Angle of repose in the numerical modeling of ballast particles focusing on particle-dependent specifications: Parametric study

The discrete element method (DEM) is widely used in the realistic simulation of the shapes of particles. Researchers have considered the simplification of particle shapes owing to the high computational cost of such simulation. In this regard, the modeling of calibrated particles is a major challenge owing to the simultaneous effects of particle properties. The angle-of-repose test is a standard test method used to calibrate the bulk behavior of simulated particles. In the present study, the hollow-cylinder (slump) test was modeled for the verification of discrete element simulations. In this regard, a sensitivity analysis was conducted for all effective parameters, namely the static friction, rolling friction, restitution coefficient, sphericity, roundness, particle size distribution, and number of ballast particles. The results indicate that the rolling friction, roundness, number of particles, and size of particles are the most important parameters in the determination of the angle of repose (AOR). For particles in the range of ballast (20–60 mm), the effect of the number of particles on the angle of repose is reduced when the number is greater than 426. Additionally, it is concluded that angular particles can be replaced with sub-angular particles (R ≈ 0.2–0.45) with a higher rolling friction coefficient (μ_r > 0.14).     

三方程线性弹性-阻尼DEM模型及碰撞参数确定

建立了一种考虑法向接触力、切向接触力(含静滑动摩擦力及动滑动摩擦力)和力矩(含由切向力产生的力矩及静滚动摩擦力矩和动滚动摩擦力矩)的三方程线性弹性-阻尼离散单元模型,并将该模型应用到颗粒物料的三维数值模拟中,讨论了模型中几个重要碰撞参数--刚性系数、阻尼系数及摩擦系数的选择及其对计算结果的影响,同时也探讨了时间步长等计算参数对模拟结果的影响.为了验证算法和参数选择的正确性,本文对几个有代表性的颗粒系统进行了数值试验研究,并对计算结果进行了细致的分析,验证了新模型和参数选择的正确性.     

Determining the angle of repose of sand under low-gravity conditions using discrete element method

This study is a comparative investigation of data, collected through experimental and numerical means, related to the flow of sand particles through a hopper under low-gravity conditions. During a parabolic airplane flight simulating low-gravity conditions, we determined effects of gravity on the angle of repose of sand pile particles by flowing dry sand from a hopper. The gravity effects on the angle of repose of the sand were negligible. Two-dimensional discrete element method (DEM) was used to simulate the angle of repose. Results were compared to observations made during the low-gravity experiments. Effects of varying parameters such as the friction coefficient and coefficient of rolling friction were determined by running various DEM simulations. Moreover, the effect of the elemental radius on the angle of repose was investigated using DEM. The angle of repose is influenced by certain changes in the friction coefficient and rolling friction values, but the elemental radius has only a negligible effect on the angle of repose within the range of variation. Results show that the DEM model used for this study might be applicable to determine terramechanical interactions under lunar surface gravity conditions, provided that parameters are adjusted and an extended period of simulation is achieved.     

粗粒土离散元非球趋真颗粒模型

颗粒形状对粗粒土的物理力学特性有着显著的影响。离散元法广泛应用于粗粒土宏观物理力学特性的细观机理研究。为了考虑颗粒形状的影响,亟待发展计算高效的离散元非球趋真颗粒模型。本文基于X射线CT扫描技术并结合数字图像处理技术,对光滑和棱角性两类典型粗粒土(鹅卵石与碎石)进行三维重构,并提出了两类趋真颗粒模型,分别采用扩展超椭球模型和球多面体模型进行趋真逼近;开展了两类颗粒试样的3D打印和单轴压缩试验,分析了配位数和局部孔隙率分布等细观特性;基于离散元开源程序SudoDEM开展了两类试样的离散元模拟,并将模拟细观分析结果与物理试验进行了对比。结果表明,提出的两类趋真颗粒模型能够较好地对粗粒土颗粒进行离散元建模。     

