蝴蝶翅膀形狀、翅膀撓曲變形與翅膀身體耦合運動之飛行動力機制

Abstract

本研究受蝴蝶飛行特色啟發，結合生物力學與流體力學，以翅膀形狀、翅膀撓曲變形與翅膀身體耦合運動解析蝴蝶飛行動力機制；研究成果可為昆蟲飛行機制與仿生拍撲微飛行器之操控設計提出嶄新見解。 有別於一般昆蟲，蝴蝶拍翅頻率低，飛行時身體有足夠的時間響應翅膀動作，使翅膀與身體一起做上下起伏的耦合運動。此外，蝴蝶的前、後翅部分交疊，構成一片大翅膀；大面積翅膀在拍翅時會因自身撓性而變形，且前翅相對於後翅的掃掠動作同時改變整個翅膀形狀。本研究因此建立三維動態量測實驗，利用高速攝影機量測蝴蝶的飛行動作與翅膀形變，並開發應用於數值模擬之撓性翅膀曲面擬合重建技術，以實驗與數值方法分析翅膀身體運動交互作用與翅膀形狀對飛行的影響。 研究結果顯示，蝴蝶腹部相對於頭胸部的上下擺動透過翅膀與身體耦合運動增加拍翅產生之氣動力。當翅膀下拍時，往上擺的腹部使頭胸部相對於蝴蝶質心下移，增加翅膀相對於質心的下拍速度；上拍時，往下擺的腹部使頭胸部相對於質心上移，增加翅膀相對於質心的上拍速度。此建設性耦合運動增加翅膀的來流速度與攻角，從而產生較強的翼前緣與翼後緣渦漩，提升下拍時的升力與上拍時的推力。過去文獻指出，蝴蝶的腹部擺動相對於拍翅有一個約0.1週期的延遲相位差，本研究發現此相位差使翅膀與身體產生完全建設性耦合，使整個下拍與上拍階段翅膀相對於質心的拍翅速度最大化，並產生最大之升推力。本研究結果解釋蝴蝶採用0.1腹部擺動延遲相位差做飛行的原因。 在翅形部分，蝴蝶前翅相對於後翅的掃掠動作同時改變整個翅膀的掃掠角與展弦比。透過分離掃掠角與展弦比效應，本研究發現掃掠角與展弦比具有不同的流場與氣動力機制。後掠翅膀由於具有較大的展向流與翼尖渦漩，翼前緣渦漩貼附於翅膀，增加下拍升力；小展弦比翅膀在尾流區引起較大低壓，提供尾流吸力而增加下拍升力，在拍撲轉換階段，此尾流低壓引起強烈的誘導氣流，回拍的翅膀捕捉此氣流發生尾流捕獲，增加上拍推力。此外，透過可變形翅膀模擬，雖然下拍初期翅膀沿翼展軸向下的扭曲(twisting)延後翼前緣渦漩的生成，下拍中期翅膀會因氣動力向上拱曲(camber)與彎曲(bending)，接著於下拍後期因彈性與慣性而向下拱曲與彎曲；此二次向下的拱彎曲增加翅膀下表面之高壓，增加升力；在上拍階段，翅膀沿翼展軸之向上扭曲將氣動力引導至水平方向，增加推力。結合以上效應，蝴蝶前翅向後的掃掠產生最大升力與最小推力，前翅向前的掃掠產生最小升力與最大推力；與剛性翅膀相比，撓曲變形翅膀的升力與推力皆有提升。 目前微飛行器設計之最大困難在於如何於微小體積下，增加翅膀機構的運動自由度以提升飛行機動性。透過本研究成果，未來微飛行器可將身體分為兩個部分，運用身體後端相對於前端的腹部擺動，在固定的拍翅動作下增加翅膀相對於質心的拍翅速度；同時也可將翅膀拆分為兩個部分重疊的前後翅，利用前翅掃掠控制整個翅膀形狀，並運用適當的拱曲、彎曲與扭曲，調控飛行氣動力。

