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.     

基于扩展多面体的离散单元法及其作用于圆桩的冰载荷计算

对于具有复杂几何形态的多面体单元,线性接触模型不能准确地计算不同接触模式下的作用力,且接触变形和作用力方向也不易判断.基于闵可夫斯基和(Minkowski sum)方法的扩展多面体单元能够准确描述非规则颗粒单元的几何形态,并可精确计算单元间的接触碰撞作用.该方法具有接触判断简单、计算效率高的特点.它将基本多面体和扩展球体相叠加以形成具有光滑棱边和角点的扩展多面体单元.考虑扩展多面体单元相互作用过程中角点、棱边和平面之间的不同接触模式,发展了相应的非线性黏弹性接触模型. 该接触模型将不同接触模型下的法向刚度统一表述为单元接触中接触点处等效曲率半径的函数;黏滞力和切向弹性力接触模型则借鉴球体单元非线性接触模型的处理方法. 为检验扩展多面体的可靠性,对碎冰区冰块对圆桩结构的冰载荷进行了离散元分析. 采用沃洛诺伊(Voronoi)切割算法获得了碎冰的初始随机分布状态,并考虑了海冰在运动过程中的海水浮力和拖曳力.计算表明该扩展多面体单元可描述海冰在海流拖曳下的运动过程以及圆桩结构的动冰力特性.在此基础上进一步分析了冰速和冰块尺寸对圆桩冰力的影响,并确定了冰力在圆桩上的分布规律. 最后,讨论了目前扩展多面体单元在计算冰载荷方面的局限性和改进方法.      

基于超二次曲面的非球形离散单元模型研究

通过对颗粒体系接触过程的运动学和动力学分析,建立了一种基于超二次曲面的非球形离散单元模型,该模型避免了球形接触模型描述颗粒形状的局限性,使离散单元法更接近物理事实,并在此基础上提出了计算求解模型的数值方法,实现了对复杂形状的颗粒体系的模拟计算。将所建立的数值计算方法进行了编程实现,并对模型和算法进行了算例测试,证实了本文所建立的非球形离散单元模型的可行性和正确性。测试结果表明,本文的模型能够比较准确地模拟复杂颗粒体系的真实运动,可为复杂颗粒体系的模拟研究提供一种新的数值计算方法。     

碎石料直剪实验的组合颗粒单元数值模拟

通过构造三维组合颗粒单元来描述颗粒间的互锁效应,对非规则颗粒材料的力学行为进行了离散元数值模拟,并通过碎石料的直剪实验进行了验证.该组合颗粒的质量与碎石块具有相同的概率分布特性,其几何形态则由不同数目、镶嵌尺寸、组合方位和粒径的球形颗粒进行随机构造.组合颗粒单元在局部与整体坐标之间的转动、力矩和方位关系通过四元素方法进行确定;颗粒之间的作用力采用具有Mohr-Coulomb摩擦定侓的Hertz-Mindlin 非线性接触模型,并考虑了非线性法向粘滞力的影响.在不同的法向应力下,对碎石料在直剪实验中的剪切应力和剪胀现象进行了离散元模拟,计算结果与实测结果相吻合;此外,在不同的法向应力和接触摩擦系数下,对碎石料的有效摩擦系数进行了计算和讨论.本文工作验证了组合颗粒单元在非规则颗粒材料的离散元模拟中的可行性.     

