AN INVESTIGATION OF THE PERFORMANCE POTENTIAL OF A LIQUID OXYGEN EXPANDER CYCLE ROCKET ENGINE by DYLAN THOMAS STAPP RICHARD D. BRANAM, COMMITTEE CHAIR SEMIH M. OLCMEN AJAY K. AGRAWAL A THESIS Submitted in partial fulfillment of the requirements for the degree of Master of Science in the Department of Aerospace Engineering and Mechanics in the Graduate School of The University of Alabama TUSCALOOSA, ALABAMA 2016 Copyright Dylan Thomas Stapp 2016 ALL RIGHTS RESERVED ABSTRACT This research effort sought to examine the performance potential of a dual-expander cycle liquid oxygen-hydrogen engine with a conventional bell nozzle geometry. The analysis was performed using the NASA Numerical Propulsion System Simulation (NPSS) software to develop a full steady-state model of the engine concept. Validation for the theoretical engine model was completed using the same methodology to build a steady-state model of an RL10A-3- 3A single expander cycle rocket engine with corroborating data from a similar modeling project performed at the NASA Glenn Research Center. Previous research performed at NASA and the Air Force Institute of Technology (AFIT) has identified the potential of dual-expander cycle technology to specifically improve the efficiency and capability of upper-stage liquid rocket engines. Dual-expander cycles also eliminate critical failure modes and design limitations present for single-expander cycle engines. This research seeks to identify potential LOX Expander Cycle (LEC) engine designs that exceed the performance of the current state of the art RL10B-2 engine flown on Centaur upper-stages. Results of this research found that the LEC engine concept achieved a 21.2% increase in engine thrust with a decrease in engine length and diameter of 52.0% and 15.8% respectively compared to the RL10B-2 engine. A 5.89% increase in vacuum specific impulse was also observed. The implications of these results could lead to significant launch cost savings and replacement of aging expander cycle technology in the rocket propulsion industry. ii In order to fully validate the results of this research, more knowledge is required regarding the heat transfer characteristics of supercritical oxygen for rocket thrust chamber cooling. Future work in this topic will focus on experimental LOX heat transfer research and model optimization to improve heat transfer estimations in the baseline model developed in this research and further explore the optimal performance potential and limitations of the LEC engine. iii DEDICATION This thesis is dedicated to my family, friends, and mentors that have supported me through the process of writing this thesis and throughout my entire education. iv LIST OF ABBREVIATIONS AND SYMBOLS A Cross-sectional area Ac Combustion chamber average cross-sectional area Ach Cooling channel area �! Nozzle exit area AFIT Air Force Institute of Technology Ainj Injector face area ∗ �! �� � Nozzle throat area AUSEP Advanced Upper Stage Engine Program a Gear ratio or speed of sound SA or As Surface Area CEA (NASA) Chemical Equilibrium with Applications CPS Cryogenic Propulsion Stage �! Constant pressure specific heat CV Cooling Volume c General constant �∗ Characteristic velocity D Diameter Dc Cooling channel diameter for Colburn Equation DEAN Dual-Expander Aerospike Nozzle v Dhyd Hydraulic diameter DoD Department of Defense D-W Darcy Weisbach Equation EELV Evolved Expendable Launch Vehicle EOS Equation of State F Thrust FPL Full Power Level f Fuel/Oxidizer ratio or general function fD Darcy friction factor g0 Gravitational acceleration constant Hch Cooling channel representative height Hp Pump head h Enthalpy he Enthalpy at exit h0 Enthalpy at entrance hgr Bartz gas reference heat transfer coefficient hl Colburn liquid heat transfer coefficient Δh Change in enthalpy I Impulse �!" Specific impulse k Loss coefficient kcf Colburn heat transfer constant kgr Combustion gas reference constant vi L Length L* Characteristic length Lc Combustion chamber length Lf Fuel pump torque LEC LOX Expander Cycle LeRC (NASA) Lewis Research Center LH2 Liquid Hydrogen LOX or LO2 Liquid Oxygen Lox Ox pump torque Lp Pump torque LRPS Liquid Rocket Propulsion System Lt Turbine torque Δl Station segment length M Mach number Me Exit Mach number MFSOV Main Fuel Shut-Off Valve �!"# Molecular weight MOC Method of Characteristics MOCV Main Oxidizer Control Valve � Mass flow rate m0 Initial mass mf Final mass N Number of injector elements or number of cooling channels vii NASA National Aeronautics and Space Administration NIST National Institute of Standards and Technology NPSS Numerical Propulsion System Simulation Np Pump shaft speed NRA NASA Research Announcement Nt Turbine shaft speed O/F Oxidizer to Fuel ratio (Mixture Ratio) P Pressure or perimeter �! Chamber pressure �!! Cooling channel perimeter �! Nozzle exit pressure Ploss Losses in pump pressure P0 or Pa Ambient pressure Pp,exit Pump exit pressure P&W Pratt and Whitney (Rocketdyne) ΔPdyn Change in dynamic pressure � Energy flux �!" Rate of energy entering system �!"