Development of a Hypersonic Aerothermoelastic Framework and Its Application to Flutter and Aerothermoelastic Scaling of Skin Panels by Daning Huang A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Aerospace Engineering) in the University of Michigan 2019 Doctoral Committee: Professor Peretz P. Friedmann, Chair Professor Carlos E. S. Cesnik Professor Bogdan Epureanu Professor Joaquim R. R. A. Martins Daning Huang [email protected] ORCID iD: 0000-0001-7049-3494 © Daning Huang 2019 To future humans as a multi-planetary species. ii Acknowledgments This dissertation marks a significant milestone in my career. I wish to thank all who made this work possible. First, I wish to sincerely thank my advisor Professor Peretz Friedmann for his guidance and support throughout my graduate studies. His wisdom and insights have significantly influenced my research philosophy and prepared me better to become an independent re- searcher. I am grateful to the members of my doctoral committee, Professor Carlos Cesnik, Professor Joaquim Martins, and Professor Bogdan Epureanu, for their time and effort spent on this research. Particularly, Prof. Cesnik is the first person to introduce me into the field of aeroelasticity and has continuously supported my academic career; Prof. Mar- tins has been very helpful and responsive to my technical and academic requests over the years; Prof. Epureanu’s students have provided valuable insights into my research. I would also like to thank the Aerospace faculty, especially Profs. Anthony Waas and Karthik Du- raisamy, for their help in my academic career. This research was funded through the Francois-Xavier Bagnoud Center for Rotary and Fixed Wing Air Vehicle Design. Partial support was provided by the Rackham Predoctoral Fellowship awarded by the University of Michigan. I would like to express my gratitude to the Multidisciplinary Design Optimization Lab- oratory, led by Prof. Martins, for allowing me to use the ADflow code; also to Dr. Gaetan Kenway and Eirikur Jonsson for their professional help and advice in computational aeroe- lasticity and general software engineering. Dr. Tomer Rokita, who I had the privilege to work with for the past few years, is deeply thanked for his insight and friendship. Prof. Jack McNamara and Dr. Ahbijit Gogulapati are acknowledged for their help and advice con- cerning aerothermoelasticity. Dr. Ryan Klock is thanked for providing me with ABAQUS user functions for aerothermoelastic analysis. I would like to thank all my colleagues in my research group with Prof. Friedmann, for their continued support and understanding throughout our years together: Dr. Michael Chia, Dr. Nicolas Lamorte, Dr. Eric Muir, Dr. Ashwani Padthe, Ryan Patterson, Abhinav Sharma, and Puneet Singh. I would also like to express my appreciation for the kindness and helpfulness of the Aerospace Department staff, especially Denise Phelps, who has been of great help and constant support with the administrative affairs. iii I am also grateful to the friends here at the University of Michigan and across the world for enlightening interactions and friendship. I decided not to put any names here - an exhaustive list would be too long for this section while any omissions would be unfair and inappropriate. The life has been amazing. As a chaotic dynamical system, it brings about the crossing of our trajectories that originate from different parts of the world. Finally, I owe immense gratitude to my parents, Guanle Huang and Minjian Pan, for bringing me to this exciting world and helping me get this far. Last but certainly not least, I thank my significant other, Junyi Geng, for her unwavering love, support, and understand- ing, since our encounter a decade ago. iv TABLE OF CONTENTS Dedication ....................................... ii Acknowledgments ................................... iii List of Figures ..................................... ix List of Tables ...................................... xii List of Appendices ................................... xiii List of Acronyms .................................... xiv List of Symbols ..................................... xvii Abstract ......................................... xxiii Chapter 1 Introduction, Background and Objectives .................... 1 1.1 Challenges in Air-Breathing Hypersonic Flight .............. 1 1.2 Literature Review .............................. 8 1.2.1 Design and Analysis of Hypersonic Structures .......... 8 1.2.2 Fully-Coupled Analysis of Fluid-Structural-Thermal Interaction . 10 1.2.3 Reduced Order Modeling for Hypersonic Aerothermodynamics . 14 1.2.4 Scaling Laws for Aeroelastic and Aerothermoelastic Testing ... 17 1.3 Objectives .................................. 22 1.4 Key Novel Contributions .......................... 