為了探討拍翼產生的非定常態空氣動力機制，本文針對淡江微型拍翼飛行器（FWMAV）「淡江金探子」系列的升力，進行了較為全面的數值與實驗研究。
    第一種方法是20 cm翼展「淡江金探子」之二維準定常態拍翼的運動學研究。其中可變形機翼的運動學實驗資料轉換為不同時間的有效攻角，並通過勢流理論計算出變形後機翼的升力係數值變化。在此，分析並描繪出機翼軌跡以及下行程和上行程拍翼運動的升力向量，初步顯示二維準定常態分析不足以充分描繪拍翼流場之全貌。
第二種方法是進行「淡江金探子」在風洞中之三維流場CFD模擬。藉由數值和實驗升力數據的比較，希望顯示Dickinson升力機制中的平移和旋轉升力現象。比較包括將3D翼面上產生的流線與之前的煙跡實驗數據進行比對，觀察到反向Kármán渦街，發現結果定性一致；使用3D立體攝影和COMSOL Multiphysics模擬對拍翼的動態運動進行比較，結果亦定性一致，然而CFD模擬已疲於描述拍翼行程轉換之轉翼現象；與風洞力規升力訊號比較，亦顯示初步的三維CFD模擬，還有改善空間，或者需要類似PIV三維流場觀測之協助。
第三種方法是在PIV量測之外創新利用肥皂膜觀察10 cm翼展拍翼MAV「微型金探子」流場，量化出非定常下洗流的數值。拍翼機採用正交方式穿過皂膜，該皂膜色彩圖像特徵具有拍翼流場特殊的物理意義。根據質量守恆定律以及高斯定律，推導出皂膜的顏色或厚度場與拍翼穿突皂膜引起的3D下洗流的定量關係。透過編寫MATLAB程式將標準波長圖表中的紅-綠-藍（RGB）顏色值與高速攝影機記錄下的拍翼皂膜彩色圖像進行比對，成功將色彩場轉換為皂膜厚度場，以及相關之時變下洗值與升力變化，涵括了平移升力與旋轉升力機制；皂膜下洗值約為風洞力規升力訊號數據之66%，且變化趨勢一致。
拍翼流場是具有多個物理耦合的力學領域。由於機翼隨著時間的往復拍動並旋轉扭曲，因此對於這種可撓翼之移動邊界流動問題，本文上述三項工作成果有助於解釋升力的產生機制，從而提供設計開發拍翼機重要的參考。

To investigate the unsteady-state aerodynamics of flapping wings, this study explored the lift of the Tamkang University’s "Golden Snitch" series, namely flapping wing micro-air-vehicle (FWMAV), by performing comprehensive numerical and experimental research.
Three methods were adopted. The first method involved investigating the kinematics of the two-dimensional quasi-steady-state flapping wing movement of a "Golden Snitch" with a 20-cm wingspan. The kinematics data of the elastic wing were converted to the effective angle of attack data at different time periods. Next, the potential flow theory was used to calculate changes in the lift coefficient of the transformed wings. In addition, the wing trajectory and lift vectors of the upstroke and downstroke flapping wing movements have been investigated. The results showed that the two-dimensional quasi-steady-state analysis was insufficient for illustrating the entire of the flapping wing flow field.
Regarding the second method, a computational fluid dynamics (CFD) simulation was performed to examine the three-dimensional (3D) flow field of a "Golden Snitch" in a wind tunnel. Comparing the simulation and experimental data enabled the study to demonstrate the translational and rotational lift in the Dickinson’s lift mechanism. The flow feature generated around the 3D wing surface were compared with the data of the previous smoke-tracing test; a reverse Kármán vortex street was observed, indicating the result was qualitatively consistent with that in the first method. 3D video recording and COMSOL Multiphysics were used to simulate the kinematics of flapping wing movements and compare the results with that in the first method, verifying a qualitatively consistency of the results. However, the CFD simulation was hardly capable of describing the flapping phenomena during the stroke reversals. Compared with the lift signals acquired from the wind tunnel, the 3D CFD simulation still required improvement or should be complemented with methods similar to particle image velocimetry (PIV) for 3D flow field observation. 
