De Schampheleire Sven, De Kerpel Kathleen, Ameel Bernd, De Jaeger Peter, Bagci Ozer, De Paepe Michel
Department of Flow, Heat and Combustion Mechanics, Ghent University, Sint-Pietersnieuwstraat 41, Ghent 9000, Belgium.
NV Bekaert SA, Bekaertstraat 1, Zwevegem 8500, Belgium.
Materials (Basel). 2016 May 25;9(6):409. doi: 10.3390/ma9060409.
It is long known that for high-velocity fluid flow in porous media, the relation between the pressure drop and the superficial velocity is not linear. Indeed, the classical Darcy law for shear stress dominated flow needs to be extended with a quadratic term, resulting in the empirical Darcy-Forchheimer model. Another approach is to simulate the foam numerically through the volume averaging technique. This leads to a natural separation of the total drag force into the contribution of the shear forces and the contribution of the pressure forces. Both representations of the total drag lead to the same result. The physical correspondence between both approaches is investigated in this work. The contribution of the viscous and pressure forces on the total drag is investigated using direct numerical simulations. Special attention is paid to the dependency on the velocity of these forces. The separation of the drag into its constituent terms on experimental grounds and for the volume average approach is unified. It is shown that the common approach to identify the linear term with the viscous forces and the quadratic term with the pressure forces is not correct.
长期以来，人们都知道在多孔介质中高速流体流动时，压降与表观速度之间的关系并非线性。实际上，用于剪切应力主导流动的经典达西定律需要用一个二次项进行扩展，从而得到经验性的达西 - 福希海默模型。另一种方法是通过体积平均技术对泡沫进行数值模拟。这导致总阻力自然地分离为剪切力的贡献和压力的贡献。两种总阻力的表示方式都得出相同的结果。本文研究了这两种方法之间的物理对应关系。使用直接数值模拟研究了粘性力和压力对总阻力的贡献。特别关注这些力对速度的依赖性。基于实验和体积平均方法，将阻力分离为其组成项的方式得以统一。结果表明，将线性项与粘性力以及二次项与压力力相识别的常见方法是不正确的。
