Superquadric DEM-SPH coupling method for interaction between non-spherical granular materials and fluids

The research on the coupling method of non-spherical granular materials and fluids aims to predict the particle–fluid interaction in this study. A coupling method based on superquadric elements is developed to describe the interaction between non-spherical solid particles and fluids. The discrete element method (DEM) and the smoothed particle hydrodynamics (SPH) are adopted to simulate granular materials and fluids. The repulsive force model is adopted to calculate the coupling force and then a contact detection method is established for the interaction between the superquadric element and the fluid particle. The contact detection method captures the shape of superquadric element and calculates the distance from the fluid particle to the surface of superquadric element. Simulation cases focusing on the coupling force model, energy transfer, and large-scale calculations have been implemented to verify the validity of the proposed coupling method. The coupling force model accurately represents the water entry process of a spherical solid particle, and reasonably reflects the difference of solid particles with different shapes. In the water entry process of multiple solid particles, the total energy of the water entry process of multiple solid particles tends to be stable. The collapse process of the partially submerged granular column is simulated and analyzed under different parameters. Therefore, this coupling method is suitable to simulate fluid–particle systems containing solid particles with multiple shapes.     

凹形多面体离散单元的水平集函数接触算法

多面体模型理论上可构造任意颗粒形态,然而受单元接触算法的限制,仅用于凸形颗粒材料的离散元模拟。对于具有凹形特征的多面体单元,单个接触点的搜索算法难以精确计算单元间的作用力。考虑多面体单元间存在单个或多个接触点的计算特性,本文发展了适用于凸形和凹形多面体颗粒材料的水平集函数接触算法。该方法通过点-三角形单元距离计算方法和奇-偶数判定方法建立多面体单元的零水平集函数和空间水平集函数,并对水平集函数进行三线性插值,可得到多面体单元间的单个或多个接触点。为检验水平集函数接触算法的可靠性,对球形和凹形多面体颗粒材料的堆积和倒塌过程进行离散元模拟,并分析颗粒形状对堆积密度和休止角的影响规律。     

NUMERICAL CALCULATION OF LONDON-VAN DER WAALS ADHESION FORCE DISTRIBUTIONS FOR DIFFERENT SHAPED PARTICLES

A basic method to calculate van der Waals dispersion force distributions for submicron superquadric particles in particle-wall systems is presented. The force distribution is achieved by rotating particles through a large number of arbitrary spatial orientations, each time keeping constant the contact distance to the wall surface while calculating the dispersion force. To accomplish this, the use of 2D particle shape suffices, that is, through using an inter-dimensional function, which has been determined previously. A further development of the method within digital image analysis may lead to possible applications to forecasting the macroscopic properties of particle systems, for example, flowability, agglomeration behavior or dispersibility. For small ranges of superquadric particle shapes, each with a different size, the way from determining the inter-dimensional function up to applying image analysis is shown in an example.     

椭球颗粒体系剪切过程中自由体积的分布与演化

颗粒材料是一种复杂的多体相互作用体系, 由大量离散的颗粒和其周围的自由体积组成. 虽然颗粒的自由体积与颗粒材料的力学性能和变形特征的相关性已得到证实, 但是由于表征上的困难, 目前对非球形颗粒体系的局部自由体积的认识还不够充分. 本文采用连续离散耦合分析方法进行了不同主轴长度的椭球颗粒试样的三轴剪切数值模拟, 基于Set Voronoi算法对剪切过程中的颗粒试样进行了Voronoi元胞分割, 分析了颗粒试验在剪切过程中自由体积的统计分布特性和演化规律, 研究了颗粒形态对自由体积的影响. 剪切过程中Voronoi元胞的各向异性逐渐增强, 且各项异性增强程度随颗粒非球度的增加而增大, 表明非球颗粒在剪切过程中经历更加强烈的重排列. 具有不同非球度的椭球颗粒体系的局部孔隙比均服从k?Γ分布, 且这个分布仅与颗粒体系的全局孔隙比相关, 不受颗粒形态和剪切状态的影响. 局部孔隙比的波动呈现非对称拉普拉斯分布, 非对称参数刻画了局部自由体积收缩和膨胀的博弈, 其与全局孔隙比呈线性关系.      