The third method outside PIV measurement in an innovative method utilizing a soap film to observe the flow field of flapping wing MAV "Micro Snitch" with a 10-cm wingspan, thereby quantifying unsteady-state downwash data. An orthogonal method was used to pass the MAV through a soap film, the color image features of which reflected a specific physical meaning of the MAV flow field. The law of conservation of mass and Gauss theory applied to the soap-film, the quantitative relationship between the color or thickness field of the soap-film and the corresponding 3D downwash induced by the penetrating flapping wing was derived successfully. MATLAB was then used to compare the RBG color values in the standard thickness graph and the soap film color image captured from a high-speed camera. The color field was successfully converted to the soap film thickness field, and related changes in the downwash values and lift over time were determined, including changes in the translational and rotational lift mechanisms. The downwash values of the soap film were approximately 66% of the lift signal values acquired from the wind tunnel, and the two types of value exhibited consistent variation trends.
A flow field generated through wing flapping pertains to mechanics and multiple physical couplings. Because the wings of an MAV flap, rotate, and twist with time, moving boundary flow problems associated with such flexible wings can be examined using the three proposed methods, which help to explain the mechanism of lift generation. The study results can serve as a reference for developing flapping-wing MAVs.

目 錄
	中文摘要	Ⅰ
	英文摘要	III	
目 錄		V
	圖目錄		VIII
	表目錄		XIV
