Analysis of instantaneous dynamic states of vibrated granular materials

The behavior of granular materials subjected to continuous vertical vibrations is dependent on a variety of factors, including how energetically the containment vessel is shaken as well as particle properties. Motivation for the investigation reported here is based on phenomenon in which bulk solids attain an increase in density upon relaxation. The results of a detailed, discrete element study designed to examine the dynamic state of a granular material is presented, in which particles are represented as inelastic, frictional spheres. The phase in which the assembly finds itself immediately before vibrations are stopped is quantified by computing depth profiles of the translational energy ratio R in conjunction with profiles of solids fraction ν and granular temperature T. The use of particles that are more frictional tends to hinder or delay thermalization, while particle restitution coefficient plays a role when the flow is collision dominated. The structure before vibrations are applied plays an important role in determining the depth profiles and the phase pattern only at low accelerations. On the other hand, large accelerations can easily dislodge the poured configuration very quickly so that the initial condition is not major factor in the phase pattern.     

On flows of granular materials

This article reviews the behavior of materials made up of a large assemblage of solid particles under rapid and quasi static deformations. The focus is on flows at relatively high concentrations and for conditions when the interstitial fluid plays an insignificant role. The momentum and energy exchange processes are then primarily governed by interparticle collisions and Coulomb-type frictional contact. We first discuss some physical behavior —dilatancy, internal friction, fluidization and particle segregation — that are typical to the understanding of granular flows. Bagnold's seminal Couette flow experiments and his simple stress analysis are then used to motivate the first constitutive theories that use a microstructural variable — the fluctuation energy or granular temperature — governing the subscale fluctuating motion. The kinetic theories formalize the derivation of the field equations of bulk mass, momentum and energy, and permit derivation of constitutive relations for stress, flux of fluctuation energy and its dissipation rate for simple particle assemblages and when frictional rubbing contact can be ignored. These statistical considerations also show that formulation of boundary conditions needs special attention. The frictional-collisional constitutive behavior in which both Coulomb-type rubbing contact and collisional encounters are significant are discussed. There is as yet no rigorous formulation. We finally present a phenomenological approach that describes rapid flows of granular materials under simultaneous transport of heat and close with a summary of stability analyses of the basic flow down an inclined plane.Dedicated to Professor Dr.-Ing. Franz Gustav Kollmann on the occasion of his sixtieth brithday     

Shear bands in dense metallic granular materials

In this paper, the phenomenon of strain localization, i.e., shear banding, in densely distributed metallic assemblies has been studied. A discrete element methodology for analyzing metallic granular materials has been put forward. In this numerical model, elastoplastic contact, as well as friction, rolling resistance and cohesion between spheres, are explicitly taken into account. The calculations reveal that the shear banding mechanism in dense assemblies can be thought as an instability triggered by initial imperfections. Within a band, the motion, deformation and rearrangement of spheres soften the resistance of the aggregate, as these mechanisms create additional geometric imperfections. Additionally, the simulations showed that the shear-band width does not change conclusively with the friction, rolling resistance and plasticity parameters. However, cohesive strength, even in small amounts, drastically increased the shear-band width. Finally, the shear-band thickness and inclination angles are strongly dependent on the degree of initial imperfection. Whereas for a perfect assembly the shear band inclinations were consistently around 60°, more heterogeneous assemblies lead to shear band angles closer to the continuum mechanics solution, which is 45°. This was found to be in agreement with recent experimental observations.     

Shock waves in dense granular flows down a chute

Large scale, three dimensional computer simulations of monosized, viscoelastic, spherical glass particles flowing in an inclined duct were performed using a phenomenological model based on the modified Kelvin–Maxwell model. The particle flow rate in the model duct was regulated using a stationary wedge located in the middle of the duct. At low flow rates of glass particles, a continuous flow was observed similar to that excited by steadily and rapidly adding glass particles to the top of a heap. However, at high flow rates, a totally different situation arises where a flow with a different nature was established in the duct. The situation was found to be analogous to the case of a supersonic gas flow in a duct, where a curved-bow shock was observed to have formed on the upper edges of the duct adjacent to the wedge. In addition, in supersonic granular flows the viscous and conductance effects spread the shock changes over a finite shock layer.     

