基于模态分解的转静干涉平面叶栅非定常流场时空分布分析

周向鑫; 李滕; 杨维建; 林永康; 张涛; 姚建尧

doi:10.21656/1000-0887.450121

基于模态分解的转静干涉平面叶栅非定常流场时空分布分析

doi: 10.21656/1000-0887.450121

1.
重庆大学航空航天学院, 重庆 400044
2.
北京航空航天大学航空发动机研究院, 北京 102206
3.
太行实验室, 成都 610213

（我刊编委严波推荐）

基金项目:

国家科技重大专项 J2022-IV-0010-0024

中央高校基本科研业务费 2023CDJXY-007

详细信息

作者简介:
周向鑫(1993-), 男, 硕士生(E-mail: xiangxinzhou@cqu.edu.cn)

通讯作者:
姚建尧(1981-), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: yaojianyao@cqu.edu.cn)

中图分类号: V211.3
计量
- 文章访问数: 64
- HTML全文浏览量: 30
- PDF下载量: 9
- 被引次数: 0
出版历程
- 收稿日期: 2024-04-29
- 修回日期: 2024-09-04
- 刊出日期: 2025-02-01

Spatiotemporal Characterization of Unsteady Cascade Flow Fields Driven by Rotor Stator Interaction Using Modal Decomposition

1.
College of Aerospace Engineering, Chongqing University, Chongqing 400044, P.R.China
2.
Research Institute of Aero-Engine, Beihang University, Beijing 102206, P.R.China
3.
Taihang Laboratory, Chengdu 610213, P.R.China

(Recommended by YAN Bo, M.AMM Editorial Board)

摘要

摘要: 由转静干涉引起的非定常流动是造成叶片/叶盘强迫响应的主要激励来源，更加准确和全面地表征转静干涉非定常流场的时空分布特征对流固耦合振动分析具有重要的意义，利用本征正交分解(POD)和动力学模态分解(DMD)等模态分析方法可以有效地从复杂流动系统中识别和提取激励成分. 该文以典型的1.5级涡轮平面叶栅为例，采用POD方法和DMD方法获得二维转静干涉流场的流动模态和时间系数，对叶片通道流场的时空分布特性进行分析. 结果表明：两种模态分解方法均能有效辨识流动特征，实现流场的合理减缩. 利用模态能量排序的POD方法可以准确识别占据流场主导地位的流动结构；而基于频率特征的DMD方法可以快速识别流场中各阶模态对应的激振频率和激励阶次. 模态分解方法相较于传统FFT方法，不受采样位置的影响，兼顾全场流动识别和局部特征分析，可为叶轮机械非定常激励耦合振动快速分析提供帮助.
- 瞬态流场 /
- 本征正交分解 /
- 动力学模态分解 /
- 转静干涉 /
- 非定常激励
Abstract: The unsteady flow caused by the rotor-stator interaction is the primary excitation source for the forced response of the blade/blisk. A more accurate and comprehensive characterization of the spatiotemporal features of the rotor-stator interaction unsteady flow field is of significance for the analysis of fluid-structure interaction vibrations. The typical modal analysis methods such as the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD) were employed to effectively identify and extract the excitation components from complex flow systems. With a 1.5-stage turbine cascade as the example, the POD method and the DMD method were used to obtain the flow modes and temporal bases of the 2D rotor-stator interaction flow field, and analyse the spatiotemporal characterization of the blade channel. The results show that, the both modal decomposition methods can effectively identify the flow characteristics and realize the reasonable reduction of the flow field. The POD method, with the modal energy ranking, can accurately identify the dominant flow structures in the flow field. Meanwhile, the DMD method based on frequency characteristics can rapidly pinpoint the excitation frequencies and engine orders of each mode in the flow field. Compared to the fast Fourier transform (FFT) methods, the modal decomposition techniques are not influenced by the sampling locations and effectively combine full-field flow recognition with local feature analysis. This approach facilitates swift analysis of unsteady excitation-coupled vibrations in turbomachinery.
- transient flow field /
- proper orthogonal decomposition /
- dynamic mode decomposition /
- rotor-stator interaction /
- unsteady excitation
edited-by

edited-by
注释:

1) （我刊编委严波推荐）

HTML全文

图 1 不同网格特征截面压力对比

Figure 1. Comparison of pressures in characteristic sections of different meshes

下载: 全尺寸图片幻灯片

图 2 1.5级二维叶栅模型网格

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 2. The 1.5-stage 2D cascade mesh grid

