Time effect and prediction of broken rock bulking coefficient on the base of particle discrete element method

Bulking characteristics of gangue are of great significance for the stability of goafs in mining overburden in the caving zones.In this paper,a particle discrete element method with clusters to represent gangue was adopted to explore the bulking coefficient time effect of the broken rock in the caving zone under three-dimensional triaxial compression condition.The phenomena of stress corrosion,deformation,and failure of rock blocks were simulated in the numerical model.Meanwhile,a new criterion of rock fragments damage was put forward.It was found that the broken rock has obvious viscoelastic properties.A new equation based on the Burgers creep model was proposed to predict the bulking coefficient of broken rock.A deformation characteristic parameter of the prediction equation was analyzed,which can be set as a fixed value in the mid-and long-term prediction of the bulking coefficient.There are quadratic function relationships between the deformation characteristic parameter value and Talbot gradation index,axial pressure and confining pressure.

Effects of rotational speed and fill level on particle mixing in a stirred tank with different impellers

The particle mixing was studied in a cylindrical stirred tank with elliptical dished bottom by experiments and simulations.The impeller types used were double helical ribbon(HR) + bottom HR,pitched blade ribbon + bottom HR,inner and outer HR + bottom HR,and pitched blade ribbon + Pfaudler + bottom HR labeled as impellers Ⅰ to Ⅳ,respectively.The quantitative correlations among the rotational speed,fill level and power consumption for impeller Ⅰ and impeller Ⅱ were obtained by experiments to validate the discrete element method(DEM) simulations.The particle mixing at different operating conditions was simulated via DEM simulations to calculate the mixing index using the Lacey method,which is a statistical method to provide a mathematical understanding of the mixing state in a binary mixture.The simulation results reveal that as the rotational speed increases,the final mixing index increases,and as the fill level increases,the final mixing index decreases.At the same operating conditions,impeller Ⅲ is the optimal combination,which provides the highest mixing index at the same revolutions.

DEM simulation of particle flow on a single deck banana screen

A mathematical study of particle flow on a banana screen deck using the discrete element method (DEM) was presented in this paper. The motion characteristics and penetrating mechanisms of particles on the screen deck were studied. Effects of geometric parameters of screen deck on banana screening process were also investigated. The results show that when the values of inclination of discharge and increment of screen deck inclination are 10° and 5° respectively, the banana screening process get a good screening performance in the simulation. The relationship between screen deck length and screening efficiency was further confirmed. The conclusion that the screening efficiency will not significantly increase when the deck length L≥430 mm (L/B ≥ 3.5) was obtained, which can provide theoretical basis for the optimization of banana screen.

Influence of vibration mode on the screening process

The screening of particles with different vibration modes was simulated by means of a 3D discrete element method (3D-DEM). The motion and penetration of the particles on the screen deck were analyzed for linear, circular and elliptical vibration of the screen. The results show that the travel velocity of the particles is the fastest, but the screening efficiency is the lowest, for the linear vibration mode. The circular motion resulted in the highest screening efficiency, but the lowest particle travel velocity. In the steady state the screening efficiency for each mode is seen to increase gradually along the longitudinal direction of the deck. The screening efficiency increment of the circular mode is the largest while the linear mode shows the smallest increment. The volume fraction of near-mesh size particles at the underside is larger than that of small size particles all along the screen deck. Linear screening mode has more near-mesh and small size particles on the first three deck sections, and fewer on the last two sections, compared to the circular or elliptical modes.

Discrete element modeling of the effect of particle size distribution on the small strain stiffness of granular soils

Discrete element modeling was used to investigate the effect of particle size distribution on the small strain shear stiffness of granular soils and explore the fundamental mechanism controlling this small strain shear stiffness at the particle level. The results indicate that the mean particle size has a negligible effect on the small strain shear modulus. The observed increase of the shear modulus with increasing particle size is caused by a scale effect. It is suggested that the ratio of sample size to the mean particle size should be larger than 11.5 to avoid this possible scale effect. At the same confining pressure and void ratio, the small strain shear modulus decreases as the coefficient of uniformity of the soil increases. The Poisson＇s ratio decreases with decreasing void ratio and increasing confining pressure instead of being constant as is commonly assumed. Microscopic analyses indicate that the small strain shear stiffness and Poisson＇s ratio depend uniquely on the soil＇s coordination number.

