ABSTRACT Title of Thesis: Modeling and Optimization of Turbine-Based Combined-Cycle Engine Performance Joshua Clough, Master of Science, 2004 Thesis Directed By: Prof. Mark Lewis Aerospace Engineering The fundamental performance of several TBCC engines is investigated from Mach 0- 5. The primary objective of this research is the direct comparison of several TBCC engine concepts, ultimately determining the most suitable option for the first stage of a two-state-to-orbit launch vehicle. TBCC performance models are developed and optimized. A hybrid optimizer is developed, combining the global accuracy of probabilistic optimization with the local efficiency of gradient-based optimization. Trade studies are performed to determine the sensitivity of TBCC performance to various design variables and engine parameters. The optimization is quite effective, producing results with less than 1% error from optimizer repeatability. The turbine- bypass engine (TBE) provides superior specific impulse performance. The hydrocarbon-fueled gas-generator air turborocket and hydrogen-fueled expander- cycle air turborocket are also competitive because they may provide greater thrust-to- weight than the TBE, but require some engineering problems to be addressed before being fully developed. MODELING AND OPTIMIZATION OF TURBINE-BASED COMBINED-CYCLE ENGINE PERFORMANCE By Joshua Clough Thesis submitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillment of the requirements for the degree of Master of Science 2004 Advisory Committee: Professor Mark Lewis, Chair Professor Christopher Cadou Professor Ken Yu ? Copyright by Joshua Clough 2004 PREFACE ?The existing technological ability and scientific background accumulated in many years of work will be lost if a small but continuing effort in this field is not maintained? -Antonio Ferri, speaking on the future of airbreathing engines at the 4 th AGARD Colloquium, in 1960. In the early 1960?s, NASA was working its way to the Moon, with the Apollo program utilizing large rockets to accelerate humans to orbit by brute force and raw power. These efforts, combined with the growing role of ICBMs in the US military, seemingly spelled the end of advanced airbreathing engine research. Yet at the same time, AGARD held its 4 th colloquium, this time focusing on the science and research behind high Mach number air breathing engines. More than 40 years later, we are at a similar cross-roads, where grand interplanetary programs are reducing (if not removing) funding from airbreathing engine research. Yet the science behind these engines has not changed, and airbreathing engines hold as much promise now as they did to Ferri that day in Milan. ii DEDICATION To my grandfather, Poppy, who is part of the reason I am here today. iii ACKNOWLEDGEMENTS This material is based upon work supported by a National Science Foundation Graduate Research Fellowship. Additional support is provided by the Space Vehicles Technology Institute, one of the NASA Constellation University Institute Programs, under grant NCC3-989, with joint sponsorship from the Department of Defense. Appreciation is expressed to Claudia Meyer of the NASA Glenn Research Center, program manager of the University Institute activity, and to Drs. John Schmisseur and Walter Jones of the Air Force Office of Scientific Research. The author would also like to thank Dr. Ryan Starkey of the University of Maryland for the use of his GA optimizer, Bonnie McBride of NASA Glenn Research Center for the use of CEA and Tom Lavelle of NASA Glenn Research Center for his assistance with CEA and engine modeling. On a more personal level, many people aided me, both directly and indirectly, in the completion of this work. I would like to thank my advisor, Mark Lewis, for his guidance, encouragement, and support over the past two and a half years. I would also like to thank Ryan Starkey for all of his help with Linux, optimization, locating sources, and general advice regarding this thesis. I owe a good deal of my sanity over the past years to my office-mates: Neal, Dan, Jesse, Justin, Andrew, Marc, Kerrie, Dave, Amardip, Andy, Greg? thanks for everything. Finally, I would like to thank my wife Ann for her amazing tolerance for ?techno-babble?, putting up with my late nights and early mornings, neck rubs, snacks, and support on every level. Thank you. iv TABLE OF CONTENTS Preface........................................................................................................................... ii Dedication....................................................................................................................iii Acknowledgements...................................................................................................... iv Table of Contents.......................................................................................................... v List of Tables .............................................................................................................viii List of Figures.............................................................................................................. ix List of Symbols........................................................................................................... xii List of Acronyms .......................................................................................................xiii Chapter 1: Introduction................................................................................................. 1 1.1 Background................................................................................................... 1 1.1.1 RLV Concepts....................................................................................... 1 1.1.2 Airbreathing Engines ............................................................................ 1 1.1.3 Combined Cycle Engines...................................................................... 3 1.2 Project Description........................................................................................ 3 1.2.1 Motivation............................................................................................. 3 1.2.2 Objective............................................................................................... 4 1.3 Previous Work .............................................................................................. 5 1.3.1 1913-1960: Early Ramjet and TBCC Development ............................. 5 1.3.2 1960-1990: Apollo, Cold War Era........................................................ 6 1.3.3 1990-Present: RLV Concepts for Access-to-Space .............................. 8 1.3.4 1990-Present: TBCC Engine Studies.................................................. 10 1.3.5 1990-Present: TBCC Engine Comparisons ........................................ 11 Chapter 2: Engine Cycles............................................................................................ 14 2.1 Brayton Cycle ............................................................................................. 14 2.2 Ramjet......................................................................................................... 15 2.2.1 Flowpath ............................................................................................. 16 2.2.2 Operation............................................................................................. 16 2.2.3 Constraints .......................................................................................... 17 2.3 Turbojet....................................................................................................... 18 2.3.1 Flowpath ............................................................................................. 19 2.3.2 Operation............................................................................................. 20 2.3.3 Constraints .......................................................................................... 20 2.4 Turbine-Bypass Engine............................................................................... 21 2.4.1 Flowpath ............................................................................................. 22 2.4.2 Operation............................................................................................. 23 2.4.3 Constraints .......................................................................................... 24 2.5 Air Turborocket .......................................................................................... 25 2.5.1 Gas Generator ATR Flowpath ............................................................ 26 2.5.2 Expander-Cycle ATR Flowpath ......................................................... 27 2.5.3 Operation............................................................................................. 27 2.5.4 Constraints .......................................................................................... 29 Chapter 3: Engine Analysis ........................................................................................ 30 v 3.1 General Analysis......................................................................................... 30 3.2 Component Analysis................................................................................... 32 3.2.1 Inlet ..................................................................................................... 32 3.2.2 Fan/Compressor .................................................................................. 34 3.2.3 Turbine................................................................................................ 34 3.2.4 TBE Bypass Duct................................................................................ 35 3.2.5 Burner/Afterburner/Gas Generator ..................................................... 37 3.2.6 Expander ............................................................................................. 38 3.3 Assumptions................................................................................................ 39 Chapter 4: Engine Optimization ................................................................................. 41 4.1 Program Structure ....................................................................................... 41 4.2 Optimization ............................................................................................... 42 4.2.1 Gradient-Based Optimization ............................................................. 