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。     

颗粒流动力学及其离散模型评述

颗粒流是由众多颗粒组成的具有内在相互作用的非经典介质流动. 自然界常见颗粒流都是密集流, 颗粒间接触形成力链, 诸多力链相互交接构成支撑整个颗粒流重量和外载荷的网络, 其局部构型及强度在外载荷下演化, 是颗粒流摩擦特性和接触应力的来源.本文介绍球形颗粒间无粘连作用时的Hertz法向接触理论和Mindlin-Deresiewicz切向接触理论. Campbell依据是否生成较为稳定的力链把颗粒流分为弹性流和惯性流两大类, 其中弹性-准静态流和惯性-碰撞流分别对应准静态流和快速流, 作为两种极端流动情况通常处理成连续体, 分别采用摩擦塑性模型和动理论予以描述, 但是表征接触力链的颗粒弹性参数并不出现这两个模型和理论框架中, 如何进一步考虑颗粒弹性参数将非常困难. 目前离散动力学方法逐渐成为复现其复杂颗粒流动现象、提取实验不可能获得的内部流动信息进而综合起来探索颗粒流问题的一种有效工具, 其真实性强于连续介质理论的描述. 软球模型对颗粒间接触力简化处理, 忽略了切向接触力对法向接触力及其加载历史的依赖, 带来了法向和切向刚度系数如何标度等更艰难的物理问题, 但由于计算强度小而广泛应用于工程问题中. 硬球模型不考虑颗粒接触变形, 因而不能描述颗粒流内在接触应变等物理机理, 仅适用于快速颗粒流, 这不仅仅是由于两体碰撞的限制. 因此基于颗粒接触力学的离散颗粒动力学模型是崭新的模型,适用于准静态流到快速流整个颗粒流态的模拟, 可以细致考虑接触形变及接触力的细节,建立更为合理的颗粒流本构关系, 进而有力的促进颗粒流这一非经典介质流动的研究.      

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。     

基于LuGre摩擦模型的接触约束法旋转柔性梁斜碰撞研究

基于接触约束法和LuGre摩擦模型对在重力场作用下作大范围旋转运动的柔性梁系统和斜坡发生含摩擦斜碰撞的动力学问题进行研究. 首先运用刚柔耦合的多体系统动力学理论对大范围运动的柔性梁进行离散化和动力学建模, 在碰撞时采用冲量动量法求出跳跃速度, 其次在法向上引入接触约束求解出碰撞力, 在切向上采用LuGre摩擦模型分两种方式求解摩擦力, 第一种是在滑动时摩擦力由摩擦系数和碰撞力计算得出, 黏滞状态下引入切向约束计算拉格朗日乘子反应实际摩擦力, 根据黏滞/滑动切换判断计算出碰撞过程摩擦力(与Coulomb摩擦模型计算摩擦力一致); 第二种根据LuGre摩擦模型摩擦系数和法向碰撞力计算其摩擦力, 从而在碰撞时无需黏滞/滑动切换, 采用相同的摩擦力计算公式. 通过与Coulomb摩擦模型对比发现, LuGre摩擦模型描述碰撞切向摩擦过程更精确, LuGre摩擦模型黏滞时建立约束方程和碰撞采用统一的摩擦力公式这两种建模方式描述的斜碰撞动力学特性没有区别, 进而说明采用法向接触约束和LuGre摩擦模型具有满足碰撞非嵌入情况、避免黏滞/滑动切换、描述摩擦力相对准确的优势.      

考虑颗粒转矩的接触网络诱发各向异性分析

颗粒材料的宏观力学行为与接触网络的组构各向异性密切相关, 根据接触点的滑动与否、转动与否和强弱力情况, 可以将颗粒间的接触系统分为不同的子接触网络. 一般而言, 不同的子接触网络在颗粒体系中的传力机制不同, 对宏观力学响应的贡献也有不同. 采用离散单元法(discrete element method, DEM)模拟了不同抗转动系数$\mu_r$下颗粒材料三轴剪切试验, 分析了剪切过程中不同子接触网络的组构张量的演变规律, 并探究了颗粒抗转动效应对子接触网络各向异性指标演变规律的影响. 研究发现: 剪切过程中转动、非转动接触的组构张量变化不是独立的, 受到颗粒间滑动与否的影响; 非滑动、强接触网络是颗粒间的主要传力结构, 非滑动接触网络的接触法向和法向接触力各向异性均随$\mu_r$的增大而增大, 其对宏观应力的贡献程度随$\mu_r$的增大而减小;强接触网络的接触法向各向异性随$\mu_r$的增大而增大, 但法向接触力各向异性随$\mu_r$的增大无明显变化, 强接触网络对宏观应力的贡献程度在不同$\mu_r$情况下均相同.      

