基于降阶模型的上游尾流波形识别方法

张珺; 李立州

doi:10.13224/j.cnki.jasp.20250043

基于降阶模型的上游尾流波形识别方法

doi: 10.13224/j.cnki.jasp.20250043

张珺^1,,
李立州^2,*, ,

1.
太原学院数学系，太原 030032
2.
中北大学航空宇航学院，太原 030051

基金项目: 国家自然科学基金（51775518）

详细信息

作者简介:
张珺（1980-），女，副教授，硕士，研究方向为应用数学和力学。E-mail：catzhangjun@163.com

通讯作者:
李立州（1977-），男，教授，博士，研究方向为计算力学理论和方法、流固耦合方法。E-mail：lilizhou@163.com

中图分类号: V231.3
计量
- 文章访问数: 109
- HTML浏览量: 67
- PDF量: 8
- 被引次数: 0
出版历程
- 收稿日期: 2025-01-22
- 网络出版日期: 2026-07-03

Upstream wake wave identification based on reduced order model

Zhang Jun^1
,,
Li Lizhou^{2,*
, ,}

1.
Department of Mathematic，Taiyuan University，Taiyuan 030032，China
2.
School of Aerospace Engineering，North University of China，Taiyuan 030051，China

摘要

摘要:
当涡轮发动机工作时，旋转的上游尾流和下游背压波动使叶片受到波动压力，是影响发动机性能的关键因素，因此研究尾流背压波动及其效应非常重要，然而发动机内部结构复杂，直接进行发动机尾流背压波形测量是非常困难的。尾流背压激励的叶片气动力降阶模型与载荷识别理论中结构响应有着相同的时域反卷积形式，为此基于气动力降阶模型，提出通过叶片气动力识别尾流和背压波形的流场状态间接测量方法。二维叶片的算例表明：一阶Volterra级数降阶模型能够表征尾流激励下叶片气动力，基于该降阶模型的Tikhonov正则化方法能够根据叶片气动力识别尾流的总压波形。
- 尾流背压扰动 /
- 载荷识别 /
- 气动力降阶模型（ROM） /
- Tikhonov正则化 /
- Volterra级数
Abstract:
When turbine engines work, the rotating upstream wake and downstream back pressure waves force blades to fluctuate, which is a key factor of the engine's performance. Therefore, it is important to study the wake and backpressure waves and their effects. However, as the structures of engines are so complex, it is difficult to directly measure the fluctuations of upstream and downstream flows when engines is working. It is found that the aerodynamic ROM of the blades force to the upstream wakes and downstream pressure waves has the time domain deconvolution, which is widely used in structural load identification. Therefore, an indirect measurement method for identifying upstream wake and downstream pressure waves is proposed here based on the aerodynamic ROM. An identification example of a 2D blade indicates that the first-order Volterra ROM can predicate the aerodynamic force of the blade under wake excitation. The Tikhonov regularization method based on the Volterra ROM can identify the total pressure wave of the upstream wake.
- wake and back pressure perturbations /
- load identification /
- aerodynamic (reduced order model) ROM /
- Tikhonov regularization /
- Volterra series

HTML

图 1 尾流激励的叶片

Figure 1. Blade excited by wake

下载: 全尺寸图片幻灯片

图 2 尾流激励叶片气动力输入简化

Figure 2. Simplification of wake excitation input for blade aerodynamic force

下载: 全尺寸图片幻灯片

图 3 二维叶片CFD模型

Figure 3. 2D blade CFD model

下载: 全尺寸图片幻灯片

图 4 进口总压脉冲下叶片气动力的核函数

Figure 4. Kernel of blade aerodynamic force due to inlet total pressure pulse

下载: 全尺寸图片幻灯片

图 5 进口总压波动

Figure 5. Inlet total pressure wave

下载: 全尺寸图片幻灯片

图 6 进口总压波动下叶片的气动力

Figure 6. Aerodynamic force of the blade due to the inlet total pressure wave

下载: 全尺寸图片幻灯片

图 7 采用“L”曲线法求得a=9.88×10⁻³

Figure 7. a =9.88×10⁻³ obtained by L-curve method

下载: 全尺寸图片幻灯片

图 8 识别到的上游尾流总压波形

Figure 8. Identified upstream wake total pressure wave

下载: 全尺寸图片幻灯片

参考文献(29)

