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Volume 55 Issue 2
Feb.  2023
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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): 299-308 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): 299-308 doi: 10.6052/0459-1879-22-523


doi: 10.6052/0459-1879-22-523
  • Received Date: 2022-11-03
  • Accepted Date: 2023-01-09
  • Available Online: 2023-01-09
  • Publish Date: 2023-02-18
  • 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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  • [1]
    Afonso F, Vale J, Oliveira É, et al. A review on non-linear aeroelasticity of high aspect-ratio wings. Progress in Aerospace Sciences, 2017, 89: 40-57 doi: 10.1016/j.paerosci.2016.12.004
    杨超, 杨澜, 谢长川. 大展弦比柔性机翼气动弹性分析中的气动力方法研究进展. 空气动力学学报, 2018, 36(6): 1009-1018 (Yang Chao, Yang Lan, Xie Changchuan. Development of aerodynamic methods in aeroelastic analysis for high aspect ratio flexible wings. Acta Aerodynamica Sinica, 2018, 36(6): 1009-1018 (in Chinese) doi: 10.7638/kqdlxxb-2018.0237
    郭洪涛, 陈德华, 吕彬彬等. 大展弦比机翼跨声速静气动弹性风洞试验. 空气动力学学报, 2017, 35(6): 841-845 (Guo Hongtao, Chen Dehua, Lü Binbin, et al. Wind tunnel test on transonic static areoelasticity of high-aspect-ratio wing. Acta Aerodynamica Sinica, 2017, 35(6): 841-845 (in Chinese)
    叶正寅, 王刚, 张伟伟. 流固耦合力学基础及其应用, 第2版. 哈尔滨: 哈尔滨工业大学出版社, 2016: 165-170

    Ye Zhengyin, Wang Gang, Zhang Weiwei. Fundamentals of Fluid-Structure Coupling and Its Application, 2rd Edition. Harbin: Harbin Institute of Technology Press, 2016: 165-170 (in Chinese))
    孙岩, 王昊, 江盟等. NNW-FSI软件静气动弹性耦合加速策略设计与实现. 航空学报, 2021, 42(9): 625738 (Sun Yan, Wang Hao, Jiang Meng, et al. Design and implementation of coupling acceleration strategy in static aeroelastic module of NNW-FSI software. Acta Aeronautica et Astronautica Sinica, 2021, 42(9): 625738 (in Chinese)
    贾欢. 大规模结构高效静气弹多学科优化设计研究. [博士论文]. 西安: 西北工业大学, 2016