散体系统冲击破碎的动力学分析

针对球形粒子组成的散体系统,基于离散单元法,将球形粒子离散成弹簧-球单元系统,给出了离散单元的运动方程,建立了离散单元之间的弹性力和接触力的计算模型,并用Mohr -Coulomb型破坏准则判断粒子的破碎。运用上述方法,对圆筒内由脆性材料组成的散体系统在冲击载荷下的挤压破碎过程进行了数值模拟;计算过程中,跟踪散体系统中每个粒子在不同时刻的破碎情况;分析了散体系统冲击破碎过程数值模拟结果的主要影响因素。结果显示:数值模拟过程中需综合考虑计算精度和计算时间之间的平衡;相同的计算条件下,颗粒的初始堆积方式不同,计算得到的散体系统的破碎程度不同。     

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.     

Modelling of gas–solid turbulent channel flow with non-spherical particles with large Stokes numbers

This paper describes a complete framework to predict the behaviour of interacting non-spherical particles with large Stokes numbers in a turbulent flow. A summary of the rigid body dynamics of particles and particle collisions is presented in the framework of Quaternions. A particle-rough wall interaction model to describe the collisions between non-spherical particles and a rough wall is put forward as well. The framework is coupled with a DNS-LES approach to simulate the behaviour of horizontal turbulent channel flow with 5 differently shaped particles: a sphere, two types of ellipsoids, a disc, and a fibre. The drag and lift forces and the torque on the particles are computed from correlations which are derived using true DNS.The simulation results show that non-spherical particles tend to locally maximise the drag force, by aligning their longest axis perpendicular to the local flow direction. This phenomenon is further explained by performing resolved direct numerical simulations of an ellipsoid in a flow. These simulations show that the high pressure region on the acute sides of a non-spherical particle result in a torque if an axis of the non-spherical particle is not aligned with the flow. This torque is only zero if the axis of the particle is perpendicular to the local direction of the flow. Moreover, the particle is most stable when the longest axis is aligned perpendicular to the flow.The alignment of the longest axis of a non-spherical particle perpendicular to the local flow leads to non-spherical particles having a larger average velocity compared to spherical particles with the same equivalent diameter. It is also shown that disc-shaped particles flow in a more steady trajectory compared to elongated particles, such as elongated ellipsoids and fibres. This is related to the magnitude of the pressure gradient on the acute side of the non-spherical particles. Finally, it is shown that the effect of wall roughness affects non-spherical particles differently than spherical particles. Particularly, a collision of a non-spherical particle with a rough wall induces a significant amount of rotational energy, whereas a corresponding collision with a spherical particle results in mostly a change in translational motion.     

Construction of irregular particles with superquadric equation in DEM

Non-spherical particles are widely present in industrial production, and significantly affect the macro and micro characteristics of granular materials. Although the superquadric equation can be used to construct non-spherical particles, its disadvantage is that the particle shape is geometrically symmetric and strictly convex. In this study, two composed approaches are used to describe geometrically asymmetric and concave particle shapes, including a multi-superquadric model and a poly-superquadric model. The multi-superquadric model is a combination of several superquadric elements, and can construct concave and geometrically asymmetric particle shapes.The poly-superquadric model is a combination of eight one-eighth superquadric elements, and can construct convex and geometrically asymmetric particle shapes. Both composed models are based on superquadric equations, and Newton's iterative method is used to calculate the contact force between the elements. Furthermore, superquadric elements, multi-superquadric elements,and poly-superquadric elements are applied for the formation of complex granular beds, and the influences of particle shape on the packing fraction can be successfully captured by the proposed models.     

