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基于POD和代理模型的静气动弹性分析方法

李凯 杨静媛 高传强 叶坤 张伟伟

李凯, 杨静媛, 高传强, 叶坤, 张伟伟. 基于POD和代理模型的静气动弹性分析方法. 力学学报, 2023, 55(2): 1-10 doi: 10.6052/0459-1879-22-523
引用本文: 李凯, 杨静媛, 高传强, 叶坤, 张伟伟. 基于POD和代理模型的静气动弹性分析方法. 力学学报, 2023, 55(2): 1-10 doi: 10.6052/0459-1879-22-523
Li Kai, Yang Jingyuan, Gao Chuanqiang, Ye Kun, Zhang Weiwei. Static aeroelastic analysis based on proper orthogonal decomposition and surrogate model. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 1-10 doi: 10.6052/0459-1879-22-523
Citation: Li Kai, Yang Jingyuan, Gao Chuanqiang, Ye Kun, Zhang Weiwei. Static aeroelastic analysis based on proper orthogonal decomposition and surrogate model. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 1-10 doi: 10.6052/0459-1879-22-523

基于POD和代理模型的静气动弹性分析方法

doi: 10.6052/0459-1879-22-523
基金项目: 国家自然科学基金(12272306)和中央高校基本科研业务费专项资金(D5000200542)资助项目
详细信息
    通讯作者:

    张伟伟, 教授, 主要研究方向为智能空气动力学、气动弹性力学. E-mail: aeroelastic@nwpu.edu.cn

  • 中图分类号: V211.3

STATIC AEROELASTIC ANALYSIS BASED ON PROPER ORTHOGONAL DECOMPOSITION AND SURROGATE MODEL

  • 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.

     

  • 图  1  静气动弹性分析框架

    Figure  1.  The flowchart of static aeroelastic

    图  2  计算网格

    Figure  2.  The computational grid

    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

    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 (continued)

    图  4  马赫数和迎角

    Figure  4.  Mach number and angle of attack

    图  5  前4阶POD模态

    Figure  5.  The first 4 POD modes

    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

    图  9  Q = 10 kPa时位移云图对比

    Figure  9.  Comparison of displacement contour at Q = 10 kPa

    图  10  Q = 10 kPa时位移误差云图

    Figure  10.  Error contour for displacement at Q = 10 kPa

    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/bCFD-LE
    dz/mm
    ROM-LE
    dz/mm
    R (LE)/%CFD-TE
    dz/mm
    ROM-TE
    dz/mm
    R (TE)/%
    0.10.07420.07835.53830.24010.25365.6400
    0.20.21880.22231.59930.56450.58443.5342
    0.30.54310.55091.43051.20821.23532.2456
    0.41.21991.19891.71662.20122.18610.6855
    0.52.22592.21770.36973.49973.44751.4941
    0.63.73943.62822.97355.12115.07340.9309
    0.75.52605.49860.49577.11937.10350.2215
    0.87.88027.78031.26849.37939.37000.0995
    0.910.412710.26061.460711.745911.71070.2997
    0.9912.867612.55822.404514.066813.79331.9443
    下载: 导出CSV

    表  2  动压为10 kPa时, 误差对比情况

    Table  2.   Comparison of the relative error at Q = 100000 Pa

    Y/bCFD-LE dz/mmROM-LE dz/mmR (LE)/%CFD-TE dz/mmROM-TE dz/mmR (TE)/%
    0.10.17030.17653.62950.55240.57163.4702
    0.20.49640.49041.21671.29221.31271.5903
    0.31.23051.23480.35272.75722.76880.4214
    0.42.75882.66633.35305.01164.87122.8021
    0.55.04984.90162.93507.91627.70642.6499
    0.68.42538.06954.222811.585111.22313.1247
    0.712.438512.10502.681216.037115.67662.2479
    0.817.731917.18023.111321.133120.64882.2917
    0.923.345622.56253.354426.459525.75422.6656
    0.9928.922427.56184.704331.705730.30524.4172
    下载: 导出CSV

    表  3  计算时间对比

    Table  3.   Comparison of computational time

    ApproachTime costTotal 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.
    $\begin{gathered} (400 \times 6{\text{ + 18} } \times {\text{240} }+ \\ {\text{ 180} } \times {\text{30 + 10} } \times {\text{10} } \times \\ 7 \times {\text{30 + 0} }{\text{.3} }) \div 60 = \\ {\text{ 552} }{\text{.005} } \\ \end{gathered}$
    下载: 导出CSV
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  • 收稿日期:  2022-11-03
  • 录用日期:  2023-01-09
  • 网络出版日期:  2023-01-09

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