下载: 全尺寸图片幻灯片

图 3 非定常计算监测点压力变化

Figure 3. Pressure changes at the monitoring point during calculation

下载: 全尺寸图片幻灯片

图 4 第2至9阶POD模态能量分布

Figure 4. Energy distribution of the 2nd to 9th modes of POD

下载: 全尺寸图片幻灯片

图 5 某时刻转子压力场POD重构模型

Figure 5. The reconstruction POD model for the rotor pressure

下载: 全尺寸图片幻灯片

图 6 第2至9阶DMD模态能量分布

Figure 6. Energy distribution of the 2nd to 9th modes of DMD

下载: 全尺寸图片幻灯片

图 7 某时刻转子压力场DMD重构模型

Figure 7. The reconstruction DMD model for the rotor pressure field

下载: 全尺寸图片幻灯片

图 8 1 ∶ 1 ∶ 1模型第2至5阶POD模态空间分布

Figure 8. The 2nd to 5th POD modes of the 1 ∶ 1 ∶ 1 model

下载: 全尺寸图片幻灯片

图 9 1 ∶ 1 ∶ 1模型第2至5阶POD模态时间系数和频率成分

Figure 9. Time coefficients and frequencies of the 2nd to 5th POD modes of the 1 ∶ 1 ∶ 1 model

下载: 全尺寸图片幻灯片

图 10 6 ∶ 7 ∶ 7模型第2至5阶POD模态空间分布

Figure 10. The 2nd to 5th POD modes of the 6 ∶ 7 ∶ 7 model

下载: 全尺寸图片幻灯片

图 11 6 ∶ 7 ∶ 7模型第2至5阶POD模态时间系数和频率成分

Figure 11. Time coefficients and frequencies of the 2nd to 5th POD modes of the 6 ∶ 7 ∶ 7 model

下载: 全尺寸图片幻灯片

图 12 1 ∶ 1 ∶ 1模型第2至5阶DMD模态空间分布

Figure 12. The 2nd to 5th DMD modes of the 1 ∶ 1 ∶ 1 model

下载: 全尺寸图片幻灯片

图 13 1 ∶ 1 ∶ 1模型第2至5阶DMD模态时间系数和频率成分

Figure 13. Time coefficients and frequencies of the 2nd to 5th DMD modes of the 1 ∶ 1 ∶ 1 model

下载: 全尺寸图片幻灯片

图 14 6 ∶ 7 ∶ 7模型第2至5阶DMD模态空间分布

Figure 14. The 2nd to 5th DMD modes of the 6 ∶ 7 ∶ 7 model

下载: 全尺寸图片幻灯片

图 15 6 ∶ 7 ∶ 7模型第2至5阶DMD模态时间系数和频率成分

Figure 15. Time coefficients and frequencies of the 2nd to 5th DMD modes of the 6 ∶ 7 ∶ 7 model

下载: 全尺寸图片幻灯片

图 16 不同模型各阶POD模态激励阶次分布

Figure 16. Engine order distributions of POD modes of 2 different models

下载: 全尺寸图片幻灯片

表 1 Aachen涡轮几何参数

Table 1. Aachen turbine geometric parameters

geometric parameter	stator blade	rotor blade
number of blades	36	41
chord length /m	0.062	0.06
blade width /m	0.044 25	0.054
aspect ratio	0.887	0.917
blade pitch /m	0.047 6	0.041 8
tip diameter /m	0.6	0.6
rotation speed /(r/min)	0	3 500

下载: 导出CSV

表 2 网格无关性验证

Table 2. Mesh-independent verification

mesh scheme	number of meshes	minimum mesh edge length/m
mesh A	448 263	2.292×10^-4
mesh B	501 563	1.779×10^-4
mesh C	654 499	1.146×10^-4

下载: 导出CSV

表 3 前5阶1 ∶ 1 ∶ 1模型DMD模态增长率和缩减频率

Table 3. Growth rates and reduced frequencies of the 1st 5 DMD modes of the 1 ∶ 1 ∶ 1 model

mode	growth rate	reduced frequency/Hz
1	3.00×10^-8	0
2, 3	-1.95×10^-5	2 791
4, 5	6.57×10^-5	5 582

下载: 导出CSV

表 4 两种模型流体激励阶次

Table 4. Engine orders of 2 models

1∶1∶1 model		6∶7∶7 model
F/Hz	engine order	F/Hz	engine order
2 791	0	2 392	1
5 582	0	2 791	0
8 373	0	4 784	2
11 164	0	5 582	0

下载: 导出CSV

参考文献(47)

