颗粒流动模型研究进展

颗粒流动在自然界中和各种工业过程中广泛存在,但人们对于其机理认识的还不深入。描述颗粒运动的模型有很多,连续介质模型应用简单但准确性比较低,离散微粒学模型是近来人们研究的一个热点,以每个颗粒为考察对象,能够更准确地反应颗粒系统的性质。本文介绍了描述颗粒流动的模型,概述了各模型的理论和应用,通过对多种模型的比较可以看到,每个模型都有一定的使用范围,要更准确、更方便地描述颗粒系统的运动,还要进行深入地研究。     

A coupled SDPH–FVM method for gas‐particle multiphase flow: Methodology

This paper describes a novel methodology that combines smoothed discrete particle hydrodynamics (SDPH) and finite volume method (FVM) to enhance the effective performance in solving the problems of gas‐particle multiphase flow. To describe the collision and fluctuation of particles, this method also increases a new parameter, namely, granular temperature, according to the kinetic theory of granular flow. The coupled framework of SDPH–FVM has been established, in which the drag force and pressure gradient act on the SDPH particles and the momentum sources of drag force are added back onto the FVM mesh. The proposed technique is a coupled discrete‐continuum method based on the two‐fluid model. To compute for the discrete phase, its SDPH is developed from smoothed particle hydrodynamics (SPH), in which the properties of SPH are redefined with some new physical quantities added into the traditional SPH parameters, so that it is more beneficial for SDPH in representing the particle characteristics. For the continuum phase, FVM is employed to discretize the continuum flow field on a stationary grid by capturing fluid characteristics. The coupled method exhibits strong efficiency and accuracy in several two‐dimensional numerical simulations. Copyright © 2016 John Wiley & Sons, Ltd.     

Enhanced continua and discrete lattices for modelling granular assemblies

This article discusses the derivation of continuum models that can be used for modelling the inhomogeneous mechanical behaviour of granular assemblies. These so-called kinematically enhanced models are of the strain-gradient type and of the strain-gradient micro-polar type, and are derived by means of homogenizing the micro-structural interactions between discrete particles. By analysis of the body wave dispersion curves, the enhanced continuum models are compared to corresponding discrete lattice models. Accordingly, it can be examined up to which deformation level the continuum models are able to accurately describe the discrete particle behaviour. Further, the boundary conditions for the enhanced continuum models are formulated, and their stability is considered. It is demonstrated how to use the body wave dispersion relations for the assessment of stability.     

A particle‐based method for mechanical analyses of planar fiber‐based materials

A new discrete element model to deal with rapid deformation and fracture of flat fibrous materials is derived. The method is based on classical mechanical theories and is a combination of traditional particle dynamics and nonlinear engineering beam theory. It is assumed that a fiber can be seen as a beam that is represented by discrete particles, which are moving according to Newton's laws of motion. Damage is dealt with by fracture of fiber‐segments and fiber–fiber bonds when the potential energy of a segment or bond exceeds the critical fracture energy. This allows fractures to evolve as a result of material properties only. To validate the model, four examples are shown and compared with analytical results found in literature. Copyright © 2013 John Wiley & Sons, Ltd.     

Application of particle simulation methods to composite materials: a review

Particle simulation methods represent deformation of an object by motion of particles, and their Lagrangian and discrete nature is suitable for explicit modeling of the microstructure of composite materials. They also facilitate handling of large deformation, separation, contact, and coalescence. Mesh-free particle methods will thus be appropriate for a part of issues throughout the lifecycle of composite materials despite their high calculation cost. This study focuses on three particle simulation methods, namely, smoothed particle hydrodynamics, moving particle semi-implicit method, and discrete element method, and reviews approaches for modeling composite materials through these methods. Applicability of each method as well as advantages and drawbacks will be discussed from the viewpoint of engineering of composite materials. This reviewing study suggests capability of particle simulation methods to handle multiphysics and to predict various complex phenomena that necessitate explicit modeling of the material’s microstructure consisting of reinforcements (inclusions), matrix, and voids.     

Analytical model of thermal stresses in two- and three-component materials II

The paper deals with an analytical model of thermal stresses in isotropic solid continuum represented by periodically distributed isotropic spherical particles in an isotropic infinite matrix, with or without an isotropic spherical envelope on the particle surface. The isotropic multi-particle–(envelope)–matrix system to represent a model system regarding the analytical modelling is applicable to two and three types of two- and three-component isotropic materials, respectively. The thermal stresses as functions of microstructural parameters (particle volume fraction, particle radius, inter-particle distance, envelope thickness) originate during a cooling process as a consequence of the difference in thermal expansion coefficients. The analytical modelling based on fundamental equations of mechanics of solid continuum represents a combination of different mathematical techniques applied to the equilibrium and compatibility equations, where a solution for a radial stress, and consequently for tangential and shear stresses is obtained. Finally, as an application example, the analytical model of the thermal stresses in the multi-particle–matrix system is applied to the SiC–Si₃N₄ ceramics representing a two-component material which consists of SiC particles and Si₃N₄ matrix.     

