flutter and forced response of turbomachinery with frequency mistuning and aerodynamic asymmetry

172 Pages·2008·5.3 MB·English

FLUTTER AND FORCED RESPONSE OF
TURBOMACHINERY WITH FREQUENCY MISTUNING
AND AERODYNAMIC ASYMMETRY
by
Tomokazu Miyakozawa
Department of Mechanical Engineering and Materials Science
Duke University
Date:
Approved:
Robert E. Kielb, Supervisor
Kenneth C. Hall
Earl H. Dowell
Laurens E. Howle
Lawrence N. Virgin
Dissertation submitted in partial fulfillment of the
requirements for the degree of Doctor of Philosophy
in the Department of Mechanical Engineering and Materials Science
in the Graduate School of
Duke University
2008
ABSTRACT
FLUTTER AND FORCED RESPONSE OF
TURBOMACHINERY WITH FREQUENCY MISTUNING
AND AERODYNAMIC ASYMMETRY
by
Tomokazu Miyakozawa
Department of Mechanical Engineering and Materials Science
Duke University
Date:
Approved:
Robert E. Kielb, Supervisor
Kenneth C. Hall
Earl H. Dowell
Laurens E. Howle
Lawrence N. Virgin
An abstract of a dissertation submitted in partial fulfillment of the
requirements for the degree of Doctor of Philosophy
in the Department of Mechanical Engineering and Materials Science
in the Graduate School of
Duke University
2008
Copyright (cid:13)c 2008 by Tomokazu Miyakozawa
All rights reserved
Abstract
This dissertation provides numerical studies to improve bladed disk assembly design
for preventing blade high cycle fatigue failures. The analyses are divided into two
major subjects. For the first subject presented in Chapter 2, the mechanisms of
transonic fan flutter for tuned systems are studied to improve the shortcoming of
traditional method for modern fans using a 3D time-linearized Navier-Stokes solver.
Steady and unsteady flow parameters including local work on the blade surfaces are
investigated. It was found that global local work monotonically became more unsta-
ble on the pressure side due to the flow rollback effect. The local work on the suction
side significantly varied due to nodal diameter and flow rollback effect. Thus, the
total local work for the least stable mode is dominant by the suction side. Local work
on the pressure side appears to be affected by the shock on the suction side. For the
second subject presented in Chapter 3, sensitivity studies are conducted on flutter
and forced response due to frequency mistuning and aerodynamic asymmetry using
the single family of modes approach by assuming manufacturing tolerance. The un-
steady aerodynamic forces are computed using CFD methods assuming aerodynamic
symmetry. The aerodynamic asymmetry is applied by perturbing the influence coeffi-
cient matrix. These aerodynamic perturbations influence both stiffness and damping
while traditional frequency mistuning analysis only perturbs the stiffness. Flutter
results from random aerodynamic perturbations of all blades showed that manu-
facturing variations that effect blade unsteady aerodynamics may cause a stable,
perfectly symmetric engine to flutter. For forced response, maximum blade ampli-
tudes are significantly influenced by the aerodynamic perturbation of the imaginary
part (damping) of unsteady aerodynamic modal forces. This is contrary to blade
frequency mistuning where the stiffness perturbation dominates.
