How swimming style affects schooling of two fish-like wavy hydrofoils

TL;DR

This study investigates how different swimming styles influence the schooling behavior of two fish-like hydrofoils, revealing optimal conditions for efficiency, stable formations, and flow control through extensive simulations.

Contribution

It provides a comprehensive analysis of the effects of swimming style parameters on fish schooling dynamics using high-fidelity simulations, highlighting optimal configurations for efficiency and stability.

Findings

Higher wavelength increases thrust and lateral force.

Maximum efficiency at intermediate wavelength (λ* = 2).

Stable side-by-side formation observed at D=0.

Abstract

Fish swimming style and schooling behaviour are two important aspects of underwater locomotion. How swimming style affects fish schooling is investigated by a representative problem setup consisting of two tethered NACA0012 hydrofoils undulating in a free stream flow at various wavelengths $ \lambda^* = 0.8 - 8 $, front-back distance $ D = 0,\ 0.25,\ 0.5,\ 0.75 $, phase difference $ \phi/\pi = 0,\ 0.5,\ 1,\ 1.5 $, and lateral gap distance $ G = 0.25,\ 0.3,\ 0.35 $ with fixed Reynolds number $ Re = 5000 $, Strouhal number $ St = 0.4 $, and maximum amplitude $ A_{max} = 0.1 $. In total, 336 cases were simulated by open-source software IBAMR based on immersed boundary method. The increase in wavelength generally leads to higher thrust and lateral force, consistent with a previous study regarding a single swimmer. The highest Froude efficiency is obtained at intermediate wavelength $ \lambda^* = 2 $ for either individual or two foils as a group. At side-by-side arrangement $ D = 0 $, the thrust force upon the two foils can be equivalent, indicating a stable formation. At staggered arrangement, $ D > 0 $, the follower can take significant advantage of the leader in locomotion performance by tuning phase difference. The follower's benefit decreases with relative distance. Various combinations of wavelength and relative distance can lead to distinct flow structures, indicating a tunable stealth capacity of the schooling swimmers.