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 dis- crete 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 polydis- perse 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 par- ticles 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.

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.

Enhancing mixing of particles by baffies in a rotating drum mixer

Baffles with shape of ＂-＂ （single baffle）, ＂＋＂ （cross-baffles with four arms） and （baffles with 6 arms） are used to enhance the mixing of particles in a rotating drum mixer. A micro-dynamics study of mixing and segregation ofa bi-disperse system of two particle sizes in the rotating drum with these three kinds of baffles is carried out using the discrete element method （DEM）. The effect of the baffles on mixing, and the mechanisms of mixing enhancement by the baffles are discussed and analyzed. Simulation results show that in an unbaffled drum mixer, particle convection, particle diffusion, and size segregation of hi- disperse particles, all play important roles in the mixing process; whereas size segregation will be largely restrained when the drum mixer has a baffle, regardless of its shape, and the degree of mixing is higher than that in an unbaffled drum mixer. The different mixing characteristics for ＂-＂ shaped baffle, ＂＋＂ baffle, and baffle are revealed by the simulation results. For ＂＋＂ or style baffles, there is an optimal size of baffles for the mixing of particles, and the ootimal mixing efficiency is higher than that for ＂-＂ baffle.

Numerical simulation of submarine landslide tsunamis using particle based methods

This paper presents the simulation of tsunamis due to rigid and deformable landslides with consideration of submerged conditions by using particle methods. The smoothed particle hydrodynamics（SPH）, as a particle based method, is for solving problems of fast moving boundaries in the field of continuum mechanics. Other particle based methods, like the discrete element method（DEM）, are suitable for modeling the displacement and the collision related to the rigid landslides. In the present work, we use the SPH and the DEM to simulate tsunamis generated by rigid and deformable landslides with consideration of submerged conditions. The viscous free-surface flows are solved by a weakly compressible SPH and the displacement and the rotation of the rigid body slides are calculated using a multi-sphere DEM allowing for modeling solids of arbitrarily complex shapes. The fluid-solid interactions are simulated by coupling the SPH and the DEM. A rheology model combining the Papanastasiou and the Herschel-Bulkley models is applied to represent the viscoplastic behavior of the non-Newtonian flow in the submarine deformable landslide cases. Submarine landslide tsunamis due to rigid and deformable landslides are both simulated as typical landslide cases in this investigation. Our simulated results and the previous experimental results in the literatures are in good agreement, which shows that the proposed particle based methods are capable of modeling the submarine landslide tsunamis.

Numerical simulation of tetrahedral particle mixing and motion in rotating drums

A regular tetrahedron is the simplest three-dimensional structure and has the largest non-sphericity. Mixing of tetrahedral particles in a thin drum mixer was studied by the soft-sphere-imbedded pseudo- hard particle model and compared with that of spherical particles. The two particle types were simulated with different rotation speeds and drum filling levels. The Lacey mixing index and Shannon information entropy were used to explore the effects of sphericity on the mixing and motion of particles. Moreover, the probability density functions and mean values and variances of motion velocities, including translational and rotational, were computed to quantify the differences between the motion features of tetrahedra and spheres. We found that the flow regime depended on the particle shape in addition to the rotation speed and filling level of the drum. The mixing of tetrahedral particles was better than that of spherical particles in the rolling and cascading regimes at a high filling level, whereas it may be poorer when the filling level was low. The Shannon information entropy is better than the Lacey mixing index to evaluate mixing because it can reflect the real change of flow regime from the cataracting to the centrifugal regime, whereas the mixing index cannot.

Energy dissipation mechanism and experiment of particle dampers for gear transmission under centrifugal loads

As a passive means of vibration reduction, particle damping is mainly applied to the horizontal or vertical steady field. However, it is seldom applied to centrifugal fields. Under high speed and heavy loading, the vibration of tooth surfaces of gear transmissions becomes more severe shortening gear service life and augmenting noise. Under centrifugal loading, the particle system exhibits different characteristics, for example, particles are extruded at the end farthest from the center. We investigated gears with drilled via holes filled with damping particles. Using the discrete-element method, we developed an energy dissipation model for the particle system accounting for friction and inelastic collisions. Energy dissipation and damping characteristics of this system were analyzed. Experiments were also conducted with the gear system having different particle filling rates. The results show that this filling rate is an important parameter associated with particle damping in a centrifugal field. An unsuitable filling rate would significantly reduce damping effectiveness. With changes in rotation speed and load, the gear transmission system has different optimal filling rates. The results provide guidelines for the application of particle damping in centrifugal fields of gear transmissions.

