Mode transition of a coupled rigid-flexible system in a uniform flow

The interaction between a rigid-flexible system and ambient fluid was simulated numerically at Re = 300 by the immersed boundary method. The rigid-flexible system consists of a stationary rigid plate upstream and a closed flexible filament downstream. For different filament lengths, four typical regimes for the motions of the flexible filament were observed. As the length increases, the flexible filament successively experiences the plate-like (P) mode, the cylinder-like (C) mode, the slender-shape (S) mode and finally enters the wriggling (W) mode. It was demonstrated by the frequency spectra that when the filament length increases up to a critical value, the second harmonic becomes dominant, corresponding to the transition from the S mode to the W mode, and at the transition point, the drag exerted on the rigid-flexible system becomes minimum. The occurrence of the S-W mode transition was found to be caused by the increased inertia of the filament.