基于水平集-离散元方法的球谐函数颗粒材料缓冲性能分析

在自然环境与工业领域中,颗粒材料是一种常见的缓冲材料,其中大量形态各异的非球形颗粒表现出复杂的力学特性并应用于不同工程领域。本文采用球谐函数构造不同球面度和表面凹凸特性的非规则颗粒,通过水平集方法计算球谐函数颗粒间的接触点和碰撞力,并对冲击过程中球形和凹形颗粒的缓冲性能进行离散元分析。数值结果表明,颗粒床厚度、冲击速度和颗粒形状显著影响球谐函数颗粒材料的缓冲性能。颗粒床底部的冲击力峰值随着颗粒床厚度和表面凹凸性的增加而降低,同时冲击力峰值随着冲击速度和颗粒球面度的增加而增加。与球形颗粒相比,球谐函数颗粒具有凹凸表面和多接触点特性,这有利于冲击荷载向四周扩展并提高凹形颗粒的缓冲效果。     

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 modified discrete element method for concave granular materials based on energy-conserving contact model

The development of a general discrete element method for irregularly shaped particles is the core issue of the simulation of the dynamic behavior of granular materials. The general energy-conserving contact theory is used to establish a universal discrete element method suitable for particle contact of arbitrary shape. In this study, three dimentional (3D) modeling and scanning techniques are used to obtain a triangular mesh representation of the true particles containing typical concave particles. The contact volume-based energy-conserving model is used to realize the contact detection between irregularly shaped particles, and the contact force model is refined and modified to describe the contact under real conditions. The inelastic collision processes between the particles and boundaries are simulated to verify the robustness of the modified contact force model and its applicability to the multi-point contact mode. In addition, the packing process and the flow process of a large number of irregular particles are simulated with the modified discrete element method (DEM) to illustrate the applicability of the method of complex problems.     

A discrete contact model for complex arbitrary-shaped convex geometries

The shape of particles has a significant influence on the behavior of suspensions, as the particle-fluid, particle-particle, and particle-wall interactions depend on it. However, the simultaneous consideration of complex particle shapes and four-way coupling remains a major challenge. This is mainly due to a lack of suitable contact models. Contact models for complex shapes have been proposed in literature, and most limit the accuracy of the particle-fluid interaction. For this reason, this paper presents a novel contact model for complex convex particle shapes for use with partially saturated methods, in which we propose to obtain necessary contact properties, such as the indentation depth, by a discretization of the contact area. The goal of the proposed model is to enable comprehensive and accurate studies of particulate flows, especially with high volume fractions, that lead to new insights and contribute to the improvement of existing industrial processes. To ensure correctness and sustainability, we validate the model extensively by studying cases with and without fluid. In the latter case, we use the homogenized lattice Boltzmann method. The provided investigations show a great agreement of the proposed discrete contact model with analytical solutions and the literature.     

Influence of particle shape on the microstructure evolution and the mechanical properties of granular materials

In order to study the influence of particle shape on the microstructure evolution and the mechanical properties of granular materials, a two-dimensional DEM analysis of samples with three particle shapes, including circular particles, triangular particles, and elongated particles, is proposed here to simulate the direct shear tests of coarse-grained soils. For the numerical test results, analyses are conducted in terms of particle rotations, fabric evolution, and average path length evolution. A modified Rowe's stress–dilatancy equation is also proposed and successfully fitted onto simulation data.     

考虑等效曲率的超二次曲面单元非线性接触模型

基于连续函数包络的超二次曲面单元可有效地描述自然界和工业生产中的非球体颗粒形态, 并通过非线性迭代方法精确计算单元间的接触力. 对于具有复杂几何形态的超二次曲面单元, 线性接触模型不能准确地计算不同接触模式下的作用力. 考虑超二次曲面单元相互作用时不同颗粒形状及表面曲率的影响, 本文发展了相应的非线性黏弹性接触模型. 该模型将不同接触模式下的法向刚度和黏滞力统一表述为单元间局部接触点处等效曲率半径的函数; 切向接触作用则借鉴基于Mohr-Coulomb摩擦定律的球体单元非线性接触模型的计算方法. 为检验超二次曲面单元接触模型的可靠性, 对球形颗粒间的法向碰撞、椭球体颗粒间的斜冲击过程、圆柱体的静态堆积和椭球体的动态卸料过程进行离散元模拟, 并与有限元数值结果及试验结果进行对比验证. 计算表明, 考虑接触点处等效曲率半径的超二次曲面非线性接触模型可准确地计算单元间的接触碰撞作用, 并合理地反映非球形颗粒体系的运动规律. 在此基础上进一步分析了不同长宽比和表面尖锐度对卸料过程中颗粒流动特性的影响, 为非球形颗粒材料的流动特性分析提供了一种有效的离散元方法.      

