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Optimization of Multi-foil Based on RBF Mesh Deformation Method and Modified Particle Swarm Optimization Algorithm
Received date: 2013-01-06
Revised date: 2013-04-28
Online published: 2013-07-02
This paper applies the Bezier and B-spline parameterization methods and particle swarm optimization (PSO) algorithm and radial basis function (RBF) mesh deformation method to multi-foil optimization based on the computational fluid dynamic (CFD) method and mesh generation technique, and the results are validated by wind tunnel tests. Comparing the definitions and properties of the Bezier curve and B-spline, the latter is found to be better than the former in description abilities and local supporting characteristics. The optimization results of three complex functions show that the convergence rate and result of the modified PSO (MPSO) algorithm is better than the original PSO algorithm. A robust, less time-consuming RBF mesh deformation method is built, which is fit for the mesh variation variation in multi-foil optimization. Two-element and three-element multi-foils are optimized by the MPSO algorithm, which increases the maximum lift coefficient and stall angle of attack of the multi-foil. The increase of maximum lift coefficient of the two-element foil is 4.1% (with Bezier) and 4.46% (with B-spline). The increase of the three-element foil is 6.74%. Therefore, it is shown that the B-spline parameterization method is better than Bezier for two-element multi-foil optimization, and the optimization process is valid and reliable.
BAI Junqiang , LIU Nan , QIU Yasong , CHEN Yingchun , LI Yalin , ZHOU Tao . Optimization of Multi-foil Based on RBF Mesh Deformation Method and Modified Particle Swarm Optimization Algorithm[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2013 , 34(12) : 2701 -2715 . DOI: 10.7527/S1000-6893.2013.0247
[1] Garner P L, Meredith P T, Stoner R C. Areas for future CFD development as illustrated by transport aircraft applications. AIAA-1991-1527, 1991.
[2] Wild J, Brezillon J, Amoignon O, et al. Advanced high-lift design by numerical methods and wind tunnel verification within the European project EUROLIFT Ⅱ. AIAA-2007-4300, 2007.
[3] Reckzeh D. Aerodynamic design of the high-lift-wing for a megaliner aircraft. Aerospace Science and Technology, 2003(7): 107-119.
[4] Tang Z, Periaux J, Bugeda G, et al. Lift maximization with uncertainties for the optimization of high-lift devices. International Journal for Numerical Methods in Fluids, 2010, 64: 119-135.
[5] Wang J F, Wu Y Z, Periaux J. Combinatorial optimization using genetic algorithms and game theory for high lift configuration in aerodynamics. AIAA-2003-295, 2003.
[6] Benini E, Ponza R, Massaro A. High-lift multi-element airfoil shape and setting optimization using multi-objective evolutionary algorithms. Journal of Aircraft, 2011, 48(2): 683-696.
[7] Cai J Y. Multi-foil optimization design and high lift device molding technology basing on control theory method. Shanghai: Department of Mechanics and Engineering Science, Fudan University, 2011. (in Chinese) 蔡锦阳. 基于控制理论的多段翼型优化设计及增升装置成型技术. 上海: 复旦大学力学与工程科学系, 2011.
[8] van Dam C P. The aerodynamic design of multi-element high-lift systems for transport airplanes. Progress in Aerospace Sciences, 2002(38): 101-144.
[9] Eyi S, Lee K D, Rogers S E, et al. High-lift design optimization using Navier-Stokes equations. Journal of Aircraft, 1996, 33(3): 499-504.
[10] Yan C. Computational fluid dynamics and its application. Beijing: Beihang University Press, 2006: 17-243. (in Chinese) 阎超. 计算流体力学方法及应用. 北京: 北京航空航天大学出版社, 2006: 17-243.
[11] Zhu X X. The molding technology of free curve and surface. Beijing: Science Press, 2000: 66-112. (in Chinese) 朱心雄. 自由曲线曲面造型技术. 北京: 科学出版社, 2000: 66-112.
[12] Unser M, Aldroubi A, Eden M. B-spline signal processing: part Ⅰ-theory. IEEE Transactions on Signal Processing, 1993, 41(2): 821-833.
