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Experimental Investigation of Three-Dimensional Mechanisms in Low-Pressure Turbine Flutter Damian Vogt Doctoral Thesis 2005

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  • Experimental Investigation of Three-Dimensional Mechanisms in

    Low-Pressure Turbine Flutter

    Damian Vogt

    Doctoral Thesis 2005

  • Akademisk avhandling som med tillstnd av Kungliga Tekniska Hgskolan i Stockholm framlgges till offentlig granskning fr avlggande av teknisk doktorsexamen i energiteknik, fredagen den 27e maj 2005, kl. 10.00 i salen M3, Brinellvgen 64, Kungliga Tekniska Hgskolan, Stockholm. Avhandlingen frsvaras p engelska. TRITA-KTV-2005-01 ISSN 1100/7990 ISRN KTH-KRV-R-05-01-SE ISBN 91-7178-034-3 2005 Damian Vogt

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    Abstract The continuous trend in gas turbine design towards lighter, more powerful and more reliable engines on one side and use of alternative fuels on the other side renders flutter problems as one of the paramount challenges in engine design. Flutter denotes a self-excited and self-sustained aeroelastic instability phenomenon that can lead to material fatigue and eventually damage of structure in a short period of time unless properly damped. The design for flutter safety involves the prediction of unsteady aerodynamics as well as structural dynamics that is mostly based on in-house developed numerical tools. While high confidence has been gained on the structural side unanticipated flutter occurrences during engine design, testing and operation evidence a need for enhanced validation of aerodynamic models despite the degree of sophistication attained. The continuous development of these models can only be based on the deepened understanding of underlying physical mechanisms from test data. As a matter of fact most flutter test cases treat the turbomachine flow in two-dimensional manner indicating that the problem is solved as plane representation at a certain radius rather than representing the complex annular geometry of a real engine. Such considerations do consequently not capture effects that are due to variations in the third dimension, i.e. in radial direction. In this light the present thesis has been formulated to study three-dimensional effects during flutter in the annular environment of a low-pressure turbine blade row and to describe the importance on prediction of flutter stability. The work has been conceived as compound experimental and computational work employing a new annular sector cascade test facility. The aeroelastic response phenomenon is studied in the influence coefficient domain having one blade oscillating in various three-dimensional rigid-body modes and measuring the unsteady response on several blades and at various radial positions. On the computational side a state-of-the-art industrial numerical prediction tool has been used that allowed for two-dimensional and three-dimensional linearized unsteady Euler analyses. The results suggest that considerable three-dimensional effects are present, which are harming prediction accuracy for flutter stability when employing a two-dimensional plane model. These effects are mainly apparent as radial gradient in unsteady response magnitude from tip to hub indicating that the sections closer to the hub experience higher aeroelastic response than their equivalent plane representatives. Other effects are due to turbomachinery-typical three-dimensional flow features such as hub endwall and tip leakage vortices, which considerably affect aeroelastic prediction accuracy. Both effects are of the same order of magnitude as effects of design parameters such as reduced frequency, flow velocity level and incidence. Although the overall behavior is captured fairly well when using two-dimensional simulations notable improvement has been demonstrated when modeling fully three-dimensional and including tip clearance. Keywords: turbomachinery, flutter, aeroelastic instability, aeroelastic testing, CFD, linearized unsteady numerical method, 3D aerodynamic effects

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    Preface The thesis is based on the following papers: 1 Vogt, D.M., Fransson, T.H., 2000

    Aerodynamic Influence Coefficients on an Oscillating Turbine Blade in Three-Dimensional High Speed Flow Paper presented at the 15th Symposium on Measuring Techniques in Transonic and Supersonic Flows in Cascades and Turbomachines, Florence, Italy

    2 Vogt, D.M., Fransson, T.H., 2002 A New Turbine Cascade for Aeromechanical Testing Paper presented at the 16th Symposium on Measuring Techniques in Transonic and Supersonic Flows in Cascades and Turbomachines, Cambridge, UK

    3 Fransson, T.H., Vogt, D.M., 2003

    A New Facility for Investigating Flutter in Axial Flow Turbomachines Paper presented at the 8th National Turbine Engine High Cycle Fatigue (HCF) Conference, Monterey, California, USA

    4 Vogt, D.M., Fransson, T.H., 2004a

    Effect of Blade Mode Shape on the Aeroelastic Stability of a LPT Cascade Paper presented at the 9th National Turbine Engine High Cycle Fatigue (HCF) Conference, Pinehurst, North Carolina, USA

    5 Vogt, D.M., Fransson, T.H., 2004b

    A Technique for Using Recessed-Mounted Pressure Transducers to Measure Unsteady Pressure Paper presented at the 17th Symposium on Measuring Techniques in Transonic and Supersonic Flows in Cascades and Turbomachines, Stockholm, Sweden

    6 Mrtensson, H., Vogt, D.M., Fransson, T.H., 2005

    Assessment of a 3D Linear Euler Flutter Prediction Tool using Sector Cascade Test Data ASME Paper GT2005-68453

    7 Vogt, D.M., Mrtensson, H., Fransson, T.H., 2005 Validation of a Three-Dimensional Flutter Prediction Tool Paper submitted to the NATO Symposium on Evaluation, Control and Prevention of High Cycle Fatigue in Gas Turbine Engines for Land, Sea and Air Vehicles, Seville, Spain

    The involvement of Prof. Torsten Fransson and Mr. Hans Mrtensson in the above publications consisted in problem formulation and discussion of results. For all publications the underlying material was part of the work elaborated in this thesis.

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    Acknowledgements I would like to express my gratitude to my supervisor Prof. Torsten Fransson at the Chair of Heat and Power Technology at the Royal Institute of Technology, Stockholm, who made this work possible and established a stimulating environment. To Hans Mrtensson at Volvo Aero, Trollhttan, I would to like to express my gratitude for giving the right inputs at the right time and providing valuable feedback. Besides that he was also one of the few persons who genuinely appreciated my old Volvo cars. Special thanks goes to Karl-Erik Andersson, retired designer at former ABB STAL, Finspng, who assisted during the design of the test facility. Staying with the facility I would like to thank the technicians in the lab, Rolf Bornhed, Stellan Hedberg, Christer Blomqvist, Bernt Jansson and last but not least Jan-Inge Ringstrm, who not only provided first class technical support but also contributed to my adaptation to the Swedish culture. The work would not have been possible without a considerable amount of manufacturing jobs that were placed outside the lab at various workshops in Sweden. The jobs were rarely standard and required often special diligence. Many thanks to all involved technicians for performing excellent work and for being open to sometimes uncommon ideas. Financial support for the present work has been provided through the Swedish Gas Turbine Center (GTC) and the EU funded project DAIGTS (contract number ENK5-CT2000-00065), which is greatly acknowledged. Special thanks goes to Lic. Eng. Sven Gunnar Sundkvist, director of GTC, as well as Dr. Andrew Minchener, technical monitor of DAIGTS, who followed the respective parts with great interest. I would like to thank my colleagues Bjrn Laumert, Jrgen Jacoby, Kai Freudenreich, Markus Jcker, Mikkel Myhre, Olivier Bron and all the ones that I have not mentioned in persona for fruitful discussions, mutual motivation and just good fun time. Special thanks is directed to all my friends from back home for being good friends. Invaluable thanks goes to my family at home, who gave me continuous support and besides that provided me with the necessary culinary fuel. Special thanks goes also to Annas family here in Sweden for taking me on board in the various senses of the word and introducing me to Swedish habits. Finally I would like to express my sincere gratitude to my dearest Anna, who supported me with love, patience and motivation and for giving birth to our son Leo, the most wonderful little boy in the world.

