Fluid flow through packings of rotating obstacles

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.