蝴蝶轉彎之飛行動態與流場機制

Abstract

本文探討蝴蝶身體姿態和左右翅膀拍撲與偏移動作對轉彎軌跡與空氣動力的影響，透過觀察大白斑蝶(Idea leuconoe)飛行動態，建構三維運動數值模擬，歸納蝴蝶高操控性飛行的不對稱流場結構與重要動作參數。 首先以三台高速攝影機建立生物動態實驗，觀測五隻大白斑蝶的轉彎飛行，並計算動作角度函數，分別為身體姿態的偏航、俯仰與滾轉角，以及左右翅膀的拍撲、掃掠、旋轉與前翅偏移角。結果顯示身體於0.3週期時開始向右偏轉，俯仰姿態與前飛動態有相同趨勢，滾轉角則無明顯變化。左右翅膀可看作以對稱掃掠及旋轉動作飛行；然而一週期內翅拍撲幅度相對外翅增加20.31%，並且外翅會先向前再向後偏移，內翅則有相反趨勢；兩翅不對稱拍撲和偏移角為轉彎關鍵的飛行參數。 由真實生物動態給定物理模型動作函數，建構六自由度運動之三維數值模型，模擬與實驗量測飛行速度具一致性。研究結果顯示，滾轉角為影響空氣作用力方向的主要因素，而與固定翼傾斜轉彎有相似機制；外翅於下拍提供法向力，內翅提供垂直力，兩翅於上拍共同產生水平推力。進一步分析流場結構，研究發現翅膀不對稱動作以及側向來流速度為影響流場結構的兩大因素。拍撲幅度差異使內翅先產生較大動力，而不對稱偏移動作和側向來流則透過影響展向流傳遞方向，提高外翅翼前緣渦漩強度與穩定貼附時間，進而使兩翅先後產生最大升力。下拍初期內翅升力為外翅之1.53倍，下拍後期外翅升力則為內翅之1.93倍。 最後針對翅膀拍撲和偏移動作進行參數分析，由空氣動力矩結果顯示，拍撲幅度差異可透過產生負滾轉力矩穩定滾轉姿態，避免過度傾斜；不對稱偏移動作改變翅膀面積和壓力中心位置，產生順偏航力矩以降低逆偏航效應。 本研究使用數值模擬，由不對稱流場結構觀點分析蝴蝶的飛行力學，提供轉彎飛行一嶄新解釋方式。蝴蝶於轉彎透過翅膀拍撲和偏移動作，調控偏航和滾轉姿態穩定的動作機制，可提供微飛行器對於高操控性飛行設計上之重要參考。

This thesis analyzes how the body motion, wing flapping, and forewing-deviation motion affect turning trajectories and aerodynamic forces. Through observing the flight posture of Idea leuconoe, a three-dimensional numerical simulation is established to discuss the asymmetric flow structure and vital wing parameters of butterflies’ maneuvering flight. In the biological experiment, three high-speed cameras are used to capture the feature points of butterflies. The posture of a butterfly is defined by yaw, pitch, and roll angles. Also, the wing motion is expressed by flapping, sweeping, rotation, and deviation angles. The flight dynamic indicates that in turning flight, the yaw angle increases at 0.3 period, and the pitch postures are similar to those in forward flight. In wing motion analysis, the sweeping and rotation motion between the left and right wings are symmetric during turning. However, compared to the outer wing, the flapping amplitude of the inner wing increases by 20.31%. In addition, the outer forewing deviates forward and backward during the flight. In contrast, the inner forewing has the opposite deviation motion. In summary, the crucial flight parameters are asymmetric flapping and deviation wing motion. With the analysis results of the biological experiment, a three-dimensional simulation model with six degrees of freedom is developed to analyze flight performance. The flight velocity calculated by simulation conforms with the experiment results. The simulation results reveal that the roll angle has a significant influence on the direction of aerodynamic forces, which is similar to the banked turn mechanism of aircraft. During the downstroke, the outer wing mainly provides the centripetal force, and the vertical force is mostly produced by the inner wing. During the upstroke, the inner and outer wings both generate thrust for acceleration. Also, the results indicate that asymmetric wing motion and lateral velocity have main implications on the flow field structure. The flapping amplitude difference results in stronger force generation by the inner wing. Besides, the forewing-deviation motion and lateral inflow increase the strength of the leading edge vortex and extend the attachment time due to the direction change of spanwise flow. The flow mechanism makes the inner wing generate a force 1.53 times larger than the outer wing in the early stage of the downstroke, contributing to the force increase of the outer wing in the later stage of the downstroke. Parameter analyses of flapping and deviation motion are applied in the discussion of flight stability. The aerodynamic moment results show that the difference in the flapping amplitude between wings results in a negative roll moment, stabilizing the roll posture. Asymmetric forewing-deviation motion changes the wing area and the center of pressure, counteracting adverse yaw by producing a yaw moment. This research analyzes the flight mechanics of butterflies from the perspective of asymmetric flow field structure with numerical simulation, offering a different explanation for turning flight. The asymmetric wing motion control can be applied to stabilize the roll and yaw posture, providing new insights into the stability design of flapping micro aerial vehicles in maneuvering flight.