Propulsion Performance and Wake Dynamics of Heaving Foils under Different Waveform Input Perturbations

Abstract

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 square. 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.

Tailbeat perturbations improve swimming efficiency in self-propelled flapping foils

“…A later study by Gao et al. (2021) using computational fluid dynamics (CFD) simulations with a rigid foil flapping in a flow confirmed the increase of thrust with superimposed rhythmic perturbations, but not of efficiency. This poses a question about the factors influencing efficiency since Quinn, Lauder & Smits (2014) show that the specific stiffness of a foil itself can significantly improve it.…”

“…In addition to optimising kinematic properties like the Strouhal number (defined as the ratio of the product of vortex shedding frequency and width of the wake to the swimming velocity) (Triantafyllou, Triantafyllou & Yue 2000), recent research has unveiled that rhythmic perturbations, often considered as ‘noise’ and neglected, can indeed have a positive influence on the hydrodynamic performance of the tethered flapping swimmer (Lehn et al. 2017; Gao, Huang & Pan 2021). Lehn et al.…”

Tailbeat perturbations improve swimming efficiency by reducing the phase lag between body motion and the resulting fluid response

“…In most studies, the high-frequency components, which are typically low in amplitude, are often disregarded in simplified body wave models due to their similarity to noise ( 36 ). As a result, few studies have investigated the role of these high-frequency and low-amplitude perturbations in kinematics ( 37 , 38 ). Lehn et al ( 37 ) found that combining high-frequency and low-amplitude perturbations to flexible flapping foils can increase thrust and efficiency.…”

“…However, it is unclear whether this improvement is mainly due to the flexibility of the foil or the perturbations, as certain stiffness of the foil can also significantly improve efficiency ( 15–17 ). Furthermore, some studies that examined the performance of a flapping rigid foil found that perturbations can enhance thrust but not the efficiency of swimming ( 38 ), thus calling into question the mechanism that allows for increased efficiency with perturbations. In addition, previous studies have primarily investigated how perturbation frequency impacts swimming efficiency, while there is a lack of research exploring the effect of perturbation amplitude, to thrust production and efficiency, as well as the combined impact of both frequency and amplitude.…”

Hydrodynamic performance of manta rays under different motion parameter

“…At present, studies on perturbation parameters are still limited to two-dimensional flapping foils, and no studies have been conducted for three-dimensional real-life organisms. Lehn [19] first added sinusoidal perturbation to the flapping foil to show that applying perturbation can improve thrust and propulsion efficiency, and Gao [20][21][22] conducted numerical studies on the effects of perturbation parameters on the hydrodynamics of heaving foils and obtained the effects of phase difference, perturbation frequency on flap thrust, efficiency, and wake structure.…”