以力元理論之觀點剖析昆蟲飛行的氣動力機制

Abstract

本論文主要以力元（源）理論方法，來探討仿生撲翼下流場結構與翼翅之間的受力關係，即所謂的非定常空氣動力學。了解昆蟲飛行之高升力機制，除可滿足人類對飛行的求知慾外，有助於微飛行器（MAVs）之發展。故多年來持續吸引著國內外學者進行探討。但一直到最近，學術界對於昆蟲飛行機制的探討仍停留在以非黏流之理論或準定常(Quasi-steady)分析非定常問題，透過實驗量測與數值計算結果搭配所獲得的流場結構來解讀各式昆蟲飛行的升力與推力機制，但這些方法之問題在於無法清楚得知整個流場與翅膀受力之間的關係，因此對於昆蟲飛行之高升力機制仍存在許多爭議性的解釋。1992年張建成教授提出一種診斷流場之力元理論，並於2008年與朱錦洲教授將此理論推展至多個物體流場之研究，對此問題提供一個理想的解決方案。 力元（源）理論法乃是引入一輔助勢流於Navier-Stokes方程式中，將其作內積並求體積分，進而求得整體壓力項對物體所造成的外力，其完整呈現物體本身運動所造成的力-加速度項、物體運動項，以及外部流場所影響的-表面渦度項以及整體流場渦度項。引出升阻力的概念，不但清楚區別各流場中的每一個流元(fluid element)對物體受力的貢獻，更清楚的分解出物體加速以及流場渦漩對物體所造成的影響。本文先探討二維簡化下蜻蜓與果蠅單一翅膀懸停拍翅之氣動力機制。結果顯示昆蟲拍翅過程中，相位角在對稱模式下有最大的渦度升力(環境渦度+表面渦度)；但就平均總升力而言，在超前模式下達到最大值。雖然相位角在超前模式下失去部分環境渦度升力，卻大幅提升了加速度升力。此外吾人提出騎乘升力元素 “Riding on the lift-elements”之概念，此即果蠅懸停拍翅在回轉過程中獲得額外升力的機制。此說法對於探討非定常流場與翼翅加速之間的受力關係有著非常重要的幫助。由於生物運動之複雜性，本文更進一步剖析蜻蜓前後翅撲拍運動時所造成周圍複雜之流場與飛行時所需的升、推力關係。透過多體力元理論獲得雙翅交互作用下之非定常氣動力來源，包括間接非定常效應：前後翅膀本身加速度項與表面速度貢獻；以及直接非定常效應：流場中的渦度項與翅膀表面渦度貢獻。搭配渦度與環境渦度力元分佈圖瞭解蜻蜓如何透過改變前後翅膀平移相位角以獲得高升力與高推力，同時明確指出，流場渦度的融合對於前後翅膀撲拍受力之互助與互制機制，並提供完整且透徹的解釋。此成果為力元的分析在仿生流力應用上奠立了堅實的基礎，且提供該領域一嶄新之研究視野。 本論文組織安排如下：第一章闡述過去研究仿生主題之背景與目的，並做相關的文獻回顧。第二章介紹所使用的數值模擬程式（Fluent）架構與理論背景，以及引入力元理論法所需的使用者自訂函數，同時詳細說明動態網格法則。第三章介紹力元理論與多體力元理論。第四章為實驗方法與配置。第五章分析蜻蜓與果蠅懸停飛行下之氣動力機制。第六章剖析蜻蜓前後翅拍動交互作用下之氣動力機制。第七章為結論與未來展望。

Birds, insects, and fish are generally acknowledged as flying and swimming experts. The efficiency of flying and swimming that these animals perform is surpassing any artificial mechanisms. Recently, numerous and experimental works have been devoted to the study of aerodynamics of insect wings, but there still exit puzzling and unsatisfactory explanations about the high-lift mechanisms of the hovering motion even for two-dimensional flow. It is now unsteadiness that has been recognized as the cause of the lift of an insect in hovering motion. But it is difficult to solely identify the vortex wake with the generation of high lift, as there are other unsteady contributions to the lift in the hovering motion. Some time ago, Chang (1992) proposed a diagnostic force theory to distinguish the contributions of individual fluid elements to hydrodynamic forces. The theory starts from the D’Alembert theorem that the incompressible potential flow predicts no force exerted on a body if the incident flow is a constant uniform stream. It is noteworthy that incompressible potential flow means that there is no single fluid element possessing nonzero vorticity or dilation. It is therefore considered that for incompressible flow, any fluid element with nonzero vorticity or dilation may be considered as a source of the hydrodynamic force. The force theory was recently extended to be applicable to flow about many bodies with applications to separated flow about bluff bodies (Chang, Yang ＆ Chu, 2008). First, we revisit two simplified models of hovering motion for fruit fly and dragonfly from the perspective of force decomposition. The unsteady aerodynamics is analysed by examining the lift force and its four constituent components, including one from the vorticity within the flow, one from the surface vorticity, and two contributions credited to the motion of the insect wing. According to the phase difference in the models, a hovering motion can be classified into one of three types: symmetric, advanced and delayed rotations. It is shown that the symmetric rotation has the maximum vorticity lift (from volume and surface vorticity), but the optimal average lift is attained for an advanced rotation, which, compared to the symmetric rotation, increases the force contribution due to the unsteady surface motion at the expense of sacrificing contribution from the vorticity. By identifying the variations of the vorticity lift with flow characteristics, we may further explore the detailed mechanisms associated with the unsteady aerodynamics at different phases of hovering motion. For the different types of rotation, the insect wing shares the same mechanism of gaining lift when in the phase of driving with a fuller speed, but exhibits different mechanisms at turning from one phase of motion to another.