43 4.2.2 Probabilistic Optimization .................................................................. 47 4.2.3 Hybrid Optimization ........................................................................... 50 4.2.4 Objective Function.............................................................................. 51 4.2.5 Rubber Engine .................................................................................... 53 Chapter 5: Optimization Results................................................................................. 55 5.1 Input Conditions.......................................................................................... 55 5.2 TBE Trade Studies...................................................................................... 57 5.2.1 Bypass Ratio ....................................................................................... 57 5.2.2 Compressor Staging Ratio .................................................................. 64 5.2.3 Compressor Efficiency........................................................................ 69 5.2.4 Turbine Efficiency .............................................................................. 72 5.2.5 Fuel Inlet Temperature........................................................................ 74 5.3 GG-ATR Trade Studies .............................................................................. 77 5.3.1 Gas Generator Equivalence Ratio....................................................... 78 5.3.2 Turbine Efficiency .............................................................................. 82 5.3.3 Reactant Inlet Temperature................................................................. 86 5.4 EX-ATR Trade Studies............................................................................... 88 5.4.1 Fuel Inlet Temperature........................................................................ 89 5.4.2 Turbine Efficiency .............................................................................. 92 5.4.3 Chamber pressure................................................................................ 95 5.5 Engine Comparison..................................................................................... 98 5.5.1 Hydrocarbon-Fueled TBCC Comparison ........................................... 99 5.5.2 Hydrogen-Fueled TBCC Comparison .............................................. 102 5.6 Practical Implications of the Air Turborocket .......................................... 105 5.6.1 Turbine Separation / Power Transmission........................................ 106 5.6.2 Turbine-Compressor Balancing........................................................ 108 5.6.3 EX-ATR Fuel Heating ...................................................................... 109 5.6.4 Engine Cooling ................................................................................. 109 5.7 ?Non-rubber? engine performance ........................................................... 110 5.8 Summary................................................................................................... 111 5.8.1 TBE................................................................................................... 111 5.8.2 GG-ATR ........................................................................................... 112 5.8.3 EX-ATR............................................................................................ 113 vi 5.8.4 Overall............................................................................................... 114 Chapter 6: Conclusions............................................................................................. 115 6.1 TBCC Optimization and Comparison....................................................... 115 6.1.1 Compressor Exit Temperature Limit ................................................ 115 6.1.2 Ramjet Threshold.............................................................................. 115 6.1.3 TBCC Comparison............................................................................ 116 6.1.4 Assumed Parameter Sensitivity ........................................................ 118 6.1.5 Fuel Selection.................................................................................... 119 6.2 Accomplishments...................................................................................... 119 6.2.1 TBCC Performance Models.............................................................. 119 6.2.2 Hybrid Optimizer.............................................................................. 120 6.2.3 TBCC Performance Comparison ...................................................... 120 6.3 Future Work.............................................................................................. 121 References................................................................................................................. 123 vii LIST OF TABLES Table 3.1: Assumed stoichiometric fuel ratios ........................................................... 40 Table 4.1: DOT non-default input parameters............................................................ 44 Table 4.2: GA non-default input parameters .............................................................. 49 Table 5.1: TBE bypass ratio trade study input parameters ......................................... 58 Table 5.2: TBE compressor efficiency values ............................................................ 70 Table 5.3: TBE turbine efficiency values ................................................................... 72 Table 5.4: GG-ATR equivalence ratio trade study input parameters ......................... 78 Table 5.5: EX-ATR fuel temperature trade study input parameters........................... 89 Table 5.6: TBCC engine comparison input parameters.............................................. 99 viii LIST OF FIGURES Figure 1.1: Specific Impulse as a function of Mach number for various engines 1 ....... 2 Figure 1.2: Nord Aviation?s Griffon II TBCC-powered aircraft 3 ............................... 6 Figure 1.3: Sketch of P&W J58 ?bleed bypass? engine 9 .............................................. 8 Figure 1.4: SAIC?s ICM-3 RLV concept 12 ................................................................... 9 Figure 1.5: Boeing?s FASST concept 13 ........................................................................ 9 Figure 2.1: Pressure-volume and temperature-entropy diagrams for the ideal Brayton cycle 26 ................................................................................................................. 14 Figure 2.2: Ramjet flowpath ...................................................................................... 15 Figure 2.3: Turbojet flowpath .................................................................................... 19 Figure 2.4: TBE flowpath ........................................................................................... 22 Figure 2.5: GG-ATR (bottom) and EX-ATR (top) flowpaths.................................... 26 Figure 3.1: Inlet diagram............................................................................................. 33 Figure 4.1: TBCC program flowchart......................................................................... 42 Figure 4.2: A comic representation of ?hill-climbing? optimization 33 ....................... 44 Figure 4.3: Graphical representation of constraint tolerance, courtesy of the DOT User Manual 33 ..................................................................................................... 45 Figure 5.1: Specific impulse vs. Mach for TBE with fixed and variable bypass ratios ............................................................................................................................. 58 Figure 5.2: Thrust vs. Mach for TBE with fixed and variable bypass ratios............. 59 Figure 5.3: Bypass ratio vs. Mach for TBE with fixed and variable bypass ratios ... 59 Figure 5.4: Compressor ratio vs. Mach for TBE with fixed and variable bypass ratios ............................................................................................................................. 60 Figure 5.5: Burner equivalence ratio vs. Mach for TBE with fixed and variable bypass ratios........................................................................................................ 60 Figure 5.6: Afterburner equivalence ratio vs. Mach for TBE with fixed and variable bypass ratios........................................................................................................ 61 Figure 5.7: Compressor inlet and exit temperature vs. Mach number for a compression ratio of 1.1...................................................................................... 63 Figure 5.8: Specific impulse vs. Mach for TBE with fixed compressor staging ratios ............................................................................................................................. 65 Figure 5.9: Thrust vs. Mach for TBE with fixed compressor staging ratios ............. 65 Figure 5.10: Bypass ratio vs. Mach for TBE with fixed compressor staging ratios.. 66 Figure 5.11: Compressor ratio vs. Mach for TBE with fixed compressor staging ratios.................................................................................................................... 66 Figure 5.12: Burner equivalence ratio vs. Mach for TBE with fixed compressor staging ratios ....................................................................................................... 67 Figure 5.13: Afterburner equivalence ratio vs. Mach for TBE with fixed compressor staging ratios ....................................................................................................... 67 Figure 5.14: Specific impulse vs. Mach for TBE with varying compressor efficiency ............................................................................................................................. 71 Figure 5.15: Close-up compressor efficiency sensitivity............................................ 72 ix Figure 5.16: Specific impulse vs. Mach for TBE with varying turbine efficiency.... 73 Figure 5.17: Close-up of turbine efficiency sensitivity .............................................. 73 Figure 5.18: Specific impulse vs. Mach for TBE with varying hydrocarbon fuel inlet temperatures........................................................................................................ 75 Figure 5.19: Close-up of specific impulse vs. Mach for TBE with varying hydrocarbon fuel inlet temperatures ................................................................... 