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.

Flow-induced coupled vibrations of an elastically mounted cylinder and a detached flexible plate

“…The present code was validated with several benchmark cases by Thekkethil & Sharma (2019) and used in a series of fish-inspired biomimetic studies (Thekkethil, Sharma & Agrawal 2018Gupta et al 2021). Further validations of the code are presented in figure 2, with good agreement between the present and published results on periodic variation of the displacements of the cylinder Y c (figure 2a) and plate-tip Y p (figure 2b).…”

“…The present code was validated with several benchmark cases by Thekkethil & Sharma (2019) and used in a series of fish-inspired biomimetic studies (Thekkethil, Sharma & Agrawal 2018, 2020; Gupta et al. 2021).…”

Level set function–based immersed interface method and benchmark solutions for fluid flexible‐structure interaction

“…For the separate verification of the fluid flow solver, a one‐way coupled fluid and moving rigid‐structure problem is considered where a forced motion is prescribed to the structure (used as the BC at the fluid‐solid interface). The FVM‐ and LS‐IIM‐based present fluid flow solver has been validated/verified in our previous works() for an oscillating cylinder, pitching foil, and undulating foil. The earlier solver used the conventional advection and reinitialisation equations for level set function, whereas the present solver uses the minimum distance and winding number algorithm–based approach.…”

An Overview of Computational Fluid Structure Interaction: Methods and Applications

“…Recently Thekkethil et al [33] performed a unified hydrodynamics study based on various types of motions (pitch, heave and undulation) through an in-house code based on Level Set Immersed boundary formulation. Apart from solving regular Navier stokes equation, two separate equations based on advection velocity at the interface and level-set function were used to classify the domains.…”