AEROTHERMODYNAMIC CYCLE DESIGN AND OPTIMIZATOIN METHOD FOR AICRAFT ENGINES A Thesis Presented to The Academic Faculty by Sean T Ford In Partial Fulfillment of the Requirements for the Degree Masters of Science in the School of Aerospace Engineering Georgia Institute of Technology December 2014 Copyright © 2014 by Sean T Ford AEROTHERMODYNAMIC DESIGN AND OPTIMIZATION METHOD FOR AIRCRAFT ENGINES Approved by: Dr. Dimitri Mavris, Advisor School of Aerospace Engineering Georgia Institute of Technology Dr. Brian Kestner GE Aviation Dr. Jeff Schutte School of Aerospace Engineering Georgia Institute of Technology Date Approved: 31 July 2014 ACKNOWLEDGEMENTS There are many people I would like to acknowledge, who without their support I would not have come so far. First is my advisor Professor Dimitri Mavris who provided me with the opportunity to pursue this thesis and has guided me on many aspects of not just this thesis but my education. His tireless leadership and mentorship has been a great source of encouragement. He has taught me not only the skills and knowledge to be a better engineer, but a better overall person. I would also like to acknowledge the community at ASDL including Dr. Jeff Schutte. They have been an amazing source of help and guidance throughout this process. And last but most definitely not least I would like to acknowledge Dr. Brian Kestner. He has been a constant source of help through this thesis and my education at Georgia Tech. He has been instrumental in helping me push further than I thought possible. Without his help and occasional kicks in the right direction I would not have made it so far. iii TABLE OF CONTENTS ACKNOWLEDGEMENTS ........................................................................................................... iii LIST OF TABLES ....................................................................................................................... viii LIST OF FIGURES ....................................................................................................................... ix NOMENCLATURE ...................................................................................................................... xi CHAPTER 1: Introduction and Motivation .................................................................................... 1 1.1 The Need for a New Engine Architecture ................................................................. 2 1.2 The Need for an Optimization Method ..................................................................... 4 CHAPTER 2: Background Information.......................................................................................... 6 2.1 Variable Cycle Engines and Variable Geometry ...................................................... 7 2.1.1 VCE History.............................................................................................................. 7 2.1.2 Variable Geometry .................................................................................................... 8 2.1.2.1 Variable Area Bypass Injector ........................................................................... 8 2.1.2.2 Variable Area Nozzle ........................................................................................ 9 2.1.2.3 Variable Inlet Guide Vanes ............................................................................. 10 2.1.2.4 Variable Nozzle Area Turbine ......................................................................... 11 2.2 Current Paradigms in Aero Propulsion Design and Cycle Analysis ....................... 12 2.3 Optimization Techniques for an Engine Model ...................................................... 15 2.4 Research Questions and Hypotheses ...................................................................... 19 CHAPTER 3: Research Formulation ............................................................................................ 23 3.1 Solver Based Optimization Overview .................................................................... 23 iv 3.1.1 SBO Process............................................................................................................ 25 3.1.1.1 Objective Identification and Definition of Optimum ...................................... 26 3.1.1.2 Setup ................................................................................................................ 27 3.1.1.3 Execution ......................................................................................................... 28 3.1.2 MDP ........................................................................................................................ 28 3.1.2.1 Requirements and Technology Definition Phase ............................................ 28 3.1.2.2 Setup Phase ...................................................................................................... 28 3.1.2.3 Execution Phase ............................................................................................... 29 3.1.2.4 MDP Initial Iterate ........................................................................................... 29 3.2 Theoretical Framework ........................................................................................... 30 3.2.1 Thrust and Efficiency .............................................................................................. 31 3.2.2 Cycle Solver: Modified Newton-Raphson Method ................................................ 35 3.2.3 Local Linear Approximation................................................................................... 38 3.2.4 Mathematical Treatment of Optimization Problem ................................................ 39 3.2.5 Practical Treatment of Optimization Problem ........................................................ 40 3.3 Assumptions and Limitations ................................................................................. 42 3.4 OMDP Optimization Strategies .............................................................................. 43 3.5 Procedure ................................................................................................................ 44 CHAPTER 4: Implementation ...................................................................................................... 46 4.1 Modeling Environment ........................................................................................... 46 4.2 SBO Setup for NPSS .............................................................................................. 47 4.3 Selection of Objective Function and Optimization Variables ................................ 49 4.4 Model Concepts ...................................................................................................... 50 4.4.1 Analytical Model Description and Solver Setup .................................................... 50 4.4.2 SFTF Engine Model Description and Solver Setup ................................................ 53 v 4.4.2.1 Solver Setup for SBO with SDP ...................................................................... 55 4.4.2.2 Solver Setup for OMDP .................................................................................. 56 CHAPTER 5: Results ................................................................................................................... 60 5.1 Experiments 1-3, Solver Based Optimization Proof of Concept ............................ 60 5.1.1 Setup and Implementation ................................................................................... 60 5.1.2 Results ................................................................................................................. 61 5.2 Experiment 4, SDP Engine Model Optimization .................................................... 66 5.2.1 Setup and Implementation ................................................................................... 67 5.2.2 Results ................................................................................................................. 68 5.3 Experiments 5-10: Engine Model Optimization with SBO and OMDP ................. 71 5.3.1 Experiment 5: Intra-point Optimization, Single Variable, Single Objective .......... 73 5.3.1.1 Results ............................................................................................................. 73 5.3.2 Experiment 6 Cross-point Optimization, Single Variable, Single Objective ......... 76 5.3.3 Experiment 7: Intra-point Optimization, Multi-variable, Multi-objective.............. 80 5.3.4 Experiment 8: Cross-point Optimization, Multi-variable, Single Objective .......... 86 5.3.4.1 Results ............................................................................................................. 86 5.3.5 Experiment 9: Cross-point Optimization, Single Variable, Multi-objective .......... 90 5.3.5.1 Results ............................................................................................................. 91 5.3.6 Experiment 10: Optimization Starting Point Study ................................................ 91 CHAPTER 6: Conclusions ........................................................................................................... 96 6.1 Research Questions and Hypotheses ...................................................................... 96 6.2 Research Contributions ........................................................................................... 97 6.3 Recommendations for Future Work.......................................................................