Numerical investigations on the force generation and wake structures of a nonsinusoidal pitching foil

We numerically investigate the force generation and wake structures of a nonsinusoidal periodic pitching foil under a thickness-based Reynolds number of Re_D=255. We consider various nonsinusoidal periodic trajectories of pitching motion, such as the sawtooth and square trajectories, using an adjustable parameter, K. Similar to previous studies on sinusoidal pitching foils, the present results for the nonsinusoidal pitching foil indicate that the transition from a Bénard–von Kármán wake to a reverse Bé nard–von Kármán wake precedes the actual drag–thrust transition. In addition, the symmetry breaking of a reverse Bé nard–von Kármán wake is observed. As K increases, the drag–thrust transition of the nonsinusoidal pitching foil advances gradually and it becomes easy to destabilize the wake structures produced by the oscillating foil. Since K physically describes how rapidly the foil reverses its pitching direction, we argue that the initial velocity of vortex shedding from the foil increases with K and results in the aforementioned phenomena. The present work provides helpful findings for better understanding the kinematic behaviour of actual animals and for designing bio-inspired robotics.