Effects of time-varying flexibility on the propulsion performance of a flapping foil

In this paper, we numerically investigate the effects of time-varying bending stiffness on the propulsion performance of a flapping foil using a fully coupled fluid-structure interaction model. The flow field is simulated using a Navier-Stokes solver while the structural dynamics is resolved by a nonlinear beam model. The force generation, the passive deformation and the flow field of the flexible foil are significantly affected by the time dependency of flexibility. Here, both the actuation at the leading edge and the stiffness of the foil vary sinusoidally and the phase ϕ between them plays an important role in determining the performance of the foil. At ϕ = 0 degree, the maximum time-averaged thrust coefficient can be increased by approximately 52% whereas the highest propulsion efficiency remains almost the same as that of the foil with a constant flexibility. This is of significance when the size of the wing is often constrained. Additionally, the foil with time-varying stiffness generates considerable lift force, which is attributed to the non-symmetrical deformations and deflected vortex-shedding patterns. Finally, the force generation due to added mass is discussed using a simplified model.