Inspired from flight characteristics of butterfly, this study analyzes the flight mechanisms of wing shape, wing deformation and wing-body coupled motion in butterfly flight via biomechanics and fluid dynamics. The results provide new insights into flight of insect and control design of bionic flapping micro-aerial vehicles (MAVs). Unlike other insects, the flapping frequency of butterfly is small, making the body of a butterfly have sufficient time to respond to its wing movement and leading the wing and the body to do up-and-down coupled motion together during flight. In addition, the forewing and hindwing of a butterfly overlap partly, forming a large wing. When flapping, this large wing deforms due to wing flexibility, and a forewing-sweeping motion relative to a hindwing changes the shape of the entire wing. We hence established a 3D kinematics-measured experiment by using high-speed cameras to capture the flying motion and the wing deformation of butterflies, and developed a flexible-wing surface fitting-and-reconstruction technology for numerical simulation to analyze the wing-body coupled motion and the wing-shape effect. The results show that the up-and-down abdominal oscillation relative to the head-thorax of a butterfly increases aerodynamic forces via the wing-body coupled motion. During downstroke, an upward-oscillating abdomen makes the head-thorax move downward relative to the center of mass, increasing the downward wing-flapping speed relative to the center of mass. During upstroke, a downward-oscillating abdomen makes the head-thorax move upward relative to the center of mass, increasing the upward wing-flapping speed relative to the center of mass. This constructive wing-body coupled motion increases the incoming airflow speed and the angle of attack of the wing, results in stronger leading- and trailing-edge vortices, and increases lift in the downstroke and thrust in the upstroke. Previous literature has pointed out that the abdominal oscillation of butterflies has a delayed phase difference of about 0.1 period relative to the wing-flapping motion. We found that this phase difference produces a completely constructive wing-body couple motion, which maximizes the wing-flapping speed during the entire downstroke and upstroke and maximizes the lift and the thrust. This result provides a physical elucidation on why natural butterflies always utilize 0.1 abdomen-oscillating delayed phase for flight. As for the wing-shape effect, the forewing-sweeping motion relative to the hindwing simultaneously changes the wing-swept angle and aspect ratio of the entire wing. On separating the effects of wing-swept angle and aspect ratio, we found that the wing-swept angle and aspect ratio have distinct flow fields and aerodynamic mechanisms. A swept-backward wing increases the lift in the downstroke because of a leading-edge vortex attachment due to spanwise flow and wing-tip vortex. A small aspect ratio wing causes a large low-pressure in a wake, which provides a suction force and increases the lift in the downstroke; at wing-reversal stage, this low-pressure in the wake generates a strong induced flow, and the flapping wings captures this induced flow, enhancing wake-capture effect and increasing the thrust in the upstroke. In addition, in deformable-wing simulation, although the downward-twisting along wingspan axis in the early stage of downstroke delays the generation of leading-edge vortex, the wing cambers and bends upward due to aerodynamic forces in the mid-downstroke, and then cambers and bends downward due to elasticity and inertia forces in the later stage of downstroke. This secondary downward camber and bending increase the high-pressure on the lower surface of the wing; the lift thereby increases. During the upstroke, the upward-twisting along wingspan axis alters aerodynamic force into horizontal direction, increasing the thrust. Combining the above effects, the backward-sweeping forewing produces the maximum lift and the minimum thrust; the forward-sweeping forewing produces the minimum lift and the maximum thrust. Compared with rigid-wing, both the lift and thrust in the deformable wing increase. The biggest difficulty in the current design of MAVs is how to increase the degree of freedom of wing mechanism to improve flight maneuverability within a small volume. With the results of this study, we recommend that the body of a MAV can be designed with two parts; one can oscillate the rear part relative to the front part, i.e., abdominal oscillation, to increase the wing-flapping speed relative to the center of mass under a fixed wing-flapping motion. Also, the wing of a MAV can be designed with two partly-overlapping forewing and hindwing; one can use the forewing-sweeping motion, wing camber, bending and twisting to control the entire wing shape of the MAV, and further to regulate the aerodynamic forces.