LIKE-DOUBLET INJECTORS: THE EFFECTS OF VARYING THE IMPINGEMENT DISTANCE AND AN ANALYSIS OF THE PRIMARY ATOMIZATION ZONE by BRIAN A. SWEENEY A DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Mechanical and Aerospace Engineering to The School of Graduate Studies of The University of Alabama in Huntsville HUNTSVILLE, ALABAMA 2016 ABSTRACT School of Graduate Studies The University of Alabama in Huntsville Degree Doctor of Philosophy College/Dept. Engineering/Mechanical and Aerospace Engineering Name of Candidate Brian A. Sweeney Title Like-Doublet Injectors: The Effects of Varying the Impingement Distance and an Analysis of the Primary Atomization Zone This research explored how the jet breakup length to impingement distance ratio affects the spray characteristics of like-doublet injectors and consisted of cold-flow experiments using water at atmospheric pressure. A combination of three impingement angles, four jet velocities, and four jet breakup length to impingement distance ratios between one-half and two were tested. The breakup characteristics, sheet lengths and ligament wavelengths were determined from high-speed videos of the spray while droplet statistics were collected with a Phase Doppler Particle Analyzer. The sheet breakup characteristics were altered when the ratio transitioned from greater than one to equal to one and dramatically changed when the ratio became less than one. A robust impingement and `steady' sheet formed when the ratio was greater than one. While an `unsteady' sheet formed when the ratio equaled one due to intermittent jet breakup at the impingement point. Finally, no sheet was formed for ratios less than one. The flat sheet experienced two breakup modes separated by a transition Weber number. Empirical sheet breakup correlations based upon the Weber number and impingement angle were determined for both breakup modes. The mean wavelength between the shed ligaments was equal for iv ACKNOWLEDGMENTS I would like to acknowledge the Alabama Space Grant Consortium, NASA Training Grant NNX10AJ80H for funding the first three years of my Ph.D. program as a Space Grant Graduate Fellow. Their support allowed me to complete my coursework, select a research topic, and finish the first part of the experimental test program. I would also like to thank my advisor Dr. Robert Frederick for his continual guidance, insight and support of this research topic and myself as a graduate student. In addition, my committee members consisting of Dr. Keith Hollingsworth, Dr. Kader Frendi, Dr. David Lineberry, and Dr. Jason Cassibry have provided key advice and help in all aspects of this research including but not limited to experiment design, data analysis, and presentation of the results. Also, Mr. Tony Hall, the PRC Facility Engineer, provided his expertise and assistance in the modification of the test facility. Finally, I would like to thank my family for their unwavering support as I embarked on this degree program. In particular, I would like to thank my wife Renae for her support and patience as I spent long hours finishing this research project and degree program. vi TABLE OF CONTENTS List of Figures xii List of Tables xviii List of Symbols xx Chapter 1 Introduction 1 1.1 Overview of Combustion Instability . .7 1.1.1 Characteristics of Combustion Instability . 12 1.1.2 Physical Manifestation of Combustion Instability . 16 1.1.3 Excitation Mechanisms . 20 1.1.4 Function of the Injector in Combustion Instability . 22 1.1.5 Damping and Controlling Combustion Instability . 28 1.1.5.1 Passive Control . 29 1.1.5.2 Active Control . 34 1.2 Characteristics of Liquids and Liquid Flow . 36 1.2.1 Bulk Modulus and Density . 36 1.2.2 Viscosity . 36 1.2.3 Surface Tension . 38 1.2.4 Vapor Pressure and Cavitation . 39 vii 1.2.5 Relevant Dimensionless Number Groups . 41 1.2.6 Laminar and Turbulent Flow Regimes . 43 1.3 Liquid Jet Breakup . 46 1.3.1 Breakup Regimes . 48 1.3.2 Jet Breakup Length . 53 1.3.3 Acoustic Excitation of Liquid Jets . 58 1.4 Like-Doublet Impinging Injectors . 61 1.4.1 Like-Doublet Injector Design . 62 1.4.2 Atomization Process of Impinging Liquid Jets . 71 1.4.2.1 Primary Atomization . 72 1.4.2.2 Secondary Atomization . 86 1.4.2.3 Droplet Size . 88 2 Research Objective and Test Plan 93 2.1 Research Objective . 93 2.2 Test Plan . 96 2.2.1 The Jet Breakup Length to Impingement Distance Ratio for Like-Doublet Injectors . 96 2.2.2 Analysis of Like-Doublet Atomization using Visual Observation and Dynamic Mode Decomposition . 98 3 Experimental Technique: Test Facility, Instrumentation, and Data Analysis 101 3.1 Experimental Setup . 