Oliveira Rafael S, Andrade José S, Andrade Roberto F S
Instituto de Física, Universidade Federal da Bahia, 40210-210 Salvador, Brazil.
Centro de Formação de Professores, Universidade Federal do Recôncavo da Bahia, 45300-000 Amargosa, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Mar;91(3):033002. doi: 10.1103/PhysRevE.91.033002. Epub 2015 Mar 3.
We investigate through numerical simulation the nonstationary flow of a Newtonian fluid through a two-dimensional channel filled with an array of circular obstacles of distinct sizes. The disks may rotate around their respective centers, modeling a nonstationary, inhomogeneous porous medium. Obstacle sizes and positions are defined by the geometry of an Apollonian packing (AP). To allow for fluid flow, the radii of the disks are uniformly reduced by a factor 0.6≤s≤0.8 for assemblies corresponding to the four first AP generations. The investigation is targeted to elucidate the main features of the rotating regime as compared to the fixed disk condition. It comprises the evaluation of the region of validity of Darcy's law as well as the study of the nonlinear hydraulic resistance as a function of the channel Reynolds number, the reduction factor s, and the AP generation. Depending on a combination of these factors, the resistance of rotating disks may be larger or smaller than that of the corresponding static case. We also analyze the flow redistribution in the interdisk channels as a result of the rotation pattern and characterize the angular velocity of the disks. Here, the striking feature is the emergence of a stable oscillatory behavior of the angular velocity for almost all disks that are inserted into the assemblies after the second generation.
我们通过数值模拟研究了牛顿流体在充满不同尺寸圆形障碍物阵列的二维通道中的非定常流动。圆盘可以绕其各自的中心旋转，模拟非定常、非均匀的多孔介质。障碍物的尺寸和位置由阿波罗尼斯填充（AP）的几何形状定义。为了使流体能够流动，对于对应于前四代AP的组件，圆盘的半径统一缩小0.6≤s≤0.8倍。该研究旨在阐明旋转状态与固定圆盘条件相比的主要特征。它包括评估达西定律的有效区域，以及研究作为通道雷诺数、缩小因子s和AP代的函数的非线性水力阻力。根据这些因素的组合，旋转圆盘的阻力可能大于或小于相应静态情况的阻力。我们还分析了由于旋转模式导致的盘间通道中的流动重新分布，并表征了圆盘的角速度。在此，引人注目的特征是，对于几乎所有在第二代之后插入组件的圆盘，角速度都出现了稳定的振荡行为。
