Vortical structures around a flexible oscillating panel for maximum thrust in a quiescent fluid

It has been agreed that a proper level of flexibility in moving appendages like a fin of swimming animals enhances their propulsive performance. However, a few efforts have been spent to characterize the criterion, as a simple guideline for designing a biomimetic propulsor, at which the beneficial effect of compliance is maximized. Recently, it was reported that a sinusoidally pitching panel produces the enhanced thrust when the passively bending angle of a trailing edge lags behind its pitching angle by around π/2 due to its compliance. To understand its mechanism, we perform a series of particle image velocimetry measurements around a panel pitching in quiescent water, while varying its compliance, planform shape and pitching frequency. For all the planform shapes and frequencies considered, with a phase delay of about π/2, the region of high streamwise velocity with thrust-generating momentum is retained farther (in the streamwise direction) in the wake, caused by the large effective pitching angle during the accelerating stage of pitching rotation. When the panel is stiffer (or the phase delay is smaller than π/2) than the optimal condition, however, a strong interaction between the trailing-edge vortices (TEVs) formed successively at each half strokes pushes the surrounding fluid into the transverse direction, thereby accelerating the decay of thrust-generating streamwise velocity. This interaction between TEVs is weak for the case of optimal compliance. On the other hand, in the case of over-compliance, the trailing edge of the panel rotates opposite to the pitching direction, which indicates that the inertial work required to rotate the panel during the stroke-reversal becomes excessive at the expense of rotational circulation which eventually weakens the thrust.