23 1.5 Outline of the Document .......................... 24 2 Approaches to Modeling Hypersonic Aerothermodynamics .......... 26 2.1 Governing Equations ............................ 27 2.1.1 The Navier-Stokes Equations ................... 27 2.1.2 Dimensional Analysis of the Fluid Problem ............ 29 2.2 Computational Fluid Dynamics ....................... 32 2.2.1 Compressible Reynolds-Averaged Navier-Stokes Equations ... 32 2.2.2 Arbitrary Lagrangian-Eulerian Formulation ............ 34 2.2.3 Overview of the ADflow Code ................... 37 2.3 Analytical Models .............................. 38 2.3.1 Pressure Distribution ........................ 38 v 2.3.2 Heat Flux Distribution ....................... 41 2.4 Reduced Order Modeling .......................... 42 2.4.1 Modeling Strategies ........................ 42 2.4.2 The POD-Kriging Method ..................... 45 2.4.3 Conventional ROM and Its Limitations .............. 46 2.4.4 Scaled and Corrected Fluid ROM Formulation .......... 48 2.4.5 Efficient ROM Sample Generation ................. 51 3 Structural Dynamic Model ............................ 55 3.1 Governing Equations ............................ 55 3.1.1 Basic Assumptions ......................... 55 3.1.2 Kinematics and Constitutive Relations ............... 56 3.1.3 Hamilton’s Principle ........................ 59 3.1.4 Dimensional Analysis of the Structural Problem ......... 60 3.2 Finite Element Formulation ......................... 64 3.2.1 Element Matrices and Loading Vectors .............. 65 3.2.2 Equations of Motion for the Structural Problem .......... 68 3.2.3 Solution of the Nonlinear Structural Problem ........... 70 4 Heat Conduction Model .............................. 74 4.1 Governing Equations ............................ 74 4.1.1 Heat Conduction in Shallow Shells ................ 74 4.1.2 Dimensional Analysis of the Thermal Problem .......... 77 4.2 Finite Element Formulation ......................... 78 4.2.1 Galerkin Formulation of the Governing Equation ......... 80 4.2.2 Element Matrices and Loading Vectors .............. 81 4.2.3 Equations of Motion for the Thermal Problem ........... 82 4.2.4 Solution of the Nonlinear Thermal Problem ............ 83 5 Fully-Coupled Aerothermoelastic Analysis ................... 86 5.1 Overview of the HYPATE Framework ................... 86 5.2 Exchange of Information Between the Physical Domains ......... 87 5.3 Transient Response ............................. 88 5.3.1 Loosely-Coupled Schemes ..................... 89 5.3.2 Time Accuracy Analysis of Coupling Schemes .......... 92 5.3.3 Energy Balance Analysis of Coupling Schemes .......... 95 5.4 Quasi-Steady Response ........................... 97 5.4.1 Decomposition of Transient Aerothermoelastic Response ..... 97 5.4.2 Linearized Stability Analysis .................... 100 5.4.3 Tightly-Coupled Scheme ...................... 102 5.4.4 Computational Considerations ................... 104 6 Refined Aerothermoelastic Scaling Laws .................... 107 6.1 Analytical Approach Revisited ....................... 107 6.1.1 Dimensional Analysis of the Aerothermoelastic Problem ..... 107 6.1.2 Limitations of Complete Aerothermoelastic Scaling ....... 110 vi 6.1.3 Strategies for Refined Aerothermoelastic Scaling ......... 111 6.2 Two-Pronged Approach for Refined Scaling Laws ............. 112 6.2.1 Objectives ............................. 112 6.2.2 Design Variables and Constraints ................. 114 6.2.3 Formulation of Optimization Problem ............... 115 6.3 Solution Strategies for the MO Problem .................. 116 6.3.1 Surrogate-Based Optimization ................... 118 6.3.2 Multi-Objective Optimization Using the BO Algorithm ...... 120 6.3.3 Implementation Details ....................... 128 7 Verification Results for the HYPATE Computational Framework ....... 130 7.1 Results for Aerothermodynamic Solutions ................. 130 7.1.1 Case Description .......................... 130 7.1.2 Generation of the Fluid ROM ................... 131 7.1.3 The ROM-Based Fluid Solutions ................. 134 7.2 Results for Aeroelastic Response ...................... 138 7.2.1 The CFD-Based Aeroelastic Solutions ............... 138 7.2.2 The ROM-Based Aeroelastic Solutions .............. 141 7.2.3 Linearized Stability Analysis of Panel Flutter Problem ...... 145 7.3 Results for Aerothermoelastic Response .................. 149 7.3.1 Case Description .......................... 149 7.3.2 The CFD-Based Aerothermoelastic Response ........... 149 7.3.3 The ROM-Based Aerothermoelastic Response .......... 153 8 Results for Aerothermoelastic Behavior of Skin Panels ............. 157 8.1 Effect of Boundary Layer Thickness .................... 157 8.1.1