On Discretization Effects within Particle Representations of Massive Forming Processes

Particle methods can be used for the simulation of large deformations under large deformation rates which are e.g. characteristic for massive forming processes. Particles' dynamics have to be carefully chosen in order to describe heat and heat flows in a correct thermodynamic way. In the following, mesoscopic particle systems are used, which solve this problem by using internal variables and in addition so-called hidden mechanical degrees of freedom ( [1], [2]). Another problem of particle methods is the influence of a symmetric discretization of the continuum on the shear planes and yielding. An appropriate interpretation of the simulation results requires a differentiation into physical phenomena and those resulting from the discretization. These circumstances and possible correctives are shown using some examples. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variational multirate integration in multi-body dynamics

For systems that contain slow and fast dynamics, variational multirate integration schemes are used. These schemes split the system into parts which are simulated using two time grids consisting of micro and macro nodes. This formulation can be extended for multi-body systems. The rigid multi-body system is described by the so called director formulation and constraints describing the joints connecting the bodies. With the Lagrange multiplier method, the constraints are introduced into the equations of motion. A way to implement the null space method into the variational multirate framework is shown and the influence on the number of unknowns is investigated. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computation of Screening Phenonema in a Vertical Tumbling Cylinder

Granular materials are an integral part of our environment. Due to their wide variety of applications in industrial and technological processes, they have captured a great interest in the recent research, see [1] and [2]. The related studies are often based on numerical simulations and it is considered as challenging to investigate computational phenomena of dense granular systems. Particle screening is an essential technology in many industrial fields and important in granular studies. The particular problem of interest is the separation of round shape particles of different geometrical sizes using a rotating tumbling vertical cylinder. The concept of discrete element method (DEM) that considers the motion of each single particle individually is applied in this study. Particle-to-particle and particle-to-wall collisions will appear under the tumbling motion of the rotating structure. The normal and frictional forces between particles themselves and particles and surrounding walls of the structure are calculated according to the rules of a penalty method, which employs spring-damper models for this purpose. As a result of collisions, the particles will dissipate kinetic energy due to the normal and frictional contact losses. Particle distribution and sifting rate of the separated particles have been studied taking into consideration different rotational speeds of the machine, various damping and frictional coefficients and different sizes of holes in the sifting plates at different levels of the structure. In an attempt to better understand the mechanism of the particle transport between the different layers of the sifting system, different computational studies have been performed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A numerical method to compute the dissolution of second phases in ternary alloys

Dissolution of stoichiometric multi-component particles in ternary alloys is an important process occurring during the heat treatment of as-cast aluminium alloys prior to hot extrusion. A mathematical model is proposed to describe such a process. In this model an equation is given to determine the position of the particle interface in time, using two diffusion equations which are coupled by nonlinear boundary conditions at the interface. Some results concerning existence, uniqueness, and monotonicity are given. Furthermore, for an unbounded domain an analytical approximation is derived. The main part of this work is the development of a numerical solution method. Finite differences are used on a grid which changes in time. The discretization of the boundary conditions is important to obtain an accurate solution. The resulting nonlinear algebraic system is solved by the Newton-Raphson method. Numerical experiments illustrate the accuracy of the numerical method. The numerical solution is compared with the analytical approximation.     

Comparison of non-cohesive resolved and coarse grain DEM models for gas flow through particle beds

The Discrete Element Method (DEM) is a widely used approach for modelling granular systems. Currently, the number of particles which can be tractably modelled using DEM is several orders of magnitude lower than the number of particles present in common large-scale industrial systems. Practical approaches to modelling such industrial system therefore usually involve modelling over a limited domain, or with larger particle diameters and a corresponding assumption of scale invariance. These assumption are, however, problematic in systems where granular material interacts with gas flow, as the dynamics of the system depends heavily on the number of particles. This has led to a number of suggested modifications for coupled gas–grain DEM to effectively increase the number of particles being simulated. One such approach is for each simulated particle to represent a cluster of smaller particles and to re-formulate DEM based on these clusters. This, known as a representative or ‘coarse grain’ method, potentially allows the number of virtual DEM particles to be approximately the same as the real number of particles at relatively low computational cost. We summarise the current approaches to coarse grain models in the literature, with emphasis on discussion of limitations and assumptions inherent in such approaches. The effectiveness of the method is investigated for gas flow through particle beds using resolved and coarse grain models with the same effective particle numbers. The pressure drop, as well as the pre and post fluidisation characteristics in the beds are measured and compared, and the relative saving in computational cost is weighed against the effectiveness of the coarse grain approach. In general, the method is found perform reasonably well, with a considerable saving of computational time, but to deviate from empirical predictions at large coarse grain ratios.     

