DEM simulation on the one-dimensional compression behavior of various shaped crushable granular materials

In order to investigate the effects of particle shape on the compression behavior of granular materials, a series of simulations was conducted using a two-dimensional discrete element method employing moment springs. Fracturable granular assemblies were constructed from particles of the same shape and size. The range of possible particle shapes includes disk, ellipse and hexagon, with different aspect ratios. Simulations of single particle crushing tests on elliptical particles showed that crushing could be classified into three types: cleavage destruction, bending fracture and edge abrasion, depending on the manner of compression. A series of simulations of one-dimensional compression tests was then conducted on six types of crushable particle assemblies; the three types of crushing mentioned above were also observed, but their rates of occurrence depended on the particle shape. Cleavage destruction was mainly observed with circular and elliptical particles; bending fracture was observed only with elongated particles; edge abrasion was frequently observed with angular particles. Despite the difference in crushing type, all samples, when subjected to intense compression, converged to a critical grading with unique void ratio, grain size distribution and aspect ratio, with a similar distribution of number of contact points.     

Experimental and numerical evaluation of the transport behaviour of a moving fuel bed on a forward acting grate

The objective of this study is to evaluate experimentally and numerically the transport behaviour of a moving bed on a forward acting grate. Therefore, the grate was operated with expanded clay and wood chips without combustion. Frequency and amplitude of the grate bars and feed rate were subject to change. Experimental findings showed that large particles have shorter residence times than small particles which is due to segregation on the grate. Additionally, the experiments indicated that increased frequencies of the grate bars lead to reduced residence times whereas the amplitude had no significant effect. The motion of a packed bed e.g., its particles was described numerically by the discrete element method (DEM). Thus, detailed data on all the particle’s paths and velocities are available. These data were used within the mean velocity method (MVM) and the tracking method (TM) to estimate the residence time of a packed bed. Both methods confirmed the dependency of the residence time on particle size, however, better predictions were obtained by the Tracking Method. The mean residence times varies from 40 to 120 min depending on the particle size. B. Peters is an Academic visitor to the Lituanian Energy Institute.     

Evaluation of the Residence Time of a Moving Fuel Bed on a Forward Acting Grate

The objective of this study is to identify numerical approaches and to employ them to evaluate the residence time of a moving bed on a forward acting grate. Obtaining residence times of fuel particles on a grate favours more reliable design of grate furnaces. The moving bed was represented by spherical particles, whereby a varying size accounts for the variety of particle geometries in a combustion chamber. In order to describe accurately the motion of a moving bed e.g. its particles, the discrete element method was applied. Thus, detailed data on all the particle’s paths and velocities are available. These data were used within two statistical approaches to estimate the residence time of a moving bed. One approach is based on a spatial averaging procedure, while the other relies on tracking the particle’s path. Both methods yielded satisfactory agreement with measurements, however, better predictions were obtained by tracking particles.Academic visitor to the Lithuanian Energy Institute     

Dynamic simulation of the flow of suspensions of two-dimensional particles with arbitrary shapes

A boundary-element method is implemented for simulating the motion of two-dimensional rigid particles with arbitrary shapes suspended in a viscous fluid in Stokes flow. The numerical implementation results in a system of linear equations for the components of the hydrodynamic traction over boundary elements distributed over the particle surfaces, and for the velocity of translation and angular velocity of rotation of the particles about designated centers. The linear system is solved by the method successive substitutions based on a physically motivated iterative procedure that involves decomposing the influence matrix into diagonal blocks consisting of physical particle clusters, and performing updates by matrix-vector multiplication using the inverses of the diagonal blocks. The iterations are found to converge as long as the particles are separated by a sufficiently large distance that depends on the particle shape and level of discretization. The stiffness of the governing equations due to lubrication forces developing between intercepting particles is removed by preventing the particles from approaching one another by less than a specified distance. Simulations are carried out for doubly-periodic suspensions of circular and elliptical particles in simple shear flow. The simulation algorithm is found to be successful for particles with moderate aspect ratios, and for small and moderate areal fractions up to 0.25. Higher areal fractions require long simulation times due to the large size of spontaneously forming particle clusters. The results illustrate the performance of various aspects of the boundary-element method and provide insights into the effect of the particle areal fraction and aspect ratio on the rheological properties of the suspension and on the geometrical properties of the evolving microstructure.     