密集颗粒物质的介观结构

密集颗粒物质由大量颗粒组成的多体相互作用体系,在一定条件下,颗粒互相连接,形成相对稳定的介观尺度结构,其几何和动力学性质较大程度上决定了颗粒体系的宏观物理和力学性质,因此开展颗粒的介观结构研究具有重要的理论价值,是科学的前沿之一.自然界的堆石坝、堰塞体和碎屑流,以及工程中的高温气冷堆堆芯颗粒流和先进核裂变能系统(ADS嬗变)的颗粒散裂靶等都是典型的颗粒体系,研究颗粒体系宏观力学性质是灾害预测和调控技术的关键.本文首先介绍颗粒接触力理论和简化模型的研究进展,接着介绍介观尺度结构分析方法与测量技术,颗粒体系Jamming转变、软点和颗粒微位移测量技术等,最后列举了几个关键的科学问题.颗粒介质中很多基本力学问题的解决需要借鉴物理和数学等学科的最新成果,建立新的概念和范式,从新的角度、思路、理念去认识颗粒介质的基本问题.同时,颗粒介质的基础研究还要紧密结合工程应用领域的大量相关的核心技术,与工程领域专家共同合作,使得颗粒介质的研究有的放矢,更具生命力.     

The mesoscopic structures of dense granular materials

密集颗粒物质由大量颗粒组成的多体相互作用体系,在一定条件下,颗粒互相连接,形成相对稳定的介观尺度结构,其几何和动力学性质较大程度上决定了颗粒体系的宏观物理和力学性质,因此开展颗粒的介观结构研究具有重要的理论价值,是科学的前沿之一.自然界的堆石坝、堰塞体和碎屑流,以及工程中的高温气冷堆堆芯颗粒流和先进核裂变能系统（ADS嬗变）的颗粒散裂靶等都是典型的颗粒体系,研究颗粒体系宏观力学性质是灾害预测和调控技术的关键.本文首先介绍颗粒接触力理论和简化模型的研究进展,接着介绍介观尺度结构分析方法与测量技术,颗粒体系Jamming转变、软点和颗粒微位移测量技术等,最后列举了几个关键的科学问题.颗粒介质中很多基本力学问题的解决需要借鉴物理和数学等学科的最新成果,建立新的概念和范式,从新的角度、思路、理念去认识颗粒介质的基本问题.同时,颗粒介质的基础研究还要紧密结合工程应用领域的大量相关的核心技术,与工程领域专家共同合作,使得颗粒介质的研究有的放矢,更具生命力.     

Mixing in horizontally heterogeneous flows

An experimental study of mixing across density interfaces produced by laterally heterogenous turbulence is presented in this paper. The turbulence is generated by a flow or air bubles rising through a density interface produced by brine and fresh water. The mixing efficiency, , of the process is measured comparing the increase in potential energy with the available kinetic energy. We find that there is a decrease in the global mixing efficiency of the process with the length of the tank, the shape of (Ri) depends also on the air flow producing the turbulence, showing a geometrical limit to the ammount of kinetic energy which may be used for mixing.     

A kinetic model for rapid flows of granular materials

A kinetic model for rapid flows of granular material is considered. An evolution equation for the first order distribution function is developed which includes the effects of intergranular friction force in an average sense. The collision operator is approximated by the BGK relaxation model. The fundamental equations of motion including an equation for dynamics of the fluctuation energy are derived and discussed. The gravity and the plane Couette flows of granular materials are treated as examples of the applications of the present theory.     