	第一章 緒 論	1
1-1	研究背景	1
1-1-1	拍翼機構設計	2
1-1-2	拍翼氣動力研究	3
1-2	文獻回顧	5
1-2-1	翼翅結構	5
1-2-2	拍翼流場理論	6
1-2-3	升力計算	10
1-2-4	拍翼流場實驗	14
1-3	研究動機與目的	16
1-4	論文架構	20
	第二章 二維準定常態拍翼軌跡升力研究	22
2-1	拍翼氣動力理論	22
2-2	三維軌跡擷取實驗設備	24
2-2-1	拍翼機規格	24
2-2-2	風洞系統	26
2-2-3	資料處理軟體	26
2-3	三維拍翼軌跡截取方法	27
2-3-1	實驗流程	27
2-3-2	翼膜標記點採樣模式	29
2-3-3	翼膜軌跡風洞實驗	30
2-3-4	標記點還原三維翼膜	32
2-3-5	翼面形變量	35
2-4	二維翼中線軌跡	37
2-4-1	翼中線特性	37
2-4-2	翼中線軌跡行為	43
2-5	準定常態二維翼面升力計算流程	46
2-6	實驗結果	49
2-6-1	二維翼中線姿態與升力關係	49
2-6-2	地面座標升力關係	52
2-6-3	機身座標升力關係	58
2-6-4	升力係數變化	59
2-6-5	翼拱與升力關係	62
2-6-6	翼面角度	64
2-7	小結		65
	第三章 三維拍翼非定常流模擬	68
3-1	拍翼流場數值解特性	68
3-2	COMSOL多重耦合軟體計算驗證	69
3-2-1	實驗條件	69
3-2-2	控制方程式	70
3-2-3	邊界條件	70
3-2-4	網格設定	71
3-2-5	網格測試結果	72
3-3	升力模擬	75
3-3-1	求解程序	75
3-3-2	升力比對	75
3-3-3	數值模擬和風洞數據的流線比較	77
3-3-4	數值和風洞數據之間的空氣動力比較	79
3-3-5	立體攝影三維軌跡與數值模擬的翼膜輪廓比較	81
3-4	小結		85
	第四章 皂膜流場顯像	90
4-1	皂膜顯像實驗特質	90
4-2	實驗設備	92
4-2-1	皂膜設備	92
4-2-2	光學設備	94
4-2-3	機械設備	98
4-2-4	分析軟體MATLAB	101
4-3	皂膜參數	101
4-3-1	薄膜干涉	102
4-3-2	圓柱體尾流實驗_運動黏滯係數	104
4-4	皂膜流場顯像理論架構	106
4-4-1	理論分析	106
4-4-2	統御方程式-偏微分方程組	108
4-4-3	簡化計算升力的方法	111
4-4-4	Gauss Theorem之應用	111
4-4-5	Rankine-Froude動量射流理論	112
4-4-6	皂膜流動之物理意義	114
4-5	皂膜流場可視化實驗步驟	116
4-6	實驗結果	121
4-7	小結	 123
	第五章 結論	125
	參考文獻	131
論文作者(馮愛蓮)著述目錄	142
  
	圖目錄
圖 1-1、初探者	4
圖 1-2、Eagle II	4
圖 1-3、第三代金探子	4
圖 1-4、淡江金探子	4
圖 1-5、伊氏拍翼機	4
圖 1-6、昆蟲拍翼氣動力五種機制：(a)延遲失速delayed stall	7
圖 1-7、模擬昆蟲懸停運動在不同時間發生翼面旋轉產生的升力趨勢，上中下分別為“提前”旋轉、“恰好”旋轉、“遲延”旋轉：(a)二維翼面姿態與升力；(b)總升力曲線(紅線)，平移運動升力貢獻(藍線)，總升力與平移升力差值(黑線)，黑點標示旋轉升力，空心圈標示尾跡捕獲貢獻；(c)移動速度(綠線)與角速度(紫色並列線)變化	9
圖 1-8、昆蟲翼面運動分析：平移；旋轉；掃掠	11
圖 1-9、數值方法研究蝙蝠飛行的空氣動力機制	12
圖 1-10、蜻蜓翼動態軌跡追蹤。上圖為蜻蜓翼標記點，圖A為不同時間的翼弦截線，翼根為0%，翼尖為100%，圖B為不同時間的翼展截線，翼前緣為0%，翼後緣為100%	13
