simplified lab-scale charging experiment. A comparative study between spheres, with rolling friction to account for shape, and polyhedra is conducted for shape and size polydisperse particle systems. It was found that shape polydispersity mainly influenced the topography of the burden, whereas the size polydispersity mainly influenced the inter-layer percolation, i.e. localized particle diffusion, hence the local spatial packing density. The differences between the spherical particle models and polyhedral particle models on the burden topography are also quantitatively and qualitatively presented, especially on the role of particle shape on the push-up of coke in the centre. This study demonstrates that modelling particle shape effects using spheres with rolling friction is insufficient to fully describe the complex behaviour of shaped particles in a blast furnace, as the particle shape has a noteworthy influence on the burden characteristics.

Industrial-scale discrete element simulations typically generate Gigabytes of data per time step, which implies that even opening a single file may require 5 - 15 minutes on conventional magnetic storage devices. Data science’s inherent multi-disciplinary nature makes the extraction of useful information challenging, often leading to undiscovered details or new insights. This study explores the potential of statistical learning to identify potential regions of interest for large scale discrete element simulations. We demonstrate that our in-house knowledge discovery and data mining system (KDS) can decompose large datasets into i) regions of potential interest to the analyst, ii) multiple decompositions that highlight different aspects of the data, iii) simplify interpretation of DEM generated data by focusing attention on the interpretation of automatically decomposed regions, and iv) streamline the analysis of raw DEM data by letting the analyst control the number of decomposition and the way the decompositions are performed. Multiple decompositions can be automated in parallel and compressed, enabling agile engagement with the analyst’s processed data. This study focuses on spatial and not temporal inferences.