泡沫金属有效导热系数的数学模型

Effective Thermal Conductivity Model for High Porosity Open-Cell Metal Foams

通过修正Kelvin提出的十四面三维结构作为金属泡沫的几何模型,利用数值求解几何模型内的稳态傅里叶导热方程,文中提出了泡沫金属的有效导热系数的数学模型.首先,利用实验数据修正了十四面体节点与骨架半径随孔隙率的变化关系.然后,把泡沫金属分成4层,利用数值模拟确定了每层有效导热系数的计算式.最后,基于Fourier定律,建立了泡沫金属的有效导热系数.研究结果表明:文中提出的模型计算泡沫金属有效导热系数与实验值的误差都在±10%之内.本文的研究结果,对于泡沫金属的热力设计和应用具有很好的指导意义.

Using the numerical simulation method,a mathematical model for effective thermal conductivity of high porosity open-cell metal foams is proposed by modifying the 3D tetradecahedron structure. Firstly,the ratio of the edge length of node to the radius of ligament of 3D tetradecahedron is calibrated with the experimental data. The geometrical model is divided into four distinctive layers along the heat transfer direction. An empirical model to estimate the effective thermal conductivity of four layers is then determined by fitting the numerical results. Finally,the mathematical model for effective thermal conductivity of metal foams is proposed based on the Fourier law. Compared with the experimental data,the present model has high accuracy with RMS deviation of less than 10%. The finding of this study can help guide the thermal design and application of porous media.