圖 1-11、準定常態法(quasi-steady model)：(a)刀片單元理論(blade element theory)；(b) 誘導氣流(actuator disc theory )；(c)渦流理論(vortex theory)	14
圖 2-1、Joukowski勢流，ζ座標轉換為z座標	23
圖 2-2、翼型參數	24
圖 2-3、塑膠減速齒輪傳動套件：(a)分解圖(b)實體機構	24
圖 2-4、拍翼式飛行器之翼膜形狀大小	25
圖 2-5、PET聚對苯二甲酸乙二醇酯	25
圖 2-6、風洞系統	26
圖 2-7、三維分析軟體Kwon 3D	27
圖 2-8、計算分析與圖形表式軟體MATLAB	27
圖 2-9、軌跡截取實驗流程圖	28
圖 2-10、三維軌跡截取實驗風洞拍攝圖。左圖：30 cm ×30 cm ×80 cm風洞系統實驗裝置，包括拍翼機、兩台高速CCD、鹵素燈，右圖：翼翅上標記為第一組9點標記	31
圖 2-11、影像擷取攝影系統示意圖	32
圖 2-12、(a)座標定位鋁框；(b)翼膜標記點；(c)輸出標記點XYZ 軌跡座標	33
圖 2-13、左圖為真實曲面，右圖(a)(b)(c)(d)分別為鄰近法'nearest'、線性法'linear'、自然法'natural'、立方法'cubic'等四種演算法，擬合出的曲面形狀範例圖	34
圖 2-14、18個標記點分佈圖(紅色小方框)，黑線為翼前緣，粗線表示翼根位置	34
圖 2-15、第三組18個標記點翼膜以立方法'cubic'演算所繪三維擬合面，底部為翼面等高線圖，色標顏色定義如右側色條	35
圖 2-16、第一組9標記點20°攻角翼面高度圖，每畫面間隔1/8週期，時間間隔1/140 s	38
圖 2-17、第二組11個標記點20°攻角翼面高度圖，每畫面間隔1/8週期，時間間隔1/140 s	39
圖 2-18、第三組18個標記點20°攻角翼面高度圖，每畫面間隔1/8週期，時間間隔1/140 s	40
圖 2-19、第四組18標記點30°攻角翼面高度圖，每畫面間隔1/8週期，時間間隔1/140 s	41
圖 2-20、第五組16個標記點10 cm翼展翼面高度圖，每畫面間隔1/8週期，時間間距為1/250 s	42
圖 2-21、三維翼膜截線：（a）翼面俯視圖，由右而左紅線為翼根到翼尖每1 cm取一條翼剖線，紅色小圓圈為翼面18個標記點；（b）翼面側視圖，右下方桃紅色粗線為翼根位置，黑色線段為翼前緣	43
圖 2-22、由左到右翼根到翼尖每隔1 cm，翼面十一條弦線方向截線上的升力係數曲線與翼面十一條平均升力係數(右下)關係圖	44
圖 2-23、第一組9個標記點，20 cm翼展20°攻角，一週期內翼中線拍動圖，左圖為下行程，右圖為上行程，每條線間隔千分之一秒[14]。	44
圖 2-24、第二組11個標記點，20 cm翼展20°攻角，一週期內翼中線拍動圖，左圖為上行程，右圖為下行程，每條線間隔千分之一秒	45
圖 2-25、第三組18個標記點，20 cm翼展20°攻角，一週期內翼中線拍動圖，左圖為下行程，右圖為上行程，每條線間隔千分之一秒	45
圖 2-26、第四組20 cm翼展30°攻角，一週期內翼中線拍動圖，左圖為下行程，右圖為上行程，每條線間隔千分之一秒	45
圖 2-27、第五組10 cm 翼展16個標記點，20°攻角，一週期內翼中線拍動圖，左圖為下行程，右圖為上行程，每條線間隔千分之一秒	46
圖 2-28、升力係數計算流程	46
圖 2-29、翼中線座標，進行座標旋轉求出翼拱高度	47
圖 2-30、一個週期內的翼前緣軌跡座標圖：(a)翼前緣鉛直方向軌跡；(b)水平方向軌跡。暗色背景表示上行程，白色背景表示下行程	48
圖 2-31、等效風速圖：(a)翼中線軌跡的運動速度(斜箭號)，風速(水平箭號)； (b)負翼前緣速度加上水平風速為V effctive wind等效風速	48