Numerical simulation of particle motion in dense phase pneumatic conveying

A gas-solids two-dimensional mathematical model was developed for plug flow of cohesionless particles in a horizontal pipeline in dense phase pneumatic conveying. The model was developed based on the discrete element method (DEM). For the gas phase, the Navier-Stokes equations were integrated by the semi-implicit method for pressure-linked equations (SIMPLE) scheme of Patankar employing the staggered grid system. For the particle motion the Newtonian equations of motion of individual particles were integrated, where repulsive and damping forces for particle collision, the gravity force, and the drag force were taken into account. For particle contact, a nonlinear spring and dash pot model for both normal and tangential components was used. In order to get more realistic results, the model uses realistic pneumatic system and material values.     

Characterization and discrete element simulation of grading and shape-dependent behavior of JSC-1A Martian regolith simulant

Granular regolith simulants have been extensively used in the preparation of space missions to test rovers and scientific instruments. In this work, the physical and mechanical properties of the JSC-1A Martian regolith simulant (MRS) are characterized using conventional and advanced laboratory techniques. Particle images are obtained using X-ray computed tomography, from which particle shapes are characterized through a series of imaging processing techniques and are further used to generate irregularly-shaped numerical particles. The characterized particle size distribution and irregularly-shaped numerical particles are incorporated into a discrete element model to simulate grading and shape-dependent behavior of the JSC-1A MRS. The developed discrete element model is calibrated and validated against laboratory direct shear tests. Simulations without the consideration of particle shapes and simulations with a rolling resistance contact model are also performed to investigate the effect of particle shapes on the behavior of the JSC-1A MRS.     

回转窑内颗粒轴向混合运动的数值模拟

为了研究不同粒径颗粒在水平回转窑内轴向混合运动机理,采用离散元软件EDEM对窑内颗粒轴向混合过程进行数值模拟,引入颗粒接触数动态跟踪颗粒的混合过程,以大、小颗粒接触数来衡量颗粒间的混合程度。结果表明:活动层内颗粒的运动速度较大;小颗粒轴向运动的主要方式是透过大颗粒间的间隙向大颗粒群渗透。     

Reduction of discrete element models by Karhunen–Loève transform: a hybrid model approach

The term “discrete element method” (DEM) in engineering science comprises various approaches to model physical systems by agglomerates of free particles. While shapes, sizes and properties of particles may vary, in most DEM models, particles are not confined by constraints, but subject to applied forces derived from potential fields and/or contact laws. This general approach allows for widespread use of DEM models for physical phenomena including gas dynamics, granular flow, fracture and impact analysis. However, its characteristic feature, combining particle restraints and forces into applied forces, does not only provide for flexible adaption of DEM to different physics, but also creates the most limiting restriction: Evaluation of the applied forces for each particle is computational expensive restraining the time sequence and sample size for numerical analyses. As an ansatz to circumvent this obstacle for a class of DEM models, we propose a model order reduction method based on coherency in the dynamics of particles. While initial flexibility of DEM is conserved, computational effort can be reduced significantly.     

