Effect of porosity on the kinematics of free-falling porous disks

The effects of porosity on the kinematics of porous disks are investigated experimentally. A new falling motion is identified, namely, spiral irregular motion, which is characterized by the irregular centerline and spiral motion around the centerline. Multifractal analysis is introduced to quantify the self-similarity and space-filling of irregular centerlines. Generally, the capacity dimension D0 decreases as the diameter ratio between the inner holes and the disk diameter χ increases. However, there is a deviation at χ = 0.2. To explain this unordinary deviation, wake is visualized by particle image velocimetry. An oblique vortex ring with high vorticity is responsible for this anomaly. With χ increasing, the angle of attack increases nonlinearly and the distance Rp between paths and centerlines decreases. However, the nutation angle does not vary monotonically with χ, and a minimum appears at χ = 0.2. The Strouhal number St and the drag coefficient Cd share the same trend with χ; hence, Cd increases monotonically with St. Both St and Cd reach a maximum at χ = 0.15. These findings can be applied to improve the aerodynamic stability of disk-shaped passive fliers and give theoretical insight into parameter selection.