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    Content 1 Introduction...................................................................................................... 23 2 Background ..................................................................................................... 25

    2.1 Description of the Flutter Phenomenon....................................................... 25 2.2 Review of Flutter Analysis Methods............................................................ 37 2.3 Review of Flutter Testing Methods.............................................................. 40

    2.3.1 Free Flutter Testing........................................................................... 40 2.3.2 Controlled Flutter Testing.................................................................. 42

    3 Fundamental Concepts.................................................................................... 49 3.1 Introduction................................................................................................. 49 3.2 Determination of Flutter Stability................................................................. 50 3.3 Aerodynamic Influence Coefficients............................................................ 53

    4 Objectives and Approach................................................................................. 57 5 Experimental Investigation of Aerodynamic Influence Coefficients................... 59

    5.1 Description of Test Setup ........................................................................... 59 5.1.1 Test Object ....................................................................................... 59 5.1.2 Test Facility....................................................................................... 61 5.1.3 Controlled Blade Oscillation .............................................................. 65 5.1.4 Conventions...................................................................................... 68 5.1.5 Measurement Setup.......................................................................... 73 5.1.6 Data Acquisition and Data Reduction Procedure............................... 79

    5.2 Validation of Test Setup.............................................................................. 80 5.2.1 Steady-State Aerodynamic Performance .......................................... 80 5.2.2 Blade Oscillation ............................................................................... 93 5.2.3 Unsteady Performance ..................................................................... 94

    6 Numerical Prediction of Aerodynamic Influence Coefficients ........................... 99 6.1 Description of Numerical Model .................................................................. 99 6.2 Validation of Numerical Method ................................................................ 102

    6.2.1 Mesh Convergence......................................................................... 102 6.2.2 Effect of Numerical Approximation .................................................. 105 6.2.3 Effect of Finite Cascade on Influence Coefficient Technique........... 106

    7 Investigation Strategy .................................................................................... 109 7.1 Flutter Testing .......................................................................................... 109 7.2 Unsteady CFD Simulations....................................................................... 110

    8 Results .......................................................................................................... 111 8.1 Steady-State Test Data ............................................................................ 111 8.2 Flutter Test Data....................................................................................... 119

    8.2.1 Aeroelastic Response at Different Modes ....................................... 119 8.2.2 Effect of Reduced Frequency on Aeroelastic Response.................. 126 8.2.3 Effect of Flow Velocity Level on Aeroelastic Response ................... 130 8.2.4 Effect of Flow Incidence on Aeroelastic Response.......................... 133

    8.3 Three-Dimensional Effects of Aeroelastic Response ................................ 136

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    8.4 Correlation of CFD Results to Test Data................................................... 144 9 Discussion ..................................................................................................... 159

    9.1 Quantification of Three-Dimensional Mechanisms during Flutter .............. 161 9.2 Assessment of CFD Prediction Accuracy of Aeroelastic Stability .............. 168

    10 Summary ..................................................................................................... 173 10.1 Conclusions.............................................................................................. 173 10.2 Recommendations and Future Work ........................................................ 176

    11 References .................................................................................................. 179 Appendix I: Blade Profile Description..................................................................... 187

    Profile Denotations ............................................................................................ 187 Profile Data........................................................................................................ 188

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    Nomenclature Latin Symbols

    a complex torsion component A matrix containing modal unsteady aerodynamic forces c blade chord

    pc specific heat at constant pressure

    Apc , normalized unsteady pressure coefficient, refdynAp pApc ,, = ; in

    case of three-dimensional consideration the angular oscillation amplitude in deg is taken as normalization basis; in case of two-dimensional plane motion the normalization is based on equivalent translational amplitude in mm for the bending modes and rotational amplitude in rad for the torsion mode

    pC averaged static pressure coefficient, refsref

    refss

    pp

    pppC

    ,,0

    ,

    =

    0pC averaged total pressure coefficient, refsref

    refs

    pp

    pppC

    ,,0

    ,00

    =

    vc specific heat at constant volume

    df infinitesimal force component

    d diameter dm infinitesimal moment component ds infinitesimal arcwise surface component, per unit span e total energy per unit volume

    er

    torsion direction (radial)

    F force, force vector HGF ,, fluxes

    G damping matrix

    hr

    complex mode shape vector

    h complex bending component

    i imaginary unit, 1=i k reduced frequency, based on full chord ufck 2=

    ik aerodynamic probe calibration coefficient i

    K stiffness matrix l nodal diameter

    mn, blade indices m mass M mass matrix M Mach number

    isoM isentropic Mach number,

    2

    11

    0 11

    2

    =

    siso p

    pM

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    nr

    normal vector to surface element N number of blades p pressure

    p mean pressure

    p~ time-varying perturbation pressure

    p complex pressure amplitude

    cp pitch

    Q conserved variables vector

    Q modal displacement vector

    r radius, radial coordinate rr

    distance from center of torsion to force realization point

    rt mode shape displacement ratio, LTrt = s span

    zytxt SSSS ,,, metric terms

    t time, time of flight T oscillation period u flow velocity

    wvu ,, Cartesian velocity components

    cycleW work per cycle; positive if the fluid is transferring work to the

    structure unstable situation zyx ,, Cartesian coordinates

    X displacement vector X& first derivative of displacement vector (velocity) X&& second derivative displacement vector (acceleration) Y radius ratio, hubshr rrY =

    Greek Symbols

    yaw flow angle pitch flow angle ratio of specific heats, vp cc= displacement torsion orthogonal mode coordinate circumferential orthogonal mode coordinate angular coordinate in cylindrical coordinate system wavelength mass ratio axial orthogonal mode coordinate number pi 3.1415927 density interblade phase angle; forward traveling wave Nl= 2 ,

    backwards traveling wave ( ) NlN = 2 pseudo time

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    mode shape rotational frequency, f 2= pressure ratio stability parameter potential

    hp phase angle of response with respect to excitation (motion); the phase angle is per definition positive if the response is leading the excitation

    Subscripts

    0 total 1 cascade inlet 2 cascade outlet 2* outlet plenum ae aerodynamic amp amplitude (magnitude of complex quantity) avg average ax axial circ_avg circumferential average damping related to damping disturbance related to disturbance dyn dynamic EA ensemble-averaged end end of separation bubble hub hub i inner ic influence coefficient max maximum phase phase of complex quantity pitch_avg pitchwise average pseudo pseudo value ref reference (r*theta) unwrapped circumferential direction s static sec secondary shr shroud start start of separation bubble twm traveling wave mode

    torsion direction

    circumferential bending direction

    circumferential component

    axial bending direction

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    Superscripts

    * normalized value T trailing edge L leading edge degree

    Abbreviations

    2D two-dimensional 3D three-dimensional A/D analog to digital AGARD Advisory Group for Aerospace Research and Development AIAA American Institute of Aeronautics and Astronautics arc normalized arcwise coordinate; negative branch on suction side,

    positive on pressure side ARC Aeronautical Research Council ASME The American Society of Mechanical Engineers avg average CFD computational fluid dynamics COT center of torsion CUED Cambridge University Engineering Department DC direct current deg degree EPFL cole Polytechnique Fdrale de Lausanne GPIB general purpose interface bus HCF high cycle fatigue HPT Heat and Power Technology FEM finite element method IBPA interblade phase angle IFASD International Forum on Aeroelasticity and Structural Dynamics Im imaginary part of complex number INFC influence coefficient ISABE International Symposium on Airbreathing Engines ISUAAAT International Symposium on Aerodynamics, Aeroacoustics and

    Aeroelasticity of Turbomachines JSME The Japan Society of Mechanical Engineers K Kelvin kg kilogram KTH Kungliga Tekniska Hgskolan (Royal Institute of Technology) LE leading edge LPT low-pressure turbine Mag magnitude MIT Massachusetts Institute of Technology MP measurement point MW mega Watt NASA National Aeronautics and Space Administration ONERA Office National dEtudes et de Recherches Arospatiales OP operating point PC personal computer

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    PS pressure side PSI Pressure System Inc. PT Platinum resistance thermometer PVC polyvinyl chloride rad radian Re real part of complex number rev revolution span spanwise coordinate; hub at span=0, tip at span=1 SS suction side tc tip clearance TE trailing edge TWM traveling wave mode UTRC United Technologies Research Center VAC Volvo Aero Corporation VDC direct current voltage VKI von Karman Institute

    Denotations of operating points

    First letter (denoting velocity level) L low subsonic M medium subsonic H high subsonic

    Second letter (denoting inflow incidence) 1 nominal, zero incidence 2 off-design 1, medium negative incidence 3 off-design 2, high negative incidence

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    List of Tables Table 5-1. Set of target design properties of test object .......................................... 59 Table 5-2. Set of blade profile parameters .............................................................. 60 Table 5-3. Probe traverse parameters..................................................................... 75 Table 6-1. CFD Mesh parameters......................................................................... 102 Table 7-1. Overview of measured test conditions (passage-averaged values) ...... 109 Table 8-1. Impact of mode shape on relative change in throat size (amplitudes

    indicated at midspan) ..................................................................................... 124

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    List of Figures Figure 2-1. Collars triangle of forces ...................................................................... 25 Figure 2-2. Graphical interpretation of mass ratio and reduced frequency .............. 26 Figure 2-3. Cross-section of a modern aero engine turbomachine (Volvo RM12);

    flutter susceptible areas indicated, area of current work highlighted; picture courtesy of Volvo Aero ..................................................................................... 27