A numerical analysis of the shear behavior of granular soil with fines

Shear behavior of granular soil with fines is investigated using the discrete element method(DEM) and particle arrangements and inter-particle contacts during shear are examined.The DEM simulation reveals that fine particles play a vital role in the overall response of granular soil to shearing.The occurrence of liquefaction and temporary reduction of strength is ascribed mainly to the loss of support from the fine particle contacts(S-S) and fine particle-to-large particle contacts(S-L) as a consequence of the removal of fine particles from the load-carrying skeleton.The dilative strain-hardening response following the strain-softening response is associated with the migration of fine particles back into the load-carrying skeleton,which is thought to enhance the stiffness of the soil skeleton.During shear,the unit normal vector of the large particle-to-large particle(L-L) contact has the strongest fabric anisotropy,and the S-S contact unit normal vector possesses the weakest anisotropy,suggesting that the large particles play a dominant role in carrying the shear load.It is also found that,during shear,fine particles are prone to rolling at contacts while the large particles are prone to sliding,mainly at the S-L and L-L contacts.     

Translation and rotation of particles in different flow pattern areas of a silo

The present paper reports the results obtained for translational and rotational velocity profiles of spherical particles for the mixed flow in a conical silo. The discrete element method (DEM) based on Hertz-Mindlin (no slip) with RVD rolling friction contact model is used for simulations. Opposite correlations are found between translational and rotational velocities in different flow areas of the silo. In particular, the abrasion caused by rotation is dominant in the funnel flow area. In addition, increase of the mass flow rate of silo can effectively reduce the abrasion induced by rotation. This highlights that understanding of dynamic characteristics of particles is helpful for optimization of silos and reduction of granular material abrasion.     

Implementation of rotational resistance models: A critical appraisal

Contact models that simulate rotational resistance at particle contacts have been proposed as a means to capture the effect of shape in DEM simulations. This contribution critically explores some key issues related to the implementation of rotational resistance models; these include the need for physically meaningful model parameters, the impact of the model on the overall numerical stability/critical time increment for the DEM model, model validation, and the assessment of model performance relative to real physical materials. The discussion is centred around a rotational resistance model that captures the resistance provided by interlocking asperities on the particle surface. An expression for the maximum permissible integration time step to ensure numerical stability is derived for DEM simulations when rotational resistance is incorporated. Analytical solutions for some single-contact scenarios are derived for model validation. The ability of this type of model to provide additional fundamental insight into granular material behaviour is demonstrated using particle-scale analysis of triaxial compression simulations to examine the roles that contact rolling and sliding have on the stability of strong force chains.     

DEM simulations of bi-disperse ellipsoids of different particle sizes

This paper presents the result of two schemes concerning computational effort reduction in discrete element simulations (DEM) of binary mixtures. Numerical triaxial compression simulations were performed. The coarse ellipsoids and the fine ellipsoids have similar shapes, but the sizes are significantly different. Computational effort reduction can be achieved by increasing the density of individual particles so that a greater time step can be used in DEM. Two different mass increase schemes are investigated. The result indicates that both schemes provide a speedup. Similar results can be produced with the correct damping.     

3-D DEM simulation of cohesive soil-pushing behavior by bulldozer blade

A numerical simulation based on discrete element method (DEM) was conducted on the excavation and pushing processes of soil by a bulldozer blade. Soil contains water and the resistance acting on the bulldozer blade is largely influenced by the cohesive force due to liquid bridges formed among soil particles. In the present study, a cohesive bond force model proposed by Utili and Nova [5] was introduced in which the microscopic behavior of cohesive force was modeled analogously with macroscopic shear failure characteristics. The dependency on the magnitude of microscopic cohesive force was verified. The behavior of particles changed greatly by taking into account the cohesive bond force. The characteristic behavior of excavated soil aggregates, such as rolling motion and intermittent collapsing, were observed in front of the blade surface.     

Calibration of granular material parameters for DEM modelling and numerical verification by blade-granular material interaction

The discrete element method (DEM) is a promising approach to model blade-granular material interactions. The accuracy of DEM models depends on the model parameters. In this study, a calibration process was developed to determine the parameter values. The particle size was the same as the real material and the particle shape was modelled using two spherical particles rigidly clumped together to form a single grain. Laboratory shear tests and compressions tests were used to determine the material internal friction angle and stiffness, respectively. These tests were replicated numerically using DEM models with different sets of particle friction coefficients and particle stiffness values. The shear test results are found to be dependent on both the particle friction coefficient and the particle stiffness. The compression test results show that it is only dependent on the particle stiffness. The combination of shear test and compression test results can be used to determine a unique set of particle friction and particle stiffness values. The calibration process was validated experimentally and numerically by modelling a blade moving through granular material. Results show that the forces acting on the blade can be accurately modelled with DEM and the maximum error is found to be 26%. The relative particle-blade displacements were used to predict the position and shape of the shear lines in front of the blade. A good qualitative correlation was achieved between the experiments and the DEM simulations.     

