A numerical approach for the characterization of the free-fall dynamics of thin disks

                                
==Abstract==

This study focuses on investigating numerically the dynamics of thin disks freely falling inside viscous and incompressible fluids. We solve the model by using the finite element method and the main falling modes are identified using the Reynolds number and dimensionless inertia moment. The results are mapped in a phase diagram for comparison with existing literature and validation of the simulations. The effect of introducing a hole in the disk geometry is investigated, analyzing variations in trajectories and Strouhal numbers. Furthermore, falling styles are quantified by examining the fluctuations of the orientation of the axis of the disks over time. Additionally, a quantitative analysis of the solid body velocities for the fluttering and tumbling modes highlights the significant differences between them. The study successfully characterizes the main falling modes through qualitative and quantitative analyses.