改进型Gappy POD翼型反设计方法
收稿日期: 2012-05-21
修回日期: 2012-08-16
网络出版日期: 2013-04-23
Improved Airfoil Inverse Design Method Based on Gappy POD
Received date: 2012-05-21
Revised date: 2012-08-16
Online published: 2013-04-23
白俊强 , 邱亚松 , 华俊 . 改进型Gappy POD翼型反设计方法[J]. 航空学报, 2013 , 34(4) : 762 -771 . DOI: 10.7527/S1000-6893.2013.0135
To improve the design accuracy of airfoils, a new sample method called the best snapshot replacement is proposed in this paper which is used during the sampling process of airfoil inverse design based on Gappy proper orthogonal decomposition (POD). Using this method, the baseline airfoil has to be replaced by an airfoil whose pressure distribution is closest to the target pressure distribution among the airfoils that have been generated. During the iteration process, a calibration step is added based on the principle that a calibration snapshot can be introduced. By the fitting error of pressure distribution estimated by POD. Then the target pressure distribution can be calibrated using this snapshot. Airfoil inverse design examples demonstrate that the new sample method can generate a set of snapshots which spans a space closer to the design target. Compared with the original method this calibration iteration method can improve the accuracy of design result obviously, while how to choose the optimal number of modes remains to be a difficult point for airfoil inverse design based on Gappy POD.
[1] Su W. Aerodynamic optimization design based on computational fluid dynamics and surrogate model. Xi'an: School of Aeronautics, Northwestern Polytechnical University, 2007. (in Chinese) 苏伟. 基于CFD技术和代理模型的气动外形优化设计方法研究. 西安: 西北工业大学航空学院, 2007.
[2] Takanashi S. An iterative procedure for three-dimensional transonic wing design by the integral equation method. AIAA-1984-2166, 1984.
[3] Hua J. Study of transonic airfoil and wing design. Xi'an: School of Aeronautics, Northwestern Polytechnical University, 1989. (in Chinese) 华俊. 跨音速机翼和翼型的设计研究. 西安: 西北工业大学航空学院, 1989.
[4] Van Egmond J A. Numerical optimization of target pressure distribution for subsonic and transonic airfoil design. AGARD CP-463 Reference 17, 1990.
[5] Van den Dam R F, Van Egmond J A, Sloof J W. Optimization of target pressure distributions. AGARD-780 Reference 3. 1990.
[6] Van den Dam R F. Constrained spanload optimization for minimum drag of multi-lifting surface configuration. AGARD-463 Reference 16, 1990.
[7] Holmes P, Lumley J L, Berkooz G. Turbulence, coherent structures, dynamical systems and symmetry. Cambridge: Cambridge University Press, 1996: 86-113.
[8] Legresley P, Alonso J. Investigation of non-linear projection for POD based reduced order models for aerodynamics. AIAA-2001-926, 2001.
[9] Fukanaga K. Introduction to statistical pattern recognition. New York: Academic Press, 1990: 399-440.
[10] Sirvoich L, Kirby M. Low-dimensional procedure for the characterization of human face. Journal of the Optical Society for America, 1987, 4(3): 519-524.
[11] Patrick A, Legresley P, Alonso J. Airfoil design optimization using reduced order models based on proper orthogonal decomposition. AIAA-2000-2545, 2000.
[12] Zhao S Y, Huang M K. Application of simulated annealing method and reduced order models based on POD to airfoil inverse design problems. Acta Aerodynamica Sinica, 2007, 25(2): 236-240. (in Chinese) 赵松原, 黄明恪. 模拟退火算法和降阶POD计算模态在翼型设计优化中的应用. 空气动力学学报, 2007, 25(2): 236-240.
[13] Everson R, Sirovich L. The karhunen-loeve procedure for Gappy data. Journal of the Optical Society of American, 1995, 12(8): 1657-1664.
[14] Sirovich L, Kirby M. Turbulence and dynamics of coherent structures. Part 1: coherent structures. Quarterly of Applied Mathematics, 1987, 45(3): 561-571.
[15] Nathan E M, Lawrence S U. An application of gappy POD for subsonic cavity flow PIV data. Experiments in Fluids, 2007, 42(1): 79-91.
[16] Daniele V, Georgr E K. Gappy data and reconstruction procedures for flow past a cylinder. Journal of Fluid Mechanics, 2004, 519: 315-336.
[17] Bui-Thanh T, Damodaran M, Willcox K. Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition. AIAA Journal, 2004, 42(8): 1501-1516.
[18] Drela M. Xfoil: an analysis and design system for low Reynolds number airfoils. New York: Springer, 1989: 1-12.
[19] Hicks R M, Henne P A. Wing design by numerical optimization. AIAA-1977-1247, 1977.
[20] Sobieczky H. Parametric airfoil and wings. Notes on Numerical Fluid Mechanics, 1998, 68: 71-88.
[21] Piegl L, Tiller W. The nurbs book. Heidelberg: Springer, 1997: 411-413.
[22] Duan Y H, Cai J S, Liu Q H. Surrogate model based optimization for airfoil design. Acta Aeronautica et Astronautica Sinica, 2011, 32(4): 617-627. (in Chinese) 段焰辉, 蔡晋生, 刘秋洪. 基于代理模型方法的翼型优化设计. 航空学报, 2011, 32(4): 617-627.
[23] Kulfan B M, Bussoletti J E. Fundamental parametric geometry representations for airfoil component shapes. AIAA-2006-6948, 2006.
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