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Extensions to the Time Lag Models for Practical Application to Rocket The Pennsylvania State University The Graduate School College of Engineering EXTENSIONS TO THE TIME LAG MODELS FOR PRACTICAL APPLICATION TO ROCKET ENGINE STABILITY DESIGN A Dissertation in Mechanical Engineering by Matthew J. Casiano © 2010 Matthew J. Casiano Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2010 The dissertation of Matthew J. Casiano was reviewed and approved* by the following: Domenic A. Santavicca Professor of Mechanical Engineering Co-chair of Committee Vigor Yang Adjunct Professor of Mechanical Engineering Dissertation Advisor Co-chair of Committee Richard A. Yetter Professor of Mechanical Engineering André L. Boehman Professor of Fuel Science and Materials Science and Engineering Tomas E. Nesman Aerospace Engineer at NASA Marshall Space Flight Center Special Member Karen A. Thole Professor of Aerospace Engineering Head of the Department of Mechanical and Nuclear Engineering *Signatures are on file in the Graduate School iii ABSTRACT The combustion instability problem in liquid-propellant rocket engines (LREs) has remained a tremendous challenge since their discovery in the 1930s. Improvements are usually made in solving the combustion instability problem primarily using computational fluid dynamics (CFD) and also by testing demonstrator engines. Another approach is to use analytical models. Analytical models can be used such that design, redesign, or improvement of an engine system is feasible in a relatively short period of time. Improvements to the analytical models can greatly aid in design efforts. A thorough literature review is first conducted on liquid-propellant rocket engine (LRE) throttling. Throttling is usually studied in terms of vehicle descent or ballistic missile control however there are many other cases where throttling is important. It was found that combustion instabilities are one of a few major issues that occur during deep throttling (other major issues are heat transfer concerns, performance loss, and pump dynamics). In the past and again recently, gas injected into liquid propellants has shown to be a viable solution to throttle engines and to eliminate some forms of combustion instability. This review uncovered a clever solution that was used to eliminate a chug instability in the Common Extensible Cryogenic Engine (CECE), a modified RL10 engine. A separate review was also conducted on classic time lag combustion instability models. Several new stability models are developed by incorporating important features to the classic and contemporary models, which are commonly used in the aerospace rocket industry. The first two models are extensions of the original Crocco and Cheng concentrated combustion model with feed system contributions. A third new model is an extension to the Wenzel and Szuch double- time lag model also with feed system contributions. iv The first new model incorporates the appropriate injector acoustic boundary condition which is neglected in contemporary models. This new feature shows that the injector boundary can play a significant role for combustion stability, especially for gaseous injection systems or a system with an injector orifice on the order of the size of the chamber. The second new model additionally accounts for resistive effects. Advanced signal analysis techniques are used to extract frequency-dependent damping from a gas generator component data set. The damping values are then used in the new stability model to more accurately represent the chamber response of the component. The results show a more realistic representation of stability margin by incorporating the appropriate damping effects into the chamber response from data. The original Crocco model, a contemporary model, and the two new models are all compared and contrasted to a marginally stable test case showing their applicability. The model that incorporates resistive aspects shows the best comparison to the test data. Parametrics are also examined to show the influence of the new features and their applicability. The new features allow a more accurate representation of stability margin to be obtained. The third new model is an extension to the Wenzel and Szuch double-time lag chug model. The feed system chug model is extended to account for generic propellant flow rates. This model is also extended to incorporate aspects due to oxygen boiling and helium injection in the feed system. The solutions to the classic models, for the single-time lag and the double-time lag models, are often plotted on a practical engine operating map, however the models have presented some difficulties for numerical algorithms for several reasons. Closed-form solutions for use on these practical operating maps are formulated and developed. These models are incorporated in a graphical user interface tool and the new model is compared to an extensive data set. It correctly predicts the stability behavior at various operating conditions incorporating the influence of injected helium and boiling oxygen in the feed system. v TABLE OF CONTENTS LIST OF FIGURES ................................................................................................................. vii LIST OF TABLES ................................................................................................................... xi NOMENCLATURE ................................................................................................................ xii ACKNOWLEDGEMENTS ..................................................................................................... xxv Chapter 1 Introduction............................................................................................................ 1 1.1 Motivation .................................................................................................................. 1 1.2 Background ................................................................................................................ 3 1.2.1 Time-Lag-Based Combustion Instability Models ........................................... 3 1.2.2 Liquid-Propellant Rocket Engine Throttling ................................................... 4 1.3 Objective .................................................................................................................... 5 Chapter 2 Liquid-Propellant Rocket Engine Throttling ......................................................... 8 2.1 Throttling Review ...................................................................................................... 11 2.1.1 High-Pressure-Drop Injectors.......................................................................... 11 2.1.2 Dual-Manifold Injectors .................................................................................. 30 2.1.3 Gaseous Injection ............................................................................................ 41 2.1.4 Multiple Chambers .......................................................................................... 47 2.1.5 Pulse Modulation ............................................................................................. 49 2.1.6 Throat Throttling ............................................................................................. 54 2.1.7 Variable Area Injectors ................................................................................... 58 2.1.8 Hydrodynamically Dissipative Injectors ......................................................... 70 2.1.9 Combined Methods ......................................................................................... 72 2.2 Review Summary ....................................................................................................... 73 2.2.1 High-Pressure-Drop Injectors Summary ......................................................... 73 2.2.2 Dual-Manifold Injectors Summary ................................................................. 74 2.2.3 Gaseous Injection Summary ............................................................................ 76 2.2.4 Multiple Chambers Summary ......................................................................... 77 2.2.5 Pulse Modulation Summary ............................................................................ 77 2.2.6 Throat Throttling Summary ............................................................................ 78 2.2.7 Variable Area Injectors Summary ................................................................... 79 2.2.8 Hydrodynamically Dissipative Injectors Summary......................................... 80 Chapter 3 Time Lag Stability Models .................................................................................... 81 3.1 Research Goal, Strategy, and Objectives ................................................................... 85 3.2 Gunder and Friant Time Lag Model .......................................................................... 89 3.3 Summerfield Time Lag Model ................................................................................... 91 3.4 Crocco and Cheng Monopropellant Time Lag Chug Model ...................................... 93 3.5 Crocco and Cheng Bipropellant Time Lag Model ..................................................... 105 3.6 Notes on Crocco and Cheng Chug Time Lag Models ............................................... 110 vi 3.7 Natanzon Monopropellant Chug Time Lag Model .................................................... 111 3.8 Crocco and Cheng Longitudinal High Frequency Time Lag Model .........................
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