    Figure 2-4. Influence phenomenon during blade row flutter in turbomachines ........ 28 Figure 2-5. Nodal diameters of a disk, traveling wave mode shape and

    corresponding instantaneous blade row geometry............................................ 29 Figure 2-6. Campbell diagram indicating the occurrence of flutter (arrows); adapted

    from Fransson (1999)....................................................................................... 29 Figure 2-7. Unshrouded and shrouded bladed disk assemblies.............................. 30 Figure 2-8. Blade first-order eigenmodes................................................................ 30 Figure 2-9. Graphical representation of critical reduced frequency versus torsion axis

    location for a 2D section of a cascade (Panovsky-Kielb method); from Chernysheva et al. (2003) ................................................................................ 31

    Figure 2-10. Flutter stability versus mode shape displacement ratio for assessing the effect of mode shape on stability; from Peng and Vahdati (2002) ..................... 32

    Figure 2-11. Possible vibration modes for blade packages; from Ewins (1988)....... 33 Figure 2-12. Effect of phase angle between bending and torsion mode on the

    aerodynamic work performed; adapted from Frsching (1991)......................... 33 Figure 2-13. Effect of multistage coupling on flutter stability (2D simulations); from

    Hall et al. (2003)............................................................................................... 36 Figure 2-14. Free flutter test setup for single mode testing; Urban et al. (2000)...... 41 Figure 2-15. Free-flutter test setup for variable mode testing; Kirschner et al. (1976)

    ......................................................................................................................... 41 Figure 2-16. Annular non-rotating cascade for traveling wave mode and influence

    coefficient testing.............................................................................................. 43 Figure 2-17. Purdue 3-stage experimental compressor; Frey and Fleeter (1999) ... 43 Figure 2-18. UTRC Oscillating Cascade Wind Tunnel (OCWT); Carta (1983)......... 44 Figure 2-19. NASA Lewis Transonic Oscillating Cascade; Buffum and Fleeter (1991)

    ......................................................................................................................... 45 Figure 2-20. Controlled flutter testing by aerodynamic excitation; Crawley (1981) .. 46 Figure 2-21. Example of type of blade oscillation device......................................... 47 Figure 3-1. System of orthogonal modes ................................................................ 50 Figure 3-2. Indexing of blades in cascade............................................................... 53 Figure 3-3. Effect of interblade phase angle on traveling wave mode response;

    superposition of influence coefficients from blades -1, 0 and +1....................... 54 Figure 3-4. Schematic influence of blade pairs on blade row aeroelastic stability ... 55 Figure 3-5. Characteristic variation of stability versus interblade phase angle (S-

    curve) ............................................................................................................... 56 Figure 5-1. Test object............................................................................................ 60 Figure 5-2. Measurement setup.............................................................................. 61 Figure 5-3. Test facility ........................................................................................... 63 Figure 5-4. Inlet and outlet flexible sidewalls........................................................... 63 Figure 5-5. Test section; upstream lateral sidewalls removed................................. 64 Figure 5-6. Blade oscillation principle ..................................................................... 65 Figure 5-7. Kinematics of oscillation actuator; bending mode shown ...................... 66

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    Figure 5-8. Oscillation actuator device (opened) and oscillating blade.................... 67 Figure 5-9. Blade oscillation actuator...................................................................... 67 Figure 5-10. Blade indexing and cascade coordinates............................................ 68 Figure 5-11. Test rig coordinate system.................................................................. 69 Figure 5-12. Local on-blade coordinate system ...................................................... 70 Figure 5-13. Definition of flow angles...................................................................... 71 Figure 5-14. Definition of blade oscillation .............................................................. 72 Figure 5-15. Head of aerodynamic 4-hole probe, calibration coefficients and

    calibration surfaces .......................................................................................... 74 Figure 5-16. Distribution of static pressure taps...................................................... 75 Figure 5-17. Distribution of unsteady pressure measurement points on non-

    oscillating blades (recessed-mounted transducers) .......................................... 76 Figure 5-18. Distribution of unsteady pressure measurement points on oscillating

    blade (recessed-mounted transducers) ............................................................ 77 Figure 5-19. Oscillating and non-oscillating blades used for fast-response pressure

    measurements ................................................................................................. 77 Figure 5-20. Dynamic calibration procedure and transfer characteristic .................. 78 Figure 5-21. Cascade flow field and periodicity assessment traverses ................... 81 Figure 5-22. Inlet flow field characteristics; low subsonic ........................................ 82 Figure 5-23. Inlet flow field characteristics; medium subsonic................................. 83 Figure 5-24. Inlet flow field characteristics; high subsonic....................................... 84 Figure 5-25. Outlet flow field characteristics; low subsonic ..................................... 85 Figure 5-26. Outlet flow field characteristics; medium subsonic .............................. 86 Figure 5-27. Outlet flow field characteristics; high subsonic.................................... 87 Figure 5-28. Inlet flow field periodicity data at different spanwise positions; low

    subsonic........................................................................................................... 88 Figure 5-29. Outlet flow field periodicity data at different spanwise positions; low

    subsonic........................................................................................................... 89 Figure 5-30. Outlet flow field periodicity data at midspan for different velocity levels

    ......................................................................................................................... 90 Figure 5-31. Blade loading periodicity data at different spanwise positions; low

    subsonic........................................................................................................... 91 Figure 5-32. Blade loading periodicity data at midspan for different velocity levels . 92 Figure 5-33. Blade oscillation data.......................................................................... 93 Figure 5-34. Power spectra of wind tunnel acoustics; blade oscillating at 44Hz...... 94 Figure 5-35. Aerodynamic response on blade -1 measured with oscillating blade at

    two different indices.......................................................................................... 95 Figure 5-36. Aerodynamic response on blade +1 measured with oscillating blade at

    two different indices.......................................................................................... 96 Figure 6-1. Simulation of flutter in the traveling wave mode domain ..................... 101 Figure 6-2. Coarse, medium and fine meshes used; midspan shown ................... 103 Figure 6-3. Medium meshes with different node distribution; midspan shown....... 103 Figure 6-4. Steady loading and unsteady response on blade 0 at midspan and close

    to hub for different meshes............................................................................. 104 Figure 6-5. Comparison of unsteady response on blades +1 through -1 using

    different numerical schemes (TWM simulation) .............................................. 105 Figure 6-6. Test section and single passage traveling wave mode model............. 106 Figure 6-7. Comparison of unsteady response on blades +2 through -2 from TWM

    and INFC simulation....................................................................................... 107 Figure 7-1. Computational meshes used for 3D simulations ................................. 110

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    Figure 8-1. Effect of flow velocity level on steady blade loading; low subsonic to high subsonic; operating point 1 (zero incidence)................................................... 112

    Figure 8-2. Termination lines of pressure side separation bubble from steady loading data; low subsonic velocity level ..................................................................... 113

    Figure 8-3. Effect of off-design operation on steady blade loading; low subsonic; operating points L1 through L3....................................................................... 114

    Figure 8-4. Blade surface flow visualization results and corresponding steady-state blade loading data; operating point L1............................................................ 115

    Figure 8-5. Blade surface flow visualization results and corresponding steady-state blade loading data; operating point L2............................................................ 117

    Figure 8-6. Blade surface flow visualization results and corresponding steady-state blade loading data; operating point L3............................................................ 118

    Figure 8-7. Unsteady response on blades +2 through -2 at midspan; operating point L1; axial bending, k=0.1 ................................................................................. 120

    Figure 8-8. Unsteady response on blades +2 through -2 at midspan; operating point L1; circumferential bending, k=0.1.................................................................. 122

    Figure 8-9. Unsteady response on blades +2 through -2 at midspan; operating point L1; torsion, k=0.1............................................................................................ 123

    Figure 8-10. Comparison of product of blade loading and its second derivative to aeroelastic response data .............................................................................. 125

    Figure 8-11. Effect of reduced frequency on unsteady response on blades +1, 0, -1; operating point L1; axial bending................................................................... 126

    Figure 8-12. Effect of reduced frequency on unsteady response on blades +1, 0, -1; operating point L1; circumferential bending ................................................... 127

    Figure 8-13. Effect of reduced frequency on unsteady response on blades +1, 0, -1; operating point L1; torsion ............................................................................. 128

    Figure 8-14. Effect of flow velocity level on unsteady response on blades +1, 0, -1; operating points L1, M1 and H1; axial bending.............................................. 130

    Figure 8-15. Effect of flow velocity level on unsteady response on blades +1, 0, -1; operating points L1, M1 and H1; circumferential bending .............................. 131

    Figure 8-16. Effect of flow velocity level on unsteady response on blades +1, 0, -1; operating points L1, M1 and H1; torsion ........................................................ 132

    Figure 8-17. Effect of flow incidence on unsteady response on blades +1, 0, -1; operating points L1, L2 and L3; axial bending ................................................ 133

