Effect of input perturbation on the performance and wake dynamics of aquatic propulsion in heaving flexible foils

In this paper we consider the effects of adding high-frequency, low-amplitude perturbations to a smooth sinusoidal base input signal for a heaving panel in a closed loop flow tank. Specifically, 0.1 cm amplitude sinusoidal perturbation waves with frequency f(p) ranging from 0.5 to 13.0 Hz are added to 1 cm heave sinusoids with base frequencies, f(b), ranging from 0.5 to 3.0 Hz. Two thin foils with different flexural stiffness are heaved with the combined input signals in addition to both the high-heave and low-heave signals independently. In all cases, the foils are heaved in a recirculating water channel with an incoming velocity of V-x = 10 cm/s and a Reynolds number based on the chord length of Re = 17 300. Results demonstrate that perturbations increase the net axial force, in the streamwise direction, in most cases tested (with the exception of some poor performing flexible foil cases). Most significantly, for a base frequency of 1 Hz, perturbations at 9 Hz result in a 780.7% increase in net streamwise force production. Generally, the higher the perturbation frequency, f(p) the more axial force generated. However, for the stiffer foil, a clear peak in net force exists at f(p) = 9 Hz, regardless of the base frequency. For the stiffer foil, swimming efficiency at a 1 Hz flapping frequency is increased dramatically with the addition of a perturbation, with reduced efficiency increases at higher flapping frequencies. Likewise, for the flexible foil, swimming efficiency gains are greatest at the lower flapping frequencies. Perturbations alter the wake structure by increasing the vorticity magnitude and increasing the vortex shedding frequency; i.e., more, stronger vortices are produced in each flapping cycle.