Discrete element modeling of granular hopper flow of irregular-shaped deformable particles

Many natural and engineered granular materials have relatively deformable particles. Besides particle size and shape, particle deformability is another salient factor that significantly impacts the material’s flow behavior. In this work, the flow of irregular-shaped deformable particles in a wedge-shaped hopper is investigated using discrete element simulations. A bonded-sphere model is developed to simultaneously capture irregular particle shapes and particle-wise deformations (e.g., compression, deflection, and distortion). Quantitative analysis of the effects of irregular shapes and particle deformations shows that the increase in particle stiffness tends to increase initial packing porosity and decrease the flow rate in the hopper. Rigid particles tend to have clogging issues, whereas deformable particles have less chance to, indicating particle deformation reduces the critical bridging width in the hopper flow. Detailed analysis of stress fields is also conducted to provide insights into the mechanism of particle flow and clogging. Stresses and discharge rates calculated from numerical simulations are compared and show good agreement with Walker’s theory and the extended Beverloo formula. Simulations with various particle shape combinations are also performed and show that the initial packing porosity decreases with an increasing percentage of fibers while the discharge rate has a complex dependency on particle shapes.     

3D finite element simulation of the matter flow by surface diffusion using a level set method

Within the context of the sintering process simulation, this paper proposes a numerical strategy for the direct simulation of the matter transport by surface diffusion, in two and three dimensions. The level set formulation of the surface diffusion problem is first established. The resulting equations are solved by using a finite element method. A stabilization technique is then introduced, in order to avoid the spurious oscillations of the grain boundary that are a consequence of the dependence of the surface velocity on the fourth‐order derivative of the level set function. The convergence and the accuracy of this approach are proved by investigating the change in an elliptic interface under surface diffusion. Cases in direct relation with the sintering process are analyzed besides: sintering between two grains of the same size or of two different sizes. Finally, 3D simulations involving a small number of particles show the ability of the proposed strategy to deal with strong deformations of the grain surface (formation of necks) and to access directly important parameters such as the closed porosity rate. Copyright © 2010 John Wiley & Sons, Ltd.     

基于三维流场模型的含孔隙复合材料弹性常数有限元预测模型

为预测含孔隙复合材料单向层合板的有效弹性常数, 基于孔隙周边纤维分布和形态与三维Rankine椭圆体绕流流场的相似性, 提出了一种基于三维Rankine椭圆体绕流流场比拟的含孔隙复合材料弹性常数计算模型与方法。建立了含孔隙复合材料的有限元单胞计算模型, 用流场的速度变化比拟单胞内纤维体积分数的变化, 用流线形状比拟孔隙周边纤维的形态。通过对单胞施加周期性边界条件, 结合孔隙形态的概率分布模型和刚度平均法, 计算了含孔隙复合材料单向层合板的弹性常数。计算结果与实验数据有较好的一致性, 数值计算可以有效反映孔隙对复合材料单向层合板弹性常数的影响。      

Steady-state granular flow in a 3D cylindrical hopper with flat bottom: macroscopic analysis

The information of a hopper flow at a particle scale, obtained from discrete particle simulation, is used to investigate the macroscopic dynamic behaviour of granular flow in a cylindrical hopper with flat bottom by means of an averaging technique. The macroscopic properties including velocity, mass density, stress and couple stress are quantified under the cylindrical coordinate framework, and an effort is made to link these variables to the microscopic variables considered. The velocity and density distributions are first illustrated to match qualitatively the experimental and numerical results, confirming the validity of the proposed averaging method. Four components of stress, T_zz, T_rr, T_rz and T_zr, and two dominant components of couple stress, M_{r θ} and M_{z θ}, are then investigated in detail. It is shown that large vertical normal stress is mainly observed in the region close to the bottom corner, large radial normal stress is observed within the particle bed as well as the bottom corner, and large shear stresses in the region adjacent to the vertical wall. The four stresses are relatively small in a region close to the orifice. Their magnitudes are mainly contributed by the interaction forces between particles and between particles and walls. However, the transport of particles also plays a significant role at the orifice, especially, in the vertical normal stress. The couple stress can be ignored except for the regions close to the vertical and bottom walls, where the most dominant components are M_{r θ} adjacent to the vertical wall and M_{z θ} close to the bottom wall. The magnitudes of these macroscopic variables depend on the geometric and physical parameters of the hopper and particles such as the orifice size and wall roughness of the hopper, and the friction and damping coefficients between particles although their spatial distributions are similar.     