    Figure 8-18. Effect of flow incidence on unsteady response on blades +1, 0, -1; operating points L1, L2 and L3; circumferential bending................................. 134

    Figure 8-19. Effect of flow incidence on unsteady response on blades +1, 0, -1; operating points L1, L2 and L3; torsion........................................................... 135

    Figure 8-20. Spanwise variation of aeroelastic response on blade +1; operating point L1................................................................................................................... 137

    Figure 8-21. Spanwise variation of aeroelastic response on blade -1; operating point L1................................................................................................................... 138

    Figure 8-22. Blade surface flow visualization results and corresponding unsteady response amplitudes on primary surfaces; operating point L1; axial bending . 140

    Figure 8-23. Blade surface flow visualization results and corresponding unsteady response amplitudes on primary surfaces; operating point L1; torsion............ 141

    Figure 8-24. Spanwise variation of aeroelastic response on blade +1; operating points L2 and L3, axial bending ...................................................................... 142

    Figure 8-25. Blade surface flow visualization results and corresponding unsteady response amplitudes; operating points L2 and L3; axial bending.................... 143

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    Figure 8-26. Comparison of predicted and measured steady loading; nominal low subsonic (L1) and high subsonic (H1) ............................................................ 144

    Figure 8-27. Comparison of measured and predicted unsteady response on blades +2 through -2 at midspan; operating point L1; axial bending, k=0.1................ 145

    Figure 8-28. Comparison of measured and predicted unsteady response on blades +2 through -2 at midspan; operating point L1; circumferential bending, k=0.1 147

    Figure 8-29. Comparison of measured and predicted unsteady response on blades +2 through -2 at midspan; operating point L1; torsion, k=0.1 .......................... 148

    Figure 8-30. Comparison of measured and predicted unsteady response on blade -1 at different reduced frequencies; operating point L1; axial bending ................ 149

    Figure 8-31. Effect of model detailing on prediction of steady-state flow field; operating point L1........................................................................................... 150

    Figure 8-32. Effect of model detailing on prediction of aeroelastic response on blades +1 through -1; operating point L1; axial bending; k=0.1....................... 151

    Figure 8-33. Effect of model detailing on prediction of aeroelastic response on blades +1 through -1; operating point L1; torsion; k=0.1 ................................. 152

    Figure 8-34. Comparison of measured and predicted unsteady response on blade -1 close to hub and close to tip; operating point L1; axial bending; k=0.1 ........... 153

    Figure 8-35. Comparison of measured and predicted unsteady response on blade -1 close to hub and close to tip; operating point L1; torsion; k=0.1...................... 154

    Figure 8-36. Comparison of predicted and measured steady loading at various incidence; low subsonic.................................................................................. 155

    Figure 8-37. Comparison of measured and predicted unsteady response on blades +1 through -1 at high negative incidence; operating point L3; axial bending ... 156

    Figure 8-38. Comparison of measured and predicted unsteady response on blade 0 at high negative incidence; operating point L3; circumferential bending and torsion ............................................................................................................ 157

    Figure 9-1. Fragmenting of profile into arcwise regions......................................... 159 Figure 9-2. Torsion mode representation of rigid-body modes .............................. 160 Figure 9-3. Spanwise distribution of stability contribution of blade -1; IBPA=0deg; low

    subsonic L1; k=0.1 ......................................................................................... 161 Figure 9-4. Variation of stability contribution of blade -1 with interblade phase angle;

    low subsonic L1; k=0.1; axial bending ............................................................ 163 Figure 9-5. Variation of stability contribution of blade +1; IBPA=90deg; low subsonic;

    k=0.1; axial bending ....................................................................................... 164 Figure 9-6. Graphical quantification of three-dimensional effects with respect to

    effects of reduced frequency and flow incidence ............................................ 165 Figure 9-7. Variation of stability contribution in span, reduced frequency and

    operating point for blade pair 1; low subsonic; axial bending ........................ 166 Figure 9-8. Variation of stability contribution in span, reduced frequency and

    operating point for blade pair 1; low subsonic; torsion .................................. 167 Figure 9-9. Comparison of measured and predicted arcwise stability contribution at

    midspan on blade -1; IBPA=90deg; operating point L1; axial bending ............ 168 Figure 9-10. Comparison of measured and predicted arcwise stability contribution at

    midspan on blade -1; IBPA=90deg; operating point L1; circumferential bending....................................................................................................................... 169

    Figure 9-11. Comparison of measured and predicted arcwise stability contribution at midspan on blade -1; IBPA=90deg; operating point L1; torsion ...................... 169

    Figure 9-12. Comparison of measured and predicted stability plot at midspan; IBPA=0deg; shaded areas mark stable regions.............................................. 170

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    Figure 9-13. Comparison of measured and predicted stability plot at midspan; IBPA=90deg; shaded areas mark stable regions............................................ 172

    Figure 10-1. Proposition for real and locally deforming test objects ...................... 177 Figure 10-2. Predicted steady-state total pressure distribution from inviscid and

    viscous models............................................................................................... 178

  • Page 22 Doctoral Thesis / Damian Vogt

  • Doctoral Thesis / Damian Vogt Page 23

    1 Introduction Flutter denotes a self-excited and self-sustained aeroelastic instability phenomenon that involves vibration of a structure when exposed to a fluid flow. In turbomachines flutter is prone to occur in the parts of the engine where long and slim blades are exposed to aggressive blade loading such as in the fore part of compressors or the aft part in turbines. Unless properly damped, it can result in material fatigue and eventually to damage of engine components in a short period of time. Depending on the extent of the instability, failure may be caused due to excessive stress or high cycle fatigue (HCF) in case of limit cycle oscillations. In the present work the focus has been put on flutter in low-pressure turbines (LPT). Safety and economical aspects rather than efficiency concerns therefore drive the assessment of the flutter phenomenon. The relevance of the problem has been indicated by El-Aini (1997) stating that although 90% of potential HCF occurrences are uncovered during engine development the remaining 10% stand for one third of the total engine development costs. Field experience as the one presented by Sieg (2000) has shown that during the last decades as much as 46% of fighter aircrafts were not mission-capable in certain periods due to high cycle fatigue related mishaps. The design for aeroelastic stability is therefore one of the paramount tasks in engine design. Aeroelastic stability denominates the ability of a system to resettle back to a stable situation upon stochastic excitation rather than escalating and leading to occurrence of high cycle fatigue. The goal for design engineers is to ensure aeroelastic stability over as wide part of the operating range as possible and by this guarantee flutter-free operation of the turbomachine. Designing for aeroelastic stability involves the prediction of unsteady aerodynamic forces that are due to blade oscillation and their reciprocal influence on the oscillation mode. Traditionally this process has involved empirical correlations that have been based on experience from existing engines and tuned such as to allow for predictive assessment of new designs. Such methods have long been applied with good confidence within families of similar engines but have failed, as soon as similarity of a new design no longer could be guaranteed. Analytical methods for determining aeroelastic stability have successfully been employed for lightly loaded components such as fans and low-pressure compressor stages but have failed for highly loaded turbine blades. Detailed assessment of the unsteady aerodynamic flow field during flutter for various blade geometries has been made possible with the advances in computational power during the last decades and the emerge of computational fluid dynamics (CFD). In conjunction with modern finite element (FEM) analysis methods for predicting structural modes design tools have been made available that opened up for an intimate treatment of the aeroelastic design problem. These advanced aeroelastic design methods allowed for designing new generations of flutter-safe engines by eliminating most of the known flutter occurrences. Consequently increased confidence in flutter prediction methods has led to pushing engines to higher power densities and more aggressive blade loading. Flutter related mishaps in the recent engine generation however indicate that the prediction tools

  • Page 24 Doctoral Thesis / Damian Vogt

    have been used beyond their range of validity and that noticeable limitations exist. The problem is especially apparent when analyzing highly loaded compressors but is also encountered in low-pressure turbines. As a matter of fact flutter problems are mostly treated in two-dimensional manner for the sake of simplicity indicating that the blade-to-blade geometry is modeled at a certain section rather than the generally complex three-dimensional geometry of turbomachine blading. It is however believed that part of the encountered limitations in predicting aeroelastic stability is due to three-dimensional effects that are present in real engines but not captured by the models. Although more advanced numerical tools have recently made it possible to treat the aeroelastic problems in three-dimensional environment the validation is still progressing due to the lack of experimental data. The present work contributes by investigating three-dimensional aerodynamic effects on the aerodynamic damping during flutter based on a compound experimental and numerical approach.

