Hydrogen peroxide vapor for small satellite propulsion

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Content HYDROGEN PEROXIDE V APOR FOR SMALL SATELLITE PROPULSION Brandie L. Rhodes Submitted to the Faculty of the USC Graduate School in Partial Fullfillment of the Requirements for the Degree of DOCTOROFPHILOSOPHY DepartmentofAstronauticalEngineering University of Southern California Los Angeles, California August 2019 CONTENTS LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix ACKNOWLEDGMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Small Satellite Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Green Monopropellants . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.1.1 Hydrogen Peroxide . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Laser Absorption Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Hydrogen Peroxide Vapor Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.1 Catalytic Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4 Thermal Transpiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.5.1 Hydrogen Peroxide Vapor Propulsion System . . . . . . . . . . . . . . . . 13 1.5.2 Laser Vapor Diagnostic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.5.3 Reaction Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.5.4 Performance Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.5.5 Catalytic Thermal Transpiration . . . . . . . . . . . . . . . . . . . . . . . 15 2. HYDROGEN PEROXIDE V APOR PROPULSION SYSTEM . . . . . . . . . . . . . . . 16 2.1 Theoretical Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.1 Vapor Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.1.2 Effects of Liquid Mole Fraction on Performance . . . . . . . . . . . . . . 19 2.1.3 Effects of Tank Temperature on Performance . . . . . . . . . . . . . . . . 20 2.2 Prototype 1: Proof of Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.1 Design and Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 ii 3. LASER DIAGNOSTIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.1 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Water Line Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3 Subtracting the Influence of Absorption by Atmospheric Water Vapor . . . . . . . 34 3.4 Water Diagnostic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4. REACTION RATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.0.1 Literatures Studies of H 2 O 2 Vapor Heterogeneous Reactions . . . . . . . . 39 4.0.2 Literatures Studies of H 2 O 2 Liquid Heterogeneous Reactions . . . . . . . . 39 4.1 Experimental Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.1.1 Catalysts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1.2 H 2 O 2 diagnostic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.2 Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.3 Experiment: Reaction of H 2 O 2 on Platinum and Silver Surfaces at Ambient Tem- peratures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.3.1 Baseline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.3.2 Platinum on Alumina Spheres . . . . . . . . . . . . . . . . . . . . . . . . 44 4.3.3 Silver Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.3.4 Platinum Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.4 Experiment: Reaction of H 2 O 2 on Platinum on Alumina Spheres at Elevated Tem- peratures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.4.1 Baseline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.4.2 Determination of Arrhenius Constants . . . . . . . . . . . . . . . . . . . . 49 4.5 Role of Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.6 Modification of Reaction Rates to Account for Diffusion and Boundary Conditions 53 4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5. PERFORMANCE OPTIMIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.1 Prototype 2: Focus on Catalyst and Chamber Construction . . . . . . . . . . . . . 56 5.1.1 Design and Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.1.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.1.3 Heat Transfer Analysis using Finite Element Modeling . . . . . . . . . . . 62 5.1.3.1 Modeling Results . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 iii 5.2 Prototype 3: Focus on Robust Components and Minimal Pressure Drop for Thrust Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.2.1 Design and Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.2.1.1 Catalyst Chamber/ Nozzle . . . . . . . . . . . . . . . . . . . . . 66 5.2.2 Thrust Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.2.3.1 O-ring Variant . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.2.3.2 Spacer Variant . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.2.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.2.4.1 Comparison with Theoretical Nozzle . . . . . . . . . . . . . . . 82 5.2.5 Comparison with Theoretical Catalyst Temperature . . . . . . . . . . . . . 85 5.2.5.1 Heat Transfer Analysis using Finite Element Modeling . . . . . 86 5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 6. CATALYTIC THERMAL TRANSPIRATION . . . . . . . . . . . . . . . . . . . . . . . 90 6.0.1 Theoretical Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 6.0.1.1 Effects of Thermal Transpiration Membrane Pore Radius . . . . 93 6.0.1.2 Effects of Tank Temperature . . . . . . . . . . . . . . . . . . . 94 6.1 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.1.1 Catalyst and Membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 7. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 7.1 Thesis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 7.2 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 7.3 Final Thoughts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 APPENDICES A. Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 B. V olume and Surface Area for Reaction Rate Calculations . . . . . . . . . . . . . . . . . 117 C. Prototype 2 Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 D. Prototype 3 Thrust Measurement Experimental Data . . . . . . . . . . . . . . . . . . . . 121 D.1 Kalrez R O-ring Variant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 D.2 Vespel R Spacer Variant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 iv E. Prototype 3 Mass Flow Rate Experimental Data . . . . . . . . . . . . . . . . . . . . . . 132 E.1 Kalrez R O-ring Variant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 E.2 Vespel R Spacer Variant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 F. Prototype 3 Thrust Measurement Mass Flow Rate Correction . . . . . . . . . . . . . . . 139 G. Isentropic Nozzle Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 v LIST OF TABLES 1.1 Propulsion Systems with Flight Heritage on Small Satellites<100 kg . . . . . . . . . 3 1.2 Monopropellant Specific Impulse Comparison . . . . . . . . . . . . . . . . . . . . . 4 1.3 H 2 O 2 Material Compatibility Classification . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 H 2 O 2 Properties (90% by mass) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1 Test Control Variables, Catalyst Temperature Zones, and Maximum Catalyst Tem- perature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.1 Measured H 2 O 2 cross sections with 95% confidence interval . . . . . . . . . . . . . . 38 4.1 Literature H 2 O 2 Vapor Reaction Rate Constants and Activation Energies . . . . . . . 39 4.2 Platinum on Alumina Sphere Reaction Rate Constants . . . . . . . . . . . . . . . . . 45 4.3 Poisoning of Silver Mesh at Room Temperature . . . . . . . . . . . . . . . . . . . . 46 4.4 Conditioning of Silver Mesh at Elevated Temperatures . . . . . . . . . . . . . . . . . 46 4.5 Platinum on Alumina Sphere Activation Energies and Pre-exponential Factors . . . . 49 4.6 Ratio of Theoretical to Experimental H 2 O 2 Consumption . . . . . . . . . . . . . . . 50 4.7 COMSOL Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.8 COMSOL Reaction Rate Constants and ERCs for 0.5 sccm Helium Bubbler Flow Rate 54 4.9 Experimental Engineering Reaction Rates (ERCs) Compared with Literature . . . . . 55 5.1 SSCD Nozzle Average Catalyst Temperatures for Different Catalyst Materials and Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.2 MCD Nozzle Average Catalyst Temperatures and Chamber Pressures for 7 Silver Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.3 COMSOL Model Average Catalyst Temperatures . . . . . . . . . . . . . . . . . . . 64 5.4 COMSOL Model Average Catalyst Temperatures for Various Heat Transfer Condi- tions at a Tank Temperature of 80 C . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.5 Measured Nozzle Throat and Exit Diameters . . . . . . . . . . . . . . . . . . . . . . 68 5.6 Steady State Tank and Chamber Pressures and Maximum Average Catalyst Temper- ature for O-ring MCD Nozzle Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.7 Thrust and I sp for O-ring MCD Nozzle Tests . . . . . . . . . . . . . . . . . . . . . . 73 vi 5.8 H 2 O 2 Steady State Tank Pressures, Maximum Average Catalyst Temperature, Steady State Thrust, and Steady State I sp for O-Ring SSCD Nozzle Tests . . . . . . . . . . . 74 5.9 H 2 O 2 Steady State Tank Pressures, Maximum Average Catalyst Temperature, Steady State Thrust, and Steady State I sp for Spacer SSCD Nozzle Tests . . . . . . . . . . . 77 5.10 H 2 O Steady State Tank Pressures, Maximum Average Catalyst Temperature, Steady State Thrust, and Steady State I sp for Spacer SSCD Nozzle Tests . . . . . . . . . . . 78 5.11 H 2 O 2 Steady State Tank Pressures, Maximum Average Catalyst Temperature, Steady State Thrust, and Steady State I sp for Spacer SSCO Nozzle Tests . . . . . . . . . . . 80 5.12 H 2 O Steady State Tank Pressures, Maximum Average Catalyst Temperature, Steady State Thrust, and Steady State I sp for Spacer SSCO Nozzle Tests . . . . . . . . . . . 81 5.13 Comparison of the Spacer Variant Nozzle Experimental Mass Flow Rate, Thrust, and I sp with that of an Isentropic Nozzle in Continuum Flow . . . . . . . . . . . . . . . . 83 5.14 Comparison of the Spacer Variant Nozzle Experimental Mass Flow Rate, Thrust, and I sp with that of an Isentropic Nozzle in Free Molecular Flow . . . . . . . . . . . . . . 85 5.15 COMSOL Catalyst Temperatures for Prototype 2 and 3 . . . . . . . . . . . . . . . . 87 6.1 Thermal Transpiration Flow Coefficients . . . . . . . . . . . . . . . . . . . . . . . . 92 6.2 Thermal Transpiration Membrane Attributes . . . . . . . . . . . . . . . . . . . . . . 97 6.3 Mass Flow Rate with and without Transpiration Membrane for Tank Temperatures of 60 C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.4 Catalyst Chamber Temperatures with and without a Membrane . . . . . . . . . . . . 