自從1976年Richard T. Whitcomb的研究報告指出加裝了翼尖小翼(Winglet)的飛機，其空氣動力性能較加裝一般翼尖裝置更能明顯提高後，翼尖小翼便成為改善飛機空氣動力性能的主要方法；因為，購買一架飛機的成本之高而令飛機的服役年數必須長達一、二十年以上，方符合經濟利益，所以不大改變機體結構，而又能顯著提升飛機性能，便成為翼尖小翼的最大優勢。翼尖小翼的概念相當簡單─阻擋下翼面上翻的翼尖渦流，減低下洗流效應的影響，故能減低誘導阻力；一般長程客機巡航時，誘導阻力佔總阻力的百分比可高達35％左右，如能有效降低誘導阻力，對總體性能的提高來說是相當可觀的。
　　本論文以計算流體力學的方式，利用現有的、強大的計算流體力學商業軟體FLUENT進行對加裝了最新翼尖小翼概念─螺旋狀翼尖小翼的機翼之模擬，探討其應用於一般商務客機於次音速馬赫下、不同攻角時，其空氣動力性能之變化；同時亦嘗試施加噴流在翼尖附近，以期進一步提升飛機之總體性能。吾人採用之機翼乃Gulfstream Ⅳ此一小型長程客機的主翼參數，而其翼剖面則是採用Whitcomb所設計的超臨界翼剖面(Supercritical Airfoil)，以此做為基準，比較未安裝、安裝螺旋狀翼尖小翼和安裝且施加噴流三種情況在巡航馬赫數0.8時，攻角0度到13度之間的升力係數、阻力係數和升阻比；其中螺旋狀翼尖小翼又依其環狀小翼的位置分為前旋與後旋兩種情況。
　　翼尖渦流對飛安的影響眾所周知，施加次音速流速的噴流於翼尖部分則是希望加速潰散翼尖渦流，並研究其對空氣動力性能的影響，而最終的目的是要找出減阻最多並且有效潰散渦流強度的最佳化結果，不僅提升飛行效率，也能改善飛行安全，甚而提高機場的使用效率。

Since 1976 Richard T. Whitcomb has shown that the efficiency of the aircraft equipped with winglet is better than other devices set at the wingtip, winglets are now incorporated into most new commercial and military transport jets. The concept of the winglet is very simple, disconnecting the roll-up vortices from the lower wing surface. A typical civil transport aircraft reveals that the skin friction and lift induced drag together represent more than 80% of the total drag, they constitute of two main sources of drag, approximately one half and one third of the total drag for a typical long range aircraft at cruise conditions.
In this thesis, use computational method, and employ FLUENT software as flow solver. Using in computation the geometry of the wing is of Gulfstream IV, and its airfoil is chosen of Whitcomb’s supercritical airfoil. And the scale of spiroid winglet is described by using the height of wing span. In our case the height of spiroid winglet is about 4% of wing span. The cases we calculated including eight angles of attack, 0, 2, 4, 7, 9, 11, and 13 degrees. The three different configurations are the bare wing of no wing tip device, the wingtip equipped with spiroid winglet, and blowing on the spiroid winglet. From literature the maximum cruising speed of Gulfstream IV is of Mach number 0.85 and the economic cruising speed is of Mach number 0.8. So the speed in this computation is set at 0.8 of Mach number.
     The goal of blowing at the wingtip is to advance the customary time of decaying trailing vortices and reduce the strength of trailing vortices. We wonder what happened as the spiroid winglet and blowing at wingtip coupled together, and finally find a optimal result that reduced the total drag as well as the strength of the trailing vortex, thus the flight become safer, the fuel consumption become more efficiency, and the capacity of the airport could be bigger.

Contents

Chapter 1 Introduction................................1
Chapter 2 Literature Review...........................6
2-1 Trailing Vortices.................................6
2-2 The Constituting of Drags.........................9
2-3 Development of Winglet...........................12
2-4 Introduction of Fow Control......................17
Chapter 3 Numerical Method...........................20
3-1 Preprocessing....................................20
3-2 Flow Solver......................................25
3-3 Verification.....................................31
Chapter 4 Results and Discussion.....................37
Chapter 5 Conclusion.................................55
References...........................................58