The particle finite element method: a powerful tool to solve incompressible flows with free‐surfaces and breaking waves

Particle Methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal forces applied to it. Particle Methods may be used for both, discrete and continuous problems. In this paper, a Particle Method is used to solve the continuous fluid mechanics equations. To evaluate the external applied forces on each particle, the incompressible Navier–Stokes equations using a Lagrangian formulation are solved at each time step. The interpolation functions are those used in the Meshless Finite Element Method and the time integration is introduced by an implicit fractional‐step method. In this manner classical stabilization terms used in the momentum equations are unnecessary due to lack of convective terms in the Lagrangian formulation. Once the forces are evaluated, the particles move independently of the mesh. All the information is transmitted by the particles. Fluid–structure interaction problems including free‐fluid‐surfaces, breaking waves and fluid particle separation may be easily solved with this methodology. Copyright © 2004 John Wiley & Sons, Ltd.     

Study on a large-scale discrete element model for fine particles in a fluidized bed

The discrete element method (DEM) is widely used to comprehend complicated phenomena such as gas–solid flows. This is because the DEM enables us to investigate the characteristics of the granular flow at the particle level. The DEM is a Lagrangian approach where each individual particle is calculated based on Newton’s second law of motion. However, it is difficult to use the DEM to model industrial powder processes, where over a billion particles are dealt with, because the calculation cost becomes too expensive when the number of particles is huge. To solve this issue, we have developed a coarse grain model to simulate the non-cohesive particle behavior in large-scale powder systems. The coarse grain particle represents a group of original particles. Accordingly, the coarse grain model makes it possible to perform the simulations by using a smaller number of calculated particles than are physically present. As might be expected, handling of fine particles involving cohesive force is often required in industry. In the present study, we evolved the coarse grain model to simulate these fine particles. Numerical simulations were performed to show the adequacy of this model in a fluidized bed, which is a typical gas–solid flow situation. The results obtained from our model and for the original particle systems were compared in terms of the transient change of the bed height and pressure drop. The new model can simulate the original particle behavior accurately.     

A coupled discrete element‐finite difference approach for modeling mechanical response of fluid‐saturated porous materials

A model of fluid‐saturated poroelastic medium was developed based on a combination of the discrete element method and grid method. The developed model adequately accounts for the deformation, fracture, and multiscale internal structure of a porous solid skeleton. The multiscale porous structure is taken into account implicitly by assigning the porosity and permeability values for the enclosing skeleton, which determine the rate of filtration of a fluid. Macroscopic pores and voids are taken into account explicitly by specifying the computational domain geometry. The relationship between the stress–strain state of the solid skeleton and pore fluid pressure is described in the approximations of simply deformable discrete element and Biot's model of poroelasticity. The developed model was applied to study the mechanical response of fluid‐saturated samples of brittle material. Based on simulation results, we constructed a generalized logistic dependence of uniaxial compressive strength on loading rate, mechanical properties of fluid and enclosing skeleton, and on sample dimensions. The logistic form of the generalized dependence of strength of fluid‐saturated elastic–brittle porous materials is due to the competition of two interrelated processes, such as pore fluid pressure increase under solid skeleton compression and fluid outflow from the enclosing skeleton to the environment. Copyright © 2015 John Wiley & Sons, Ltd.     

Micro–macro homogenization of granular materials based on the average-field theory of Cosserat continuum

This paper performs further study on the micro–macro homogenization approach of granular materials (Li et al., 2010) based on the advancement of Hill’s lemma for Cosserat continuum (Liu, 2013). Firstly, the average couple stress tensor, expressed as the volume integration of quantities over the representative volume element (RVE) in the average-field theory of Cosserat continuum, is further deduced and expressed in terms of discrete quantities on the discrete particle assembly RVE of granular materials. The expression is also discussed and compared with other typical definitions of the effective couple stress tensor for granular materials in the literature. Then, rate forms of micromechanically based constitutive models consistent with different types of RVE boundary conditions are derived and discussed. Since the presented micro–macro homogenization approach is used, not only the micro–macro energy equivalence is satisfied, but also the microstructure and its evolution can be taken into account in the constitutive formulation with no need of specifying macroscopic phenomenological constitutive model.     

Coupled lattice Boltzmann method and discrete element modelling of particle transport in turbulent fluid flows: Computational issues

This paper presents essential numerical procedures in the context of the coupled lattice Boltzmann (LB) and discrete element (DE) solution strategy for the simulation of particle transport in turbulent fluid flows. Key computational issues involved are (1) the standard LB formulation for the solution of incompressible fluid flows, (2) the incorporation of large eddy simulation (LES)‐based turbulence models in the LB equations for turbulent flows, (3) the computation of hydrodynamic interaction forces of the fluid and moving particles; and (4) the DE modelling of the interaction between solid particles. A complete list is provided for the conversion of relevant physical variables to lattice units to facilitate the understanding and implementation of the coupled methodology. Additional contributions made in this work include the application of the Smagorinsky turbulence model to moving particles and the proposal of a subcycling time integration scheme for the DE modelling to ensure an overall stable solution. A particle transport problem comprising 70 large particles and high Reynolds number (around 56 000) is provided to demonstrate the capability of the presented coupling strategy. Copyright © 2007 John Wiley & Sons, Ltd.     