75 Figure 5.20: Specific impulse vs. Mach for TBE with varying hydrogen fuel inlet temperatures........................................................................................................ 76 Figure 5.21: Close-up of specific impulse vs. Mach for TBE with varying hydrogen fuel inlet temperatures......................................................................................... 76 Figure 5.22: Specific impulse vs. Mach for GG-ATR with fixed and variable equivalence ratios................................................................................................ 79 Figure 5.23: Thrust vs. Mach for GG-ATR with fixed and variable equivalence ratios ............................................................................................................................. 80 Figure 5.24: Bypass ratio vs. Mach for GG-ATR with fixed and variable equivalence ratios.................................................................................................................... 80 Figure 5.25: Compressor ratio vs. Mach for GG-ATR with fixed and variable equivalence ratios................................................................................................ 81 Figure 5.26: Burner equivalence ratio vs. Mach for GG-ATR with fixed and variable equivalence ratios................................................................................................ 81 Figure 5.27: Specific impulse vs. Mach for GG-ATR with varying turbine efficiency ............................................................................................................................. 83 Figure 5.28: Thrust vs. Mach for GG-ATR with varying turbine efficiency ............. 83 Figure 5.29: Bypass ratio vs. Mach for GG-ATR with varying turbine efficiency.... 84 Figure 5.30: Compressor ratio vs. Mach for GG-ATR with varying turbine efficiency ............................................................................................................................. 84 Figure 5.31: Burner equivalence ratio vs. Mach for GG-ATR with varying turbine efficiency............................................................................................................. 85 Figure 5.32: Specific impulse vs. Mach for GG-ATR with varying hydrocarbon fuel inlet temperature ................................................................................................. 87 Figure 5.33: Specific impulse vs. Mach for GG-ATR with varying hydrogen fuel inlet temperature ................................................................................................. 88 Figure 5.34: Specific impulse vs. Mach for EX-ATR with varying fuel inlet temperature ......................................................................................................... 90 Figure 5.35: Thrust vs. Mach for EX-ATR with varying fuel inlet temperature....... 91 Figure 5.36: Bypass ratio vs. Mach for EX-ATR with varying fuel inlet temperature ............................................................................................................................. 91 Figure 5.37: Compressor ratio vs. Mach for EX-ATR with varying fuel inlet temperature ......................................................................................................... 92 Figure 5.38: Specific impulse vs. Mach for EX-ATR with varying turbine efficiency ............................................................................................................................. 93 Figure 5.39: Thrust vs. Mach for EX-ATR with varying turbine efficiency............. 94 Figure 5.40: Bypass ratio vs. Mach for EX-ATR with varying turbine efficiency ... 94 Figure 5.41: Compressor ratio vs. Mach for EX-ATR with varying turbine efficiency ............................................................................................................................. 95 x Figure 5.42: Specific impulse vs. Mach for EX-ATR with varying chamber pressure ............................................................................................................................. 96 Figure 5.43: Thrust vs. Mach for EX-ATR with varying chamber pressure ............. 97 Figure 5.44: Bypass ratio vs. Mach for EX-ATR with varying chamber pressure.... 97 Figure 5.45: Compressor ratio vs. Mach for EX-ATR with varying chamber pressure ............................................................................................................................. 98 Figure 5.46: Specific impulse comparison for TJ, RJ, and TBCC engines burning hydrocarbon fuel ............................................................................................... 101 Figure 5.47: Thrust comparison for TJ, RJ, and TBCC engines burning hydrocarbon fuel .................................................................................................................... 101 Figure 5.48: Compressor ratio comparison for TJ, RJ, and TBCC engines burning hydrocarbon fuel ............................................................................................... 102 Figure 5.49: Specific impulse comparison for TJ, RJ, and TBCC engines burning hydrogen fuel .................................................................................................... 104 Figure 5.50: Thrust comparison for TJ, RJ, and TBCC engines burning hydrogen fuel ........................................................................................................................... 104 Figure 5.51: Compressor ratio comparison for TJ, RJ, and TBCC engines burning hydrogen fuel .................................................................................................... 105 Figure 5.52: Marquardt's SERJ concept 7 . ................................................................. 107 Figure 5.53: "Gas Generator ATR" flowpath 24 ......................................................... 108 Figure 6.1: Possible engines for first-stage propulsion............................................. 121 xi LIST OF SYMBOLS A x = cross-sectional area at location ?x? a x = speed of sound at location ?x? C px = constant-pressure specific heat of component ?x? f x = fuel ratio of component ?x? g = acceleration due to gravity I sp = specific impulse M x = Mach number at location ?x? x m& = mass flow rate at location ?x? P x = pressure at location ?x? R = ideal gas constant T = thrust T x = temperature at location ?x? u x = velocity at location ?x? ? = bypass ratio ? = shockwave angle ? c = compressor staging ratio ? x = specific heat ratio at location ?x? ? = inert mass fraction ? x = efficiency of component ?x? ? = wedge half-angle ? = payload fraction ? c = compressor pressure ratio ? = standard deviation ? x = equivalence ratio of component ?x? Subscripts 0 = properties at beginning of inlet 2 = properties at beginning of compressor 3 = properties at end of compressor 4 = properties at beginning of turbine 5 = properties at beginning of afterburner 6 = properties at beginning of nozzle 8 = properties at beginning of bypass duct 9 = properties at end of bypass duct AB = afterburner parameters B = burner parameters a = free stream properties e = engine exit properties gg = gas generator properties n = properties normal to a shockwave t = total properties xii LIST OF ACRONYMS ATR Air turborocket CEA NASA?s Chemical Equilibrium with Applications package DOT VMA Engineering?s Design Optimization Tools package EX-ATR Expander-cycle air turborocket GA Genetic algorithm optimization GG-ATR Gas-generator air turborocket GTOW Gross take-off weight MMFD Modified method of feasible directions optimization RBCC Rocket-based combined-cycle RJ Ramjet engine RLV Reusable launch vehicle SSTO Single-stage-to-orbit TBCC Turbine-based combined-cycle engine TBE Turbine-bypass engine TJ Turbojet engine TSTO Two-stage-to-orbit xiii CHAPTER 1: INTRODUCTION 1.1 Background 1.1.1 RLV Concepts In the early days of the American space program, there were two schools of thought regarding space launch: a rocket school that believed a vertically launched, rocket-powered vehicle would be the best way to orbit; and a spaceplane school that believed the optimal launch vehicle would be powered much like a traditional passenger aircraft and fly horizontally, accelerating to orbit. Many aspects of aerospace technology have advanced over the past 50 years yet these two schools of thought still exist. In recent times, however, new concepts have emerged which combine aspects of rocket and airplane operation in order to reduce the cost and increase the safety of space launch. A particular launch vehicle concept that has received considerable attention over the past several years is the two-stage-to-orbit (TSTO) recent reusable launch vehicle (RLV). This system generally takes off horizontally, utilizing airbreathing rocket or turbine engines in the first stage. The second stage separates somewhere between Mach 4-10 and is powered by an airbreathing or pure rocket engine. 1.1.2 Airbreathing Engines Airbreathing engines are used in many RLV concepts because they utilize atmospheric oxygen in combustion, negating the need for stored oxidizer. The elimination of stored oxidizer results in a drastic increase in the fuel-efficiency of the 1 cycle, as shown by the large specific impulse of the airbreathing engines in Fig. 1.1. This benefit brings the promise of lighter, less expensive launch systems with a shorter turnaround time than traditional rocket-based systems. Figure 1.1: Specific Impulse as a function of Mach number for various engines 1 The main disadvantage of air-breathing engines, however, is that no single engine can provide consistent performance across as wide a range of Mach numbers as a rocket. As illustrated in Fig. 1.1, a turbojet is most effective to approximately Mach 3, ramjet to Mach 6, and scramjet possibly to Mach 15 or beyond 1 . A rocket is still required to leave the sensible atmosphere and accelerate to orbital velocity. A launch vehicle trying to use all of these engines separately would, at best, get thrust from one quarter of its engine system at any given time. Alternatively, the combination of multiple engine modes into a single package could produce an engine with a wider operating range, broader performance, and little additional weight. Engines of this type are called ?combined-cycle engines.? 