Table of Figures

Figure 1.1  U.S. wake-turbulence accidents and incidents, 1983-2000 [1]
-------------------------------------------------------------------------------------- 2
Figure 2.1  Trend of vortices [2]---------------------------------------------- 7
Figure 2.2  Trailing vortices formation [1]---------------------------------- 7
Figure 2.3  Effect of downwash on the local flow over a local airfoil section of a finite wing. [2]--------------------------------------10
Figure 2.4  Drag breakdown of a typical civil transport aircraft [3]-----11
Figure 2.5  Airfoil and geometry selection of wing tips [5]---------------13
Figure 2.6  Flow visualization with tufts, α=10° [9]-----------------------16
Figure 2.7  Cross flow kinetic energy at cruise downstream of several wing tips [10]------------------------------------------------------16
Figure 3.1  Detail data of Whitcomb’s supercritical airfoil [14]----------22
Figure 3.2  The geometry of Wing equipped with Forward-spiroid winglet--------------------------------------------------------------23
Figure 3.3  The geometry of Wing equipped with After-spiroid winglet--------------------------------------------------------------23
Figure 3.4  The position of blowing------------------------------------------24
Figure 3.5  The scale of our calculated field--------------------------------24
Figure 3.6  The solution loop of the segregated solver [17]--------------25
Figure 3.7  Geometric layout of the ONERA M6 wing [19]-------------32
Figure 3.8  Pressure coefficients on the wing surface at section (y/b)=0.20---------------------------------------------------------33
Figure 3.9  Pressure coefficients on the wing surface at section (y/b)=0.44---------------------------------------------------------33
Figure 3.10  Pressure coefficients on the wing surface at section (y/b)=0.65---------------------------------------------------------34
Figure 3.11  Pressure coefficients on the wing surface at section (y/b)=0.80---------------------------------------------------------34
Figure 3.12  Pressure coefficients on the wing surface at section (y/b)=0.90---------------------------------------------------------35
Figure 3.13  Pressure coefficients on the wing surface at section (y/b)=0.95---------------------------------------------------------35
Figure 3.14  Pressure coefficients on the wing surface at section (y/b)=0.99---------------------------------------------------------36
Figure 4.1  Lift coefficient versus angle of attack at M=0.8-------------40
Figure 4.2  Drag polar diagram at M=0.8----------------------------------41
Figure 4.3  Lift coefficient of blown case no.1 versus angle of attack at M=0.8---------------------------------------------------------------42
Figure 4.4  Drag polar diagram of blown case no.1 at M=0.8-------------43
Figure 4.5  Lift coefficient of blown case no.2 versus angle of attack at M=0.8---------------------------------------------------------------44
Figure 4.6  Drag polar diagram of blown case no.2 at M=0.8-------------45
Figure 4.7  Mach number contour of Bare wing-----------------------------46
Figure 4.8  Mach number contour of the wing equipped FWD-spiroid--------------------------------------------------------46
Figure 4.9  Mach number contour of the wing equipped AFT-spiroid---------------------------------------------------------47
Figure 4.10  Two secondary tip vortex of wing equipped FWD-spiroid
           at angle of attack 11°---------------------------------------------47
Figure 4.11  The contour of x-axis vorticity of Bare wing at AOA=0°-----------------------------------------------------------48
Figure 4.12  The contour of x-axis vorticity of wing equipped FWD-spiroid at AOA=0°---------------------------------------48
Figure 4.13  The contour of x-axis vorticity of wing equipped AFT-spiroid at AOA=0°----------------------------------------49
Figure 4.14  The contour of x-axis vorticity of wing equipped FWD-spiroid in the blown case no.1 at AOA=0°-----------49
Figure 4.15  The contour of x-axis vorticity of wing equipped FWD-spiroid in the blown case no.2 at AOA=0°-----------50
Figure 4.16  The contour of x-axis vorticity of wing equipped AFT-spiroid in the blown case no.1 at AOA=0°-------------50
Figure 4.17  The contour of x-axis vorticity of wing equipped AFT-spiroid in the blown case no.2 at AOA=0°-------------51

[1] “Data show That U.S. Wake-turbulence Accidents Are Most Frequent at Low Altitude and During Approach and Landing”, Flight Safety Foundation March-April 2002.
[2] Anderson, JR, John D., “Fundamentals of Aerodynamics”, 2001
[3] 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.
[4] U. La Roche, S. Palffy, “WING-GRID, a Novel Device for Reduction of Induced Drag on Wings”, presented at ICAS 96 in Sorrento, Italy.
[5]Von Bank, Nicholas C. “Trailing Vortex Diffusion Review of Technical Literature”, STS 401 October 1, 2004
[6] Lanchester, F W., “Aerodynamics ” Constable & Co, London, 1907.
[7] Whitcomb, R T., “A Design Approach and Selected Wing-Tunnel Result at High Subsonic Speed for Wing-Tip Mounted Winglets ” NASA TN D-8260, July 1976.
[8] Anderle P., F.N. Coton, L. Smrcek, V. Broz, “A Wing Tunnel Based Study of The Flow Field Behind Sailplane Winglets ,” Proceeding of the 24th ICAS, 2004.
[9] 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, 2004.
[10] Reneaux, J., “Overview on Drag Reduction Technologies for Civil Transport Aircraft”, ECCOMAS, July 2004.
[11] S. Scott Collis, Ronald D. Joslin, Avi Seifert, Vassilis Theofilis, “Issues in Active Flow Control: Theory, Control, Simulation, and Experiment”, progress in Aerospace Sciences 40(2004) 237-289.
[12] D. Douglas Boyd, JR., “Navier-Stokes Computations of a Wing-Flap Model with Blowing Normal to the Flap”, NASA/TM-2005-213542, March 2005.
[13] Scheiman, J. Shivers, J.P.: Exploratory Investigations of the Structure of the Tip Vortex of a Semispan Wing for Several Wing-Tip Modifications, NASA TN D6101, February 1971.
[14] Shipman, K.W., White Jr., R.P. Balcerak, J.C.: Drag Reduction of a Lifting Surface by Alteration of the Forming Tip Vortex, Rochester Applied Science Associates, Inc. (RASA) Report 74-06, 1974.
[15] “Jane's all the world's aircraft,” London : Sampson Low, Marston, 1930.
[16] The Whitcomb’s supercritical airfoil, available on-line; URL:
http://www.nasg.com/afdb/show-airfoil-e.phtml?id=1151
[17] FLUENT 6.2’s User Guide.
[18] The ONERA M6 Wing, available on-line; URL:
http://www.grc.nasa.gov/WWW/wind/valid/m6wing/m6wing01/m6wing01.html
[19] The ONERA M6 Wing, available on-line; URL:
    http://www.grc.nasa.gov/WWW/wind/valid/m6wing/page07.pdf
[20] Chou, H. H. “Numerical Simulation of the Flow Field Characteristics of Various Winglet Shapes” Department of Aerospace Engineering, Tamkang University, master institute, 2005.
[21] Paul Proctor “Winglet Designs to Cut Fuel Burn” Aviation Week & Space Technology, December 6, 1993.