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A Design Study of Single-Rotor Turbomachinery Cycles

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A Design Study of Single-Rotor Turbomachinery Cycles A Design Study of Single-Rotor Turbomachinery Cycles by Manoharan Thiagarajan A thesis submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Committee Dr. Peter King, Chairman Dr. Walter O’Brien, Committee Member Dr. Clint Dancey, Committee Member August 12, 2004 Blacksburg, Virginia Keywords: Auxiliary power unit, single radial rotor, specific power takeoff, compressor, burner, turbine A Design Study of Single-Rotor Turbomachinery Cycles by Manoharan Thiagarajan Dr. Peter King, Chairman Dr. Walter O’Brien, Committee Member Dr. Clint Dancey, Committee Member (ABSTRACT) Gas turbine engines provide thrust for aircraft engines and supply shaft power for various applications. They consist of three main components. That is, a compressor followed by a combustion chamber (burner) and a turbine. Both turbine and compressor components are either axial or centrifugal (radial) in design. The combustion chamber is stationary on the engine casing. The type of engine that is of interest here is the gas turbine auxiliary power unit (APU). A typical APU has a centrifugal compressor, burner and an axial turbine. APUs generate mechanical shaft power to drive equipments such as small generators and hydraulic pumps. In airplanes, they provide cabin pressurization and ventilation. They can also supply electrical power to certain airplane systems such as navigation. In comparison to thrust engines, APUs are usually much smaller in design. The purpose of this research was to investigate the possibility of combining the three components of an APU into a single centrifugal rotor. To do this, a set of equations were chosen that would describe the new turbomachinery cycle. They either were provided or derived using quasi-one-dimensional compressible flow equations. A MathCAD program developed for the analysis obtained best design points for various cases with the help of an optimizer called Model Center. These results were then compared to current machine specifications (gas turbine engine, gasoline and diesel generators). The result of interest was maximum specific power takeoff. The results showed high specific powers in the event there was no restriction to the material and did not exhaust at atmospheric pressure. This caused the rotor to become very large and have a disk thickness that was unrealistic. With the restrictions fully in place, they severely limited the performance of the rotor. Sample rotor shapes showed all of them to have unusual designs. They had a combination of unreasonable blade height variations and very large disk thicknesses. Indications from this study showed that the single radial rotor turbomachinery design might not be a good idea. Recommendations for continuation of research include secondary flow consideration, blade height constraints and extending the flow geometry to include the axial direction. Acknowledgement The author wishes to express his sincere gratitude to Dr. Peter King, major professor, for contributing valuable time, advice, and assistance to the research and to the preparation of this manuscript. Sincere thanks are due to the members of the author’s graduate committee composed of Dr. Walter O’Brien, and Dr. Clint Dancey for their advice and constructive criticism. The author also is grateful to Phoenix Integration for allowing him to use Model Center for the purpose of optimization to help in the completion of this research project. Very special thanks are due to the author’s parents for their understanding, patience, and encouragement throughout the course of this study. Heartiest thanks are also due to Rene Villanueva, An Song Nguyen, and Kevin Duffy for all their encouragement. Special appreciation goes out to Ms. Lisa Stables for all her assistance during this research. To all turbolabbers, warp speed ahead. Space is the final frontier. iii Table of contents TABLE OF FIGURES ............................................................................................................................................VII LIST OF TABLES.................................................................................................................................................... XI NOMENCLATURE .............................................................................................................................................. XIII CHAPTER 1 INTRODUCTION.........................................................................................................................1 1.1 ABOUT SMALL GAS TURBINE ENGINES ..........................................................................................................1 1.2 AUXILIARY POWER UNIT (APU) AND PURPOSE OF RESEARCH .......................................................................4 CHAPTER 2 LITERATURE REVIEW.............................................................................................................6 2.1 HISTORY OF THE APU...................................................................................................................................6 2.1.1 Project A .........................................................................................................................................6 2.1.2 The Black Box .................................................................................................................................6 2.1.3 The GTC43/44.................................................................................................................................8 2.2 IDEAL BRAYTON CYCLE AND IDEAL JET PROPULSION CYCLE........................................................................9 2.3 HOW CURRENT APUS WORK.......................................................................................................................11 CHAPTER 3 FORMULAS USED FOR THE APU ........................................................................................15 3.1 GENERAL INFORMATION .............................................................................................................................15 3.2 AMBIENT AIR AND DIFFUSER.......................................................................................................................17 3.3 COMPRESSOR ..............................................................................................................................................18 3.4 BURNER AND TURBINE................................................................................................................................22 3.4.1 Burner equations...........................................................................................................................23 3.4.2 Burner input parameters and method of solving equations ..........................................................25 3.4.3 Turbine equations .........................................................................................................................28 3.4.4 Turbine input parameters..............................................................................................................29 3.4.4.1 Subsonic turbine............................................................................................................................................ 30 3.4.4.2 Supersonic turbine ........................................................................................................................................ 31 3.4.5 Method of solving turbine equations.............................................................................................32 3.4.6 Burner and turbine output summary .............................................................................................35 3.5 OVERALL APU PROPERTIES........................................................................................................................37 CHAPTER 4 RESULTS OF ANALYSIS.........................................................................................................39 4.1 SIMPLE ONE-DIMENSIONAL FLOW ...............................................................................................................39 4.1.1 Burner ...........................................................................................................................................40 4.1.1.1 Constant area flow with drag and heat addition ............................................................................................ 40 4.1.1.2 Constant area flow with only heat addition................................................................................................... 41 iv 4.1.2 Variable area flow ........................................................................................................................42 4.2 SINGLE ROTOR APU RESULTS .....................................................................................................................43 4.2.1 Model Center and input/output constraints ..................................................................................43 4.2.2 Results from Model Center............................................................................................................46 4.2.2.1 Case 1: Without the stress and |(P0-P5)/P5| constraints. ................................................................................. 46 4.2.2.2 Case 2: With the stress constraint but without the |(P0-P5)/P5| constraint...................................................... 48 4.2.2.3 Case 3:
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