101 C.1 Prototype 2, SSCD nozzle, 7 Sheets Silver Mesh Catalyst . . . . . . . . . . . . . . . 118 C.2 Prototype 2, SSCD nozzle, 3 Sheets Silver Mesh Catalyst . . . . . . . . . . . . . . . 118 C.3 Prototype 2, SSCD nozzle, 14 Sheets Silver Mesh Catalyst . . . . . . . . . . . . . . 119 C.4 Prototype 2, SSCD nozzle, 7 Sheets Platinum Mesh Catalyst . . . . . . . . . . . . . 119 C.5 Prototype 2, SSCD nozzle, 3 Sheets Platinum Mesh Catalyst . . . . . . . . . . . . . 119 C.6 Prototype 2, SSCD nozzle, Platinum Sphere Catalyst . . . . . . . . . . . . . . . . . . 119 C.7 Prototype 2, MCD nozzle, 7 Sheets Silver Mesh Catalyst . . . . . . . . . . . . . . . 120 D.1 H 2 O 2 Propellant: O-ring Variant, MCD Nozzle Test Steady State Values . . . . . . . 122 D.2 H 2 O 2 Propellant: O-ring Variant, SSCD Nozzle Test Steady State Values . . . . . . . 124 D.3 H 2 O 2 Propellant: Spacer Variant, SSCD Nozzle Test Steady State Values . . . . . . . 126 vii D.4 H 2 O Propellant: Spacer Variant, SSCD Nozzle Test Steady State Values . . . . . . . 127 D.5 H 2 O 2 Propellant: Spacer Variant, SSCO Nozzle Test Steady State Values . . . . . . . 129 D.6 H 2 O Propellant: Spacer Variant, SSCO Nozzle Test Steady State Values . . . . . . . 130 E.1 H 2 O 2 Propellant: O-ring Variant, MCD Nozzle Mass Flow Rate Test Series . . . . . . 132 E.2 H 2 O 2 Propellant: O-ring Variant, MCD Nozzle Mass Flow Rate Test Series . . . . . . 133 E.3 H 2 O 2 Propellant: O-ring Variant, SSCD Nozzle Mass Flow Rate Test Series . . . . . 134 E.4 H 2 O 2 Propellant: O-ring Variant, SSCD Nozzle Mass Flow Rate Test Series . . . . . 137 E.5 H 2 O Propellant: O-ring Variant, SSCD Nozzle Mass Flow Rate Test Series . . . . . . 137 E.6 H 2 O 2 Propellant: O-ring Variant, SSCO Nozzle Mass Flow Rate Test Series . . . . . 137 E.7 H 2 O Propellant: O-ring Variant, SSCO Nozzle Mass Flow Rate Test Series . . . . . . 138 F.1 Loaded vs. Calculated Propellant V olume . . . . . . . . . . . . . . . . . . . . . . . . 139 viii LIST OF FIGURES 1.1 Hydrogen peroxide molecule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Basic schematic of a laser absorption experimental set-up. . . . . . . . . . . . . . . . 8 1.3 Visual representation of a heterogeneous catalytic reaction, where A represents the reactant and B the product. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Illustration of one stage in a Knudsen compressor. . . . . . . . . . . . . . . . . . . . 12 1.5 Thermal transpiration effect within a simple thruster design. . . . . . . . . . . . . . . 13 2.1 Schematic of vapor-fed H 2 O 2 propulsion system. . . . . . . . . . . . . . . . . . . . . 16 2.2 Vapor pressure of a liquid H 2 O 2 /H 2 O solution at 60 C. . . . . . . . . . . . . . . . . 19 2.3 Vacuum specific impulse of a vapor and liquid system with a throat diameter of 0.79 mm, an exit diameter of 4.78 mm, and a tank temperature of 60 C. . . . . . . . . . . 20 2.4 Vacuum thrust of a vapor and liquid system with a throat diameter of 0.79 mm, an exit diameter of 4.78 mm, and a tank temperature of 60 C. . . . . . . . . . . . . . . 20 2.5 Vacuum specific impulse of a vapor and liquid system with a throat diameter of 0.79 mm, an exit diameter of 4.78 mm, and a liquid H 2 O 2 mole fraction of 0.9. . . . . . . 21 2.6 Vacuum thrust of a vapor and liquid system with a throat diameter of 0.79 mm, an exit diameter of 4.78 mm, and a liquid H 2 O 2 mole fraction of 0.9. . . . . . . . . . . . 21 2.7 Hydrogen peroxide vapor thruster Prototype 1: CAD model with transparent tank lid (left), test unit (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.8 Platinum wire catalyst bed within the MACOR R catalyst chamber. . . . . . . . . . . 23 2.9 Measured catalyst temperatures for each test run. . . . . . . . . . . . . . . . . . . . . 24 2.10 Measured tank temperatures for each test run. . . . . . . . . . . . . . . . . . . . . . 24 2.11 Measured tank pressures for each test run. . . . . . . . . . . . . . . . . . . . . . . . 25 2.12 Change in temperature during the warm-up zone for tests 1 - 4. . . . . . . . . . . . . 26 2.13 Change in temperature during the rapid reaction zone (data and linear fit). . . . . . . 26 2.14 Vapor mole fraction over test time. The circles mark the beginning of the rapid reac- tion zone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.15 Fraction of platinum sites, Pt(s), available at varying catalyst temperatures. . . . . . . 28 ix 3.1 Experimental set-up including paths for the laser, vapor, dry air, and data. . . . . . . . 32 3.2 Absorption of H 2 O vapor at 1420.015 nm as a function of the concentration of H 2 O vapor in the flow cell at ambient temperature conditions. . . . . . . . . . . . . . . . . 33 3.3 Absorption spectrum of atmospheric H 2 O vapor absorption in the region of spectral interest at ambient pressure and temperature. The absorption was fit to a V oight profile to allow subtraction of this feature from the data. . . . . . . . . . . . . . . . . 35 3.4 The H 2 O 2 + H 2 O spectrum from 1419.955 nm to 1420.065 nm as a function of H 2 O 2 concentration in the flow cell at ambient temperature. The spectrum has been cor- rected to remove the atmospheric H 2 O vapor absorption as discussed above. . . . . . 35 3.5 A Doppler profile fit to the H 2 O peak at 1420.015 nm and the small H 2 O 2 peak on the shoulder of that H 2 O peak. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.6 Absorption of H 2 O 2 vapor at six measured cross sections as a function of the H 2 O 2 vapor concentration in the flow cell at ambient temperatures. From left to right, then top to bottom the wavelengths shown are 1419.958, 1419.967, 1419.999, 1420.029, 1420.047, and 1420.059 nm. See Table 3.1 for values of the cross sections inferred from these data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.1 Diagram of the reaction rate experimental set-up. . . . . . . . . . . . . . . . . . . . . 40 4.2 Absorbance of H 2 O 2 at 1420.059 nm through the bypass tube, 0 , and through the catalyst tube, , for the 2.35 mm platinum on alumina sphere with a 3/1.5 helium flow cell to bubbler ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.3 Destruction of H 2 O 2 on platinum on alumina spheres for varying residence times and catalyst sizes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.4 Rate constant determination for different platinum on alumina sphere catalyst sizes. . 45 4.5 H 2 O 2 destruction for conditioned silver mesh catalysts. . . . . . . . . . . . . . . . . 47 4.6 Minimal destruction of H 2 O 2 on platinum catalyst even at elevated temperatures. . . . 48 4.7 Temperature dependence for different platinum on alumina sphere sizes and helium flow rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.8 COMSOL diffusion-controlled model: flow velocity (left), H 2 O 2 concentration (right). 53 4.9 COMSOL gas only finite reaction rate model: (1) flow velocity, (2) H 2 O 2 concentra- tion for 3.05 mm platinum on alumina sphere, (3) H 2 O 2 concentration for silver mesh (4) H 2 O 2 concentration for platinum mesh. . . . . . . . . . . . . . . . . . . . . . . . 54 5.1 Hydrogen peroxide vapor thruster Prototype 2: test unit (left), CAD model (right). . . 57 5.2 Prototype 2: SSCD nozzle (left), MCD nozzle (right). . . . . . . . . . . . . . . . . . 58 x 5.3 Catalyst temperatures for the tests using the SSCD nozzle and 7 sheets silver mesh at tank temperatures of 60 C, 70 C, and 80 C. . . . . . . . . . . . . . . . . . . . . . 59 5.4 Tank pressures for tests using the SSCD nozzle and 7 sheets silver mesh at tank temperatures of 60 C, 70 C, and 80 C. . . . . . . . . . . . . . . . . . . . . . . . . 59 5.5 Top, middle, and bottom catalyst temperatures in the MCD nozzle with 7 sheets silver mesh and a tank temperature of 60 C. . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.6 Catalyst temperatures for the tests with the MCD nozzle and 7 sheets silver mesh at tank temperatures of 60 C, 70 C, and 80 C. . . . . . . . . . . . . . . . . . . . . . 61 5.7 Catalyst chamber pressures for tests with the MCD nozzle and 7 sheets silver mesh at tank temperatures of 60 C, 70 C, and 80 C. . . . . . . . . . . . . . . . . . . . . 61 5.8 Vapor pressure relation developed by Scatchard et al. [51] compared to experimental data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.9 Adiabatic temperature compared with experimental values for catalyst temperature. . 62 5.10 COMSOL geometry featuring MCD catalyst chamber: full model (left), sectioned at plane (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.11 COMSOL model slice temperature for 80 C tank temperature (location at plane indicated in Figure 5.10): MCD nozzle (left), SSCD nozzle (right). . . . . . . . . . . 65 5.12 Hydrogen peroxide vapor thruster Prototype 3: test unit (left), CAD model (right). . . 67 5.13 Prototype 3 mounting configurations: o-ring (left), spacer (right). . . . . . . . . . . . 67 5.14 Spacer variant nozzles: SSCD (left), SSCO (right). . . . . . . . . . . . . . . . . . . . 68 5.15 Prototype 3 thruster on torsional pendulum thrust stand. . . . . . . . . . . . . . . . . 69 5.16 Top, middle, and bottom catalyst temperatures in the O-ring MCD nozzle with 7 sheets silver mesh and a tank temperature of 80 C during a thrust measurement test series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.17 Tank and catalyst chamber pressure in the Spacer MCD nozzle with 7 sheets silver mesh and a tank temperature of 80 C during a thrust measurement test series. . . . . 71 5.18 Measured thrust for all O-ring MCD nozzle thrust measurement test runs. . . . . . . . 71 5.19 Average catalyst temperature for all O-ring MCD nozzle thrust measurement test runs. 72 5.20 O-ring MCD nozzle mass flow rate calculated from known propellant load and test run length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.21 Evidence of leak between manifold and catalyst chamber in 80 C tank temperature run of O-ring SSCD nozzle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 xi 5.22 Measured thrust for all O-ring SSCD nozzle thrust measurement test runs. . . . . . . 75 5.23 Catalyst temperature for all O-ring SSCD nozzle thrust measurement test runs. . . . . 75 5.24 Thermocouple placement on Spacer SSCD nozzle. . . . . . . . . . . . . . . . . . . . 76 5.25 Temperature measured at the bottom of the catalyst chamber and throat for a 60 C tank experiment series on the Spacer SSCD nozzle running H 2 O 2 . Thermocouple placement shown in Figure 5.24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.26 Measured thrust for all H 2 O 2 Spacer SSCD nozzle thrust measurement test runs. . . . 