流体力学与飞行力学

CST气动外形参数化方法研究

  • 关晓辉 ,
  • 李占科 ,
  • 宋笔锋
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  • 西北工业大学 航空学院, 陕西 西安 710072

收稿日期: 2011-06-27

  修回日期: 2011-08-29

  网络出版日期: 2012-04-20

A Study on CST Aerodynamic Shape Parameterization Method

  • GUAN Xiaohui ,
  • LI Zhanke ,
  • SONG Bifeng
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  • College of Aeronautics,Northwestern Polytechnical University,Xi’an 710072,China

Received date: 2011-06-27

  Revised date: 2011-08-29

  Online published: 2012-04-20

摘要

类别形状函数变换(CST)方法是通过类别函数和形状函数来表示几何外形的新型气动外形参数化方法。通过考察参数化过程线性系统的条件数以及对翼型的表示误差,研究了Bernstein多项式阶数(BPO)对CST方法单值性和精度的影响,并将CST方法与B样条法、Hicks-Henne法和参数化翼型(PARSEC)法的参数数量和表示精度进行了对比。使用基于CST参数化方法的远场组元(FCE)激波阻力优化方法对超声速机翼进行外形优化,优化后的机翼其激波阻力降低达61%。研究结果表明:CST方法具有参数少,精度高的优点;为保证表示精度,同时避免病态参数化过程,应使用4阶以上、10阶以下的Bernstein多项式定义形状函数。

本文引用格式

关晓辉 , 李占科 , 宋笔锋 . CST气动外形参数化方法研究[J]. 航空学报, 2012 , (4) : 625 -633 . DOI: CNKI:11-1929/V.20111011.1411.005

Abstract

Class-shape-transformation (CST) is a new shape parameterization method which represents the geometries of aircraft shapes with a class function and a shape function. Based on the condition numbers of linear systems and the representation residuals in the parameterization process, a study is performed on the influence of the bernstein polynomial order (BPO) on the numerical uniqueness and the precision of the CST method. Comparisons of parameter number and representation precision between the CST method and B-spline, Hicks-Henne and parametric section(PARSEC) methods are represented in this paper, as well as a supersonic wing shape optimization case using the far-field composite-element (FCE) wave drag optimization method which yields a 61% reduction of wave drag. It is suggested that the CST parameterization is chara-cterized by high precision and low parameter number. In order to achieve sufficient precision and avoid ill-conditioned parameterization, the shape function should be defined by bernstein polynomials of at least 4th order, but no more than 10th order.

参考文献

[1] Mousavi A, Castonguay P, Nadarajah S K. Survey of shape parameterization techniques and its effect on three-dimensional aerodynamic shape optimization. AIAA-2007-3837, 2007.
[2] Samareh J A. Survey of shape parameterization techniques for high-fidelity multidisciplinary shape optimization. AIAA Journal, 2001, 39(5): 877-884.
[3] Sripavadkul V, Padulo M, Guennov M. A comparison of airfoil shape parameterization techniques for early design optimization. AIAA-2010-9050, 2010.
[4] Kulfan B M, Bussoletti J E. "Fundamental" parametric geometry representations for aircraft component shapes.AIAA-2006-6948, 2006.
[5] Kulfan B M. Recent extensions and applications of the "CST" universal parametric geometry representation method. AIAA-2007-7709, 2007.
[6] Kulfan B M. A universal parametric geometry representation method-"CST". AIAA-2007-62, 2007.
[7] Lane A K, Marshall D D. A surface parameterization method for airfoil optimization and high lift 2D geometries utilizing the CST methodology. AIAA-2009-1461, 2009.
[8] Ceze M, Hayashi M, Volpe E. A study of the CST parameterization characteristics. AIAA-2009-3767, 2009.
[9] Straathof M H, van Tooren M J L, Voskuijl M, et al. Aerodynamic shape parameterisation and optimisation of novel configurations. Proceedings of the RAeS Aerodynamic Shape Parameterisation and Optimisation of Novel Configurations Conference. London: Royal Aeronautical Soc., 2008: 1-14.
[10] Straathof M H, van Tooren M J L, Voskuijl M, et al. Development and implementation of a novel parametrization technique for multidisciplinary design initialization. AIAA-2010-3004, 2010.
[11] Straathof M H, van Tooren M J L. Extension to the class-shape-transformation method based on B-splines. AIAA Journal, 2011, 49(4): 780-790.
[12] Demengel G, Pouget J P. Mathematiques des courbes et des surfaces. Wang X D, translated. Beijing: Commercial Press, 2000: 109-112(in Chinese) Demengel G, Pouget J P. 曲线与曲面数学. 王向东, 译. 北京: 商务印书馆, 2000: 109-112.
[13] Li Y, Zhang K F, Yu J F. Technology and applications of computer aided geometric design. Xi’an: Northwestern Polytechnical University Press, 2007: 30-32. (in Chinese) 李原, 张开富, 余剑锋. 计算机辅助几何设计技术及应用. 西安:西北工业大学出版社,2007: 30-32.
[14] Piegl L, Tiller W. The NURBS book. Heidelberg: Springer, 1997: 411-413.
[15] Hicks R, Henne P. Wing design by numerical optimization. Journal of Aircraft, 1978, 15(7): 407-412.
[16] Sobieczky H, Parametric airfoils and wings. Notes on Numerical Fluid Mechanics, 1998, 68: 71-88.
[17] Jones R T. Theory of wing-body drag at supersonic speeds. NACA-RM-A53H18A, 1953.
[18] Chin W C. Supersonic wave-drag of planar singularity distributions. AIAA Journal, 1978,16(5): 482-487.
[19] Nikolic V, Jumper E J. Zero-lift wave drag calculation using supersonic area rule and its modifications. AIAA-2004-217, 2004.
[20] Kulfan B M. New supersonic wing far-field composite-element wave-drag optimization method, "FCE". AIAA-2008-132, 2008.
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