STRUCTURE AND THERMODYNAMICS OF GRANULAR MATERIALS

颗粒介质由大量离散的粗颗粒聚集而成,如自然界中的粗砂和碎屑堆积体等. 在工程实践中,人们依据经验和实验数据建立了许多模型,虽然可以满意地描述某些力学现象,但是对颗粒介质力学性质全貌的认识以及颗粒介质物理本质的理解仍远远不够. 颗粒介质长程无序、短程有序的结构和复杂的能量转化过程,注定了其独特的力学性质. 该文综述了颗粒介质结构探测和表征技术、热力学理论和固态-流态转变方面的新进展,特别介绍了清华大学近5 年来开展的颗粒介质结构模型化方法和双颗粒温度热力学理论. 最后,提出了开展结构分析-热力学理论的联合研究思路,以期更加深入认识颗粒介质的力学特性,探究颗粒介质的热力学根源,改善现有唯象研究现状.     

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.     

一种改进的颗粒移动床μ(I)拟流体模型及应用

颗粒移动床在工业领域应用广泛, 发展实用可靠的颗粒移动床模型具有理论和应用价值. 本文基于颗粒流μ(I)模型, 补充局部颗粒体积分数与颗粒局部压力和局部颗粒流密度的关系式, 将移动床内密集颗粒处理成可压缩拟流体, 建立了颗粒流单相可压缩流μ(I)模型, 并建立了颗粒流?壁面摩擦条件, 在计算中对颗粒流拟黏度和拟压力项进行正则化处理. 采用上述模型与方法对3种典型散料在移动床缩口料仓内的流动进行模拟, 与实验对比, 得到了玻璃珠、刚玉球和粗沙的μ(I)模型参数, 分析了3种不同散料在料仓内的颗粒速度、体积分数等分布特性, 模拟结果较好地揭示了料仓内不同物料的整体流和漏斗流特性; 进而以玻璃珠为例, 对移动床颗粒单管绕流流动进行了模拟, 所得结果合理揭示了管流附近的流动特性. 计算结果表明, 对于本文的计算工况, 颗粒体积分数变化最大范围为0.510 ~ 0.461, 绝大部分区域流动惯性数小于0.1, 改进的单相μ(I)模型能合理预测出密集颗粒流移动床内的流动特性, 方法可行且较多相流算法能明显减小计算量.      

基于应力波动的修正非局部流变模型

基于Pouliquen提出的非局部流变模型,考虑颗粒流中某个位置重新排列引起的自激发过程,详细分析颗粒介质中应力波动幅值的概率密度分布形式以及剪切速率与体积分数的耦合作用,提出一种修正的非局部流变模型.采用此修正非局部流变模型对斜面剪切颗粒流的流动特性进行了预测,颗粒流动的临界厚度、平均流动速度及剪切速率廓线的预测结果与实验结果定量吻合.此修正模型的提出为复杂的密集颗粒流的描述和表征提供了一种新的研究思路.     

稀疏两相湍流的惯性颗粒倾向性弥散

气相采用大涡模拟、颗粒相采用拉格朗日轨道模型的方法对后台阶突扩流、充分发展 槽道流和圆湍射流3种典型的稀疏气固两相流动进行了数值模拟，研究了颗粒倾向性弥散的 特征和规律. 研究表明颗粒的跟随性和倾向性相联系，颗粒惯性和大涡结构同时决定颗粒的 倾向性分布特征. Stokes数量级为1(气相时间参考尺度取为宏观特征时间尺度)左右的颗 粒，倾向性分布特征最强烈. 颗粒倾向分布于低涡量(或是低脉动速度)的湍流区域.     

颗粒材料计算力学专题序

颗粒材料广泛地存在于自然环境、工业生产和日常生活等诸多领域, 其受加载速率、约束条件等因素的影响具有复杂的力学行为. 颗粒材料常与流体介质、工程结构物耦合作用并共同组成复杂的颗粒系统, 并呈现出非连续性、非均质性的复杂力学特性. 目前, 离散元方法已成为解决不同工程领域颗粒材料问题的有力工具, 然而其在真实颗粒形态的构造、接触算法、颗粒与流体及工程结构的耦合模型、多介质和多尺度问题, 以及高性能大规模计算等方面仍面临着诸多亟待解决的问题.《力学学报》组织了“颗粒材料计算力学”专题的7篇综述或研究论文, 分别从研究进展、理论模型及工程应用方面反映了颗粒材料计算力学研究领域上的最新研究进展, 为颗粒材料计算力学交叉领域的研究提供参考.      

