Force decomposition of vortex–plate interaction via dynamic mode decomposition

This study investigates the dynamics of two tandem flexible plates flapping in a uniform flow, focusing on how variations in their phase angle affect thrust generation. Considerable emphasis is given to the interactions between the wakes of the two plates and their subsequent effects on the performance of the rear plate. By applying Dynamic Mode Decomposition (DMD) alongside vortex dynamics analysis, the force exerted on the rear plate is quantitatively assessed in relation to the surrounding flow structures. The results show a decline in the rear plate's thrust when it enters a “locked vortex” state, primarily due to diminished leading-edge suction. The analysis also reveals a strong correlation between the dominant mode f^∗=1 and the time-averaged forces, which aligns with the observed vortex–plate interaction patterns. Furthermore, the study demonstrates that the time-averaged horizontal force on the rear plate is largely influenced by low-frequency dominant modes, underscoring the importance of these interactions for optimizing propulsion systems.