一种改进的B样条翼型参数化方法
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摘要
翼型设计是空气动力学研究的一项重要内容,翼型的参数化结果将影响翼型的优化设计。为了减少翼型优化中的设计变量,保证优化结果的光滑性与C2连续,在优化过程中控制翼型几何特性的变化范围,提出了一种改进的B样条参数化方法。用一条三次非均匀B样条曲线表示翼型,翼型数据的参数化过程中主要运用了B样条曲线拟合算法,并且在一般的B样条曲线拟合算法的基础上加入了对曲线的法向约束,通过迭代得到最终的参数化结果。实验结果表明,该方法可以很好的拟合典型的翼型数据,得到的翼型参数化结果不仅光滑,满足C2条件,而且所得翼型函数的参数个数比传统的参数化方法有了进一步的减少,更有利于之后翼型的优化设计。
Airfoil design is a crucial issue of aerodynamic research, the parameterization of airfoil will affect the airfoil optimization design. In order to reduce the number of variables in the airfoil optimization, eliminate the unfairness phenomenon, preserve the C2 continuity condition, and control the geometric characteristics of the airfoil in the optimization process, in this paper, we present an improved method for airfoil parameterization by B-spline. The method represents airfoil by a cubic non-uniform B-spline curve. Fitting of airfoil data by B-spline curve is mainly by least square method and the normal constraints. And the final result is obtained by iteration. Experiments show that the proposed method can be well fitted to the typical airfoil data, the resulting curve is fair and C2 continuity, and has few parameters of airfoil function compared with the classical airfoil parametric methods.
Airfoil design is a crucial issue of aerodynamic research, the parameterization of airfoil will affect the airfoil optimization design. In order to reduce the number of variables in the airfoil optimization, eliminate the unfairness phenomenon, preserve the C2 continuity condition, and control the geometric characteristics of the airfoil in the optimization process, in this paper, we present an improved method for airfoil parameterization by B-spline. The method represents airfoil by a cubic non-uniform B-spline curve. Fitting of airfoil data by B-spline curve is mainly by least square method and the normal constraints. And the final result is obtained by iteration. Experiments show that the proposed method can be well fitted to the typical airfoil data, the resulting curve is fair and C2 continuity, and has few parameters of airfoil function compared with the classical airfoil parametric methods.
引文
[1]刘周,朱自强,付鸿雁,等.高升阻比翼型的设计[J].空气动力学学报,2004,22(4):410-414.
[2]王晓璐,朱自强,刘周,等.基于N-S方程的翼型双设计点双目标优化设计[J].北京航空航天大学学报,2006,32(5):503-507.
[3]Song W,Keane A J.A study of shape parameterization methods for airfoil optimization,AIAA 2003-4482[R].Reston:American Institute of Aeronautics and Astronautics,2004.
[4]Hicks R M,Hennet P A.Wing design by numerical optimization[J].Journal of Aircraft,1978,15(7):407-412.
[5]Sobieczky H.Parametric airfoils and wings[M]//Notes on Numerical Fluid Mechanics(NNFM):Recent Development of Aerodynamic Design Methodologies.Germany:Vieweg Teubner Verlag,1990:71-87.
[6]Kulfan B M,Bussoletti J E.“Fundamental”parametric geometry representations for aircraft component shapes,AIAA 2006-6948[R].Reston:American Institute of Aeronautics and Astronautics,2006.
[7]Lepine J,Guibauh F,Trepanier J Y,et al.Optimized nonuniform rational B-spline geometrical representation for aerodynamic design of wings[J].American Institute of Aeronautics and Astronautics,2001,39(11):570-577.
[8]邓金秋,冯仁忠.利于翼型优化设计的超临界翼型参数化方法[J].北京航空航天大学学报,2011,37(5):368-373.
[9]Sobester A,Keane A J.Airfoil design via cubic splines–Ferguson’s curves revisited,AIAA 2007-2881[R].Reston:American Institute of Aeronautics and Astronautics,2007.
[10]夏成林,邬弘毅,郑兴国,等.带多个形状参数的三次均匀B样条曲线的扩展[J].图学学报,2011,32(2):73-79.