DEM analysis of the effect of electrostatic interaction on particle mixing for carrier-based dry powder inhaler formulations

Particle interactions play a significant role in controlling the performance of dry powder inhalers （DPIs）, which mainly arise through van der Waals potentials, electrostatic interactions, and capillary forces. Our aim is to investigate the influence of electrostatic charge on the performance of DPIs as a basis for improv- ing the formulation of the particle ingredients. The mixing process of carrier and active pharmaceutical ingredient （API） particles in a vibrating container is investigated using a discrete element method （DEM）. The number of APl particles attaching to the carrier particle （i.e., contact number） increases with increas- ing charge and decreases with increasing container size. The contact number decreases with increasing vibrational velocity amplitude and frequency. Moreover, a mechanism governed by the electrostatic force is proposed for the mixing process. This mechanism is different from that previously proposed for the mixing process governed by van der Waals forces, indicating that long-range and short-range adhesive forces can result in different mixing behaviours.

Numerical simulation of polygonal particles moving in incompressible viscous fluids

A two-dimensional coupled lattice Boltzmann immersed boundary discrete element method is introduced for the simulation of polygonal particles moving in incompressible viscous fluids. A collision model of polygonal particles is used in the discrete element method. Instead of a collision model of circular particles, the collision model used in our method can deal with particles of more complex shape and efficiently simulate the effects of shape on particle–particle and particle–wall interactions. For two particles falling under gravity, because of the edges and corners, different collision patterns for circular and polygonal particles are found in our simulations. The complex vortexes generated near the corners of polygonal particles affect the flow field and lead to a difference in particle motions between circular and polygonal particles. For multiple particles falling under gravity, the polygonal particles easily become stuck owing to their corners and edges, while circular particles slip along contact areas. The present method provides an efficient approach for understanding the effects of particle shape on the dynamics of non-circular particles in fluids.

Use of multiscale particle simulations in the design of nuclear plant decommissioning

The application of a digital modelling method that can faithfully take account of three-dimensional shape and inherent physical and chemical properties of each particulate component provides an essential tool in decommissioning design. This is useful in handling of high, medium and low level radioactive waste. The processes involve making decisions on where to cut existing plant components and then how to pack these components into boxes, which are then cemented and kept for long term storage as the level of radioactive declines with time. We illustrate the utility of the method and its ability to take data at plant scale （m-scale） and then deduce behaviours at sub millimetre scale in the packed containers. A variety of modelling approaches are used as a part of this approach including cutting algorithms, geometric and dynamic （distinct element） force models, and lattice Boltzmann methods. These methods are applicable to other complex particulate systems including simulation of waste, building recycling, heap leaching and related minerals processes. The paper introduces the basic concepts of this multi-scale and multi-model approach.

Application of DEM modified with enlarged particle model to simulation of bead motion in a bead mill

We applied the discrete element method （DEM） of simulation modified by an enlarged particle model to simulate bead motion in a large bead mill. The stainless-steel bead mill has inner diameter of 102 mm and mill length of 198 mm. The bead diameter and filling ratio were fixed respectively at 0.5 mm and 85%. The agitator rotational speed was changed from 1863 to 3261 rpm. The bead motion was monitored experimentally using a high-speed video camera through a transparent mill body. For the simulation, enlarged particle sizes were set as 3-6 mm in diameter. With the DEM modified by the enlarged particle model, the motion of enlarged particles in a mill was simulated.The velocity data of the simulated enlarged particles were compared with those obtained in the experiment. The simulated velocity of the enlarged particles depends on the virtual frictional coefficient in the DEM model. The optimized value of the virtual frictional coefficient can be determined by considering the accumulated mean value. Results show that the velocity of the enlarged particles simulated increases with an increase in the optimum virtual frictional coefficient, but the simulated velocity agrees well with that determined experimentally by optimizing the virtual frictional coefficient in the simulation. The computing time in the simulation decreases with increased particle size.