以力元理論觀點探討真實果蠅懸停之氣動力機制

本論文主要是以張建成教授於1992年所發表之力元理論，來分析低雷諾數下果蠅懸停撲拍之非定常氣動力特性。力元理論可檢視流場中非零渦度流元與物體受力之間關係，同時可將物體運動時之受力中提煉出勢流力以及其它具有物理意義之受力貢獻。本文將分別檢視三種不同懸停模式(對稱、超前與延遲)下各個升力元素之變化，同時與二維簡化模式下(Hsieh, Chang & Chu, 2009, vol. 623, pp. 121–148)進行比對。不同於二維假設，在所探討之三種運動模式中附加質量力皆具升力貢獻，而翅膀主要升力來源來自於環境渦度。為了進一步探討翅膀三個運動階段包括：撲拍中期、翻轉前期與翻轉後期之前緣渦、翼尖渦、後緣渦與根部渦漩等三維渦漩結構與翅膀高升力之間的關係。透過以翅膀旋轉軸做為中心，將流場以同心圓進行環狀切割，分別探討各個環狀切割流場中之升力元素變化。吾人更進一步發現在複雜三維翅膀翻轉階段時之流場中所存在之高升力機制。貼附於翅膀前緣端之前緣渦撲拍中期時之升力來源，即動態失速機制。當翅膀於翻轉前期，翼尖渦、後緣渦與根部渦漩相連成渦環狀並向尾流脫落，前緣渦沿著翅膀表面朝向翼尖方向運動。當翅膀於翻轉後期時，翅膀將有兩次騎乘升力元素機制，原本由三個渦漩組成之渦環結構提供升力，而前一週期之前緣渦平貼於翅膀迎風面上卻提供負升力元素，當翅膀持續加速時，原前緣渦將會因翅膀旋轉朝向翅膀翼尖與後緣端，並與新生成之後緣渦融合產生額外之正升力貢獻。三種撲拍模式翻轉時刻的不同將引致兩個騎乘升力元素機制之發生時間點不同。此外，將流場沿著翼展方向進行傳統壓力積分法(Pressure Force Analysis, PFA)與流元的渦度與物體受力作連結(Vorticity Force Analysis, VFA)進行二維特性之探討(Lee, Hsieh, Chang & Chu; 2012)。透過比較VFA與PFA在不同截面之間的差異，提供不同於過去三維真實流場卻以二維分析方法之新見解。

關鍵字

非常定空氣動力學；果蠅:懸停

並列摘要

In this study, the force element theory proposed by Prof. Chang C. C. (1992) is used to analyze three-dimensional unsteady aerodynamics for hovering flapping flight of fruit-fly at low-Reynolds-number flows. The theory enables us to quantify the contributions to the forces exerted on the wing in terms of fluid elements with non-zero vorticity, and extract potential forces such as added mass and inertial forces from the total forces. The variations of the lift force and its constituent components for three different type motions, including symmetric, advanced and delayed rotations, are carefully examined. In conjunction with the previous results of Hsieh, Chang and Chu (J. Fluid Mech, 2009, vol. 623, pp. 121–148), we further compare each force contribution with the results under simplified two-dimensional assumptions. It is shown that the lift is almost supported by vorticity in the flow field, and the added-mass forces have positive contribution for these three-type motions.To understand the lift force generation relative to three-dimensional vortex structures, such as leading-edge vortex (LEV), trailing-edge vortex (TEV), tip vortex (TV) and Root vortex (RV) during different hover motion stages, we divide whole flow domain into annularity column regions with same center of circle, which is the rotation center of the wing. Except a well-known high lift mechanism generated, the delayed-stall vortex, during the midstroke for three different types of rotation, the insect wing will take advantage of wake vortices to gain extra lift force, termed as “riding on lift elements” at two different time instant, as performing turning stage. Besides, the line of force analysis of the pressure force analysis (PFA) and the vorticity force analysis (VFA) is pursued by dividing flow domain into some regions along spanwise direction of the wing. From comparison of differences between PAF and VFA, we could isolate two-dimension characteristics from three dimensional flows, further survey feasibility of two-dimensional analyses on flapping motions in unsteady ﬂow.

並列關鍵字

Unsteady Aerodynamics ； FruitFly ； hovering

參考文獻

[26] 楊適壕 2007多體力源理論及其應用，國立臺灣大學應用力學研究所博士論文。

[28] 胡校碩 2011果蠅撲翅運動之仿生模擬與力元分析，國立臺灣大學應用力學研究所碩士論文。

[1] Peng Bai, Er-jie Cui, Hui-ling Zhan (2009) “Aerodynamic Characteristics, Power Requirements and Camber Effects of the Pitching-Down Flapping Hovering” Journal of Bionic Engineering 6 120–134

[2] Sane, S. P. (2003) "Review - The aerodynamics of insect flight.", J. Exp. Biol. 206, 4191-4208

[4] Michael H. Dickinson et al. (1999)” Wing Rotation and the Aerodynamic Basis of Insect Flight ” Science 284, 1954

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以力元理論觀點探討真實果蠅懸停之氣動力機制

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