A coupled sliding and rolling friction model for DEM calibration

The accuracy of dense Discrete Element Method (DEM) simulations is sensitive to initial density, contact orientation, particle size and shape, and interparticle interaction parameters including contact stiffness, cohesion, coefficients of friction, and coefficients of restitution. Although studies have characterized the effects of individual particle interaction parameters on mechanical responses of loaded granular material, research combining DEM parameters for calibration is scarce. Robust DEM calibration methodology combining sliding and rolling friction coefficients was developed and validated to predict bulk residual soil strength of initially dense DEM particle assemblies.     

CFD-DEM simulation of spouting of corn-shaped particles

Three dimensionally coupled computational fluid dynamics (CFD) and discrete element method (DEM) were used to investigate the flow of corn-shaped particles in a cylindrical spouted bed with a conical base. The particle motion was modeled by the DEM, and the gas motion by the k-? two-equation turbulent model. A two-way coupling numerical iterative scheme was used to incorporate the effects of gas–particle interactions in terms of momentum exchange. The corn-shaped particles were constructed by a multi-sphere method. Drag force, contact force, Saffman lift force, Magnus lift force, and gravitational force acting on each individual particle were considered in establishing the mathematical modeling. Calculations were carried out in a cylindrical spouted bed with an inside diameter of 200 mm, a height of 700 mm, and a conical base of 60°. Comparison of simulations with experiments showed the availability of the multi-sphere method in simulating spouting action with corn-shaped particles, but it depended strongly on the number and the arrangement of the spherical elements. Gas–solid flow patterns, pressure drop, particle velocity and particle concentration at various spouting gas velocity were discussed. The results showed that particle velocity reaches a maximum at the axis and then decreases gradually along the radial direction in the whole bed. Particle concentration increases along the radial direction in the spout region but decreases in the fountain region, while it is nearly constant in the annulus region. Increasing spouting gas velocity leads to larger pressure drop, remarkably increased speed of particle moving upward or downward, but decreased particle concentration.     

Rolling/sliding of a particle on a flat wall in a linear shear flow at finite Re

Recently Lee and Balachandar proposed analytically-based expressions for drag and lift coefficients for a spherical particle moving on a flat wall in a linear shear flow at finite Reynolds number. In order to evaluate the accuracy of these expressions, we have conducted direct numerical simulations of a rolling particle for shear Reynolds number up to 100. We assume that the particle rolls on a horizontal flat wall with a small gap separating the particle from the wall (L = 0.505) and thus avoiding the logarithmic singularity. The influence of the shear Reynolds number and the translational velocity of the particle on the hydrodynamic forces of the particle was investigated under both transient and the final drag-free and torque-free steady state. It is observed that the quasi-steady drag and lift expressions of Lee and Balachandar provide good approximation for the terminal state of the particle motion ranging from perfect sliding to perfect rolling. With regards to transient particle motion in a wall-bounded shear flow it is observed that the above validated quasi-steady drag and lift forces must be supplemented with appropriate wall-corrected added-mass and history forces in order to accurately predict the time-dependent approach to the terminal steady state. Quantitative comparison with the actual particle motion computed in the numerical simulations shows that the theoretical models quite effective in predicting rolling/sliding motion of a particle in a wall-bounded shear flow at moderate Re.     

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.     

