基于RBF动网格方法和改进粒子群优化算法的多段翼型优化
收稿日期: 2013-01-06
修回日期: 2013-04-28
网络出版日期: 2013-07-02
基金资助
国家级项目
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
采用经风洞试验验证的计算流体力学（CFD）方法和网格生成策略，对Bezier曲线、B样条曲线参数化方法、粒子群优化（PSO）算法以及径向基函数（RBF）动网格技术在二维多段翼型设计中的应用进行了研究。通过对比研究Bezier曲线和B样条参数化方法可知，B样条曲线在描述能力和局部支柱特性等方面优于Bezier曲线。利用3个复杂函数对PSO算法进行测试，结果表明：改进的PSO（MPSO）算法在收敛速度方面明显优于标准PSO算法，且收敛结果也优于标准PSO算法。同时建立了鲁棒性高、耗时短且适用于多段翼型优化的RBF动网格方法。运用MPSO算法分别对两段翼型和三段翼型进行了优化设计，提高了设计多段翼型的最大升力系数和失速迎角。两段翼型的最大升力系数增加量分别为4.1%（Bezier参数化方法）和4.46%（B样条参数化方法），三段翼型的最大升力系数增量为6.74%。对于本文的算例，B样条参数化方法明显优于Bezier曲线，同时也证明了本文所建立优化流程的可靠性。
白俊强 , 刘南 , 邱亚松 , 陈迎春 , 李亚林 , 周涛 . 基于RBF动网格方法和改进粒子群优化算法的多段翼型优化[J]. 航空学报, 2013 , 34(12) : 2701 -2715 . DOI: 10.7527/S1000-6893.2013.0247
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.
[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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