Geometry Control System for Exploratory Shape Optimization Applied to High-Fidelity Aerodynamic ...

157 Pages·2015·7.06 MB·English

Geometry Control System
for Exploratory Shape Optimization
Applied to High-Fidelity Aerodynamic Design
of Unconventional Aircraft
by
Hugo Gagnon
A thesis submitted in conformity with the requirements
for the degree of Doctor of Philosophy
Graduate Department of Aerospace Science and Engineering
University of Toronto
Copyright (cid:13)c 2015 by Hugo Gagnon
Abstract
Geometry Control System
for Exploratory Shape Optimization
Applied to High-Fidelity Aerodynamic Design
of Unconventional Aircraft
Hugo Gagnon
[email protected]
Doctor of Philosophy
Graduate Department of Aerospace Science and Engineering
University of Toronto
2015
This thesis represents a step forward to bring geometry parameterization and con-
trol on par with the disciplinary analyses involved in shape optimization, particularly
high-fidelity aerodynamic shape optimization. Central to the proposed methodology
is the non-uniform rational B-spline, used here to develop a new geometry generator
and geometry control system applicable to the aerodynamic design of both conven-
tional and unconventional aircraft.
The geometry generator adopts a component-based approach, where any number
of predefined but modifiable (parametric) wing, fuselage, junction, etc., components
can be arbitrarily assembled to generate the outer mold line of aircraft geometry. A
unique Python-based user interface incorporating an interactive OpenGL windowing
system is proposed. Together, these tools allow for the generation of high-quality, C2
continuous (or higher), and customized aircraft geometry with fast turnaround.
The geometry control system tightly integrates shape parameterization with vol-
ume mesh movement using a two-level free-form deformation approach. The frame-
work is augmented with axial curves, which are shown to be flexible and efficient at
parameterizing wing systems of arbitrary topology. A key aspect of this methodol-
ii
ogy is that very large shape deformations can be achieved with only a few, intuitive
control parameters. Shape deformation consumes a few tenths of a second on a single
processor and surface sensitivities are machine accurate.
The geometry control system is implemented within an existing aerodynamic op-
timizer comprising a flow solver for the Euler equations and a sequential quadratic
programming optimizer. Gradients are evaluated exactly with discrete-adjoint vari-
ables. The algorithm is first validated by recovering an elliptical lift distribution on
a rectangular wing, and then demonstrated through the exploratory shape optimiza-
tion of a three-pronged feathered winglet leading to a span efficiency of 1.22 under a
height-to-span ratio constraint of 0.1.
Finally, unconventional aircraft configurations sized for a regional mission are
compared against a conventional baseline. Each aircraft is optimized by varying wing
section and wing planform (excluding span) under lift and trim constraints at a single
operating point. Based on inviscid pressure drag, the box-wing, C-tip blended-wing-
body, and braced-wing configurations considered here are respectively 22%, 25%, and
45% more efficient than the tube-and-wing configuration.
iii
À mon grand-père, un inventeur
et ma grand-mère, une colombe
iv
Acknowledgements
I am eternally grateful to Dr. David Zingg for believing in my capabilities and pro-
viding me with a world-class academic environment. His love and passion for science
are contagious, and I feel truly privileged to have benefited from his supervision and
mentorship.
I would like to extend my gratitude to Ms. Joan DaCosta, who has been excep-
tionally welcoming and comforting when I first arrived at the Institute five years
ago. Special thanks to Ms. Gail Holliwell for patiently and professionally handling
all things bureaucratic. I also want to thank Ms. Rosanna McGregor for the relent-
less “good morning!”, which invariably made me smile no matter how tedious my
commute to the Institute was.
ThecamaraderieanddedicationofotherstudentsattheInstitute, especiallythose
from the Computational Aerodynamics Group, has made my stay enjoyable and my
work feasible. There are too many names to enumerate, but I am nevertheless com-
pelled to mention Dr. Jason Hicken, who has been for me a constant source of in-
spiration. To my close friend, David Fernandez, I feel lucky and humbled to have
gotten the chance to know the sophisticated person that you are; to Dr. John Gatsis,
thank you for your continued encouragement and thorough explanation of ILU de-
composition and preconditioning (which is, to this day, the best that I ever had);
to Ramy Rashad, I look forward to continue sharing with you lively discussions on
optimization and aviation in general. I wish you all the very best in life.
