Validation of a discrete element model using magnetic resonance measurements

The discrete element model(DEM)is a very promising modelling strategy for two-phase granular systems.However,owing to a lack of experimental measurements,validation of numerical simulations of two-phase granular systems is still an important issue.In this study,a small two-dimensional gas- fluidized bed was simulated using a discrete element model.The dimensions of the simulated bed were 44 mm×10 mm×120 mm and the fluidized particles had a diameter dp=1.2 mm and density p=1000 kg/m3.The comparison between D...     

Multi-scale magnetic resonance measurements and validation of Discrete Element Model simulations

This short review describes the capabilities of magnetic resonance (MR) to image opaque single- and two-phase granular systems, such as rotating cylinders and gas-fluidized beds operated in different fluidization regimes. The unique capability of MR to not only image the solids’ distribution (voidage) but also the velocity of the particulate phase is clearly shown. It is demonstrated that MR can provide measurements over different length and time scales. With the MR equipment used for the studies summarized here, temporal and spatial scales range from sub-millisecond to hours and from a few hundred micrometres to a few centimetres, respectively. Besides providing crucial data required for an improved understanding of the underlying physics of granular flows, multi-scale MR measurements were also used to validate numerical simulations of granular systems. It is shown that predictions of time-averaged properties, such as voidage and velocity of the particulate phase, made using the Discrete Element Model agree very well with MR measurements.     

Simulation and calibration of granules using the discrete element method

The discrete element method(DEM), developed by Cundall and Strack(1979) to solve geomechanical problems, is used to simulate the mechanical behavior of granules. According to the DEM, an individual granule can be modeled as a realistic mechanical system consisting of primary particles bonded by interaction forces.Granulometric properties of the model material, zeolite 4A, have been measured to determine their macro properties. To investigate the compression behavior, a compression test was performed using a strength tester on single granules between two pistons. A modeled granule consisting of more than 22,000 primary particles was generated. The micro properties of the modeled granule have been precisely set to allow its macro properties to be equivalent to the macro properties of zeolite 4A granules. To calibrate the mechanical properties, diametrical compression was simulated using two rigid walls stressed at a constant stressing velocity. The force–displacement curve of the modeled granule at compression has been calibrated by the experimental curve of zeolite 4A.     

Simulation and calibration of granules using the discrete element method

The discrete element method (DEM), developed by Cundall and Strack (1979) to solve geomechanical problems, is used to simulate the mechanical behavior of granules. According to the DEM, an individual granule can be modeled as a realistic mechanical system consisting of primary particles bonded by interaction forces.Granulometric properties of the model material, zeolite 4A, have been measured to determine their macro properties. To investigate the compression behavior, a compression test was performed using a strength tester on single granules between two pistons. A modeled granule consisting of more than 22,000 primary particles was generated. The micro properties of the modeled granule have been precisely set to allow its macro properties to be equivalent to the macro properties of zeolite 4A granules. To calibrate the mechanical properties, diametrical compression was simulated using two rigid walls stressed at a constant stressing velocity. The force–displacement curve of the modeled granule at compression has been calibrated by the experimental curve of zeolite 4A.     

A discrete element model for simulating saturated granular soil

A numerical model is developed to simulate saturated granular soil, based on the discrete element method. Soil particles are represented by Lagrangian discrete elements, and pore fluid, by appropriate discrete elements which represent alternately Lagrangian mass of water and Eulerian volume of space. Macro-scale behavior of the model is verified by simulating undrained biaxial compression tests. Micro-scale behavior is compared to previous literature through pore pressure pattern visualization during shear tests. It is demonstrated that dynamic pore pressure patterns are generated by superposed stress waves. These pore-pressure patterns travel much faster than average drainage rate of the pore fluid and may initiate soil fabric change, ultimately leading to liquefaction in loose sands. Thus, this work demonstrates a tool to roughly link dynamic stress wave patterns to initiation of liquefaction phenomena.     