[13] Unser M, Aldroubi A, Eden M. B-spline signal processing: partⅡ-efficient design and applications. IEEE Transactions on Signal Processing, 1993, 41(2): 834-848.
[14] Zhang W H, Yang J G, Zhu J H. Simultaneous topology and shape optimization of pressure loaded structures. Acta Aeronautica et Astronautica Sinica, 2009, 30 (12): 2335-2341.(in Chinese) 张卫红, 杨军刚, 朱继宏. 压力载荷下的结构拓扑优化-形状协同优化. 航空学报, 2009, 30(12): 2335-2341.
[15] Huang J T, Gao Z H, Bai J Q, et al. Laminar airfoil aerodynamic optimization design based on delaunay graph mapping and FFD technique. Acta Aeronautica et Astronautica Sinica, 2012, 33(10): 1817-1826. (in Chinese) 黄江涛, 高正红, 白俊强, 等. 应用Delaunay图映射与FFD技术的层流翼型气动优化设计. 航空学报, 2012, 33(10): 1817-1826.
[16] Huang J T, Gao Z H, Bai J Q, et al. Study of robust winglet design based on arbitrary space shape FFD technique. Acta Aeronautica et Astronautica Sinica, 2013, 34(1): 37-45. (in Chinese) 黄江涛, 高正红, 白俊强, 等. 基于任意空间属性FFD技术的融合式翼梢小翼稳健性气动优化设计. 航空学报, 2013, 34(1): 37-45.
[17] Ma X Y, Fan Z L, Wu W H, et al. Aerodynamic shape optimization for wing based on NURBS. Acta Aeronautica et Astronautica Sinica, 2011, 32(9): 1616-1621.(in Chinese) 马晓永, 范召林, 吴文华, 等. 基于NURBS方法的机翼气动外形优化. 航空学报, 2011, 32(9): 1616-1621.
[18] Boer A D, Schoot V D, Bijl H. Mesh deformation based on radial basis function interpolation. Computers and Structures, 2007, 85: 784-795.
[19] Allen C B, Rendall T C S. Unified approach to CFD-CSD interpolation and mesh motion using radial basis functions. AIAA-2007-3804, 2007.
[20] Li L, Niu B. The particle swarm optimization algorithm. Beijing: Metallurgical Industry Press, 2009: 25-29.(in Chinese) 李丽, 牛奔. 粒子群优化算法. 北京: 冶金工业出版社, 2009: 25-29.
[21] Li D, Xia L. Application of improved particle swarm optimization algorithm to aerodynamic design. Acta Aeronautica et Astronautica Sinica, 2012, 33(10): 1809-1816. (in Chinese) 李丁, 夏露. 改进的粒子群优化算法在气动设计中的应用. 航空学报, 2012, 33(10): 1809-1816.
[22] Sun M J, Zhan H. Synthesis airfoil optimization by particle swarm optimization based on global information. Acta Aeronautica et Astronautica Sinica, 2010, 31(11): 2166-2173. (in Chinese) 孙美建, 詹浩. 基于全局信息的粒子群算法翼型综合优化设计. 航空学报, 2010, 31(11): 2166-2173.
[23] Ji Z, Liao H L, Wu Q H. The algorithm and application of particle swarm. Beijing: Science Press, 2008: 16-71. (in Chinese) 纪震, 廖惠连, 吴青华. 粒子群算法及应用. 北京: 科学出版社, 2008: 16-71.
[24] Liu H, Abraham A, Clerc M. Chaotic dynamic characteristics in swarm intelligence. Applied Soft Computing, 2007(3): 1019-1026.
[25] Coelho L D S. A quantum particle swarm optimizer with chaotic mutation operator. Chaos, Solitons and Fractals, 2008, 37: 1409-1418.
[26] Hu W, Li Z S. A simpler and more effective particle swarm optimization algorithm. Journal of Software, 2007, 18(4): 861-868. (in Chinese) 胡旺, 李志蜀. 一种更简化而高效的粒子群优化算法. 软件学报, 2007, 18(4): 861-868.
[27] Smith A M O. High-lift aerodynamics. Journal of Aircraft, 1975, 12(6): 501-530.
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