 | May M. Linearized flutter investigations of mistuned turbomachinery blading: Diss. / Deutsches Zentrum für Luft- und Raumfahrt, Institut für Aeroelastik, Göttingen. - Köln: DLR, Bibliotheks- und Informationswesen, 2011. - xix, 168 p.: ill. - (Forschungsbericht; 2011-02). - Ref.: p.145-156. - ISSN 1434-8454
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List of Figures ............................................... xix
List of Tables ................................................ xxi
Nomenclature ................................................ xxiii
1 Introduction ................................................. 1
1.1 Aeroelastic Phenomena in Turbomachines .................. 1
1.2 State of the Art ........................................ 3
1.3 Objectives and Outline of the Present Work .............. 5
2 Theoretical Concepts ......................................... 7
2.1 Driven Harmonic Oscillator .............................. 7
2.1.1 Equation of Motion and Physical Interpretation ... 8
2.1.2 Damping Definitions and Identification .......... 10
2.1.3 Energy Considerations ........................... 12
2.2 Aeroelastic Modeling of Turbomachinery Blading ......... 15
2.2.1 Structural Eigenbehavior of the Rotationally
Symmetric Rotor ................................. 16
2.2.2 Unsteady Aerodynamic Loads ...................... 21
2.2.3 Influence Coefficients .......................... 22
2.2.4 Flutter Stability Equations ..................... 25
2.2.5 Aeroelastic Similarity Parameters ............... 26
2.3 Energy Method as Solution Strategy ..................... 28
2.3.1 Work per Cycle and Generalized Aerodynamic
Force ........................................... 28
2.3.2 Aerodynamic Damping and Local Excitation ........ 30
2.4 Reduced Order Modeling ................................. 33
2.4.1 State Space Representation ...................... 34
2.4.2 Frequency Mistuning and Aerodynamic Asymmetry ... 38
2.4.3 Multidisciplinary Design Optimization ........... 44
2.4.4 Coupling of Eigenmode Families .................. 47
3 Numerical Methods ........................................... 49
3.1 Aerodynamic Time and Frequency Domain Approaches ....... 49
3.1.1 Nonlinear Flow Simulations ...................... 51
3.1.2 Time-Linearization .............................. 51
3.1.3 Harmonic Balancing .............................. 52
3.2 Standard Numerical Tools ............................... 54
3.2.1 G3DMESH ......................................... 54
3.2.2 TRACE ........................................... 55
3.2.3 Lin3D ........................................... 55
3.2.4 elsA ............................................ 56
3.2.5 CalculiX ........................................ 56
3.3 Implementation of AEturbo .............................. 57
4 Presentation of Test Cases .................................. 59
4.1 FUTURE - TUD 11/2 Stage Compressor ...................... 60
4.2 NACA-3506-EPFL Annular Cascade ......................... 62
4.3 AeroLight - DLR Transonic Compressor Rotor ............. 64
4.4 BliDes-UHBR Fan in DLR Test Rig ........................ 66
5 Capabilities and Limits of Linear Aerodynamic Methods ....... 69
5.1 Computational Efficiency ............................... 69
5.2 Reliability ............................................ 73
5.2.1 Dependency on Steady-State Flow Field ........... 73
5.2.2 Amplitude Limitations ........................... 76
5.2.3 Shock Motion .................................... 77
6 Sensitivity Analysis with Respect to Flutter-Free Design .... 83
6.1 Preliminary Investigations ............................. 83
6.2 Variation of Similarity Parameters ..................... 86
6.2.1 Reduced Frequency ............................... 86
6.2.2 Mass Ratio ...................................... 88
6.3 Mode Shape Variations .................................. 91
6.3.1 Linear and Quadratic Patterns ................... 91
6.3.2 Amplitude Variations of Mode Shape .............. 92
6.3.3 Complexity of Mode Shape ........................ 92
6.4 Mistuning Influence .................................... 94
6.4.1 Individual Blade Mistuning ...................... 94
6.4.2 Harmonic Mistuning Pattern ...................... 94
6.4.3 Alternate Mistuning Pattern ..................... 95
6.4.4 Optimal Mistuning ............................... 95
6.4.5 Frequency Mistuning vs. Aerodynamic Asymmetry ... 95
6.5 Coupling of Eigenmode Families ........................ 104
6.5.1 Aeroelastic Coupling with Mode Family IF ....... 104
6.5.2 Aeroelastic Coupling with Mode Family IT ....... 104
6.6 Design Rules to Stabilize Flutter Cases ............... 107
7 Flutter Analysis of a Highly Loaded Transonic Fan .......... 109
7.1 Steady CFD Simulations ................................ 109
7.1.1 Performance Map ................................ 109
7.1.2 Operating Points ............................... 109
7.2 Pre-stressed Normal Modes Analysis .................... 112
7.3 Unsteady СГО Simulations .............................. 114
7.3.1 Aeroelastic Stability Diagrams ................. 114
7.3.2 Local Excitation Mechanisms .................... 115
7.3.3 Design Tool To Predict the Flutter Boundary .... 118
7.4 Evaluation of the Mistuning Characteristics ........... 124
7.4.1 Individual Blade Responses to Traveling Wave
Excitation ..................................... 124
7.4.2 Standing Wave Modes of Instrumented Blisk ...... 126
7.4.3 Individual Blade Modes of Instrumented Blisk ... 130
7.5 Model Updating with Experimental Data ................. 132
7.5.1 Updating Procedure ............................. 132
7.5.2 Application to the Aeroelastic ROM ............. 134
7.6 Evaluation of Results ................................. 138
7.6.1 Identification of Significant Parameters ....... 138
7.6.2 Aeroelastic Characterization of the
Underlying Configuration ....................... 139
8 Conclusion ................................................. 141
8.1 Summary of Results .................................... 141
8.2 Future Work ........................................... 142
References ................................................. 156
A Conventions ................................................ 157
A.1 Numbering of Passages ................................. 157
A.l.l Sign of Inter-Blade Phase Angle and Nodal
Diameter ....................................... 157
A.1.2 Effective Direction of Influence
Coefficients ................................... 159
A.2 Work per Oscillation Cycle ............................ 160
A.2.1 Real Approach .................................. 160
A.2.2 Complex Approach ............................... 161
В Unsteady Data of UHBR Fan ................................... 163
B.1 Results of Time-Linearized CFD Simulations ............ 163
B.l.l Speedline at 50% Rotational Speed .............. 164
B.1.2 Speedline at 74% Rotational Speed .............. 165
B.1.3 Speedline at 82% Rotational Speed .............. 166
B.1.4 Speedline at 93% Rotational Speed .............. 167
B.1.5 Speedline at 100% Rotational Speed ............. 168
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