Actively flapping tandem flexible flags in a viscous flow

Abstract

The active flapping motions of fish and cetaceans generate both propulsive and manoeuvring forces. The tail fin motions of the majority of fish can essentially be viewed as a combined pitch-and-heave motion. Downstream bodies are strongly influenced by the vortices shed from an upstream body. To investigate the interactions between flexible bodies and vortices, the present study examined tandem flexible flags in a viscous flow by using an improved version of the immersed boundary method. The upstream flag underwent passive flapping in a uniform flow while the downstream flag flapped according to a prescribed pitching and heaving motion of the leading edge. The influences of the active flapping motion on the system dynamics were examined in detail, including the frequency, the phase angle, the bending coefficient and the amplitudes of the pitching and heaving motion. The variation of the drag coefficient of the downstream flag was explored together with the instantaneous vorticity contours and the body shapes. Both the slalom mode and the interception mode were identified according to the vortex–flexible body interactions, corresponding to the low- and high-drag situations, respectively. The underlying mechanism was discussed and compared with previous studies.