77 5.27 Measured thrust for all H 2 O Spacer SSCD nozzle thrust measurement test runs. . . . 78 5.28 Catalyst temperature for all H 2 O 2 Spacer SSCD nozzle thrust measurement test runs. 78 5.29 Measured thrust for all H 2 O 2 Spacer SSCO nozzle thrust measurement test runs. . . . 79 5.30 Measured thrust for all H 2 O Spacer SSCO nozzle thrust measurement test runs. . . . 80 5.31 Catalyst temperature for all H 2 O 2 Spacer SSCO nozzle thrust measurement test runs. 80 5.32 Average normalized thrust for all Prototype 3 thrust measurement tests. . . . . . . . . 81 5.33 Average normalized I sp for all Prototype 3 thrust measurement tests. . . . . . . . . . 82 5.34 Average catalyst temperatures for all Prototype 2 and 3 thrust measurement tests. . . . 86 5.35 Kalrez R O-Ring variant COMSOL model slice temperature for 80 C tank tempera- ture: MCD nozzle (left), SSCD nozzle (right). . . . . . . . . . . . . . . . . . . . . . 87 5.36 Vespel R Spacer variant COMSOL model slice temperature for 80 C tank tempera- ture: SSCD nozzle (left), SSCO nozzle (right). . . . . . . . . . . . . . . . . . . . . . 88 6.1 Chamber pressure and mass flow with a transpiration phase for a tank temperature of 60 C. The mass flow rate and pressure without the membrane is 1.14 10 -6 kg/s and 20.9 torr, respectively, for all pore sizes. . . . . . . . . . . . . . . . . . . . . . . 93 6.2 Thrust with and without a transpiration phase for a tank temperature of 60 C. . . . . 94 6.3 Chamber pressure and mass flow with and without a transpiration phase for a pore diameter of 0.7m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 6.4 Thrust with and without a transpiration phase for a pore diameter of 0.7m. . . . . . 95 6.5 Hydrogen peroxide vapor thruster for thermal transpiration studies: test unit (left), CAD model with transparent manifold (right). . . . . . . . . . . . . . . . . . . . . . 96 6.6 Catalyst chamber with integrated thermal transpiration membrane. Temperature mea- surement locations indicated with numbers. . . . . . . . . . . . . . . . . . . . . . . . 96 xii 6.7 Catalyst chamber temperatures for thermal transpiration experiment set-up with no membrane installed: thermocouple 1 = solid line, 2 = dashed line, and 3 = dotted line (number based on Figure 6.6). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.8 System pressures for thermal transpiration experiment with no membrane installed: tank pressure = solid line, upstream of catalyst chamber = dashed line, and down- stream of silver catalyst = dotted line. . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.9 Catalyst chamber temperatures for thermal transpiration experiment with membrane A installed: thermocouple 1 = solid line, 2 = dashed line, and 3 = dotted line (number based on Figure 6.6). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.10 System pressures for thermal transpiration experiment with membrane A installed: tank pressure = solid line, upstream of catalyst chamber = dashed line, and down- stream of silver catalyst = dotted line. . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.11 Catalyst chamber temperatures for thermal transpiration experiment with membrane B installed: thermocouple 1 = solid line, 2 = dashed line, and 3 = dotted line (number based on Figure 6.6). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.12 System pressures for thermal transpiration experiment with membrane B installed: tank pressure = solid line, upstream of catalyst chamber = dashed line, and down- stream of silver catalyst = dotted line. . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.13 Chamber pressure and mass flow with and without a transpiration phase for a pore diameter of 0.7m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.14 Thrust with and without a transpiration phase. Higher pressures lead to higher thrust. 102 D.1 Thrust for a 80 C tank test run using calibration 1 (taken at the beginning of the test day) and calibration 2 (taken at the end of the test day). The average of the steady state mean was reported as the thrust value. . . . . . . . . . . . . . . . . . . . . . . . 121 E.1 H 2 O 2 Propellant: O-ring Variant, SSCD nozzle mass flow rate calculated from known propellant load and test run length. . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 E.2 H 2 O 2 spacer SSCD nozzle mass flow rate calculated from known propellant load and test run length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 E.3 H 2 O spacer SSCD nozzle mass flow rate calculated from known propellant load and test run length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 E.4 H 2 O 2 spacer SSCO nozzle mass flow rate calculated from known propellant load and test run length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 E.5 H 2 O spacer SSCO nozzle mass flow rate calculated from known propellant load and test run length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 xiii ACKNOWLEDGMENT Reflecting back on the last few years, I am humbled by the amount of support I have received from mentors, friends, colleagues, and family. My achievements in this degree, including this dissertation, would not have been possible without their contributions. I would like to extend my deepest gratitude to my advisor, Paul Ronney, for his wisdom on a variety of topics spanning from combustion to life as an astronaut trainee, his understanding and flexibility regarding my work/research/university balance, and his invaluable contributions to my research. I am also deeply indebted to my supervisor at the Aerospace Corporation, Randy Villahermosa, for providing unparalleled support from the very beginning to the very end of this process. Furthermore, I would also like to thank Geoff Reber for championing both my PhD application as well as my first research proposal at the Aerospace Corporation. The concepts explored in this thesis would not have been possible without his guidance. I would also like to extend my sincere thanks to all of my Aerospace Corporation colleagues who have contributed to this work by helping collect and analyze data as well as always being willing to gather in a conference room or lab for an in-depth discussion. Specifically I would like to thank my publication co-authors, Evan Ulrich (LabVIEW and electronics champion), John DeSain (laser connoisseur), and Andrea Hsu Schouten (thrust measurement guru). Many thanks also extend to David Hinkley, Brian Brady, Lee Steffeney, Andrew Blackney, Hannah Weiher, Tom Curtiss, John Quinn, Chuck Gustafson, and several other members of the iLab, Propulsion, Machine Shop, Small Satellite, and Guidance and Controls groups. I am also exceedingly grateful to my Combustion Physics Lab PhD cohorts: Si Shen, Jakrapop “Boom” Wongwiwat, Ashkan Davani, Eugene Kong, Yang Shi, Zhenghong “Harris” Zhou, and Patharapong “Winry” Bhuripanyo. Your camaraderie and insights were invaluable. Special thanks to Professors Dan Erwin, Garrett Reisman, Mike Gruntman, Fokion Egolfopoulos, Joseph Kunc, who graciously served on my qualification and/or dissertation committees. Finally this work could not have been completed without the research and academic support from the Aerospace Corporation’s Technical Investment and Fellowship Program. xiv ABSTRACT Propulsion is a critical capability for artificial satellites, allowing for constellation management, extended mission durations, and orbit reconfiguration. However due to volume and power con- straints as well as safety requirements, only a limited number of CubeSats have launched with on-board propulsion systems. With the recent trend towards smaller satellites but more plentiful constellations, new propulsion concepts need to be developed and executed to enable these smaller platforms to perform more broad missions. This body of work details the development of the first vacuum-evaporated monopropellant propulsion system. The iterative design and optimization process is documented for three working prototypes, all specifically designed to meet small satellite volume and power limitations. Hy- drogen peroxide (H 2 O 2 ) was chosen as the monopropellant of study and its vapor properties and decomposition reaction was examined extensively to understand the behavior within the thruster body and specifically the catalyst chamber. Theoretical studies showed the H 2 O 2 vapor thruster concept had the potential to provide the highest vacuum specific impulse of any H 2 O 2 system (>200 s), while retaining the advantages of small size and simple construction typical of liquid monopropellant systems. For a nominally- sized thruster, the theoretical thrust could be varied from 0.5 to 8 mN simply by changing the temperature of the tank in which the liquid H 2 O 2 is stored. The first prototype found that when vapor was allowed to flow over the catalyst its temperature increases slowly at first then rapidly when the vapor H 2 O 2 mole fraction exceeded approximately 0.5 and a catalyst temperature of about 130 C was reached. An analysis of the equilibrium state on the catalyst indicated that this temperature corresponded to the condition where the surface coverage shifts from predominantly H 2 O to a significant fraction of open platinum sites where H 2 O 2 could adsorb and react. To better understand the behavior of the H 2 O 2 vapor within the propulsion system, an H 2 O 2 vapor concentration diagnostic was developed using near-infrared laser absorption. The spectral features of low pressure H 2 O 2 vapor were examined near the Doppler-broadened limit. An ad- vantageous portion of the spectra near 1420 nm containing several distinct H 2 O 2 peaks and one well-known water (H 2 O) peak (for calibration) was identified and the cross-sections of these peaks determined. Specifically the peak at 1420.06 nm was recommended as the most advantageous sin- gle line for determining H 2 O 2 concentration due to its high strength and distance from interfering xv absorbers. The cross section values were then employed to measure vapor-phase concentrations of H 2 O 2 upstream and downstream of several known catalyst materials, specifically silver mesh, platinum mesh, and platinum on alumina spheres. Using those data, the global reaction rates were deter- mined as a function of catalyst surface area, residence time, and temperatures from ambient to 120 C. The kinetics, approximated as a gas-phase reaction, were found to be first order. Silver mesh showcased the