Unified hydrodynamics study for various types of fishes-like undulating rigid hydrofoil in a free stream flow

Abstract

A generic kinematic model is presented for a unified hydrodynamics study covering the various types of motion found in real as well as hypothetical fish-like undulation. Undulating motion is presented here as a generic motion, considering chordwise forced flexibility—modelled by wavelength of undulation λ*—of a rigid NACA0012 hydrofoil in a free-stream flow. Using a level-set immersed boundary method-based in-house code, a non-dimensional study is presented for various wavelengths, λ* (0.8–8.0), and frequency of undulation, St (0.2–0.7), at a constant maximum amplitude of undulation of 0.1 and Reynolds number of 5000. A unified cause-and-effect-based analysis is presented with the help of flow patterns and propulsive performance parameters. Pressure contour demonstrates how the travelling wave distributes momentum in the streamwise direction and reduces the lateral force coefficient. Vorticity contours elucidate the mechanism of formation of reverse von Kármán vortex street and the secondary vortices. A correlation is proposed for thrust coefficient as a function of λ* and St. Good qualitative agreement is observed between the simulated results at smaller λ*-based undulating and larger λ*-based pitching foil and the published results for the anguilliform and thunniform fishes, respectively. The agreement with the real fishes is presented for the relative magnitude of thrust coefficient, propulsive efficiency, dynamic stabilization, and signal of the prey fish for the predator fish. Similar to propulsive performance of real fishes, larger (smaller) flexibility-based undulation (pitching) results in larger propulsive efficiency (thrust generation)—which can be used for the design of fish-like biomimetic propulsion system.