An erosion model for the discrete element method

A shear impact energy model (SIEM) of erosion suitable for both dilute and dense particle flows is proposed based on the shear impact energy of particles in discrete element method (DEM) simulations. A number of DEM simulations are performed to determine the relationship between the shear impact energy predicted by the DEM model and the theoretical erosion energy. Simulation results show that nearly one-quarter of the shear impact energy will be converted to erosion during an impingement. According to the ratio of the shear impact energy to the erosion energy, it is feasible to predict erosion from the shear impact energy, which can be accumulated at each time step for each impingement during the DEM simulation. The total erosion of the target surface can be obtained by summing the volume of material removed from each impingement. The proposed erosion model is validated against experiment and results show that the SIEM combined with DEM accurately predicts abrasive erosions.     

Random packing of tetrahedral particles using the polyhedral discrete element method

The random packing of tetrahedral particles is studied by applying the discrete element method (DEM), which simulates the effects of friction, height ratio, and eccentricity. The model predictions are analyzed in terms of packing density and coordination number (CN). It is demonstrated that friction has the maximal effect on packing density and mean CN among the three parameters. The packing density of the regular tetrahedron is 0.71 when extrapolated to a zero friction effect. The shape effects of height ratio and eccentricity show that the regular tetrahedron has the highest packing density in the family of tetrahedra, which is consistent with what has been reported in the literature. Compared with geometry-based packing algorithms, the DEM packing density is much lower. This demonstrates that the inter-particle mechanical forces have a considerable effect on packing. The DEM results agree with the published experimental results, indicating that the polyhedral DEM model is suitable for simulating the random packing of tetrahedral particles.     

Simulation of particle flow in a bell-less type charging system of a blast furnace using the discrete element method

A three-dimensional model was established by the discrete element method （DEM） to analyze the flow and segregation of particles in a charging process in detail. The simulation results of the burden falling trajectory obtained by the model were compared with the industrial charging measurements to validate the applicability of the model. The flow behavior of particles from the weighing hopper to the top layer of a blast furnace and the heaping behavior were analyzed using this model. A radial segregation index （RSI） was used to evaluate the extent of the size segregation in the charging process. In addition, the influence of the chute inclination angle on the size segregation and burden profile during the charging process was investigated.     

Representative elementary volume analysis of polydisperse granular packings using discrete element method

The representative elementary volume (REV) for three-dimensional polydisperse granular packings was determined using discrete element method simulations. Granular mixtures of various sizes and particle size distributions were poured into a cuboid chamber and subjected to uniaxial compression. Findings showed that the minimum REV for porosity was larger compared with the REV for parameters such as coordination number, effective elastic modulus, and pressure ratio. The minimum REV for porosity and other parameters was found to equal 15, 10, and 5 times the average grain diameter, respectively. A study of the influence of sample size on energy dissipation in random packing of spheres has also confirmed that the REV size is about 15 times the average grain diameter. The heterogeneity of systems was found to have no effect on the REV for the parameters of interest for the narrow range of coefficient of uniformity analyzed in this paper. As the REV approach is commonly applied in both experimental and numerical studies, determining minimum REV size for polydisperse granular packings remains a crucial issue.     

Modeling soil-bulldozer blade interaction using the discrete element method (DEM)

Limited studies have been conducted to establish scaling relationships of soil reaction forces and length scales of bulldozer blades using the Discrete Element Method (DEM) technique. With a DEM-based similitude scaling law, performance of industry-scale blades can be predicted at reduced simulation efforts provided a calibrated and validated DEM soil model is developed. DEM material properties were developed to match soil cone penetration testing. The objectives of the study were to develop a DEM soil model for Norfolk sandy loam soil, establish a scaled relationship of soil reaction forces to bulldozer blade length scales (n = 0.24, n = 0.14, n = 0.10, and n = 0.05), and validate the DEM-predicted soil reaction forces on the scaled bulldozer blades to the Norfolk sandy loam soil bin data. Using 3D-scanned and reconstructed DEM soil aggregate shapes, Design of Experiment (DOE) of soil cone penetration testing was used to develop a soil model and a soil-bulldozer blade simulation. A power fit best approximated the relationship between the DEM-predicted soil horizontal forces and the bulldozer blade length scale (n) (R² = 0.9976). DEM prediction of soil horizontal forces on the bulldozer blades explained the Norfolk sandy loam soil data with a linear regression fit (R² = 0.9965 and slope = 0.9634).     

