Direct numerical simulation and macroscopic modeling of heat and fluid flow in porous media

采用二维和三维数值计算方法，模拟了粘性和多孔惯性对牛顿流体和非牛顿流体在多孔介质中流动时压降的影响。将各种周期排列的正方形和圆形杆体作为微观多孔结构的二维模型，而将放置在无限大范围内的立方体集合作为其三维模型。将一整套二维和三维动量方程与孔洞尺度上的连续性方程一起处理，以模拟无限多个规则排列的障碍物的流动。对得到的微观数值结果进行了处理，提取了压力梯度-质量流量之间的宏观关系。结果表明，通过读取无因次压力梯度-雷诺数曲线中的截距确定的修正渗透率与Christopher和Midlman基于水力半径概念的公式非常接近。通过比较基于二维和三维模型的结果，发现只有三维模型才能准确地捕捉到多孔惯性对压降的影响。利用二维周期阵列研究了多孔介质中的热弥散。所得到的高Peclet数范围的关联式与现有的实验数据符合得很好。

Two- and three-dimensional numerical calculations have been conducted to simulate the viscous and porous inertia effects on the pressure drop in Newtonian and non-Newtonian fluid flows through porous media. Various periodic arrangements of square and circular rods are proposed as two-dimensional models of microscopic porous structure, whereas a collection of cubes placed in a region of infinite extent is proposed as its three-dimensional model. A full set of two- and three-dimensional momentum equations are treated along with the continuity equation at a pore scale, so as to simulate a flow through an infinite number of obstacles arranged in a regular pattern. The microscopic numerical results, thus obtained, are processed to extract the macroscopic relationship between the pressure gradient-mass flow rate. It has been found that the modified permeability determined by reading the intercept in the dimensionless pressure gradient versus Reynolds number plot closely follows Christopher and Middleman's formula based on a hydraulic radius concept. Upon comparing the results based on the two- and three-dimensional models, it has been found that only the three-dimensional model can capture the porous inertia effects on the pressure drop, correctly. Thermal dispersion in porous media is also investigated using a two-dimensional periodic array. The resulting correlation for high Peclet number range agrees well with available experimental data.