highest reaction rate, with a rate constant of 10.7 s -1 and an average destruction of 76%. The same catalyst materials were also investigated in the second thruster prototype. Silver mesh led to the highest catalyst temperatures (>236 C), specifically when 3 - 7 sheets were com- pacted into the chamber. Sheet numbers outside this range resulted in lower temperatures. Heat transfer proved to be the primary concern in the system, with substantial effects on catalyst tem- perature and overall system performance. Finite element modeling was used to identify heat paths in the design and make improvements to decrease catalyst chamber heat loss. Thrust measurements were conducted for the third and final prototype design, which featured the lowest pressure drop and most compatible valve and sensor package (when compared to the prior prototypes). Depending on the thruster design and tank temperature, thrust varied from 0.5 mN to 2.5 mN and specific impulse varied from 55 s to 80 s. Comparison of experimental results to theory revealed substantial thrust losses, most likely due to a large subsonic boundary layer that forms at low Reynolds numbers. Comparisons of the H 2 O 2 vapor system to a steam variant using the same thruster body and nozzle, revealed a 60% better performance by the H 2 O 2 vapor. Improvements in catalyst temperature and nozzle design were suggested to further increase that performance differential. Lastly, the potential integration of a thermal transpiration pump into the catalyst chamber was explored. The third H 2 O 2 vapor thruster prototype was modified slightly to allow for pressure measurement directly upstream and downstream of the catalyst chamber. A microfiber membrane, pore diameter< 1m, was added to the chamber ahead of the catalyst. A combination of theoret- ical and experimental studies show a potential 30 - 60% increase in thrust and mass flow rate by incorporating the thermal transpiration pump. xvi CHAPTER 1 INTRODUCTION The successful launch of the first artificial satellite, Sputnik 1, marked humanity’s entrance into the Space Age. Sputnik 1 stayed on orbit for< 3 months and had approximately 1 W of power on-board. However even with its low power and short mission, valuable information about upper atmosphere density and characteristics about the ionosphere were extracted from the drag and radio signal propagation. While those early satellites had few capabilities, they demonstrated the potential of Earth-orbiting satellites. As of 2019, there are approximately 5000 satellites on orbit, 7 of them in orbit around celestial bodies other than Earth, performing a variety of missions including Earth observation, communication, navigation, weather, and exploration [1]. Government and commercial satellites, such as Geostationary Positioning System satellites (GPS, mass 1,600 kg, volume 10.3 m 3 ), have propulsion systems to allow for them to point in- struments, re-position once on orbit, and/or maintain their position within a constellation. Without this capability, satellites in low earth orbit would loose altitude and re-enter the Earth’s atmosphere due to drag. Typically a satellite’s usable life is considered over once it has exhausted its propellant and no longer has the ability to adjust its orbit. These highly capable satellites come with a high cost, e.g., GPS III, the first of which launched in 2018, is estimated to cost $577 million each [2]. This matches with the traditional way satellites have been built over the last several decades: develop a highly reliable, expensive satellite with as much new technology as possible and load that satellite on a dedicated, highly reliable, expensive launch vehicle (cost $100 million). Once on orbit, the satellite operates continuously for decades. However, in recent years this model has been threatened by two major changes: (1) the development of weapons that can destroy on-orbit satellites, and (2) universities and small companies entering the space industry. Both of these changes have pushed the industry towards greater numbers of smaller, more affordable but less capable satellites. High launch costs are, in part, due to the non-standard and complex structures necessary for large satellite integration into the launch vehicle. This led to the invention of the CubeSat standard, which allowed for the integration and launch of multiple unique small satellites and payloads within one vehicle [3]. The CubeSat form factor (mass 4 kg, volume 0.003 m 3 ) has effectively lowered the barrier of entry to space and dramatically changed how satellites are built 1 2 and launched. 1.1 Small Satellite Propulsion As the small satellite industry matures, customers are looking to expand their capabilities beyond academic learning experiences or technology demonstrations. As was done for their larger predecessors, propulsion systems need to be integrated into these platforms to enable a broader range of missions. These capabilities include: (1) constellation management, (2) formation flying, (3) rendezvous, (4) extended mission durations, and (5) orbit reconfiguration. Small satellite propulsion presents a unique set of challenges. Due to volume constraints and shared launch conditions, trade-offs between subsystem performance, footprint, and power must be made. Additional complexities include subsystem reliability and propellant hazards. Due to these unique and challenging requirements, a limited number of propulsion systems have succeeded in transitioning from development to flight test. Table 1.1 lists systems that have undergone flight testing on satellites under 100 kg, with their respective propellants and performance. This is by no means an exhaustive list, primarily due to non-uniform reporting and the secretive nature of some projects, but it gives an indication of the variety in systems and manufacturers. A more detailed summary of the current state of the art in small satellite propulsion can be found in Lemmer [4]. Compared to all other propulsion options, cold gas systems have the most flight heritage in small satellites, most likely due to the simple design and ease of integration. A typical cold gas system uses pressurized inert gas, which is released through a nozzle to generate thrust. In general these systems fall in the 1-100 mN range with specific impulse (I sp ) values from 30-75 s [4]. In an electromagnetic system, such as the ones developed by Busek and George Washington University (GWU), acceleration is achieved by the interaction of electric and magnetic fields in a plasma [11]. Examples of these systems include pulsed plasma thrusters, vacuum arc thrusters, and magnetic nozzle thrusters. Electromagnetic systems provide very low thrust, micronewton range, with I sp values from 500 to 3000 s. Power requirements in these types of systems vary with thrust level and performance, anywhere from 2 to 50 W. Electromagnetic systems have proven to be very popular among small satellite propulsion manufacturers due to the flexible power constraints, solid propellant, and proven larger-scale operation. While electric propulsion technologies, like electro- magnetic systems, offer great promise, the high cost of manufacturing these systems along with the need for advancements in power processing unit (PPU) technologies, electric power generation and storage, and thermal management currently limit the development and implementation of these 3 Table 1.1: Propulsion Systems with Flight Heritage on Small Satellites<100 kg Prop. Type / Manufacturer Propellant Thrust I sp Satellite Cold Gas / SFL [4] Sulfur hexafluoride 12.5-50 mN 45 s CanX-2 & 5 Cold Gas / Aerospace Corp. [4] Xenon 100 mN 30 s MEPSI-3 Cold Gas / Microspace [4] Argon 1 mN/nozzle 32 s POPSAT-HIP1 Cold Gas / TNO [4] Nitrogen 6 mN 69 s Delfi-n3xt Cold Gas / Marotta [5] Nitrogen 2.4 N at 154 bar 70 s NASA ST-5 Warm Gas / Nanospace [4] Butane 0.1 - 1 mN/nozzle 50-75 s TW-1 Warm Gas / SSTL [6] Butane 100 mN 45 s SNAP-1 Warm Gas / Aerospace Corp. [7] Water 3-5 mN Not Reported AeroCube OCSD Solid Motor / Pacific Scientific [8] Not Reported >1 N 210 s PacSciSat Pulsed Plasma / Busek [4] PTFE 500N 700 s Falcon-Sat 3 Ion + Cold Gas / Univ. of Tokyo [9] Xenon 300N 1000 s PROCYON & HODOYOSHI-4 Vacuum Arc / GWU [4] Metal 1-20N 3000 s BRICSat-P FEEP / Enpulsion [10] Indium 250N 4000 s Not Reported Monoprop / ECAPS [4] LMP-103S 1 N 225 s SkySat propulsion systems on small satellites. Monopropellant systems, such as the one developed by Ecological Advanced Propulsion Systems (ECAPS), utilize the chemical energy stored in a propellant to create thrust. Typical monopropellant thrusters pump-feed or pressure-feed liquid propellant to a catalyst chamber where the liquid reacts with the catalyst creating a high pressure, high temperature gas. This gas is then expanded through a nozzle to generate thrust. Monopropellant systems offer a wide range of thrust levels, anywhere from a few millinewtons to hundreds of newtons, with I sp values from 150 to 4 300 s. This versatility, matched with flight heritage, low power requirements, and off-the-shelf components, are attractive qualities for small satellite manufacturers. 1.1.1 Green Monopropellants Hydrazine (N 2 H 4 ) is the most commonly used monopropellant on larger satellites,e.g., GPS satellites, Wideband Global Satcom satellites, Advanced Extremely High Frequency satellites, etc. However due to its toxic nature and the requirement for extensive safety precautions during loading and operation, it has not been readily adopted for small satellite applications. Environmentally friendly “green” propellants, such as hydroxylammonium nitrate (HAN), ammonium dinitramide (ADN), and hydrogen peroxide (H 2 O 2 ) show promise due to their low toxicity, low volatility, and low vapor pressure. These green propellants are a better fit with the low cost build and launch requirements of the small satellite community, which often includes a “do no harm” clause for integration into a launch vehicle as a secondary payload. This “do no harm” methodology ensures that multiple passengers on a launch do not cause adverse effect to each other, but can force strict rules in terms of pressure vessels, toxicity, and stored energy. Sackheim et al. [12] describes several green propulsion systems including two targeted at small satellite manufacturers: the Aerojet 1 N AF-M315E thruster developed under the NASA green propellant infusion mission and the ECAPS LMP-103S 1 N propulsion system currently flying on SkySat. These systems employ, respectively, propellants based on HAN and ADN. In terms of liquid H 2 O 2 , Platt [13] and Pasini et al. [14] have developed systems operating in the 5 mN to 10 N thrust range, representing the corporate interests of Micro Aerospace Solutions and ALTA S.p.A. Table 1.2 shows a comparison of the specific impulse of hydrazine and the aforementioned green propellants. Table 1.2: Monopropellant Specific Impulse Comparison Propellant I sp (s) Hydrazine (100%) 245 [12] AF-M315E (HAN based) 250 [12] LMP-103S (ADN based) 250 [12] H 2 O 2 (98%) 185 [15] While H 2 O 2 has the lowest specific impulse of the green propellants listed, it does have a 5 unique property that proves useful for low thrust propulsion: a reactive vapor phase. The applica- tions and benefits of this property will be discussed in Chapter 2. 