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研究生：	王地寶 Wang, Di-Bao
論文名稱：	低雷諾數下二維機翼氣動力過渡現象之實驗研究與數學模型建立 Experimental Study and Mathematical Modeling of Aerodynamic Transition for 2-D Airfoil at Low Reynolds Numbers
指導教授：	蕭飛賓 Hsiao, Fei-Bin
學位類別：	碩士 Master
系所名稱：	工學院 - 航空太空工程學系 Department of Aeronautics & Astronautics
論文出版年：	2003
畢業學年度：	91
語文別：	英文
論文頁數：	126
中文關鍵詞：	拓樸、尖點劇變、劇變論、氣動力過渡、低雷諾數、驟變
外文關鍵詞：	Topology, Sudden Change, Cusp Catastrophe, Catastrophe Theory, Low Reynolds Number, Aerodynamic Transition
相關次數：	點閱：58 下載：2
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　　本論文以理論及實驗之方法研究NACA 633-018二維機翼在雷諾數由1.32×10^4 至1.09×10^5間空氣動力係數及流場的過渡特性。在理論部分，本研究將劇變論應用於氣動力過渡問題之數學模型建立，從探討函數局部奇異性出發，用連續函數來敘述氣動力特性之非連續行為；同時利用劇變模型來預測在過渡區域尚未被發現的氣動力特性。在實驗部分，風洞實驗量測結果成功地驗證了劇變論在氣動力過渡問題上的適用性，並且藉由視流觀察提供了該理論在此處之物理本質。最後，本文從尖點劇變模型出發，對本機翼之氣動力過渡現象予以更明確之定義及闡釋。

　　結合實驗觀測結果與此數學模型，可推論氣動力係數驟變現象與其變化特性隨雷諾數及攻角的過渡行為，本質上乃是流場拓樸結構之相變過程。由劇變模型所預測之氣動力驟變點與實驗量測所得結果相當吻合，且誤差範圍在攻角小於0.5度，在雷諾數小於2000。這在相當程度上表示在氣動力過渡過程中機翼升力或阻力與雷諾數及攻角構成一個三次超曲面的關係，可信其將來必定能為相關之氣動力過渡研究開創一個新的研究方向。

　In this thesis, the theoretical and the experimental approaches were performed to study the transitional characteristics of aerodynamic coefficients and flow field of the NACA 633-018 airfoil at Re ranging from 1.32×10^4 ~ 1.09×10^5. For theoretical approach, the catastrophe theory was applied to model the aerodynamic transition problem and to predict some aerodynamic characteristics undiscovered before. The so-called catastrophe theory describes the discontinuous phenomena with continuous functions based on the study of singularities of nonlinear functions. Results of aerodynamic loading measurement well verified the validity of the catastrophe theory on the aerodynamically transitional problems and flow visualization provided some physical essences of the flow field about the theory employed here. Finally, the aerodynamic transition of the airfoil was redefined and reexamined through the cusp catastrophe model.

　Combining the mathematical model and the experimental results, it can be deduced that the transition and sudden change of aerodynamic coefficients, in essence, is a phase-changing process of the topological structure of the flow field. The predicted sudden-changing points of the aerodynamic coefficients match very well with the experimental results within the error margin of α less than 0.5 degree and Re less than two thousand. It indicates that the lift or drag and Re as well as α actually constitutes a cubic hypersurface relationship during the transitional process, which is believed to be a new direction of related aerodynamic researches.

I.	INTRODUCTION …………………………………………………………………………1
	1.1 The Road toward Low Re …………………………………………………………1
	1.2 Known Aerodynamic Characteristics of Low Re Up to Date ………………2
	1.3 Catastrophe Theory ………………………………………………………………7
	1.4 Motivation …………………………………………………………………………8
	1.5 Objectives …………………………………………………………………………9
		
II.	MATHEMATICAL MODELING ………………………………………………………………10
	2.1 Description and Dimensional Analysis of Flow Field ………………… 10
	2.2 Introduction and Application of Catastrophe Theory ………………	12
	2.3 Cusp-Catastrophe Model for Lift and Drag…………………………………14
	2.3.1 Mathematical Modeling ………………………………………………………14
	2.3.2 Discussion of Cusp-Catastrophe Model for Lift and Drag……………17
	2.4 Identification of the Cusp Catastrophe Model for Lift or Drag…… 19
		
III.	EXPERIMENTAL ARRANGEMENT ………………………………………………………… 22
	3.1 Wind Tunnel ………………………………………………………………………22
	3.2 Experimental Apparatus ……………………………………………………… 23
	3.3 Flow Visualization …………………………………………………………… 25
	3.4 Data Processing …………………………………………………………………26
	3.5 Testing Plan …………………………………………………………………… 30
		
IV.	RESULTS AND DISCUSSIONS ……………………………………………………………31
	4.1 Aerodynamic Characteristics with α for Each Re ………………………31
	 4.1.1 Aerodynamic Behavior at Supercritical Mode……………………………29
	 4.1.2 Aerodynamic Behavior at Critical Mode …………………………………34
	 4.1.3 Aerodynamic Behavior at Subcritical Mode …………………………… 39
	 4.1.4 Synthetic Discussion for Three Modes ………………………………… 39
	4.2 Aerodynamic Characteristics with Re for Eachα ……………………… 43
	 4.2.1 Aerodynamic Coefficients with Re forα = 0° ~ 6.2°…………………43
	 4.2.2 Aerodynamic Coefficients with Re forα = 7.2° ~ 11.5° ……………46
	 4.2.3 Aerodynamic Coefficients with Re forα = 12.5° ~ 14.6°……………48
	4.3 Reexamination of the Aerodynamic Transition ……………………………48
		
V.	CONCLUDING REMARKS ………………………………………………………………… 52
	
REFERENCES ………………………………………………………………………… 55
	
APPENDICES………………………………………………………………………………59
   A. Dimensional Analysis of the Flow Field Around an Airfoil ………………… 59
   B. Identification and Calculation of the Cusp Catastrophe Model …………… 62
   C. Calculation for Number of Significant Figures of This Experiment…………65
   D. The Uncertainty of Wind Speed, Forces and Moments ……………………………67
   E. Mechanical Analysis among Model, Supporter and Balance………………………69
   F. Blockage Correction ……………………………………………………………………71
	
TABLES……………………………………………………………………………………73
	
FIGURES……………………………………………………………………………… 74
	
VITA …………………………………………………………………………………125
PUBLICATION LISTS……………………………………………………………………126
                                    

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校內：2004-07-21公開
校外：2004-07-21公開

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