Effects of the closed domain area on the dynamics of a closed flexible filament behind a rigid plate

In this study, the effects of the closed domain area on the dynamics of a coupling system consisting of a plate and a flexible filament were investigated. Numerical simulations were performed utilizing the immersed boundary method and a penalty method was adopted to conserve the closed domain area. The drag variation was investigated across various length ratio (Lr) and area reduction (Ar), and the maximum drag reduction of 30.26% was achieved at Lr = 2.0 and Ar = 0%. For a small area reduction like Ar <= 10%, the drag of the system with Lr < 1.75 was lower than that of a fully filled state, but it had a significant increase because of vortex shedding variation for Lr >= 1.75. When Ar exceeded 30%, the system drag closely approached that of the bare plate. Furthermore, the maximum width of the shape envelope was employed to renormalize the drag and considered to roughly estimate drag. In addition, the effects of the bending coefficient (gamma) on filament shapes were concluded. For gamma < 0.01, the filament was closer to the plate as Ar increased. However, for gamma > 0.01, the filament globally bent and flapped like an elastic rod for high Ar avoiding the occurrence of large curvature.