﻿ 二元可变后缘翼型的鲁棒优化设计
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1. 北京航空航天大学 航空科学与工程学院, 北京 100191;
2. 北京机电工程研究所, 北京 100074

Robust design optimization of a two-dimensional airfoil with deformable trailing edge
ZHENG Yuning1, QIU Zhiping1, HUANG Ren1 , YUAN Kaihua2
1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. Beijing Electron-Mechanical Engineering Institute, Beijing 100074, China
Abstract:In order to improve the aerodynamic stability of a two-dimensional airfoil with deformable trailing edge during the change of external conditions, a robust optimization method considering the uncertainty was proposed. Based on class-shape function transformation (CST) method, a parametric model was established to represent the geometry of a two-dimensional airfoil with a deformable trailing edge. The differences between robust optimization method and deterministic optimization method were discussed. Taking into account the uncertain airfoil geometry and inlet Mach number, the robust optimization method was applied to maximize the mean value of the lift-to-drag ratio and minimize its standard deviation. The actuation power requirement of the optimized airfoil with a deformable trailing edge was calculated. The results show that the robust optimization method can help to improve the aerodynamic performance of morphing airfoil and reduce the sensitivity of this performance to inlet Mach number simultaneously and to reduce the actuation power requirement of the robust optimal airfoil.
Key words: class-shape function transformation (CST) method     deformable trailing edge     uncertainty     robust optimization     actuation power

1 翼型的参数化方法

CST参数化方法使用翼型几何参数(前缘半径、后缘角和后缘位置)作为部分控制参数,由于具有设计变量少、可调节、设计空间大等优点,适合与遗传算法相结合解决气动优化的问题.翼型的几何曲线可表示为

C(x/c)一般可表示为

S(x/c)通常由n阶Bernstein多项式加权作为形状函数表达式:

 Rle—翼型前缘半径;β—上表面曲线在后缘处切线倾角; zte/c—后缘点的初始位置.图 1 翼型几何控制参数Fig. 1 Parameters for airfoil geometry control

 图 2 NACA0012翼型的拟合结果Fig. 2 Fitting result for NACA0012 airfoil

 图 3 可变后缘操纵面简化模型Fig. 3 Simplified model for the control surface of deformable trailing edge

 图 4 可变后缘翼型示意图Fig. 4 Schematic diagram of airfoil with deformable trailing edge
2 网格生成和流场求解

 图 5 C型结构网格Fig. 5 C-type structured grid
 图 6 压力分布计算结果和试验结果的对比Fig. 6 Comparison of pressure distribution between experiment and CFD
3 优化设计方法 3.1 确定性优化设计方法

3.2 鲁棒性优化设计方法

3.3 基于代理模型的遗传算法

3.4 鲁棒性优化过程

 图 7 翼型鲁棒优化设计流程图Fig. 7 Flow chart of robust airfoil optimization
4 算例及结果分析 4.1 算 例

4.2 优化结果分析

 图 8 翼型外形和压力分布对比Fig. 8 Geometry profile and pressure distribution comparison

 图 9 权重系数变化时的Pareto前沿Fig. 9 Pareto front varied with weight coefficient

 翼型 μ(K) σ(K) xm/c Δzte ΔE/J NACA0012 14.4129 4.3406 确定性翼型 17.4048 4.9497 0.5040 -0.0113 1.3833 鲁棒性翼型 17.5594 3.5625 0.5370 -0.0121 1.0685

 图 10 翼型升阻比随马赫数的变化Fig. 10 Lift to drag ratio varied with Mach number

 图 11 翼型几何形状对比Fig. 11 Comparison of airfoil geometry shape

 图 12 鲁棒性翼型几何形状随马赫数的变化Fig. 12 Robust airfoil geometry shape varied with Mach number

5 结 论

1) 在CST参数化建模方法基础上引入变形控制参数,可以实现用较少的设计变量表达变后缘翼型的气动外形,使得用遗传算法进行翼型优化设计成为可能.

2) 可变后缘翼型的优化结果表明,后缘的连续光滑变形改善了翼型的气动性能,而采用加权法处理多目标鲁棒优化问题,很好地均衡了性能优化和鲁棒性要求,在保持气动性能的基础上又改善了性能的稳定性.

3) 与确定性优化翼型相比,鲁棒性优化翼型后缘变形量将随马赫数变化,并且在相同马赫数条件下变形所需的驱动能更低.

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#### 文章信息

ZHENG Yuning, QIU Zhiping, HUANG Ren, YUAN Kaihua

Robust design optimization of a two-dimensional airfoil with deformable trailing edge

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(5): 897-903.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0387