[1]	李其汉, 王延荣. 航空发动机结构强度设计问题[M]. 上海: 上海交通大学出版社, 2014. LI Qihan, WANG Yanrong. The Design Problem of Aero-Engine Structure Strength[M]. Shanghai: Shanghai Jiao Tong University Press, 2014. (in Chinese)
[2]	MAILACH R, VOGELER K. Aerodynamic blade row interactions in an axial compressor, part Ⅱ: unsteady profile pressure distribution and blade forces[J]. Journal of Turbomachinery, 2004, 126 (1): 45-51. doi: 10.1115/1.1649742
[3]	周正贵, 胡骏. 轴流压气机动静叶片排非定常气动力分析[J]. 航空动力学报, 2003, 18 (1): 46-50. doi: 10.3969/j.issn.1000-8055.2003.01.008 ZHOU Zhenggui, HU Jun. The analysis of unsteady blade force in a rotor/stator axial compressor[J]. Journal of Aerospace Power, 2003, 18 (1): 46-50. (in Chinese) doi: 10.3969/j.issn.1000-8055.2003.01.008
[4]	王英锋, 胡骏, 王志强. 转静干涉对叶片非定常表面压力的影响[J]. 推进技术, 2010, 31 (2): 198-203. WANG Yingfeng, HU Jun, WANG Zhiqiang. Effect of stator-rotor interactions on the blades surface pressure[J]. Journal of Propulsion Technology, 2010, 31 (2): 198-203. (in Chinese)
[5]	杨彤, 王松涛, 姜斌. 弯曲叶片造型对涡轮叶栅作用力影响的非定常数值研究[J]. 推进技术, 2013, 34 (6): 760-767. YANG Tong, WANG Songtao, JIANG Bin. Unsteady numerical study of effects on turbine blade forces for the bowed blade[J]. Journal of Propulsion Technology, 2013, 34 (6): 760-767. (in Chinese)
[6]	张小博, 王延荣, 黄钟山, 等. 转静干涉下转子叶片的非定常压力频谱[J]. 航空动力学报, 2016, 31 (7): 1695-1703. ZHANG Xiaobo, WANG Yanrong, HUANG Zhongshan, et al. Frequency spectrum of unsteady pressure on rotor blade with rotor-stator interaction[J]. Journal of Aerospace Power, 2016, 31 (7): 1695-1703. (in Chinese)
[7]	LI H D, HE L. Blade aerodynamic damping variation with rotor-stator gap: a computational study using single-passage approach[J]. Journal of Turbomachinery, 2005, 127 (3): 573-579. doi: 10.1115/1.1928932
[8]	MONK D J, KEY N L, FULAYTER R D. Reduction of aerodynamic forcing through introduction of stator asymmetry in axial compressors[J]. Journal of Propulsion and Power, 2016, 32 (1): 134-141. doi: 10.2514/1.B35704
[9]	MAILACH R, MVLLER L, VOGELER K. Rotor-stator interactions in a four-stage low-speed axial compressor, part Ⅱ: unsteady aerodynamic forces of rotor and stator blades[J]. Journal of Turbomachinery, 2004, 126 (4): 519-526. doi: 10.1115/1.1791642
[10]	JIA H, XI G, MVLLER L, et al. Unsteady blade loading with clocking in multistage axial compressors, part 1[J]. Journal of Propulsion and Power, 2010, 26 (1): 25-36. doi: 10.2514/1.36914
[11]	FURTH F, VOGT D M, BLADH R, et al. Unsteady forcing vs. efficiency: the effect of clocking on a transonic industrial compressor[C]//Proceedings of the ASME 2013 Fluids Engineering Division Summer Meeting. Incline Village, Nevada, USA: ASME, 2013.
[12]	LIU J, QIAO W Y, DUAN W H. Investigation of unsteady aerodynamic excitation on rotor blade of variable geometry turbine[J]. International Journal of Rotating Machinery, 2019, 2019 : 4396546.
[13]	TYLER J M, SOFRIN T G. Axial flow compressor noise studies[R]. 1962.
[14]	ADAMCZYK J. Model equation for simulating flows in multistage turbomachinery: NASA-TM-86869[R]. 1985.
[15]	LENGANI D, SELIC T, SPATARO R, et al. Analysis of the unsteady flow field in turbines by means of modal decomposition[C]//Proceedings of the ASME Turbo Expo 2012 : Turbine Technical Conference and Exposition. Copenhagen, Denmark: ASME, 2012.
[16]	COURTIADE N, OTTAVY X, GOURDAIN N. Modal decomposition for the analysis of the rotor-stator interactions in multistage compressors[J]. Journal of Thermal Science, 2012, 21 (3): 276-285. doi: 10.1007/s11630-012-0545-2
