The pappus angle as a key factor in the entire separation of a vortex ring from a dandelion seed’s pappus

Abstract

A separated vortex ring is the main aerodynamic feature of the dandelion seed which enables its flight. However, recent research on simply modeled dandelion seeds with a pappus angle of 180° (flat porous disk) shows that the vortex ring is not entirely separated from the pappus. This significantly differs from what is observed in a real dandelion seed and would prevent us from fully understanding its flight mechanism. In this work, the two key structural features of the pappus that are considered in the work of others, i.e., the circular disk-like geometry and the porosity, were expected to be insufficient to form an entirely separated vortex ring. Therefore, refined numerical simulations were conducted on model pappi with different pappus angles, which are more similar to real dandelion seeds than flat porous disks. A stable and entirely separated vortex ring and a small vortex ring above the central disk were observed. The lower pappus angle increases the radial pressure gradient toward the central axis between the root of the filaments. When the net effect of this pressure gradient is large enough to overcome the effect of the pressure gradient away from the central axis below the pappus, the streamlines near the root of the filaments deflect to the central axis and the vortex ring is lifted and separates entirely. It is concluded that an appropriate pappus angle is another key feature for forming an entirely separated vortex ring. This more in-depth flow mechanism is of considerable reference value for future research.