減少飛機飛行時的阻力是飛機製造商的一個主要的目標，飛機在巡航時，摩擦阻力和升力誘導的阻力是造成阻力的兩個重要的關鍵。在翼尖形成的渦流是當升力存在時，所造成的一個不可避免的產物，產生翼尖渦流需要能量，而機翼和空氣之間能量轉換就是由誘導阻力轉移而來，另外，由大型飛機產生的強大翼尖渦流會增加它後方小型飛機的危險性，例如波音747客機所產生的翼尖渦流有能力使太靠近它的輕型飛機失去控制，某些意外就因為這樣而發生，這也是飛機在起飛和降落時需要間隔很大的空間的原因。翼尖渦流可以由移動或是減低的方法來做修正，這些修正方法可以用翼尖的裝置如翼尖小翼來達到。
在這篇論文中，以計算模擬的方式，利用FLUENT軟體當作求解器，討論當不同翼尖小翼外型時，在翼尖附近的流場情形，目標是了解各種翼尖小翼對渦流結構所造成的變化。吾人選擇用ATR-72的機翼當作基準，附加上各種不同外型的翼尖小翼，在馬赫數等於0.2與0.41時，從0度到16度之間各種不同的攻角的情形下，比較其升力、阻力的變化，而其中包含了一種新的翼尖小翼外型，叫做螺旋狀翼尖小翼，吾人也設計出一些不同外型的螺旋狀翼尖小翼，其中包括不同的cant angle、不同的螺旋半徑和不同的翼尖小翼的機翼剖面，試著找出一種能減少最多阻力的最佳外型，進而達到省油的目的。

Drag reduction is one of the main objectives of the transport aircraft manufacturers. The drag breakdown of a transport aircraft at cruise shows that the skin frictional drag and the lift-induced drag constitute the two main sources of drag. The vortices produced in the wing tip are unavoidable products by the presence of lift. Generation of tip vortices requires energy, and transfer of this energy from wing to air is induced drag. Large induced drag will reduce airplane endurance while cruising, and also increase the fuel consumption.
Furthermore, wing tip vortices on large aircraft can be so powerful as to endanger smaller aircraft flying behind them. For large airplanes such as Boeing 747, these tip vortices can be powerful enough to cause small airplanes following too closely to be out of control. The energy of the vortices can be modified through displacement and reduction. These modifications can potentially be achieved by the use of wing tip devices such as winglets.
In this paper, use computational method, and regard FLUENT software as flow solver. Investigating wings with different shapes of winglet, the situation of the flow field near the wing tip. The objective of this work is to gain a greater understanding of how the wing tip device modifies the vortex structure. Use ATR-72 wing as the datum, and add different types of winglet shape, at Mach number equal to 0.2 and 0.41, with different angles of attack, to compare the differences in CL and CD. It is including a new winglet appearance－spiroid winglet. I also design different kinds of spiroid winglet, including spiroid winglets with different cant angles, different sprial radius, and different spiroid winglet airfoil section, hope to find a optimize shape which can reduce the drag most, and then achieve the aerodynamic performance and fuel-efficient goals.

Contents

Chapter 1	Introduction......1
Chapter 2	Literature Review......4
	2-1  Understanding Drag......4
	2-2  Drag Distribution......7
	2-3  Winglet's History and Development......9
Chapter 3	Numerical Method......11
	3-1  Grid Generation......11
	3-2  Flow Solver......17
	3-3  Verification......21
Chapter 4	Results and Discussion......33
Chapter 5	Conclusion......58
References......60