Swirling flows in circular-to-rectangular transition ducts

Miniature axisymmetric supersonic nozzles were produced with exit Mach numbers ranging from 1.0 to 2.8 by forming Pyrex^® capillary tubing of 0.6 and 1.2 mm inside diameter into converging-diverging channels. The nozzle contours were measured and were found to compare favorably to ideal solutions given by the axisymmetric method of characteristics. In addition, the surfaces of these nozzles were quite smooth, providing featureless flows at perfect expansion. Schlieren visualization and pitot pressure measurements of the resulting microjets were compared to the literature available for jets produced by larger-scale nozzles. A postponed transition to turbulence is noted in these microjets due to their low Reynolds number. The pitot pressure on centerline is nearly uniform at perfect expansion over core lengths up to 12 nozzle exit diameters. Supersonic microjet nozzles thus provide a more effective small-scale high-pressure gas delivery device than do sonic nozzles of comparable scale at equivalent mass flow rates. Supersonic microjets may therefore have several industrial applications.List of symbols ^* boundary layer displacement thickness, mm - d diameter of nozzle exit, mm - L length of nozzle diverging section, mm - L _c inviscid core length, mm - L _s supersonic region length, mm - M _c convective Mach number - M _e exit Mach number - P _b backpressure at nozzle exit, (equal to ambient pressure in this experiment) - P _e exit pressure of the supersonic jet - P _be exit pressure ratio (P _b /P _e ) - P _p impingement pressure (pitot pressure) - P ₀ stagnation pressure supplied to nozzle - P _n overall pressure ratio (P ₀/P _b ,) - r radial dimension (cylindrical coordinate system), mm - r ₀ radius of throat, mm - Re _d Reynolds number, based on nozzle exit diameter - V _e exit velocity, m/s - x axial dimension (cylindrical coordinate system), mm This research was sponsored by National Science Foundation Grant DMI 9400119, as part of a study of the assist-gas dynamics of laser cutting.     

Topological evolution in dense granular materials: A complex networks perspective

One of the great challenges in the science of complex materials – materials capable of emergent behavior such as self-organized pattern formation – is deciphering their “inherent” structural design principles as they deform in response to external loads. We have been exploring the efficacy of techniques from complex networks to the study of dense granular materials as a means to: (i) uncover such design principles and (ii) identify suitable metrics that quantify the evolution of structure during deformation. Herein, we characterize the developing network structure and loss of connectivity in a quasistatically deforming granular medium from the perspective of complex networks. Attention is paid to the evolution of the contact and contact force networks at the local or mesoscopic level, i.e., a particle and its immediate neighbors, as well as the macroscopic level. We explore network motifs and other topological properties at these multiple length scales, in an attempt to find that which best correlates with the constitutive properties of nonaffine deformation and dissipation, spatially and with respect to strain. Key processes or rearrangement events that cause loss of connectivity within the material domain, e.g. microbanding and force chain buckling, are investigated. Network statistics of these processes, previously shown to be major sources of energy dissipation and nonaffine deformation, are then tied to corresponding trends observed in the evolving macroscopic network. It is shown that consideration of the unweighted contact network alone is insufficient to tie dissipation to loss of material connectivity.     

