Modification of the fundamental theorem for transport phenomena in porous media
Modification of the fundamental theorem for transport phenomena in porous media
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DOI：
10.1016/j.ijheatmasstransfer.2017.08.067
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发表时间：
2017-12-01
影响因子：
5.2
通讯作者：
Takatsu, Yasuyuki
中科院分区：
文献类型：
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作者：
Takatsu, Yasuyuki
为了研究多孔介质中的对流，基于宏观控制方程进行了大量的分析和数值模拟。在推导宏观控制方程时，使用梯度（或散度）的局部体积平均值定理对多孔介质固有的现象（例如达西流阻、福希海默流阻和色散）进行建模。该定理已被广泛接受为多孔介质对流理论的基础。然而，有人提出了与定理（体积平均值的连续导数和达西定律的压力修正）的正确性有关的某些问题。在本研究中，我们修改了梯度（或散度）的局部体积平均值的传统定理来解决上述问题。首先，我们引入点质量的概念来描述流体相运动的参考点，并推导出对应于多孔介质连续体的宏观场中的雷诺输运定理。然后，我们检查一点散度的定义，得到使用流体粒子的速度矢量u和数量B的微观描述与使用点质量粒子的参考速度矢量u(0)和参考数量B-0的宏观描述之间的关系，并推导出梯度（或散度）的局部体积平均值的修正定理。此外，我们借助修正定理推导了多孔介质的控制方程。 (C) 2017 Elsevier Ltd. 保留所有权利。
To examine convection in porous media, numerous analyses and numerical simulations have been conducted based on the macroscopic governing equations. In deriving the macroscopic governing equations, the phenomena intrinsic to porous media, such as Darcy's flow resistance, Forchheimer's flow resistance, and dispersion, are modeled using the theorem of the local volume average of a gradient (or a divergence). The theorem has been widely accepted as fundamental in the theory of convection in porous media; however, certain questions relating to the correctness of the theorem (the continuous derivative of the volume average and the pressure correction for Darcy's law) have been raised. In this study, we modify the conventional theorem for the local volume average of a gradient (or a divergence) to solve the aforementioned questions. First, we introduce the concept of a point mass to describe the reference point for the movement of the fluid phase, and we derive the Reynolds transport theorem in the macroscopic field that corresponds to the continuum of porous media. Then, we examine the definition of divergence at a point to obtain the relation between the microscopic description that employs the velocity vector u and quantity B of the fluid particle and the macroscopic description that employs the reference velocity vector u(0) and the reference quantity B-0 of the point-mass particle, and we derive the modified theorem for the local volume average of a gradient (or a divergence). Furthermore, we derive the governing equations for porous media with the aid of the modified theorem. (C) 2017 Elsevier Ltd. All rights reserved.