Discrete element simulation of dynamic behaviour of partially saturated sand

The discrete element method (DEM) together with the finite element method (FEM) in LS-DYNA was employed to investigate the dynamic behaviour of sand under impact loading. In this approach, the partially saturated sand was modelled in DEM with capillary forces being taken into account through an implicit capillary contact model, while other solids were simulated using FEM. A slump test was first performed with dry sand to calibrate the contact parameters in DEM. Low velocity impact tests were then conducted to investigate the effect of water saturation on the shape and height of sand piles after impact, and to validate the simulations. It was found in the experiments that an increasing water saturation (in the range between 10 and 30 %) affected the height of sand pile for a given drop height due to an increasing cohesion between particles. The simulations captured the experimental ejecta patterns and sand pile height. Finally, a low confinement split Hopkinson pressure bar test from earlier literature was modelled; the DEM–FEM simulations could reproduce the trends of experimentally observed stress–strain curves of partially saturated sand under high strain rate loading, indicating that it was feasible to model dynamic behaviour of dry and wet sand with low saturation (<20 %) in LS-DYNA; however, a number of questions remain open about the effect of grain shape, grain crushing and viscosity.     

Discrete element method simulation analysis of the generation mechanism of cooperative behavior of disks falling in a low-density particle bed

Pacheco-Vázquez and Ruiz-Suárez reported an interesting cooperative behavior for disks falling in a particle bed. This behavior involved the formation of upward and downward convex configurations during the falling of five steel disks into a bed of polystyrene particles. We used discrete element method simulations to investigate the generation mechanism for this cooperative behavior. Particles with a diameter of 5.0 mm and a density of 14.0 kg/m³ were placed randomly in a container with a width of 900 mm or 2700 mm and a height of 2700 mm. Model spheres with the same mass and diameter as the steel disks with a diameter of 25.4 mm and a thickness of 5.0 mm were then dropped into the particle bed, and we investigated the cooperative behavior of the model spheres. Similar cooperative behaviors were observed for the containers with widths of 900 mm and 2700 mm, indicating that the container side walls do not affect the occurrence of this behavior when the width is larger than 900 mm. The falling velocity of each disk was strongly dependent on the packing fractions over the disk and the flow velocity of the bed particles around the disks. Based on these results, the generation mechanism of the upward and downward convex configurations is discussed.     

Discrete element numerical simulation of fly ash triboelectrostatic separation in a nonlinear electric field

Fly ash is solid waste produced by thermal power generation, and its carbon content is a key factor affecting its recycling. Due to the large difference in fly ash quality and insufficient tribocharging, the parallel plate electric field with constant electric field strength cannot meet the practical needs of efficient decarbonization of fly ash particles with wide charge range or small charge to mass ratio (CMR). Therefore, a nonlinear electric field structure is proposed. The separation process of fly ash particles in the nonlinear electric field is explored through the establishment of geometric model and the application of CFD-DEM coupled calculation method, and the main influencing factors of fly ash electrostatic dry separation are studied. The results show that the nonlinear electric field structure is feasible to achieve high efficiency decarbonization of fly ash. With the increase of air flow velocity, the loss on ignition of positive electrode first increases and then decreases. The loss on ignition (LOI) of positive electrode products is directly proportional to the voltage and the CMR of the input, but inversely proportional to the feed quantity. Air flow velocity of 20 m/s, voltage of 30 kV, charge-mass ratio of 1.1–1.2 nC/g and feed quantity of 5000/s are suitable conditions for efficient decarbonization of fly ash. Compared with parallel plates, hyperbolic nonlinear electric field has higher decarbonization efficiency and lower energy consumption in experiment.     

