Study on energy extraction of Kármán gait hydrofoils from passing vortices

Abstract

How swimming fish extract energy from environmental vortices is still an open question. In this work, fish swimming in unsteady flow is numerically investigated by using the immersed boundary lattice Boltzmann method. The swimming fish is modeled as a forced Kármán gait hydrofoil, and the vortical flow is generated by a stationary circular cylinder. We calculate the Fourier spectra of hydrodynamic forces on the hydrofoil surface and found that there is a coupling between lateral force and drag, which results from a nonlinear wave interaction. The Kármán gait hydrofoil adjusts the lateral force by applying lateral excitation to the vortical flow and improves the drag/thrust through nonlinear wave interaction. We find that suppressing the harmonic energy of the viscous mode is the key ingredient to extract energy from the passing vortex. In turn, the downstream distance LN and foil-vortex phase φ determine whether the viscous harmonic energy can be suppressed. If the viscous mode harmonic is strong, the interaction between the vortex shedding mode and the viscous mode leads to a series of combined modes, which extract energy from the fundamental mode. These combined modes that appear in the fluid force spectra reduce the efficiency of energy extraction.