2 1.1.3 Combined Cycle Engines A combined-cycle engine is an engine which integrates the components and operating modes of multiple engines into a single, common flowpath, in order to provide superior performance to any individual engine across a wider flight range. Combined-cycle engines come in two main forms: rocket-based combined-cycle (RBCC) and turbine-based combined-cycle (TBCC). As indicated by their names, RBCC engines integrate airbreathing components and modes with a pure-rocket core, while TBCC engines generally build multiple modes around a turbojet core. RBCC engines begin in ducted rocket (also referred to as ?air-augmented? or ?ejector? rocket) mode, burning stored fuel and oxidizer, to lift off and accelerate to a speed where a ramjet is more effective. In ramjet mode, atmospheric oxygen alone is combusted with fuel, accelerating to hypersonic speeds, where a conversion to scramjet operation is more effective. To reach orbit, a final rocket mode is required. TBCC engines, alternatively, utilize a turbojet mode for low-speed propulsion. 1.2 Project Description 1.2.1 Motivation Despite 50 years of study and development, many questions about TBCC engines remain unanswered. The work discussed here all falls under a single, broad question: are airbreathing engines better suited for launch vehicles than rockets? Looking specifically at TBCC engines, several more questions may be asked: ? Which form of TBCC engine is best? 3 ? What defines the ?best? engine? ? How does engine performance vary with Mach number? ? How does engine performance vary with bypass ratio? ? ?compression ratio? ? ?fuel type? ? ?component efficiency? All of these questions should be addressed before a TBCC-powered RLV can be developed. Computational cycle models provide an inexpensive, powerful means to investigate these engines by addressing the questions above before investing resources into hardware. Although many TBCC engines and vehicles have been studied, such cycle models, which allow for fundamental trade studies on engine performance and direct comparison between engines, are still unavailable. 1.2.2 Objective The objective of this project is to develop a series of fundamental TBCC performance models, in order to better understand the performance trades encountered in the design of these engines, with the goal of selecting the optimum propulsion system for the first stage of a TSTO launch vehicle. The primary contribution of this project will be a direct, ?apples-to-apples? comparison between the most promising TBCC concepts. The design space will be limited to true ?combined-cycle? engines, which utilize turbomachinery in some form and combine all operating modes into a common flowpath that will operate from take-off to Mach 5. As such, scramjet operation will not be considered. This is in line with the 4 conclusions of similar engine research, which shows that 1 st -stage scramjet integration is not feasible for at least another 20 years. 1.3 Previous Work 1.3.1 1913-1960: Early Ramjet and TBCC Development The ramjet was first conceived shortly after the Wright brothers? first flight. Lake patented the first ramjet cycle in the United States in 1909, but France?s Ren? Lorin was the first to publish, in 1913 2 . Both looked only at subsonic flight, and Lorin concluded that performance would be poor. Extensive ramjet ground-testing took place throughout the 20?s and 30?s, but the first successful ramjet flight did not occur until 1940, with the German V-1 ?buzz-bomb?. Ren? Leduc developed the first manned ramjet-powered aircraft in 1935, but due to World War II, didn?t fly the Leduc 010 until 1949 3 . The Leduc 010 had a top speed of Mach 0.84, so while it obviously didn?t take advantage of the benefits of shockwaves for compression, it did demonstrate the feasibility of ramjet propulsion for manned aircraft. It was also immediately apparent that ramjets require separate low-speed propulsion, as the Leduc 010 required a carrier craft to bring it up to speed before the ramjet engine was effective and the aircraft could be released. Addressing this problem, France?s Nord Aviation built on Leduc?s work through the 1950?s, with the development of the Griffon II. As shown in Fig 1.2, the Griffon II used a turboramjet engine, integrating a preexisting turbojet core with an afterburner/ram-burner. Under the power of this turboramjet engine, the Griffon II flew from the ground up to Mach 2.1, demonstrating the feasibility of TBCC engines. 5 Figure 1.2: Nord Aviation?s Griffon II TBCC-powered aircraft As the Griffon II was being built in France, similar designs were proposed in the United States. In 1951, Republic Aviation submitted their design for the turboramjet powered AP-57 (XF-103) to the USAF 4 . The proposed turboramjet used a Wright XJ-67-W-1 core with bypass to an afterburner/ram-burner, but development stopped when their contract was cancelled in 1957. 1.3.2 1960-1990: Apollo, Cold War Era From 1960-1990, combined-cycle engine research was almost non-existent. In the 1960?s and early 1970?s, NASA?s primary focus was on rocket propulsion for the Apollo moon program. Most advanced air-breathing engine research of the 1960?s and 1970?s was focused on ramjets for cruise, as this period also represents the height of the Cold War 5 . Some of the more prominent ramjet-powered cruise missiles were the USAF Bomarc, Navy Talos, and Britain?s Bloodhound. Further information about these missiles and many others can be found in Refs. 3 and 5. Another major focus of advanced airbreathing research during this time was the development of scramjet engines. Scramjet research was the main focus of programs such as NASA?s Hypersonic Research Engine (HRE); the joint Navy, John?s 6 Hopkins/APL SCRAM program; and the National Aero-Space Plane program. There were, however, a few notable programs from 1960-1990 which dealt primarily with combined-cycle engines. Zipkin and Nucci presented their analysis of several ?Composite Airbreathing Systems? at the 4 th AGARD colloquium on ?High Mach Number Airbreathing Engines? in 1960. They performed a vehicle-level analysis to determine the impact of air-breathing/rocket multistage vehicles for satellite launch and long-range cruise. Their analysis was primarily system level, with very little information on the specifics of the airbreathing engines, but they concluded that a horizontally launched air- breathing first stage can provide twice the payload fraction of a traditional, vertically launched rocket 6 . From 1965-1967, under the NASA-sponsored Synerjet program, Marquardt, Rocketdyne, and Lockheed jointly examined several combined-cycle engine and vehicle concepts. This study was originally limited to integrating only ramjet and rocket components, but found that the addition of a low-pressure ratio fan greatly increased the payload capacity of their candidate vehicles. This program also intended to focus on single-stage-to-orbit (SSTO) concepts, but actually found that TSTO vehicles were the only technologically feasible option 7 . One of the most successful TBCC examples from the United States is Lockheed?s SR-71 program, which ran from the early 1960?s to 1989 8 . The SR-71 was propelled by two Pratt & Whitney J58 ?bleed bypass? engines, illustrated in Fig. 1.3 9 . 7 Figure 1.3: Sketch of P&W J58 ?bleed bypass? engine These engines allowed the inlet air to bypass the combustor and turbine by bleeding part of the flow off of the compressor and ducting it back into an afterburner/ram- burner. Powered by the J58 engines, the SR-71 was able to take off and fly up to a top speed of Mach 3+. 1.3.3 1990-Present: RLV Concepts for Access-to-Space Over the past decade, combined-cycle engines have been reexamined for space launch to respond to the demand for cheaper, safer launch vehicles to replace the Space Shuttle. Bowcutt, Gonda, et al. and Hatakeyama, McIver, et al., compared many RLV concepts on the basis of cost, performance, and operational parameters, finding that airbreathing launch systems require almost twice the development costs but half the operating costs of traditional launch systems 10,11 . For a launch program longer than approximately 10 years, the TSTO airbreathing RLV system would be the least expensive of all options. 8 Figure 1.4: SAIC?s ICM-3 RLV concept 12 Figure 1.5: Boeing?s FASST concept SAIC?s ICM-3 concept, Fig. 1.4, is a TSTO RLV utilizing RBCC 1 st -stage propulsion and pure rocket 2 nd -stage. Escher and Christensen concluded that the optimal staging Mach number for this system is Mach 7.2 12 . As illustrated in Fig 1.5, Boeing?s ?Flexible Aerospace System Solution for Transformation? (FASST) concept is similar to the ICM-3, except utilizing a turbojet-powered 1 st -stage and RBCC- powered 2 nd -stage. The staging Mach number for the FASST vehicle was chosen to be Mach 4, the limit of NASA?s Revolutionary Turbine Accelerator (RTA) 1 st -stage engine 13 . A final example of TSTO RLV comes from Mehta and Bowles at NASA Ames, who found that a TBCC-powered 1 st -stage and pure rocket-powered 2 nd -stage, separating at Mach 10, is the best option for reducing the cost and increasing the safety and reliability of space launch 14 . 9 1.3.4 1990-Present: TBCC Engine Studies Bossard and Thomas 15,16 and Christensen 17,18 have published several studies specifically focused on the solid-fuel gas generator air turborocket. This engine is primarily used in missile and rocket applications, but a similar form can be applied to non-military systems. The details of liquid-fueled air turborocket operation will be discussed in the following chapter. In 1997, Bossard and Thomas designed turbomachinery specifically for the solid-fuel air turborocket. They concluded that the fuel type and chemistry drives the turbomachinery design. The use of this turbomachinery for missile propulsion provided three times the thrust of a comparable turbojet and over twice the specific impulse of a comparable pure-rocket system. In 1999, Christensen compared the solid-fuel air turborocket, turbojet, and solid rocket motor on the basis of range and flight time for a missile system. He concluded that, for a given range, the turborocket system reduced the turbojet flight time by a factor of three. Similarly, for a given volume, the turborocket produced double the flight time and range of a solid rocket. Bossard and Thomas studied the influence of turbomachinery characteristics on turborocket performance in 2000. They found that the turborocket is less sensitive to variations in compressor and turbine efficiency, but more prone to problems with surge and stall. Finally, in 2001, Christensen examined the accuracy of different engine chemistry models for the air turborocket turbine. He found that the turbine flow is non-ideal and reacting. An assumption otherwise would falsely predict two separate fuel ratios corresponding to maximum specific impulse, when in reality there is only one. 10 NASA?s now-defunct Revolutionary Turbine Accelerator (RTA) program represents the most recent work in TBCC development in the United States. The goal of this program was to develop a turbine-based engine capable of flying at Mach 4+ with a minimum thrust-to-weight of 7 19 . This program also planned to improve the maintainability and operability of these engines, enabling the ?airplane-like? operation of the RLV concepts mentioned previously. The first stage of the RTA program was the RTA-1 test bed, which was a ?turbofan ramjet? based on an existing General Electric YF120 core. More advanced engines and flight tests were planned, but the program was cancelled in mid-2004. 