Duke University Dissertation Template

186 Pages·2016·11.77 MB·English

by  Jing Li

Multi-Row Aerodynamic Interactions
and Mistuned Forced Response
of an Embedded Compressor Rotor

by
Jing Li
Department of Mechanical Engineering and Materials Science
Duke University

Date:_______________________
Approved:

___________________________
Robert Kielb, Supervisor

___________________________
Earl Dowell

___________________________
Kenneth Hall

___________________________
Jeffrey Thomas

___________________________
Thomas Witelski

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

2016

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ABSTRACT
Multi-Row Aerodynamic Interactions
and Mistuned Forced Response
of an Embedded Compressor Rotor

by
Jing Li
Department of Mechanical Engineering and Materials Science
Duke University

Date:_______________________
Approved:

___________________________
Robert Kielb, Supervisor

___________________________
Earl Dowell

___________________________
Kenneth Hall

___________________________
Jeffrey Thomas

___________________________
Thomas Witelski

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

2016
Copyright by
Jing Li
2016
Abstract
This research investigates the forced response of mistuned rotor blades that can
lead to excessive vibration, noise, and high cycle fatigue failure in a turbomachine. In
particular, an embedded rotor in the Purdue Three-Stage Axial Compressor Research
Facility is considered. The prediction of the rotor forced response contains three key
elements: the prediction of forcing function, damping, and the effect of frequency
mistuning. These computational results are compared with experimental aerodynamic
and vibratory response measurements to understand the accuracy of each prediction.
A state-of-the-art time-marching computational fluid dynamic (CFD) code is
used to predict the rotor forcing function. A highly-efficient nonlinear frequency-
domain Harmonic Balance CFD code is employed for the prediction of aerodynamic
damping. These allow the compressor aerodynamics to be depicted and the tuned rotor
response amplitude to be predicted. Frequency mistuning is considered by using two
reduced-order models of different levels of fidelity, namely the Fundamental Mistuning
Model (FMM) and the Component Mode Mistuning (CMM) methods. This allows a cost-
effective method to be identified for mistuning analysis, especially for probabilistic
mistuning analysis.
The first topic of this work concerns the prediction of the forcing function of the
embedded rotor due to the periodic passing of the neighboring stators that have the

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same vane counts. Superposition and decomposition methods are introduced under a
linearity assumption, which states that the rotor forcing function comprises of two
components that are induced by each neighboring stator, and that these components
stay unchanged with only a phase shift with respect to a change in the stator-stator
clocking position. It is found that this assumption captures the first-order linear relation,
but neglects the secondary nonlinear effect which alters each stator-induced forcing
functions with respect to a change in the clocking position.
The second part of this work presents a comprehensive mistuned forced
response prediction of the embedded rotor at a high-frequency (higher-order) mode.
Three steady loading conditions are considered. The predicted aerodynamics are in
good agreement with experimental measurements in terms of the compressor
performance, rotor tip leakage flow, and circumferential distributions of the stator wake
and potential fields. Mistuning analyses using FMM and CMM models show that the
extremely low-cost FMM model produces very similar predictions to those of CMM. The
predicted response is in good agreement with the measured response, especially after
taking the uncertainty in the experimentally-determined frequency mistuning into
consideration. Experimentally, the characteristics of the mistuned response change
considerably with respect to loading. This is not very well predicted, and is attributed to
un-identified and un-modeled effects. A significant amplification factor over 1.5 is
observed both experimentally and computationally for this higher-order mode.

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Contents
Abstract ......................................................................................................................................... iv
List of Tables ................................................................................................................................. ix
List of Figures ................................................................................................................................ x
List of Abbreviations .................................................................................................................xvi
Acknowledgements ................................................................................................................... xix
1 Introduction ................................................................................................................................ 1
1.1 Turbomachinery Forced Response ................................................................................ 1
1.1.1 Aerodynamic Forcing Functions ............................................................................... 4
1.1.2 Aerodynamic Damping ............................................................................................ 15
1.1.3 Modeling of Forced Response ................................................................................. 17
1.1.4 Effect of Mistuning .................................................................................................... 19
1.2 Purdue Three-Stage Axial Compressor Research Facility ........................................ 23
1.3 Outline of the Current Work ......................................................................................... 27
2 Forcing Function Decomposition and Superposition ......................................................... 29
2.1 Background ..................................................................................................................... 30
2.2 Research Objectives ........................................................................................................ 34
2.3 Numerical Approach ..................................................................................................... 39
2.4 Time-Averaged Aerodynamics .................................................................................... 42
2.5 Linear Superposition of 2-Row Solutions ................................................................... 46
2.6 Linear Decomposition and Superposition of 3-Row Solutions ................................ 53

