Interactions between Flight Dynamics and Propulsion Systems of Air-Breathing Hypersonic Vehicles by Derek J. Dalle A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Aerospace Engineering) in the University of Michigan 2013 Doctoral Committee: Professor James F. Driscoll, Chair Michael A. Bolender, Air Force Research Laboratory Associate Professor Joaquim R. R. A. Martins Assistant Professor David J. Singer ©Derek J. Dalle 2013 DEDICATION This dissertation is dedicated to Sara Spangelo, who showed me that graduate school is more than fun, games, doing re- search, and writing papers. Among other things, it was also a lot of running, eating, running, and making pretty graph- ics. She also strongly recommended that I dedicate this dis- sertation to her. ii Acknowledgments I would like to thank Professor Driscoll for guiding me through the Ph.D. program and being a great advisor. My experience here was about as close to perfect as I could hope to expect, and Jim is more responsible for that than anyone else. My colleague Dr. Sean M. Torrez, who was also a Ph.D. student of Professor Driscoll, was essential in the creation of the MASIV and MASTrim models. Also, we made a very good team. I would also like to thank my committee for their support and work in reviewing my thesis. This research was funded by the Air Force Research Laboratory/Air Vehicles Directorate grant FA 8650-07-2-3744 for the Michigan/AFRL Collaborative Center in Control Sciences. iii TABLE OF CONTENTS Dedication ....................................... ii Acknowledgments ................................... iii List of Figures ..................................... vii List of Tables ...................................... x List of Appendices ................................... xi List of Abbreviations ................................. xii Nomenclature ..................................... xiii Abstract ......................................... xvii Chapter 1 Introduction ..................................... 1 1.1 Motivation..................................2 1.2 Background.................................5 1.2.1 Applications............................6 1.2.2 Component Analysis........................6 1.2.3 Flight Dynamics..........................9 1.2.4 Coupling between Propulsion and Flight Dynamics........ 11 1.2.5 Vehicle Sizing........................... 12 1.2.6 Optimization............................ 14 1.2.7 Economics............................. 15 1.3 New Aspects................................ 16 1.4 Outline................................... 17 2 Dual-Mode Ram-Scramjet Models ......................... 18 2.1 SAMURI: A Method for 2D Supersonic Flow............... 19 2.1.1 Oblique Shocks and Discretized Expansion Fans......... 20 2.1.2 Riemann Interactions........................ 23 2.1.3 Compressible Boundary Layers.................. 25 2.1.4 Algorithm.............................. 26 2.1.5 Range of Model Validity...................... 27 2.2 Inlet..................................... 30 iv 2.2.1 Comparison to 2D CFD...................... 34 2.2.2 Comparison to Experimental Data................. 35 2.2.3 Inlet Design Methodology..................... 37 2.3 Isolator................................... 40 2.4 Combustor.................................. 42 2.5 Nozzle.................................... 45 3 Dual-Mode Ramjet-Scramjet Vehicles ....................... 49 3.1 Vehicle Design............................... 50 3.1.1 Fuselage Design.......................... 51 3.1.2 Control Surfaces.......................... 52 3.1.3 Mass Properties and Center of Mass................ 53 3.2 External Aerodynamics........................... 55 3.3 Engine Integration.............................. 57 4 Flight Dynamics of Hypersonic Vehicles ...................... 60 4.1 Equations of Motion............................ 60 4.1.1 State Variables and Control Variables............... 61 4.1.2 Trimmed Flight Conditions.................... 63 4.1.3 Linearized Equations........................ 63 4.2 Operating Maps............................... 64 4.3 Turning Flight................................ 68 4.4 Summary.................................. 76 5 Unstart and Ram-Scram Transition ........................ 78 5.1 Introduction................................. 78 5.2 Ram-Scram Transition and Unstart..................... 81 5.3 Ram Mode and the MASIV Combustor Model............... 86 5.3.1 The MASIV Engine Unstart Method................ 86 5.3.2 Ram-Scram Predictions for a Lab-Scale Geometry........ 87 5.4 Vehicle results................................ 89 5.4.1 Unstart margin for the MAX-1 vehicle............... 89 5.4.2 Ram-scram Transition....................... 92 5.4.3 Jumps at the Ram-Scram Boundary................ 