【作者】 雷雅洁；

【导师】 张端明；

【作者基本信息】 华中科技大学 ， 凝聚态物理， 2004， 硕士

【摘要】 颗粒材料是由大量宏观颗粒组成的系统,例如砂子,粉尘,咖啡等。颗粒系统中的问题可以粗略地分为准静态问题(沙堆,静力的分布,压缩,断裂的传播等)和运动问题(所有流动,对流,分层,堆积模式,流化床等)[1]。本文针对后一类问题,对由大量不同尺寸颗粒组成的非均匀混合颗粒系统进行了研究,研究涉及近平衡和远平衡两种动力学条件。这里应该强调指出的是,为了解决有关非均匀颗粒系统的物理问题,本文基于有关实验事实,借助于稠密气体的动力学理论和分形理论,首次提出了非均匀颗粒系统的具有分形特征的速度分布函数。对于处于近平衡条件下的颗粒系统,近年来,人们从稠密气体动力学[2]的概念出发,提出了适于描述颗粒流中物理特性关系的颗粒流体动力学[3-6]。这一理论将颗粒看作大小相等、表面光滑的球,且不计颗粒的大小和表面形状对颗粒流性质的影响。但是,实验表明,由于颗粒被研细过程是随机无序的,形成的颗粒大小不相等,表面不光滑,其某些物理量具有分形特性[7-8]。本文在本课题组已建立的颗粒系统分形模型的基础上[9-10],在近平衡条件下,提出了非均匀颗粒系统具有分形特征的速度分布函数。并以此研究了混合颗粒系统中的热传导,研究发现此混合系统的有效热导率将随着固体体积百分比,系统结构特征参数和分形维数的变化而变化。计算机科学的发展使得人们对颗粒系统的研究跨入了远平衡状态的范畴,它更加真实地反映了颗粒系统的动力学演化[11-14]。已有的模拟结果与颗粒流体动力学的预言在很多方面出现了不同:颗粒系统的速度分布偏离了高斯分布,空间密度分布也出现了各向异性。在此基础上,本文利用Monte Carlo方法和分形理论对非均匀混合颗粒系统进行了动力学模拟。模拟结果表明,颗粒系统中代表粒度大小分布的分形维数可以作为系统非均匀性的量度,它对系统的动力学行为影响极大。随着的增大,系统的速度分布远离高斯分布越明显,粒子的成团化更加加强。本文的工作将对颗粒系统的研究从简单均匀的颗粒系统推广到了具有实际意义的非均匀混合颗粒系统。更重要的是,混合颗粒系统的理论预测为今后的实验工作提出新的课题。更多还原

【Abstract】 Granular-material system here is two-phase systems composed of macroscopical particles with different sizes (e.g. coffee, powders, and detritus, etc.). Problems in granular systems are roughly divided into quasi-static (sand piles, distribution of static forces, compaction, and fracture propagation, etc.) and dynamical ones (all kinds of flows, convection, and segregation, pattern formation, and fluidized beds, etc.) [1]. Aiming at the latter, the research has been made for the non-uniform granular system, which was dealt with in the different dynamics regimes: quasi-equilibrium regime and far from equilibrium one. It should to be emphasized that, for resolving the physical problems on non-uniform granular system, the velocity distribution function with the fractal character was originally put forward with the dense-gas kinetic theory and fractal theory. In the quasi-equilibrium regime, granular hydrokinetics theory [3-6] is brought forward based on dense-gas kinetic theory [2]. In this theory, particles are looked as slick balls with uniform size; granular sizes and surface forms will not bring any influences to the characteristics of the system. However, experiments showed that, for many materials, in the procession of macroscopical comminution, the geometrical and mathematical characteristics exhibited the self-similarity [7-8]. On the base of the fractal model for non-uniform granular system [9-10], the velocity distribution function with the fractal character was put forward under the quasi-equilibrium regime. Furthermore, we investigated the thermal conductivity in the mixed system. Found that the thermal conductivity changed with the solid fraction , structural character parameter and fractal dimension .The increasing power of computer awakened an interest in the “granular gases” simulation, in the far from equilibrium regime, which more really reflects the dynamics <WP=5>characteristics of granular systems [11-14]. The numerical results performed many different properties from the granular hydrokinetics theory: the velocity distribution deviates the Gaussian and the spatial clusterization arises. Monte Carlo simulation made in this paper also exhibited that the degree of inhomogeneity in the granularity distribution signed by the fractal dimension of size distribution has great influences on the dynamics actions of the system. The velocity distribution deviates obviously from the Gaussian distribution and the particles cluster more pronounced with the larger value of in the system. The work in this paper generalized the research from the simple granular system to the non-uniform one. The more important is that the predictions in our work make the new programs for correlative experiments.更多还原