航空学报 > 2010, Vol. 31 Issue (9): 1746-1751

基于多级响应面法的翼梢小翼气动优化设计

姜琬1, 金海波1, 孙卫平2   

  1. 1. 南京航空航天大学 航空宇航学院 2. 中航工业特种飞行器研究所
  • 收稿日期:2009-09-08 修回日期:2010-01-13 出版日期:2010-09-25 发布日期:2010-09-25
  • 通讯作者: 金海波

Aerodynamic Optimization for Winglets Based on Multi-level Response Surface Method

Jiang Wan1, Jin Haibo1, Sun Weiping2   

  1. 1. College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics2. Specialty Vehicle Institute of China Aviation Industry
  • Received:2009-09-08 Revised:2010-01-13 Online:2010-09-25 Published:2010-09-25
  • Contact: Jin Haibo

摘要: 为了提高数值计算效率和准确性,提出了基于多级响应面法的确定翼梢小翼气动外形参数的一种优化方法。建立某水陆两用飞机带融合式翼梢小翼的机翼参数化模型后,先用Plackett-Burman试验设计筛选设计参数,并根据设计参数对目标函数的影响将其划分为3个等级:显著因素、次显著因素和不显著因素。为了逼近存在最大响应值的区域,用最速上升法确定95%概率水平上显著因素的设计中心点。最后用多级响应面法确定各级设计参数的最优设计点。该方法以采用计算流体力学(CFD)的计算结果为基础,选择了8个设计变量,共进行了68次试验。优化设计得到的最大升阻比为20.680 56,数值计算直接算得的最大升阻比为20.680 31,相对误差0.001%,证实了优化模型的有效性。加装小翼后,最大升阻比增加了5.62%,总阻力减少了4.13%,翼根弯矩增加了2.88%。

关键词: 翼梢小翼, 气动优化, 响应面法, Plackett-Burman设计, 最速上升法, Box-Behnken设计

Abstract: In order to improve the efficiency and accuracy of the numerical calculation for the aerodynamic design of winglets, an optimization method based on multi-level response surfaces is proposed. After the establishment of the initial parameterized model of a wing with a blended winglet for an amphibious aircraft, the Plackett-Burman design is used to screen the design parameters and divide them into three grades according to their respective effect on the objective function: the significant factors, sub-significant factors, and non-significant factors. Subsequently the steepest ascent method is applied to obtain the design center point of the significant factors above the 95% probability level. Finally the optimum design parameters are obtained by the multi-level response surface method. The method is based on the computational fluid dynamics (CFD) results. Eight design parameters are selected and sixty-eight experiments are performed. The maximum lift-drag ratio of the optimization design is 20.680 56, and that of the direct numerical experiment is 20.680 31. The relative deviation is 0.001%, which confirms the effectiveness of the optimization model. After the installation of the winglets, the maximum lift-drag ratio is increased by 5.62% with an accompanying decrease of 4.13% in total resistance and an increase of 2.88% in wing-root bending moment.

Key words: winglet, aerodynamic optimization, response surface method, Plackett-Burman design, steepest ascent method, Box-Behnken design

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