A macroscopic model that accounts for the effect of momentum dispersion on flows in porous media is proposed. The model is based on the pore scale prevalence hypothesis (PSPH). The effects of macroscopic velocity gradient on momentum transport are approximated using a Laplacian term. A local Reynolds number Re d , which characterizes the strength of momentum dispersion, is introduced to calculate the effective viscosity. The characteristic length used in defining Re d is the pore size, while the characteristic velocity is the mixing velocity. A Taylor expansion is made for the effective viscosity with respect to Re d . The two leading-order terms of the Taylor series are adopted in the present PSPH momentum-dispersion model. The model constants are determined from the direct numerical simulation results of a flow in the same porous medium bounded by two walls. The effective viscosity approaches the molecular viscosity when the porosity is increased to 1. It approaches infinity when the porosity approaches 0. The benchmark studies show that the effects of the macroscopic velocity gradient can be approximated by the Laplacian term. The proposed PSPH momentum-dispersion model is highly accurate in a wide range of Reynolds and Darcy numbers as well as porosities.

中文翻译：

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基于孔隙尺度普遍性假设的多孔介质中动量分散的数值模拟

提出了一个宏观模型，该模型解释了动量色散对多孔介质中流动的影响。该模型基于孔隙尺度普遍性假设 (PSPH)。宏观速度梯度对动量传输的影响使用拉普拉斯项来近似。引入了表征动量分散强度的局部雷诺数 Re d 来计算有效粘度。用于定义 Re d 的特征长度是孔径，而特征速度是混合速度。对 Re d 的有效粘度进行泰勒展开式。目前的 PSPH 动量色散模型采用了泰勒级数的两个前导项。模型常数是根据同一多孔介质中流动的直接数值模拟结果确定的，该结果由两壁包围。当孔隙率增加到 1 时，有效粘度接近于分子粘度。当孔隙率接近 0 时，它接近无穷大。基准研究表明，宏观速度梯度的影响可以用拉普拉斯项来近似。所提出的 PSPH 动量色散模型在广泛的雷诺数和达西数以及孔隙度范围内都非常准确。