Influence of complex driving motion on propulsion performance of a heaving flexible foil

This study explores the effects of complex driving motion on the propulsion performance of a flexible foil heaving in the flight regimes of natural flyers. Such a fluid-structure interaction problem is numerically studied using an immersed boundary lattice Boltzmann method (IBLBM) based numerical framework. It is found that, at the Reynolds number 200 and when the foil's bending stiffness and mass ratio are moderate, adding an extra driving motion of doubled frequency to a purely harmonic motion on the foil's leading edge can enhance the thrust and propulsive efficiency by about 860% and 70%, respectively. The improvement in thrust increases with the extra-driving-motion amplitude. When the extra-driving-motion amplitude is fixed, there exists an optimal extra-driving-motion phase angle. As the foil becomes much stiffer or lighter, the improvement in the propulsion performance turns less. On the other hand, as the foil becomes much more flexible or heavier, drag instead of thrust is generated, and extra driving motion brings no improvement. Although the extra driving motion can improve the foil's propulsion performance in flows of different Reynolds numbers, the increasing rate of the thrust reduces with the Reynolds number. Through this study, details about the competitions among various forces exerted on the foil and their roles in the foil's dynamics are also revealed.