泥石流及其运动方程

本文简单介绍了泥石流及其防治和研究简况．对于泥石流运动方程，介绍了Ｂｉｎｇｈａｍ模型、日本高桥保的颗粒流膨胀体模型、美国Ｃｈｅｎ的塑性颗粒流膨胀体模型以及作者的非牛顿塑性膨胀体模型，并介绍了美国ＭａｃＡｒｔｈｕｒ和Ｈａｍｉｌｔｏｎ对泥石流运动的数值模拟．最后，对泥石流运动研究进行了展望     

泥石流及其运动方程

本文简单介绍了泥石流及其防治和研究简况．对于泥石流运动方程，介绍了Ｂｉｎｇｈａｍ模型、日本高桥保的颗粒流膨胀体模型、美国Ｃｈｅｎ的塑性颗粒流膨胀体模型以及作者的非牛顿塑性膨胀体模型，并介绍了美国ＭａｃＡｒｔｈｕｒ和Ｈａｍｉｌｔｏｎ对泥石流运动的数值模拟．最后，对泥石流运动研究进行了展望     

筒仓泄料过程中阻塞现象的数值模拟

基于颗粒材料离散颗粒模型及颗粒流方案,通过数值试验研究了筒仓泄料过程中影响颗粒流发生阻塞的若干因素,给出了阻塞概率随筒仓底部开口半径及倾角、颗粒间摩擦系数及颗粒粒径分布的关系曲线.基于颗粒簇的概念,进一步研究了颗粒形状的影响,并对颗粒材料阻塞时的力链分布特征进行简要分析.     

金属颗粒磁带宏观性质的细观力学估计

金属颗粒之间的磁场相互作用对金属颗粒磁带的高密度记录性能有显著的影响. 为了有效 地估计该影响，在单畴颗粒的Stoner-Wohlforth模型基础上将新近提出的细观力学相 互作用直推法(Zheng & Du, J. Mech. Phys. Solid. 2001) 推广到非均匀磁记录材料中，得到了磁带宏观性质的率形式解析表达， 能有效地计及颗粒之间的相互作用、颗粒形状的统计分布和体积分数对磁介质性能的 影响. 得到的理论结果与数值模拟和有关的实验观测结果相当一致.     

聚合物分子模型的Brown动力学模拟

介绍了研究聚合物分子模拟流变性质的Brown动力学模拟方法,综述了有关这方面的研究工作．在通常情况下,将分子模型的数值模拟与求解流动守恒方程的数值解法相结合,便有可能用分子模型去代替连续介质力学的本构方程,来模拟聚合物流体的复杂流动．本文介绍了这一方法的产生背景、最新进展以及优点．     

Gravity-driven dry granular slow flows down an inclined moving plane: a comparative study between two concepts of the evolution of porosity

Two concepts in modeling the effects of the evolution of porosity in dry granular flows are investigated to illuminate their performance and limitations. To this end, the thermodynamic analysis, based on the Müller-Liu entropy principle, and the quasi-linear theory, are employed to deduce the ultimate constitutive models and the restrictions on their thermodynamic consistencies. The models are employed to study an isothermal dry granular slow flow down an inclined moving plane, of which the results are compared with the experimental outcomes. Results show that, while the two models deliver appropriate equilibrium expressions of the Cauchy stress tensor for compressible grains, the model in which the evolution of porosity is treated kinematically yields a spherical stress tensor for incompressible grains. Only the model with a dynamic evolution of porosity can give rise to a non-spherical stress tensor at equilibrium. Moreover, whilst the former model can better capture the characteristics of flows with slow to moderate speeds, the latter model is more able to describe the features of very rapid flows like avalanches. The present study illustrates the essential difference between the two concepts in modeling the effects of the evolution of porosity, and can be extended for further studies on other microstructural effects in granular flows.     

COMPUTATIONAL FLUID DYNAMICS FOR DENSE GAS-SOLID FLUIDIZED BEDS: A MULTI-SCALE MODELING STRATEGY

Dense gas-particle flows are encountered in a variety of industrially important processes for large scale production of fuels, fertilizers and base chemicals. The scale-up of these processes is often problematic and is related to the intrinsic complexities of these flows which are unfortunately not yet fully understood despite significant efforts made in both academic and industrial research laboratories. In dense gas-particle flows both (effective) fluid-particle and (dissipative) particle-particle interactions need to be accounted for because these phenomena to a large extent govern the prevailing flow phenomena, i.e. the formation and evolution of heterogeneous structures. These structures have significant impact on the quality of the gas-solid contact and as a direct consequence thereof strongly affect the performance of the process. Due to the inherent complexity of dense gas-particles flows, we have adopted a multi-scale modeling approach in which both fluid-particle and particle-particle interactions can be properly accounted for. The idea is essentially that fundamental models, taking into account the relevant details of fluid-particle (lattice Boltzmann model) and particle-particle (discrete particle model) interactions, are used to develop closure laws to feed continuum models which can be used to compute the flow structures on a much larger (industrial) scale. Our multi-scale approach (see Fig. 1 ) involves the lattice Boltzmann model, the discrete particle model, the continuum model based on the kinetic theory of granular flow,and the discrete bubble model. In this paper we give an overview of the multi-scale modeling strategy, accompanied by illustrative computational results for bubble formation. In addition, areas which need substantial further attention will be highlighted.     