1.3.5 1990-Present: TBCC Engine Comparisons Several recent studies have compared specific TBCC engines on various benchmarks. In 1990, Stricker and Essman used computational studies to compare dry and afterburning turbojet, turboramjet, and air turborocket engines on the basis of both installed and uninstalled engine performance for both cruise and acceleration. They concluded that, although the air turborocket was able to produce greater thrust at the same specific impulse, the afterburning turbojet was superior because it provided competitive performance with much lower technological risk than the other engines 20 . In 1995, under France?s PREPHA program, Lepelletier, Zendron, et al. compared several RBCC and TBCC engines for SSTO launch systems. They found that despite producing the highest specific impulse, a turbojet-based system was the heaviest of all, to the point of infeasibility. The other concepts were to be studied further; specifically considering an expander-cycle air turborocket in addition to the gas generator air turborocket originally studied 21 . In 2001, Dupolev, Lanshin, et al. 11 compared many international RLV engine and vehicle designs from the past 15-20 years. The designs were compared on the basis of payload fraction and categorized by separation Mach number. For near term technology (2005-2010), it was concluded that a system with a separation Mach number of approximately 6, like Russia?s MIGAKS concept, would be best. For more advanced technological capabilities (2015-2020), the optimal staging Mach number would range between 8 and 10, with a scramjet mode added to the first stage propulsion system 22 . Over the past few years, Japan?s ATREX program has also produced several TBCC analysis projects similar to the one at hand. In 2001, Isomura and Omi, Kobayashi, Sato, and Tanatsugu, and Kobayashi and Tanatsugu all presented their findings from the comparison of TBCC engines for the 1 st -stage of a TSTO RLV 23-25 . Isomura and Omi compared a precooled turbojet and expander-cycle air turborocket up to Mach 6, looking at trade studies on the variation of thrust and specific impulse with fan and compressor pressure ratio, compressor efficiency, turbine inlet temperature, and turbine efficiency. The trade studies showed that improvements in turbine efficiency will do little to improve turborocket performance and that both engines share similar technological limitations. Both engines were able to produce similar thrust at transonic and high-speed conditions, but the turbojet was found to be more efficient below Mach 3 while the turborocket was more efficient above Mach 3 23 . Kobayashi, Sato, and Tanatsugu used genetic algorithm optimization to determine the optimal propulsion system for the 1 st -stage of a TSTO system, based on minimum gross take-off weight (GTOW). Their baseline vehicle was a more traditional cylindrical fuselage, delta-wing configuration with the candidate engines 12 (precooled turbojet, precooled expander-cycle turborocket, precooled gas generator turborocket, and turboramjet) mounted on pylons beneath the wing. They concluded that the turborocket cycles were limited by low turbine efficiency and the precooled turbojet produced the lowest GTOW. The greatest limitation of the Turboramjet was the requirement of a large ram-duct, which could be alleviated with more extensive engine-airframe integration 24 . Kobayashi and Tanatsugu performed a similar analysis, optimizing for maximum payload fraction in stead of minimum GTOW. They concluded that the precooled turbojet was superior to the turborocket and turboramjet cycles, but also examined the limitations of the turborocket cycles more closely. The stored oxidizer required by the gas generator enhanced its ability to maintain a high turbine inlet temperature, but incurred a specific impulse penalty that made it the worst performing option of all. Both the gas generator and expander-cycle turborockets were also limited by the turbine efficiency, but only the expander-cycle would benefit from increased turbine inlet temperature 25 . 13 CHAPTER 2: ENGINE CYCLES 2.1 Brayton Cycle The open Brayton cycle is the ideal thermodynamic cycle upon which all modern aircraft engines are based. The term ?open? refers to the fact that the engine exhaust and inlet are not connected, leaving an open-loop with a constant influx of fresh air. This is in contrast to, for example, the closed-loop refrigeration cycle, where a fixed mass of refrigerant continually flows through the condenser, evaporator, etc. Figure 2.1: Pressure-volume and temperature-entropy diagrams for the ideal Brayton cycle The ideal Brayton cycle, as depicted by T-s and P-v diagrams in Fig 2.1, consists of three basic processes: adiabatic compression (1-2), isobaric heat addition (2-3), and adiabatic expansion (3-4). The term ?open? refers to the fact that the cycle loop is not actually closed from step (4) to step (1). For actual aircraft engines, these processes are, of course, non-ideal and occur in separate engine components. The thermal efficiency of a Brayton cycle engine can be expressed as a function of the compression ratio from step (1) to (2), and the specific heat ratio of the working fluid 26 . 14 ? ? ? 1 1 2 , 1 ? ? ? ? ? ? ? ? ? ? ?= P P Braytonth (2.1) As illustrated by Eq. 2.1, the cycle efficiency of a Brayton engine can be maximized by increasing the pressure as which heat is added. With this relation in mind, aircraft engines will generally attempt to produce the highest pressure ratio possible, in order to attain the highest possible cycle efficiency. As will be seen shortly, however, the pressure ratio is generally limited by other engine constraints. 2.2 Ramjet The ramjet is the simplest form of airbreathing engine. It uses the kinetic energy of the aircraft alone to compress the freestream air, requiring no moving parts. The compression process is performed using shockwaves and/or a diffuser section, converting kinetic energy of the freestream air into internal energy in the form of increased temperature and pressure. As such, ramjets are most effective at high speeds, and cannot produce static thrust. Figure 2.2: Ramjet flowpath 15 2.2.1 Flowpath A typical ramjet flowpath is illustrated in Fig. 2.2. Freestream air (0) passes through the inlet, from stations (1) to (5). Fuel is then mixed and combusted with the inlet air from stations (5) to (6), further increasing its internal energy. After combustion, the hot, high pressure products expand through a nozzle from (6) to (e), converting the increased internal energy to excess kinetic energy. The increase in kinetic energy of the air across the engine produces thrust, propelling the vehicle forward. 2.2.2 Operation For a given trajectory, ramjet performance is defined primarily by the inlet geometry and combustor fuel flow-rate. For this project the inlet geometry is fixed, so the only variable defining ramjet operation is the fuel-air equivalence ratio. The equivalence ratio is defined as a ?ratio of ratios? between the fuel-air ratio seen in the combustor and the stoichiometric ratio for that fuel type. . . stoich burn f f ?? (2.2) Theoretically, equivalence ratio can range from zero to infinity, where ratios above 1.0 are referred to as ?fuel rich? because there will be excess fuel left over after combustion. The use of equivalence ratio, in lieu of fuel-air ratio, in this project allows a more direct comparison between operation with both hydrogen and hydrocarbon fuels, as their stoichiometric fuel-air ratios differ significantly. 16 2.2.3 Constraints At low speeds, RJ performance is limited by the inlet?s ability to provide sufficient pressure ratio to the engine. As discussed for the general Brayton cycle, a lower pressure ratio corresponds to lower cycle efficiency. In general, RJs are best suited to supersonic flight, where the inlet can take advantage of high pressure ratios across shockwaves in the inlet. As indicated in the previous work, subsonic RJ operation is possible, but is more often limited to flight speeds above approximately Mach 2. At high speeds, RJ operation is limited by dissocciative and high temperature effects in the combustor. This constraint is affected by a combination of flight speed and equivalence ratio, generally limiting ramjet operation to approximately Mach 6. At this speed, the temperature in the combustor is high enough that the water produced by the combustion of hydrogen and oxygen will dissociate back into the reactants. Additionally, the reactant molecules will dissociate into their atomic forms, and the energy from combustion will remain stored in the exhaust gas, in stead of being converted to thrust while expanding through the nozzle. Thus, this limit is primarily chemical, not material, in nature. RJit TT ,lim6 ? (2.3) The temperature limit can be alleviated by reducing the strength of the shockwaves in the inlet, thus maintaining supersonic flow throughout the combustor. This type of engine is generally referred to as a ?supersonic combustion ramjet,? or ?scramjet.? Scramjet operation is most effective above Mach 5, so it will not be considered further for this project. 