On the financial side of things, my gratitude goes to the Governments of Quebec
and Ontario, as well as the University of Toronto.
Finally, but foremost, I would like to acknowledge the unconditional love and
support that I have received from my family. My father has passed onto me the
value of higher education, and my mother has always given me unfaltering strength.
Brothers, thank you for taking interest in what I do. And to you, Nandita, you have
been a pillar in this journey that I shall never forget; thank you for sharing your life,
love, and friendship with me.
Jalal-Hugo Gagnon
University of Toronto Institute for Aerospace Studies
August 2014
v
Contents
Abstract ii
List of Tables viii
List of Figures ix
List of Symbols and Acronyms xi
1 Introduction 1
1.1 The Future of Aviation: an Environmental Perspective . . . . . . . . 1
1.2 A Case for Unconventional Aircraft . . . . . . . . . . . . . . . . . . . 2
1.3 Geometry Control in Shape Optimization . . . . . . . . . . . . . . . . 5
1.4 Thesis Objectives and Outline . . . . . . . . . . . . . . . . . . . . . . 8
2 Generation of Aircraft Geometry 11
2.1 Modeling Paradigms . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Non-Uniform Rational B-Spline Library . . . . . . . . . . . . . . . . . 15
2.3 Component-Based Aircraft Design . . . . . . . . . . . . . . . . . . . . 20
2.4 Object-Oriented Programming Interface . . . . . . . . . . . . . . . . 34
3 Geometry Control System for Shape Exploration 39
3.1 Review of Shape Deformation Techniques . . . . . . . . . . . . . . . . 40
3.2 Two-level Free-Form Deformation . . . . . . . . . . . . . . . . . . . . 44
3.3 Axial Deformation Tailored to Wing Design . . . . . . . . . . . . . . 49
4 High-Fidelity Aerodynamic Shape Optimization 57
4.1 Function Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2 Gradient Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3 Mesh-Movement and Mesh-Adjoint Solution Strategy . . . . . . . . . 64
4.4 Wing Twist Validation . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.5 Three-Pronged Feathered Winglet . . . . . . . . . . . . . . . . . . . . 70
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5 Applications to Unconventional Aircraft Design 77
5.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2 Tube-and-Wing Configuration . . . . . . . . . . . . . . . . . . . . . . 88
5.3 Box-Wing Configuration . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.4 Blended-Wing-Body Configuration . . . . . . . . . . . . . . . . . . . 94
5.5 Braced-Wing Configuration . . . . . . . . . . . . . . . . . . . . . . . 98
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6 Conclusions and Recommendations 105
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
References 129
Appendices 130
A Interactive User Interface 131
A.1 IPython . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
A.2 OpenGL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
B Transformation Matrices 134
B.1 Translation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
B.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
B.3 Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
B.4 Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
C Unconventional Aircraft 136
C.1 Airfoil Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
C.2 3-Views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
C.3 Drag Minimization Convergence Histories . . . . . . . . . . . . . . . . 142
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List of Tables
3.1 Wall-clock time breakdown of axial-curve-driven FFD . . . . . . . . . 55
4.1 Number of FFD volume cross-sections versus span efficiency . . . . . 69
5.1 Total aircraft wetted area . . . . . . . . . . . . . . . . . . . . . . . . 79
5.2 Empty weight per wetted area . . . . . . . . . . . . . . . . . . . . . . 86
5.3 Grid size properties of the aircraft configurations . . . . . . . . . . . 88
5.4 Performance and drag reduction of the unconventional aircraft relative
to the conventional baseline . . . . . . . . . . . . . . . . . . . . . . . 103
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List of Figures
2.1 Effect of weight modification on the shape of a NURBS curve . . . . 17
2.2 Rational basis functions of the red NURBS curve of Figure 2.1 . . . . 18