  • Doctoral Thesis / Damian Vogt Page 25

    2 Background

    2.1 Description of the Flutter Phenomenon

    Flutter denotes an unstable vibration phenomenon of a structure that is exposed to fluid flow. In a condition of instability initially small vibrations at the verge of flutter induce unsteady aerodynamic forces that feed energy into the structure leading to rapidly growing in magnitude by each cycle. Normally the escalation of the instability cannot be prevented leading to excessive structural oscillations and material failure. The difference between flutter and resonant vibrations in turbomachines is that the flow unsteadiness leading to structural oscillation is induced by the motion of the structure itself rather than an external source. The existence of flutter is yielding from a balance between the unsteady forcing by the fluid, the inertial and damping forces of the structure respectively and the elastic forces of the structure. Flutter is occurring if this balance attains unstable condition meaning that the fluid is feeding energy into the structure leading to larger oscillation amplitude and consequently to even larger aerodynamic forcing. From a phenomenological point of view the assessment of the flutter involves steady and unsteady aerodynamics as well as structural dynamics and is embraced by the science of aeroelasticity. A graphical interpretation of the phenomenological interaction leading to flutter has been given by Collar (1946) as depicted in Figure 2-1.

    Figure 2-1. Collars triangle of forces Structures, which are long, slim and exposed to high aerodynamic loading are prone to flutter as the unsteady aerodynamic forces gain in magnitude relative to the structural forces. Within the aeronautic field flutter was first observed on wings as airplanes reached higher velocities in the first half of last century. Soon it was recognized that the ratio between wing mass and the mass of surrounding air inside a circle with radius half chord has a noticeable influence. This ratio, referred to as mass ratio, is given by

  • Page 26 Doctoral Thesis / Damian Vogt

    20

    4

    c

    m

    = , Eq. 2-1

    where m is the mass per unit blade span, 0 the air density and c the blade chord. As the mass ratio decreases flutter susceptibility increases. In turbomachines the mass ratio attains comparatively large values and thus does not gain the same importance. Meldahl (1946) has found that flutter in turbomachine blade rows occurs above certain flow velocities and that it is rather the ratio of flow velocity, blade chord and oscillation frequency that dominates flutter stability. The ratio is known as reduced frequency and relates the time of flight for a fluid particle needed to travel across blade chord to the oscillation period as is

    u

    fc

    T

    tk

    2== , Eq. 2-2

    where f is the oscillation frequency, c the blade chord and u the flow velocity.

    Another though equivalent interpretation of the reduced frequency is that it relates to the blade chord to the wavelength drawn out by a sinusoidal oscillation as given by

    c

    k = , where f

    uu

    2== Eq. 2-3

    Small values of reduced frequency indicate that the time of flight is short compared to the oscillation period, in other words that the flow is able to settle to changed conditions and thus has a quasi-steady character. For each setup a value of critical reduced frequency can be found below which flutter can occur. For a certain oscillation frequency this indicates that the value of critical reduced frequency is approached as flow velocity increases. For turbomachine blades critical reduced frequencies have been reported in the range between 0.1 and 1.0. A graphical interpretation of mass ratio and reduced frequency is included in Figure 2-2.

    0 20 40 60 80 100 120 140 160 180 200

    20

    10

    0

    10

    20

    30

    Mass ratio Reduced frequency

    Figure 2-2. Graphical interpretation of mass ratio and reduced frequency

    0 m

    c c

  • Doctoral Thesis / Damian Vogt Page 27

    The occurrence of flutter in turbomachines is almost exclusively limited to blades in the fore and aft part of the engine (Srinivasan, 1997) such as fans, low-pressure compressor (LPC) and low-pressure turbine (LPT). Figure 2-3 shows a typical aero engine turbomachine denoting the areas susceptible to flutter. The area of interest of the present work (LPT) is highlighted in the figure.

    Figure 2-3. Cross-section of a modern aero engine turbomachine (Volvo RM12); flutter susceptible areas indicated, area of current work highlighted; picture courtesy

    of Volvo Aero Given the blade row environment in turbomachines the phenomenon of flutter usually involves an arrangement of blades and for that reason a blade row rather than a single blade is regarded. The motion of each single blade is influencing instantaneously the flow field in its direct neighborhood inducing a response on itself and on its direct neighbors as depicted in Figure 2-4. This phenomenon is referred to as aerodynamic coupling. In one of the early studies Bellenot and Lalive dEpinay (1950) have recognized that an arrangement of blades might become aeroelastically unstable although a comparable isolated blade would not flutter. Several efforts have been dedicated to the coupling phenomena with the aim to understand the effect of coupling on cascade aeroelastic stability. Triebstein (1976), Kirschner et al. (1976) and Carta and St.Hilaire (1980) can be cited as early studies addressing the coupling phenomena in blade rows. All investigations concluded that the aerodynamic response on the blades in an oscillating blade row is influenced to a large degree by coupling effects. Szchnyi (1985) has indicated that the aptitude of a single blade to flutter was of the same importance as coupling effects in a cascade. In a systematic categorization of unsteady flow phenomena in turbomachines Greitzer et al. (1994) classify the phenomenon of flutter being one order of magnitude larger in extent than the blade pitch.

    Fan Low-pressure turbine (LPT)

  • Page 28 Doctoral Thesis / Damian Vogt

    100 50 0 50 100 150

    100

    50

    0

    50

    100

    +3

    +2

    +1

    0

    1

    2

    3

    Figure 2-4. Influence phenomenon during blade row flutter in turbomachines The coupling influence is thereby largely affected by the relative motion between two adjacent blades. In a traditional approach as for example given by Crawley (1988) the oscillatory motion of a tuned blade row during flutter can be characterized as a traveling wave mode indicating that all blades oscillate in the same mode, amplitude and frequency but at a certain phase lag between two adjacent blades. The phase lag between two adjacent blades is referred to as interblade phase angle and can take discrete values that yield from the kinematical constraint to fulfill full cycle periodicity as is

    N

    l= 2 , Nl ,...3,2,1= Eq. 2-4

    The order of the traveling wave is given by parameter l also referred to as nodal diameter. For each nodal diameter pattern a pair of traveling waves is induced, a

    forward traveling wave with N

    l= 2 and a backwards traveling wave with

    =

    N

    lN 2 . An example of nodal diameter patterns and corresponding cascade

    geometries is depicted in Figure 2-5.

    stator stator rotor

  • Doctoral Thesis / Damian Vogt Page 29

    100 0 100

    300

    200

    100

    0

    100

    200

    300

    400

    100 0 100

    300

    200

    100

    0

    100

    200

    300

    400

    Nodal diameter pattern Blade row Nodal diameter pattern Blade row

    Nodal diameter 1=l Nodal diameter 3=l

    Figure 2-5. Nodal diameters of a disk, traveling wave mode shape and corresponding instantaneous blade row geometry

    The excitation of structural modes in the turbomachine environment is traditionally assessed by means of a Campbell diagram as the one shown in shown in Figure 2-6. The diagram depicts structural vibration characteristics and engine order excitation lines versus rotational speed and allows recognizing potential vibration problems at crossings between these lines. As flutter occurrences are not bound to engine order lines and therefore can occur at any rotational speed the predictive assessment of flutter gets one additional unknown dimension.

    Figure 2-6. Campbell diagram indicating the occurrence of flutter (arrows); adapted from Fransson (1999)

    The vibration properties of blade rows depend largely on the structural setup of the assembly. From a general perspective a turbomachine blade row can mechanically be modeled as a disk with blades fixed to it. Depending on whether the blades are interconnected to each other above the root the assembly is referred to as unshrouded bladed disk or shrouded bladed disk as shown in Figure 2-7. The location of the shroud may vary from part span to full span, i.e. tip shroud.

    + - +

    +

    + -

    -

    -

    Flutter occurrences

    Synchronous vibrations

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    Unshrouded Shrouded

    Figure 2-7. Unshrouded and shrouded bladed disk assemblies. Unshrouded bladed disk assemblies result in blades being freestanding. The oscillation modes of such assemblies can be separated into blade-dominated or disk-dominated modes. The former summarizes the modes that are either blade global modes such as bending or torsion or local blade modes as for example corner modes or stripe modes. In disk-dominated modes the individual blades play a subordinate role and are rather to be seen as passive element attached to a rotor disk. To assess blade dominated modes the single blades can in a simplified manner be modeled as beams. The three mode shapes with lowest frequencies, which are of greatest interest in the present context, are accordingly two bending modes and one torsion (twisting) mode defined by the position of the elastic axes. With relation to the blade these modes are referred to as flap, edgewise bending and torsion (twisting) as depicted in Figure 2-8. All modes feature a certain eigenfrequency at rest, which change with the rotational speed of the turbomachine due to centrifugal forces. Other modes include stripe mode (in-plane oscillation) as well as local deformation modes such as corner modes.

