Effect of perturbations with different phases on the propulsive performance of rigid heaving foils

What effect does the addition of high-frequency, low-amplitude perturbation signals with various phase differences have on a flapping foil that originally performs only a sinusoidal heaving motion? To answer this question, we use numerical simulations to investigate the propulsion performance and wake structure of a rigid NACA0012 heaving foil under sinusoidal perturbation signals with various phase differences. Numerical calculations show that adding perturbations with any phase difference is beneficial for increasing the heaving foil thrust. Especially at a base frequency of 0.5 Hz, the addition of a 12 Hz perturbation frequency with a phase difference of π/2 increases the axial thrust to 873% of the original. We also find for the first time that additional perturbation enhances the propulsion efficiency of a rigid sinusoidal heaving foil (at a phase difference of π). From the analysis of the wake structure, we find that the base frequency determines the initial shape of the wake structure, but with the increase in the perturbation frequency, the wake structure evolves into either a deflected 2S wake or chaotic wake after experiencing some intermediate stages.