101 3.2 Injector Design . 107 viii 3.3 Instrumentation . 115 3.3.1 Feedline Instrumentation . 115 3.3.2 Spray Characterization . 117 3.3.2.1 High-Speed Camera . 118 3.3.2.2 Phase Doppler Particle Analyzer . 119 3.4 Data Analysis . 124 3.4.1 Matlab Analysis . 125 3.4.1.1 Low-Speed Data Analysis . 125 3.4.1.2 High-Speed Data Analysis . 126 3.4.2 Image Analysis . 127 3.4.3 PDPA Analysis . 131 3.4.4 Dynamic Mode Decomposition . 134 3.5 Uncertainty Analysis . 145 4 Results { Part 1: The Jet Breakup Length to Impingement Distance Ratio for Like-Doublet Injectors 150 4.1 Single Jet . 150 4.2 Like-Doublet . 156 4.2.1 Spray Characteristics . 156 4.2.2 Sheet Breakup Length . 160 4.2.3 Ligament Wavelength . 172 4.2.4 Droplet Size . 178 ix 5 Results { Part 2: Analysis of Like-Doublet Atomization using Visual Observation and Dynamic Mode Decomposition 186 5.1 Single Jet Analysis . 186 5.1.1 Physical Characteristics of the Single Jet . 187 5.1.2 DMD Analysis of the Single Jet . 188 5.1.3 Feed System Coupling . 195 5.2 Like-Doublet Analysis . 200 5.2.1 Physical Characteristics of the Like-Doublet Spray . 201 5.2.2 DMD Analysis of the Like-Doublet Spray . 210 m 5.2.2.1 Like-Doublet: vj = 5 =s ............... 211 m 5.2.2.2 Like-Doublet: vj = 10 =s .............. 219 m 5.2.2.3 Like-Doublet: vj = 20 =s .............. 226 5.2.3 Feed System Coupling . 233 6 Conclusion 236 6.1 Summary of Results . 236 6.1.1 Part 1: The Effects of Varying the Impingement Distance for Like-Doublet Injectors . 236 6.1.2 Part 2: A Visual and DMD Analysis of the Turbulent Jet and Like-Doublet Spray . 239 6.2 Future Work . 243 APPENDIX A: Test Conditions 246 x A.1 Part 1: The Effects of Varying the Impingement Distance for Like-Doublet Injectors . 246 A.1.1 Single Jet Experiments . 246 A.1.2 Like-Doublet Experiments . 247 A.2 Part 2: A Dynamic Mode Decomposition Analysis of the Like-Doublet Spray.................................... 250 A.2.1 Single Jet Experiments . 250 A.2.2 Like-Doublet Experiments . 250 APPENDIX B: Like-Doublet Sheet Breakup Length & Ligament Wavelength Results 251 APPENDIX C: Like-Doublet Droplet Distribution Results 253 C.1 Tabulated Results . 253 C.2 Droplet Diameter Histograms . 255 C.2.1 30◦ Impingement Angle . 255 C.2.2 60◦ Impingement Angle . 259 C.2.3 90◦ Impingement Angle . 263 APPENDIX D: Uncertainty Analysis Results 268 D.1 Tabulated Uncertainty Results (95% Confidence) . 268 D.2 Uncertainty Plots (95% Confidence) . 271 REFERENCES 276 xi LIST OF FIGURES FIGURE PAGE 1.1 Liquid Rocket Injection and Combustion Process Diagram [3] . .4 1.2 Common Liquid Rocket Injector Types [1] . .5 1.3 F-1 Rocket Engine [9] . .9 1.4 Ariane Viking Engine [12] . 11 1.5 Transverse Combustion Instability Modes [9] . 19 1.6 Injector Dynamics Diagram [9] . 23 1.7 Cutaway of Thrust Chamber with Passive Control Devices Installed [3] 30 1.8 Various Baffle Designs [24] . 32 1.9 Various Resonance Absorber Designs [27] . 34 1.10 Jet Breakup Regimes: (a) Rayleigh, (b) 1st Wind-Induced, (c) 2nd Wind-Induced, and (d) Atomization [39] . 49 1.11 Jet Breakup Regimes as Functions of the Reynolds and Weber Numbers [40] . 50 1.12 Qualitative Jet Breakup Length vs. Injection Velocity . 54 1.13 Liquid Jet Located at Velocity Anti-Node of Standing Acoustic Wave: rms crit rms crit (a) Vac < Vac , (b) Vac > Vac [49] . 60 1.14 Schematic of a Typical Like-Doublet Injector . 63 1.15 Spray Fan Impingement of Two Like-Doublets [5] . 66 1.16 Hewitt Stability Correlation Plot [4] . 68 1.17 Like-Doublet Spray Fan Patterns: (a) Closed-Rim [61], (b) Periodic-Drop [62], (c) Opened-Rim [62],and (d) Fully-Developed [51] 74 xii 1.18 Representative Droplet Size Distribution with Locations of Several Mean Diameters [30] . 90 l 2.1 Liquid Jet Breakup Length to Impingement Distance Ratio: (a) b=li > l l 1, (b) b=li ≈ 1, (c) b=li < 1 ........................ 94 3.1 Atmospheric Spray Facility . 102 3.2 Spray Instrumentation Layout . 104 3.3 Injector Apparatus . 109 3.4 Injector Mass Flow Rate Calibration Data . 110 3.5 Calibration Data with Prediction Curves: (a) Mass Flow Rate per Orifice and (b) Injection Velocity . 114 3.6 Breakup Length Measurements: (a) Jet and (b) Flat Sheet . 129 3.7 Atomization Frequency Measurements . 130 3.8 Geometry of: (a) Sphere and (b) Ellipsoid . 131 m m m 4.1 Single Jet Snapshots: (a) vj = 5 =s, (b) vj = 10 =s, (c) vj = 15 =s, m and (d) vj = 20 =s ............................ 151 4.2 Single Turbulent Jet Breakup Length . 154 4.3 Spray Snapshots: 30◦ Impingement Angle . 158 4.4 Spray Snapshots: 60◦ Impingement Angle . 159 4.5 Spray Snapshots: 90◦ Impingement Angle .