Evaluation of Different Methods to Compute Excitation Signals Based on Measured Targets in Agricultural Machines

Basis for a strength calculation of a mechanical system is the knowledge of the outer excitation. In the case of agricultural machines it is either not possible or financially not affordable to measure such variables directly at the wheels. Therefore, measureable output parameters are defined as targets and they are used to calculate the input variables in an inverse process. Trailed agricultural machines are characterized by nonlinearities like complex tires, bearing slackness or elasticity of hydraulic components. All these phenomena have to be included in a MBS (multi-body simulation) in order to describe the behaviour of the real system. As shown in this paper, the results of a test track can be reproduced with a model consisting of rigid and flexible bodies. The excitation signals can be calculated in different ways. A well known method and a new approach are evaluated. By using mathematical methods in combination with a virtual test rig, time and costs can be reduced compared to a real test rig. Another advantage is that inner variables can be calculated, which cannot be taken out from the physical system. Key words: virtual test rig, virtual iteration, multi-body simulation, inverse problem (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

胶体有效粘滞系数的理论研究

胶体是自然界和工业应用中的常见对象。胶体领域的一个中心理论问题是如何根据胶体系统的微结构来确定胶体的流变性质。由于处理多粒子系统边值问题的困难,现有的胶体理论都局限于低颗粒浓度。该文中发展了变换场方法,用该方法可以计算含胶体颗粒的不可压缩粘滞流体的有效粘滞系数,颗粒可以是固体也可以是流体。在低颗粒浓度,该理论预测与爱因斯坦关于悬浮体的公式以及Taylor关于乳浊液的公式完全吻合。在高颗粒浓度,该文的结果与Nunan和Keller的结果相一致,其方法可以用于预测非球形颗粒悬浮体的有效粘滞系数。     

Coalescing systems of non-Brownian particles

A well-known result of Arratia shows that one can make rigorous the notion of starting an independent Brownian motion at every point of an arbitrary closed subset of the real line and then building a set-valued process by requiring particles to coalesce when they collide. Arratia noted that the value of this process will be almost surely a locally finite set at all positive times, and a finite set almost surely if the initial value is compact: the key to both of these facts is the observation that, because of the topology of the real line and the continuity of Brownian sample paths, at the time when two particles collide one or the other of them must have already collided with each particle that was initially between them. We investigate whether such instantaneous coalescence still occurs for coalescing systems of particles where either the state space of the individual particles is not locally homeomorphic to an interval or the sample paths of the individual particles are discontinuous. We give a quite general criterion for a coalescing system of particles on a compact state space to coalesce to a finite set at all positive times almost surely and show that there is almost sure instantaneous coalescence to a locally finite set for systems of Brownian motions on the Sierpinski gasket and stable processes on the real line with stable index greater than one.     

A numerical study of two coaxial axi-symmetric particles undergoing steady equal rotation in the slip regime

The problem of two axi-symmetric particles (separated by a certain distance) that rotate about their common axis of symmetry in an infinite viscous fluid with slip boundary conditions at their surfaces have been studied numerically. Aerosol particles are usually nonspherical with the exception of liquid droplets in certain cases, and the shape of particles has a significant impact on frictional drag (for particle translation) and torque (for particle rotation), and, hence, on Brownian motion, and the deposition, sampling and coagulation of particles. The effects of the rotation of particles prior to their collision and coagulation have usually been ignored in favor of simpler calculations. The study of two-particle systems should give more information about the interaction between particles that cannot be understood from the study of single particles alone. In this work, the Laplace equation (resulting from the steady Stokes equation) with slip boundary conditions is converted into a Fredholm integral equation of the second kind via the use of Green's function. The integral equations are then solved by the singularity subtraction method. The local stresses are calculated at each nodal point and the torques are then calculated from the summation of the local stresses. Explicit numerical results for the local stresses and torques are reported for three systems of two axi-symmetric particles, i.e. sphere-sphere, sphere-spheroid, and spheroid-spheroid. While the formulation of the problem is quite general, the results reported here have been limited to calculations for systems in which both particles have identical angular velocities. The numerical method is, however, valid for arbitrary axi-symmetric particles and its modification to systems containing other shaped particles or differing angular velocities is straightforward. Numerical results of the torques for each system studied show in every case that the presence of slip results in a reduction in the torques. As a consequence, the impact of the slip on the torques and local stresses is substantial and cannot be ignored. The distance between the centers of the particles (the separation distance) also plays an important role in determining the values of the torques and local stresses. In the systems that have been studied here, as the particles get further apart, the torques on both particles increase.     