圖 2-32、相對風速時間變化圖：(a)水平與鉛直方向等效風速Vx(上)、Vy(下)，無窮遠風速為3 m/s ；(b)相對風速值，暗色背景表示上行程，白色背景表示下行程	48
圖 2-33、等效攻角 由翼傾角α與等效風向角β向量相加組成	49
圖 2-34、一拍翼週期內角度與時間關係圖：(a)翼面傾角；(b)相對風向角	49
圖 2-35、一拍翼週期內翼面傾角(短虛線)、相對風向角(長虛線)與相對攻角(實線)三者相位關係，暗色背景表示上行程，白色背景表示下行程	50
圖 2-36、星號點線為翼中線姿態，細箭號為瞬時相對風速VEW，粗箭號為升力係數，升力係數方向定義為垂直風速方向	50
圖 2-37、上下行程升力變化，上排為下行程，下排為上行程	51
圖 2-38、紅色箭號為升力係數大小，綠色箭號為飛行方向：(a)0.001-0.011 s正升力期；(b)0.012-0.022 s負升力期；(c)0.023-0.043 s第二正升力期；(d)0.044-0.056 s上行程負升力期；(e)0.057-0.068 s上行程正升力期	52
圖 2-39、9個標記點，翼中線剖面與瞬時升力係數表現黑色曲線表示翼中線瞬態形狀，翼前緣位置以黑色圓點標示，箭號表示準定常態模式下升力係數的大小與方向	53
圖 2-40、9個標記點，翼中線剖面與相對風速圖，黑色曲線表示翼中線瞬態形狀，翼前緣位置以黑色圓點標示，箭號表示準定常態模式下等效風速的大小與方向	53
圖 2-41、9個標記點，升力係數鉛直分量與時間關係圖	53
圖 2-42、11個標記點，翼中線剖面與瞬時升力係數表現，黑色曲線表示翼中線瞬態形狀，翼前緣位置以黑色圓點標示，箭號表示準定常態模式下升力係數的大小與方向	54
圖 2-43、11個標記點，翼中線剖面與相對風速圖，黑色曲線表示翼中線瞬態形狀，翼前緣位置以黑色圓點標示，箭號表示準定常態模式下等效風速的大小與方向	54
圖 2-44、11個標記點，升力係數鉛直分量與時間關係圖	54
圖 2-45、18個標記點，翼中線與瞬時升力係數表現，黑色曲線表示翼中線瞬態形狀，翼前緣位置以黑色圓點標示，箭號表示準定常態模式下升力係數的大小與方向	55
圖 2-46、18個標記點，翼中線剖面與相對風速圖，黑色曲線表示翼中線瞬態形狀，翼前緣位置以黑色圓點標示，箭號表示準定常態模式下等效風速的大小與方向	55
圖 2-47、18個標記點，升力係數鉛直分量與時間關係圖	55
圖 2-48、30 °攻角18點，翼中線剖面與瞬時升力係數表現，黑色曲線表示翼中線瞬態形狀，翼前緣位置以黑色圓點標示，箭號表示準定常態模式下升力係數的大小與方向	56
圖 2-49、30°攻角18點，翼中線剖面與相對風速圖，黑色曲線表示翼中線瞬態形狀，翼前緣位置以黑色圓點標示，箭號表示準定常態模式下等效風速的大小與方向	56
圖 2-50、30°攻角18個標記點，升力係數鉛直分量值	56
圖 2-51、10 cm翼展，16個標記點升力係數表現，黑色曲線表示翼中線瞬態形狀，翼前緣位置以黑色圓點標示，箭號表示準定常態模式下升力係數的大小與方向	57
圖 2-52、10 cm翼展翼中線剖面與相對風速圖，黑色曲線表示翼中線瞬態形狀，翼前緣位置以黑色圓點標示，箭號表示準定常態模式下等效風速的大小與方向	57
圖 2-53、10 cm翼展，升力係數鉛直分量與時間關係圖	57
圖 2-54、9個標記點機身座標下的翼前緣軌跡，右側為下行程，左側為上行程。翼中線剖面(黑線)，相對風速(藍色箭號)，升力係數(紅色箭號)	59
圖 2-55、11個標記點機身座標下的翼前緣軌跡，右側為下行程，左側為上行程。翼中線剖面(黑線)，相對風速(藍色虛線箭號)，升力係數(紅色實線箭號)	59
圖 2-56、18個標記點機身座標下的翼前緣軌跡，右側為下行程，左側為上行程。翼中線剖面(黑線)，相對風速(虛線箭號)，升力係數(紅色箭號)	60
圖 2-57、10cm翼展機身座標翼前緣軌跡，右側下行程，左側上行程。翼中線剖線，相對風速(藍色箭號)，升力係數(紅色箭號)	60