Dynamic coupling of fluid and structural mechanics for simulating particle motion and interaction in high speed compressible gas particle laden flow

In this work, structural finite element analyses of particles moving and interacting within high speed compressible flow are directly coupled to computational fluid dynamics and heat transfer analyses to provide more detailed and improved simulations of particle laden flow under these operating conditions. For a given solid material model, stresses and displacements throughout the solid body are determined with the particle–particle contact following an element to element local spring force model and local fluid induced forces directly calculated from the finite volume flow solution. Plasticity and particle deformation common in such a flow regime can be incorporated in a more rigorous manner than typical discrete element models where structural conditions are not directly modeled. Using the developed techniques, simulations of normal collisions between two 1 mm radius particles with initial particle velocities of 50–150 m/s are conducted with different levels of pressure driven gas flow moving normal to the initial particle motion for elastic and elastic–plastic with strain hardening based solid material models. In this manner, the relationships between the collision velocity, the material behavior models, and the fluid flow and the particle motion and deformation can be investigated. The elastic–plastic material behavior results in post collision velocities 16–50% of their pre-collision values while the elastic-based particle collisions nearly regained their initial velocity upon rebound. The elastic–plastic material models produce contact forces less than half of those for elastic collisions, longer contact times, and greater particle deformation. Fluid flow forces affect the particle motion even at high collision speeds regardless of the solid material behavior model. With the elastic models, the collision force varied little with the strength of the gas flow driver. For the elastic–plastic models, the larger particle deformation and the resulting increasingly asymmetric loading lead to growing differences in the collision force magnitudes and directions as the gas flow strength increased. The coupled finite volume flow and finite element structural analyses provide a capability to capture the interdependencies between the interaction of the particles, the particle deformation, the fluid flow and the particle motion.     

Discrete element-embedded finite element model for simulation of soft particle motion and deformation

The motion and deformation of soft particles are commonly encountered and important in many applications. A discrete element-embedded finite element model (DEFEM) is proposed to solve soft particle motion and deformation, which combines discrete element and finite element methods. The collisional surface of soft particles is covered by several dynamical embedded discrete elements (EDEs) to model the collisional external forces of the particles. The particle deformation, motion, and rotation are independent of each other in the DEFEM. The deformation and internal forces are simulated using the finite element model, whereas the particle rotation and motion calculations are based on the discrete element model. By inheriting the advantages of existing coupling methods, the contact force and contact search between soft particles are improved with the aid of the EDE. Soft particle packing is simulated using the DEFEM for two cases: particle accumulation along a rectangular straight wall and a wall with an inclined angle. The large particle deformation in the lower layers can be simulated using current methods, where the deformed particle shape is either irregular in the marginal region or nearly hexagonal in the tightly packed central region. This method can also be used to simulate the deformation, motion, and heat transfer of non-spherical soft particles.     

Numerical study of the sedimentation of spheroidal particles

The gravity-driven motion of rigid particles in a viscous fluid is relevant in many natural and industrial processes, yet this has mainly been investigated for spherical particles. We therefore consider the sedimentation of non-spherical (spheroidal) isolated and particle pairs in a viscous fluid via numerical simulations using the Immersed Boundary Method. The simulations performed here show that the critical Galileo number for the onset of secondary motions decreases as the spheroid aspect ratio departs from 1. Above this critical threshold, oblate particles perform a zigzagging motion whereas prolate particles rotate around the vertical axis while having their broad side facing the falling direction. Instabilities of the vortices in the wake follow when farther increasing the Galileo number. We also study the drafting-kissing-tumbling associated with the settling of particle pairs. We find that the interaction time increases significantly for non-spherical particles and, more interestingly, spheroidal particles are attracted from larger lateral displacements. This has important implications for the estimation of collision kernels and can result in increasing clustering in suspensions of sedimenting spheroids.     

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.