【作者】 周强；

【导师】 张洪武；

【作者基本信息】 大连理工大学 ， 计算力学， 2011， 博士

【摘要】 颗粒材料的热传导问题是工程科学中面临的重要课题之一,为许多研究者所关注。一般认为,颗粒材料由离散颗粒随机组合而成,其宏观性质由颗粒的形状、尺寸、材料属性以及空间分布等参数决定。为反映其非均质特征,通常将颗粒材料模型化为离散颗粒集合体,采用离散单元法进行数值模拟。离散元法实施的关键在于准确地描述颗粒间的接触行为。因此,修正接触传热模型以提高其反映颗粒物理特征的能力,对于提高模拟颗粒体传热行为的离散元法的准确性大有裨益。由于工程实际中的颗粒体由大量颗粒构成,采用离散元法模拟其热传导问题所需的计算量往往难以承受。采用多尺度计算方法可以在准确描述颗粒材料特性的同时将计算成本控制在可接受的范围之内,因此相关研究具有重要的实际工程意义。本文从接触传热模型和多尺度计算两方面入手,讨论了颗粒材料热传导问题的数值模拟方法,主要工作包括：通过引入接触面热阻模型,在离散元分析中考虑了颗粒表面性质对颗粒集合热传导能力的影响；发展了周期性颗粒材料各向异性热传导模拟的表征元法；发展了颗粒材料热传导分析的多尺度有限元法。具体内容如下：简单介绍了颗粒材料以及描述颗粒的形状和表面特性、颗粒体的密度、孔隙比、应力、应变等基本参量。讨论了离散元方法的要点,并以颗粒集合直剪数值试验为例对离散元模拟的实施进行了说明。在离散元方法中引入了接触面热阻模型,在离散元分析中计入了接触面性质对颗粒集合温度分布和热传导性能的影响,并讨论了数值模拟的主要实施步骤。计算结果显示,颗粒表面性质是影响颗粒集合热传导能力的重要参数,良好的接触面属性有助于提高颗粒集合的整体传热性能。使用所发展的离散元方法对颗粒材料内的热传导问题进行了模拟,分析了颗粒尺寸、颗粒集合体分比、配位数和所受压缩载荷大小对颗粒体传热性能的影响,结果表明上述参数在适当条件下均可影响颗粒体的传热性能。从应用的角度出发,由较大尺寸颗粒组成的密实颗粒材料,在强压缩载荷作用下将表现出相对良好的热传导性能。针对拓扑结构确定的颗粒材料,发展了其热传导模拟的表征元法。以表征元为研究对象,讨论了获取能够表征颗粒材料各向异性有效热传导系数的均匀化策略：建立了平均热流密度与颗粒位置、颗粒接触对的热流率之间的关系；又以最优拟合的方式描述了颗粒体的平均温度梯度；以离散元模拟获取平均热流密度和平均温度梯度,通过求解傅立叶热传导方程计算有效热传导系数。有效热传导系数矩阵特征值之间的差异显示了颗粒体热传导性能各向异性的程度,反映了颗粒体内部空间结构的复杂性以及单体颗粒属性之间的差异。有效热容系数则根据表征元上的体积平均得到。与离散元分析数据的比较显示,所发展方法可有效地进行颗粒材料的热传导模拟。发展了颗粒材料热传导分析的多尺度有限元法。对于拓扑结构确定的颗粒材料,其细观热传导信息通过以接触对为基本单元的网络模型反映,热传导模拟则在其宏观粗网格模型上进行。多尺度有限元法的核心是由粗网格单元多尺度基函数建立宏、细观网格模型间的联系,而多尺度基函数则需通过求解粗网格单元上的边值问题数值构造。通过多尺度基函数,颗粒接触对的细观热传导性质被计入粗网格单元的热传导系数阵和热容系数阵中,并在粗网格模型的热传导模拟中得以体现。由于多尺度基函数建立了细观温度场与粗网格单元节点温度之间的联系,颗粒温度可在模拟过程中以降尺度计算直接获得。数值模拟显示,所发展方法可在保证一定计算精度的同时显著提高计算效率。更多还原