圖 2-58、二維軌跡實驗升力係數與力規量測升力係數比較	60
圖 2-59、一週期內，翼面旋轉角速度與時間關係圖。白色區域為下行程，藍色區域為上行程	61
圖 2-60、不同標記點翼拱高度變化，點線為9個標記點，虛線為11個標記點，實線為18個標記點	62
圖 2-61、翼拱高度與等效攻角的關係	63
圖 2-62、翼拱對升力係數的影響	63
圖 2-63、拍翼行程角Φ、攻角α、掃掠角θ一週期內的變化	64
圖 3-1、拍翼機翼膜	70
圖 3-2、風洞與拍翼機模型：(a)全風洞與完整拍翼機模型，風洞大小30 cm× 100 cm×30 cm，翼膜大小215.3 mm×65 mm×0.024 mm，翼前緣位於(0,0,0)，拍翼機置中，灰色剖面為風洞對稱平面；(b)實際模擬大小，右半側風洞與右單翼	71
圖 3-3、ㄧ般網格網格配置圖。翼根以x軸為旋轉軸，旋轉20°：(a)右翼面；(b) 右半風洞	72
圖 3-4、風洞網格配置圖：(a)精細網格；(b)極精細網格	72
圖 3-5、三種網格密度下的升力曲線圖：(a) ㄧ般網格；(b) 精細網格；(c) 極精細網格	74
圖 3-6、拍翼行程角90°，單一翼翅不同拍翼週期的平均升力值，風速2 m/s最後五次拍翼週期，變異性5％	77
圖 3-7、拍翼行程角53°，單一翼翅不同拍翼週期的平均升力模擬值，風速3 m/s最後五次拍翼週期，變異性21％	77
圖 3-8、「淡江金探子」風洞中煙線渦流。機身傾角20°；拍翼行程角53°；上游風速1 m/s拍翼頻率= 14 Hz：(a)下行程；(b)上行程	78
圖 3-9、「淡江金探子」CFD模擬渦流。機身傾角20°；拍翼行程角53°；上游風速1 m/s；拍翼頻率14 Hz：(a)下行程；(b)上行程；翼面上紅，黃，綠顏色顯示翼膜位移的最大值到最小值；在流場中紅，黃，綠箭頭則分別顯示翼膜速度的最大值到最小值	78
圖 3-10、顯示三個拍翼週期的升力圖。藍色實線表示模擬結果，棕色虛線表示風洞實驗使用六軸力規的測量值：（a）拍翼頻率為14 Hz；拍翼行程角度為53°；風洞入口風速為1 m/s；（b）拍翼頻率為15 Hz；拍翼行程角度為53°；風洞入口風速為2 m/s；（c）拍翼頻率為15 Hz；拍翼行程角度為53°；風洞入口風速為3 m/s	80
圖 3-11、「淡江金探子」風洞實驗翼膜曲面3D立體圖	82
圖 3-12、「淡江金探子」的翼中線的2D輪廓圖，L.E.和T.E.分別表示翼前緣和翼後緣：（a）下行程；（b）上行程	83
圖 3-13、COMSOL模擬「淡江金探子」翼膜曲面3D立體圖	84
圖 3-14、COMSOL模擬「淡江金探子」翼中線的2D輪廓圖，L.E.和T.E.分別表示翼前緣和翼後緣：（a）下行程；（b）上行程	85
圖 3-15、風速為1 m/s和拍翼頻率為14 Hz的三維流向結構圖：（a-g）水平截面速度場；（h-u）流向橫截面速度場	86
圖 3-16、風速為1 m/s和拍翼頻率為14 Hz的三維流動結構圖：（a-u）不同弦長沿流向橫截面速度場	87
圖 4-1、壓克力框架(單位：mm)	93
圖 4-2、皂膜液體：(a)DAWN清潔劑；(b)和盛超級泡泡水	93
圖 4-3、(a)彩色高速攝影機Phantom Miro EX4；(b)影像控制軟體PCC；(c)型號參數；d)單幀畫素(H×V)與影格率(fps)	94
圖 4-4、不同光源下，皂膜干涉條紋圖：(a)石英燈；(b) LED燈	95
圖 4-5、不同光源下，皂膜干涉條紋(圖 4-4) 的RGB三色強度分布圖，由左到右顯示直立皂膜由上而下色彩週期性變化對應的RGB值：(a)石英燈；(b) LED燈	95
圖 4-6、第一代反射式矩形EPS燈箱：(a)右側視圖；(b)左側視圖。	97
圖 4-7、第二代直射式三角形燈箱	97
