Enhancing propulsion performance of a flexible heaving foil through dynamically adjusting its flexibility

This study investigates how dynamically adjusting the bending stiffness of a heaving foil affects its propulsion performance in a flow of Reynolds number 200. The foil is forced to oscillate sinusoidally at the leading edge, and its bending stiffness is tuned in a square-wave manner. Such a fluid-structure interaction (FSI) problem is explored using an immersed boundary lattice Boltzmann method (IBLBM) based numerical framework. The results reveal that when the lower and upper bounds of the foil's time-dependent bending stiffness are moderate, the net thrust can be evidently enhanced compared to those in the corresponding constant-bending-stiffness cases, while the propulsion efficiency is not apparently ameliorated. The most significant enhancement is observed when the bending stiffness has lower and upper bounds of the same duration (i.e. a duty cycle of 1/2) and also it remains at the lower bound during stroke reversals (corresponding to an actuation phase angle of pi/2). When the two bounds simultaneously increase or decrease, however, dynamically adjusting the bending stiffness fails to improve the net thrust. Through this study, competitions among various forces/moments, including the inertial force, tension force, bending moment and fluid loading, acting on the foil and their influences on the foil's dynamics are also unveiled.