Transient effects during transitions of bio-inspired flapping foils between two different schooling configurations

Recently, there has been considerable interest in developing novel energy-saving vehicles that use flapping foils propulsion systems inspired by biology. Facing increasingly complex application tasks, the coordination of multiple vehicles will be a hot issue in the future this research field. We are inspired by changes in configurations of biological collective behavior (known as schooling) in nature, focused on studying transient effects during transitions of three-dimensional bio-inspired flapping foils between two different bionic schooling configurations. Numerical simulations employing the immersed boundary-lattice Boltzmann method (IB-LBM) for unsteady hydrodynamics of flapping foils in schooling transitions were performed. Effects of different mutual transition modes between tandem and diamond schooling configurations on their thrust performance were investigated. Meanwhile, we present hydrodynamics of flapping foils in a schooling with different downstream flapping frequencies under the best transition mode. The results show that during transitions between two schooling configurations, there is an optimal energy-saving transition mode. It has nothing to do with the length of transition distance. Different downstream flapping frequencies will affect the interacting vortices between fluid and structure and then affect transient effects during schooling transition. Although the transition modes were specified, our research takes the transients effects of schooling transitions as an influencing factor to be considered for formations changes, which will provide a new idea for the design bio-inspired vehicle cluster formation.

The performance of a flapping foil for a self-propelled fishlike body

Several fish species propel by oscillating the tail, while the remaining part of the body essentially contributes to the overall drag. Since in this case thrust and drag are in a way separable, most attention was focused on the study of propulsive efficiency for flapping foils under a prescribed stream. We claim here that the swimming performance should be evaluated, as for undulating fish whose drag and thrust are severely entangled, by turning to self-propelled locomotion to find the proper speed and the cost of transport for a given fishlike body. As a major finding, the minimum value of this quantity corresponds to a locomotion speed in a range markedly different from the one associated with the optimal efficiency of the propulsor. A large value of the feathering parameter characterizes the minimum cost of transport while the optimal efficiency is related to a large effective angle of attack. We adopt here a simple two-dimensional model for both inviscid and viscous flows to proof the above statements in the case of self-propelled axial swimming. We believe that such an easy approach gives a way for a direct extension to fully free swimming and to real-life configurations.

Contrasting thrust generation mechanics and energetics of flapping foil locomotory states characterized by a unified - scaling

Self-propelled flapping foils with distinct locomotion-enabling kinematic restraints exhibit a remarkably similar Strouhal number ( $St$ )-Reynolds number ( $Re$ ) dependence. This similarity has been hypothesized to pervade diverse forms of oscillatory self-propulsion and undulatory biolocomotion; however, its genesis and implications on the energetic cost of locomotion remain elusive. Here, using high-resolution simulations of translationally free and restrained foils that self-propel as they are pitched, we demonstrate that a generality in the $St$ - $Re$ relationship can emerge despite significant disparities in thrust generation mechanics and locomotory performance. Specifically, owing to a recoil reaction induced passive heave, the fluid's inertial response to the prescribed rotational pitch, the principal source of thrust in unidirectionally free and towed configurations, ceases to produce thrust in a bidirectionally free configuration. Rather, the thrust generated from the leading edge suction mechanics self-propels a bidirectionally free pitching foil. Owing to the foregoing distinction in the thrust generation mechanics, the $St$ - $Re$ relationships for the bidirectionally and unidirectionally free/towed foils are dissimilar and pitching amplitude dependent, but specifically for large reduced frequencies, converge to a previously reported unified power law. Importantly, to propel at a given mean forward speed, the bidirectionally free foil must counteract the out-of-phase passive heave through a more intense rotational pitch, resulting in an appreciably higher power consumption over the range $10 \leq Re \leq 10^3$ . We highlight the critical role of thrust in introducing an offset in the $St$ - $Re$ relation, and through its amplification, being ultimately responsible for the considerable disparity in the locomotory performance of differentially constrained foils.

Investigation on Hydrodynamic Performance of Flapping Foil Interacting with Oncoming Von Kármán Wake of a D-Section Cylinder

Flapping foils are studied to achieve an efficient propeller. The performance of the flapping foil is influenced by many factors such as oncoming vortices, heaving amplitude, and geometrical parameters. In this paper, investigations are performed on flapping foils to assess its performance in the wake of a D-section cylinder located half a diameter in front of the foil. The effects of heaving amplitude and foil thickness are examined. The results indicate that oncoming vortices facilitate the flapping motion. Although the thrust increases with the increasing heaving amplitude, the propelling efficiency decreases with it. Moreover, increasing thickness results in higher efficiency. The highest propelling efficiency is achieved when the heaving amplitude equals ten percent of the chord length with a symmetric foil type of NACA0050 foil. When the heaving amplitude is small, the influence of the thickness tends to be more remarkable. The propelling efficiency exceeds 100% and the heaving amplitude is 10% of the chord length when the commonly used equation is adopted. This result demonstrates that the flapping motion extracts some energy from the oncoming vortices. Based on the numerical results, a new parameter, the energy transforming ratio (RET), is applied to explicate the energy transforming procedure. The RET represents that the flapping foil is driven by the engine or both the engines and the oncoming vortices with the range of RET being (0, Infini) and (−1, 0), respectively. With what has been discussed in this paper, the oncoming wake of the D-section cylinder benefits the flapping motion which indicates that the macro underwater vehicle performs better following a bluff body.