Quasi-real-time simulation of rotating drum using discrete element method with parallel GPU computing

Real-time simulation of industrial equipment is a huge challenge nowadays. The high performance and fine-grained parallel computing provided by graphics processing units (GPUs) bring us closer to our goals. In this article, an industrial-scale rotating drum is simulated using simplified discrete element method (DEM) without consideration of the tangential components of contact force and particle rotation. A single GPU is used first to simulate a small model system with about 8000 particles in real-time, and the simulation is then scaled up to industrial scale using more than 200 GPUs in a 1D domain-decomposition parallelization mode. The overall speed is about 1/11 of the real-time. Optimization of the communication part of the parallel GPU codes can speed up the simulation further, indicating that such real-time simulations have not only methodological but also industrial implications in the near future.     

Parallel computing of discrete element method on multi-core processors

This paper describes parallel simulation techniques for the discrete element method (DEM) on multi-core processors. Recently, multi-core CPU and GPU processors have attracted much attention in accelerating computer simulations in various fields. We propose a new algorithm for multi-thread parallel computation of DEM, which makes effective use of the available memory and accelerates the computation. This study shows that memory usage is drastically reduced by using this algorithm. To show the practical use of DEM in industry, a large-scale powder system is simulated with a complicated drive unit. We compared the performance of the simulation between the latest GPU and CPU processors with optimized programs for each processor. The results show that the difference in performance is not substantial when using either GPUs or CPUs with a multi-thread parallel algorithm. In addition, DEM algorithm is shown to have high scalability in a multi-thread parallel computation on a CPU.     

Numerical analysis on tractive performance of off-road wheel steering on sand using discrete element method

This paper presents a numerical analysis on steering performance including tractive parameters and lug effects. To explore the difference between the turning and straight conditions of steering, a numerical sand model for steering is designed and appropriately established by the discrete element method on the basis of triaxial tests. From the point of mean values and variation, steering traction tests are conducted to analyze the tractive parameters including sinkage, torque and drawbar pull and the lug effects resulting from type, intersection and central angle. Analysis indicates that steering motion has less influence on the sinkage and torque. When the slip ratio exceeds 20%, the steering drawbar pull becomes increasingly smaller than in the straight condition, and the increase of steering radius contributes to a decline in mean values and a rise in variation. The lug effect of central angle is less influenced by the steering motion, but the lug intersection is able to significantly increase the steering drawbar pull along with the variation reduced. However, the lug inclination reduces the steering drawbar pull along with the variation raised in different degrees.     

Calibration of discrete element modeling: Scaling laws and dimensionless analysis

In this paper, dynamic similarity conditions are derived for discrete element simulations by non-dimensionalising the governing equations. These conditions must be satisfied so that the numerical model is a good representation of the physical phenomenon. For a pure mechanical system, if three independent ratios of the corresponding quantities between the two models are set, then the ratios of other quantities must be chosen according to the similarity principles. The scalability of linear and non-linear contact laws is also investigated. Numerical tests of 3D uni-axial compression are carried out to verify the theoretical results. Another example is presented to show how to calibrate the model according to laboratory data and similarity conditions. However, it is impossible to reduce computer time by scaling up or down certain parameters and continue to uphold the similarity conditions. The results in this paper provide guidelines to assist discrete element modelers in setting up the model parameters in a physically meaningful way.     

Modeling particle sedimentation in viscous fluids with a coupled immersed boundary method and discrete element method