【Abstract】 Thermal conduction within granular materials is one of the challenging research topics in engineering. The thermal properties of granular materials have been discussed in many relevant studies. The macroscopic behavior of granular materials depends on the shape, size, material properties and distribution of the random packed particles, etc. The discrete element method (DEM) is widely used to simulate the behavior of granular materials, of which the key feature is to model the behavior between two particles in contact accurately. Therefore, the thermal DEM simulations of granular materials will benefit from introducing the thermal contact model with a comprehensive consideration of the physical properties of the particles. On the other hand, the computational efforts is far beyond the computer capability, which is required by the quantitatively determination of motions within granular assemblies consisting of the huge number of particles. The advantages of the multi-scale strategy of granular materials lie not only in the reliable description on the material behaviors but also in the acceptable computational efforts of simulations. It is thus necessary to develop the relevant methods.The present work focuses on the developments of numerical methods to simulating the thermal conduction within granular materials, including:a DEM study on the thermal conduction within granular assemblies with the introduction of the thermal contact resistance, a homogenization technique to model the thermal conduction of periodic granular materials based on the analyses on the granular represent volume element (RVE) and a multi-scale method to simulate the thermal conduction within granular materials consisting of a large number of particles. The major works and findings are summarized as follows:First, a brief introduction to granular assemblies is provided, including the definitions of the particle shape and surface roughness, the density, solid volume fraction, stress and strain tensor of the granular assemblies, etc. The key features of the DEM are discussed with the numerical direct shear tests performed.Next, a thermal contact model is introduced into the DEM to study the thermal conduction within granular materials. The numerical examples indicate that the surface properties affect the thermal conductivity (ETC) of the granular assemblies and a smooth particle surface enhances the ETC. The effect on the ETC of the particle size, external load, solid volume fraction and coordination number of granular assemblies have also been investigated via the DEM simulations. The simulation results imply that any of the parameters could be the decisive factor to the ETC of the granular assemblies. From a practice view, a dense granular assembly consisting of relative large particles will exhibit good heat transfer behaviors under heavy compressions.Then, a homogenization technique is proposed to simulate the thermal conduction of periodic granular materials. The ETC and the effective volumetric heat capacity (EVHC) can be obtained from the granular RVE using homogenization techniques. The average heat flux can be formulated by the positions and heat flows of particles in contact within the RVE as well as the "best fit" average temperature gradient. The ETC of the granular RVE can be computed from solving the heat equation with the average heat flux and temperature gradient obtained from DEM simulations. Moreover, the difference between the three eigenvalues reveals the anisotropy of the ETC, which exhibits the complexity of granular materials. Analogously, the EVHC can be calculated by averaging over all particles in the granular RVE. The ETC and EVHC obtained are then employed to simulate the thermal conduction procedure in periodic granular materials using finite element methods. The similar temperature profiles and heat flux given by both the DEM and DEM simulations verify the proposed techniques.Finally, a multi-scale method is developed to simulate the thermal conduction within granular materials consisting of a large number of particles. The heat exchange between the two particles in contact is simplified as the heat flow through a truss element so that a network can be used to model these assemblies. Based on multi-scale finite element method, the fundamental idea of the method is to construct the numerical base functions considering both the topology and the material properties of the particles via solving the boundary value problems on the coarse meshes. With the thermal conduction and the heat capacity matrices computed from the contributions of all the contact pairs corresponding to the coarse element, the thermal conduction problem can be solved using the same technique as the finite element method. Moreover, the temperature of every particle can be simultaneously obtained from the downscaling computation during the simulation procedure. The numerical tests indicate that the developed method can provide fairly accurate results with the great reduction of computational efforts for solving the thermal conduction problems within granular materials.更多还原