Table of Figures

Figure 2.1  Higher pressure air on the wing lower surface flowing around wingtip to upper surface [5]......6
Figure 2.2  Spanwise flow on a finite wing – solid lines, upper surface; dashed line, lower surface [5]......6
Figure 2.3  Drag breakdown of a typical transport aircraft [7]......8
Figure 3.1  Three dimensional wing model (1)......13
Figure 3.2  Three dimensional wing model (2)......13
Figure 3.3  Wing and outer boundary......14
Figure 3.4  Two dimensional grids on the wing model......14
Figure 3.5  Three dimensional unstructured grids......15
Figure 3.6  Three dimensional wing and winglet model......15
Figure 3.7  Three dimensional wing and spiroid winglet model (1)......16
Figure 3.8  Three dimensional wing and spiroid winglet model (2)......16
Figure 3.9  Geometric layout of the ONERA M6 wing [13]......23
Figure 3.10  The ONERA M6 wing model......24
Figure 3.11  Pressure contours on the surface of the ONERA M6 wing [13]......25
Figure 3.12  Pressure contours on the surface of the ONERA M6 wing......25
Figure 3.13  Pressure coefficients on the wing surface at section 1 (y/b=0.20) [13]......26
Figure 3.14  Pressure coefficients on the wing surface at section 1 (y/b=0.20)......26
Figure 3.15  Pressure coefficients on the wing surface at section 2 (y/b=0.44) [13]......27
Figure 3.16  Pressure coefficients on the wing surface at section 2 (y/b=0.44)......27
Figure 3.17  Pressure coefficients on the wing surface at section 3 (y/b=0.65) [13]......28
Figure 3.18  Pressure coefficients on the wing surface at section 3 (y/b=0.65)......28
Figure 3.19  Pressure coefficients on the wing surface at section 4 (y/b=0.80) [13]......29
Figure 3.20  Pressure coefficients on the wing surface at section 4 (y/b=0.80)......29
Figure 3.21  Pressure coefficients on the wing surface at section 5 (y/b=0.90) [13]......30
Figure 3.22  Pressure coefficients on the wing surface at section 5 (y/b=0.90)......30
Figure 3.23  Pressure coefficients on the wing surface at section 6 (y/b=0.95) [13]......31
Figure 3.24  Pressure coefficients on the wing surface at section 6 (y/b=0.95)......31
Figure 3.25  Pressure coefficients on the wing surface at section 7 (y/b=0.99) [13]......32
Figure 3.26  Pressure coefficients on the wing surface at section 7 (y/b=0.99)......32
Figure 4.1  Pressure distribution on the wing......38
Figure 4.2  Pressure distribution on the wing and winglet......39
Figure 4.3  Pressure distribution on the wing and spiroid winglet......39
Figure 4.4  Velocity vectors near wing tip at 0˚ angle of attack......40
Figure 4.5  Pathlines (Ⅰ)......40
Figure 4.6  Pathlines (Ⅱ)......41
Figure 4.7  Pathlines (Ⅲ)......41
Figure 4.8  Pathlines (Ⅳ)......42
Figure 4.9  Pathlines (Ⅴ)......42
Figure 4.10  Vorticity contour of wing......43
Figure 4.11  Vorticity contour of wing and winglet......43
Figure 4.12  Vorticity contour of wing and spiroid winglet......44
Figure 4.13  Velocity vectors near wing tip at 10˚ angle of attack......44
Figure 4.14  Pathlines at 10˚ angle of attack......45
Figure 4.15  Lift coefficient versus angle of attack at M=0.41......46
Figure 4.16  Drag polar diagram at M=0.41......47
Figure 4.17  Lift coefficient versus angle of attack at M=0.2......48
Figure 4.18  Drag polar diagram at M=0.2......49
Figure 4.19  Wing and spiroid winglet with cant angle=45∘......50
Figure 4.20  Wing and spiroid winglet with cant angle=15∘......50
Figure 4.21  Wing and spiroid winglet with larger radius......51

List of Tables

Table 4.1  CD values of different wing and winglet shapes at various angles of attack for M=0.41......52
Table 4.2  CL values of different wing and winglet shapes at various angles of attack for M=0.41......53
Table 4.3  CD values of different wing and winglet shapes at various angles of attack for M=0.2......54
Table 4.4  CL values of different wing and winglet shapes at various angles of attack for M=0.2......55
Table 4.5  L/D values of different wing and winglet shapes at various angles of attack for M=0.41......56
Table 4.6  L/D values of different wing and winglet shapes at various angles of attack for M=0.2......57

References
[1]  Green, J.E., “Civil Aviation and the Environmental Challenge ”, The Aeronautical Journal, June 2003.
[2]  Report of the group of personalities, “European Aeronautics: a Vision for 2020 ”, January 2001.
[3]  The Spiriod-Tipped Wing, 2001, available on-line; URL:
    http://www.aviationpartners.com/company/concepts.html
[4]  Kravchenko, S.A., “The Application of the Wing Tip Lifting Surfaces for Practical Aerodynamic ”, Proceeding of the 20th ICAS, Napoli, Italy, 1996, Vol. 20/V2.
[5]  Maughmer, Mark D., “About Winglets ”, available on-line; URL:
http://www.mandhsoaring.com/articles/WL-Soaring.pdf
[6]  Mohammad, Reza Soltani, Kaveh Ghorbanian, and Mehdi Nazarinia, “Experimental Investigation of the Effect of Various Winglet Shapes on the Total Pressure Distribution Behind a Wing ”, Proceeding of the 24th ICAS, Yokohama, Japan, 2004.
[7]  Thiede, P., “Aerodynamic Drag Reduction Technologies ”, Proceedings of the CEAS/Drag Net European Drag Reduction Conference, 19-21 June 2000, Potsdam, Germany, 1st Ed., Springer, 2001.
[8]  Kroo, I., “Drag Due to Lift: Concepts for Prediction and Reduction ”, Annual Review of Fluid Mechanics, Vol. 333, pp. 587-617, 2001.
[9]  Lanchester, F W., “Aerodynamics ”, Constable & Co, London,  
1907.
[10]  Whitcomb, R T., “A Design Approach and Selected Wing-TunnelResult at High Subsonic Speed for Wing-Tip Mounted Winglets ” NASA TN D-8260, July 1976.
[11]  Anderle, P., F.N. Coton, L. Smrcek, and V. Broz, “A Wing Tunnel Based Study of the Flow Field Behind Sailplane Winglets ”, Proceeding of the 24th ICAS, Yokohama, Japan, 2004.
[12]  Abbott, I., and A. Von Doenhoff, “Theory of Wing Sections: Including a Summary of Airfoil Data ”, New York, Dover Publications, 1959.
[13]  The ONERA M6 Wing, available on-line; URL:
http://www.grc.nasa.gov/WWW/wind/valid/m6wing/m6wing01/m6wing01.html
[14]  The ONERA M6 Wing, available on-line; URL:
    http://www.grc.nasa.gov/WWW/wind/valid/m6wing/page07.pdf
[15]  Catalano, F.M., H.D. Ceron-Munoz, “Experimental Analysis of Aerodynamics Characteristics of Adaptative Multi-Winglets ”, Proceeding of the 24th ICAS, Yokohama, Japan, 2004.