1.1.1.1 Hydrogen Peroxide Hydrogen peroxide is typically known for its household and medical uses in dilute solutions as a disinfectant or bleaching agent [16, 17] and is a known product of photochemical reactions in urban atmospheres [18]. At higher concentrations it can be used as a rocket propellant; in the presence of a catalyst, H 2 O 2 will decompose exothermically into water (H 2 O) and oxygen (O 2 ): H 2 O 2 !H 2 O + 1 2 O 2 (1.1) The temperature of these product gases depend on the initial H 2 O 2 liquid concentration. At concentrations above 67% by mass the heat generated will evaporate all of the water produced in the reaction. At a concentration of 98% by mass the adiabatic reaction temperature is approxi- mately 950 C, leading to the specific impulse provided in Table 1.2. When selecting materials to use in H 2 O 2 systems, it is extremely important to consider the effect the material may have on the propellant. Utilizing an incompatible material could initiate rapid undesirable decomposition and potentially fire or overpressurization. One common method to rank H 2 O 2 material compatibility is presented in Table 1.3, where a class 1 material is considered the most compatible and therefore the most desirable for storage and system design. A class 4 material will cause excessive decomposition, material deterioration, or form impact sensitive mixtures. Catalysts used in propulsion system design fall in the class 4 category [19]. Hydrogen peroxide resembles water in several ways [20]; it is a clear, colorless liquid with only a slightly higher viscosity. It also remains in its liquid state from -11 C to 140 C at 1 atm (for 90% by mass H 2 O 2 ). However, unlike water, H 2 O 2 contracts when frozen solid. Additional prop- erties are provided in Table 1.4. Figure 1.1 shows an image of the H 2 O 2 molecule with dimensions [21]. 6 Table 1.3: H 2 O 2 Material Compatibility Classification Class Definition Typical Materials 1 Materials satisfactory for unrestricted use Aluminum (Al), Al 1100, Polytetrafluoroethylene (PTFE), Mylar R , Pyrex R 2 Materials satisfactory for repeated short-time contact Al 6061, Stainless steel (SS) 316, Silicon, Kel-F R , Polyvinylchloride (PVC), LEXAN TM , Fluorolube 3 Materials should be used only for short-time contact SS 17-7, PTFE cloth, Polyurethane, Fluorel R 4 Materials not recommended for use Copper, Gold, Iron, Nickel, Platinum, Silver, Titanium, Silicone oil Reference: [19] Table 1.4: H 2 O 2 Properties (90% by mass) Molecular Weight 32.4 Specific Gravity 1.39 at 20 C Vapor pressure 5 Torr at 30 C Heat of Vaporization 1372 J/g Heat capacity 2.43 J/g/ C for 0-18.5 C Surface tension 0.07553 N/m Refractive index 1.398 at 20 C Reference: [20, 22] Figure 1.1: Hydrogen peroxide molecule. Safety Precautions High concentration H 2 O 2 is a strong oxidizer and can behave volatilely in certain situations. 7 In order to avoid dangerous scenarios, the following four rules are recommended for storage and handling: Never contaminate Never confine Never contact Always have water available Contamination results from H 2 O 2 exposure to any of the following: (1) incompatible mate- rials, (2) heat, and (3) energy. The decomposition rate of H 2 O 2 increases with temperature by 2.3 times per 10 C rise [21]. Therefore H 2 O 2 stored at 20 C will decompose approximately 1% per year. Tests have shown that H 2 O 2 contact with clean textiles and wood will not cause a fire, how- ever if these materials have any catalytic contaminates, such as rust or dust, spontaneous ignition can occur and can cause serious burns. Water should be used as a protective medium and large quantities should be readily available when working with H 2 O 2 [20]. Decomposition of H 2 O 2 results in oxygen production as shown in Equation 1.1. The in- troduction of a contaminate could result in an extremely rapid over-pressurization and pressure vessel failure. Venting and/or active pressure management as well as contamination prevention is necessary. Hydrogen peroxide contact with skin will cause stinging and capillary embolism, i.e., a whitening of the skin, which will typically disappear after a few hours. The skin should be thor- oughly rinsed with water to reduce the irritation. Prolonged contact may produce blisters and burns. Gloves, safety glasses, and protective clothing are recommended when handling high con- centration H 2 O 2 . 1.2 Laser Absorption Spectroscopy Absorption spectroscopy is one way to determine the concentration, and therefore the behav- ior of a vapor, such as H 2 O 2 vapor. This technique measures a sample’s absorbance of radiation as a function of wavelength. Planck’s law, Equation 1.2, provides one of the fundamental relations for radiation; it ex- plains the spectral-energy distribution of radiation emitted by a blackbody. Planck assumed that the sources of radiation are atoms/molecules in a oscillatory state and that the vibrational energy of each atom may have any of a series of discrete values, but never any value in between. When 8 an atom changes from one state of energy to another, the discrete amount of energy is equal to the product of the radiation frequency and a constant: E =E upper E lower =h (1.2) whereh is the Planck constant and is the frequency of radiation. The wavelength associated with the discrete transitions, or lines, and the spacing between those lines is determined by molecular parameters, such as internuclear spacing and bond angles. The absorbance and linewidth depend upon the sample’s composition, temperature, and pressure. Since each molecule has its own unique absorption spectrum, absorption spectroscopy can be an excellent method for determining concentration of species within a mixture. Typical absorption experiments are done using a laser as a radiation source. Figure 1.2 shows the general schematic for an absorption experiment. The laser provides the incident light at the desired wavelength, I 0 , and the detector collects the transmitted light, I. Figure 1.2: Basic schematic of a laser absorption experimental set-up. Beer’s law describes the relationship between the incident and transmitted laser intensities: I =I 0 e nL (1.3) where I and I 0 are the transmitted and initial intensity, respectively, is the absorption cross section,L is the path length andn is the number density of absorbing molecules. To determine a sample with an unknown concentration, the incident and transmitted inten- sities are collected with a detector and the path length is measured. The absorption cross section of a molecule determines how much electromagnetic radiation it can absorb and is dependent on molecule, wavelength, temperature, and pressure. Due to the complex nature of radiation ab- sorption within molecules, typically the cross section is determined experimentally with a known mixture diluted with an inert bath gas. For common molecules, such as H 2 O, cross section values 9 can be found in literature, with sites like HITRAN [23] providing a useful summary of previous experimental studies. However for more complex molecules and those difficult to obtain known concentrations, such as H 2 O 2 , cross sections values are not readily available. 1.3 Hydrogen Peroxide Vapor Kinetics In order to model the H 2 O 2 decomposition process, it is necessary not only to define the products of the reaction, but also the speed at which they are produced. This is often represented by a global reaction rate constant, k, as seen in Eqn. 1.4. The reaction equation can then be expressed in terms of that rate constant. H 2 O 2 k !H 2 O + 1 2 O 2 (1.4) d[H 2 O 2 ] dt =k[H 2 O 2 ] (1.5) The rate constant is generally represented by an Arrhenius equation, which provides the temperature dependence: k =A 0 exp E A ~ RT (1.6) where A 0 is the pre-exponential factor, E a is the activation energy, ~ R is the universal gas constant, andT is temperature. The pre-exponential factor describes how often molecular colli- sions occur, which then leads to the splitting of the molecule and the generation of products. The activation energy is the minimum required energy for the decomposition to occur. Decomposition can result from heat, generally referred to as thermal decomposition, or via contact with a catalytic surface,i.e., catalytic decomposition. Experimental studies of vapor phase H 2 O 2 decomposition performed by Gigu` ere and Lui [24] as well as Conway [25] show that cat- alytic decomposition dominates over thermal decomposition for temperatures under 450 C. There- fore low temperature studies can effectively neglect thermal decomposition influences on reaction rate. 1.3.1 Catalytic Decomposition The catalytic decomposition process is typically broken down into seven steps; a visual representation is shown in Figure 1.3: 10 1. External diffusion: diffusion of the reactant from the bulk gas through the boundary layer to the outside of the catalyst 2. Internal diffusion: diffusion of the reactant into the catalyst material 3. Adsorption: adhesion of molecules to the catalyst 4. Actual decomposition: formation of products 5. Desorption: release of molecules from the catalyst 6. Internal diffusion: diffusion of the products from the catalyst material 7. External diffusion: diffusion of products through the boundary layer to the bulk gas Figure 1.3: Visual representation of a heterogeneous catalytic reaction, where A represents the reactant and B the product. Therefore, the overall decomposition velocity depends on the slowest step in this process, which will indicate if the reaction is diffusion-limited or reaction-limited. Holub et al. [26] stated that the torturous path associated with the catalyst bed prevents the formation of a velocity bound- ary layer and Koopmans [27] extended this assumption to the