基于代理模型方法的翼型优化设计

doi:CNKI:11-1929/V.20101221.0954.056

Abstract

Abstract: This article presents a two-step optimization based on a surrogate model for the aerodynamic shape optimization in a viscous flow. The first-step employs the genetic algorithm (GA) to search the range of the global optimal solution. The surrogate model gappy proper orthogonal decomposition (POD) is used to replace computational dluid dynamics to estimate the flow solution, and an improvement is made on the snapshots to raise the accuracy of the gappy POD. The second-step optimization employs the steepest descent algorithm (SDA) based on the Navier-Stokes equations to refine the result of the first-step optimization. The Hicks-Henne bump function, by which the airfoil shape is parameterized, is improved to overcome its inherent flaw at the trailing edge of the airfoil. Finally, the results of the inverse design for different shapes of the airfoil and the optimal design in different states of freestream flow demonstrate that the two-step optimization is efficient and practical for the airfoil design in the viscous flow.

Key words: optimal design, Navier-Stokes equation, genetic algorithm, steepest descent algorithm, surrogate model

CLC Number:

V211.41⁺2

DUAN Yanhui, CAI Jinsheng, LIU Qiuhong. Surrogate Model Based Optimization for Airfoil Design[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2011, 32(4): 617-627.

References

[1] 王晓鹏. 遗传算法及其在气动优化设计中的应用研究. 西安: 西北工业大学, 2000. Wang Xiaopeng. Researches on genetic algorithm and its application in aerodynamics shape optimization. Xi’an: Northwestern Polytechnical University, 2000. (in Chinese)

[2] 王一伟, 钟星立, 杜特专. 翼型多目标气动优化设计方法[J]. 计算力学学报, 2007, 24(1): 98-103. Wang Yiwei, Zhong Xingli, Du Tezhuan. Multi-objective optimization of airfoils[J]. Chinese Journal of Computational Mechanics, 2007, 24(1): 98-103. (in Chinese)

[3] 杨旭东, 乔志德, 朱兵. 气动/几何约束条件下翼型优化设计的最优控制理论方法[J]. 计算物理, 2006, 23(1): 66-73. Yang Xudong, Qiao Zhide, Zhu Bing. An optimal control method for aerodynamic design of airfoil with multi-constraint conditions[J]. Chinese Journal of Computational Physics, 2006, 23(1): 66-73. (in Chinese)

[4] 熊俊涛, 乔志德, 杨旭东, 等. 基于黏性伴随方法的跨声速机翼气动优化设计[J]. 航空学报, 2007, 28(2): 281-286. Xiong Juntao, Qiao Zhide, Yang Xudong, et al. Optimum aerodynamic design of transonic wing based on viscous adjoint method[J]. Acta Aeronautica et Astronautica Sinica, 2007, 28(2): 281-286. (in Chinese)

[5] 余刚, 李栋. 基于混合遗传算法和复合形法的翼型优化设计[J]. 科学技术与工程, 2007, 10(7): 2292-2296. Yu Gang, Li Dong. Optimization design of airfoil based on hybrid genetic algorithm and compound form method[J]. Science Technology and Engineering, 2007, 10(7): 2292-2296. (in Chinese)

[6] 杨维维, 陈小前, 姚雯, 等. 基于多方法协作优化算法的飞机总体优化设计[J]. 航空计算技术, 2006, 35(6): 1-5. Yang Weiwei, Chen Xiaoqian, Yao Wen, et al. Plane system design optimization based on multimethod collaborative optimization[J]. Aeronautical Computing Technique, 2006, 35(6): 1-5. (in Chinese)

[7] 熊俊涛, 乔志德, 韩忠华. 基于响应面法的跨声速机翼气动优化设计[J]. 航空学报, 2006, 27(3): 399-403. Xiong Juntao, Qiao Zhide, Han Zhonghua. Optimum aero-dynamic design of transonic wing based on response surface methodology[J]. Acta Aeronautica et Astronautica Sinica, 2006, 27(3): 399-403. (in Chinese)

[8] 穆雪峰, 姚卫星, 余雄庆, 等. 多学科设计优化中常用代理模型的研究[J]. 计算力学学报, 2005, 22(5): 608-613. Mu Xuefeng, Yao Weixing, Yu Xiongqing, et al. A survey of surrogate models used in MDO[J]. Chinese Journal of Computational Mechanics, 2005, 22(5): 608-613. (in Chinese)

[9] 王晓峰, 席光. 基于Kriging模型的翼型气动性能优化设计[J]. 航空学报, 2005, 26(5): 545-550. Wang Xiaofeng, Xi Guang. Aerodynamic optimization design for airfoil based on Kriging model[J]. Acta Aeronautica et Astronautica Sinica, 2005, 26(5): 545-550. (in Chinese)

[10] Mazaheri K, Khayatzadeh P, Meshed S T. Laminar airfoil shape optimization using an improved genetic algorithm. AIAA-2008-913, 2008.

[11] Holmes P, Lumley J L, Berkooz G. Turbulence, coherent structures, dynamical systems and symmetry[M]. Cambridge: Cambridge University Press, 1996: 86-113.

[12] Sirvoich L, Kirby M. Turbulence and the dynamics of coherent structures. Part 1: coherent structures[J]. Quarterly of Applied Mathematics, 1987, 45(3): 561-571.

[13] LeGresley P A, Alonso J J. Improving the performance of design decomposition methods with POD. AIAA-2004-4465, 2004.

[14] LeGresley P A,Alonso J J. Dynamic domain decomposition and error correction for reduced order models. AIAA-2003-0250, 2003.

[15] 赵松原, 黄明恪. 模拟退火算法和POD降阶模态计算在翼型反设计中的应用[J]. 空气动力学学报, 2007, 25(2): 236-241. Zhao Songyuan, Huang Mingke. Application of simulated annealing method and reduced order models based on POD to airfoil inverse design problems[J]. Acta Aerodynamic Sinica, 2007, 25(2): 236-241. (in Chinese)

[16] Everson R, Sirovich L. The Karhunen-Loeve procedure for gappy data[J]. Journal of the Optical Society of American, 1995, 12(8): 1657-1664.

[17] Bui-Thanh T, Damodara M. Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition[J]. AIAA Journal, 2004, 42(8): 1505-1516.

[18] Cai X. A comparison of two POD methods for airfoil design optimization. AIAA-2005-4912, 2005.

[19] Zhang J M, Wang C F, Lum K Y. Multidisciplinary design of S-shaped intake. AIAA-2008-7060, 2008.

[20] Hicks R M, Henne P A. Wing design by numerical optimization[J]. Journal of Aircraft, 1987, 15(7): 407-412.

[21] Liu F, Zheng X Q. A strongly coupled time-marching method for solving the Navier-Stokes and k-ω Turbulence model equations with multigrid[J]. Journal of Computational Physics, 1996, 128(0211): 289-300.

Surrogate Model Based Optimization for Airfoil Design

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