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2.6.1 Linear Decomposition ............................................................................................... 54
2.6.2 Stator-Stator Interaction ........................................................................................... 59
2.6.3 Linear Superposition Based on Decomposed 3-Row Results ............................. 61
3 Higher-Order Mode Mistuned Forced Response ................................................................ 65
3.1 Background ..................................................................................................................... 66
3.2 Research Objectives ........................................................................................................ 68
3.3 Steady and Unsteady Aerodynamics .......................................................................... 69
3.3.1 Numerical Models ..................................................................................................... 70
3.3.2 Compressor Performance ......................................................................................... 73
3.3.3 Rotor Tip Leakage Flow ........................................................................................... 81
3.3.4 Characterization of Stator Aerodynamic Forcing Functions ............................... 85
3.3.5 Rotor Forcing Function ............................................................................................. 92
3.3.5.1 Influence of the Tip Leakage Flow .................................................................. 92
3.3.5.2 Individual Stator Contributions ....................................................................... 96
3.3.5.3 Additional Traveling-Wave Forcing Functions ........................................... 101
3.3.6 Rotor Tuned Resonant Response .......................................................................... 102
3.4 Mistuned Forced Response Prediction ...................................................................... 104
3.4.1 Experimental Vibratory Response Measurement System ................................. 105
3.4.2 Mistuning Theories ................................................................................................. 106
3.4.3 Problem Description ............................................................................................... 108
3.4.3.1 Frequency Mistuning....................................................................................... 108
3.4.3.2 Structural Coupling ......................................................................................... 111

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3.4.3.3 Aerodynamic Coupling ................................................................................... 115
3.4.4 Prediction of Aeroelastic Eigenvalues .................................................................. 117
3.4.5 Prediction of Mistuned Forced Response ............................................................ 122
3.4.5.1 Results Presentation......................................................................................... 122
3.4.5.2 Mistuned Forced Response Prediction ......................................................... 125
3.4.5.3 Low Average Mistuned Response ................................................................. 133
3.4.5.3 Mistuned Forced Response Sensitivity Analysis ......................................... 135
4 Conclusions and Future Work ............................................................................................. 139
4.1 Conclusions ................................................................................................................... 139
4.2 Future Work .................................................................................................................. 144
Appendix A: Estimate of Hysteretic Damping ..................................................................... 147
Appendix B: Acoustic Resonance in Forced Response ........................................................ 149
Bibliography .............................................................................................................................. 153
Biography ................................................................................................................................... 166

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List of Tables
Table 1-1: Material properties of the P3S compressor blisk. ................................................. 26
Table 2-1: Node count per passage for the coarse, medium, and fine meshes. .................. 40
Table 2-2: Computationally resolved normalized corrected mass flow rate in comparison
with experimental value. ........................................................................................................... 42
Table 2-3: Percentage difference of the superposed R2 forcing amplitude compared
against 3-row CFD solutions for CL-1, CL-3, and CL-5. ........................................................ 53
Table 2-4: Percentage difference of the R2 1T/44EO modal force amplitude between the
superposed and CFD-resolved results. .................................................................................... 64
Table 3-1: Summary of predicted and measured performances of LL, PE, and HL
operating points on the 68% Nc speed line. ............................................................................ 74
Table 3-2: Summary of R2 1CWB/88EO modal forces at LL. .............................................. 101
Table 3-3: Summary of predicted and measured loading, modal forcing, damping, and
tuned forced response at LL, PE, and HL. ............................................................................. 104
Table 3-4: Summary of tuned R2 1CWB structural characteristics. ................................... 115
Table 3-5: Summary of measured and predicted mistuned responses. ............................ 128
Table B-1: Inputs and results for the acoustic resonance condition calculations. ............ 151

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List of Figures
Figure 1-1: An example Campbell diagram (adapted from Miyakozawa, [5]). ................... 3
Figure 1-2: Schematic of primary sources of aerodynamic excitations to an embedded
rotor in a subsonic compressor. .................................................................................................. 5
Figure 1-3: Purdue Three-Stage Axial Compressor Research Facility (adapted from Ball,
[72]). .............................................................................................................................................. 23
Figure 1-4: PS3 Compressor flow path cross-sectional view, blading, and measurement
stations (adapted from Ball, [72]). ............................................................................................. 25
Figure 1-5: Schematic of two compressor stator designs: (a) cantilevered stator vane, and
(b) shrouded stator vane. ........................................................................................................... 25
Figure 1-6: Campbell diagram of R2. 1T/44EO and 1CWB/88EO crossings are shown. ... 27
Figure 2-1: (a) Schematic of the P3S compressor, (b) R2 Campbell diagram, and (c) P3S
compressor 74% Nc speed line. ................................................................................................. 37
Figure 2-2: Schematic of six clocking configurations defined by Key ([35]) in terms of the
S1 percentage vane pitch (%vp) location relative to S2. ........................................................ 38
Figure 2-3: Normalized time-averaged absolute total pressure contours upstream of the
S2 LE for clocking configurations of (a) CL-1, (b) CL-3, and (c) CL-5. ................................ 39
Figure 2-4: Unsteady CFD models of 2-row and 3-row forced response problems. ......... 40
Figure 2-5: Predicted steady-state mid-span airfoil loading using coarse, medium, and
fine meshes. .................................................................................................................................. 41
Figure 2-6: Mid-span time-averaged pressure coefficient distributions for (a) S1, (b) R2,
and (c) S2 resolved by 2-row and 3-row CFD simulations. .................................................. 42
Figure 2-7: Predicted (by 2-row and 3-row CFD simulations) and measured S1 exit wake
profiles at 80% span. ................................................................................................................... 43
Figure 2-8: Predicted (by 2-row and 3-row CFD simulations) and measured S1 exit
casing potential profiles. ............................................................................................................ 44

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