密集颗粒体系的颗粒运动及结构测量技术

颗粒材料由大量粗颗粒堆积形成, 是复杂的多体相互作用体系, 呈现出颗粒尺度的结构不均匀和动力学不均匀性的基本特征, 这决定了颗粒材料具有很多独特的宏观性质. 借鉴学科历史的发展途径, 基于统计力学, 从颗粒结构和动力学开始建立颗粒材料体系的宏观连续介质力学理论框架是必然途径.但是, 颗粒材料的基本特征决定了从基本理论到实验手段上, 表征与建立颗粒材料结构与性能的相关性都极其困难.这是由于现有测试分析手段所描述的颗粒系统组织结构过于简单化, 缺乏对颗粒结构和动力学的真正认识, 从而制约了颗粒物质研究的发展.因此, 开展颗粒体系结构和动力学性质的测量, 是理解和认识颗粒材料重要物理和力学问题的基础和依据.笔者来自不同的科研院所, 近十年来开展了颗粒体系结构和动力学性质的测量研究, 主要集中于以下两个方向: (1)数字图像测速法、散斑能见度光谱法和X射线- CT等非侵入式测量技术在颗粒运动方面的应用; (2)体积响应谱、力学谱(有效质量和内耗等)和声速测量技术等直接或间接测量颗粒接触力和颗粒结构技术.本文综述了这些实验手段的基本原理及其特点、取得的主要成果, 以及国际最新进展和困难. 最后是对全文的总结, 结合笔者开展测量的经验和教训, 提出了自己的看法, 并试图展望颗粒材料测量技术研究的前景.      

Measurement techniques of grain motion and inter-grain structures in dense granular materials

颗粒材料由大量粗颗粒堆积形成, 是复杂的多体相互作用体系, 呈现出颗粒尺度的结构不均匀和动力学不均匀性的基本特征, 这决定了颗粒材料具有很多独特的宏观性质. 借鉴学科历史的发展途径, 基于统计力学, 从颗粒结构和动力学开始建立颗粒材料体系的宏观连续介质力学理论框架是必然途径.但是, 颗粒材料的基本特征决定了从基本理论到实验手段上, 表征与建立颗粒材料结构与性能的相关性都极其困难.这是由于现有测试分析手段所描述的颗粒系统组织结构过于简单化, 缺乏对颗粒结构和动力学的真正认识, 从而制约了颗粒物质研究的发展.因此, 开展颗粒体系结构和动力学性质的测量, 是理解和认识颗粒材料重要物理和力学问题的基础和依据.笔者来自不同的科研院所, 近十年来开展了颗粒体系结构和动力学性质的测量研究, 主要集中于以下两个方向: (1)数字图像测速法、散斑能见度光谱法和X射线- CT等非侵入式测量技术在颗粒运动方面的应用; (2)体积响应谱、力学谱(有效质量和内耗等)和声速测量技术等直接或间接测量颗粒接触力和颗粒结构技术.本文综述了这些实验手段的基本原理及其特点、取得的主要成果, 以及国际最新进展和困难. 最后是对全文的总结, 结合笔者开展测量的经验和教训, 提出了自己的看法, 并试图展望颗粒材料测量技术研究的前景.     

Structural stability and jamming of self-organized cluster conformations in dense granular materials

We examine emergent, self-organized particle cluster conformations in quasistatically deforming dense granular materials from the perspective of structural stability. A structural mechanics approach is employed, first, to devise a new stability measure for such conformations in equilibrium and, second, to use this measure to explore the evolving stability of jammed states of specific cluster conformations, i.e. particles forming force chains and minimal contact cycles. Knowledge gained on (a) the spatial and temporal evolution of stability of individual jammed conformations and (b) their relative stability levels, offer valuable clues on the rheology and, in particular, self-assembly of granular materials. This study is undertaken using data from assemblies of nonuniformly sized circular particles undergoing 2D deformation in two biaxial compression tests: a discrete element simulation of monotonic loading under constant confining pressure, and cyclic loading of a photoelastic disk assembly under constant volume. Our results suggest that the process of self-assembly in these systems is realized at multiple length scales, and that jammed force chains and minimal cycles form the basic building blocks of this process. In particular, 3-cycles are stabilizing agents that act as granular trusses to the load-bearing force chain columns. This co-evolutionary synergy between force chains and 3-cycles proved common to the different materials under different loading conditions. Indeed, the remarkable similarities in the evolution of stability, prevalence and persistence of minimal cycles and force chains in these systems suggest that these structures and their co-evolution together form a generic feature of dense granular systems under quasistatic loading.     

