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Purchased from American Institute of Aeronautics and Astronautics Liquid Rocket Thrust Chambers: Aspects of Modeling, Analysis, and Design Purchased from American Institute of Aeronautics and Astronautics This page intentionally left blank Purchased from American Institute of Aeronautics and Astronautics Liquid Rocket Thrust Chambers: Aspects of Modeling, Analysis, and Design Edited by Vigor Yang Pennsylvania State University University Park, Pennsylvania Mohammed Habiballah Office National d'Etudes et de Recherches Aerospatiales Chatillon, France James Hulka Jacobs-Sverdrup Technology, Inc. Huntsville, Alabama Michael Popp Pratt and Whitney Space Propulsion West Palm Beach, Florida Volume 200 PROGRESS IN ASTRONAUTICS AND AERONAUTICS Paul Zarchan, Editor-in-Chief MIT Lincoln Laboratory Lexington, Massachusetts Published by the American Institute of Aeronautics and Astronautics, Inc. 1801 Alexander Bell Drive, Reston, Virginia 20191-4344 Purchased from American Institute of Aeronautics and Astronautics Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. Printed in the United States of America. All rights reserved. Reproduction or translation of any part of this work beyond that permitted by Sections 107 and 108 of the U.S. Copyright Law without the permission of the copyright owner is unlawful. 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ISBN 1-56347-223-6 Purchased from American Institute of Aeronautics and Astronautics Progress in Astronautics and Aeronautics Editor-in-Chief Paul Zarchan MIT Lincoln Laboratory Editorial Board David A. Bearden Richard C. Lind The Aerospace Corporation University of Florida John D. Binder Richard M. Lloyd viaSolutions Raytheon Electronics Company Steven A. Brandt Frank K. Lu U.S. Air Force Academy University of Texas at Arlington Fred R. DeJarnette Ahmed K. Noor North Carolina State University NASA Langley Research Center Philip D. Hattis Albert C. Piccirillo Charles Stark Draper Laboratory Institute for Defense Analyses Abdollah Khodadoust Ben T. Zinn The Boeing Company Georgia Institute of Technology Peter H. Zipfel Air Force Research Laboratory Purchased from American Institute of Aeronautics and Astronautics This page intentionally left blank Purchased from American Institute of Aeronautics and Astronautics Table of Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. xvii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. xix Chapter 1 Propellant Injection Systems and Processes . . . . . . . . .. 1 Jackson I. Ito GenCorp Aerojet Propulsion Division, Sacramento, California Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1 Rocket Application Design Requirements . . . . . . . . . . . . . . . . . . .. 2 Thrust Level and Operating Pressure . . . . . . . . . . . . . . . . . . . . . .. 2 Propellant Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3 Engine Cycle or Feed S y s t e m . . . . . . . . . . . . . . . . . . . . . . . . . .. 4 Common Combustion Device Development Risks . . . . . . . . . . . . . .. 6 Combustion Instability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 6 Combustion Chamber Overheating and Burnout . . . . . . . . . . . . . . . .. 7 Injector Face Erosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 8 Low Thrust Chamber Assembly Performance . . . . . . . . . . . . . . . . .. 8 Unsafe Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9 Injection System Design Considerations . . . . . . . . . . . . . . . . . . . .. 9 Engine Pressure Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10 Nozzle Expansion R a t i o . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10 Contraction Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10 Chamber Length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10 Injection Element and P a t t e r n . . . . . . . . . . . . . . . . . . . . . . . . . .. 10 Critical Combustion Processes . . . . . . . . . . . . . . . . . . . . . . . . . .. 10 Injector Manifold Distribution . . . . . . . . . . . . . . . . . . . . . . . . .. 11 Injector Spray Atomization . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 Propellant Droplet Vaporization. . . . . . . . . . . . . . . . . . . . . . . . .. 13 Bipropellant Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13 Candidate Injectors for Liquid Rocket Applications . . . . . . . . . . . . .. 13 Coaxial Jet I n j e c t o r s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 14 Impinging Jet Injectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15 Parallel Jet (Showerhead) Injectors . . . . . . . . . . . . . . . . . . . . . . .. 16 Injector Design Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 16 Conclusions and Recommendations........................ 17 References....................................... 17 Chapter 2 Design and Dynamics of Jet and Swirl Injectors . . . . . .. 19 Vladimir Bazarov Moscow Aviation Institute, Moscow, Russia and Vigor Yang and Puneesh Puri Pennsylvania State University, University Park, Pennsylvania Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21 Classification of Injectors and Methods of Mixture Formation . . . . . . . .. 22 vii Purchased from American Institute of Aeronautics and Astronautics VIM Liquid Injectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 24 Gas-Liquid I n j e c t o r s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 32 Intensification of Propellant Atomization and Mixing in Liquid Injectors . . 41 Intensification of Propellant Atomization and Mixing in Gas-Liquid Injectors . 45 Theory and Design of Liquid Monopropellant Jet Injectors.......... 45 Flow Characteristics................................ 45 Effect of Injector Configuration.......................... 46 Flow Coefficient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 47 Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 49 Theory and Design of Gaseous Monopropellant Jet Injectors. . . . . . . .. 51 Flow Characteristics................................ 