    0.3

    0.4

    0.4

    0.4

    0.4

    0.4

    0.4

    0.4

    0.4

    0.4

    0.02 0.01 0 0.01 0.02

    0

    0.01

    0.02

    0.03

    0.04

    0.39

    0.4

    0.41

    0.42

    0.43

    0.44

    0.45

    0.46

    0.47

    0.48

    0.01 0 0.01 0.02 0.030

    0.01

    0.02

    0.03

    0.04

    0.05

    0.3

    0.4

    0.4

    0.4

    0.4

    0.4

    0.4

    0.4

    0.4

    0.01 0 0.01 0.02 0.03

    0

    0.01

    0.02

    0.03

    0.04

    Flap Edgewise bending Torsion

    Figure 2-8. Blade first-order eigenmodes Several researchers have addressed the mode shape as major influence for flutter stability. Bendiksen and Friedmann (1982) have analytically studied a cascade oscillating in bending and torsion modes over a large range of flow regime and showed that bending and torsion stabilities develop differently. Systematic studies on the influence of mode shape have been carried out by Panovsky and Kielb (2000), Nowinski and Panovsky (2000) and Tchernycheva et al. (2001) employing a

  • Doctoral Thesis / Damian Vogt Page 31

    graphical method referred to as Panovsky-Kielb method that assesses the aeroelastic stability on a two-dimensional section of a cascade. The method assumes pure rigid-body modes and is based on representing any possible modes as torsion modes with respective center of torsion resulting in so-called stability maps. An example of such map is included in Figure 2-9 specifying the critical reduced frequency below which flutter could occur for a given center of torsion.

    Figure 2-9. Graphical representation of critical reduced frequency versus torsion axis location for a 2D section of a cascade (Panovsky-Kielb method); from Chernysheva

    et al. (2003) The Panovsky-Kielb plots illustrate efficiently the effect of mode shape on flutter stability; as can be seen in Figure 2-9 there are regions of high gradients around the blade suggesting that a small change in torsion axis location does have a detrimental effect on the magnitude of critical reduced frequency. It can be noted as interesting fact that stability maps are of similar nature for different types of turbine geometries as resulted from a study performed by Tchernycheva et al. (2001). Kielb et al. (2003) therefore draw the conclusion that standard maps for turbine mode shape stability can be used in the preliminary aeroelastic design thus omitting time-consuming unsteady aeroelastic analyses in a first stage and performing structural dynamic analyses only. Peng and Vahdati (2002) have employed a ratio of mode shape displacement of blade leading and trailing edge as included in Figure 2-10 such as to assess the effects of mode shape on stability. The result indicates that although the method is different in its roots from the above-presented graphical tool it leads to similar conclusion of the mode shape affecting greatly flutter stability.

    Reference blade Example: flutter

    is predicted below k=0.4 if the reference blade is oscillating around this center of torsion (motion indicated) Reduced frequency k here based on semi-chord

  • Page 32 Doctoral Thesis / Damian Vogt

    Figure 2-10. Flutter stability versus mode shape displacement ratio for assessing the effect of mode shape on stability; from Peng and Vahdati (2002)

    Further kinematical constraints might be imposed due to tying blades together to blade packages such as to increase structural stiffness. This method is commonly employed for suppressing flutter both due to an increased mechanical stiffness of the assembly and due to restricting the coupling of the blades to few interblade phase angles. The measures can extend over the entire circumference as in the case of shrouded rotors or part-span shrouds or to cyclic symmetric sectors as in the case of sectored vane assemblies. Ewins (1988) has given a schematic description of blade assembly modes as shown in Figure 2-11.

  • Doctoral Thesis / Damian Vogt Page 33

    Figure 2-11. Possible vibration modes for blade packages; from Ewins (1988) Chernysheva et al. (2003) conclude from a theoretical analysis that although sectoring of blades to blade packages might increase stability the existence of unstable regions might not be suppressed completely. Corral et al. (2003) have performed a computational analysis on pairs of low-pressure turbine blades. Their main finding is that aeroelastic stability of welded pairs of blades is greater than for single airfoils especially for torsion and circumferential bending modes, which indicated that sectoring of blades is an efficient mean to increase flutter stability. Structural coupling of blades might lead to the occurrence of coupled modes that combine two modes under a certain phase angle. In this case the phase angle between the involved modes detrimentally affects aeroelastic stability. Bendiksen and Friedmann (1982) have analyzed the problem analytically concluding that the coupled bending and torsion flutter affects the flutter boundary significantly. A tendency of the two modes to coalesce could however not be observed as flutter has been approached. Frsching (1991) has elucidated the effect of phase angle between bending and torsion mode on the work performed from a quasi-steady consideration; for a phase difference of zero degree the total work examined by the fluid equals to zero. Positive work results for a phase angle of 90deg, see Figure 2-12.

    Figure 2-12. Effect of phase angle between bending and torsion mode on the aerodynamic work performed; adapted from Frsching (1991)

    negative work

    positive work

    positive work

    negative work

    Direction of oscillation

    Direction of force

    positive work

    positive work

    Phase angle 0deg total work zero

    Phase angle 90deg total work positive

  • Page 34 Doctoral Thesis / Damian Vogt

    In addition to reduced frequency and mode shape it has been observed that flow incidence has a dominant effect on aeroelastic stability. On one hand it affects directly the mean loading of the blades and has identical effects in turbomachine blade rows as it has for isolated airfoils. Generally it has been shown from several investigations that higher angles of attack lead to reduced stability. Carta and St.Hilaire (1980) have performed systematic studies on the influence of incidence, reduced frequency and interblade phase angle on a linear research compressor cascade finding that critical reduced frequency decreases with increasing angle of attack. They stated however clearly that this was not due to an incidence-induced separation. Szchnyi (1985) has shown the effect of reduced stability at high angles of attack from tests in a compressor cascade. Above a certain angle of attack though the flow may separate around the leading edge of the blade profile leading to the aeroelastic stability being dominated by the separated flow behavior. Buffum et al. (1998) have investigated a compressor cascade at high mean incidence and shown that the character of damping largely depends on the state of flow around the leading edge, which in turn was directly influenced by flow incidence; a high angle of attack led to separated flow that had a destabilizing effect whereas attached flow acted stabilizing in this region. Peng and Vahdati (2002) have drawn the conclusion that high incidence leads to destabilizing from an analytical study of a compressor at near stall and near choke. Ellenberger and Gallus (1999) have drawn the conclusion from a compressor cascade experiment on torsional flutter that although a shock-induced separation was present the shock rather than the separation bubble dominated the stability character. He (1996) investigated the effect of separated flow experimentally in a cascade of low-pressure turbine blades at various incidence angles with one blade oscillating in torsion mode and found that a large separation bubble on the pressure acted destabilizing. However it is interesting to notice that the region downstream of the reattachment point acted stabilizing, which balanced the negative effect of the separation bubble. Queune and He (2000) have performed flutter testing on a steam turbine profile in bending mode and at massive part-span separation. The tests yielded that the separated region featured reduced stability compared to attached flow.

  • Doctoral Thesis / Damian Vogt Page 35

    Closer attention shall at this position be drawn to the space adjacent to the regarded blade row. Due to the oscillation of the blades a varying pressure field is established up- and downstream of the blade row that can induce acoustic resonance in the adjacent ducts. Whitehead (1973) draws the distinction between three regions of acoustic resonance flutter:

    1) subcritical flutter where acoustic waves can not propagate in the duct 2) acoustic resonance flutter where a pair of waves are just at the verge to

    propagate 3) supercritical flutter where at least one pair of waves can propagate.

    Acoustic resonances can only exist over a certain range of interblade phase angles in which the traveling wave mode pattern matches the resonance pattern and therefore suggest the distinct influence of higher blade indices. The practical implication is that the acoustic resonance adds one degree of freedom to the aeroelastic system, which might be effective for extraordinary coupling of blades during flutter. Acoustic resonance flutter is almost exclusively of relevance in empty ducts adjacent to the regarded blade row as adjacent blade rows tend to suppress resonant behavior (Whitehead, 1973). Wu et al. (2003) have recently underlined the relevance of aeroacoustic flutter for a high bypass-ratio jet engine where the aeroacoustic properties of the inlet duct triggered flutter of the fan, which was observed as sharp and local drop in the flutter stability margin referred to as flutter bite. Up to this point the phenomenon has exclusively been discussed in the extent of a single blade row. In the turbomachine environment the adjacent blade rows are affecting the flutter properties in various ways. On one side they are inducing flow disturbances that are overlaid to the unsteadiness induced by the oscillating blade row and by this diffusing the line between flutter and forced response. Frey and Fleeter (1999) have addressed the phenomenon of combined gust and flutter in a low-speed rotating compressor facility with the blades oscillated in torsion mode and the inflow having been subjected to a 2/rev inlet distortion. The influence of gust on flutter stability has been found being dependent on the phase lag between the two mechanisms leading to either a constructive or destructive constellation meaning that flutter stability is decreased in the latter case.