A test problem for molecular dynamics integrators

We derive a test problem for evaluating the ability of time-steppingmethods to preserve the statistical properties of systems inmolecular dynamics. We consider a family of deterministic systemsconsisting of a finite number of particles interacting on acompact interval. The particles are given random initial conditionsand interact through instantaneous energy- and momentum-conservingcollisions. As the number of particles, the particle density,and the mean particle speed go to infinity, the trajectory ofa tracer particle is shown to converge to a stationary Gaussianstochastic process. We approximate this system by one describedby a system of ordinary differential equations and provide numericalevidence that it converges to the same stochastic process. Wesimulate the latter system with a variety of numerical integrators,including the symplectic Euler method, a fourth-order Runge-Kuttamethod, and an energyconserving step-and-project method. Weassess the methods' ability to recapture the system's limitingstatistics and observe that symplectic Euler performs significantlybetter than the others for comparable computational expense.     

Numerical simulation of dynamic sand dunes

The physics of granular materials is interesting from many points of view because they exhibit a wealth of phenomena that have both fluid and solid aspects [C.S. Campbell, Annu. Rev. Fluid. Mech. 22 (1990) 57, H.M. Jaeger, S.R. Nagel, R.P. Behringer, Phys. Today 494 (1996) 32]. Recently a difficult pattern was observed if sand falls in the space between two plates and passes an obstacle [Y. Amarouchene, J.F. Boudet, H. Kellay, Phys. Rev. Lett. 86 (2001) 4286]. The interesting behaviour occurs on top of the obstacle where a dynamic dune with a parabolic tip is formed. Inside this parabola, a triangular region of non- or very slow flowing sand is observed. Using factor analysis it is possible to extract latent parameters from a dynamic process. Applying a three factor model we can clearly identify the inner triangle (1st factor) and the outer parabolic pattern (3rd factor). The second factor we interpret as shock wave. Most interactions between particles take place in a relatively small region. We show that the pattern formation process depends on the restitution coefficients (particle–particle and particle–obstacle) and also on the particle size. These findings cannot be observed if standard velocity profiles are used to analyse the data. Our findings show, that most interactions take place in a relatively small area correlating with the particle size. If the interactions between different particles and particle–obstacle are elastic the formation of a non-flowing triangular region is more difficult as if inelastic collisions are used. The factor curves also clearly show that a pattern formation process has to be finished, before the next pattern can be formed.     

Modal analysis reduction of multi-body systems with generic damping

Modal analysis of multi-body systems is broadly used to study the behavior and controller design of dynamic systems. In both cases, model reduction that does not degrade accuracy is necessary for the efficient use of these models. Previous work by the author addressed the reduction of modal representations by eliminating entire modes or individual modal elements (inertial, compliant, resistive). In that work, the bond graph formulation was used to model the system and the modal decomposition was limited to systems with proportional damping. The objective of the current work is to develop a new methodology such that model reduction can be implemented to modal analysis of multi-body systems with non-proportional damping that were not modeled using bond graphs. This extension also makes the methodology applicable to realistic systems where the importance of modal coupling terms is quantified and potentially eliminated. The new methodology is demonstrated through an illustrative example.     

NEW METHOD FOR EFFECTIVE VISCOSITY OF COLLOIDAL DISPERSIONS WITH PERIODIC MICROSTRUCTURES

1IntroductionTherheologyofcolloidaldispersionisofinterestinmanyphsicalandtechnologicalproblems,andforthisreasonithasbeenstudiedextensively,expeciallywhenthesystemcallI)edescribedbythelillearNavier-StokesequationsforincompressibleNewtonianfiuicl[1--6J.ColIoidaldispersioncanbesubdividedintotwoclasses,namely,suspensionandemulsi.I,[7'8].Asuspensionisadispersionwithfinerigidparticlessuspendedinafluid.Inanemulsion,pallidparticlesareimmersedinanotherfluid.Animportantprobleminthisfieldistodeters-f…     

两球形颗粒间横向毛细力的格子Boltzmann研究

采用以Shan-Chen多组分模型为基础的格子Boltzmann-伪固体模型对两颗粒间的浮体和浸润横向毛细力展开数值模拟研究,其中流体-固体间的相互作用及颗粒润湿性质在介观层次上采用简单形式得以充分考虑．三维测试表明,与已有理论解相比,成功再现了横向毛细力与颗粒间距的“1/L”关系,并确认了浸润横向毛细力与表面张力间的线性关系．这表明可进一步应用该模型研究横向毛细力作用下的颗粒自聚集等现象.     