[17]	SCHRAPE S, GIERSCH T, NIPKAU J, et al. Tyler-Sofrin modes in axial high pressure compressor forced response analyses[C]//Proceedings of the 14 th International Symposium on Unsteady Aerodynamics, Aeroacoustics & Aeroelasticity of Turbomachines. Stockholm, Sweden, 2015.
[18]	FIGASCHEWSKY F, KVHHORN A, BEIROW B, et al. Analysis of mistuned forced response in an axial high-pressure compressor rig with focus on Tyler-Sofrin modes[J]. The Aeronautical Journal, 2019, 123 (1261): 356-377. doi: 10.1017/aer.2018.163
[19]	SIROVICH L. Turbulence and the dynamics of coherent structures, part Ⅰ: coherent structures[J]. Quarterly of Applied Mathematics, 1987, 45 (3): 561-571. doi: 10.1090/qam/910462
[20]	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[J]. 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 application[J]. Advances in Mechanics, 2011, 41 (6): 686-701. (in Chinese)
[21]	BENNER P, GUGERCIN S, WILLCOX K. A survey of projection-based model reduction methods for parametric dynamical systems[J]. SIAM Review, 2015, 57 (4): 483-531. doi: 10.1137/130932715
[22]	王金城, 齐进, 吴锤结. 含压力基Navier-Stokes方程最优动力系统建模和分析[J]. 应用数学和力学, 2020, 41 (8): 817-833. WANG Jincheng, QI Jin, WU Chuijie. Modelling and analysis of optimal dynamical systems of incompressible Navier-Stokes equations with pressure base functions[J]. Applied Mathematics and Mechanics, 2020, 41 (8): 817-833. (in Chinese)
[23]	SCHMID P J. Dynamic mode decomposition of numerical and experimental data[J]. Journal of Fluid Mechanics, 2010, 656 : 5-28. doi: 10.1017/S0022112010001217
[24]	王建明, 明晓杰, 王涵, 等. 方柱/板结合部马蹄涡流动结构的动力学模态分解[J]. 应用数学和力学, 2018, 39 (1): 64-76. WANG Jianming, MING Xiaojie, WANG Han, et al. Dynamic mode decomposition of horseshoe vortex flow structures around square prism-plate junctions[J]. Applied Mathematics and Mechanics, 2018, 39 (1): 64-76. (in Chinese)
[25]	EPUREANU B I, HALL K C, DOWELL E H. Reduced-order models of unsteady viscous flows in turbomachinery using viscous-inviscid coupling[J]. Journal of Fluids and Structures, 2001, 15 (2): 255-273. doi: 10.1006/jfls.2000.0334
[26]	EPUREANU B I. A parametric analysis of reduced order models of viscous flows in turbomachinery[J]. Journal of Fluids and Structures, 2003, 17 (7): 971-982. doi: 10.1016/S0889-9746(03)00044-6
[27]	LI T, DENG S, ZHANG K, et al. A nonintrusive parametrized reduced-order model for periodic flows based on extended proper orthogonal decomposition[J]. International Journal of Computational Methods, 2021, 18 (9): 2150035. doi: 10.1142/S0219876221500353
[28]	LI T, PAN T, ZHOU X, et al. Non-intrusive reduced-order modeling based on parametrized proper orthogonal decomposition[J]. Energies, 2023, 17 (1): 146. doi: 10.3390/en17010146
[29]	WEI H, CAO Z, LI T, et al. Parametric modelling of unsteady load for turbine cascade and its application in clocking effect optimization and load-reduction[J]. Aerospace Science and Technology, 2022, 127 : 107669. doi: 10.1016/j.ast.2022.107669
[30]	KOU J, ZHANG W. Dynamic mode decomposition with exogenous input for data-driven modeling of unsteady flows[J]. Physics of Fluids, 2019, 31 (5): 057106. doi: 10.1063/1.5093507
[31]	HU C, QIAO T, ZHENG S, et al. Improved prediction of coherent structure in an intermediate turbine duct[J]. International Journal of Mechanical Sciences, 2023, 256 : 108497. doi: 10.1016/j.ijmecsci.2023.108497
