In this work, we consider the momentum transport of a incompressible fluid in a like Beavers and Joseph (1967) system. For this purpose, in the context of the volume averaging method, we use a one-domain approach (ODA). Thus, the momentum generalized transport equations (GTE), which are written in terms of position-dependent effective medium coefficients, are valid everywhere in the system and contains two Brinkman corrections in addition to a Darcy’s term. The ODA predictions are tested against the results obtained from averaging the local profiles resulting from pore-scale simulations. One of the key points for solving the ODA remains on the prediction of the permeability, which in this work is obtained either by solving the associated local closure problem or from pore-scale profiles. Our analysis shows that the GTE for momentum transport accurately predicts the average velocity profiles everywhere in the system. To this end, the first and the second Brinkman’s corrections, as well as a position-dependent intrinsic permeability tensor in Darcy’s term must be included.

在这项工作中，我们考虑了类似 Beavers 和 Joseph (1967) 系统中不可压缩流体的动量传递。为此，在体积平均方法的上下文中，我们使用单域方法 (ODA)。因此，以与位置相关的有效介质系数的形式编写的动量广义输运方程 (GTE) 在系统中的任何地方都有效，并且除达西项外还包含两个 Brinkman 修正。官方发展援助的预测是针对通过平均孔隙尺度模拟产生的局部剖面而获得的结果进行测试的。解决 ODA 的关键点之一仍然是渗透率的预测，在这项工作中，这是通过解决相关的局部闭合问题或从孔隙尺度剖面获得的。我们的分析表明，动量传输的 GTE 准确地预测了系统中各处的平均速度分布。为此，必须包括第一次和第二次 Brinkman 修正，以及达西项中与位置相关的固有渗透率张量。