摘 要

泡沫金属内固相变过程在诸多领域得到广泛的应用，例如新能源、航空航天领域、相变储能、电子器件冷却等领域。目前泡沫金属内相变材料融化过程研究尚不充分，这是因为固液相变本身的非线性性，以及泡沫金属作为开孔式多孔介质结构的复杂性所导致的。为此本文借助一种介观的计算方法——格子Boltzmann方法，研究无泡沫金属的纯相变过程，在此基础上添加规则的方形体多孔介质，为了更趋近于真实的泡沫金属，本文采用Rhino配合Grasshopper编程方法，构造了完全不规则的多孔介质作为研究对象，进行数值模拟。

首先，本文在保证质量守恒、动量守恒、能量守恒的基础上，基于REV尺度（Representative elementary volume，表征体元），建立了开孔式泡沫金属中固液相变流动与传热的数学模型。针对液态相变材料的流动过程选用Brinkmann-Forchheimer-Darcy渗流模型作为控制方程，相变过程引用焓法处理。从介观角度，除微观流体粒子的演化描述的速度分布函数外，针对融化相变过程而言引入温度演化方程，并以含液率作为加权参数计算焓值，判断相变材料的所处状态。通过选取速度分布和能量分布的源项以及平衡态演化方程，解决固液相变的非线性性问题和自然对流对固液相变的影响问题。本文将该模型的计算解与经典解进行比较。

对纯相变过程的模拟研究结果为：（1）在融化过程开始阶段，热传导占主导地位；（2）随着融化过程进行，热对流所占比重逐渐增大；（3）由于热浮升力影响，致使方腔上部换热能力强，融化速率快；（4）通过加热进入系统的能量主要被相变过程所吸收；（5）Ra对相变过程初期影响不大，但后期随Ra数增加，融化速率逐渐增强，但强化传热的幅度减弱，主要是因为温度场和速度场的协同作用变差的缘故；（6）一方面，Pr数对固液相变的影响与Pr数范围有关，与高Pr数范围(Prgt;1)相比，在低Pr数范围(Prlt;1)内增加Pr数会导致传热增加；另一方面，Pr数对熔融传热过程的影响与自然对流的强度有关，自然对流越强，影响越大。

添加方形体多孔介质骨架后：（1）以加强系统的传热性能为目的，多孔介质骨架与相变材料的比值必须大于某一个临界值； （2）孔隙率对固液相变的过程有着深远影响，一方面孔隙率降低，使融化率得到增加，增强系统热传导性能，另一方面孔隙率过低会阻碍自然对流，因此要综合考虑、优化设计；（3）Ste数越大，相变潜热越小，融化速率越快，反之相反；（4）在孔隙率相同的情况下 ，改变骨架排列方式，对流动过程影响较大，其主要影响是改变流动阻力所导致的：顺排结构的流动阻力大于叉排结构，所以左壁面Nu数较高，且准静态阶段融化率较高。

相比于方形体多孔介质，泰森多边形的多孔介质研究结果如下：（1）孔密度对固液相变的影响要与孔隙率和Ra数有直接关系；（2）固液相变过程几乎不受骨架结构的影响。

关键词：固液相变、多孔介质、格子Boltzmann方法

Abstract

The solid phase transition process in foam metal has been widely used in many fields, such as new energy, aerospace, phase change energy storage, electronic device cooling and so on. At present, the research on the melting process of phase change materials in foam metal is not enough, which is due to the non-linearity of solid-liquid phase transition and the complexity of foam metal as open-cell porous media. Therefore, with the help of a mesoscopic calculation method-lattice Boltzmann method, this paper studies the pure phase transition process of non-foam metal, and adds regular square porous media on this basis. In order to approach the real foam metal, this paper uses Rhino combined with Grasshopper programming method to construct almost completely irregular porous media as the research object for numerical simulation.

Firstly, on the basis of continuity equation, momentum equation and energy equation, the mathematical model of solid-liquid phase transition flow and heat transfer in open-cell metal foam is established based on REV-scale (Representative elementary volume,. Brinkmann-Forchheimer-Darcy percolation model is selected as the governing equation for the flow process of liquid phase change materials, and the enthalpy method is used to deal with the phase change process. From the mesoscopic point of view, in addition to the velocity distribution function described by the evolution of microscopic fluid particles, the temperature evolution equation is introduced for the melting phase transition process, and the liquid holdup is used as a weighted parameter to calculate the enthalpy to judge the state of phase change materials. By selecting the source term of velocity distribution and energy distribution and the equilibrium evolution equation, the problems of nonlinearity of solid-liquid phase transition and the influence of natural convection on solid-liquid phase transition are solved. In this paper, the calculated solution of the model is compared with the classical solution.

The simulation results of the pure phase transition process are as follows: (1) heat conduction is dominant at the beginning of the melting process; (2) with the progress of the melting process, the proportion of thermal convection increases gradually; (3) due to the influence of thermal floating lift, the heat transfer capacity in the upper part of the square cavity is strong and the melting rate is fast. (4) the energy entering the system through heating is mainly absorbed by the phase transition process. (5) with the increase of Ra, the melting rate increases gradually, but the extent of enhanced heat transfer decreases, which is due to the deterioration of the synergistic effect of temperature field and velocity field. (6) on the one hand, the influence of Pr number on solid-liquid phase transition is related to the range of Pr number, on the other hand, the influence of Pr number on melting heat transfer process is related to the intensity of natural convection, the stronger the natural convection is, the greater the influence is.

After adding the square porous media skeleton: (1) if the heat transfer performance of the system is to be enhanced, the ratio of the porous media skeleton to the phase change material must be greater than a certain critical value; (2) porosity has a far-reaching influence on the process of solid-liquid phase transition. on the one hand, reducing porosity enhances the heat conduction performance of metal skeleton, but the decrease of porosity will lead to the decrease of storage capacity of phase change materials. therefore, it should be optimized according to the specific purpose. (3) the larger the Ste number is, the smaller the latent heat of phase transition is and the faster the melting rate is. On the contrary, (4) in the case of the same porosity, changing the arrangement of the skeleton has a great influence on the flow process, which is mainly caused by the change of flow resistance.

Compared with square porous media, the research results of Tyson polygonal porous media are as follows: (1) GH programming, compared with other advanced languages, has many advantages such as simplicity and intuition; (2) the effect of pore density on solid-liquid phase transition is directly related to porosity and Ra number; (3) the solid-liquid phase transition process is almost not affected by the skeleton structure.

Keywords: solid-liquid phase change, porous media, lattice Boltzmann method

目 录

摘 要 I