Fabric rates of elliptical particle assembly in monotonic and cyclic simple shear tests: a numerical study

This paper aims to investigate the evolutions of microscopic structures of elliptical particle assemblies in both monotonic and cyclic constant volume simple shear tests using the discrete element method. Microscopic structures, such as particle orientations, contact normals and contact forces, were obtained from the simulations. Elliptical particles with the same aspect ratio (1.4 and 1.7 respectively for the two specimens) were generated with random particle directions, compacted in layers, and then precompressed to a low pressure one-dimensionally to produce an inherently anisotropic specimen. The specimens were sheared in two perpendicular directions (shear mode I and II) in a strain-rate controlled way so that the effects of inherent anisotropy can be examined. The anisotropy of particle orientation increases and the principal direction of particle orientation rotates with the shearing of the specimen in the monotonic tests. The shear mode can affect the way fabric anisotropy rate of particle orientation responds to shear strain as a result of the initial anisotropy. The particle aspect ratio exhibits quantitative influence on some fabric rates, including particle orientation, contact normal and sliding contact normal. The fabric rates of contact normal, sliding contact normal, contact force, strong and weak contact forces fluctuate dramatically around zero after the shear strain exceeds 4 % in the monotonic tests and throughout the cyclic tests. Fabric rates of contact normals and forces are much larger than that of particle orientation. The particle orientation based fabric tensor is harder to evolve than the contact normal or contact force based because the reorientation of particles is more difficult than that of contacts.     

The effect of relative refractive index on monosized particle movement under laser radiation pressure

The purpose of this study is to investigate the fundamental characteristics of particle movement under laser radiation pressure from the viewpoint of particle separation. In this study, the radiation pressure exerted on a spherical particle was calculated by using a simple geometrical optics model and the simulation of particle movement in a laser beam was performed. Further, the movement of particles under the laser radiation pressure was experimentally observed to confirm the accuracy of simulation. As a result, it was possible to simulate particle movement with the two-dimensional equations of motion by considering radiation pressure, viscous drag, gravity, and buoyancy as the forces acting on a particle. The possibility of particle separation according to the refractive index was suggested since the difference in laser radiation pressure was large enough to discriminate the particles.     

Two-dimensional oscillatory motion of inertially focused particles in microfluidic flows

Inertially focused particles flowing in microchannels form an evenly spaced streamline on each channel face due to hydrodynamic interaction. Previous studies of this interaction have only reported the oscillatory pairwise dynamics of focused particles, which was limited to the one-dimensional (1D) streamwise direction. Thus, despite its practical and intellectual importance, there remains a lack of comprehensive research on the pairwise oscillation, due to the difficulty of high-resolution observation. Here, I explore the hydrodynamic interaction between inertially focused particles in microfluidic flows to determine the ordering mechanism. Direct numerical simulation (DNS) is applied to a pressure-driven flow of a pair of particles due to the lack of established formulas for the inertial focusing of finite-sized particles; in particular, only DNS allows the author to simulate the microscale flow structures. I describe the unique periodic oscillations of the pairwise particles as they flow downstream. Upon the formation of a train structure in the steady state, the following particle shows periodic oscillations on a two-dimensional (2D) limit cycle around its equilibrium position, whereas the leading particle exhibits 1D oscillation at a specific distance downstream. The 2D oscillatory motion of the following particle is produced by a combination of the lift forces and the disturbance flow induced by the leading particle, coupled with forward/backward transport by the main flow. Thus, the spacing of the particle train is a function of the particle size and flow conditions, leading to even spacing between inertially focused particles. The finding of the asymmetric oscillatory dynamics of the pairwise system provides direct evidence for the self-assembly mechanism of inertially focused particles. I highlight a mostly overlooked aspect of the lift forces: that they stabilize focused streamlines that might otherwise break apart due to finite-particle-induced disturbance flows.     

