STATIC AEROELASTIC ANALYSIS BASED ON PROPER ORTHOGONAL DECOMPOSITION AND SURROGATE MODEL
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摘要: 静气动弹性问题考虑弹性结构与定常气动力间的相互耦合作用, 对飞行器的性能和安全具有显著的影响. 在现代飞行器设计阶段, 计算流体力学(CFD)/计算结构力学(CSD)直接耦合方法是精确考察静气动弹性影响的重要手段. 然而, 基于CFD技术的气动力仿真手段在耦合过程中计算量大且耗时长, 难以满足设计阶段的需求. 因此, 为了兼顾计算精度与效率, 文章采用本征正交分解(POD)和Kriging代理模型相结合的模型降阶方法, 替代CFD求解过程并耦合有限元分析(FEA)方法, 建立了高效、准确的静气动弹性分析框架. 相较于传统的以模态法为主的静气动弹性分析方法, 该方法能够解决更为复杂的静气动弹性问题以及提供静气动弹性变形过程中的气动分布载荷. 针对典型三维跨声速HIRENASD机翼模型开展的马赫数、迎角变化的算例验证表明: 由建立的静气动弹性分析方法与CFD/CSD直接耦合方法计算得到机翼翼梢处的静变形量间的相对误差在5%以内; 同时该方法预测静平衡位置处的气动分布载荷的误差在5%以内, 静气动弹性分析的计算效率至少提升了6倍.Abstract: The static aeroelastic problem is concerned with those physical phenomena which involve significant mutual interaction between elastic and aerodynamic forces, which has dramatical influence on the overall flight performance and security of the aircraft. The computational fluid dynamics (CFD) and computational structural dynamics (CSD) coupling method is an essential and accurate tool to account for the impact of static aeroelastic problems in the design of the advanced aircraft. However, aerodynamic loads based on CFD simulation require a large computational cost and time, which cannot meet the need of the design stage. Therefore, many aerodynamic reduced order models based on CFD have been proposed in order to maintain a balance between the computational accuracy and efficiency. Then, an efficient and accurate steady aerodynamic reduced order model for the static aeroelastic analysis is developed in this work, using proper orthogonal decomposition (POD) and Kriging surrogate model to replace the CFD simulations and couple the finite element analysis (FEA). Compared with the conventional static aeroelastic analysis with the modal method, the proposed approach can deal with more complex static aeroelastic problems and predict the aerodynamic distribution loads in the static aeroelastic deformation. Then, the performance of the proposed approach is evaluated by a transonic flow with multiple Mach numbers and angles of attack past a three dimensional HIRENASD wing configuration, which is initiated by Aachen University's Department of Mechanics to provide a benchmark test case for computational aeroelastic code validation. Results demonstrate that the relative error for the static displacement at the wing tip (Y/b = 0.99) of the CFD/CSD coupling method and the proposed approach is within 5%. In addition, the error for predicting aerodynamic distribution loads in the position of static equilibrium is within 5% and the computational efficiency is improved by the proposed approach at least 6 times for the static aeroelastic analysis.
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图 3 不同截面位置处的压力系数与试验数据的对比
Figure 3. Comparison of the computational pressure coefficient with experimental data in different sections
3 不同截面位置处的压力系数与试验数据的对比(续)
3. Comparison of the computational pressure coefficient with experimental data in different sections (continued)
图 6 不同动压和展向下机翼变形量对比
Figure 6. Comparison of the displacement of wing at different dynamic pressure and span
图 7 Q = 40055.4 Pa时压力分布云图对比
Figure 7. Comparison of pressure distribution contour at Q = 40055.4 Pa
图 8 Q = 40055.4 Pa时压力分布的误差云图
Figure 8. Error contour for pressure distribution at Q = 40055.4 Pa
表 1 动压为40055.4 Pa时, 误差对比情况
Table 1. Comparison of the relative error at Q = 40055.4 Pa
Y/b CFD-LE
dz/mmROM-LE
dz/mmRLE/% CFD-TE
dz/mmROM-TE
dz/mmRTE/% 0.1 0.0742 0.0783 5.5383 0.2401 0.2536 5.6400 0.2 0.2188 0.2223 1.5993 0.5645 0.5844 3.5342 0.3 0.5431 0.5509 1.4305 1.2082 1.2353 2.2456 0.4 1.2199 1.1989 1.7166 2.2012 2.1861 0.6855 0.5 2.2259 2.2177 0.3697 3.4997 3.4475 1.4941 0.6 3.7394 3.6282 2.9735 5.1211 5.0734 0.9309 0.7 5.5260 5.4986 0.4957 7.1193 7.1035 0.2215 0.8 7.8802 7.7803 1.2684 9.3793 9.3700 0.0995 0.9 10.4127 10.2606 1.4607 11.7459 11.7107 0.2997 0.99 12.8676 12.5582 2.4045 14.0668 13.7933 1.9443 
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表 2 动压为10 kPa时, 误差对比情况
Table 2. Comparison of the relative error at Q = 10 kPa
Y/b CFD-LE dz/mm ROM-LE dz/mm RLE/% CFD-TE dz/mm ROM-TE dz/mm RTE/% 0.1 0.1703 0.1765 3.6295 0.5524 0.5716 3.4702 0.2 0.4964 0.4904 1.2167 1.2922 1.3127 1.5903 0.3 1.2305 1.2348 0.3527 2.7572 2.7688 0.4214 0.4 2.7588 2.6663 3.3530 5.0116 4.8712 2.8021 0.5 5.0498 4.9016 2.9350 7.9162 7.7064 2.6499 0.6 8.4253 8.0695 4.2228 11.5851 11.2231 3.1247 0.7 12.4385 12.1050 2.6812 16.0371 15.6766 2.2479 0.8 17.7319 17.1802 3.1113 21.1331 20.6488 2.2917 0.9 23.3456 22.5625 3.3544 26.4595 25.7542 2.6656 0.99 28.9224 27.5618 4.7043 31.7057 30.3052 4.4172
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表 3 计算时间对比
Table 3. Comparison of computational time
Approach Time cost Total time/h CFD/FEA (1) There are 100 steady cases and time cost for each case is about 400 min;
(2) There are 7 cases for each steady case and time cost for each case is about 240 min.$\begin{gathered} (10 \times 10 \times 400 + 10 \times \\ 10 \times 7 \times 240) \div 60= \\ 3446.67 \\ \end{gathered}$ ROM/FEA (1) Time cost for each CFD case and ROM training are about 30 and 0.3 min, respectively;
(2) There are 6 steady cases, 18 cases for static analysis and 180 CFD cases for training sample;
(3) Time cost for each static analysis is about 30 min.$\begin{gathered} (400 \times 6{\text{ + 18} } \times {\text{240} }+ \\ {\text{ 180} } \times {\text{30 + 10} } \times {\text{10} } \times \\ 7 \times {\text{30 + 0} }{\text{.3} }) \div 60 = \\ {\text{ 552} }{\text{.005} } \\ \end{gathered}$
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