Numerical techniques have increasingly been used to model fluid–particle two-phase flows. Coupling the immersed boundary method (IBM) and discrete element method (DEM) is one promising approach for modeling particulate flows. In this study, IBM was coupled with DEM to improve the reliability and accuracy of IBM for determining the positions of particles during the sedimentation process within viscous fluids. The required ratio of the particle diameter to the grid size (D/dx) was determined by comparing the simulation results with the analytical solution and experimental data. A dynamic mesh refinement model was utilised in the IBM model to refine the computational fluid dynamics grid near the particles. In addition, an optimum coupling interval between the IBM and DEM models was determined based on the experimental results of a single particle sedimentation within silicon oil at a Reynolds number of 1.5. The experimental results and the analytical solution were then utilised to validate the IBM–DEM model at Reynolds numbers of 4.1, 11.6, and 31.9. Finally, the validated model was utilised to investigate the sedimentation process for more than one particle by modeling the drafting-kissing-tumbling process and the Boycott phenomenon. Benchmark tests showed that the IBM–DEM technique preserves the advantages of DEM for tracking a group of particles, while the IBM provides a reliable and accurate approach for modeling the particle–fluid interaction.     

Discrete element modelling of pebble beds: With application to uniaxial compression tests of ceramic breeder pebble beds

In this paper, a discrete element simulation scheme for pebble beds in fusion blankets is presented. Each individual pebble is considered as one element obeying equilibrium conditions under contact forces. We study not only the rearrangement of particles but also the overall behaviour of an assembly under the action of macroscopic compressive stresses. Using random close packing as initial configurations, the discrete element simulation of the uniaxial compression test has been quantitatively compared to experiments. This method yields the distribution of the inter-particle contact forces. Moreover, the micro-macro relations have been investigated to relate the microscopic information, such as the maximum contact force and the coordination number inside the assembly, to the macroscopic stress variables.     

The elastic response of a cohesive aggregate—a discrete element model with coupled particle interaction

A model is presented for the deformation of a cohesive aggregate of elastic particles that incorporates two important effects of large-sized inter-particle junctions. A finite element model is used to derive a particle response rule, for both normal and tangential relative deformations between pairs of particles. This model agrees with the Hertzian contact theory for small junctions, and is valid for junctions as large as half the nominal particle size. Further, the aggregate model uses elastic superposition to account for the coupled force–displacement response due to the simultaneous displacement of all of the neighbors of each particle in the aggregate. A particle stiffness matrix is developed, relating the forces at each junction to the three displacement degrees of freedom at all of the neighboring-particle junctions. The particle response satisfies force and moment equilibrium, so that the model is properly posed to allow for rigid rotation of the particle without introducing rotational degrees of freedom. A computer-simulated sintering algorithm is used to generate a random particle packing, and the stiffness matrix is derived for each particle. The effective elastic response is then estimated using a mean field or affine displacement calculation, and is also found exactly by a discrete element model, solving for the equilibrium response of the aggregate to uniform-strain boundary conditions. Both the estimate and the exact solution compare favorably with experimental data for the bulk modulus of sintered alumina, whereas Hertzian contact-based models underestimate the modulus significantly. Poisson's ratio is, however, accurately determined only by the full equilibrium discrete element solution, and shown to depend significantly on whether or not rigid particle rotation is permitted in the model. Moreover, this discrete element model is sufficiently robust, so it can be applied to problems involving non-homogeneous deformations in such cohesive aggregates.     

Using the discrete element method to assess the mixing of polydisperse solid particles in a rotary drum

Despite the wide applications of powder and solid mixing in industry, knowledge on the mixing of polydisperse solid particles in rotary drum blenders is lacking. This study investigates the mixing of monodisperse, bidisperse, tridisperse, and polydisperse solid particles in a rotary drum using the discrete element method. To validate the model developed in this study, experimental and simulation results were compared. The validated model was then employed to investigate the effects of the drum rotational speed, particle size, and initial loading method on the mixing quality. The degree of mixing of polydisperse particles was smaller than that for monodisperse particles owing to the segregation phenomenon. The mixing index increased from an initial value to a maximum and decreased slightly before reaching a plateau for bidisperse, tridisperse, and polydisperse particles as a direct result of the segregation of particles of different sizes. Final mixing indices were higher for polydisperse particles than for tridisperse and bidisperse particles. Additionally, segregation was weakened by introducing additional particles of intermediate size. The best mixing of bidisperse and tridisperse particles was achieved for top–bottom smaller-to-larger initial loading, while that of polydisperse systems was achieved using top–bottom smaller-to-larger and top–bottom larger-to-smaller initial loading methods.