# Rate of energy exiting system � Specific energy flux R Gas constant Re Reynolds number ROCETS ROCet Engine Transient Simulation Software viii rc Combustion chamber radius �! Nozzle exit radius ∗ �! �� � Nozzle throat radius SLS Space Launch System SSME Space Shuttle Main Engine T Temperature Tcw Cold wall temperature for Colburn Equation Te Exit temperature Tg Gas temperature Tgr Gas reference temperature for Bartz Equation Thw Hot wall temperature for Colburn Equation T/W Thrust-to-Weight Ratio t Time tch Cooling channel wall thickness V Velocity Vc Combustion chamber volume Veq Equivalent velocity ΔV Change in velocity �!"## Power losses in turbopump �! Pump power �! Turbine power xstep Numerical integration step ε Expansion ratio ix εc Chamber ratio εn Nozzle expansion ratio � Ratio of specific heats ηc Combustion chamber efficiency ηp Pump efficiency ηt Turbine efficiency λ Nozzle efficiency µ Dynamic viscosity µgr Combustion gas reference constant ρ Density ϕB Bartz heat transfer correction factor ϕcurv Colburn heat transfer correction factor x ACKNOWLEDGMENTS It is with great pleasure that I thank the family, friends, and faculty that have assisted me in this research. In particular, I am indebted to Lt. Col. (Ret.) Dr. Richard Branam, the chairman of my thesis committee, for his guidance and wisdom through the research process. I would also like to thank the other members of my thesis committee, Dr. Semih Olcmen and Dr. Ajay Agrawal, for their time in reviewing my thesis and their valuable recommendations. My gratitude is particularly extended to my parents, Denny and Nancy Stapp for providing me with the work ethic and financial support to get me through the past 17 years of school. I would not be where I am today without their wisdom and encouragement. I would also like to thank my fiancé, Naz Syed, for her continuing moral support throughout my college career and in writing this thesis. Finally, I am grateful to my friends and fellow graduate students who toiled through this effort alongside me and set a high bar for me to strive after. xi TABLE OF CONTENTS ABSTRACT .................................................................................................................................... ii DEDICATION ............................................................................................................................... iv LIST OF ABBREVIATIONS AND SYMBOLS ........................................................................... v ACKNOWLEDGMENTS ............................................................................................................. xi LIST OF TABLES ........................................................................................................................ xv LIST OF FIGURES .................................................................................................................... xvii 1 INTRODUCTION .................................................................................................................... 1 1.1 Research Motivation and Concept Overview .................................................................... 1 1.2 Problem Statement ............................................................................................................. 5 1.3 Research Objectives ........................................................................................................... 6 1.4 Document Overview .......................................................................................................... 7 2 BACKGROUND AND PREVIOUS RESEARCH .................................................................. 8 2.1 Demand and Cost Implications for Improvement of LRPS ............................................... 8 2.2 Liquid Rocket Propulsion ................................................................................................ 11 2.2.1 LRPS Design ............................................................................................................. 11 2.2.1.1 Engine Cycles .................................................................................................... 15 2.2.1.2 Nozzle Theory .................................................................................................... 19 2.2.1.3 Combustion Chamber Theory ............................................................................ 24 2.2.1.4 Cooling Jacket Theory ....................................................................................... 34 2.2.1.5