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

通过二维和三维数值计算，模拟了粘性和孔隙惯性对牛顿流体和非牛顿流体在多孔介质中流动压降的影响。提出了各种周期性安排的方形和圆形杆的微观多孔结构的二维模型，而一个集合的立方体放置在一个区域的无限范围内提出了其三维模型。一套完整的二维和三维的动量方程被视为沿着与连续性方程在孔隙尺度，以模拟通过无限数量的障碍物排列在一个规则的模式。微观数值结果，从而获得，处理，以提取的压力梯度-质量流量之间的宏观关系。已经发现，通过阅读无因次压力梯度与雷诺数图中的截距确定的修改的渗透率紧密地遵循基于水力半径概念的Christopher和Middleman公式。在比较基于二维和三维模型的结果时，已经发现，只有三维模型可以正确地捕获多孔惯性对压降的影响。多孔介质中的热色散也使用一个二维的周期性阵列进行了研究。高Peclet数范围内得到的相关性与现有的实验数据吻合良好。

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.