Hygrothermomechanical evaluation of porous media under finite deformation. Part I - finite element formulations

The coupled thermomechanical responses of fluid-saturated porous continua subjected to finite deformation are investigated. Field equations governing the transient response of the media are derived from a continuum thermodynamics mixture theory based on mass balance, momentum balance and energy balance laws as well as the Clausius-Duhem inequality. Finite element procedures for the two-dimensional response, employing updated Lagrangian formulations for the solid skeleton deformation and the weak formulations for fluid and thermal transport equations, are implemented in a fully implicit form. Temperature-dependent mechanical properties for the non-linear solid matrix, characterized by Perzyna's viscoplastic model, are assumed. An iterative scheme based on the full Newton-Raphson method is presented for simultaneously solving the coupled non-linear equations.     

Effect of size distribution on mixing of a polydisperse wet granular material in a belt-driven enclosure

We use a recently developed coupled fluid–particle discrete element model to study mixing of a wet granular material in a two dimensional setting. The particles are modeled as linearly elastic disks and are considered to be immersed in a Newtonian fluid. The fluid–particle interaction is modeled using a linear drag model under the assumption that the fluid inertia is small compared to particle inertia. The granular slurry is driven by a belt moving at constant velocity in a square cavity. In the simulations, we consider three types of size distributions: monodisperse, bidisperse with several particle size ratios, and polydisperse Gaussian distributions with several different standard deviations. Mixing is characterized using both strong and weak measures. Size segregation is observed only in the bidisperse simulations. The energy required for mixing polydisperse slurries decreases with increasing standard deviation of the particle sizes. Finally, we show the benefits of engineering certain polydisperse particle size distributions towards minimizing energy consumption.     

A nonlocal multiscale discrete‐continuum model for predicting mechanical behavior of granular materials

A three‐dimensional nonlocal multiscale discrete‐continuum model has been developed for modeling mechanical behavior of granular materials. In the proposed multiscale scheme, we establish an information‐passing coupling between the discrete element method, which explicitly replicates granular motion of individual particles, and a finite element continuum model, which captures nonlocal overall responses of the granular assemblies. The resulting multiscale discrete‐continuum coupling method retains the simplicity and efficiency of a continuum‐based finite element model, while circumventing mesh pathology in the post‐bifurcation regime by means of staggered nonlocal operator. We demonstrate that the multiscale coupling scheme is able to capture the plastic dilatancy and pressure‐sensitive frictional responses commonly observed inside dilatant shear bands, without employing a phenomenological plasticity model at a macroscopic level. In addition, internal variables, such as plastic dilatancy and plastic flow direction, are now inferred directly from granular physics, without introducing unnecessary empirical relations and phenomenology. The simple shear and the biaxial compression tests are used to analyze the onset and evolution of shear bands in granular materials and sensitivity to mesh density. The robustness and the accuracy of the proposed multiscale model are verified in comparisons with single‐scale benchmark discrete element method simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

Future continuum models for granular materials in penetration analyses

This paper presents an investigation on future continuum models for granular materials in penetration analyses. A two-dimensional discrete element method has been used to numerically simulate penetration tests on a granular ground. The stress paths of soil elements in the ground have been studied, and then used to highlight the main features of granular materials based on most-advanced knowledge in soil mechanics. The study shows that the penetration makes the soil near the penetrometer undergo a significant changes of stresses in both magnitude and direction. The soil of large deformation rate may arrive at a stress state slightly over the strength envelope obtained from conventional tests. As a result, shear dilatancy, rate-dependency, non-coaxiality and particle crushing are the four main features that future continuum models should capture for granular materials in penetration analyses.     

A nonlocal lattice particle model for J2 plasticity

In virtue of their intrinsic integro-differential formulation of underlying physical behavior of materials, discontinuous computational methods are more beneficial over continuum-mechanics-based approaches for materials failure modeling and simulation. However, application of most discontinuous methods is limited to elastic/brittle materials, which is partially due to their formulations are based on force and displacement rather than stress and strain measures as are the cases for continuous approaches. In this article, we formulate a nonlocal maximum distortion energy criterion in the framework of a lattice particle model for modeling of elastoplastic materials. Similar to the maximum distortion energy criterion in continuum mechanics, the basic idea is to decompose the energy of a discrete material point into dilatational and distortional components, and plastic yielding of bonds associated with this material point is assumed to occur only when the distortional component reaches a critical value. However, the formulated yield criterion is nonlocal since the energy of a material point depends on the deformation of all the bonds associated with this material point. Formulation of equivalent strain hardening rules for the nonlocal yield model was also developed. Compared to theoretical and numerical solutions of several benchmark problems, the proposed formulation can accurately predict both the stress-strain curves and the deformation fields under monotonic loading and cyclic loading with different strain hardening cases.