Effect of Front and Rear Rotor Stages on Aeroelasticity in Multi-Stage Environment

  • Xiaobo Zhang
  • Yanrong Wang
  • Xianghua Jiang
  • Zhizhong Fu
Original Paper


An energy method based on the mixing-plane model and phase lagged boundary condition has been developed to estimate the flutter characteristics of rotor blades in multi-stage environment. The effects of front and rear rotor stages on the aerodynamic damping of the rotor blades have been investigated using this method. The results show that the mixing-plane model enables to consider the averaging effect of the other stages on the aeroelasticity of the checked rotor blades without having to perform the unsteady full annual multi-stage (FAMS) flow computations. Comparing with the isolated rotor blade, the upstream and downstream rotor stages have a significant influence on the aeroelasticity of the rotor blade with altering the intensity and location of the shock wave and separation flow region on suction surface. It is worth to point out that the neighbor rotor stages reduce the effect of the inter-blade phase angle (IBPA) on the aerodynamic damping. Moreover, the impact of the rear rotor stage on aerodynamic damping of the rotor blade is more remarkable than that of the front one. Compared to the measured data, the capability of this method used in the aeroelasticity assessment of a multi-stage turbomachine has been validated. Furthermore, the relationship between the aerodynamic damping and the motion of the shock wave has been revealed, which can assist the compressor design.


Aeroelasticity Multi-stage turbomachine Front and rear rotor stages Mixing-plane model 

List of symbols


First bending mode shape


First torsion mode shape


Fourier coefficient


Aerodynamic modal damping ratio


Blade chord length, m


Aerodynamic force vector


Imaginary unit


Inter-blade phase angle


Inlet guided vane

\( \vec{n} \)

Surface unit normal vector


Nodal diameter


Pressure, pa


Modal amplitude of the selected mode shape


Blade surface area, m2


Vibration period, s


Time, s

\( \vec{v} \)

Velocity, m/s


Work, J


Inter-blade phase angle


Natural angular frequency of the blade, rad/s


Damping ratio


Time difference, s



This work is supported by the National Nature Science Foundation of China (No. 51475022).


  1. 1.
    Hsu K, Hoyniak D (2012) Full-annulus multi-row flutter analyses. ASME Paper No. GT2012-68631.
  2. 2.
    Zhang CA, Ye ZY, Liu F, Shi AM (2010) Numerical Researches on Aeroelastic Problem of a Rotor due to IGV/Fan Interaction. AIAA Paper No. 2009-865.
  3. 3.
    Yang H, Shen Z, Zhen Y (2016) Influence of up-and downstream blades on the rotor blade flutter characteristics. J Aerosp Power 31(5):1170–1177. (in Chinese) CrossRefGoogle Scholar
  4. 4.
    Buffum DH (1995) Blade row interaction effects on flutter and forced response. J Propul Power 11(2):205–212. CrossRefGoogle Scholar
  5. 5.
    Hall KC, Silkowski PD (1997) The influence of neighboring blade rows on the unsteady aerodynamic response of cascades. J Turbomach 119(1):85–93. CrossRefGoogle Scholar
  6. 6.
    Li HD, He L (2003) Blade aerodynamic damping variation with rotor-stator gap: a computational study using single-passage approach. J Turbomach 127(3):573–579. CrossRefGoogle Scholar
  7. 7.
    Ekici K, Voytovych DM, Hall KC (2005) Time-linearized navier-stokes analysis of flutter in multistage turbomachines. AIAA Paper No. 2005-836.
  8. 8.
    Huang XQ, He L, Bell DL (2006) Influence of upstream stator on rotor flutter stability in a low pressure steam turbine stage. Proc Inst Mech Eng Part A J Power Energy 220(1):25–35. CrossRefGoogle Scholar
  9. 9.
    Namba M, Nishino R (2006) Flutter analysis of contra-rotating blade rows. AIAA J 44(11):2612–2620. CrossRefGoogle Scholar
  10. 10.
    Namba M, Kubo A (2008) Aerodynamically coupled flutter of multiple blade rows. ASME Paper No. GT2008-50315.
  11. 11.
    Rahmati MT, He L, Li YS (2015) The blade profile orientations effects on the aeromechanics of multirow turbomachines. J Eng Gas Turbines Power 138(6):062606. CrossRefGoogle Scholar
  12. 12.
    Sayma AI, Vahdati M, Imregun M (2000) An integrated nonlinear approach for turbomachinery forced response prediction. Part I: formulation. J Fluids Struct 14:87–101. CrossRefGoogle Scholar
  13. 13.
    Sayma AI, Vahdati M, Imregun M (2000) An integrated nonlinear approach for turbomachinery forced response prediction. Part II: case studies. J Fluids Struct 14:103–125. CrossRefGoogle Scholar
  14. 14.
    Culver R, Liu F (2009) Mixing-plane method for flutter computation in multi-stage turbomachines. AIAA Paper No. 2009-862.
  15. 15.
    Huang XQ, Zhang X, Zhang HM (2014) Blade flutter prediction method based on hybrid unsteady/steady flow analysis in a multi-stage environment. J Eng Thermophys (in Chinese) 35(7):1304–1308 (Accession number for EI: 20143118012541) Google Scholar
  16. 16.
    Carta FO (1967) Coupled blade-disk-shroud flutter instability in turbojet engine rotors. J Eng Gas Turbines Power 89(3):419–426. CrossRefGoogle Scholar
  17. 17.
    Micallef D, Witteck D, Wiedermann A, Kluß D, Mailach R (2012) Three-dimensional viscous flutter analyses of a turbine cascade in subsonic and transonic flows. ASME Paper No. GT2012-68396.
  18. 18.
    Zhang XW, Wang YR, Xu KN (2011) Flutter prediction in turbomachinery with energy method. Proc Inst Mech Eng Part G 225(9):995–1002. CrossRefGoogle Scholar
  19. 19.
    Zhang XW, Wang YR, Xu KN (2012) Mechanisms and key parameters for compressor blade stall flutter. J Turbomach 135(2):024501. CrossRefGoogle Scholar
  20. 20.
    Fu ZZ, Wang YR, Jiang XH, Wei DS (2014) Tip clearance effects on aero-elastic stability of axial compressor blades. J Eng Gas Turbines Power 137(1):012501. CrossRefGoogle Scholar
  21. 21.
    Moffatt S, He L (2003) Blade forced response prediction for industrial gas turbines: Part 1—methodologies. ASME Paper No. GT2003-38640.
  22. 22.
    Erdos JI, Alzner E, McNally W (1977) Numerical solution of periodic transonic flow through a fan stage. AIAA J 15(11):1559–1568. CrossRefzbMATHGoogle Scholar
  23. 23.
    He L (1990) An euler solution for unsteady flows around oscillating blades. J Turbomach 112(4):714–722. CrossRefGoogle Scholar
  24. 24.
    Zhang XB, Wang YR, Wang NM, Tian AM (2016) Effects of turbulence model on flutter prediction of a transonic fan. AIAA Paper No. 2016-3836.
  25. 25.
    Vedeneev VV, Kolotnikov M, Makarov P (2015) Experimental validation of numerical blade flutter prediction. J Propul Power 31(5):1–11. CrossRefGoogle Scholar

Copyright information

© The Korean Society for Aeronautical & Space Sciences and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of Energy and PowerBeihang UniversityBeijingChina
  2. 2.Collaborative Innovation Center for Advanced Aero-EngineBeijingChina
  3. 3.Beijing Key Laboratory of Aero-Engine Structure and StrengthBeijingChina

Personalised recommendations