    Jia Huan. High efficient multidisciplinary design optimization of static aeroelasticity for large-scale structure. [PhD Thesis]. Xi’an: Northwestern Polytechnical University, 2016 (in Chinese))
    杜子亮, 万志强, 杨超. 模态选取对静气动弹性分析的影响. 航空学报, 2015, 36(4): 1128-1137 (Du Ziliang, Wan Zhiqiang, Yang Chao. Effect of modal selection on static aeroelastic analysis. Acta Aeronautica et Astronautica Sinica, 2015, 36(4): 1128-1137 (in Chinese)
    Mian HH, Wang G, Ye ZY. Numerical investigation of structural geometric nonlinearity effect in high-aspect-ratio wing using CFD/CSD coupled approach. Journal of Fluids and Structures, 2014, 49: 186-201 doi: 10.1016/j.jfluidstructs.2014.04.011
    Gordnier RE, Chimakurthi SK, Cesnik CES, et al. High-fidelity aeroelastic computations of a flapping wing with spanwise flexibility. Journal of Fluids and Structures, 2013, 40: 86-104 doi: 10.1016/j.jfluidstructs.2013.03.009
    Ye K, Ye ZY, Li CN, et al. Effects of the aerothermoelastic deformation on the performance of the three-dimensional hypersonic inlet. Aerospace Science and Technology, 2019, 84: 747-762 doi: 10.1016/j.ast.2018.11.015
    张伟伟, 寇家庆, 刘溢浪. 智能赋能流体力学展望. 航空学报, 2021, 42(4): 524689 (Zhang Weiwei, Kou Jiaqing, Liu Yilang. Prospect of artificial intelligence empowered fluid mechanics. Acta Aeronautica et Astronautica Sinica, 2021, 42(4): 524689 (in Chinese)
    Lucia DJ, Beran PS, Silva WA. Reduced-order modeling: new approaches for computational physics. Progress in Aerospace Sciences, 2004, 40(1-2): 51-117 doi: 10.1016/j.paerosci.2003.12.001
    张伟伟, 叶正寅. 基于CFD的气动力建模及其在气动弹性中的应用. 力学进展, 2008, 38(1): 77-86 (Zhang Weiwei, Ye Zhengyin. On unsteady aerodynamic modeling based on CFD technique and its applications on aeroelastic analysis. Advances in Mechanics, 2008, 38(1): 77-86 (in Chinese) doi: 10.3321/j.issn:1000-0992.2008.01.005
    陈刚, 李跃明. 非定常流场降阶模型及其应用研究进展与展望. 力学进展, 2011, 41(6): 686-701 (Chen Gang, Li Yueming. Advances and prospects of the reduced order model for unsteady flow and its applications. Advances in Mechanics, 2011, 41(6): 686-701 (in Chinese) doi: 10.6052/1000-0992-2011-6-lxjzJ2011-009
    Ghoreyshi M, Jirasek A, Cummings RM. Reduced order unsteady aerodynamic modeling for stability and control analysis using computational fluid dynamics. Progress in Aerospace Sciences, 2014, 71: 167-217 doi: 10.1016/j.paerosci.2014.09.001
    杨执钧, 黄锐, 刘豪杰等. 大长细比导弹的气动弹性降阶模型. 力学学报, 2017, 49(3): 517-527 (Yang Zhijun, Huang Rui, Liu Haojie, et al. Aeroelastic model of reduced-order for a slender missile. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 517-527 (in Chinese) doi: 10.6052/0459-1879-16-358
    Kou JQ, Zhang WW. Data-driven modeling for unsteady aerodynamics and aeroelasticity. Progress in Aerospace Sciences, 2021, 125: 100725 doi: 10.1016/j.paerosci.2021.100725
    Dowell EH. A Modern Course in Aeroelasticity, 6th edn., Switzerland: Springer, 2022: 447-471
    Yang JY, Liu YL, Zhang WW. Static aeroelastic modeling and rapid analysis of wings in transonic flow. International Journal of Aerospace Engineering, 2018, 2018: 5421027
    Lindhorst K, Haupt MC, Horst P. Efficient surrogate modelling of nonlinear aerodynamics in aerostructural coupling schemes. AIAA Journal, 2014, 52(9): 1952-1966 doi: 10.2514/1.J052725
    Lindhorst K, Haupt MC, Horst P. Reduced-order modelling of non-linear, transient aerodynamics of the HIRENASD wing. The Aeronautical Journal, 2016, 120(1226): 601-626 doi: 10.1017/aer.2016.12
    朱强华, 杨恺, 梁钰等. 基于特征正交分解的一类瞬态非线性热传导问题的新型快速分析方法. 力学学报, 2020, 52(1): 124-138 (Zhu Qianghua, Yang Kai, Liang Yu, et al. A novel fast algorithm based on model order reduction for one class of transient nonlinear heat conduction problem. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 124-138 (in Chinese) doi: 10.6052/0459-1879-19-323
    赵丹阳, 刘韬, 李红霞等. 可降解聚合物血管支架结构优化设计. 力学学报, 2017, 49(6): 1409-1417 (Zhao Danyang, Liu Tao, Li Hongxia, et al. Optimization design of degradable polymer vascular stent structure. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(6): 1409-1417 (in Chinese) doi: 10.6052/0459-1879-17-214
    Crowell AR, Mcnamara JJ. Model reduction of computational aerothermodynamics for hypersonic aerothermoelasticity. AIAA Journal, 2012, 50(1): 74-84 doi: 10.2514/1.J051094
    Chen X, Liu L, Long T, et al. A reduced order aerothermodynamic modeling framework for hypersonic vehicles based on surrogate and POD. Chinese Journal of Aeronautics, 2015, 28(5): 1328-1342 doi: 10.1016/j.cja.2015.06.024
    赵旋, 张伟伟, 邓子辰. 融入压力分布信息的气动力建模方法. 力学学报, 2022, 54(9): 2616-2626 (Zhao Xuan, Zhang Weiwei, Deng Zichen. Aerodynamic modeling method incorporating pressure distribution information. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 2616-2626 (in Chinese) doi: 10.6052/0459-1879-22-170
    杨倩, 郭晓峰, 李芹等. 基于 POD 和代理模型的热气防冰性能预测方法. 航空学报, 2023, 44: 126992 (Yang Qian, Guo Xiaofeng, Li Qin, et al. Hot air anti-icing performance estimation method based on POD and surrogate model. Acta Aeronautica et Astronautica Sinica, 2023, 44: 126992 (in Chinese)
    韩忠华. Kriging模型及代理优化算法研究进展. 航空学报, 2016, 37(11): 3197-3225 (Han Zhonghua. Kriging surrogate model and its application to design optimization: A review of recent progress. Acta Aeronautica et Astronautica Sinica, 2016, 37(11): 3197-3225 (in Chinese)
    蒋跃文. 基于广义网格的CFD方法及其应用. [博士论文]. 西安: 西北工业大学, 2013

    Jiang Yuewen. Methodology of generalized mesh and its application to solve the Navier-Stokes equations. [PhD Thesis]. Xi’an: Northwestern Polytechnical University, 2013 (in Chinese))
    Dhondt G. Calculix: A free software three-dimensional structural finite element program. http://www.calculix.de, 2022-08-30
    Rendall TCS, Allen CB. Unified fluid−structure interpolation and mesh motion using radial basis functions. International Journal for Numerical Methods in Engineering, 2008, 74(10): 1519-1559 doi: 10.1002/nme.2219
    Ballmann J. Experimental analysis of high Reynolds number structural dynamics in ETW//46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, AIAA, 2008: 84
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