Numerical computations of conductivity over agglomerated continuum percolation models

In order to clarify how the percolation theory governs the conductivities in real materials which consist of small conductive particles, e.g., nanoparticles, with random configurations in an insulator, we numerically investigate the conductivities of continuum percolation models consisting of overlapped particles using the finite difference method as a sequel of our previous article [S. Matsutani, Y. Shimosako, Y. Wang, Int. J. Mod. Phys. C 21 (2010) 709–729]. As the previous article showed the shape effect of each particle by handling different aspect ratios of spheroids, in this article we numerically show influences of the agglomeration of the particles on conductivities after we model the agglomerated configuration by employing a simple numerical algorithm which simulate an agglomerated configuration of particles by a natural parameter. We conclude that the dominant agglomeration effect on the conductivities can be interpreted as the size effect of an analyzed region. We also discuss an effect of shape of the agglomerated clusters on its universal property.     

SOIL EROSION AND DEGRADATION BASED ON SAND PARTICLES TRANSPORT CAUSED BY WIND BLOWING

Abstract In this paper, the effect of sand particles transport caused by wind blowing and its role in the land degradation and desertification process is considered. For the modeling of the 3D landscape, a grayscale height map has been used, the vegetation has been modeled using a Lindenmayer system, and the sand particles have been modeled as a 3D mesh‐free particles system. It was assumed that both the sand motion and the wind motion are incompressible continuum systems and their behavior follows the Navier–Stokes equations. To simulate the sand transport, the Navier–Stokes equations are discretized using the moving particle Semi‐implicit (MPS) method. Different types of revegetation patterns (windbreakers) have been used to show some effective measures preventing soils from erosion.     

Investigation of discrete stress distribution for dry powder compaction using Discrete Element Method and weighted Voronoi tesselation

Powder compaction of granular material plays a substantial role in the manufacturing process of ceramics industry and powder metallurgy industry. The compaction behaviour is ruled by granular flow and densification of deformable particles. Discrete element method (DEM) allows to investigate the powder compaction process numerically on the microscale by modeling the forces on the particle level and simulating the particle motion. Three-dimensional data about particle size distribution and spatial structure of the particle packing can be extracted from micro-computed tomography (µCT). An average stress tensor can be computed from DEM results, evaluating the contact forces and the distances from the particle center to the contact point with respect to an average cell volume. A weighted Voronoi tesselation of the polydisperse particle assembly is proposed for mapping a cell volume to each individual particle. With this approach all structural information of the particle system can be transferred from a discrete particle model to a heterogeneous volume model of micro-structure. Discrete stress distributions for uniaxial powder compaction are presented. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulating bistable biochemical systems by means of reactive multiparticle collision dynamics

Based on a reactive multiple particle collision method, we construct a mesoscopic dynamics model to simulate chemical system. The validity of the reactive multiple particle collision method under various conditions in a double-feedback bi-stable chemical system is studied. Then, we extend it to simulate diffusion-limited reactions with fast reaction rate in cellular environment. Using the improved method, we observe bi-stable behavior with randomly distributed reactants and spatial domain separation of opposite phases. The particle-based mesoscopic method is computationally efficient, although hydrodynamic interactions and fluctuation are both properly accounted for. Stochastic effects shown to play dominant roles in biochemical dynamics are also considered. The improved method could be used to explore a variety of reactions with disparate scale of reaction rates.     

Functional large deviations for burgers particle systems

We consider Burgers particle systems, i.e., one‐dimensional systems of sticky particles with discrete white‐noise‐type initial data (not necessarily Gaussian), and describe functional large deviations for the state of the systems at any given time. For specific functionals such as maximal particle mass, particle speed, rarefaction interval, momentum, and energy, the research was initiated by Avellaneda and E [1, 2] and pursued further by Ryan [14]. Our results extend those of Ryan and contain many other examples. © 2006 Wiley Periodicals, Inc.     

不同大小粒子之间相互作用的直接数值模拟

应用改进的拉格朗日乘子/虚拟区域算法对不同大小的两个圆形粒子在二维方槽中的沉降过程和相互作用进行了直接数值模拟,并进行了实验验证．结果表明不同大小的两个粒子在沉降过程中的相互作用可以描述为追尾、接触、旋转和分离4个过程,只有当两个粒子尺度差异很小时,才会重复进行DKT过程．在两个粒子相互作用的过程中,小粒子的运动受到大粒子的影响更剧烈一些,而相反大粒子运动包括运动轨迹和速度所受到的影响则相对较小．