diffusion boundary layer. For a liquid molecule, further support of this theory is supplied by Oehmichen et al. [28]. They reported that for liquid concentrations above 30% by mass, decomposition rate was independent of liquid stir- ring speed, which indicates a reaction-limited system. This is explained by the enhanced mixing due to the formation of gaseous product bubbles in the liquid reactants. As the bubbles break away 11 from the surface, the gap is immediately filled with liquid. For a vapor phase reaction, both the reactant and product are in the gas phase and therefore the studies of Oehmichen et al. [28] would not apply. And while the Holub et al. [26] theory on the torturous path still holds, the assumption for a reaction-limited process is not as strong. Nor has there been many experimental studies in the area, with most research focus on liquid heterogeneous systems or vapor homogeneous systems. Once the reactant makes it to the surface the following reaction scheme can be used. A +site k ad * ) k de Asite kreac !B +site (1.7) whereA is the reactant,B is the product,site represents the active sites at the catalyst that promote reaction, k de is the reactant desorption rate, k ad is the reactant adsorption rate, and k reac is the reaction/product desorption rate. The rate of adsorption depends on the concentration of the reactants, the availability of active sites, and the sticking probability, while the rate of desorption depends on the fraction of active sites to which a molecule is chemisorbed. Pasini et al. [29] assumed fast equilibrium adsorption and first-order finite-rate product desorption for their one-step H 2 O 2 decomposition reaction, seen in Equation 1.8, which had good correlation with experimental results. Other researchers, including Zhou and Hitt [30], Krejci et al. [31], and Corpening et al. [32], have also utilized a global reaction rate, single step assumption for the decomposition of H 2 O 2 . H 2 O 2 +site k ad * ) k de siteH 2 O 2 (ads) kreac !H 2 O + 0:5O 2 (1.8) Experimental and theoretical studies [33–36] into the intermediate reactions in the H 2 O 2 decomposition process and their associated rates have yielded little consensuses. Plauck et al. [36] used a combination of density functional theory and kinetic experiments to identify 17 elementary steps with several different reaction pathways for their H 2 O 2 reaction mechanism. It was concluded that the key parameter governing H 2 O 2 decomposition is the breaking of the O-O bond in the adsorbed H 2 O 2 molecule or the intermediate species, adsorbed hydroperoxyl (OOH). 1.4 Thermal Transpiration Thermal transpiration or thermal creep is a rarefied gas dynamic phenomenon which causes gas molecules to flow through a membrane or capillary tubes when a temperature gradient is 12 present. The flow initiates and maintains a pressure difference between the cold and hot sides. Since this is a rarified gas effect the pores of the path must have a radius on the order of the mean free path of the gas molecules. A small pore size can be accomplished with a nanoporous mem- brane. As the gas moves from the cold side to the hot side of the flow path the temperature and pressure of the gas increases. Knudsen [37] was first to use the thermal transpiration effect to develop a miniature pump in the 1900s. He was able to demonstrate a compression ratio of ten by using a series of tubes each with a transpiring phase to heat and compress the gas and then a cooling phase where the temperature was dropped but the pressure was retained. An illustration of one stage employing this concept with temperature and pressure lines can be seen in Figure 1.4. Figure 1.4: Illustration of one stage in a Knudsen compressor. While several studies have investigated thermal transpiration, most use electrical power to generate the temperature gradient [38–40]. In a small satellite, power is limited and the usage of it in a transpiration application might not be feasible. For example, the Optical Communications and Sensor Demonstration Cubesat, which included a water thruster for proximity operations, had an average power input of 4.5 W from its solar cells [41]. In a thruster application, instead of using electrical power to create the required temperature differential, the high temperature product gases of the chemical reaction could be used, as is shown in Figure 1.5. Some studies utilizing a chemical reaction to initiate thermal transpiration have already been done at the University of Southern California. Zeng et al. [42], Wang et al. [43], and Ochoa et al. 13 Figure 1.5: Thermal transpiration effect within a simple thruster design. [44] used the catalytic reaction of a hydrocarbon/ air mixture to create the temperature difference to run a small thermal transpiration pump. Zeng et al. [42] used propane as the feedstock propellant, utilizing the self-sustained catalytic combustion to maintain the necessary temperature difference for thermal transpiration and passive pumping. Utilizing a passive catalytically-activated thermal transpiration pump could increase the pres- sure, and in the case of a monopropellant propulsion system, the thrust, with no additional moving parts. Small moving parts add complexity and failure points in a system due to heat loss, friction loss, and manufacturing difficulties. This has been witnessed by researchers studying miniature internal combustion engines and electrical generators for handheld portable devices [45, 46]. 1.5 Thesis Overview In the remainder of this thesis, the viability of H 2 O 2 vapor as a propellant for small satel- lite propulsion is systematically investigated. The following sections provide an outline of the upcoming chapters. 1.5.1 Hydrogen Peroxide Vapor Propulsion System In Chapter 2, the H 2 O 2 vapor propulsion system concept is introduced. The theoretical performance parameters are calculated and compared with a liquid-fed design. A prototype sys- tem including a tank, heater, platinum catalyst, and nozzle (to be referred to as Prototype 1) was constructed and five exploratory test runs were conducted. These tests explored the impact of pro- pellant concentration and tank temperature on performance. Analysis of the vapor mole fraction 14 and percentage of open catalyst sites provide insights into the dynamic behavior of the system. 1.5.2 Laser Vapor Diagnostic In Chapter 3, an H 2 O 2 vapor diagnostic is developed using a near-infrared diode laser as a non-invasive measure of concentration. Knowledge of concentration is necessary for determining the performance and reaction rates of H 2 O 2 on specific catalysts. The absorption spectra of vapors of concentrated H 2 O 2 / H 2 O mixtures (without a carrier gas) were characterized at wavelengths from 1390 to 1470 nm. Low pressures were employed to examine these spectral features near the Doppler-broadened limit. An advantageous portion of the spectra near 1420 nm containing several distinct H 2 O 2 peaks and one well-known H 2 O peak (for calibration) was identified and the cross sections determined. These cross section values are employed, using Beer’s law (Equation 1.3), to obtain H 2 O 2 concentration. 1.5.3 Reaction Rates In Chapter 4, the diagnostic developed in Chapter 3 was used to determine the reaction rates of three common H 2 O 2 catalysts: platinum on alumina spheres, silver mesh, and platinum mesh. Hydrogen peroxide vapor was transported to the catalyst via a helium carrier gas, which flowed through a reservoir of high concentration liquid H 2 O 2 . After reacting on the catalyst, the product gas composition was measured using laser absorption in a multi-pass flow cell. The global reaction rate was determined as a function of catalyst surface area, residence time, and temperatures from 21 to 120 C. Rates were first characterized for a perfectly-mixed reactor following Equation 1.5, and then using a multiphysics model to incorporate diffusion and boundary layer interaction. 1.5.4 Performance Optimization In Chapter 5, two further iterations of the H 2 O 2 vapor propulsion system are presented with the focus on catalyst design, heat transfer, pressure drop, and material compatibility. The catalyst materials characterized in Chapter 4 were tested in the Prototype 2 configuration and the thruster experimental results were compared to the reaction rate studies. A heat transfer model was created and used to understand the heat flow through the system to identify potential improvements that could be implemented on the next iteration. Prototype 3 built on the lessons learned from Prototype 2 and was the subject of several thrust measurement campaigns using a torsional pendulum thrust stand. Specific impulse is calcu- 15 lated using the measured thrust and mass flow rate. Nozzle design was considered and efforts to minimize heat loss were implemented. 1.5.5 Catalytic Thermal Transpiration In Chapter 6, the implementation of a catalytically-activated thermal transpiration mem- brane into a slightly modified Prototype 3 H 2 O 2 catalyst chamber is investigated. The theoretical performance and an experimental series varying membrane pore diameter and tank temperature are compared. CHAPTER 2 HYDROGEN PEROXIDE V APOR PROPULSION SYSTEM Traditional satellite propulsion systems used over the past several decades were designed for mas- sive satellites when compared with CubeSats (e.g., GPS IIF weighed upwards of 1,600 kg and measured 10.3 m 3 , whereas a standard 3U cubesat weighs 4 kg and measures 0.003 m 3 ). Therefore the requirements and design trades of these existing systems are drastically different than those of a smaller, CubeSat propulsion system. While scaling these systems down can decrease the thrust to a more desirable range for small satellites, doing that maintains all of the attributes of the larger system and introduces additional complexities. In the proposed thruster 1 , a schematic of which is shown in Figure 2.1, reactive H 2 O 2 vapor is vacuum-evaporated from the surface of the stored liquid. The vapor flows to a catalyst bed where a chemical reaction occurs producing hot product gases, which then can be utilized to generate thrust. This propellant feed system represents the mirror image of a tradition monopropellant, which pressure-feeds liquid propellant to the catalyst. This design has the potential to provide millinewtons of thrust with low tank pressure (< 2 psia), no additional pressurant gas system, and minimal power requirements. A vapor system utilizes all of the liquid propellant (i.e., none stays trapped