17 2.3 Turbojet The turbojet engine can be defined as a ramjet that has been corrected for low- speed flight. At low speeds, a diffuser alone cannot sufficiently provide the high compression ratio that is required for efficient Brayton cycle operation. A turbojet engine utilizes a mechanical compressor to increase the temperature and pressure of the inlet air, providing a higher pressure ratio than could be delivered by the inlet alone and increasing the overall cycle efficiency. The compressor is driven by a turbine, which draws power from the expansion of combustion products. The use of mechanical compression allows the turbojet to operate at static conditions, as evidenced by most commercial and military aircraft flying today. The temperature increase, and thus pressure ratio, cycle efficiency and operation, of a TJ is primarily limited by the turbine inlet temperature. The heat addition from the combustor must be limited so that the material limits of the turbine are not exceeded. The turbine is made up of many fine blades that operate on the hot gases immediately downstream of the combustor. As such, these blades are more difficult to cool and are more sensitive to high temperature than the combustion chamber itself. The turbine inlet temperature limit is defined by the turbine materials and cooling and is generally lower than the combustion limit seen in a ramjet. Afterburners are sometimes added to turbojets, injecting and combusting additional fuel downstream of the turbine. This increases the temperature of the air further and adds additional fuel mass to the flow, both of which increase the thrust of an engine. Afterburners are most common in military aircraft, which can sometimes afford sacrifices in fuel efficiency in exchange for additional thrust. 18 Figure 2.3: Turbojet flowpath 2.3.1 Flowpath A turbojet flowpath, as shown in Fig. 2.3, begins in the same manner as the ramjet. The freestream air (0) moves across the inlet, from stations (1) to (2), undergoing some compression if the aircraft is in flight. The compressor acts in a similar manner to the inlet, increasing the temperature and pressure of the air from station (2) to (3). The main difference being that the compressor is mechanically driven by the turbine, allowing it to increase the internal energy of the flow, even at zero velocity. The compressed air then enters the combustor, which operates in the same manner as the ramjet. The combustion products then expand through a turbine from stations (4) to (5), whose sole purpose is to drive the compressor. The turbine operates in reverse from the compressor, converting the energy of the combustion products into shaft work. The afterburner acts in the same manner as a ramjet combustor, from stations (5) to (6). Finally, as in the ramjet, thrust is provided by the acceleration of the engine exhaust through a nozzle from stations (6) to (e). 19 2.3.2 Operation As with the RJ, TJ operation is defined by the inlet geometry and fuel-air equivalence ratio. However, the turbomachinery also introduces the compressor pressure ratio as an additional design parameter. The pressure ratio is defined as the fractional increase in total pressure across the compressor. 2 3 t t c P P ?? (2.4) High compressor pressure ratios provide two benefits for TJ operation. By increasing the combustor pressure, they help reduce dissocciative effects and allow for more efficient combustion at higher temperatures. Additionally, high compression ratios lead to higher engine pressure ratios, and, as shown in the Brayton cycle analysis, higher cycle efficiency. High pressure ratios are generally desirable, but a single compressor stage can only provide a finite pressure ratio, so higher pressure ratios also require multiple compressor stages, and thus greater engine weight and complexity. This factor is neglected in the current analysis but is nonetheless important. 2.3.3 Constraints The primary constraint on TJ operation, as mentioned before, is the maximum turbine inlet temperature (T 4 ) limit. turbit TT ,lim4 ? (2.5) For a given inlet and trajectory, T 4 can only be decreased by reducing the compressor pressure ratio or fuel-air equivalence ratio. At very high speeds, the material limit of the compressor is also a factor. Turbines are generally actively cooled, but that is 20 more difficult for a compressor, so its temperature limit is generally lower than that of the turbine. As the air temperature increases across the compressor, this limit is first reached at the compressor exit. compit TT ,lim3 ? (2.6) As the engine analysis will be performed automatically, a negative turbine exit temperature could, hypothetically, be calculated. This would be physically impossible, and in fact, even a very low turbine exit temperature would be unrealistic. Thus, the turbine exit temperature is constrained so that is must be greater than a specified minimum. turb TT min,5 ? (2.7) This constraint is required because otherwise, the computer model could allow a design that combines a high compressor pressure ratio with a low turbine inlet temperature, forcing the turbine to expand to a negative temperature in order to satisfy an energy balance with the compressor. This situation is, of course, physically impossible and, in a real engine, the compressor pressure ratio would be relaxed in order to relieve the requirements on the turbine. However, as that feedback is not present in the engine models here (which will be discussed in detail in the following chapter), a constraint on minimum temperature is required. 2.4 Turbine-Bypass Engine The primary objective of any TBCC engine is to increase the upper speed limit of a traditional turbojet by alleviating or eliminating the turbine inlet temperature limit. The turbine-bypass engine (TBE) does this by bypassing the 21 combustor and turbine altogether at high speeds. The TBE is a form of afterburning turbojet that combines the operation of TJ and RJ cycles. At high speeds, the turbomachinery of the afterburning turbojet becomes less important, as the inlet alone can provide the necessary compression. At this point, the flow through the compressor is ducted around the combustor and turbine, directly into the afterburner. The amount of bypass flow can vary, with increasing amounts causing the afterburner to operate more like a RJ combustor. This operation could theoretically allow a single engine to operate from take-off up to Mach 6, the theoretical limit of RJ performance. Figure 2.4: TBE flowpath 2.4.1 Flowpath Figure 2.4 depicts a typical TBE flowpath. The inlet operates in the same manner as in the ramjet and turbojet, compressing the freestream (0) from station (1) up to the compressor face (2). The first compressor stage compresses the entire inlet flow from location (2) to (8). At this point, bypass flow is bled off of the compressor into the bypass duct. The non-bypass flow will then pass through a second compressor stage, from location (8) to (3). The non-bypass, or ?core,? section of the 22 TBE is simply a TJ engine, and may be treated as such. The non-bypass flow may be treated as compressing in a single step, from (2) to (3). The combustor and turbine of the TBE also act in an identical manner to the TJ. The bypass flow will pass through a duct from (8) to (9), undergoing an area change in order to better condition the flow for the afterburner. The turbine and bypass exit flows then mix and enter the afterburner at station (5). The afterburner, from (5) to (6), and nozzle, stations (6) to (e), act in exactly the same manner as the RJ burner and nozzle. 2.4.2 Operation In addition to the traditional TJ parameters, TBE operation is also characterized by the bypass and compressor staging ratios. The bypass ratio for the TBE is defined as the ratio of bypass mass-flow to inlet mass-flow: 0 m m ? bypass TBE & & ? (2.8) At a bypass ratio of 0, all air will pass through the core and the engine will perform like a pure turbojet engine. At a bypass ratio of 1, all inlet air will move directly to the afterburner and the engine will behave like a ramjet. Intermediate bypass ratios, however, provide the most interest as they combine the operation of both engines, possibly providing performance superior to either engine alone. The TBE uses a two-stage compressor, where the first stage acts on the entire inlet flow and the second stage acts only on the core flow. The first stage is often referred to as a ?fan? because it generally operates with a low pressure ratio and high flow-rate. The distribution between the two compressor stages is characterized by the 23 compressor staging ratio (? c ). The compressor staging ratio is defined as the fraction of compression occurring in the first stage: totalc stgc c , 1., ? ? ? ? (2.9) Variations in compressor staging affect only the bypass flow. At a staging ratio of 0, all compression occurs in the second stage and the bypass flow enters the afterburning without undergoing any mechanical compression. This configuration is sometimes referred to as ?turboramjet?, where a turbojet core is essentially propelling an attached ramjet. This is also the only form of TBE that allows full ramjet operation (?=1), as some non-bypass flow would be required to operate the fan stage for other configurations. At a staging ratio of 1, all compression occurs in the first stage and the inlet flow is compressed entirely before bypass. Assuming a given bypass ratio, the flow into the combustor will always undergo the same total compression for any staging ratio. 2.4.3 Constraints In addition the constraints of the previous engines, the bypass duct introduces constraints that are specific to the TBE. For reasonable engine packaging, the area change in the duct must be lower than a factor of 100 ? representing no more than an order of magnitude change in diameter for an axisymmetric duct. Additionally, to prevent backflow in the bypass duct, the ratio of turbine exhaust pressure to duct exhaust pressure is constrained to be less than 10. As this engine employs a ram- burner (not scram-burner), the bypass velocity is constrained to be subsonic at the duct exit. Finally, the afterburner fuel is assumed to react with only the fresh bypass 24 air, which translates to the afterburner equivalence ratio being less than or equal to the bypass ratio. 10001.0 9 8 ?? A A (2.10) 10 9 5 ? P P (2.11) 0.1 9 ?M (2.12) ??? AB (2.13) 2.5 Air Turborocket While the TBE alleviates the turbine inlet temperature limit of a traditional turbojet by utilizing bypass flow at high speeds, the air turborocket (ATR) eliminates this limit altogether by isolating the turbine from the inlet and compressor flow and supplying it with stored, hot, high pressure gas. The hot gas alone passes through the turbine, which still drives the compressor, drawing inlet air into the combustor, where it reacts with the excess fuel in the hot gas leaving the turbine. The use of this stored gas also requires operation with much lower turbine and compressor pressure ratios, reducing the number of turbomachinery stages, and thus engine weight. This leads to a greater sensitivity to turbine efficiency in the ATR as the turbine working fluid is no longer air. The ATR also addresses the problem of low thrust of the TBE by combining elements of turbojet and rocket engines to produce an engine with higher thrust-to-weight across a wider range of Mach numbers than a traditional turbojet engine, with higher specific impulse than a traditional rocket. 