Volume 46 Issue 2
Feb.  2025
Turn off MathJax
Article Contents
ZHOU Xiangxin, LI Teng, YANG Weijian, LIN Yongkang, ZHANG Tao, YAO Jianyao. Spatiotemporal Characterization of Unsteady Cascade Flow Fields Driven by Rotor Stator Interaction Using Modal Decomposition[J]. Applied Mathematics and Mechanics, 2025, 46(2): 223-240. doi: 10.21656/1000-0887.450121
Citation: ZHOU Xiangxin, LI Teng, YANG Weijian, LIN Yongkang, ZHANG Tao, YAO Jianyao. Spatiotemporal Characterization of Unsteady Cascade Flow Fields Driven by Rotor Stator Interaction Using Modal Decomposition[J]. Applied Mathematics and Mechanics, 2025, 46(2): 223-240. doi: 10.21656/1000-0887.450121

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

doi: 10.21656/1000-0887.450121
  • Received Date: 2024-04-29
  • Rev Recd Date: 2024-09-04
  • Publish Date: 2025-02-01
  • 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.
  • (Recommended by YAN Bo, M.AMM Editorial Board)
  • loading
  • [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)
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(16)  / Tables(4)

    Article Metrics

    Article views (145) PDF downloads(26) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return