iv
Contents
Abstract iv
List of Figures xi
List of Tables xviii
Nomenclature xix
Acknowledgements xxii
1 Background 1
1.1 High Cycle Fatigue Failure . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Recent Turbofan Configurations . . . . . . . . . . . . . . . . . . . . . 2
1.3 Flutter and Forced Response Analysis . . . . . . . . . . . . . . . . . . 3
1.4 Research Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Numerical Study of Transonic Fan Flutter 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Traditional Design Approach . . . . . . . . . . . . . . . . . . . 7
2.1.2 Related Previous Research . . . . . . . . . . . . . . . . . . . . 9
2.1.3 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 Work & Aerodynamic Damping . . . . . . . . . . . . . . . . . 11
2.3 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.1 Nominal 18 Bladed, 20 Bladed, & Drooped Leading Edge 18
Bladed Fans . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.2 Mass Ratio of Composite Blade . . . . . . . . . . . . . . . . . 12
v
2.3.3 Flow Conditions (Rotational Speed & Flow Rollbacks) . . . . 13
2.4 Steady Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.1 Mach Number . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.1.1 Pressure Side Mach Contour . . . . . . . . . . . . . . 14
2.4.1.2 Suction Side Mach Contour . . . . . . . . . . . . . . 15
2.4.1.3 91% Span Mach Contour . . . . . . . . . . . . . . . . 17
2.4.1.4 91% Span Pressure Side Mach Number . . . . . . . . 21
2.4.1.5 91% Span Suction Side Mach Number . . . . . . . . 24
2.4.2 Static Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.2.1 Pressure Side Static Pressure Contour . . . . . . . . 27
2.4.2.2 Suction Side Static Pressure Contour . . . . . . . . . 27
2.4.2.3 91% Span Static Pressure Contour . . . . . . . . . . 28
2.4.2.4 91% Span Pressure Side Static Pressure . . . . . . . 30
2.4.2.5 91% Span Suction Side Static Pressure . . . . . . . . 33
2.5 Unsteady Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5.1 Aerodynamic Damping versus Interblade Phase Angle . . . . . 36
2.5.1.1 Local Work versus Interblade Phase Angle . . . . . . 38
2.5.2 Least Stable Damping & Flutter Boundary . . . . . . . . . . . 39
2.5.2.1 Interpolation of Flutter Boundary . . . . . . . . . . . 39
2.5.3 Fan Characteristic Map . . . . . . . . . . . . . . . . . . . . . 39
2.5.3.1 Numerically Measured Flutter Boundary . . . . . . . 39
2.5.3.2 Experimentally Measured Flutter Boundary . . . . . 42
2.5.4 Local Work (1ND FTW) . . . . . . . . . . . . . . . . . . . . . 43
2.5.4.1 Fraction of Local Work on Pressure & Suction Surfaces 43
vi
2.5.4.2 Pressure Side Local Work Contour . . . . . . . . . . 45
2.5.4.3 91% Span Pressure Side Local Work . . . . . . . . . 46
2.5.4.4 Span-Wise Pressure Side Local Work . . . . . . . . . 47
2.5.4.5 Suction Side Local Work Contour . . . . . . . . . . . 50
2.5.4.6 91% Span Suction Side Local Work . . . . . . . . . . 52
2.5.4.7 Span-Wise Suction Side Local Work . . . . . . . . . 52
2.5.5 Unsteady Pressure Amplitude (1ND FTW) . . . . . . . . . . . 55
2.5.5.1 Pressure Side Unsteady Pressure Amplitude Contour 55
2.5.5.2 91% Span Pressure Side Unsteady Pressure Amplitude 55
2.5.5.3 Suction Side Unsteady Pressure Amplitude Contour 56
2.5.5.4 91% Span Suction Side Unsteady Pressure Amplitude 56
2.5.6 Unsteady Pressure Phase (1ND FTW) . . . . . . . . . . . . . 62
2.5.6.1 91% Span Pressure Side Unsteady Pressure Phase . . 62
2.5.6.2 91% Span Suction Side Unsteady Pressure Phase . . 62
2.5.7 Comparisons of All Flow Parameters (1ND FTW) . . . . . . . 67
2.5.7.1 Pressure Side . . . . . . . . . . . . . . . . . . . . . . 67
2.5.7.2 Suction Side . . . . . . . . . . . . . . . . . . . . . . . 67
2.6 VariationsofStabilityMarginduetoMistuning&AerodynamicAsym-
metric Perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.6.1 Investigated Speed Line . . . . . . . . . . . . . . . . . . . . . 71
2.6.1.1 72.5% Speed . . . . . . . . . . . . . . . . . . . . . . 71