25 The ATR comes in two main forms, characterized by the source of the hot gas. In a ?gas generator ATR? (GG-ATR), the source of this gas is the combustion of stored fuel and oxidizer in a gas generator. An ?expander-cycle ATR? (EX-ATR), on the other hand, utilizes pre-heated fuel alone, likely from engine cooling. This system ultimately serves to decouple the turbine inlet temperature from the flight speed, allowing the engine to operate across a larger range of Mach numbers than a traditional turbojet. Figure 2.5: GG-ATR (bottom) and EX-ATR (top) flowpaths 2.5.1 Gas Generator ATR Flowpath The GG-ATR, shown in the bottom half of Fig. 2.5, provides hot gas to the turbine from a gas generator, at station (4). The gas generator is essentially a rocket chamber immediately upstream of the turbine and is supplied only with stored fuel and oxidizer, at an extremely fuel-rich mixture. Only the gas generator combustion products and excess fuel expand through the turbine, from (4) to (5), providing the necessary shaft work to the compressor. The inlet and compressor operate in the same manner as the turbojet, with a single compressor stage moving inlet air into the 26 combustor, from stations (2) to (3). For the ATR, however, the inlet air flows directly to the afterburner, (5) to (6), where it mixes and burns with the excess fuel leaving the turbine. The afterburner does not have its own fuel injectors. The afterburner and nozzle are again identical to those of the TBE, TJ, and RJ. 2.5.2 Expander-Cycle ATR Flowpath The greatest limitation of the GG-ATR is the use of stored oxidizer, which greatly decreases specific impulse and creates a very high temperature flame in the gas generator. The EX-ATR eliminates these issues by using the expansion of pressurized, pre-heated, but un-combusted fuel to drive the turbine. This removes the need for oxidizer altogether, as combustion only occurs with inlet air in the afterburner. As illustrated in the top half of Fig. 2.5, the EX-ATR is almost identical to the GG-ATR, simply lacking the stored oxidizer and combustion chamber upstream of the turbine. The EX-ATR assumes that the fuel will be used for active cooling, and then pumped into a chamber upstream of the turbine (4) at a high temperature and pressure. The turbine is then powered, as in the GG-ATR, by the expansion of the hot gas. From that point onward, the two ATR cycles are identical in configuration and operation. 2.5.3 Operation Regardless of gas source, ATR cycle performance is characterized by its bypass ratio, which is defined as the ratio of mass-flow through the inlet to mass-flow through the turbine: 27 turbine inlet ATR m m ? & & ? (2.14) Theoretically, the bypass ratio can range anywhere from zero to infinity. At very low bypass ratio values, the majority of the engine mass flow comes from the stored gases, and the ATR will behave like a rocket. Similarly, at higher bypass ratio values, the gas generator or expander will simply act as a fuel injector and the engine will behave similar to a turbojet. This illustrates another major benefit of the ATR over other engines: it can provide higher thrust than a tradition turbojet engine when needed, and then scale back to more efficient operation by simply changing the propellant flow-rates in the engine. It should be noted that the higher thrust modes of the GG-ATR will also give lower specific impulse than a traditional turbojet, as stored oxidizer is being used. As with any turbine-based engine, a compressor pressure ratio and fuel flow rate are also required to fully define the cycle performance. For GG-ATR operation, a fuel-oxidizer equivalence ratio must be specified for the gas generator. This term is defined in the same manner as Eq. 2.2, but with fuel-oxidizer ratios in place of fuel- air. .,2 ,2 stoichO ggO f f ?? (2.15) As the only substance passing through the turbine of an EX-ATR is fuel, its fuel-air ratio is simply the inverse of the bypass ratio. Thus, only the bypass ratio and compression ratio are required to fully define the EX-ATR. 28 2.5.4 Constraints In addition to the applicable constraints from the other engines, the ATR is constrained so that the compressor and turbine exhaust static pressures are essentially equal. This is done to ensure proper mixing of the inlet and gas generator/expander streams, without backflow, and is expressed in Eq. 2.16, below, where ?tol? is a specified tolerance on the pressure difference. tolPP ?? 35 (2.16) Meeting this constraint forces the compressor and turbine to balance, operating in concert as they would in a more traditional engine. This constraint is specifically required for the ATR, and not the other engines, because the ATR compressor and turbine streams are, by definition, decoupled. 29 CHAPTER 3: ENGINE ANALYSIS 3.1 General Analysis Although they have different names, the aforementioned engines are all just variations on the basic afterburning turbojet engine. As such, on a system level, the analysis of each is identical. The thrust analysis presented here will begin at this level, showing the basic equations of motion that are common to all airbreathing engines. Subsequent sections will then address a component level analysis, which will vary from engine to engine. TBCC engine performance is quantified by the thrust and specific impulse. This analysis begins with the familiar thrust equation 27 : ( ) eaeee APPumum=T ??? 00 && (3.1) Equation 3.1 is simplified by assuming an ideal nozzle, where the exhaust expands isentropically to atmospheric pressure, and by defining ? as the relative amount of mass added to the inlet flow while passing through the engine. This parameter accounts for all injected propellants and has distinct, engine-specific forms, as given by Eq. 3.3. ( ) 000 1 umum=T e && ??+ (3.2) () ? ? ? ? ? +??? ? ATR TBEff TJRJf abb b 1 1 , ? ?? (3.3) Thrust is then divided by the inlet mass flow-rate and local speed of sound. The resulting term is referred to as ?normalized thrust? and is a dimensionless quantity 30 that is independent of engine size and vehicle trajectory, allowing for direct comparison between engines in a variety of applications. () 0 0 1 M a u += am T a e a ?? & (3.4) The velocity ratio in Eq. 3.4 can be further dissected using the definition of Mach number: aa eee a e RT? RT?M = a u (3.5) By canceling the ideal gas constant from the numerator and denominator and rewriting the exit temperature in terms of total temperature and Mach number, Eq. 3.5 becomes: ? ? ? ? ? ? ? 2 2 1 1 e 6 aa tee e a e M ? +T? T? M= a u (3.6) A final expression for normalized thrust is derived by inserting Eq. 3.6 into Eq. 3.4 and using the assumption of isentropic expansion to replace T te with T t6 . () 0 2 6 0 2 1 1 1 M M ? +T? T? M+= am T e 6 aa t6 e a ? ? ? ? ? ? ? ? ? & (3.7) Specific impulse is found by multiplying the normalized thrust by the local speed of sound and dividing by the weight flow rate of fuel (or fuel plus oxidizer for rocket systems). ? ? ? ? ? ? ? ? ? g a am T = mg T =I a aox+fuel sp 0. && (3.8) 31 The exit Mach number, required in order to calculate normalized thrust, is derived from the traditional isentropic pressure relation at the nozzle exit plane: 1 26 6 6 2 1 1 ? ? ? ? ? ? ? ? ? ? e e te M ? += P P (3.9) An expression for exit Mach number is found by solving Eq. 3.9 for an ideal nozzle, where P e =P a and P te =P t6 . ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1 1 2 6 6 1 6 ? ? a t6 e P P ? =M (3.10) The atmospheric and freestream properties required for Eqs. 3.7-3.10 are given by the trajectory, which will be discussed shortly. The afterburner exit properties, denoted by subscript ?6,? required in Eqs. 3.7 and 3.10 are found by calculating the temperature, pressure, and Mach number between engine components, starting from the inlet and working downstream. With these component properties, which are the topic of the following section, the values for normalized thrust and specific impulse can be calculated. 3.2 Component Analysis 3.2.1 Inlet The inlet, as shown in Fig. 3.1, is chosen to be a three-shock inlet, consisting of two oblique shocks and a terminating normal shock. When the upstream Mach number normal to a given shock is subsonic, that portion of the inlet is assumed to have no effect on the flow. 32 Figure 3.1: Inlet diagram Each portion of the inlet is treated as a two-dimensional wedge, with a given half- angle (? ). For the two oblique shocks, the shock angle (? ) is found using the tradition ? -? -M relation: () ( ) ( ) ( ) () ()??M? ?M?+ =?? cossin1 sin12 tan 2 11 22 11 ? ? ? (3.11) Once the shock angle has been calculated, the normal component of the Mach number can be calculated, and the properties behind the oblique shock can be found in the same manner as a normal shock 27,28 : ( )?sin 11 MM n = (3.12) 1 1 2 1 2 2 1 1 1 1 2 1 2 2 ? ? ? + = n n n M M M ? ? ? (3.13) ? ? ? ? ? ? ? ? + + = 2 21 2 11 12 1 1 n n M M PP ? ? (3.14) 2 1 2 2 1 2 12 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? = n n M M P P TT (3.15) ()?? ? = sin 2 2 n M M (3.16) Equations 3.12-3.16 are used to find the properties behind the two oblique inlet shockwaves. By definition, the flow upstream of the normal shock is perpendicular to the shock, so Eqs. 3.12 and 3.16 are omitted for that shock. 33 3.2.2 Fan/Compressor For the TBE, the pressure rise across the first compressor stage is given by the total compression ratio and the compressor staging ratio. The temperature rise across the compressor is based on an isentropic relation, accounting for compressor efficiency 29 . cct2t8 ??P=P (3.17) () ? ? ? ? ? ? ? ? + ? = ? 1 1 2 2 1 28 c cc tt TT ? ?? ? ? (3.18) For existing engines, this efficiency is generally known, or at last calculable, but the efficiency in the TBCC engines of this study is unknown. Thus, this value will be treated as an assumed input parameter, and will be the subject of subsequent trade studies. Properties behind the second TBE compressor stage, or behind the entire compressor for the other engines, are found in the same manner as above, with a similarly assumed efficiency. ctt PP ? 