Symmetry breaking of a closed flexible filament behind a rigid plate at low Reynolds numbers

In this paper, the motion modes transition and dynamic performance of the flow past a rigid-flexible coupling system were investigated at low Reynolds numbers. The coupling system consisted of a rigid plate and a trailing closed flexible filament and was simulated numerically using the immersed boundary method. According to whether the filament moves and the symmetry of its movement, six motion modes have been identified for different filament lengths and Reynolds numbers ( Re), i.e. symmetric and stationary (SS) mode, asymmetric and stationary (AS) mode, regular and unilateral flap (RUF) mode, transition motion (TM) mode, symmetric and bilateral flap (SBF) mode, and asymmetric and bilateral flap (ABF) mode. Moreover, symmetry breaking occurred in the AS mode, RUF mode, and ABF mode. Drag reduction was found at Re {greater than or equal to} 40, which was mainly influenced by the pressure behind the filament. However, it was weakened for the filament with Lr {greater than or equal to} 2.57 because of its large width suffered to the flow, where Lr is the ratio of the length of the filament to the width of the plate. The time-averaged lift was also found to be directly dependent on the symmetry of the filament. In addition, the motion modes were significantly affected by the bending coefficient of the filament. Symmetry breaking was prevented by the reduction of the bending coefficient before vortex shedding. Moreover, if the filament was symmetric before vortex shedding, the RUF mode and the TM mode did not appear with the increase of Re.