the discrete adjoint approach to aerodynamic shape optimization

275 Pages·2003·2.3 MB·English

THE DISCRETE ADJOINT APPROACH TO
AERODYNAMIC SHAPE OPTIMIZATION
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
Siva Kumaran Nadarajah
January 2003
(cid:176)c Copyright by Siva Kumaran Nadarajah 2003
All Rights Reserved
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I certify that I have read this dissertation and that, in
my opinion, it is fully adequate in scope and quality as a
dissertation for the degree of Doctor of Philosophy.
Antony Jameson
(Principal Adviser)
I certify that I have read this dissertation and that, in
my opinion, it is fully adequate in scope and quality as a
dissertation for the degree of Doctor of Philosophy.
Juan Alonso
I certify that I have read this dissertation and that, in
my opinion, it is fully adequate in scope and quality as a
dissertation for the degree of Doctor of Philosophy.
Robert MacCormack
Approved for the University Committee on Graduate
Studies:
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To My Parents,
T.C. Nadarajah and Sushila
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Abstract
A viscous discrete adjoint approach to automatic aerodynamic shape optimization is
developed, and the merits of the viscous discrete and continuous adjoint approaches
are discussed. The viscous discrete and continuous adjoint gradients for inverse de-
sign and drag minimization cost functions are compared with finite-difference and
complex-step gradients. The optimization of airfoils in two-dimensional flow for in-
verse design and drag minimization is illustrated. Both the discrete and continuous
adjoint methods are used to formulate two new design problems. First, the time-
dependent optimal design problem is established, and both the time accurate discrete
and continuous adjoint equations are derived. An application to the reduction of the
time-averaged drag coefficient while maintaining time-averaged lift and thickness dis-
tribution of a pitching airfoil in transonic flow is demonstrated. Second, the remote
inverse design problem is formulated. The optimization of a three-dimensional bicon-
vex wing in supersonic flow verifies the feasibility to reduce the near field pressure
peak. Coupled drag minimization and remote inverse design cases produce wings
with a lower drag and a reduced near field peak pressure signature.
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Acknowledgments
I would like to express gratitude to my mentor, Professor Antony Jameson, whose
expertise,understanding,andpatienceaddedconsiderablytomygraduateexperience.
His vast knowledge and enthusiasm have inspired me greatly, and I thank him for his
time and support.
A very special thanks to Dr. Juan Alonso. He provided me with direction, techni-
cal support and became a mentor and friend. I would like to thank the other members
ofmycommittee, Dr. IlanKroo, Dr. RobertMacCormack, andDr. MichaelSaunders
for the assistance they provided at all levels of the research project. This research
would not have been possible without the financial assistance of the Airforce Of-
fice of Scientific Research (AFOSR Grant No: F49620-98-1-022), Defense Advanced
Research Project Agency (DARPA Grant No: MDA972-01-2-0003), Advanced Simu-
lation and Computing: Department of Energy (ASC Grant No: B341491), and Mark
Yong.
I have enjoyed the encouragement and warm company of my colleagues in the
Aerospace Computing Laboratory. A special thanks to Sangho Kim for the fruitful
conversationsaboutoptimizationandtoMatthewMcMullenforthemanydiscussions
on research. Matt’s humor was a wonderful distraction from work.
Life in the San Francisco Bay Area would have been meaningless without the love
and friendship of the Sai Bay Area Young Adults. I cherish the hours of serving the
community with such kind and loving friends. I am grateful to my Guru Sri Sathya
Sai Baba for inspiring me to believe in high ideals and to live up to what I believe in.
My dream is to make my life Your message.
I am eternally grateful to my parents, T.C. Nadarajah and Sushila Nadarajah,
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and my family for their unconditional love. Thanks for encouraging me to be an
independent thinker and having confidence in my abilities to go after new things that
inspired me.
Above all, I thank Lisa Steffen, my wife and best friend, for her unbounded love
and confidence in me. Lisa gives me something to look forward to each and every
day.
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