2.6.1.2 TunedDamping&Frequencyfor0%to6%FlowRoll-
back of 72.5% Speed . . . . . . . . . . . . . . . . . . 71
2.6.2 Monte Carlo Results . . . . . . . . . . . . . . . . . . . . . . . 72
2.6.2.1 6% Flow Rollback of 72.5% Speed . . . . . . . . . . . 72
vii
2.6.2.2 Effect of Standard Deviation Level . . . . . . . . . . 74
2.6.2.3 Effect of Mass Flow Rollback . . . . . . . . . . . . . 78
2.6.2.4 Effect on Fan Characteristic Map . . . . . . . . . . . 78
3 Frequency Mistuning and Aerodynamic Asymmetric Perturbation 81
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.1.1 Mistuning Research with Aerodynamic Coupling . . . . . . . . 81
3.1.2 Aerodynamic Asymmetries Research . . . . . . . . . . . . . . 82
3.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.2.1 Modal Equation of Motion for a Bladed Disk . . . . . . . . . . 85
3.2.2 Methods of Aerodynamic Asymmetric Perturbations . . . . . 88
3.2.3 Frequency Separation Parameter . . . . . . . . . . . . . . . . 91
3.3 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.3.1 Structural Coupling Models . . . . . . . . . . . . . . . . . . . 92
3.3.2 Aerodynamic Coupling Models . . . . . . . . . . . . . . . . . 94
3.4 Flutter Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.4.1 Tuned & Symmetric Results . . . . . . . . . . . . . . . . . . . 97
3.4.1.1 Aeroelastic Frequency (System Stiffness) . . . . . . . 97
3.4.1.2 Aeroelastic Damping (System Stability) . . . . . . . 97
3.4.2 Frequency Mistuning Results . . . . . . . . . . . . . . . . . . 101
3.4.2.1 AeroelasticFrequency&DampingforCaseTwo(Flex-
ible Disk) . . . . . . . . . . . . . . . . . . . . . . . . 101
3.4.2.2 Monte Carlo Results for Case Two (Flexible Disk) . 101
3.4.2.3 Effects of Random Mistuning Level . . . . . . . . . . 102
3.4.2.4 Effects of Frequency Separation Parameter . . . . . . 102
viii
3.4.3 Aerodynamic Asymmetric Perturbation Results . . . . . . . . 107
3.4.3.1 AeroelasticFrequency&DampingforCaseTwo(Flex-
ible Disk) . . . . . . . . . . . . . . . . . . . . . . . . 107
3.4.3.2 Monte Carlo Results for Case Two (Flexible Disk) . 107
3.4.3.3 Effect of Random Aerodynamic Perturbation Levels . 108
3.4.3.4 Effects of Frequency Separation Parameter . . . . . . 110
3.4.4 Frequency Mistuning & Aerodynamic Asymmetric Perturba-
tion Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.4.4.1 AeroelasticFrequency&DampingforCaseTwo(Flex-
ible Disk) . . . . . . . . . . . . . . . . . . . . . . . . 113
3.4.4.2 Monte Carlo Results for Case Two (Flexible Disk) . 114
3.4.4.3 Effect of Random Mistuning & Aerodynamic Pertur-
bation Levels . . . . . . . . . . . . . . . . . . . . . . 114
3.4.4.4 Effects of Frequency Separation Parameter . . . . . . 118
3.5 Forced Response Results . . . . . . . . . . . . . . . . . . . . . . . . . 121
3.5.1 Tuned Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
3.5.1.1 Tuned Resonant Response . . . . . . . . . . . . . . . 121
3.5.2 Mistuning Results . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.5.2.1 Mistuned Blade Frequency, FRF & Blade Amplitude
for Flexible Disk . . . . . . . . . . . . . . . . . . . . 122
3.5.2.2 Monte Carlo Results for Flexible Disk . . . . . . . . 122
3.5.2.3 Effects of Random Mistuning Level . . . . . . . . . . 124
3.5.2.4 Effects of Nodal Diameter Excitation . . . . . . . . . 124
3.5.2.5 Effects of Frequency Separation Parameter . . . . . . 126
3.5.2.6 Effects of Structural Damping . . . . . . . . . . . . . 127
3.5.2.7 Numerical Results to Compare with Simulated Ex-
perimental Results . . . . . . . . . . . . . . . . . . . 130
ix
3.5.3 Aerodynamic Asymmetric Perturbation Results . . . . . . . . 133
3.5.3.1 Tuned Aeroelastic Eigenvalues . . . . . . . . . . . . . 133
3.5.3.2 Single Blade Perturbation . . . . . . . . . . . . . . . 133
3.5.3.3 Symmetric Group Force Perturbation . . . . . . . . . 137
3.5.3.4 Random Force Perturbation For All Blades . . . . . 139
4 Summary & Conclusions 145
Bibliography 147
Biography 150
x