Department of Mechanical and Aerospace Engineering, University of Alabama in Huntsville, Huntsville, AL 35899, USA.
Department of Mechanical and Aerospace Engineering, University of Alabama in Huntsville, Huntsville, AL 35899, USA
J R Soc Interface. 2017 Nov;14(136). doi: 10.1098/rsif.2017.0725.
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.
飞行动物拥有灵活的翅膀，在飞行过程中会发生变形。翼弦方向的柔韧性会改变机翼形状，影响有效迎角，从而影响周围的空气动力学。然而，展向柔韧性对运动的影响尚未得到充分理解。在这里，我们提出了一种俯冲展向柔性机翼的双向耦合气动弹性模型。通过在机翼的每个展向位置评估二维、非定常、不可压缩位势流模型来模拟空气动力学。通过考虑横向位移作为在机翼惯性、弹性恢复力和空气动力的动态平衡下的有效下俯，实现了双向耦合。推力是机翼变形增强和诱导阻力之间竞争的结果。对于纯粹俯冲展向柔性机翼的结果与文献中的实验和高保真数值结果吻合较好。我们的分析表明，抽象的雀形目和鹅模型的机翼展弦比对应于最佳的气动弹性响应，在最小化翅膀拍打所需功率的同时产生最大的推力。在这些最佳展弦比下，拍打频率接近机翼的第一展向固有频率，这表明这些鸟类可能受益于共振来产生推力。
