Darcy's law for two-dimensional flows: Singularities at corners and a new class of models
Darcy's law for two-dimensional flows: Singularities at corners and a new class of models
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二维流动的达西定律：拐角处的奇点和一类新模型
DOI：
10.1002/aic.15840
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发表时间：
2017
期刊：
影响因子：
3.7
通讯作者：
Shikhmurzaev Y
中科院分区：
文献类型：
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作者：
Shikhmurzaev Y
众所周知，达西流体在各向同性均质多孔介质中的流动模型在基本为二维流动形态的速度场中产生奇异性，如绕过拐角的流动。从建模的角度考虑这一问题，本研究旨在消除这种奇异性，这种奇异性不能通过达西模型的常规推广(如Brinkman方程)正则化，而不牺牲达西定律本身对单向流动的有效性，而达西定律的有效性在实验上得到了很好的证实。关键思想是，正如一个简单的类比所证实的那样，多孔基质相对于流动的渗透率不是独立于流动的常数，而是流场(其标量不变量)的函数，随着流线曲率的增加而减小。这引入了一类全新的模型，其中流场和渗透场被联系在一起，特别是必须同时发现问题。©2017美国化学工程师学会AIChE J，2017
As is known, Darcy's model for fluid flows in isotropic homogeneous porous media gives rise to singularities in the velocity field for essentially two‐dimensional flow configuration, like flows over corners. Considering this problem from the modeling viewpoint, this study aims at removing this singularity, which cannot be regularized via conventional generalizations of the Darcy model, like Brinkman's equation, without sacrificing Darcy's law itself for unidirectional flows where its validity is well established experimentally. The key idea is that as confirmed by a simple analogy, the permeability of a porous matrix with respect to flow is not a constant independent of the flow but a function of the flow field (its scalar invariants), decreasing as the curvature of the streamlines increases. This introduces a completely new class of models where the flow field and the permeability field are linked and, in particular problems, have to be found simultaneously. © 2017 American Institute of Chemical EngineersAIChE J, 2017