A spectral approach for the stability analysis of turbulent open-channel flows over granular beds

A novel Orr–Sommerfeld-like equation for gravity-driven turbulent open-channel flows over a granular erodible bed is here derived, and the linear stability analysis is developed. The whole spectrum of eigenvalues and eigenvectors of the complete generalized eigenvalue problem is computed and analyzed. The fourth-order eigenvalue problem presents singular non-polynomial coefficients with non-homogenous Robin-type boundary conditions that involve first and second derivatives. Furthermore, the Exner condition is imposed at an internal point. We propose a numerical discretization of spectral type based on a single-domain Galerkin scheme. In order to manage the presence of singular coefficients, some properties of Jacobi polynomials have been carefully blended with numerical integration of Gauss–Legendre type. The results show a positive agreement with the classical experimental data and allow one to relate the different types of instability to such parameters as the Froude number, wavenumber, and the roughness scale. The eigenfunctions allow two types of boundary layers to be distinguished, scaling, respectively, with the roughness height and the saltation layer for the bedload sediment transport.     

Investigation of proper modeling of very dense granular flows in the recirculation system of CFBs

The aim of this paper is the development of new models and/or the improvement of existing numerical models, used for simulating granular flow in CFB (circulating fluidized bed) recirculation systems. Most recent models follow the TFM (two-fluid model) methodology, but they cannot effectively simulate the inter-particle friction forces in the recirculation system, because the respective stress tensor does not incorporate compressibility of flow due to change of effective particle density. As a consequence, the induced normal and shear stresses are not modeled appropriately during the flow of the granular phase in the CFB recirculation system. The failure of conventional models, such as that of von Mises/Coulomb, is mainly caused by false approximation of the yield criterion which is not applicable to the CFB recirculation system. The present work adopts an alternative yield function, used for the first time in TFM Eulerian modeling. The proposed model is based on the Pitman–Schaeffer–Gray–Stiles yield criterion. Both the temporal deformation of the solid granular phase and the repose angle that the granular phase forms are more accurately simulated by this model. The numerical results of the proposed model agree well with experimental data, implying that frictional forces are efficiently simulated by the new model.     

Nonequilibrium identities of granular vibrating beds

We derive the integral fluctuation theorem around a nonequilibrium stationary state for frictionless and soft core granular particles under an external vibration achieved by a balance between an external vibration and inelastic collisions. We also derive the standard fluctuation theorem and the generalized Green–Kubo formula for this system.     

Particle dynamics in dense shear granular flow

The particle dynamics in an annular shear granular flow is studied using the discrete element method, and the influences of packing fraction, shear rate and friction coefficient are analyzed. We demonstrate the existence of a critical packing fraction exists in the shear granular flow. When the packing fraction is lower than this critical value, the mean tangential velocity profile exhibits a rate-independent feature. However, when the packing fraction exceeds this critical value, the tangential velocity profile becomes rate-dependent and varies gradually from linear to nonlinear with increasing shear rate. Furthermore, we find a continuous transition from the unjammed state to the jammed state in a shear granular flow as the packing fraction increases. In this transforming process, the force distribution varies distinctly and the contact force network also exhibits different features.     

Experimental study of coating flows in a partially-filled horizontally Rotating cylinder

 We describe a number of different phenomena seen in the free-surface flow inside a partially filled circular cylinder which is rotated about its horizontal axis of symmetry. At low angular velocities the flow settles into a steady two-dimensional flow with a front where the coating film coalesces with the pool at the bottom of the cylinder. This mode becomes unstable at higher angular velocities, initially to a sloshing mode on the rising side of the coating film and then to an axial instability on the front. The undulations that appear on the front grow into large-amplitude stationary patterns with cusp-like features for some parameter values. At still higher angular velocities and volume fractions, a number of different inertial instabilities and patterns appear. We present a phase diagram of the various transitions and characterize some of the more prominent instabilities and patterns in detail, along with some possible mechanisms for the observed behaviour. Received: 13 April 1996 / Accepted: 13 June 1996