[11]Brakhage K H,Lamby P.Application of B-spline techniques to the modeling of airplane wings and numerical grid generation[J].Computer Aided Geometric Design,2008,25(9):738-750.
[12]王仁宏,李崇君,朱春钢.计算几何教程[M].北京:科学出版社,2008:158-174,188-200.
[13]Jüttler B,Felis A.Least-squares fitting of algebraic spline curves via normal vector estimation[J].Advances in Computational Mathematics,2002,17(1):135-152.
[14]Farin G E.Curves and surfaces for computer-aided geometric design[M].San Diego:Academic Press,1997:53-56,172-224.
[15]伍丽峰,陈岳坪,谌炎辉,等.求点到空间参数曲线最小距离的几种算法[J].机械设计与制造,2011,(9):15-17.
[16]韩力文,杨玉婷,邱志宇.一种任意次非均匀B样条的细分算法[J].图学学报,2013,34(5):56-61.
[17]张德虎,席胜,田鼎.典型翼型参数化方法的翼型外形控制能力评估[J].航空工程进展,2014,5(3):281-288.
[18]徐进.带约束的B样条曲线曲面延伸技术[J].图学学报,2013,34(3):36-42.
[2]王晓璐,朱自强,刘周,等.基于N-S方程的翼型双设计点双目标优化设计[J].北京航空航天大学学报,2006,32(5):503-507.
[3]Song W,Keane A J.A study of shape parameterization methods for airfoil optimization,AIAA 2003-4482[R].Reston:American Institute of Aeronautics and Astronautics,2004.
[4]Hicks R M,Hennet P A.Wing design by numerical optimization[J].Journal of Aircraft,1978,15(7):407-412.
[5]Sobieczky H.Parametric airfoils and wings[M]//Notes on Numerical Fluid Mechanics(NNFM):Recent Development of Aerodynamic Design Methodologies.Germany:Vieweg Teubner Verlag,1990:71-87.
[6]Kulfan B M,Bussoletti J E.“Fundamental”parametric geometry representations for aircraft component shapes,AIAA 2006-6948[R].Reston:American Institute of Aeronautics and Astronautics,2006.
[7]Lepine J,Guibauh F,Trepanier J Y,et al.Optimized nonuniform rational B-spline geometrical representation for aerodynamic design of wings[J].American Institute of Aeronautics and Astronautics,2001,39(11):570-577.
[8]邓金秋,冯仁忠.利于翼型优化设计的超临界翼型参数化方法[J].北京航空航天大学学报,2011,37(5):368-373.
[9]Sobester A,Keane A J.Airfoil design via cubic splines–Ferguson’s curves revisited,AIAA 2007-2881[R].Reston:American Institute of Aeronautics and Astronautics,2007.
[10]夏成林,邬弘毅,郑兴国,等.带多个形状参数的三次均匀B样条曲线的扩展[J].图学学报,2011,32(2):73-79.
[11]Brakhage K H,Lamby P.Application of B-spline techniques to the modeling of airplane wings and numerical grid generation[J].Computer Aided Geometric Design,2008,25(9):738-750.
[12]王仁宏,李崇君,朱春钢.计算几何教程[M].北京:科学出版社,2008:158-174,188-200.
[13]Jüttler B,Felis A.Least-squares fitting of algebraic spline curves via normal vector estimation[J].Advances in Computational Mathematics,2002,17(1):135-152.
[14]Farin G E.Curves and surfaces for computer-aided geometric design[M].San Diego:Academic Press,1997:53-56,172-224.
[15]伍丽峰,陈岳坪,谌炎辉,等.求点到空间参数曲线最小距离的几种算法[J].机械设计与制造,2011,(9):15-17.
[16]韩力文,杨玉婷,邱志宇.一种任意次非均匀B样条的细分算法[J].图学学报,2013,34(5):56-61.
[17]张德虎,席胜,田鼎.典型翼型参数化方法的翼型外形控制能力评估[J].航空工程进展,2014,5(3):281-288.
[18]徐进.带约束的B样条曲线曲面延伸技术[J].图学学报,2013,34(3):36-42.