圖 4-8、第三代反射式半圓形EPS燈箱：(a)燈箱內面；(b)燈箱背面	97
圖 4-9、10 cm翼展規格：(a)拍翼機；(b)翼膜	98
圖 4-10、拍翼機懸空夾具：(a)三維結構圖；(b) 3D列印成品	99
圖 4-11、三相步進馬達外觀圖	100
圖 4-12、超極終端機介面	100
圖 4-13、50 cm行程，CTT-42皮帶式滑台	100
圖 4-14、MATLAB程式介面	101
圖 4-15、薄膜干涉光線路徑圖	102
圖 4-16、皂膜厚度400 nm，干涉光波長分布關係：上圖皂膜呈現的顏色；下圖可見光波長分布強度	103
圖 4-17、以D65光源照射折射率n = 1.33的皂液，皂膜厚度0 nm到1000 nm，RGB三色光強度與膜厚關係圖	103
圖4-18、圓柱流史徹荷數St (Strouhal number)與雷諾數Re (Reynolds number)關係，皂膜黏滯係數實驗，量測範圍在圖中紅色方框內	105
圖 4-19、圓柱體尾流皂膜成像圖	105
圖 4-20、皂膜顯像實驗流程圖	108
圖 4-21、拍翼機行進時，在皂膜上留下因膜厚變化，形成彩色干涉影像	109
圖 4-22、皂膜上每單位小面積內皂液厚度與皂膜液流速 (v, w) 關係	109
圖 4-23、翼面積分路徑示意圖，C為積分路徑，S為環狀積分所圈選的面積範圍	111
圖 4-24、機翼周圍的三維流場積分：(a)機翼平行皂膜移動；(b)機翼垂直穿突皂膜	112
圖 4-25、自由流在翼後緣偏轉，形成下洗速度的向量關係	113
圖 4-26、拍翼機穿透皂膜平面產生下洗流	114
圖 4-27、高斯定理求解拍翼機升力流程圖	116
圖 4-28、拍翼微飛行器皂膜可視化的實驗裝置與步驟：（a）肥皂液在直立式壓克力框架上成膜；（b）含視窗口白色EPS反射式燈箱；（c）設置燈和高速攝像機；（d）照亮EPS盒的內部空間；（e）放入黑色吸光背景，將拍翼機機翼浸入皂膜；（f）拍翼機沿滑軌移動，並擷取皂膜彩色條紋高幀率影像	118
圖 4-29、10 cm翼展拍翼機在一個拍翼週期中翼面動作與皂膜流動的影像；兩幅圖像之間的時間間隔為20 ms	119
圖 4-30、皂膜可視化圖像處理的流程圖	120
圖 4-31、皂膜彩色圖轉換成厚度圖：（a）單幀皂膜色彩圖像；（b）轉換成厚度場以灰度表示，單位nm	121
圖 4-32、10 cm翼展一週期內拍翼運動下洗流對時間的變化圖。前進速度0.15 m/s，皂膜實驗升力(帶圈曲線)與風洞實驗升力(曲線)關係，白色背景表示下行程，綠色背景表示上行程	122
圖 5-1、微拍翼飛行器經三種數值與實驗方法所得歸一化升力之比較，白色背景為下行程，灰色背景為上行程。	127
圖 5-2、微拍翼飛行器皂膜實驗與風洞力規升力歸一化比較，白色背景為下行程，灰色背景為上行程。	128
 
	表目錄
表 1-1、皂膜流場實驗發展	17
表 2-1、四種標記點：(a)9點；(b)11點；(c)18點；(d)16點。(a)(b)(c)為20 cm翼展，(d)為10 cm翼展	30
表 2-2、四組標記點位置。左圖為二維翼膜標記點位置，綠色面積為重建翼面範圍，右圖為擬合後的三維翼膜曲面，標記點所在位置以粉紅色圓圈表示	36
表 3-1、一般網格、精細網格、極精細網格元素數量	73
表 3-2、COMSOL 多重物理場軟體模組設定步驟	76
表 4-1、皂膜實驗裝置列表	92
表 4-2、石英燈型號參數	96
表 4-3、CTT-42皮帶式滑台馬達型號參數	100
表 4-4、相同圓柱體不同移動速度下之皂膜流場之史徹荷數St、雷諾數Re與運動黏滯係數ν，實驗溫度28°C	107
表 5-1、20 cm翼展拍翼流場分析方法比較	125
表 5-2、10 cm翼展拍翼流場分析方法比較	125

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