Propulsion performance and wake dynamics of heaving foils under different waveform input perturbations

A numerical simulation is used to investigate the effects of adding high frequency and low amplitude perturbations of different waveforms to the sinusoidal-based signal of the heaving foil on the propulsion performance and wake structure. We use the adjustable parameter k to achieve a heaving motion of various waveform cycle trajectories, such as sawtooth, sine, and sq3e. Adding a perturbation of whatever waveform is beneficial in increasing the thrust of the heaving foil, especially by adding a square wave perturbation with a frequency of 10 Hz, pushes the thrust up to 10.49 times that without the perturbation. However, the addition of the perturbation signal brings a reduction in propulsion efficiency, and the larger the perturbation frequency, the lower the efficiency. The wake structure of the heaving foil behaves similarly under different waveform perturbations, all going through some intermediate stages, which eventually evolve into a chaotic wake with the increase in the perturbation frequency. However, a lower frequency square wave perturbation can destabilize the heaving foil wake structure. This work further explains the effect of different waveform perturbation signals on the base sinusoidal signal and provides a new control idea for underwater vehicles.