Trajectory modes and wake patterns of freely falling plates

Abstract

The free falling of a plate is an interesting and canonical problem in the study of fluid–body interactions. In this paper, experiments with a wide range of the dimensionless moment of inertia ($I^*=0.05{-}1.6$) and the Reynolds numbers ($Re=10{-}350$) were conducted to investigate the trajectory modes and the corresponding wake patterns of freely falling plates. Experimental results show that the freely falling plates exhibit four trajectory modes including vertical falling, fluttering, tumbling, and chaotic motions. Based on massive experiments, a detailed $Re{-}I^*$ phase diagram is given and shows different trajectory regimes, which are distinguished by clear boundaries. Then, the wake patterns corresponding to different trajectory modes are investigated. When Re is rather small, plates fall vertically and the corresponding wake exhibits a stable and symmetrical pattern. With increasing Re, it is found that the plate falls vertically, whereas the corresponding wake has developed to be similar to the Kármán vortex street, thereby indicating that wake instability should be prior to the path instability. As Re and $I^*$ further increase, both trajectory mode and wake pattern are unstable. The trajectory modes and the wake patterns of the freely falling plates are summarized in one $Re{-}I^*$ phase diagram, and the onset of the wake instability is found to occur when Re is approximately 30.

Graphical abstract