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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): 299-308. 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): 299-308. 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): 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

基于POD和代理模型的静气动弹性分析方法

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.

     

    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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