[1]	Hsu C N. A study on fluid self-excited flutter and forced response of turbomachinery rotor blade[J]. Mathematical Problems in Engineering, 2014, 2014: 437158. doi: 10.1155/2014/437158
[2]	Kou Haijun, Lin Jiansheng, Zhang Junhong, et al. Dynamic and fatigue compressor blade characteristics during fluid-structure interaction: Part Ⅰ blade modelling and vibration analysis[J]. Engineering Failure Analysis, 2017, 76: 80-98.
[3]	Amoo L M. On the design and structural analysis of jet engine fan blade structures[J]. Progress in Aerospace Sciences, 2013, 60: 1-11. doi: 10.1016/j.paerosci.2012.08.002
[4]	Rastogi V, Bhagi L K, Kumar V. Dynamic modeling of underplateform damper used in turbomachinery[J]. World Academy of Science, Engineering and Technology, 2012, 61: 536-545.
[5]	Sayma A I, Vahdati M, Imregun M. An integrated nonlinear approach for turbomachinery forced response prediction. part i: formulation[J]. Journal of Fluids and Structures, 2000, 14(1): 87-101. doi: 10.1006/jfls.1999.0253
[6]	Kirschmeier B, Bryant M. Experimental investigation of wake-induced aeroelastic limit cycle oscillations in tandem wings[J]. Journal of Fluids and Structures, 2018, 81: 309-324. doi: 10.1016/j.jfluidstructs.2018.04.015
[7]	Huang X Q, He L, Bell D L. Influence of upstream stator on rotor flutter stability in a low pressure steam turbine stage[J]. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 2006, 220(1): 25-35. doi: 10.1243/095765005X69170
[8]	杨智春, 贾有. 动载荷的识别方法[J]. 力学进展, 2015, 45(1): 29-54. Yang Zhichun, Jia You. The identification of dynamic loads[J]. Advances in Mechanics, 2015, 45(1): 29-54. (in Chinese Yang Zhichun, Jia You. The identification of dynamic loads[J]. Advances in Mechanics, 2015, 45(1): 29-54. (in Chinese)
[9]	胡寅寅, 率志君, 李玩幽, 等. 设备载荷识别与激励源特性的研究现状[J]. 噪声与振动控制, 2011, 31(4): 1-5, 15. Hu Yinyin, Shuai Zhijun, Li Wanyou, et al. Status quo of study on machine’s load identification technique[J]. Noise and Vibration Control, 2011, 31(4): 1-5, 15. (in Chinese Hu Yinyin, Shuai Zhijun, Li Wanyou, et al. Status quo of study on machine’s load identification technique[J]. Noise and Vibration Control, 2011, 31(4): 1-5, 15. (in Chinese)
[10]	许锋, 陈怀海, 鲍明. 动载荷识别的广义域模态模型及其精度分析研究[J]. 计算力学学报, 2003, 20(2): 218-222. Xu Feng, Chen Huaihai, Bao Ming. Study on the general domain based modal-model of force identification and its accuracy analysis[J]. Chinese Journal of Computational Mechanics Chinese Journal of Computational Mechanics, 2003, 20(2): 218-222. (in Chinese Xu Feng, Chen Huaihai, Bao Ming. Study on the general domain based modal-model of force identification and its accuracy analysis[J]. Chinese Journal of Computational Mechanics Chinese Journal of Computational Mechanics, 2003, 20(2): 218-222. (in Chinese)
[11]	周盼, 张权, 率志君, 等. 动载荷识别时域方法的研究现状与发展趋势[J]. 噪声与振动控制, 2014, 34(1): 6-11. Zhou Pan, Zhang Quan, Shuai Zhijun, et al. Review of research and development status of dynamic load identification in time domain[J]. Noise and Vibration Control, 2014, 34(1): 6-11. (in Chinese Zhou Pan, Zhang Quan, Shuai Zhijun, et al. Review of research and development status of dynamic load identification in time domain[J]. Noise and Vibration Control, 2014, 34(1): 6-11. (in Chinese)