in the system) and the specific impulse remains constant or improves over the life of the thruster due to vacuum distillation. Additionally, many of the hydrodynamic complications (e.g., droplet and bubble formation, thermocapillary flows) that prevent full decomposition in low thrust liquid systems, do not occur in a vapor-phase propulsion system [47]. Figure 2.1: Schematic of vapor-fed H 2 O 2 propulsion system. However, working with a vacuum-evaporated vapor does imposes some strict requirements on the stored liquid monopropellant. These include: 1 United States Patent Application 20170363044 16 17 No phase separation Liquid phase at ambient conditions Low vapor pressure Low health hazard Low volatility in storage The first two requirements are necessary for the described system to function. The propel- lant must produce a usable vapor and must have liquid to enable vacuum boiling. The last three requirements allow for easier implementation by the small satellite community and less difficulty in research and development. Many monopropellants were eliminated based on these considerations. The most widely used monopropellant, hydrazine, is considered a possible human carcinogenic by the EPA, requires the use of a Self Contained Atmospheric Protection Ensemble, SCAPE, suit for humans to handle, and is highly flammable. Salt-based propellants, such as HAN and ADN, were eliminated since they would not have a reactive vapor phase. Nitrous oxide and ethylene oxide both were not considered due to their low boiling point; they are gases at room temperature. Hydrogen peroxide (H 2 O 2 ), isopropyl nitrate (C 3 H 7 NO 3 ), and nitromethane (CH 3 NO 2 ) meet the listed requirements; due to flight heritage and extensive documentation on propellant behavior, H 2 O 2 was chosen for this study. 2.1 Theoretical Performance In this section, the vapor/liquid equilibrium characteristics for H 2 O 2 are reported, then the relative performance of vapor and liquid propulsion systems are calculated using a chemical equi- librium code based on STANJAN [48]. The input parameters of the analyses are the H 2 O 2 mole fraction in the H 2 O 2 / H 2 O mixture and the liquid propellant temperature. The catalyst chamber pressure was taken to be the vapor pressure of the propellant at prescribed temperatures. The propulsion cycle analysis assumes steady flow with constant-pressure decomposition of the liquid or vapor followed by isentropic expansion of the products by a specified exit-to-throat area ratio. From the pressure, velocity, and density at the throat (defined as the location where the local sound speed is equal to the local velocity,i.e., a Mach number of unity) and the exit were calculated. This allowed for the mass flow rate, thrust, and vacuum specific impulse to be determined. 18 2.1.1 Vapor Properties Hydrogen peroxide used in propulsion applications is typically 70 - 98% H 2 O 2 mixed with water. Figure 2.2 shows the total and partial vapor pressure at 60 C of a liquid H 2 O 2 / H 2 O solution. Due to the comparably high vapor pressure of H 2 O, the liquid H 2 O 2 mole fraction has to be at 82% to get to a 50% vapor H 2 O 2 mole fraction. The vapor pressure of H 2 O was determined using the Antoine equation parameters for vapor pressure (data provided by Stull [49], coefficients calculated by Linstom and Mallard [50]). The H 2 O 2 vapor pressure was calculated using the following relation developed by Scatchard et al. [51]. log 10 (P ) = 44:5760 4025:3 T 12:996log 10 (T ) + 0:0046055T (2.1) whereP is the vapor pressure in torrs andT is the temperature in kelvins. Scatchard et al. [51] also proposed equations for H 2 O 2 /H 2 O mixtures utilizing Raoult’s law modified for non-ideal mixing. The fugacity coefficient, the correction for gas non-ideality, was removed because it was believed that corrections for gas imperfection was not of a magnitude comparable to the experimental error. Activity coefficients, , were taken from Keyes et al. [52]. P =p H 2 O x H 2 O H 2 O +p H 2 O 2 (1x H 2 O ) H 2 O 2 (2.2) H 2 O =e (1x H 2 O ) 2 ~ RT [1017+0:97(T273:15)+85(14x H 2 O )+13(12x H 2 O )(16x H 2 O )] ! (2.3) H 2 O 2 =e x 2 H 2 O ~ RT [1017+0:97(T273:15)+85(34x H 2 O )+13(12x H 2 O )(56x H 2 O )] ! (2.4) where ~ R is the gas constant in calories per kelvin per mole. 19 Figure 2.2: Vapor pressure of a liquid H 2 O 2 /H 2 O solution at 60 C. 2.1.2 Effects of Liquid Mole Fraction on Performance Increasing the liquid H 2 O 2 mole fraction of the propellant increases the vapor H 2 O 2 mole fraction and decreases the catalyst chamber total pressure, as was shown in Figure 2.2. For a vapor thruster operating in vacuum with a throat diameter of 0.79 mm, an exit diameter of 4.8 mm, and a tank temperature of 60 C, the I sp effects of altering the liquid H 2 O 2 mole fraction are shown in Figure 2.3. Figure 2.3 also shows the I sp of a liquid system assuming the same tank temperature and catalyst chamber pressure. The thrust for both systems is shown in Figure 2.4. While the thrust is comparable for the two systems (decreasing with decreasing total pressure), a vapor system has the potential to provide approximately 25% higher I sp . 20 Figure 2.3: Vacuum specific impulse of a vapor and liquid system with a throat diameter of 0.79 mm, an exit diameter of 4.78 mm, and a tank temperature of 60 C. Figure 2.4: Vacuum thrust of a vapor and liquid system with a throat diameter of 0.79 mm, an exit diameter of 4.78 mm, and a tank temperature of 60 C. 2.1.3 Effects of Tank Temperature on Performance Increasing the tank temperature increases the catalyst chamber total pressure and the vapor H 2 O 2 mole fraction. For a vapor thruster of the same design laid out in Section 2.1.2 and a liquid H 2 O 2 mole fraction of 0.9, the I sp and thrust effects of altering the tank temperature are shown in Figure 2.5 and 2.6. The figures also show the impacts on a liquid system assuming the same catalyst chamber total pressure. The slight increase in I sp in the vapor system is due to the increase 21 in vapor H 2 O 2 mole fraction. The increase in thrust for both systems correspond to the increase in total pressure. Figure 2.5: Vacuum specific impulse of a vapor and liquid system with a throat diameter of 0.79 mm, an exit diameter of 4.78 mm, and a liquid H 2 O 2 mole fraction of 0.9. Figure 2.6: Vacuum thrust of a vapor and liquid system with a throat diameter of 0.79 mm, an exit diameter of 4.78 mm, and a liquid H 2 O 2 mole fraction of 0.9. 2.2 Prototype 1: Proof of Concept A prototype device was constructed and tested to evaluate the concept of an H 2 O 2 vapor thruster for varying H 2 O 2 concentrations and tank temperatures. Heat transfer, material incom- 22 patibility, incomplete decomposition, and viscous losses will influence the behavior of an actual system and lead to lower performance than that calculated in Section 2.1. 2.2.1 Design and Construction Prototype 1 is shown in Figure 2.7. The system measures 5 x 5 x 8 cm, approximately 1/4 of a standard CubeSat unit. The body is constructed of aluminum 1100 and the catalyst chamber and nozzle were machined out of MACOR R with an interior catalyst chamber 5 mm in diameter and length. The nozzle throat diameter is 0.79 mm and the exit diameter is 4.8 mm (area ratio 36.6), the same dimensions as was used for the theoretical calculations in Section 2.1. The MACOR R catalyst chamber/nozzle was secured to the thruster body with 3 screws and a Kalrez R o-ring seal. Two flexible heaters are attached to the outside body to control the temperature of the liquid propellant. The vapor flow is controlled with two normally closed solenoid valves in series for fault protection. The valve orifice diameter is approximately 1 mm. The catalyst used was a bundle of 1 mm diameter platinum wires press-fit inside of a PTFE sleeve as shown in Figure 2.8. Figure 2.7: Hydrogen peroxide vapor thruster Prototype 1: CAD model with transparent tank lid (left), test unit (right). 23 Figure 2.8: Platinum wire catalyst bed within the MACOR R catalyst chamber. 2.2.2 Measurements Temperature measurements were made with Omega type T thermocouples in two locations: (1) on the outside bottom surface of the tank and (2) within the catalyst bed along the centerline. The manufacturer’s stated accuracy for these thermocouples is the greater of 1 C or 0.75%, with a recommended temperature range of -250 C to 350 C. Some of the highest temperatures observed during testing exceeded 350 C and thus the accuracy of these data is unknown. Propellant tank pressure measurements were made with a Honeywell TruStability TM absolute pressure sensor with a 0 - 775 Torr range having an accuracy of0.25% full scale span best-fit straight line. Noise in the tank pressure sensor was reduced using a Butterworth low pass filter with a 0.2 Hz cutoff frequency. Prior to each test, the propellant liquid concentration was measured with a MISCO refrac- tometer (accuracy0.2% by mass H 2 O 2 ). 2.2.3 Results Five test runs were performed, during some of which the tank temperature was intentionally varied. Figures 2.9, 2.10, and 2.11 show the measured catalyst temperatures, tank temperatures, and tank pressures, respectively, for these test runs. Within each run, once the propellant valve was opened, it was found that the initial rate of temperature rise within the catalyst bed was relatively slow and nearly linear. This behavior was followed by a transition to a relatively rapid but again nearly linear rate of temperature rise and finally a transition to a slower asymptotic-like approach to a maximum temperature. These regions of nearly linear behavior were deemed the “warm-up zone,” defined as the period from valve opening to when T=t< 0.4 C/s, whereT refers to the catalyst temperature andt is time and the “rapid reaction zone,” defined as the period from when T=t> 4 C/s until T=t< 3.5 C/s. The catalyst temperature ranges for these two zones are shown in Table 2.1 along with the corresponding tank temperatures, as well as the initial H 2 O 2 liquid-phase concentrations and 24 the maximum catalyst temperatures achieved in these tests. Figure 2.9: Measured catalyst temperatures for each test run. Figure 2.10: Measured tank temperatures for each test run. The temperature-time profiles during the warm-up and rapid reaction zones are shown in Figures 2.12 and 2.13, respectively. For each profile, the starting condition is the time and temper- ature at which the zone begins. For Figure 2.12 data are shown for tests 1 - 4 only because test 5 immediately entered the rapid reaction zone upon opening the valve. This is likely due to the fact that the initial H 2 O 2 concentration was higher for test 5 than tests 1 - 4. Fitting each profile within the warm-up zone with a linear regression leads to similar slopes, ranging from 0.05 to 0.07 C/s. During the times corresponding to these zones, the tank temperature was increasing for tests 1 and 25 Figure 2.11: Measured tank pressures for each test run. Table 2.1: Test Control Variables, Catalyst Temperature Zones, and Maximum Catalyst Temperature Test Starting Concentration Tank Temperature Range ( C) Warm-up Zone ( C) Rapid Reaction Zone ( C) Maximum Catalyst Temperature ( C) 1 79.3% by mass (67.0% by mol) 21 - 57 27 - 57 139 - 259 517 2 79.3% by mass (67.0% by mol) 56 - 60 81 - 119 154 - 284 428 3 79.3% by mass (67.0% by mol) 56 - 79 78 - 111 136 - 314 553 4 79.3% by mass (67.0% by mol) 42 - 62 55 - 95 132 - 261 394 5 90.0% by mass (82.7% by mol) 60 - 63 - 113 - 307 430 4, but was held constant for tests 2 and 3. These differences in operating conditions do not appear to affect the rate of temperature rise during the warm-up zone. Figure 2.13 shows the temperature- time profiles during the rapid reaction zone. Test 5 exhibits a much more rapid rise (slope = 16.4 C/s) than the other tests 1-4 (slopes ranging from 5.7-8.6 C/s), again likely due to the differences in initial H 2 O 2 concentrations. 