23 = (3.19) () ? ? ? ? ? ? ? ? + ? = ? 1 1 2 2 1 23 c c tt TT ? ? ? ? (3.20) 3.2.3 Turbine The temperature change across the turbine is specified by an energy balance between the compressor and turbine. tcpccttptt TCm=TCm ?? && (3.21) Assuming a single turbine stage, Eq. 3.21 can be re-written as follows: 34 tc t c pt pc t4t5 T m m C C T=T ?? & & (3.22) Or, for N compressor stages: ? ? ? ? ? ? ? ? ? ?? N i ti t i pt pc t4t5 T m m C C T=T & & (3.23) From Eq. 3.23, each engine has a unique expression for turbine exhaust temperature, as given below: () () () ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? +? + ? ? ? ? ? ? ? ? ? + ? ? ATRTT C C T TBE TT TT fC C T TJ f TT C C T =T tt pt pc t4 tt tt bpt pc t4 b tt pt pc t4 t5 23 28 83 23 11 1 ? ? (3.24) As in the compressor, an expression for turbine pressure change in terms of temperature change is based on an isentropic relation, accounting for turbine efficiency. 1 4 5 45 4 4 1 1 1 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ??= ? ? ? t t t tt T T PP (3.25) Once again, the exact value of this efficiency is unknown for the TBCCs of this study, and will be an assumed parameter and the subject of subsequent trade studies. 3.2.4 TBE Bypass Duct Assuming uniform density and pressure across the compressor face and unit inlet cross-sectional area, the area of the bypass and core are directly related to the bypass ratio: 35 ?= 8 A (3.26) ??=1 3 A (3.27) The bypass area change is designed such that the duct exhaust velocity will be equal to the turbine exhaust velocity, providing optimal engine efficiency. This design is analogous to the same principle used in the design of a traditional turbofan engine. It should be noted that although the exit velocity of the turbine and duct will be equal, the Mach numbers of each will generally be quite different, as the temperatures, and thus sonic velocities, of the streams will differ. The optimal duct exit area and exit properties will be found by assuming an isentropic area change. The first step in this process is to find the critical (corresponding to M=1) properties, for use as a reference point. ? ? ? ? ? ? ? + + ? 2 8 8 8 2 1 1 1 2 MC ? ? (3.28) ()12 1 88 * 8 8 ? + ? = ? ? CMAA (3.29) CTT 8 * = (3.30) 1 8 * 8 8 ? = ? ? CPP (3.31) * 8 * RTa ?= (3.32) The desired condition for the bypass exit is equal velocity to the turbine exit: 5559 RTMu ?= (3.33) The bypass exit conditions can be found by inserting the desired condition from Eq. 3.33 into the isentropic flow relations, reversing the process of Eqs.3.28-3.32. 36 2 1 8 2 * 98 9 2 1 2 1 ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ?+ = ?? a u M (3.34) ? ? ? ? ? ? ? + + ? 2 9 8 8 2 1 1 1 2 MC ? ? (3.35) ()12 1 1 9 * 9 8 8 ? + ? = ? ? CMAA (3.36) 1* 9 8 8 ? ? = ? ? CPP (3.37) 1* 9 ? = CTT (3.38) 3.2.5 Burner/Afterburner/Gas Generator The mixing and combustion for the burner, afterburner, and gas generator is handled entirely by NASA?s Chemical Equilibrium with Applications (CEA) code 30 . This code calculates the equilibrium chemical and thermodynamic properties of a mixture of gases based on the minimization of Gibb?s free energy. This code is required to determine the thermodynamic properties at the turbine and nozzle inlet, where the presence of fuel and high-temperature combustion products precludes the usual assumption of a specific heat model based on air alone. This is especially important in the turbine analysis for the ATR cycles, where the turbine working fluid is comprised entirely of excess fuel and/or combustion products. Specific details about the analysis behind CEA and its implementation can be found in Ref. 30. Reference 31 gives full details about the input, output, and usage of CEA, but those specifically pertaining to this project are given below. The combustor, gas generator, and afterburner are all modeled as infinite-area- combustor rockets in CEA. For input, CEA requires the mass-fraction and 37 temperature of each reactant, along with a chamber pressure. CEA returns many equilibrium chemical and thermodynamic properties, but the ones of interest for the engine models are: temperature, pressure, constant-pressure specific heat, and specific heat ratio. These properties are calculated at a theoretical throat, as the turbine will have choked flow to prevent backflow, and the afterburner exhausts directly to a supersonic nozzle. CEA also returns a list of all exhaust products and their relative mass fractions. The fuel inlet temperature and ATR chamber pressures are assumed values, while the burner and afterburner pressure and air temperature are based on the compressor and turbine exit properties. The TBE afterburner reactants account for the bypass air, afterburner fuel, and the turbine exhaust products. Similarly, the ATR afterburner models include all turbine exhaust products and the inlet air as reactants. This allows for an accurate model of the excess-fuel combustion of the GG-ATR. 3.2.6 Expander The expander section of the EX-ATR consists of non-reacting flow, but CEA is also employed to calculate the appropriate thermodynamic properties. This process is required because the turbine working fluid in the EX-ATR is pure fuel, so the constant-pressure specific heat and specific heat ratio are unknown. These properties are found by performing an assigned-temperature/pressure problem in CEA. This calculation requires only the fuel temperature and pressure and returns the same equilibrium thermodynamic properties as the combustion model above. 38 3.3 Assumptions Several assumptions have been made to simplify the engine analysis. The ratio of specific heats is assumed constant for each engine component, but allowed to vary between components. As mentioned previously, the specific heat and specific heat ratio of the turbine and nozzle are calculated directly in CEA. For components acting on air alone, Eq. 3.39 gives the specific heat ratio of air as a function of static temperature, and is based on a curve-fit of available data. ()? ? ? ? ? ?? ?= K>TT KT 600ln0.08381.936 6001.4? (3.39) The trajectory for every engine assumes an approximately constant dynamic pressure of about 1 atm., with an acceleration/climb phase up to Mach 2. As mentioned previously, the inlet is chosen to be a three-shock inlet, consisting of an oblique shock, turning shock, and terminating normal shock. When the Mach number normal to any one of these shocks is less than 1.0, that portion of the inlet is assumed to have no effect on the flow. The compressor and turbine are assumed to operate as disc actuators with user-specified efficiencies. The turbine is always assumed to have a moderate exit Mach number of about 0.5, to maintain a high engine exit Mach number. For the TJ and TBE, the compressor exit Mach number should be low for efficient combustion, and is assumed to be 0.05. For the ATR cycles, however, the compressor exhausts to the afterburner so a moderate exit Mach number of 0.5 is assumed, similar to the turbine. 39 Combustion is permitted with either hydrogen or hydrocarbon fuel. For hydrocarbon combustion, gaseous Jet-A is the assumed fuel. Table 3.1 gives the stoichiometric fuel-air and fuel-oxygen ratios assumed for each fuel. Table 3.1: Assumed stoichiometric fuel ratios Fuel Type Stoich. Fuel-Air Ratio Stoich. Fuel-O 2 Ratio H 2 0.0289 0.125 Jet-A 0.0678 0.293 For the TJ, RJ, and TBE burners, GG-ATR gas generator, and TBE afterburner, a fuel inlet temperature of 200 K is assumed. The ATR afterburners calculate the fuel temperature directly from the turbine exhaust. The GG-ATR gas generator pressure is assumed to be 4000 kPa (about 40 atm.). This is comparable to the gas generator pressure in the Atlas rocket 32 . As it has no combustor upstream of the turbine, the EX-ATR assumes the fuel has been used for active cooling, with an inlet temperature on the order of 1000 K, and a pressure of 2000 kPa. With the exception of the GG- ATR chamber pressure, the aforementioned values have been chosen as educated, but somewhat arbitrary estimations, and will be the subject of trade studies in Chap. 5. 40 CHAPTER 4: ENGINE OPTIMIZATION 4.1 Program Structure The TBCC engine analysis and optimization is performed using a custom computer code written in a combination of FORTRAN, C, and C++. All new code for this project, which includes the driver routine, engine models, and subroutine interfaces, is written in C++. The code also utilizes CEA and pre-existing optimization subroutines, which are written in FORTRAN 77 and C. The code performs a quasi one-dimensional thermodynamic cycle analysis, calculating the pressure, temperature, and Mach number at each position in the flowpath in order to calculate normalized thrust and specific impulse, as given by Eqs. 3.7 and 3.8, respectively. This process is repeated for a user-defined range in Mach number, such that the output consists of a list of optimum values of normalized thrust, specific impulse, and the design variables, corresponding to each value of Mach number. The code is modular, with separate driver, optimization, and analysis routines linked as shown in Fig. 4.1. The driver routine reads the main input file, in which the user specifies the engine cycle, fuel type, optimization method, Mach number range and discretization, and limits on each design variable. The driver repeats the optimization process across the user-specific range of Mach numbers, calling the appropriate optimizer, reading the optimization results, and writing them to the output file. The optimization routines communicate with each engine module separately, which, in turn, communicates directly with CEA, as needed. 41 TBCC TBCC Driver Input Output Routine Figure 4.1: TBCC program flowchart 4.2 Optimization The engine analysis is approached as an optimization problem, where the bypass ratio, compressor pressure ratio, and fuel flow rates are treated as design variables, optimized in order to maximize a given objective function at each value of Mach number, while also satisfying the constraints given in Chap.2. As such, the model produces the best possible engine performance for the given flight Mach number and component limits. The driver program allows the user to specify one of three optimization schemes: gradient-based, probabilistic, or a hybrid optimizer that combines the two. The hybrid scheme is used exclusively in this project, as it combines the strengths and combats the weaknesses of its component methods. The other methods may still be CEA Optimizer DOT GA Loop for M min