[12]	吴肖, 曾捷, 胡子康, 等. 变截面悬臂梁结构动载荷辨识方法[J]. 航空学报, 2020, 41(9): 223806. Wu Xiao, Zeng Jie, Hu Zikang, et al. Dynamic load identification method for variable cross-section cantilever structure[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(9): 223806. (in Chinese Wu Xiao, Zeng Jie, Hu Zikang, et al. Dynamic load identification method for variable cross-section cantilever structure[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(9): 223806. (in Chinese)
[13]	袁向荣, 卜建清, 满红高, 等. 移动荷载识别的函数逼近法[J]. 振动与冲击, 2000, 19(1): 58-60, 70. Yuan Xiangrong, Bu Jianqing, Man Honggao, et al. Function approaching method in moving load identification[J]. Journal of Vibration and Shock, 2000, 19(1): 58-60, 70. (in Chinese Yuan Xiangrong, Bu Jianqing, Man Honggao, et al. Function approaching method in moving load identification[J]. Journal of Vibration and Shock, 2000, 19(1): 58-60, 70. (in Chinese)
[14]	张方, 朱德懋. 动态载荷时域识别的级数方法[J]. 振动工程学报, 1996, 9(1): 1-8. Zhang Fang, Zhu Demao. Identification of dynamic load based on series expansion[J]. Journal of Vibration Engineering, 1996, 9(1): 1-8. (in Chinese Zhang Fang, Zhu Demao. Identification of dynamic load based on series expansion[J]. Journal of Vibration Engineering, 1996, 9(1): 1-8. (in Chinese)
[15]	张方, 朱德懋, 张福祥. 动载荷识别的时间有限元模型理论及其应用[J]. 振动与冲击, 1998(2): 4-7, 96. Zhang Fang, Zhu Demao, Zhang Fuxiang. The theory and application of time finite element model for dynamic load identification[J]. Journal of Vibration and Shock, 1998(2): 4-7, 96. (in Chinese Zhang Fang, Zhu Demao, Zhang Fuxiang. The theory and application of time finite element model for dynamic load identification[J]. Journal of Vibration and Shock, 1998(2): 4-7, 96. (in Chinese)
[16]	饶柱石, 施勤忠, 荻原一郎. 基于逆系统分析法的多输入-多输出系统动态载荷的优化估计[J]. 振动与冲击, 2000, 19(2): 9-12, 16. Rao Zhushi, Shi Qinzhong, Di Yuanyilang. Inverse system analysis based optimal estimation of dynamic loads for multiple-input multiple-output system[J]. Journal of Vibration and Shock, 2000, 19(2): 9-12, 16. (in Chinese Rao Zhushi, Shi Qinzhong, Di Yuanyilang. Inverse system analysis based optimal estimation of dynamic loads for multiple-input multiple-output system[J]. Journal of Vibration and Shock, 2000, 19(2): 9-12, 16. (in Chinese)
[17]	高广磊, 刘斌, 李军, 等. 船体梁总纵弯曲载荷识别方法及试验验证[J]. 武汉理工大学学报(交通科学与工程版), 2024, 48(1): 67-71. Gao Guanglei, Liu Bin, Li Jun, et al. Identification method and experimental verification of longitudinal bending load of hull beam[J]. Journal of Wuhan University of Technology (Transportation Science & Engineering), 2024, 48(1): 67-71. (in Chinese Gao Guanglei, Liu Bin, Li Jun, et al. Identification method and experimental verification of longitudinal bending load of hull beam[J]. Journal of Wuhan University of Technology (Transportation Science & Engineering), 2024, 48(1): 67-71. (in Chinese)
[18]	Zhang Jun, Liu Zhao, Li Lizhou, et al. Aerodynamic reduced-order model of shape-change blade subjected to upstream wake[J]. Journal of Aerospace Engineering, 2020, 33(5): 04020055. doi: 10.1061/(ASCE)AS.1943-5525.0001174
