Fluid–structure interaction response of flapping flexible forked plates in drag mode

Bioinspired forked plates are employed as a model system to investigate fundamental fluid–structure interaction (FSI) mechanisms in flexible flapping systems. Although extensive research has been conducted on the FSI response of flapping forked plates in thrust mode, their FSI characteristics in drag mode remain largely unexplored. In this paper, a direct-forcing immersed boundary method is implemented in OpenFOAM, supplemented by systematic validations of grid independence and numerical methodology. Simulations are performed at Re = 500 for aspect ratios ranging from 3 to 6 and dimensionless stiffness spanning several orders of magnitude. The results show that the FSI dynamics are governed by the relationship between the driving frequency and the structural natural frequencies, which defines distinct modal regimes. The maximum drag and highest energy extraction efficiency occur near the third vibration mode, highlighting the critical role of coupled spanwise-chordwise deformation. Minimum drag occurs well below the first resonant frequency. The wake topology is also strongly mode-dependent: high-order modes promote inward curling of the forked branches and merging of side-edge vortices, whereas low-order modes are dominated by vortex shedding from the inner edges. Notably, while anti-Karman vortex streets are observed at high stiffness, the flapping forked plate continues to experience net drag due to the phase relationship between structural deformation and fluid loading. Notably, inverse Karman vortex streets are observed at high stiffness while the plate still experiences net drag, indicating a mismatch between wake pattern and force generation due to the phase relationship between structural deformation and fluid loading.