[32]	CLARK S T, BESEM F M, KIELB R E, et al. Developing a reduced-order model of nonsynchronous vibration in turbomachinery using proper-orthogonal decomposition methods[J]. Journal of Engineering for Gas Turbines and Power, 2015, 137 (5): 052501. doi: 10.1115/1.4028675
[33]	CIZMAS P G A, PALACIOS A. Proper orthogonal decomposition of turbine rotor-stator interaction[J]. Journal of Propulsion and Power, 2003, 19 (2): 268-281. doi: 10.2514/2.6108
[34]	ROCHUON N, TRÉBINJAC I, BILLONNET G. An extraction of the dominant rotor-stator interaction modes by the use of proper orthogonal decomposition (POD)[J]. Journal of Thermal Science, 2006, 15 (2): 109-114. doi: 10.1007/s11630-006-0109-4
[35]	王磊, 高丽敏, 茅晓晨, 等. 基于POD方法的对转压气机叶顶非定常流场分析[J/OL]. 航空动力学报, 2023[2024-09-04]. https://doi.org/10.13224/j.cnki.jasp.20220896. WANG Lei, GAO Limin, MAO Xiaochen, et al. Analysis of tip unsteady flow field in a counter-rotating compressor based on POD method[J/OL]. Journal of Aerospace Power, 2023[2024-09-04]. https://doi.org/10.13224/j.cnki.jasp.20220896. (in Chinese)
[36]	QIAO T, YANG C, HU C. Analysis of interaction between leakage flow and upstream wake by proper orthogonal decomposition applied[J]. Journal of Physics: Conference Series, 2023, 2569 (1): 012028. doi: 10.1088/1742-6596/2569/1/012028
[37]	SUZUKI T. Spiral flow instability between a rotor and a stator in high-speed turbomachinery and its relation to fan noise[J]. Journal of Fluid Mechanics, 2023, 966 : A1. doi: 10.1017/jfm.2023.282
[38]	LIU X, WU Z, SI C, et al. Role of unsteady tip leakage flow in acoustic resonance inception of a multistage compressor[J]. Chinese Journal of Aeronautics, 2023, 36 (10): 165-181. doi: 10.1016/j.cja.2023.07.034
[39]	SONG M R, YANG B. Analysis on the unsteady flow structures in the tip region of axial compressor[J]. Proceedings of the Institution of Mechanical Engineers (Part A): Journal of Power and Energy, 2021, 235 (6): 1272-1287. doi: 10.1177/0957650921995111
[40]	DE ALMEIDA V B C, TVZVNER E, ECK M, et al. Numerical characterization of prestall disturbances in a compressor stage[J]. Journal of Turbomachinery, 2024; 146 (8): 081009. doi: 10.1115/1.4064993
[41]	TAIRA K, BRUNTON S L, DAWSON S T M, et al. Modal analysis of fluid flows: an overview[J]. AIAA Journal, 2017, 55 (12): 4013-4041. doi: 10.2514/1.J056060
[42]	TU J H, ROWLEY C W, LUCHTENBURG D M, et al. On dynamic mode decomposition: theory and applications[J]. Journal of Computational Dynamics, 2014, 1 (2): 391-421. doi: 10.3934/jcd.2014.1.391
[43]	ROWLEY C W, MEZI CĆI, BAGHERI S, et al. Spectral analysis of nonlinear flows[J]. Journal of Fluid Mechanics, 2009, 641 : 115-127. doi: 10.1017/S0022112009992059
[44]	JOVANOVI CĆM R, SCHMID P J, NICHOLS J W. Sparsity-promoting dynamic mode decomposition[J]. Physics of Fluids, 2014, 26 (2): 024103. doi: 10.1063/1.4863670
[45]	宋兆泓. 航空燃气涡轮发动机强度设计[M]. 北京: 北京航空学院出版社, 1988. SONG Zhaohong. Strength Design of Aviation Gas Turbine Engine[M]. Beijing: Beijing Aviation Institute Press, 1988. (in Chinese)
[46]	尹泽勇. 航空发动机设计手册: 第18册, 叶片轮盘及主轴强度分析[M]. 北京: 航空工业出版社, 2001. YIN Zeyong. Aero-Engine Design Manual: Vol 18, Strength Analysis of Blade Rotor and Spindle[M]. Beijing: Aviation Industry Press, 2001. (in Chinese)
[47]	寇家庆, 张伟伟, 高传强. 基于POD和DMD方法的跨声速抖振模态分析[J]. 航空学报, 2016, 37 (9): 2679-2689. KOU Jiaqing, ZHANG Weiwei, GAO Chuanqiang. Modal analysis of transonic buffet based on POD and DMD method[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37 (9): 2679-2689. (in Chinese)