A combined physical and DEM modelling approach to investigate particle shape effects on load movement in tumbling mills

The discrete element method (DEM) which is used to simulate granular flows often assumes spherical shape for particles. This assumption is legitimized by the added complexity of non-spherical shape representation, contact detection and computational cost. In this work, the difference between the dynamics of non-spherical and spherical particles was studied in detail by a combined physical and DEM modeling approach. An in-house developed DEM software called KMPC_DEM©, which was coded to handle non-spherical particles, was used to simulate the behavior of particles. To calibrate the model parameters, a model tumbling mill (100 cm diameter and 10.8 cm length) with one transparent end was used which made accurate photography possible. The tests were performed at filling of 20% and mill speed of 85% of critical speed with steel balls and wood cubes. In the simulation, each cubical particle was represented with clusters of spheres (with identical size) by particle packing algorithm for contact detection and contact-force calculation. Comparison of the simulation and experimental results showed that the difference between the measured and predicted impact toe, shoulder angle and bulk toe angle were 3, 4 and 5°, respectively. The significant change in the charge movement and structure on account of non-spherical particles was reflected in the amount of in-flight charge, and positions of shoulder, impact toe and bulk toe. It found that there was a 17% difference in the amount of in-flight of charge between cubical and spherical particles. The marked difference was attributed to higher interlocking of non-spherical particles in comparison to spherical balls. The results showed that cubical particles participated 5% more in the high energy impact action compared to that of the spherical particles. The simulation computation time increased by 35 times when the shape of particles changed from spherical to cubical.     

Experimental study and discrete element method simulation of Geldart Group A particles in a small-scale fluidized bed

Geldart Group A particles are of great importance in various chemical processes because of advantages such as ease of fluidization, large surface area, and many other unique properties. It is very challenging to model the fluidization behavior of such particles as widely reported in the literature. In this study, a pseudo-2D experimental column with a width of 5 cm, a height of 45 cm, and a depth of 0.32 cm was developed for detailed measurements of fluidized bed hydrodynamics of fine particles to facilitate the validation of computational fluid dynamic (CFD) modeling. The hydrodynamics of sieved FCC particles (Sauter mean diameter of 148 µm and density of 1300 kg/m³) and NETL-32D sorbents (Sauter mean diameter of 100 µm and density of 480 kg/m³) were investigated mainly through the visualization by a high-speed camera. Numerical simulations were then conducted by using NETL’s open source code MFIX-DEM. Both qualitative and quantitative information including bed expansion, bubble characteristics, and solid movement were compared between the numerical simulations and the experimental measurement. The cohesive van der Waals force was incorporated in the MFIX-DEM simulations and its influences on the flow hydrodynamics were studied.     

流化床法制备太阳能级多晶硅用沉积硅粒的性能研究

在流化过程中,为保证硅粒在流化床中分布状态良好,提高硅的沉积产率,同时要达到产生太阳能级纯度的多晶硅,对流化床中流化的硅粒的粒径和纯度要求是非常严格的,本文采用球磨技术,通过正交实验,对球磨时间、球磨介质、球的均匀度工艺参数对沉积硅粒的粒径影响及球磨污染程度和形貌特征进行试验研究。试验表明：选择合适的球磨罐和球磨介质,以高纯工业硅进行实验,制得的硅粒平均粒径处于145—166um和166—180um之间时,在进行流态化试验时,完全满足太阳能级多晶硅用沉积硅粒在流化床中流态化分布的要求。     

Agglomerate behavior in a recirculating fluidized bed with sheds: Effect of sheds

A Radioactive Particle Tracking (RPT) technique was used to study the effects of the internal baffles in the stripping section of the Fluid Coker?, called sheds, have on the behavior of wet agglomerates that are formed when residual oil is injected into the Coker. Vapor emitted by reacting wet agglomerates below the sheds rises and causes shed fouling. The release of vapor from agglomerates can be estimated by combining the RPT results with a coking reaction model. The study found that the sheds reduce the time agglomerates spend in the shed zone, which in turn reduces the amount of organic vapor that reaches the sheds, but at the same time increase the wetness of the agglomerates that exit to the recirculation line, which results in the loss of valuable liquid. The research also found that the best type of shed, from the point of view of agglomerate motion, is the mesh-shed. Finally, experimental data indicate that reducing the cross sectional area of the sheds from 50% to 30% increases the time that the agglomerates spend above the shed zone, and thus reduces the flow of vapor emitted below the sheds.     

Numerical study on compression processes of cohesive bimodal particles and their packing structure

In this study, the compression characteristics of bimodal cohesive particles were investigated using a discrete element method (DEM) simulation. The compression and packing processes were simulated under different conditions of size ratios of 1–4 and fine particle mixing ratios of 0–0.5. The cohesive force was expressed using the surface energy proposed by the Johnson-Kendall-Roberts (JKR) cohesion model having a surface energy of 0–0.2 J/m². The calculated results demonstrated that even in the case of cohesive particles, an increase in the particle size ratio reduced the void fraction of the powder bed during the packing and compression processes. In addition, it was found that the cohesive force decreased the contact number, especially the coarse-coarse contacts, although it had little impact on the void fraction. Our DEM simulations suggested that it is necessary to evaluate the contact numbers even under similar void fractions, which will be essential in the case of different material mixtures, such as all-solid-state batteries.     