The effect of the beam shapes on the doubly-clamped piezoelectric energy harvester

For a piezoelectric energy harvester composed of a doubly-clamped beam with arbitrary width shapes and a proof mass, the influence of beam shapes and electrode arrangements on different electric outputs is analyzed. The output performances of piezoelectric energy harvesters with rectangular shape, concave trapezoidal shape, and concave parabolic shape are compared, and an optimization way is given. The experimental results validate the effectiveness of the methods.     

Effect of particle shape on micro- and mesostructure evolution of granular assemblies under biaxial loading conditions

Discrete element method (DEM) numerical biaxial tests on samples with different particle shapes are performed to investigate how the multiscale evolves with varying particle shape. The samples used in such simulations are composed of circular, square, and elongated particles, respectively. For the numerical results, analyses are conducted in terms of microscopic evolution, i.e. particle rotation and evolution of fabric, and mesoscopic evolution, i.e. the evolution of loops and improved clustering coefficient. At the microscale, the mean particle rotation of circular particles is remarkably larger than those of square and elongated particles, and the shear band localization phenomenon is more obvious when the aspect ratio (AR) decreases. Considering the fabric evolving with particle shape, the value of anisotropy gradually increases when particle shape becomes irregular, and contacts of circular particles are pronouncedly less than those of irregular particles from the coordination number and curves of degree distribution. At the mesoscale, when the particle relationship is considered, the isotropic particles (i.e. circular and square particles) have similar evolutions of loops and modified clustering coefficient, whereas the elongated particles have remarkable three loops and modified clustering coefficient, which are both larger than those of isotropic particles.     

Scaling granular material with polygonal particles in discrete element modeling

Despite advancements in computational resources, the discrete element method (DEM) still requires considerable computational time to solve detailed problems, especially when it comes to the large-scale models. In addition to the geometry scale of the problem, the particle shape has a dramatic effect on the computational cost of DEM. Therefore, many studies have been performed with simplified spherical particles or clumps. Particle scaling is an approach to increase the particle size to reduce the number of particles in the DEM. Although several particle scaling methods have been introduced, there are still some disagreements regarding their applicability to certain aspects of problems. In this study, the effect of particle scalping on the shear behavior of granular material is explored. Real granular particles were scanned and imported as polygonal particles in the direct shear test. The effect of particle size distribution, particle angularity, and the amount of scalping were investigated. The results show that particle scalping can simulate the correct shear behavior of the model with significant improvement in computational time. Also, the accuracy of the scalping method depends on the particle angularity and particle size range.     

Fracture of granular materials composed of arbitrary grain shapes: A new cohesive interaction model

Discrete Element Methods (DEM) are a useful tool to model the fracture of cohesive granular materials. For this kind of application, simple particle shapes (discs in 2D, spheres in 3D) are usually employed. However, dealing with more general particle shapes allows to account for the natural heterogeneity of grains inside real materials. We present a discrete model allowing to mimic cohesion between contacting or non-contacting particles whatever their shape in 2D and 3D. The cohesive interactions are made of cohesion points placed on interacting particles, with the aim of representing a cohesive phase lying between the grains. Contact situations are solved according to unilateral contact and Coulomb friction laws. In order to test the developed model, 2D uniaxial compression simulations are performed. Numerical results show the ability of the model to mimic the macroscopic behavior of an aggregate grain subject to axial compression, as well as fracture initiation and propagation. A study of the influence of model and sample parameters provides important information on the ability of the model to reproduce various behaviors.     

