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Chapter 1: Introduction AIRFOIL OPTIMIZATION FOR MORPHING AIRCRAFT A Thesis Submitted to the Faculty of Purdue University by Howoong Namgoong In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2005 ii I dedicate this thesis to my father, Young Kyu Namgoong in heaven. iii ACKNOWLEDGMENTS Thanks to God for being my guidance of the journey of life. It has been a privilege to be a student of Drs. William A. Crossley and Anastasios S. Lyrintzis. I was able to open my eyes toward the world of design optimization and morphing aircraft with a tremendous help from Dr. Crossley. I learned great knowledge about aerodynamics and received precious advice from Dr. Lyrintzis. I will cherish and miss the moments that we met together for five years. Special thanks to my committee members, Dr. Scott D. King, Dr. Marc H. Williams and Dr. Terrence A. Weisshaar for their invaluable comments and lectures. I also thank to my colleagues and staffs in Purdue AAE department. This work was partially supported by the Air Force Research Laboratory, contract F33615-00-C-3051, and by a Purdue Research Foundation grant. I would like to share this great moment with my lovely wife, Miran who completes my life, and my beautiful son, Young who gives me another reason for living. I will not forget the support from my three sisters, Ran, Eun and Yoon and my brothers in law. I also like to thank my father and mother in law for their support and prayer. Lastly, my deep appreciation goes to my mother, Mal Soon Park who showed me the meaning of true love. iv TABLE OF CONTENTS Page LIST OF TABLES...........................................................................................................viii LIST OF FIGURES ........................................................................................................... ix ABSTRACT...................................................................................................................... xv CHAPTER 1 INTRODUCTION ....................................................................................... 1 1.1 Background.............................................................................................................. 1 1.1.1 Airfoil Design Methods .................................................................................... 1 1.2 Issues in Airfoil Design Optimization ..................................................................... 4 1.2.1 Objective and Constraint Functions.................................................................. 4 1.2.2 Design Variables............................................................................................... 5 1.2.3 Global Optimization.......................................................................................... 9 1.2.4 Flow Models ..................................................................................................... 9 1.3 Morphing Aircraft.................................................................................................. 11 1.3.1 Return to the First Flight................................................................................. 11 1.3.2 Definition of Morphing Aircraft ..................................................................... 12 1.3.3 Morphing Aircraft Related Programs ............................................................. 12 1.4 Motivation of Research.......................................................................................... 17 1.4.1 Global Optimization Issues in Airfoil Optimization....................................... 17 1.4.2 Morphing Airfoil Design ................................................................................ 18 v Page 1.5 Thesis Objectives................................................................................................... 19 1.6 Thesis Organization ............................................................................................... 19 CHAPTER 2 TRANSONIC AIRFOIL OPTIMIZATION.............................................. 21 2.1 Design Variables.................................................................................................... 22 2.2 Base Airfoils .......................................................................................................... 28 2.3 Trimming ............................................................................................................... 31 2.4 Objective Function................................................................................................. 32 2.5 Accuracy of Function Evaluations......................................................................... 33 2.6 Computational Cost ............................................................................................... 38 2.6.1 Parallel Genetic Algorithm ............................................................................. 38 2.6.2 Gradient Based Optimization Method ............................................................ 40 2.7 Objectives and Fitness Function Formulation ....................................................... 40 2.7.1 Objectives ....................................................................................................... 40 2.7.2 Fitness Function Formulation ......................................................................... 41 2.8 Single-point Optimization Results Comparison .................................................... 43 2.8.1 GA Results...................................................................................................... 43 2.8.2 GM Results ..................................................................................................... 53 2.9 Multi-point Optimization Results Comparison...................................................... 57 2.10 Lessons Learned from GA and GM Results........................................................ 62 2.10.1 Multimodal Design Space............................................................................. 62 2.10.2 Computational Efficiency ............................................................................. 63 2.11 Summary.............................................................................................................. 64 CHAPTER 3 AIRFOIL OPTIMIZATION FOR MORPHING AIRCRAFT.................. 65 3.1 Problem Description .............................................................................................. 65 vi Page 3.2 Objective Function Formulation............................................................................ 67 3.2.1 Aerodynamics Only Investigation (Single-objective Approach).................... 67 3.2.2 Energy Based Optimization (Multi-objective Approach)............................... 68 3.2.3 Multi-objective Optimization.......................................................................... 69 3.3 Design Variables.................................................................................................... 72 3.3.1 Optimization Algorithm.................................................................................. 73 3.3.2 Flow Solver..................................................................................................... 73 3.4 Optimization Results.............................................................................................. 74 3.4.1 Aerodynamic-only Optimization Results ....................................................... 74 3.4.2 Energy Based Optimization Results ............................................................... 76 3.4.3 Cp and Energy Comparison............................................................................. 82 3.5 Transonic Morphing Airfoil................................................................................... 88 3.5.1 Problem Definition.......................................................................................... 88 3.5.2 Objective Function.......................................................................................... 88 3.5.3 Flow Solver, Design method and Parameters................................................. 89 3.5.4 Aerodynamics-only Result.............................................................................. 89 3.5.5 Energy-based Design Results ......................................................................... 91 3.6 Summary................................................................................................................ 99 CHAPTER 4 ACTUATION ENERGY MODELING INCLUDING AERODYNAMIC WORK .................................................................................................... 100 4.1 Description of Concept ........................................................................................ 100 4.2 Formulation.......................................................................................................... 103 4.3 Sensorcraft Problem............................................................................................. 106 4.3.1 Problem Definition........................................................................................ 106 4.3.2 Stiffness Approximation ............................................................................... 107 4.4 Results and Comparison ...................................................................................... 109 vii Page 4.4.1 Effect of Aerodynamic Work Term.............................................................. 109 4.4.2 Effect of Stiffness Change ............................................................................ 122 4.5 Summary.............................................................................................................
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