﻿ 基于多点约束的大展弦比机翼静气动弹性计算
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MPC based static aeroelastic numerical method for high aspect ratio wing
Huang Wei, Lu Zhiliang, Tang Di, Guo Tongqing
Colleg of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Abstract:The steady aerodynamic loads were calculated with N-S equations and the multi-block structured grid technique was used to improve the computational efficiency. A beam model was applied to a high aspect ratio wing, and its structural deformations were evaluated by the finite element method with or without geometry nonlinearity. A multi-point constrain (MPC) method was used for the information exchange between the aerodynamic loads calculations and the structure deformations calculations. The static aeroelasticity was further considered. By successive iterations between self-developed computational fluid dynamics (CFD) solver and NASTRAN computational structural dynamics (CSD) software based on the MPC interpolation method, a quick and accurate coupled CFD-CSD method was achieved for the nonlinear static aeroelastic problem. Obviously the present method is more accurate than the conventional flexibility approach only considering single-direction deformation. Numerical analysis of a high aspect ratio wing demonstrates that spanwise deformation would have certain influence on its static aeroelastic characteristics and that geometric nonlinearity has small effect on this common airliner wing.
Key words: high aspect ratio wing     finite element method     N-S equations     static aeroelasticity     multi-block structured grid

1 气动力与结构变形计算 1.1 定常气动力N-S方程计算

1.2 结构变形计算

NASTRAN非线性106求解序列则求解考虑几何大变形和跟随力的非线性静力学方程[15].

2 流/固耦合双向数据传递MPC方法

 图 1 梁单元的多点约束Fig. 1 MPC of a beam element

 图 2 四边形单元的多点约束Fig. 2 MPC of a quadrilateral element

3 基于MPC的静气动弹性计算

1) 构建结构模型,划分气动网格,设定计算状态参数;

2) 提取所有气动表面网格点,构建气动点到结构单元的MPC,生成NASTRAN线性101/非线性106求解序列的BDF文件;

3) N-S方程计算机翼气动表面点的节点力;

4) 通过MPC,采用虚功原理将气动节点力加载到结构有限元模型,利用NASTRAN线性或非线性求解序列进行结构计算;

5) 结构计算得到结构点位移,通过MPC计算得到气动表面点的位移,利用弹性变形技术生成新的气动网格;

6) 重复步骤3)~5),直至收敛,得到给定迎角α、马赫数Ma、雷诺数Re、速压Q下考虑弹性影响的气动特性.

4 计算结果及讨论

 图 3 机翼表面的气动网格Fig. 3 Aerodynamic grids of the wing surface

 图 4 机翼的有限元模型Fig. 4 Finite element model of the wing

 图 5 柔度矩阵插值点分布Fig. 5 Point distribution of flexibility method

 图 6 翼型截面多点约束Fig. 6 MPC of a airfoil section
 图 7 机翼表面的多点约束Fig. 7 MPC of the wing surface

CFD/柔度法、CFD/NASTRAN耦合计算得到的机翼静平衡构型比较如图 8所示,图 9进一步给出了翼尖处的变形图.其中红色为没有发生结构变形的初始外形,蓝色、绿色和灰色分别代表柔度法、NASTRAN线性和非线性求解器计算的静平衡构型.图 8表明在翼根处变形很小,柔度法与NASTRAN线性、非线性求解器计算的静平衡构型有重叠区域.图 9表明在翼尖处NASTRAN线性、非线性求解器计算的静平衡构型基本重合,几何非线性影响很小;而NASTRAN线性求解序列与只考虑纵向z方向的柔度法的静平衡构型存在一定差异.

 图 8 柔度法和有限元法计算的机翼静平衡构型比较Fig. 8 Static aeroelastic sharp comparison of the flexibility and the FEM method
 图 9 柔度法和有限元法计算的翼尖变形比较Fig. 9 Wing tip deformation comparison of the flexibility and the FEM method

 图 10 机翼z方向变形比较Fig. 10 Deformation distribution of the wing in z direction
 图 11 机翼y方向变形比较Fig. 11 Deformation distribution of the wing in y direction
 图 12 机翼扭角分布比较Fig. 12 Torsion angle distribution of the wing

 计算方法 升力系数 阻力系数 柔度法 0.463 3 0.012 85 NASTRAN线性求解器 0.457 0 0.012 79 NASTRAN非线性求解器 0.456 5 0.012 78
5 结 论

1) MPC流固耦合数据交换方法只需建立气动点到结构单元的映射关系.部分MPC插值计算可以由NASTRAN完成且与Bdf文件内的求解序列无关,因而可以快速方便地与NASTRAN软件的线性、非线性求解器进行耦合计算.

2) 机翼变形只考虑升力方向会使机翼面积有所增大,使得气动力在一定程度上产生偏差.飞行器气动弹性计算时需要精确考虑三维变形.

3) 本文算例巡航状态的升力方向翼尖变形量只有半展长3%左右,几何非线性对机翼的变形以及气动力的影响较小,可以忽略不计.

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#### 文章信息

Huang Wei, Lu Zhiliang, Tang Di, Guo Tongqing

MPC based static aeroelastic numerical method for high aspect ratio wing

Journal of Beijing University of Aeronautics and Astronsutics, 2014, 40(12): 1666-1671.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0015