Granular temperature with discrete element method simulation in a bubbling fluidized bed

The Discrete Element Method (DEM) plays an important role in understanding and modeling the kinetic characteristics in granular systems. A soft-sphere method with a linear spring–dashpot model was used in the simulation of a bubbling fluidized bed. The time-averaged granular temperature and vertical particle velocity at different heights were numerically studied and compared to experimental measurements of Müller. The influence of a velocity-dependent coefficient of restitution and three drag models were also investigated in this work. Good agreement was found between the DEM simulation and Müller’s experiment, especially using the DiFelice drag model. The variable coefficient of restitution, with a sufficiently high yielding relative velocity, gives a granular temperature that is a little lower compared to that of a constant coefficient of restitution, while it predicts a more intense velocity fluctuation, with a lower yielding relative velocity. By comparing the granular temperature in the vertical direction and in the transverse direction, a strong anisotropy is found in the bed.     

Prediction of hopper discharge rate using combined discrete element method and artificial neural network

An Artificial Neural Network (ANN) was developed to predict the mass discharge rate from conical hoppers. By employing Discrete Element Method (DEM), numerically simulated flow rate data from different internal angles (20°–80°) hoppers were used to train the model. Multi-component particle systems (binary and ternary) were simulated and mass discharge rate was estimated by varying different parameters such as hopper internal angle, bulk density, mean diameter, coefficient of friction (particle-particle and particle-wall) and coefficient of restitution (particle-particle and particle-wall). The training of ANN was accomplished by feed forward back propagation algorithm. For validation of ANN model, the authors carried out 22 experimental tests on different mixtures (having different mean diameter) of spherical glass beads from different angle conical hoppers (60° and 80°). It was found that mass discharge rate predicted by the developed neural network model is in a good agreement with the experimental discharge rate. Percentage error predicted by ANN model was less than ±13%. Furthermore, the developed ANN model was also compared with existing correlations and showed a good agreement.     

hp Fast multipole boundary element method for 3D acoustics

A fast multipole boundary element method (FMBEM) extended by an adaptive mesh refinement algorithm for solving acoustic problems in three‐dimensional space is presented in this paper. The Collocation method is used, and the Burton–Miller formulation is employed to overcome the fictitious eigenfrequencies arising for exterior domain problems. Because of the application of the combined integral equation, the developed FMBEM is feasible for all positive wave numbers even up to high frequencies. In order to evaluate the hypersingular integral resulting from the Burton–Miller formulation of the boundary integral equation, an integration technique for arbitrary element order is applied. The fast multipole method combined with an arbitrary order h‐p mesh refinement strategy enables accurate computation of large‐scale systems. Numerical examples substantiate the high accuracy attainable by the developed FMBEM, while requiring only moderate computational effort at the same time. Copyright © 2016 John Wiley & Sons, Ltd.     

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

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

Thermal analysis of induction motors using 3D finite element method

Abstract

To design a reliable and economical induction motor, it is necessary to be able to predict accurately the temperature distribution within the motor. In this paper, a 3D thermal model of an induction motor is presented. Except for providing a more accurate representation of the problem, the proposed model can also reduce computer memory and time. The finite element method (FEM) is used to analyze the three dimensional (3D) heat flow equation which describes the thermal model. Galerkin's procedure is used to derive the element equations and first order tetrahedral elements are used to discretize the field region. Galerkin's time‐stepping scheme is employed to treat time differential terms. Values of surface heat transfer coefficients are obtained from the empirical formula and heat losses are revised by the factory test. Application of the proposed method to the analysis of a 9,000 HP induction motor yields temperature distribution very close to the experimental data.     

