Effects of Plunging Acceleration on the Passive Morphing of Avian-Inspired Flexible Foils

Abstract

This study investigates the dynamics of passively morphing foils under accelerated plunging, establishing mechanistic links between transient kinematics, structural compliance, and aerodynamic performance. Two-way coupled simulations are performed for three wing geometries: a symmetric NACA0012 foil and two bio-inspired geometries based on falcon and owl wing sections, across non-dimensional bending rigidity values, chordwise flexible segment extents from the trailing-edge (25%, 50%, and 75%), and transition speed parameters. The present findings reveal that flexible trailing-edge configurations exhibit improved aerodynamic performance relative to stiffer foils, and the aerodynamic benefit of trailing-edge compliance is strongly influenced by wing geometry. A geometry-specific optimal bending stiffness exists beyond which additional flexibility degrades performance. The extent of the chordwise flexible segment critically governs the aeroelastic response. Whilst a 25% flexible segment produces behaviour indistinguishable from a rigid wing, extending flexibility to 75% of the chord induces highly unsteady lift fluctuations, particularly for the NACA0012 foil, for which the root-mean-square lift coefficient increases sharply. The bio-inspired foils, in contrast, exhibit a moderate reduction in root-mean-square lift coefficient for the 50% and 75% cases, reflecting the stabilising influence of their cambered geometry. Increasing the transition speed parameter monotonically amplifies trailing-edge deflection, strengthens the leading- and trailing-edge vortices, and intensifies the coupling between structural deformation and instantaneous lift. These findings provide new physical insight into bio-inspired propulsion and manoeuvring strategies, with implications for the design of passively adaptive lifting surfaces in unsteady environments.

Figures (20)

• Figure 1: Schematic representation of the bio-inspired wing sections of (a) peregrine falcon and (b) barn owl, investigated in this study; (c) the present computational domain with dimensions and boundary conditions (not drawn to scale); (d) the zoomed insets of the fluid mesh with multiple refinement zones indicated in red, (e) the representative solid mesh for the falcon wing section; the prescribed accelerated plunging kinematics (f) displacement, and (g) the corresponding accelerations across a range of transition-speed parameter ($a_s$) values investigated.
• Figure 2: Schematic representation of the fluid-structure coupling framework.
• Figure 3: Grid independence study -- time histories of (a) normalised transverse displacement $D_y/c$ and (b) lift coefficient $C_l$ for the coarse, medium, and fine mesh configurations, with close-up views of the peak regions shown in (c) and (d), respectively. Panels (e) and (f) present the corresponding Richardson extrapolation curves for the peak values $D_{y_{\max}}/c$ and $C_{l_{\max}}$, respectively, demonstrating convergence of both quantities with mesh refinement.
• Figure 4: Time step independence study -- time histories of (a) normalised transverse displacement $D_y/c$ and (b) lift coefficient $C_l$ for the three time step sizes tested ($\Delta t =8 \times 10^{-4}$, $5 \times 10^{-4}$, and $2 \times 10^{-4}$), with close-up views of the peak regions shown in (c) and (d), respectively, demonstrating convergence of both quantities with temporal refinement.
• Figure 5: Flow solver validation -- (a) vorticity contours around the NACA0012 foil, falcon, and owl wing sections reproduced from harvey and (b) corresponding contours obtained from the present simulations, where Colorbar 1 and Colorbar 2 denote the colour scales associated with the reference and present results, respectively; (c) a comparison of the dynamic stall vortex formation angle for the three wing sections against the experimental measurements of harvey, demonstrating close agreement across all geometries.