51 Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 52 Theory and Design of Gas-Liquid Jet Injectors . . . . . . . . . . . . . . . .. 53 Theory and Design of Liquid Monopropellant Swirl Injectors . . . . . . .. 56 Flow Characteristics of Ideal Swirl Injector . . . . . . . . . . . . . . . . . .. 57 Flow Characteristics of Real Swirl Injectors . . . . . . . . . . . . . . . . . .. 66 Effect of Viscosity on Injector Operation. . . . . . . . . . . . . . . . . . . .. 68 Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 69 Theory and Design of Liquid Bipropellant Swirl Injectors . . . . . . . .. 72 Injectors with External Mixing . . . . . . . . . . . . . . . . . . . . . . . . .. 72 Injectors with Internal Mixing. . . . . . . . . . . . . . . . . . . . . . . . . .. 75 Modulation of Liquid Spray Characteristics of Swirl Injectors . . . . . . .. 77 Design of Gas Swirl Injectors . . . . . . . . . . . . . . . . . . . . . . . . . .. 85 Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 85 Selection of Geometric Dimensions and Flow Parameters............ 89 Dynamics of Liquid Rocket Injectors . . . . . . . . . . . . . . . . . . . . . .. 90 Linear Dynamics of Jet Injectors . . . . . . . . . . . . . . . . . . . . . . . .. 92 Linear Dynamics of Swirl Injectors........................ 94 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 102 References....................................... 102 Chapter 3 Atomization in Coaxial-Jet Injectors . . . . . . . . . . . . . .. 105 Lucien Vingert and Pierre Gicquel ONERA, Palaiseau, France, Michel Ledoux and Isabelle Care CORIA, Universite de Rouen, Rouen, France, and Michael Micci and Michael Glogowski Pennsylvania State University, University Park, Pennsylvania Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 105 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 106 Phenomenological Description and Literature Review............. 106 General Scheme of Jet Disintegration and Drop Formation . . . . . . . . . .. 106 Studies of Elementary Processes . . . . . . . . . . . . . . . . . . . . . . . .. 109 Numerical Simulations of the Atomization Process . . . . . . . . . . . . . .. Ill Derivation of Droplet Size Distribution Functions . . . . . . . . . . . . . . .. Ill Investigations of Atomization in Shear Coaxial Injectors . . . . . . . . . .. Ill Experimental and Theoretical Investigation at Atmospheric Pressure with Simulants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Ill Photographic Studies Using Cryogenic Fluids (Liquid/Gaseous Nitrogen) . .. 125 LOX Spray Combustion. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 130 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 136 Purchased from American Institute of Aeronautics and Astronautics !X Acknowledgment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 136 R e f e r e n c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 136 Chapter 4 Liquid Bipropellant Injectors . . . . . . . . . . . . . . . . . . .. 141 William E. Anderson, Matthew R. Long, and Stephen D. Heister Purdue University, West Lafayette, Indiana Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 141 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 143 Impinging Jet Injector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 143 General Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 143 Applications and Design Guidelines . . . . . . . . . . . . . . . . . . . . . .. 144 Mechanistic S t u d y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 148 Modeling Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 150 Bicentrifugal Swirl Injector. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 152 General Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 152 Applications and Design Guidelines . . . . . . . . . . . . . . . . . . . . . .. 152 Modeling Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 154 Pintle I n j e c t o r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 157 General Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 157 Applications and Design Guidelines . . . . . . . . . . . . . . . . . . . . . .. 159 Mechanistic Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 161 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 162 References....................................... 163 Chapter 5 Distortion and Disintegration of Liquid Streams . . . . . .. 167 William A. Sirignano and Carsten Mehring University of California, Irvine, California Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 167 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 169 Formulation of Governing Equations . . . . . . . . . . . . . . . . . . . . . .. 173 Round Jet Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 176 Temporal Stability Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . .. 177 Surface Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 179 Spatial Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 181 Nonlinear Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 183 Viscous Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 187 Spray Control via Electric Fields . . . . . . . . . . . . . . . . . . . . . . . .. 188 Coaxial Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 Planar Sheet Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 195 Linear Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 196 Fan Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 199 Simplified Breakup Theories . . . . . . . . . . . . . . . . . . . . . . . . . .. 201 Nonlinear Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 205 Annular Free F i l m s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 222 Linear Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 222 Nonlinear Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 227 Effect of Swirl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 232 Conical Free Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 234 Concluding Remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 241