Nonlinear elasto-plastic model for dense granular flow

This work proposes a model for granular deformation that predicts the stress and velocity profiles in well-developed dense granular flows. Recent models for granular elasticity [Jiang, Y., Liu, M., 2003. Granular elasticity without the Coulomb condition. Phys. Rev. Lett. 91, 144301] and rate-sensitive fluid-like flow [Jop, P., Forterre, Y., Pouliquen, O., 2006. A constitutive law for dense granular flows. Nature 441, 727] are reformulated and combined into one universal elasto-plastic law, capable of predicting flowing regions and stagnant zones simultaneously in any arbitrary 3D flow geometry. The unification is performed by justifying and implementing a Kröner–Lee decomposition, with care taken to ensure certain continuum physical principles are necessarily upheld. The model is then numerically implemented in multiple geometries and results are compared to experiments and discrete simulations.     

Simulation of mass balance behavior in a large-scale circulating fluidized bed reactor

We determine using a compound model the influence of the mass of granular matter on the behavior of a supercritical circulating fluidized bed (CFB) reactor. Population balance enables a stationary-regime modeling of the mass flow of granular matter inside a CFB unit in a large-scale. The simulation includes some important dynamic processes of gas-particle flows in fluidized bed such as attrition, fragmentation, elutriation, and fuel combustion. Numerical calculations with full boiler loading were performed of operational parameters such as furnace temperature, furnace pressure, feeding materials mass flows, and excess air ratio. Furthermore, three bed inventory masses were adopted as experimental variables in the simulation model of mass balance. This approach enables a sensitivity study of mass flows of granular matter inside a CFB facility. Some computational results from this population balance model obtained for a supercritical CFB reactor are presented that show consistency with the operational data for large-scale CFB units.     

Modelling long-term deformation of granular soils incorporating the concept of fractional calculus

Many constitutive models exist to characterise the cyclic behaviour of granular soils but can only simulate deformations for very limited cycles. Fractional derivatives have been regarded as one potential instrument for modelling memory-dependent phenomena. In this paper, the physical connection between the fractional derivative order and the fractal dimension of granular soils is investigated in detail.Then a modified elasto-plastic constitutive model is proposed for evaluating the long-term deformation of granular soils under cyclic loading by incorporating the concept of factional calculus. To describe the flow direction of granular soils under cyclic loading, a cyclic flow potential considering particle breakage is used. Test results of several types of granular soils are used to validate the model performance.     

Expanding the limits of “equilibrium” second-moment turbulence closures

The paper discusses possibilities for refinements of conventional “equilibrium” second-moment turbulence closure models, aimed at improving model performances in predicting turbulent flows of greater complexity. In focus are the invariant modelling of the low-Re-number and wall proximity effects, as well as extra strain-rates and control of the turbulence length-scale. In addition to satisfying most of the basic physical constraints, the main criterion for model validation was the quality of reproduction of flow and turbulence details, particularly, in the vicinity of a solid wall, in a broad variety of non-equilibrium flows featured by different phenomena. It is demonstrated that the new model, which includes several new modifications, but also some proposed in the past, can satisfactorily reproduce a range of attached and separating flows with strong time- or space-variations or abrupt changes of boundary conditions. Cases considered cover a wide range of Re-numbers involving in some cases also the laminar-to-turbulent or reverse transition.     

湍流转捩模式研究进展

以湍流模式理论为基础发展起来的湍流转捩模式是一种十分重要的转捩预测方法. 本文对转 捩模式的研究进行了回顾. 首先, 探讨了以低雷诺数湍流模式理论研究转捩问题的局限性, 此类模式中, 用来模拟黏性层次的阻尼函数经过修正之后, 具有一定的转捩预测能力. 但也 有观点认为这只是一种数值上的巧合而已. 其次, 指出了考虑间歇性的模式所存在的问 题. 此类模式通过各种方式将间歇因子与湍流模式进行耦合, 在一定程度上考虑了转捩的物 理机制, 可较好地模拟简单流动中的转捩过程. 但其中所包含的非局部变量使其与现代CFD 方法并不协调一致. 接着, 分析了完全由局部变量构造的新型转捩模式, 其中涉及了关 于非湍流脉动动能等转捩特征变量的新型输运方程. 最后, 对此领域的发展方向进行了 预测.