A Numerical Study On The Thermal Conduction Within Granular Materials Based On Discrete Element Method

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.