Prediction of segregation characterization based on granular velocity and concentration in rotating drum

In a binary granular system composed of two types of particles with different granule sizes and the same density, particle sorting occurs easily during the flow process. The segregation pattern structure is mainly affected by the granular velocity and granular concentration in the flow layer. This paper reports on the experimental velocity and concentration measurement results for spherical particles in a quasi-two-dimensional rotating drum. The relationship between the granular velocity along the depth direction of the flow layer and granular concentration was established to characterize structures with different degrees of segregation. The corresponding relationships between the granular velocity and concentration and the segregation pattern were further analyzed to improve the theoretical models of segregation (convection–diffusion model and continuous flow model) and provide a reference for granular segregation control in the production process.     

A novel interface‐tracking method based on Lagrangian particles for deformation analysis of a red blood cell in a capillary

A novel efficient interface‐tracking method is developed to gain an insight into the interface in a multiphase or multifluid system, called the modified particle binary level set (MPBLS) method, in which the binary level set function is defined to distinguish the different phases or fluids and further modified by Lagrangian particles scattered along the interface for achieving higher accuracy. The validation of the MPBLS method is carried out first by simulating the free motion of a red blood cell (RBC) in the rotating, shear and Poiseuille flows, respectively. Subsequently, further validations are performed by comparing with the experimental and numerical results published previously. As one of important applications, the MPBLS method is employed to investigate the deformation behaviors of RBCs with different shapes in a capillary. The simulations show that the healthy RBC gradually changes the geometric shape from a biconcave to a steady parachute shape. It is thus guaranteed that the RBC successfully traverses through the smaller capillaries compared with undeformed RBC. However, the unhealthy RBC with the circular or elliptical shape has different deformation behaviors, in which the steady parachute shape is much less concave at the rear and more convex in the front. Copyright © 2011 John Wiley & Sons, Ltd.     

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.      

Settling and spreading behaviour of particle clusters in quiescent liquids in confined vessels

Here we report experiments on particle cluster settling at high Reynolds number in quiescent liquid contained in a vessel. The particles were observed to spread at the vessel bottom surface in a near-circular annular shape after settling irrespective of the shape of the vessel cross-section and particle shape, size, and types. Effect of different parameters such as mass, type and aspect ratio of the particles, height, and viscosity of liquid was investigated on spreading behaviour. Formation of the hemispherical bottom cap of the cluster that bounces upon hitting the vessel bottom surface was found to be responsible for the final circular annular shape of the settled structure. Particle leakage from the cluster was seen in the form of a tail. In the liquid having viscosity beyond 100 cP, cluster breakage was observed that resulted in hindered settling and asymmetric shapes of finally settled particles. The observations are useful to understand the overall area over which settling and spreading of such clusters can be observed.     

Generalized closed-form model for analysis of asymmetric shaped charges

This paper presents a model that has less constraints than similar models and explains the collapse phenomenon in any desired order of geometrical asymmetries and in the presence of symmetric and asymmetric general-form wave fronts. It seems that, in this model, a complete generalized form of the classical jet formation theory has been developed. Available models that describe the symmetric jet and slug formation phenomenon are very good in such conditions. But the liner and confinement asymmetries, detonation wave front asymmetries, and other specifications, such as manufacturing tolerances, can affect the collapse and the behavior of the jet and slug. Some proposed models that describe asymmetric cases are not closed-form models or are only applicable for limited conditions, such as small asymmetries and a planar wave front. With the presented model, effects of concave, plane, and convex wave fronts on the off-axis velocity of the jet, other parameters of the jet and slug, and effects of an asymmetric wave front on jet formation for a completely symmetric liner and confinement geometry can be evaluated.     

Particle shape consideration in numerical simulation of assemblies of irregularly shaped particles

The mechanical behavior of granular materials depends much on the shape of the constituent particles. Therefore appropriate modeling of particle, or grain, shape is quite important. This study employed the method of direct modeling of grain shape (Matsushima & Saomto, 2002), in which, the real shape of a grain is modeled by combining arbitrary number of overlapping circular elements which are connected to each other in a rigid way. Then, accordingly, a discrete-element program is used to simulate the assembly of grains. In order to measure the effects of grain shape on mechanical properties of assembly of grains, three types of grains—high angular grains, medium angular grains and round grains are considered where several biaxial tests are conducted on assemblies with different grain types. The results show that the angularity of grains greatly affects the behavior of granular soil.