2.3 B-spline curve fit of a discrete airfoil . . . . . . . . . . . . . . . . . . 22
2.4 Generation of an arbitrary wing surface . . . . . . . . . . . . . . . . . 26
2.5 Merging two wings at their connecting end through shearing . . . . . 27
2.6 Wingtip surface extension created from a network of curves . . . . . . 28
2.7 Side and front views of a fuselage designed using FFD . . . . . . . . . 30
2.8 Three-dimensional rendering of the fuselage shown in Figure 2.7e . . 31
2.9 Wing-fuselage junction reapproximated with a watertight network of
four-sided surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.11 Nacelle geometry generated by revolving an airfoil 360 degrees . . . . 35
2.12 Automatic generation of ribs and spars by linear interpolation . . . . 35
2.13 Partial UML class diagram of the geometry generator. . . . . . . . . . 36
3.1 Surface deformation: from sphere to blended wing-body . . . . . . . . 46
3.2 Volume mesh movement: undeformed and deformed states of the con-
trol and computational grids . . . . . . . . . . . . . . . . . . . . . . . 49
3.3 Axial deformation: a curve deforms an object in 3D space . . . . . . 50
3.4 Axial-curve-driven FFD applied to a generic wing . . . . . . . . . . . 51
3.5 Relativeerrorbetweenanalyticalandfinite-differencedirectionalderiva-
tive as a function of step size . . . . . . . . . . . . . . . . . . . . . . . 55
4.1 Sparsity structure of a stiffness matrix distributed on 5 processors . . 66
4.2 Wing twist validation case setup . . . . . . . . . . . . . . . . . . . . . 67
4.3 Spanwise lift and twist distributions of the twist-optimized wing . . . 68
4.4 Convergence histories of the twist-only optimization . . . . . . . . . . 70
4.5 Feathered winglet shape exploration case setup . . . . . . . . . . . . 72
4.6 Convergence histories of the feathered winglet optimization . . . . . . 73
4.7 Frontal view of the optimized feathered winglet with streamtraces . . 74
4.8 Spanwise lift and drag distributions of the optimized feathered wing . 75
5.1 Tube-and-wing regional aircraft . . . . . . . . . . . . . . . . . . . . . 80
5.2 Box-wing regional aircraft . . . . . . . . . . . . . . . . . . . . . . . . 81
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5.3 Blended-wing-body regional aircraft . . . . . . . . . . . . . . . . . . . 81
5.4 Braced-wing regional aircraft . . . . . . . . . . . . . . . . . . . . . . . 82
5.5 Axial curve setup of the aircraft configurations . . . . . . . . . . . . . 84
5.6 Tube-and-wing upper surface pressure coefficient contours and normal
force distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.7 Close-up of the initial and optimized wingtip extensions . . . . . . . . 91
5.8 Tube-and-wing pressure coefficient section plots . . . . . . . . . . . . 92
5.9 Box-wing upper surface pressure coefficient contours and normal force
distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.10 Box-wing pressure coefficient section plots . . . . . . . . . . . . . . . 95
5.11 Blended-wing-bodyuppersurfacepressurecoefficientcontoursandnor-
mal force distributions . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.12 Blended-wing-body pressure coefficient section plots . . . . . . . . . . 98
5.13 Braced-wing upper surface pressure coefficient contours and normal
force distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.14 Section cut taken inboard of the wing-strut junction of Figure 5.13b . 101
5.15 Braced-wing pressure coefficient section plots . . . . . . . . . . . . . . 102
C.1 Airfoils used to generate the aircraft configurations . . . . . . . . . . 137
C.2 3-view of the initial tube-and-wing aircraft . . . . . . . . . . . . . . . 138
C.3 3-view of the initial box-wing aircraft . . . . . . . . . . . . . . . . . . 139
C.4 3-view of the initial blended-wing-body aircraft . . . . . . . . . . . . 140
C.5 3-view of the initial braced-wing aircraft . . . . . . . . . . . . . . . . 141
C.6 Convergence histories of the tube-and-wing optimization . . . . . . . 142
C.7 Convergence histories of the box-wing optimization . . . . . . . . . . 142
C.8 Convergence histories of the blended-wing-body optimization . . . . . 143
C.9 Convergence histories of the braced-wing optimization . . . . . . . . . 143
x