A non-obstructive particle damping model of DEM

The non-obstructive particle damping technology has been used successfully in many fields for vibration reduction. However, it is difficult to predict the damping characteristics due to complex collisions in the dense particle flow. The discrete element method makes it possible to consider effects of granularity such as the particle size, number of particles and friction between two particles. The validity of this numerical method is examined by a comparison of the experimental results. The discrete element method simulation system is further examined with examples for its computational complexity and effectiveness for different density parameters. It is shown that the mass ratio and material density influence the damping performance.     

Lattice Boltzmann simulation of flow past a non-spherical particle

Lattice Boltzmann method was used to predict the fluid-particle interaction for arbitrary shaped particles. In order to validate the reliability of the present approach, simulation of flow past a single stationary spherical, cylindrical or cubic particle is conducted in a wide range of Reynolds number (0.1 < Re_p < 3000). The results indicate that the drag coefficient is closely related to the particle shape, especially at high Reynolds numbers. The voxel resolution of spherical particle plays a key role in accurately predicting the drag coefficient at high Reynolds numbers. For non-spherical particles, the drag coefficient is more influenced by the particle morphology at moderate or high Reynolds numbers than at low ones. The inclination angle has an important impact on the pressure drag force due to the change of projected area. The simulated drag coefficient agrees well with the experimental data or empirical correlation for both spherical and non-spherical particles.     

Effect of lognormal particle size distributions on particle spreading in additive manufacturing

Additive manufacturing (AM) has attracted much attention worldwide in various applications due to its convenience and flexibility to rapidly fabricate products, which is a key advantage compared to the traditional subtractive manufacturing. This discrete element method (DEM) study focusses on the impact of particle polydispersity during the particle spreading process on parameters that affect the quality of the final product, like packing and bed surface roughness. The particle systems include four lognormal particle size distribution (PSD) widths, which are benchmarked against the monodisperse system with the same mean particle diameter. The results reveal that: (i) the solid volume fraction of the initial packed particle bed in the delivery chamber increases then plateaus as the PSD width increases; (ii) regardless of PSD width, the solid volume fraction of the particle bed increases with spreading layer height before compression, but decreases with layer height after compression; (iii) the bed surface roughness increases with PSD width or layer height both before and after the compression of the spreading layer; (iv) the extent of increase in solid volume fraction during compression is correlated with the extent of decrease in bed surface roughness; and (v) the broader PSDs exhibit larger fluctuations of solid volume fraction of the particle bed and bed surface roughness due to greater variability in the arrangement of particles of different sizes. The results here have important implications on the design and operation of particle-based AM systems.     

Influence of air velocity and powder bed height on local density and float–sink of spheres in a gas–solid fluidized bed

Depending on their density, large objects will either float or sink in a gas–solid fluidized bed due to the liquid–like properties and density of the fluidized bed. The float–sink technology has been applied to dry density separations in industry. It is important for optimized industrial application to understand how the air velocity and the powder bed height affect the float–sink as the key operating factors. In this study, we investigated the float–sink of spheres of various density by varying the air velocity and the powder bed height. Also, we obtained the local fluidized bed density and the buoyancy force working on the sphere at various heights. We used the weight of a stainless-steel sphere in the fluidized bed to estimate the local fluidized bed density and the buoyancy force based on Archimedes principle. We found that the spheres float–sink behavior changes dramatically with the air velocity and the powder bed height and that the spheres float–sink behavior is correlated to ΔF = F_b – F_g, where F_b is the buoyancy force and F_g is the gravity force acting on the sphere. We also found that the fluidized bed density is not constant as a function of height when the air velocity is relatively large; the local fluidized bed density is interestingly either minimal at approximately mid-height or surprisingly, gradually increases with height within the fluidized bed at higher air velocities. The possible reasons are discussed by considering the local variation of the motion of air bubbles and the fluidized medium which affect the fluid force acting on the sphere in the fluidized bed.     

Three-dimensional numerical simulation of quasi-static pebble flow

To investigate the influence of the drainage rate and the particle contact model on the main features of the pebble flow, a quasi-static pebble flow of full scale German HTR-MODUL pebble bed is performed with up to 360,000 frictional graphite spheres. The treatment of the sphere-wall boundary condition is analyzed to avoid underestimating the friction of pebble near the wall. The streamlines, diffusion of pebbles and velocity profiles of pebble flow are drawn and analyzed. It shows that the streamlines and diffusion of pebbles inside the pebble bed are barely affected by the drainage rate and the particle contact model used. However, it reveals that the drainage rate and the contact model obviously influence the pattern of velocity profiles. It demonstrates that the quasi-static pebble flow and the Hertzian model are optimal choices of the neutronic physical design of the pebble bed reactor when the residue time of pebbles is particularly concerned.     

