The Parameters Optimization of Fusion Winglet Based on Orthogonal Experiment Yue LUO 1, *, Qi WANG 1, Qi DU 1 and Hou-An DING 1

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1 2016 International Conference on Control and Automation (ICCA 2016) ISBN: The Parameters Optimization of Fusion Winglet Based on Orthogonal Experiment Yue LUO 1, *, Qi WANG 1, Qi DU 1 and Hou-An DING 1 1 School of Aircraft Engineering, Nanchang Hangkong University, Nanchang , China *Corresponding author Key words: Fusion winglet, Orthogonal experiment, Aerodynamic calculations, Parameter optimization. Abstract: The installation of winglet is an important method to reduce the induced drag, but if the winglet design is not good enough will increase weight and drag, and result in reducing the lift-drag ratio of the plane. With the small jets as the research object, referred the wing of "longhorns" to build basic airplane wing, with installation of fusion winglet. According to the 5 parameters of winglet established test models by the use of orthogonal test method, the test models were aerodynamic simulated and analyzed by Fluent, and studied the impact of 5 parameters on the lift-drag ratio. The results showed that: the setting angle has the greatest impact on the aerodynamic performance of winglet, and the model of winglet has better lift-drag characteristic which was optimized by orthogonal test, thus to provide theoretical basis for parametric design of winglet. Introduction Friction drag, pressure drag, interference drag and induced drag are the four main drag sources of aircraft. With the energy shortage problem has become increasingly prominent, it is particularly important to reduce the drag and improve the lift drag ratio as to aircraft conceptual design. Wing as one of the most important parts of the aircraft, which bears most of the aircraft lift and a part of drag[1], with installation of winglet at the end of wing, which can effectively reduce the induced drag of the aircraft, thereby improving the aerodynamic performance of the aircraft[3]. However, aerodynamic performance of winglet is influenced by many parameters, such as height, camber angle, sweep angle,setting angle, etc[3]. In this paper, with the small jet as the research object, referred the wing of "longhorns" to build basic wing, then established test models of fusion winglet by the use of orthogonal experiment method, which were aerodynamic calculated by Fluent, and optimized the parameters of winglet, it will help to improve the lift-drag ratio of the aircraft. Modeling of Fusion Winglet The model of the fusion winglet consists of basic wing and winglet, the main design parameters of the basic wing is shown in Table 1.

2 Table 1. The main design parameters of the basic wing. Name of basic wing parameters Airfoil Parameter Value NASA0614 Semispan l 8.4m Aspect ratio 7 Mean chord b 1.2m Root chord b 0 1.8m Tip chord b 1 0.6m Leading sweep 15 The establishment of 3D model of winglet is shown in Figure 1. The 5 basic parameters of winglet consist of height h, camber angle φ, sweep angle Λ, taper ratio λ(λ=b2/b3)and setting angle ψ, is shown in Figure 2. The airfoil of winglet is the same as the basic wing. The transition of fusion winglet between the basic wing and winglet is smooth, so in this paper, the tip chord of basic wing b1 is equal to the root chord of winglet b2, so that b1=b2, and b3 is the tip chord of winglet. Figure 1. 3D model of fusion winglet. camber angle φ sweep angle Λ height h root chord of winglet b 2 setting angle ψ tip chord of winglet b 3 Figure 2. Basic parameters of winglet. Establishment and Calculation of Orthogonal Test Models Orthogonal test design method is a king of optimization design technology [4], which has the advantage of being able to get a satisfactory test results with small number of test times, very short test time and very low test cost [5].

3 The symbol of the orthogonal table is Ln(q m ), L represents an orthogonal table, n represents the number of test times, m represents the number of factors, q represents the number of factor levels. So in this paper, m represents the parameters of winglet, respectively A (height), B (camber angle), C (sweep angle), D (taper ratio), E (setting angle), therefore, in this experiment design m=5. According to the parameter selection principle of winglet[3], in this experiment design, each factor takes five levels, among them the height of winglet were taken as semispan l 5%, 10%, 15%, 20%, 25%, built the comparison table of orthogonal test factors and levels is shown in Table 2. Level Table 2. The comparison table of orthogonal test factors and levels. Factor A(height) B(camber angle) C(sweep angle) E(setting angle) D(taper ratio) [mm] [ ] [ ] [ ] (5%l) (10%l) (15%l) (20%l) (25%l) According to standard orthogonal test table design the winglet test model, built the comparison table of orthogonal test L25(5 5 ), the number of tests are 25 times, but the whole combination experiment needs to be done 3125 times. Thus, the orthogonal experimental design method can greatly reduce the number of tests. Used Gambit to make the mesh generation, the model uses the unstructured tetrahedral meshes. In order to ensure calculation precision, the meshes of the surface of the wing, especially in the wing leading and trailing edges as well as winglet were make necessary encryption processing, and the external flow field of wing is a cuboid. The mesh model of winglet is shown in Figure 3, the number of total meshes are 2.3 million. The orthogonal test models were made aerodynamic calculation by Fluent, in this paper used N-S equation, the model of turbulence is k-epsilon model, the conditions of the calculation were: height H=10000m, angle of attack α=2, flight mach number Ma=0.6, mean aerodynamic chord b=1.2m, the external flow field was set as idea gas, the coupling form between velocity and pressure is SIMPLE. The orthogonal test model comparison table and calculation results is shown in Table 3. Figure 3. The mesh model of winglet.