[19]	罗骁, 李立州, 张新燕, 等. 尾流激励下的叶片气动力快速分析[J]. 振动与冲击, 2019, 38(23): 139-145. Luo Xiao, Li Lizhou, Zhang Xinyan, et al. Fast analysis of blade aerodynamic force under wake excitation[J]. Journal of Vibration and Shock, 2019, 38(23): 139-145. (in Chinese Luo Xiao, Li Lizhou, Zhang Xinyan, et al. Fast analysis of blade aerodynamic force under wake excitation[J]. Journal of Vibration and Shock, 2019, 38(23): 139-145. (in Chinese)
[20]	张珺, 李立州, 原梅妮. 径向基函数参数化翼型的气动力降阶模型优化[J]. 应用数学和力学, 2019, 40(3): 250-258. Zhang Jun, Li Lizhou, Yuan Meini. Optimization of RBF parameterized airfoils with the aerodynamic ROM[J]. Applied Mathematics and Mechanics, 2019, 40(3): 250-258. (in Chinese Zhang Jun, Li Lizhou, Yuan Meini. Optimization of RBF parameterized airfoils with the aerodynamic ROM[J]. Applied Mathematics and Mechanics, 2019, 40(3): 250-258. (in Chinese)
[21]	Li Lizhou, Zhang Xinyan, Zhang Jun, et al. Efficient ROM method for calculating blade aerodynamic forces to upstream and downstream perturbations[J]. Journal of Aerospace Engineering, 2019, 32(3): 04019011.
[22]	Li Lizhou, Zhang Jun, Luo Xiao, et al. An aerodynamic ROM of the blade subjected to wake based on Fourier method for flow[J]. International Journal for Numerical Methods in Fluids, 2019, 89(4/5): 162-179.
[23]	Li Li zhou, Yang Minglei, Luo Xiao, et al. A spline ROM of blade aerodynamic force to upstream wake[J]. Aerospace Science and Technology, 2019, 84: 650-660.
[24]	李立州, 杨明磊, 张珺, 等. 尾流激励的叶片气动力降阶模型. 计算力学学报, 2018, 35, (3): 299-303. Li Lizhou, Yang Minglei, Zhang Jun, et al. Aerodynamic ROM of blade due to upstream wake[J]. Chinese Journal of Computational Mechanics, 2018, 35(3): 299-303. (in Chinese Li Lizhou, Yang Minglei, Zhang Jun, et al. Aerodynamic ROM of blade due to upstream wake[J]. Chinese Journal of Computational Mechanics, 2018, 35(3): 299-303. (in Chinese)
[25]	罗骁, 张新燕, 张珺, 等. 基于谐波平衡法的尾流激励的叶片振动降阶模型方法[J]. 应用数学和力学, 2018, 39(8): 892-899. Luo Xiao, Zhang Xinyan, Zhang Jun, et al. A reduced-order model method for blade vibration due to upstream wake based on the harmonic balance method[J]. Applied Mathematics and Mechanics, 2018, 39(8): 892-899. (in Chinese Luo Xiao, Zhang Xinyan, Zhang Jun, et al. A reduced-order model method for blade vibration due to upstream wake based on the harmonic balance method[J]. Applied Mathematics and Mechanics, 2018, 39(8): 892-899. (in Chinese)
[26]	Balajewicz M, Nitzsche F, Feszty D. Application of multi-input Volterra theory to nonlinear multi-degree-of-freedom aerodynamic systems[J]. AIAA Journal, 2010, 48(1): 56-62. [LinkOut]
[27]	Raveh D, Mavris D. Reduced-order models based on CFD impulse and step responses: AIAA-2001-1527[R]. Anaheim, US: 19th AIAA Applied Aerodynamics Conference, 2001.
[28]	Silva W. Reduced-order models based on linear and nonlinear aerodynamic impulse responses: AIAA-1999-1262 [R]. Louisiana, US: 40th Structures, Structural Dynamics, and Materials Conference and Exhibit, 1999.
[29]	Hansen P C. Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion[M]. Philadelphia, US: Society for Industrial and Applied Mathematics, 1998.