Comparative evaluation of granules made with different binders by a fluidized bed method

Granules were prepared using three different binders, pregelatinized starch (PGS), gelatin (GEL), and polyvinylpyrrolidone (K30) by a fluidized bed method. As a quantitative measurement of mechanical strength or abrasion resistance, granules were subjected to a friability test for certain periods of time, and friability indexes (FI) as a function of time were calculated. The data obtained were analyzed by applying standard mathematical models. According to the derived parameters of the logistic and Weibull models, which fit best to the data, mechanical strength of granules made with K30 was observed to be lower than that of the granules of PGS and GEL which have similar values of model parameters. Flow properties, consolidation, and compressibility behaviors of unfriabled (UFR) and friabled (FR) granules, which were selected based upon their Weibull time parameter, were investigated as comparative. The flow rate of granules decreased due to diminishing particle size depending on binder type and friability, but the values of angle of repose were within the acceptable limits. Regarding consolidation behavior, the change of relative density vs. the number of taps, i.e., packing rate for FR granules of GEL was slower than that of its UFR form, whereas FR granules of PGS and K30 showed faster change in relative density compared to their UFR forms. According to the parameters obtained from the Heckel equation, PGS and K30 were found to produce softer, more plastic and readily deformable granules than GEL, and the compressibility of their FR forms was not influenced negatively.     

Investigating the fluidization of disk-like particles in a fluidized bed using CFD-DEM simulation

Fluidization of monodispersed disk-like particles with different aspect ratios in the fluidized bed is simulated by CFD-DEM, with disk-like particles being modeled by the super-ellipsoids. The relatively comprehensive investigations are performed in order to understand the fluidization behaviors of disk-like particles and to evaluate how the aspect ratio influences the fluidization. The results obtained demonstrate that disk-like particles with a larger aspect ratio possess stronger particle movement and more apparent fluidization. Comparisons between spherical particles and disk-like particles elucidate their differences in the fluidization behavior. Particle orientation is also investigated in this paper due to its important influence on the fluidization. Particles possess different preferred orientations in the static bed and in the fluidization state, and a reduced aspect ratio can drive particles to be in the preferred orientation. The existence of the walls will prompt particles to align their cross sections to be parallel to the plane of the walls.     

DEM simulation of the packing structure and wall load in a 2-dimensional silo

The filling and discharge of a two-dimensional wedged-bottom silo holding circular objects was modelled using DEM technique to examine the influence of method of silo filling on distribution of orientations of unit vectors normal to contact points (contact normals) and normal contact forces. It was found that packing structure determined through method of generation of grain bedding significantly influenced distribution of contact normals. Nearly hexagonal network of contact normals was obtained for central filling of silo while sprinkle filling provided higher anisotropy of contact normals. The significance of frictional conditions and number of particles in system on distribution of contact normals was analysed. Increase in number of grains reduced disturbance from boundaries on behaviour of assembly. Distribution of loads on silo bottom obtained in simulation for different wall roughness was found in qualitative agreement with experimental data.     

Modeling breakage and motion of black pepper seeds in cryogenic mill

The present investigation aims to represent three-dimensional motion and breakage phenomena of black pepper seeds in the cryogenic mill (hammer mill) using discrete element method (DEM). In DEM modeling, bonded particle model was coupled with Hertz-Mindlin contact model. Calibration method was used to select appropriate model (bond) parameters. The calibrated set of bond parameters includes 3.12?×?10¹¹?Pa?m^?1 normal stiffness; 1.56?×?10¹¹?Pa?m^?1 shear stiffness; 3.88?×?10⁸?Pa critical normal stiffness; 1.94?×?10⁸?Pa critical shear stiffness. Besides, the validity of calibrated parameters was tested in the hammer mill. The observed qualitative and quantitative results (breakage and flow pattern) of numerical and experimental approaches were in good agreement. Based on these results, a few prefatory suggestions were provided to improve the design aspects of the mill. Overall, DEM modeling offered a better understanding of particle breakage and flow pattern in the mill.     

Experiments and simulations of direct shear tests: porosity, contact friction and bulk friction

The direct shear testers, in particular the Jenike cell, are widely used to measure the bulk material properties for the design of bulk handling equipment. This paper describes a study of the Jenike shear tester using both experiments and discrete element simulations. A total of 90 tests on spherical glass beads and paired glass beads were performed to study the influence of the particle shape, stress level and packing density on the bulk friction at limiting shear. The data are thus useful for validating particle scale simulations of densely packed granular systems. In an attempt to verify the predictive capability of discrete element method, closely matching 3-dimensional discrete element simulations of the shear tests were performed and compared with the experimental observations. The comparison for single spheres shows good quantitative agreement for the limiting bulk friction when there is a good match in the sample porosity. Further research is needed to produce a comprehensive validation of the discrete element method. Several salient observations from this study provide further insight into the roles of particle shape and contact friction on the resulting packing porosity and bulk friction.