Working characteristics of self-pitching flapping foil propulsor

This work investigates the working characteristics of a large amplitude semi-passive flapping-foil with a prescribed sinusoidal heave motion and a passive pitch motion. Different from the active flapping foil with two degrees of freedom, this self-pitching flapping foil ( SPFF ) constructs a single degree of freedom spring mass system in the direction around the pitching motion axis. Because of the torsion spring attached to the foil, this kind of foil is a flow-induced vibration system, and the torsional spring stiffness, the foil inertia and the hydrodynamic added inertia should affect the propulsive performance. Its working characteristics are affected by two non-dimensional coeffificients: the frequency ratio r and spring stiffness ratio k’ according to dimensional analysis. In this paper, the fluid-structure coupling method is used to analyze the working characteristics of the self-pitching flapping foil with different parameter settings. After the verification of the numerical method, the investigation first discusses the working characteristics of the self-pitching flapping foil when the system resonates and identifies that the resonance can make the self-pitching flapping foil deviate from the ideal angle of attack, and its fluctuation of short-term average thrust coefficient becomes irregular. That leads to the performance degradation of self-pitching flapping foil and even the loss of propulsion ability. Then the influence of frequency ratio on the propulsive performance is investigated. The numerical results confirm that the semi-active flapping foil performs efficiently when the frequency ratio r is small, and the maximum efficiency can reach as high as 86%; the more suitable frequency ratio is recommended to be less than 0.5. Finally, the effect of spring stiffness ratio is discussed under a small frequency ratio. The results imply that the peak efficiency of self-pitching flapping foil is not monotonic with different spring stiffness ratio, and there is a maximum value; but self-pitching flapping foil can maintain the peak efficiency over a wider range of spring stiffness ratio, the range is 0.1 ~ 1000 in this report; Through the analysis of the performance curves of the foil with different pitching center positions, it indicates that the influence trend of pitching center position is close to that of the spring stiffness ratio.