基于PCE方法的翼型不确定性分析及稳健设计  

UNCERTAINTY QUANTIFICATION AND ROBUST DESIGN OF AIRFOIL BASED ON POLYNOMIAL CHAOS TECHNIQUE

作　　者：赵轲[1] 高正红[1] 黄江涛[1,2] 李静[1] 

机构地区：[1]西北工业大学翼型叶栅空气动力国防科技重点实验室,西安710072 [2]中国空气动力研究与发展中心,绵阳621000

出　　处：《力学学报》2014年第1期10-19,共10页Chinese Journal of Theoretical and Applied Mechanics

摘　　要：由于能够获得一个既经济又对参数变化不敏感的设计结果,稳健型设计在工程设计中备受关注.不确定性分析是稳健型设计的关键.因此研究了基于混沌多项式的不确定性分析方法,并将其与CFD方法结合,对计算空气动力学设计中的不确定性影响进行了量化分析.首先以RAE2822翼型为算例,对其跨音速马赫数不确定影响进行了分析,研究了多项式阶次对计算的影响,分析了平均流场和方差.接着结合超临界翼型的马赫数稳健型设计验证了混沌多项式方法在稳健型设计中的有效性.优化结果表明,稳健型优化后的翼型阻力系数明显降低,同时对于马赫数的敏感性显著减小.通过分析表明混沌多项式方法能够大幅提高稳健型优化设计效率,能很好地应用于气动稳定性设计.Robust design optimization has gained increasing concern in the engineering design process because it can provide an economical design that is insensitive to variations in the input variables without eliminating their causes. The key of robust design is uncertainty analysis. So in this paper the uncertainty analysis based on polynomial chaos was investigated and combined with CFD method to quantify the uncertainties in computational aerodynamic design. The transonic flow around RAE2822 airfoil is studied to test the presented method and analyze the effect of the polynomial or- der to the precision of the aerodynamic characteristic. The robust clesign of a supercritical airfoil based on the uncertainty of Mach number was conducted to validate the PCE method. It is shown by the optimization result that the drag coefficient was decreased at the design point while the sensitivity of the drag coefficient about the Mach number was weakened. It is proved that the PCE method can improve the efficiency of robust design and is a good choice for aerodynamic robust design.

关 键 词：稳健型设计 NSGA-Ⅱ 混沌多项式 埃尔米特多项式 不确定性分析 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]