3.14 Amplification ratios of Tollmien-Schlichting waves on a flight test airfoil

198 Pages·2004·4.17 MB·English

by  Peter Sturdza

AN AERODYNAMIC DESIGN METHOD FOR
SUPERSONIC NATURAL LAMINAR FLOW AIRCRAFT
a dissertation
submitted to the department of aeronautics and astronautics
and the committee on graduate studies
of stanford university
in partial fulfillment of the requirements
for the degree of
doctor of philosophy
Peter Sturdza
December 2003
c Copyright by Peter Sturdza 2004
°
All Rights Reserved
ii
I certify that I have read this dissertation and that, in my
opinion, it is fully adequate in scope and quality as a disser-
tation for the degree of Doctor of Philosophy.
Ilan M. Kroo
(Principal Advisor)
I certify that I have read this dissertation and that, in my
opinion, it is fully adequate in scope and quality as a disser-
tation for the degree of Doctor of Philosophy.
Juan J. Alonso
I certify that I have read this dissertation and that, in my
opinion, it is fully adequate in scope and quality as a disser-
tation for the degree of Doctor of Philosophy.
Sanjiva K. Lele
ApprovedfortheUniversityCommitteeonGraduateStudies.
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Abstract
The computation of boundary-layer properties and laminar-to-turbulent transition location
is a complex problem generally not undertaken in the context of aircraft design. Yet this
is just what must be done if an aircraft designer is to exploit the advantages of laminar
flow while making the proper trade-offs between inviscid drag, structural weight and skin
friction. To facilitate this process, a new tool is developed. This thesis presents a design-
oriented method for the aerodynamic analysis of supersonic wings including approximate
means for estimating transition and total drag.
The method consists of a boundary-layer solver combined with a fast and robust tran-
sition scheme based on the well-known en criterion. The boundary-layer analyses em-
ployed are computationally inexpensive but sufficiently accurate to provide guidance for
advanced design studies and to be incorporated in multidisciplinary design optimization.
The boundary-layer solver is based on an enhanced quasi-3D sweep/taper theory which is
shown to agree well with three-dimensional Navier-Stokes results.
The transition calculation scheme is implemented within the boundary-layer solver and
automatically triggers a turbulence model at the predicted transition front. The laminar
instability amplification values used in the en criterion are based on algebraic fits to linear
stability results for streamwise and crossflow modes. This parametric transition prediction
methodcomparesfavorablywithexactlineartheoryonrelevantgeometriesandsuccessfully
computes transition for a supersonic flight test.
Integration of the present design method with numerical optimization is discussed, and
airfoil section and wing/body shape optimizations are performed. Wing/body drag mini-
mizationstudiessuggestthatlow-sweepsupersonicaircraftwithextensivelaminarflowmay
have a significant drag advantage over conventional designs.
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Acknowledgments
I’m not quite sure why I returned to Stanford for the PhD; there are many reasons, but
probably the foremost was to learn more about aircraft design and multidisciplinary opti-
mization. ForthisImustthankmyadvisor,ProfessorIlanKroo. Withoutamostinteresting
Master’s year exposed to his research group and its then-intriguing group meetings (now
dreaded, of course), I just might have gone through with my desire from my undergraduate
years: to be done with school once and for all. Ironically, actually obtaining the degree was
not a strong priority (after all, PhDs are not very practical, I keep hearing), leaving me in
school for quite some time longer than I had imagined. Thus, I have a long list of people
to acknowledge.
First are the members of my defense and reading committees. Professor Juan Alonso
has been very helpful over the years particularly with CFD tools and grid generators, but
was also patient while entertaining my curiosity of adjoint methods. I would like to thank
Professor Sanjiva Lele for participating in both the reading and defense committees and
for asking all the right questions that have helped strengthen the chapter on transition
analysis. I am grateful for Professor Peter Bradshaw’s involvement in the defense as well
as his assistance and candid advice regarding boundary-layer methods. And Professor Paul
Durbin was nice enough to serve as chairman at my defense and run the proceedings very
smoothly.
None of this work would have taken place without Richard Tracy and his consistent
and heroic efforts to gather support for studying supersonic natural laminar flow aircraft
concepts. In particular, thanks go to Directed Technologies, Inc., the direct sponsor of this
research.
The field of boundary-layer transition is a vast and scary one. I must acknowledge
Professors Case van Dam of UC Davis and Helen Reed and William Saric of ASU for their
guidance and expertise. Chau-Lyan Chang and Meelan Choudhari of NASA Langley have
provided invaluable assistance with linear stability theory and their code, LASTRAC. I
am grateful to Jeffrey Viken, also of NASA Langley, for running COSAL and having the
patience to answer my many questions.
My colleagues, of course, cannot go unmentioned. Quim Martins, my office mate
throughout most of this endeavor, along with Valerie Manning, David Rodriguez, Mark
Meyer, Tara Rishko, Peter Kunz, Samy Elkayam, Gary Fay and Martin Chan have all con-
tributed in some way to the contents of this thesis. I have learned a lot from working with
