Probabilistic Aerothermal Design of Compressor Airfoils Victor E. Garzon

183 Pages·2012·2.88 MB·English

Probabilistic Aerothermal Design of Compressor
Airfoils
by
Victor E. Garzon
B.S., University of Kentucky (1994)
M.S., University of Kentucky (1998)
Submitted to the Department of Aeronautics and Astronautics
in partial ful(cid:12)llment of the requirements for the degree of
Doctor of Philosophy
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 2003
c Massachusetts Institute of Technology 2003. All rights reserved.
(cid:13)
Author
Department of Aeronautics and Astronautics
11 December 2002
Certi(cid:12)ed by
David L. Darmofal
Associate Professor of Aeronautics and Astronautics
Thesis Supervisor
Certi(cid:12)ed by
Mark Drela
Professor of Aeronautics and Astronautics
Certi(cid:12)ed by
Edward M. Greitzer
H. N. Professor of Aeronautics and Astronautics
Certi(cid:12)ed by
Ian A. Waitz
Professor of Aeronautics and Astronautics
Accepted by
Edward M. Greitzer
H. N. Slater Professor of Aeronautics and Astronautics
Chair, Committee on Graduate Students
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Probabilistic Aerothermal Design of Compressor Airfoils
by
Victor E. Garzon
Submitted to the Department of Aeronautics and Astronautics
on 11 December 2002, in partial ful(cid:12)llment of the
requirements for the degree of
Doctor of Philosophy
Abstract
Despite the generally accepted notion that geometric variability is undesirable in tur-
bomachinery airfoils, little is known in detail about its impact on aerothermal com-
pressor performance. In this work, statistical and probabilistic techniques were used
to assess the impact of geometric and operating condition uncertainty on axial com-
pressor performance. High-(cid:12)delity models of geometric variability were constructed
from surface measurements of existing hardware using principal component analy-
sis (PCA). A quasi-two-dimensional cascade analysis code, at the core of a parallel
probabilistic analysis framework, was used to assess the impact of uncertainty on
aerodynamic performance of compressor rotor airfoils. Three rotor blades with inlet
relative Mach numbers of 0.82, 0.90 and 1.25 were considered. Discrepancies between
nominal and mean loss (mean-shift) of up to 20% were observed. Loss and turning
variability were found to grow linearly with geometric noise amplitude.
A probabilistic, gradient-based approach to compressor blade optimization was
presented. Probabilistic objectives, constraints and gradients are approximated using
low-resolution Monte Carlo sampling. Test airfoils were optimized both determinis-
tically and probabilistically and then analyzed probabilistically to account for geo-
metric variability. Probabilistically redesigned airfoils exhibited reductions in mean
loss of up to 25% and in loss variability of as much as 65% from corresponding values
for deterministically redesigned airfoils. A probabilistic mean-line multi-stage axial
compressor model was used to estimate the impact of geometric variability on over-
all compressor performance. Probabilistic loss and turning models were exercised on
a six-stage compressor model. At realistic levels of geometric variability, the mean
polytropic e(cid:14)ciency was found to be upwards of 1% lower than nominal. Compres-
sor simulations using airfoils redesigned probabilistically for minimum loss variability
exhibited reductions of 30 to 40% in polytropic e(cid:14)ciency variability and mean shift.
Thesis Supervisor: David L. Darmofal
Title: Associate Professor of Aeronautics and Astronautics
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Acknowledgments
I am indebted to Prof. David Darmofal for suggesting the topic of this thesis, for his
excellent academic and technical advise and for his constant encouragement. Thanks
to Prof. Edward Greitzer and Prof. Ian Waitz for their research guidance and many
contributions to this thesis. Thanks to Prof. Mark Drela for developing MISES and
ancillary codes, and for answering countless questions about their usage. Prof. Daniel
Frey suggested principal component analysis to characterize geometric variability of
compressor airfoils. Thanks also to Dr. Ali Merchant for allowing me use of his
codes and for answering various questions about compressor design. Special thanks
to Mr. Je(cid:11) Lancaster for helping ground this thesis in reality. Mr. Robert Haimes’
guidance with system administration matters is also thankfully acknowledged.
The work reported in this thesis was made possible by the (cid:12)nancial support of
NASA Glenn Research Center through grant No. NAG3-2320.
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Contents
1 Introduction 17
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.3 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.5 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Characterization of Geometric Variability 27
2.1 Principal Component Analysis of Airfoil Measurements . . . . . . . . 28
2.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.1.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 Statistical Models of Geometric Variability . . . . . . . . . . . . . . . 37
2.3 PCA Results Vs. Number of Samples . . . . . . . . . . . . . . . . . . 38
2.4 Other Methods of Describing Geometric Noise . . . . . . . . . . . . . 40
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3 Impact of Geometric Variability On Compressor Blade Aerodynam-
ics 45
3.1 Aerodynamic Performance Assessment . . . . . . . . . . . . . . . . . 46
3.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.1.2 Blade row aerodynamic analysis: MISES . . . . . . . . . . . . 47
3.2 Probabilistic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2.1 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . 49
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3.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3.1 Integrally-bladed rotor, mid-span section . . . . . . . . . . . . 52
3.3.2 DFVLR transonic cascade . . . . . . . . . . . . . . . . . . . . 67
3.3.3 NASA rotor 37, mid-span section . . . . . . . . . . . . . . . . 73
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4 Probabilistic Optimization of Compressor Blade Sections 81
4.1 Gradient-Based Probabilistic Optimization . . . . . . . . . . . . . . . 82
4.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2.1 Objectives and Constraints . . . . . . . . . . . . . . . . . . . . 87
4.2.2 Geometric Design Modes . . . . . . . . . . . . . . . . . . . . . 88
4.2.3 IBR Rotor Mid-Span . . . . . . . . . . . . . . . . . . . . . . . 89
4.2.4 DFVLR Cascade Airfoil . . . . . . . . . . . . . . . . . . . . . 99
4.2.5 Rotor 37 Mid-Span . . . . . . . . . . . . . . . . . . . . . . . . 108
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5 E(cid:11)ect of Geometric Variability on Compressor Performance 119
5.1 Mean-Line Compressor Model . . . . . . . . . . . . . . . . . . . . . . 120
5.2 Loss Coe(cid:14)cient and Turning Angle Models . . . . . . . . . . . . . . . 122
5.3 Probabilistic Mean-Line Calculations . . . . . . . . . . . . . . . . . . 129
5.3.1 Six-stage compressor model: baseline airfoil . . . . . . . . . . 129
5.3.2 Six-stage compressor model: redesigned airfoils . . . . . . . . 132
5.4 Impact of Geometric Noise on Compressor Performance . . . . . . . . 132
5.5 Multiple-Blade Rows . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6 Summary and Recommendations 143
A Principal Component Analysis 149
A.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
A.2 Basic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
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A.3 Three-Dimensional Analysis of IBR Blade Measurements . . . . . . . 155
B Point- Vs. Flank-Milled Compressor Blade Rows 159
C Robustness Via Constrained Probabilistic Optimization 163
D Mean-Line Compressor Model 167
D.1 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
D.2 Baseline Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
D.3 Stage formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
D.4 Rotor System Jacobian . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Bibliography 175
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