  • Page 36 Doctoral Thesis / Damian Vogt

    Another effect from adjacent blade row is the influence on the aerodynamic coupling as a neighboring blade row has the ability to reflect pressure waves and thus change the coupling response. Hall et al. (2003) have modeled the coupling effect by means of spinning modes, i.e. a set of pressure and vorticity waves that propagate between blade rows. Reflection and transmission properties from adjacent blade rows were thereby computed from isolated blade row analyses. Figure 2-13 depicts the effect of multistage coupling by comparing the results of an isolated blade row analysis to a multistage analysis using two-dimensional models. Large differences can therein be recognized in the range of interblade phase angles of 90deg to 180deg. Using the same approach Chuang (2004) could show that the flutter boundary was shifted by 5% in flow margin.

    Figure 2-13. Effect of multistage coupling on flutter stability (2D simulations); from Hall et al. (2003)

    The effect of aeroelastic mistuning has early been identified as favorable and as potential method for preventing flutter. Szchnyi (1985) has found that mistuning can be an effective method to shrink the stability locus loop of aerodynamic damping. A limitation however is that the method cannot be used to change the position of the loop relative to the axis; if a single-blade flutter is prone to occur it is not possible to be remedied by mistuning. Nowinski and Panovsky (2000) have assessed the method of mistuning in an annular cascade flutter experiment and concluded that alternate mistuning represents the most stabilizing pattern. Silkowski et al. (2001) have made a similar observation of that the destabilizing influence of blade pair 1 can be broken down by arranging blades with alternating varying natural frequency around the circumference.

  • Doctoral Thesis / Damian Vogt Page 37

    2.2 Review of Flutter Analysis Methods

    Analysis methods for predicting flutter stability are employed to prevent flutter occurrences prior to operation of new engine or engine components. In detail the methods used involve the analysis of structure dynamics as well as unsteady aerodynamics and the evaluation of results with respect to aeroelastic instability. From an analytical point of view the aeroelastic problem can be described by the aeroelastic equation as given by

    [ ]{ } [ ]{ } [ ]{ } { })(tFXKXGXM ae=++ &&& Eq. 2-5 The left-hand side of the above equation reflects the structural part where M being the mass, G the structural damping and K the stiffness matrices. The right-hand side includes the unsteady aerodynamic forces that are due to the blade motion and contains the aerodynamic damping. Generally there are three different approaches used in the prediction of flutter stability. The first approach foresees an implicit analytical description of the structural and the aerodynamic part and is also referred to as reduced-order model. A simplified analytical model is thereby usually used to describe the structural part. Rather than resolving the flow around the airfoils a representation of the unsteady aerodynamic force only is employed. The aeroelastic system is then fully defined and can be reduced to an eigenvalue problem yielding dynamic behavior and occurrences of flutter instability over a parameter range of interest. The approach has its limitations in that the analytical description of the unsteady aerodynamic force is heavily simplified and therefore cannot be used with confidence for highly loaded geometries. Imregun (1995) has presented a method of using frequency response functions to determine flutter stability. Whereas a lumped parameter model was used to describe the structural part linearized unsteady aerodynamic theories presented by Smith (1972) for subsonic flow and Nagashima and Whitehead (1976) for supersonic flow have been implemented for representing the unsteady aerodynamic force. The technique was employed on a 12-bladed disk of flat plates yielding frequency response functions over a range of frequencies. The strength of the method lies in the inherent coupling of structure and flow and comparatively small computational times. Copeland and Rey (2004) have used an actuator disk model to represent a fan stage and could show that the overall aeroelastic model was tunable to experimental data. Whereas this approach could be used to assess the influences of changes from a known setup such as for example the assessment of mistuning, it did however not allow predictive application. The second approach foresees a separate i.e. decoupled treatment of the structural and the aerodynamic part. The coupling is effectuated by aerodynamic forces for the structural part and motion of the structure for the aerodynamic part. The dynamic behavior of the aeroelastic system yields from modal comparisons of the structural and the aerodynamic part. This approach has the great advantage that practically any method can be used for predicting the structural and the unsteady aerodynamic part. As the critical mode shapes of the setup are not known a priori a method must

  • Page 38 Doctoral Thesis / Damian Vogt

    be used to predict the aerodynamic damping properties for a number of possible structural modes. Rather than performing an immense number of unsteady aerodynamic predictions simplifying assumptions can be made such as linearity and non-deforming blade sections, which allows spanning of a mode space by three orthogonal modes. The evaluation of stability is then yielding from solving the modal equations, i.e. detecting unstable modal coalescences of the structural and aerodynamic system. The drawback of this method however is that the effects of aerodynamic damping on the structural modes are not taken into consideration unless the process is performed in iterative manner. On the aerodynamic side the methods can be separated depending on the flow model used and the employed temporal discretization. The different flow models cover analytical methods, linear potential methods assuming inviscid, isentropic and irrotational flow or discrete models solving either the inviscid Euler or the viscous Navier-Stokes equations on a computational mesh. Analytical models as the ones described by Whitehead (1987) are assuming flat plates and thus do not account for steady blade loading. The linear potential method (Verdon and Caspar, 1982) allows studying effects of airfoil geometry on loading and flow structure even in the transonic regime provided the shocks are weak and the condition of isentropic flow is not harmed. The discrete Euler method can be used for the same conditions as potential models but have the advantage that it can deal with rotational and non-isentropic flow, i.e. the limitation of weak shocks is no longer valid. It resolves the flow field in detail but does not reflect shear layers such as boundary layers or separated flow bubbles correctly due to absence of viscosity. The most accurate description of the flow is thus given by the Navier-Stokes model taking into account viscosity. This model is applicable to the same flows as can be treated by an Euler analysis. From the temporal discretization point of view the unsteady equations can either be solved time-marching or in a linearized manner. In the first case the characteristic equations are solved at each node of the computational mesh at each time step. Convergence is achieved if a time-periodic flow is established. Non-linear time-marching models have for example been presented by Fransson and Pandolfi (1986), Giles (1988) and Whitfield et al. (1987) employing Euler equations and Huff (1987) and Rai (1989) for Navier-Stokes equations. The linearized approach assumes small perturbations of flow variables around a steady mean value. The steady flow solution can thereby be determined from a steady non-linear flow analysis. Thereafter the perturbation equations are solved on this mean value until a steady perturbation amplitude is reached. Such models have for example been presented by Hall and Crawley (1989), Holmes and Chuang (1991), Lindstrm and Mrtensson (2001) and Petrie-Repar (2003). Whereas unsteady non-linear viscous models allow for the most accurate representation of unsteady flow they are associated with high computational costs in the order of magnitude of several days, which decreases applicability especially in the industrial environment. On the other hand it has been pointed out above how different flow phenomena such as flow separation act on flutter stability. The decision for what model to use for a certain analysis must therefore be justified by the targeted application.

  • Doctoral Thesis / Damian Vogt Page 39

    The third and last approach treats the structure and the flow as one continuum and foresees the solving the structural and the aerodynamic part in a fully coupled and time-marching manner. The boundary conditions of force for the structural part and motion for the aerodynamic part are used at the structure/flow interface. The aeroelastic equation is solved at each time step for a number of cycles and the aeroelastic stability is determined from the temporal development of characteristic variables. Divergence of the variables indicates an aeroelastic unstable situation whereas convergence indicates stability. The prominent mode shape during flutter is directly yielded from such analysis. Applications of fully coupled models have for example been presented by Vahdati and Imregun (1995) and McBean et al. (2002). Fully coupled models represent the most accurate model for the dynamic analysis of an aeroelastic system but feature the highest computational costs.

  • Page 40 Doctoral Thesis / Damian Vogt

    2.3 Review of Flutter Testing Methods

    Flutter testing can be performed on a component basis or in the frame of engine tests and finds its application in research as well as engine commissioning. Component tests feature inherently lower complexity compared to full engine tests and by this open up for a more intimate analysis of the flutter phenomenon. On the other hand such tests are performed in an idealized environment and therefore often do not model all the effects that are influencing flutter. In a cascade flutter test the effects of adjacent blade rows are for example not present. The section gives a review of different testing techniques and overview of the most prominent examples. The occurrence of flutter is an instability phenomenon involving an oscillation system comprising fluid flow and structures as outlined above. Flutter testing can either be aimed at detecting eventual instability of the system or at determining the transfer function of the system over a range of oscillation parameters. In the first case the test performed are of free-flutter type indicating that outer parameters such as flow velocity or angle of attack are changed until onset of flutter can be observed. The second case represents a forced oscillation testing method during which the system is excited in a controlled manner and the response is monitored such as to determine the transfer function. These two types of flutter testing are reviewed below.