高温熟料非稳态非热平衡渗流换热模型

回转窑卸入篦冷机的高温水泥熟料为红热半透明的多孔介质,其复杂的气固换热机理给篦冷机的工艺改进带来较大难度。针对这一问题,将高温红热颗粒等效为光学厚介质,推导了一种高温熟料颗粒间传导与辐射综合换热系数,基于渗流力学与传热学理论,建立了考虑高温熟料颗粒间热辐射效应的水泥熟料非稳态非热平衡渗流换热模型。通过对所建模型进行求解,得到了料层内熟料温度与气体温度的分布规律,比较了不同区域冷却速率的差异,获得了辐射传热因素对料层温度分布的影响。     

粉末高速压制成形密度分布的数值模拟及影响因素分析

将研究不连续体力学行为的离散单元法应用于粉末高速压制致密化过程的研究,将粉末视为黏弹性的离散颗粒,建立粉末高速压制过程颗粒接触模型及每个颗粒的基本运动方程,推导了力与位移表达的粉末高速压制黏弹性本构关系。基于PFC软件实现了铁粉高速压制过程中粉末颗粒二维流动情况及压坯密度分布的数值模拟,模拟结果的密度分布规律与实际压制的密度分布规律较为一致;利用数值模拟结果对影响压坯密度分布的摩擦因数、高径比、双向压制因素进行了具体分析。     

The discrete element method with deformable particles

This work presents a new original formulation of the discrete element method (DEM) with deformable cylindrical particles. Uniform stress and strain fields are assumed to be induced in the particles under the action of contact forces. Particle deformation obtained by strain integration is taken into account in the evaluation of interparticle contact forces. The deformability of a particle yields a nonlocal contact model, it leads to the formation of new contacts, it changes the distribution of contact forces in the particle assembly, and it affects the macroscopic response of the particulate material. A numerical algorithm for the deformable DEM (DDEM) has been developed and implemented in the DEM program DEMPack. The new formulation implies only small modifications of the standard DEM algorithm. The DDEM algorithm has been verified on simple examples of an unconfined uniaxial compression of a rectangular specimen discretized with regularly spaced equal bonded particles and a square specimen represented with an irregular configuration of nonuniform‐sized bonded particles. The numerical results have been verified by a comparison with equivalent finite element method results and available analytical solutions. The micro‐macro relationships for elastic parameters have been obtained. The results have proved to have enhanced the modeling capabilities of the DDEM with respect to the standard DEM.     

Dynamic forces on an immersed cylindrical tube and analysis of particle interaction in 2D-gas fluidized beds

The interactions of bubbles and particles with fixed cylindrical tubes in two-dimensional fluidized beds were investigated by experiments and by simulations, based on results for single bubbles impinging on a tube. The experimental results based on PIV analysis support our previous force origin model and indicate that the model is able to successfully model bubble behavior and particle motion around fixed objects. The simulation results give useful predictions, dynamic force induced on a tube consists of the force from pressure gradient, fluid viscous force and particle contact force. The predominant force component is from the pressure gradient. As bubbles directly interact with a tube, the particle contact force contribution briefly becomes predominant.Bubble behavior and particle motion are greatly affected by the state of the emulsion phase as the medium of the fluidized bed into which gas is injected. Hence the dynamic forces on immersed objects are directly affected by the state of the emulsion phase.     

Numerical investigations of strong hydrodynamic interaction between neighboring particles inertially driven in microfluidic flows

Dispersed particles traveling at a high throughput in microchannels laterally migrate and focus into a streamline at each channel face. The focusing attractors within the cross-section are determined by the balance between the lift forces. However, particles in close proximity (e.g. due to high concentration and abrupt particle contact) suffer a breakdown of distinct focusing due to excessive hydrodynamic interaction. Here, I present numerical investigations into the effects of the strong hydrodynamic interaction on the inertial focusing. The direct numerical simulation is used to calculate the focusing/defocusing of particles, specifically since the particle-induced disturbance flows vary at the particle scale and hence affect the individual particle motion. The simulated defocusing of many-body systems prefer finite inter-particle separation, in contrast with sedimentation of two mobile particles, whereby the trailing particle catches up with the leading particle due to reduced drag in its wake. I numerically demonstrate that the finite separation between nearest neighbors is a consequence of hydrodynamic repulsive motion unique to wall-bound shear flows. The author further presents direct demonstrations of the effects of the strong hydrodynamic interaction on the inertial focusing in an experimentally unachievable manner. The excessive hydrodynamic interaction drastically dissipates the near-wall focusing attractors and thus causes irreversible defocusing by breaking the balance between the lift forces. Unexpectedly, I also find that moderate hydrodynamic interaction can alter focusing speed on specific conditions, suggesting that an optimum concentration may significantly boost the inertial focusing in microfluidic-based applications.     