98 5.4.4 Region of Potential Instabilities.................. 100 5.5 Conclusions................................. 100 6 Trajectory and Design Optimization ........................ 102 6.1 Accelerating Trajectories.......................... 102 6.1.1 Trajectory Objective Functions................... 104 6.1.2 Optimal Control of Accelerating Trajectory............ 105 6.1.3 Numerical Calculation of Fuel Consumption........... 107 6.2 Sensitivities to Design Parameters..................... 109 6.2.1 Center of Mass........................... 110 6.2.2 Change in Mass........................... 113 6.2.3 Dihedral Angle........................... 115 v 6.2.4 Design Mach Number....................... 115 6.2.5 Inlet Compression Ratio...................... 120 6.2.6 Number of Inlet Ramps...................... 122 6.2.7 Conclusions from Stability Analysis................ 123 6.2.8 Performance............................ 123 6.3 Trajectory Optimization........................... 128 6.3.1 Minimum-Fuel Acceleration Profile................ 129 6.3.2 Effect of Dynamic Pressure.................... 131 6.3.3 Sensitivity of Total Fuel Consumption to Acceleration Profile.. 133 6.4 Cooptimization of Inlet and Trajectory................... 135 6.4.1 Optimization Methodology..................... 135 6.4.2 Discussion............................. 137 6.5 Conclusions................................. 139 7 Conclusions and Future Work ........................... 141 7.1 Summary.................................. 141 7.2 Future Work................................. 143 7.2.1 Three-Dimensional Extension to SAMURI............ 143 7.2.2 Improved Injection and Mixing Modeling............. 145 7.2.3 Flamelet Table Reduction..................... 145 7.2.4 Generic Vehicle Generation and Integration............ 145 7.3 Conclusions................................. 146 7.4 Closing................................... 147 Appendices ....................................... 148 Bibliography ...................................... 176 vi LIST OF FIGURES 1.1 Approximate efficiency (specific impulse) as a function of Mach number for various aerospace propulsion systems.......................3 2.1 Information flow in dual-mode ramjet/scramjet.................. 19 2.2 Two diamond airfoils, M1 = 2, α = 0....................... 20 2.3 Angle and Mach number definitions for an oblique shock............ 21 2.4 Control volume for discretized expansion with nexp = 1............. 22 2.5 Sketch of Riemann interaction........................... 23 2.6 Sketch of the boundary layer model at vertices.................. 25 2.7 Step-by-step example of SAMURI algorithm: input through step 2....... 28 2.8 Step-by-step example of SAMURI algorithm: step 2 through solution...... 29 2.9 Definitions for inlet design methodology..................... 32 2.10 Contours of temperature in Kelvins for a sample inlet solution.......... 33 2.11 Comparison of commercial CFD package (CFD++®) and SAMURI inlet so- lution: temperature for M1 = 10, α = 0...................... 34 ◦ 2.12 SAMURI solution for the Emami et al. geometry with θcowl = 6:5 ....... 35 2.13 Comparison of experiment and SAMURI inlet models.............. 36 2.14 Inlet efficiency for single-condition and multi-condition designs......... 38 2.15 Wedges traced by inlet shockwaves over a range of M1 and α.......... 38 2.16 Sketch of inlet design conditions and actual envelope............... 40 2.17 Sketch of isolator shock train types and idealization............... 41 2.18 Comparison of SAMURI results to CFD++® for the scramjet nozzle of San- giovanni et al.................................... 45 2.19 Contours of normalized temperature (T=T1) computed by SAMURI for flow in a plug nozzle at two pressure ratios....................... 47 2.20 Comparison of plug nozzle surface pressure for design case (p0;i=p1 = 60)... 48 2.21 Comparison of plug nozzle surface pressure for off-design case (p0;i=p1 = 10). 48 3.1 View of MAX-1 vehicle with stylized shocks and exhaust plume........ 49 3.2 Baseline MAX-1 flowpath dimensions. Engine width is 2.143 m........ 50 3.3 Two views of the MAX-1 vehicle showing fuselage dimensions......... 51 3.4 Tail region of MAX-1 vehicle showing positive control surface deflections... 53 3.5 Upper surface of MAX-1 vehicle showing triangulated surface......... 56 3.6 MAX-1 vehicle geometry with engine flowpath surfaces highlighted in red... 57 3.7 Overview of information flow within the MASTrim program.......... 59 vii 4.1 Operating map for steady, level flight for the MAX-1 vehicle assuming equa- torial (L = 0), eastward (χ = 90◦) flight conditions................ 65 4.2 Operating map for steady, level flight for the MAX-1 vehicle assuming con- stant dynamic pressure (q = 100 kPa) and equatorial (L = 0), eastward