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them and they have helped me avoid work as well; both are sincerely appreciated.
Special recognition goes to Stefan Bieniawski for his careful review of the manuscript—
he may very well be the only person to ever read it in its entirety. Aga Goodsell has also
provided much help with many aspects of the preparation of this thesis, including taking
considerable from her busy schedule to assist with editing and hyphenating.
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Contents
Abstract iv
Acknowledgments v
Contents ix
List of Tables x
List of Figures xv
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Design Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Present Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Sweep/Taper Boundary-Layer Analysis 9
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 The Sweep/Taper Approximation . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.2 Mathematical Development . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Present Program Description . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1 Theory in Detail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.2 Numerical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.5 Summary and Future Improvements . . . . . . . . . . . . . . . . . . . . . . 41
3 Transition Prediction Methodology 43
3.1 Introduction to Boundary-Layer Transition . . . . . . . . . . . . . . . . . . 43
3.2 Transition Analysis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.1 Linear Stability Theory . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.2 The en Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.3 Present Transition Prediction Methodology . . . . . . . . . . . . . . . . . . 49
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3.3.1 Crossflow Instability Calculation . . . . . . . . . . . . . . . . . . . . 49
3.3.2 Streamwise Instability Calculation . . . . . . . . . . . . . . . . . . . 55
3.3.3 3-D Transition Criterion . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.4 Some Real-World Considerations . . . . . . . . . . . . . . . . . . . . . . . . 68
3.4.1 Bugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.4.2 Effects of Bluntness . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.4.3 Non-Adiabatic Wall Conditions . . . . . . . . . . . . . . . . . . . . . 76
3.5 Limitations and Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4 Optimization Techniques 83
4.1 Gradient-based Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.1.1 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.1.2 Sequential Quadratic Programming . . . . . . . . . . . . . . . . . . . 85
4.1.3 Example and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.2 Response Surface Trust Region Methods . . . . . . . . . . . . . . . . . . . . 90
4.2.1 Quadratic Response Surfaces . . . . . . . . . . . . . . . . . . . . . . 91
4.2.2 Kriging Response Surfaces . . . . . . . . . . . . . . . . . . . . . . . . 92
4.3 Nelder-Mead Simplex. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.4 Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.5 Final Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5 Example Design Problem 103
5.1 Description of Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2 Results and Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.2.1 Design 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.2.2 Design 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.2.3 Design 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6 Conclusions 132
6.1 Limitations of the Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.2 NLF Design Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.3 Improvements and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.4 Final Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
A Boundary-Layer Equations 138
A.1 Notes on Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
A.2 Laminar Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
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B Quadratic Response Surface 142
C Ordinary Kriging 148
D Modified Akima Interpolation Method 153
D.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
D.2 Overview of Akima’s Univariate Methods . . . . . . . . . . . . . . . . . . . 155
D.3 Present Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
E Complex-Step Derivative Approximation Method 160
E.1 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
E.2 Implementation Issues and Observations . . . . . . . . . . . . . . . . . . . . 162
E.3 Higher-Order Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
F Shock-Expansion Method 169
G User Manual for the SWPTPRBL Program 172
G.1 Basic Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
G.2 Input File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
G.3 Output File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Bibliography 177
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List of Tables
2.1 Wing drag coefficients: Sweep/taper vs. Navier-Stokes on the Agrawal wing
for 100% laminar and 100% turbulent computations. . . . . . . . . . . . . . 40
4.1 Optimized airfoil coordinates. . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.1 Basic dimensions and properties of baseline configuration. . . . . . . . . . . 104
A.1 Conversion from the conventional cylindrical coordinate variables to Brad-
shaw’s cylindrical coordinates. . . . . . . . . . . . . . . . . . . . . . . . . . . 139
B.1 Coordinates of vertices of the “ideal” simplex up to 7 dimensions. . . . . . . 147
E.1 Execution time penalties for complex-step and algorithmic differentiation
methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
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