基于有限质点法的结构碰撞行为分析

有限质点法是以向量式力学为基础的结构分析方法,它将结构离散为质点群,并以结构质点的真实行为模拟为基本思想,研究表明该方法在结构强非线性和不连续行为分析中有明显的优势。该文将其拓展至结构的碰撞行为分析中,根据结构的离散模型提出了结构单元的接触侦测方法,建立了碰撞模型,推导了碰撞力的计算公式和质点内力的修正公式,并编制了基于有限质点法的结构碰撞行为分析程序。通过对两个算例的模拟和分析,验证了该方法进行结构接触碰撞行为分析的有效性。     

Numerical simulation of particulate cake formation in cross-flow microfiltration: Effects of attractive forces

We present a two-dimensional simulation model to explore cake formation in cross-flow filtration. The model uses the lattice Boltzmann method (LBM) for fluid computation and the discrete element method (DEM) for particle computation; they were fully coupled with the smoothed profile method. We verified our model by simulating filtration under different transmembrane pressures. We then investigated the effects of attractive forces and particle concentration on the cake formation mechanism. Generally, as the attractive interaction and particle concentration increased, the particles formed a cake layer with a looser body and rough surface, due to the decrease in the mobility of the particles in contact with the cake surface. It is concluded that the effects of particle concentration are affected by the different conditions of attractive interactions between the particles.     

风雪流滞空颗粒受力及运动行为的数值模拟

为研究稀疏风雪流系统下滞空颗粒在介质中的变加速运动行为及非线性气动特性,以运动学微分方程为基础,建立了微观层面下不同粒径、密度颗粒的三维动网格计算模型。采用时间-空间离散的数值积分方法,求解了小时空尺度下,单个雪颗粒在静止空气及梯度风场中的自由沉降与强迫运动问题。通过对比不同颗粒参数及流场环境的模拟结果发现:颗粒自由沉降所能达到的终端线速度及对应稳定时间均随平均粒径及密度的增大而增大,粒径确定的情况下,相同时间内大密度颗粒沉降距离相对更远,自由沉降初期的非线性变速运动行为可近似考虑为小时空尺度问题;剪切流条件下,较小的风速梯度可能引起颗粒在来流及自重方向运动速度的波动,所受气动外力的改变总是滞后于运动速度的变化,强风环境下颗粒将具有更好的流场跟随性,其非线性变速阶段仍可视为小时空尺度问题。滞空雪颗粒在流场中的运动行为基本满足多相流理论的局部短时空尺度均衡假定。     

Numerical simulation of gravel deposits using multi‐circle granule model

Abstract

This study proposes a new Multi‐Circle Granule Model (MCGM), based on overlapping circles with various diameters to create an irregular particle shape, to simulate the geometry‐dependent behavior of gravel particles for two‐dimensional mechanical analyses of gravel deposits. The MCGM model is implemented in a Distinct Element Method (DEM) program for numerical simulation. Two numerical examples are presented to study the effects of gravel shapes on the angles of repose in free falling tests, and on the stability of gravel tunnel excavation in trap door tests. Additionally, the numerical study reveals that the shapes of gravel significantly affect the angle of repose. Furthermore, interlocking, anisotropy, and contact numbers among the gravels are found to be key factors governing the stability of gravel tunnel excavation. These numerical simulation results of geometry‐dependent behavior are quite encouraging for the MCGM model.