Two-and three-dimensional low-aspect-ratio (AR 4) hovering airfoil/wing aerodynamics at a low Reynolds number (Re 100) are numerically investigated. Regarding fluid physics, in addition to the well-known leading-edge vortex and wake-capture mechanisms, a persistent jet, induced by the shed vortices in the wake during previous strokes, and tip vortices can significantly influence the lift and power performance. While in classical stationary wing theory the tip vortices are seen as wasted energy, here, they can interact with the leading-edge vortex to contribute to the lift generated without increasing the power requirements. Using surrogate modeling techniques, the two-and three-dimensional time-averaged aerodynamic forces were predicted well over a large range of kinematic motions when compared with the Navier-Stokes solutions. The combined effects of tip vortices, leading-edge vortex, and jet can be manipulated by the choice of kinematics to make a three-dimensional wing aerodynamically better or worse than an infinitely long wing. The environmental sensitivity during hovering for select kinematics is also examined. Different freestream strengths and orientations are imposed, with the impact on vortex generation and wake interaction investigated.

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Flying animals possess flexible wings that deform during flight. The chordwise flexibility alters the wing shape, affecting the effective angle of attack and hence the surrounding aerodynamics. However, the effects of spanwise flexibility on the locomotion are inadequately understood. Here, we present a two-way coupled aeroelastic model of a plunging spanwise flexible wing. The aerodynamics is modelled with a two-dimensional, unsteady, incompressible potential flow model, evaluated at each spanwise location of the wing. The two-way coupling is realized by considering the transverse displacement as the effective plunge under the dynamic balance of wing inertia, elastic restoring force and aerodynamic force. The thrust is a result of the competition between the enhancement due to wing deformation and induced drag. The results for a purely plunging spanwise flexible wing agree well with experimental and high-fidelity numerical results from the literature. Our analysis suggests that the wing aspect ratio of the abstracted passerine and goose models corresponds to the optimal aeroelastic response, generating the highest thrust while minimizing the power required to flap the wings. At these optimal aspect ratios, the flapping frequency is near the first spanwise natural frequency of the wing, suggesting that these birds may benefit from the resonance to generate thrust.

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