Discrete element modelling of grain flow in a planar silo: influence of simulation parameters

There is extensive engineering literature concerning the prediction of pressure and flow in a silo. The great majority of them are based on continuum theories. The friction between the stored material and the silo wall as well as the inclination of the hopper at its base are considered to be the most influential parameters for the flow pattern within the silo. In this paper, the filling and discharge of a planar silo with a hopper at its base has been modelled using DEM. The aim is to investigate the influence of DEM model parameters on the predicted flow pattern in the silo. The parametric investigation particularly focused on the hopper angle of inclination and the contact friction between particles and walls. The shape of the particles was also considered by comparing spherical and non-spherical particles, thus providing an insight into how particle interlocking might influence solids flow behaviour in silos. The DEM computations were analysed to evaluate the velocity profiles at different levels as well as the wall pressure distribution at different stages during filling and discharge. A detailed comparison reveals several key observations including the importance of particle interlocking to predict a flow pattern that is similar to the ones observed in real silos.     

Finite element analysis of 3-ply laminated conical shell for flutter

The results of the finite element analysis of 3-ply laminated conical shells with light core for linear panel flutter are presented and certain advantages of such shells discussed.     

Crack length measurements with a potential drop method: A finite element simulation

A potential drop method, as used for estimations of crack lengths during three-point-beind experiments, is studied. The mechanical state is calculated using a finite element method. The deformed body obtained is used for a subsequent calculation of the electrostatic state. Calculations are performed for both two- and three-dimensional models. The material is assumed to be elastic, linearly hardening plastic and electrostatically linear. Large deformations are considered. Further, the non-linearity caused by the load, depending on the contact area between the cylinder on which the load is applied and the specimen, is considered. The increased contact area did not influence the mechanical state very much but had a direct impact on the electrostatic state. The changes in the potential drop recordings due to deformation and electrical current passing through the load cylinder were shown to be considerable. The study explains, at least partly, the experimental observations. A more reliable registration of crack growth initiation is the main outcome of the analysis.     

Discrete element method investigation on thermally-induced shakedown of granular materials

Temperature change, as a common kind of internal perturbation performed on granular materials, has a significant effect on the bulk properties of granular materials. However, few studies on thermally-induced shakedown under a long-term thermal cycling were reported. In this work, the discrete element method was used to give insight into the thermally-induced shakedown on the fabric and stress states within non-cohesive, frictional granular assemblies. Assemblies were submitted to thermal cycling at a stationary boundary condition after experiencing a one-dimensional compression. Evolution of coordination number, entropy and anisotropy was investigated as well as boundary forces and contact forces. At the same time, effects of the heating rate, the initial vertical load and the magnitude of temperature change were examined. It demonstrates that thermal cycling induces a significant force relaxation within granular materials, while the corresponding granular fabric has a small change. In addition, the entropy and anisotropy decreases with thermal cycling. Moreover, the initial vertical load can constrain the development of thermally-induced fabric change, thereby limiting force relaxation to some degree. Both high heating rate and larger magnitudes of temperature change contribute to more significant force relaxation. However, they cause smaller fabric changes even though they provide larger perturbations.     

A method for rendering 3D finite element vector field solutionsnondivergent

The use of the method of constraints for enforcing the zero divergence condition in vectorial finite-element schemes is discussed. An earlier implementation of the method was shown to produce the correct solution for a 3-D resonant cavity problem modeled by a single finite element. Partial success in extending the method to multielement cases is reported. The reduction in matrix size alone would justify the development of the technique for general multielement grids, but it will require the implementation of a global approach to the method of constraints     

Boundary element method solutions for elastic wave scattering in 3D

Time-harmonic elastic wave scattering problems such as those encountered in ultrasonic non destructive evaluation are solved by the boundary element method (BEM). Selected results for spherical and spheroidal shaped voids and inclusions are compared with analytical and other numerical solutions. Results for ellipsoids, which require a full three-dimensional formulation, are provided as a benchmark for comparison when other numerical methods would be developed for this problem class in the future. The modelling of cracklike defects with this formulation is discussed. Recent theoretical findings regarding the fictitious eigenfrequency difficulty (FED) are confirmed by a numerical study.