    2.3.1 Free Flutter Testing

    Free flutter testing stems from a build it test it approach with the aim to detect if flutter occurs at a certain set of flow conditions. The object of investigation is thereby exposed to a well-defined fluid flow and measurements are taken such as to detect unstable oscillatory motion and eventually also aerodynamic response characteristics. Free flutter tests can be performed in real engines and test frames that are accurate models (annular rotating rigs) or on a more generic basis in simpler cascades. The former types of tests are rare due to the inherently higher complexity. If the scope of the tests is to assess the aerodynamic damping characteristics it is tried to increase aerodynamic forcing compared to structural damping, which can be achieved by suspending blades elastically or increasing blade aspect ratio. In certain cases the spring constant of the suspension and the mass of the blade are made variable such as to measure inversely aerodynamic damping. For monitoring the motion of the blades traditionally strain gauges are employed although alternative motion capturing methods such as optical techniques have been reported. Some of the few full-scale flutter tests reported in open literature have been performed in the Compressor Research Facility (CRF) at Wright Patterson Air Force Base. Sanders et al. (2002) studied the flutter properties of a transonic low aspect ratio fan blisk and found that a blade passage shock acted most destabilizing. Additionally it was found that structural dynamics was the key driver for mistuning response. Manwaring et al. (1996) employed the same facility for the investigation of forced response due to inlet distortion in a 2-stage low aspect ratio fan. Bellenot and Lalive dEpinay (1950) have employed a linear cascade consisting of five low-pressure compressor profiles with increased aspect ratio compared to their

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    counterparts in real engines such as to promote the influence of aerodynamic forcing over elastic forces. Detection of flutter as well as determination of flutter frequency was performed by means of a stroboscope. Flutter was detected above a certain flow velocity, which gave proof for the validity of reduced frequency approach as stability criteria. Urban et al. (2000) have used a seven bladed linear cascade of last stage profiles of steam turbines. The blades were elastically suspended as shown in Figure 2-14 such as to allow a torsional oscillation with the center of torsion being located upstream of the leading edge. Blade motion was monitored by means of strain gauges. In addition the blades were equipped with miniature pressure transducers such as to provide information on the unsteady loading during flutter.

    Figure 2-14. Free flutter test setup for single mode testing; Urban et al. (2000) A setup with four elastically suspended blades has been used by Kirschner et al. (1976), see Figure 2-15. Friction in the blade suspension has been minimized with the aim to cancel out the damping contribution in the aeroelastic balance. The tests performed aimed at acquiring stability characteristics of damping and frequency versus reduced flow velocity (inverse of reduced frequency) for the cascade oscillating in bending mode, torsion modes with different center of torsion as well as combined modes. The cited investigation is one of the first ones addressing the importance of blade mode shape on the aerodynamic damping.

    Test section Blade support

    Figure 2-15. Free-flutter test setup for variable mode testing; Kirschner et al. (1976)

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    As a matter of fact free flutter tests generally have lower complexity compared to controlled flutter tests. There are however several drawbacks. Firstly flutter data can only be obtained at the least stable condition, which establishes naturally. Flutter data are therefore only available for the least stable interblade phase angle. Secondly no aerodynamic damping information can be gathered at no flutter condition and thus no conclusions can be drawn on how sensitive the system is. Thirdly, as most free flutter tests employ a cascade that restricts or promotes certain blade oscillation modes, see for example the study performed by Urban et al. (2000), test data are only available for the addressed modal dimension of the system. Hennings and Send (1998) have eliminated these drawbacks by employing a linear cascade of elastically suspended compressor airfoils undergoing torsional motion that could be operated in both free oscillation as well as excited mode by forcedly oscillating one blade. The method used consisted in reducing blade displacement data to eigenvectors and finally frequency response functions to describe aeroelastic stability.

    2.3.2 Controlled Flutter Testing

    Controlled flutter testing is used for determining aerodynamic damping characteristics of a setup. The flow is thereby considered as oscillation system that similar to a structural oscillation system features inherent dynamic characteristics. By exciting the system in a controlled manner and measuring the aerodynamic response information on aerodynamic damping and consequently on aeroelastic stability can be acquired. Most controlled flutter tests excite the system via the motion of the blades although it is generally possible to induce the excitation via aerodynamic disturbance forces. In the former case the regarded setup is exposed to fluid flow while the structure is oscillated in a controlled manner and aerodynamic response data is acquired. In accordance thereof the latter method foresees as well that the setup under investigation is exposed to fluid flow however the forcing is introduced by aerodynamic disturbance forces that are terminated abruptly such as to let the structure oscillate freely. Aerodynamic damping data can then be deduced from the oscillation properties of the structure. Motion-induced controlled flutter testing is widely used for testing. Under application of the linearized theory that has been lined out above there are the following two testing methods:

    Traveling wave mode testing: all blades in the cascade are oscillated at identical mode shape and at various interblade phase angles. The response is measured on one blade.

    Influence coefficient testing: only one blade is oscillated and the

    response is measured on all the blades in cascade. The data are superimposed at different interblade phase angles according to the theory presented below such as to yield damping data in the traveling wave mode domain.

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    These two testing methods have different strengths and disadvantages. Traveling wave mode testing in an annular cascade is the one that most accurately represents the circumstances in real engines. In such setups pressure waves can freely propagate in circumferential direction, which allows the detection of acoustic resonances. The test setup gets however costly and complex firstly due to higher complexity of annular facilities and secondly due to the fact that all blades in the cascade have to be oscillated in a controlled manner. Blcs and Fransson (1986) have employed an annular non-rotating cascade shown in Figure 2-16 where all blades or only single blades could be oscillated for the systematic investigation of flutter phenomenon in compressor and turbine cascades. Flow conditions could be varied from subsonic to transonic. Controlled oscillation of the blades is achieved by a spring type suspension of the blades that are submitted to electromagnetic excitation.

    Elastic blade suspension

    Kahl and Hennings (2000) Assembled blade carrier

    Nowinski and Panovsky (2000)

    Figure 2-16. Annular non-rotating cascade for traveling wave mode and influence coefficient testing

    Another type of annular cascade has been used by Frey and Fleeter (1999) for the investigation of combined gust and flutter in low-speed tests. The facility comprises a 3-stage experimental compressor with blades that can be made oscillating in traveling wave mode at frequencies proportional to the rotational speed. Oscillation of the blades is achieved by a cam follower assembly as shown in Figure 2-17.

    Figure 2-17. Purdue 3-stage experimental compressor; Frey and Fleeter (1999)

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    A simplification of annular facilities is achieved by traveling wave mode testing in linear cascades as the complexity of the setup decreases to an easier manageable level. Linear cascades are widely used due to the fact that data can readily be compared to two-dimensional theory without the need for taking into account complex three-dimensional mean flow phenomena. Blcs and Fransson (1986) have compiled a set of 9 two-dimensional test cases, so-called standard configurations, for validation purposes. There are however two major drawbacks in the use of linear cascades. On the steady-state side passage-to-passage periodicity, which otherwise is inherently present in annular cascades, must be achieved by means of flow and geometric devices at least in the center passages to achieve acceptance of data. On the unsteady side the walls limiting the cascade induce deteriorating pressure wave reflections and prevent the establishment of acoustic resonance flutter. These drawbacks have been assessed by several studies. Carta (1983) has addressed the unsteady blade-to-blade periodicity in a cascade of 11 blades depicted in Figure 2-18 and has shown that although good unsteady periodicity could be achieved for low incidence conditions at low speed higher mean incidence led to deteriorated unsteady periodicity. In addition the presence of an acoustic resonance has been reported at a specific interblade phase angle.

    Figure 2-18. UTRC Oscillating Cascade Wind Tunnel (OCWT); Carta (1983) In a series of investigations Buffum and Fleeter (1991) and Buffum and Fleeter (1994) have investigated the influence on wind tunnel walls on the unsteady performance during flutter testing in the NASA Lewis Transonic Oscillating Cascade shown in Figure 2-19. The facility features capabilities of oscillating all blades in traveling wave mode as well as single blade modes. Oscillation is achieved in a mechanical way by means of a cam follower assembly. To reduce acoustic reflections it has been suggested to treat the tunnel walls adequately,