4 Factor Test Number Table 3. The orthogonal test model comparison table and calculation results. A (height) [mm] B (camber angle ) [ ] C (sweep angle) [ ] D (taper ratio) E (setting angle ) [ ] Lift-Drag Ratio k Analysis of Calculation Results According to the results of orthogonal experiment numerical calculation, made analysis of range values of each factor.[6,7] Figured out total response value K of each factor level, and figured out range value R of each factor based on the total response value K, then found out the order of each factor importance according to the numerical value of range value R. The results of all the individual level of each factor are accumulated, the cumulative value is the total response value K. The total response value K of level is greater, it means its performance is better. Therefore, we can figure out the optimal level of each factor according to K. For example, the factor of height is A, the level 1 of A is h=420mm, the total response value of lift-drag ratio of factor level 1 is KA1, the expression of KA1 is show in Eq. 1, the same can be used for other factors and levels. The range value R is an index to measure the importance of factors of orthogonal test[6,8], it is the difference between maximum and minimum total response values of a factor. For example, the expression RA of factor A is shown in Eq. 2, the range value R is greater means this factor is more important in the orthogonal test. (1) (2)

5 Based on calculation and analysis, the analysis table of results is shown in Table 4. Index Lift-Dra g Ratio Table 4. The analysis table of results. Factor Total Response Value of Each Level X Range The Optimal Level 1 Level 2 Level 3 Level 4 Level 5 Value R Level A B C D E Compared with the range value R of each factor based on Table 4. We can the order of R from larger to little as E>A>B>D>C, thus we could find out the descending impact of factors on lift-drag ratio was: setting angle, height, camber angle, taper ratio, sweep angle. According to the optimal level of the each factor, built the optimal parameter combination as A1B2C5D5E4. The lift-drag ratio of the optimal configuration was 9.43 which was calculated by Fluent. Because the height of the optimal configuration is 420mm which is the minimum of 5 levels, in order to ensure the accuracy of the calculation, calculated three additional models which are: basic wing, h=180mm and h=260mm(the other four parameters remain the same), the result is shown in Table 5. Table 5. The results of additional models. Model Lift Coefficient Drag Coefficient Lift-Drag Ratio Basic h=180mm h=260mm h=420mm (the optimal configuration) As seen in table 5, after the installation of winglet, the lift-drag ratio of aircraft can be increased significantly. And the height of winglet is not the smaller the better, it reaches the maximum value at about h=420mm. The results showed that: the model of winglet has better lift-drag characteristic which was optimized by orthogonal test. Conclusions (1) After the installation of winglet, the lift-drag ratio of aircraft can be increased significantly; (2) The descending impact of parameters of fusion winglet on lift-drag ratio was: setting angle, height, camber angle, taper ratio, sweep angle; (3) The model of winglet has better lift-drag characteristic which was optimized by orthogonal test. References [1] Xiao-lei Liu, Wei-ping Shi, Song Li, Study on Simulating the Drag Reduction Characteristics of Winglet, J. Engineering & Test. 2010, 50(1): 3-5. In Chinese. [2] Biao Jiang, Jie Li, Aerodynamic Analysis of Civil Aircraft Equipped with Winglet on Numerical Simulation, J. Aeronautical Computing Technique. 2011, 41(1): In Chinese. [3] Yong-quan Jiang, Aircraft Winglet Design, Aviation Industry Press, Beijing, 2009, chapter 2. [4] Hao-yang Wu, Bing-guo Chang, et al, A Special Case of Genetic Algorithm-Orthogonal Experimental Design Method, J. Journal of Software. 2001, 12(1): In Chinese. [5] Rui-jiang Liu, Ye-wang Zhang, Chong-wei Wen, Jian Tang, Study on the Design and Analysis Methods of Orthogonal Experiment, J. Experimental Technology and Managment. 2010, 9(27): In Chinese.

6 [6] Yong-ping Liao, Qin-yu Yan, Application of Orthogonal Test Method in Mechanical Industry, China Agricultural Machinery Press, Beijing, [7] Zhong-an Xu, Tian-bao Wang, et al, Brief Introduction to the Orthogonal Test Design, J. SCI/TECH Information Development & Economy. 2002, 5(12): In Chinese. [8] Jing-li Cheng, Min Zheng, Jian-qing Lou, Comparison of Several Common Optimal Experimental Design Methods, J. Research and Exploration in Laboratory. 2012, 7(31): In Chinese.

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