Transient rolling friction model for discrete element simulations of sphere assemblies

The rolling resistance between a pair of contacting particles can be modeled with two mechanisms. The first mechanism, already widely addressed in the DEM literature, involves a contact moment between the particles. The second mechanism involves a reduction of the tangential contact force, but without a contact moment. This type of rotational resistance, termed creep-friction, is the subject of the paper. Within the creep-friction literature, the term “creep” does not mean a viscous mechanism, but rather connotes a slight slip that accompanies rolling. Two extremes of particle motions bound the range of creep-friction behaviors: a pure tangential translation is modeled as a Cattaneo–Mindlin interaction, whereas prolonged steady-state rolling corresponds to the traditional wheel–rail problem described by Carter, Poritsky, and others. DEM simulations, however, are dominated by the transient creep-friction rolling conditions that lie between these two extremes. A simplified model is proposed for the three-dimensional transient creep-friction rolling of two spheres. The model is an extension of the work of Dahlberg and Alfredsson, who studied the two-dimensional interactions of disks. The proposed model is applied to two different systems: a pair of spheres and a large dense assembly of spheres. Although creep-friction can reduce the tangential contact force that would otherwise be predicted with Cattaneo–Mindlin theory, a significant force reduction occurs only when the rate of rolling is much greater than the rate of translational sliding and only after a sustained period of rolling. When applied to the deviatoric loading of an assembly of spheres, the proposed creep-friction model has minimal effect on macroscopic strength or stiffness. At the micro-scale of individual contacts, creep-friction does have a modest influence on the incremental contact behavior, although the aggregate effect on the assembly's behavior is minimal.     

Role of particle stiffness and inter-particle sliding friction in milling of particles

Discrete element method （DEM） has been used to investigate the effects of particle elastic modulus and coefficient of inter-particle sliding friction on milling of mineral particles. An autogeneous mill of 600 mm diameter and 320 mm length with 14,500 particles has been selected for the simulation. Various mill performance parameters, for example, particle trajectories, collision frequency, collision energy and mill power have been evaluated to understand the effects of particle elastic modulus and inter-particle sliding friction during milling of particles. For the given model, it has been concluded that at high energy range, as the elastic modulus and particle sliding friction increase the energy dissipated among the particles increases. The collision frequency increases with the increase in elastic modulus, however, this trend is not clearly observed with increasing inter-particle sliding friction. The power draw of the mill increases with the increase in fraction of mill critical speed.     

Discrete element modeling of inherently anisotropic granular assemblies with polygonal particles

In the present article, we study the effect of inherent anisotropy, i.e., initial bedding angle of particles and associated voids on macroscopic mechanical behavior of granular materials, by numerical simulation of several biaxial compression tests using the discrete element method (DEM). Particle shape is considered to be irregular convex-polygonal. The effect of inherent anisotropy is investigated by following the evolution of mobilized shear strength and volume change during loading. As experimental tests have already shown, numerical simulations also indicate that initial anisotropic condition has a great influence on the strength and deformational behavior of granular assemblies. Comparison of simulations with tests using oval particles, shows that angularity influences both the mobilized shear strength and the volume change regime, which originates from the interlocking resistance between particles.     

基于离散元法的干湿颗粒系统仿真

介绍了基于离散元法的干湿颗粒系统仿真软件DEMSIM。对于干颗粒系统,DEMSIM可以分析二维和三维颗粒系统的弹性和塑性接触碰撞过程;对于湿颗粒系统,DEMSIM采用传统的液桥模型;对于颗粒-流体系统,DEMSIM采用CFD-DEM细观耦合模型模拟。一系列典型算例的模拟分析,验证了干湿颗粒系统仿真软件DEMSIM的精度和有效性。     

基于离散单元法和人工神经网络的近壁颗粒动力学特征研究

颗粒与壁面的相互作用往往对颗粒流动具有显著影响. 为研究颗粒与壁面作用机理, 对滚筒内颗粒流动过程进行离散单元法(DEM)数值模拟. 基于模拟结果统计分析靠近壁面处颗粒的运动特征, 结果表明, 小摩擦系数时颗粒平动和旋转速度均近似满足正态分布, 但由于壁面影响, 摩擦系数增大时颗粒沿滚筒轴向的旋转速度偏离正态分布, 颗粒动力学理论推导壁面边界条件时应考虑速度正态分布的修正及速度脉动的各向异性. 采用人工神经网络(ANN)构建了颗粒无因次旋转温度、滑移速度和平动温度之间的函数模型, 进而可以在常规双流模型壁面边界条件中考虑颗粒旋转的影响. 基于DEM模拟及结果分析可以为壁面边界条件的理论构造和半经验修正提供基础数据和封闭模型.