Chang Sheng-Kai, Lin You-Jun, Hsu Kuan-Lun, Yang Jing-Tang
Department of Mechanical Engineering, National Taiwan University, Taipei 106319, Taiwan.
Phys Rev E. 2023 Jun;107(6-2):065105. doi: 10.1103/PhysRevE.107.065105.
The effect of wing shape on a forward-flying butterfly via decoupled factors of the wing-swept angle and the aspect ratio (AR) was investigated numerically. The wing-shape effect is a major concern in the design of a microaerial vehicle (MAV). In nature, the wing of a butterfly consists of partially overlapping forewing and hindwing; when the forewing sweeps forward or backward relative to the hindwing, the wing-swept angle and the AR of the entire wing simultaneously change. The effects of the wing-swept angle and AR on aerodynamics are coupled. To decouple their effects, we established wing-shape models with varied combinations of the wing-swept angle and AR based on the experimental measurement of two butterfly species (Papilio polytes and Kallima inachus) and developed a numerical simulation for analysis. In each model, the forewing and hindwing overlapped partially, constructing a single wing. Across the models, the wing-swept angle and AR of these single wings varied sequentially. The results show that, through our models, the effects of the wing-swept angle and AR were decoupled; both have distinct flow mechanisms and aerodynamic force trends and are consistent in the two butterfly species. For a fixed AR, a backward-swept wing increases lift and drag because of the enhanced attachment of the leading-edge vortex with increased strength of the wingtip vortex and the spanwise flow. For a fixed wing-swept angle, a small AR wing increases lift and decreases drag because of the large region of low pressure downstream and the wake-capture effect. Coupling these effects, the largest lift-to-drag ratio occurs for a forward-swept wing with the smallest AR. These results indicate that, in a flapping forward flight, sweeping a forewing forward relative to a hindwing is suitable for cruising. The flow mechanisms and decoupled and coupled effects of the wing-swept angle and the AR presented in this paper provide insight into the flight of a butterfly and the design of a MAV.
通过翼展后掠角和展弦比（AR）的解耦因素，对向前飞行的蝴蝶的翼形效应进行了数值研究。翼形效应是微型飞行器（MAV）设计中的一个主要关注点。在自然界中，蝴蝶的翅膀由部分重叠的前翅和后翅组成；当前翅相对于后翅向前或向后扫掠时，整个翅膀的翼展后掠角和展弦比会同时发生变化。翼展后掠角和展弦比对空气动力学的影响是相互耦合的。为了解耦它们的影响，我们基于对两种蝴蝶（柑橘凤蝶和枯叶蛱蝶）的实验测量，建立了具有不同翼展后掠角和展弦比组合的翼形模型，并开发了用于分析的数值模拟。在每个模型中，前翅和后翅部分重叠，构成一个单一的翅膀。在所有模型中，这些单一翅膀的翼展后掠角和展弦比依次变化。结果表明，通过我们的模型，翼展后掠角和展弦比的影响被解耦；两者都有独特的流动机制和空气动力趋势，并且在这两种蝴蝶中是一致的。对于固定的展弦比，后掠翼会增加升力和阻力，这是因为随着翼尖涡和展向流强度的增加，前缘涡的附着增强。对于固定的翼展后掠角，小展弦比的翅膀会增加升力并减小阻力，这是因为下游有大面积的低压区域以及尾流捕获效应。综合这些影响，最大升阻比出现在展弦比最小的前掠翼上。这些结果表明，在向前扑翼飞行中，前翅相对于后翅向前扫掠适合巡航。本文中呈现的翼展后掠角和展弦比的流动机制以及解耦和耦合效应，为蝴蝶飞行和微型飞行器设计提供了见解。