26 Figure 2.12: Change in temperature during the warm-up zone for tests 1 - 4. Figure 2.13: Change in temperature during the rapid reaction zone (data and linear fit). Equation 2.2 was used to infer an estimate of the liquid concentration and therefore the vapor concentration delivered to the catalyst with respect to time. Results are shown in Figure 2.14 for tests 2, 3, and 5, with the beginning of the rapid reaction zone marked with a circle on each test profile. Tests 1 and 4 were excluded from this analysis since the tank temperature was varied during these tests. The location of these circles correspond to H 2 O 2 vapor mole fractions between 0.45 and 0.55. This suggest that rapid reaction initiates when the concentration of H 2 O 2 vapor arriving at the catalyst bed exceeds that of H 2 O vapor. Table 2.1 shows that for all 5 tests the catalyst temperature at the beginning of the rapid reaction zone is between 113 and 154 C. In the following, it is shown that this temperature range corresponds to conditions where enough H 2 O 27 has desorbed from the catalyst surface that a sufficiently large fraction of the surface is Pt sites available for reaction with H 2 O 2 vapor. Thus, for rapid reaction, two conditions must be satisfied: (1) a sufficiently high concentration of H 2 O 2 vapor compared to H 2 O vapor (approximately 50% H 2 O 2 ) and (2) a sufficiently high density of active catalyst sites (approximately 90%). Figure 2.14: Vapor mole fraction over test time. The circles mark the beginning of the rapid reaction zone. The concentration of active Pt sites on the catalyst bed is based on the equilibrium between the rates of adsorption and desorption of H 2 O on the surface. The rate of adsorption of H 2 O on platinum is collisionally limited with a sticking probability (S) of 0.75 [53]. The rate of collisions of gas molecules on a surface (in units of moles per square meter per second) is given by P p 2M ~ RT (2.5) whereP is the pressure,M is the molecular mass, ~ R the universal gas constant, andT the absolute temperature. A fraction of these collisions equal to (1 - H 2 O ) is with platinum sites not already occupied by H 2 O, thus the adsorption rate of H 2 O on the surface is given by d[H 2 O] s dt = SP (1 H 2 O ) p 2MRT (2.6) where [H 2 O] s is the surface concentration of H 2 O in units of moles per square meter, which in turn can be written as H 2 O , where is the total number of platinum sites per unit area of the catalyst surface (approximately 2.5 x 10 -5 moles/m 2 for a smooth platinum surface). The rate of 28 desorption of H 2 O from a platinum surface is given by d[H 2 O] s dt =Z[H 2 O] s exp E a ~ RT (2.7) whereZ is the frequency factor (10 13 /s) andE a is the activation energy (40,300 J/mole) [53]. At equilibrium, the rates of adsorption and desorption are of equal magnitudes and thus H 2 O = 1 1 + Z p 2M ~ RT SP exp Ea RT (2.8) The fraction of available Pt sites is simply 1 H 2 O , which is shown in Figure 2.15 for the aforementioned rate constants. It can be seen that the availability of Pt sites is very low near room temperature, increasing to 50% near 70 C and 90% at 130 C. This analysis strongly suggests that, as mentioned above, the transition to rapid reaction corresponds to a transition from surface coverage dominated by H 2 O to a surface with a significant fraction of sites available for H 2 O 2 to adsorb on the surface and react. Figure 2.15: Fraction of platinum sites, Pt(s), available at varying catalyst temperatures. 2.3 Summary The theoretical evaluation and initial prototype proved that the H 2 O 2 vapor thruster concept is feasible, beneficial, and implementable. The effects of tank temperature and liquid and vapor concentrations on thrust and specific impulse were measured. From the experiments the mini- mum H 2 O 2 vapor mole fraction and the minimum catalyst bed temperature needed to promote the 29 transition to rapid reaction were inferred. This information was then leveraged in the design of Pro- totypes 2 and 3 to promote immediate rapid reaction and minimize time to steady state conditions (to be covered in Chapter 5). CHAPTER 3 LASER DIAGNOSTIC To characterize the H 2 O 2 vapor thruster performance, it is important to quantify the concentration of H 2 O 2 vapor in the vicinity of the catalyst bed and the amount of unreacted vapor present in the exhaust. From this information the thruster efficiency can be determined and chemical kinetics of the catalytic reaction can be inferred. For relevance to propulsion applications, a traditional spectroscopic approach using highly diluted samples at relatively high total pressures contained in a stagnant vessel is not appropri- ate because (1) the H 2 O 2 vapor may decompose on a time scale shorter than the measurement duration; (2) individual absorption lines cannot be determined in higher-pressure systems due to collisional broadening and (3) such conditions would not provide spectra that are representative of those present in low-pressure vapor-phase propulsion applications. Additional considerations for measuring H 2 O 2 spectra are (1) the diagnostic must be able to differentiate between H 2 O 2 and H 2 O, a difficult task because the molecules have similar O-H bond characteristics and therefore some similar spectral features and (2) the diagnostic must not cause decomposition of H 2 O 2 . Using absorption spectroscopy to measure concentrations of H 2 O 2 has been employed pre- viously, however, the focus of most of these studies has been in the ultraviolet (UV) or far infrared regions. The UV region has been of particular interest due to the impact of H 2 O 2 photolysis in the atmosphere at UV wavelengths. As early as the 1930s, Fergusson et al. [54] measured broadband absorption cross sections from 200 to 500 nm. Recently Kahan et al. [55] compared cross section measurements from six different studies spanning 40 years. The mid to far infrared, including the fundamental 3 and 6 bands, have also been explored and these data are available in the HITRAN database [23]. One of the spectral regions of H 2 O 2 notably lacking in the literature is the near infrared (NIR), which is an ideal wavelength region for in-situ measurements because H 2 O 2 is a strong absorber in this region and because of the availability and robustness of commercially-available NIR diode lasers with optical fiber couplings. Using a high-resolution diode laser and low total pressures, individual H 2 O 2 absorption lines can be resolved near their Doppler-broadened limit, which eliminates issues that arise with broadband measurements, primarily the need to account for H 2 O vapor in the sample. Parker et al. [56] investigated two NIR lines near 1506 nm of the 30 31 vapor from a 50/50 H 2 O 2 solution bubbled with helium at a total pressure of 50 Torr. They were able to identify the individual absorption lines without H 2 O interference, but for only four different H 2 O 2 concentrations, thus limiting the statistical confidence in these data. Other studies in the NIR investigated broadband spectra and discrete transitions [16, 17, 57–59], but cross sections were not measured. Johnson et al. [57] published quantitative broadband spectra for the 1 + 5 combination band, which covers 1390 - 1450 nm. This combination band has also been observed by Gigu` ere [58] at low resolution in the gas phase and the spectra was partially assigned. Corveleyn et al. [16] also made broadband NIR measurements, particularly for a strong H 2 O 2 peak near 1420 nm previously observed by Gigu` ere. Based on the aforementioned broadband studies, a preliminary spectral survey in the 1390 to 1470 nm range was conducted. The spectrum near 1420 nm contained several distinct H 2 O 2 peaks and one well-known H 2 O peak, making this region particularly advantageous for measurements of H 2 O 2 vapor concentration in the presence of H 2 O vapor. Consequently, the objective of this work is to investigate the spectrum of H 2 O 2 vapor near 1420 nm at high resolution. Concentrated low pressure vapor is used in order to minimize collisional broadening of this spectrum. 3.1 Experiment A diagram of the apparatus is shown in Figure 3.1. A Newport tunable diode laser, TLB- 6725, capable of spanning 1390 to 1470 nm was used for this study due its high power of 45 mW, excellent 0.01 nm tuning resolution, and narrow, stable linewidths (<200 kHz). The laser beam was split into two beams using a CaF 2 flat with one beam directed to a wavemeter to record the wavelength and the other beam into a Herriott-type multipass cell [60] of 10 cm length and radius 2 cm. The multipass cell was configured to provide 17 passes, yielding a total beam path length within the cell of 170 cm. After the beam exited the cell, it was directed through a short-focus lens and onto an infrared detector. Liquid H 2 O 2 was placed under vacuum and the vapor passed through this multipass flow cell. To minimize H 2 O 2 decomposition, the only materials within the flow path were passivated borosilicate glass, Teflon TM , and stainless steel. The concentration of H 2 O 2 was varied by changing the H 2 O 2 liquid temperature, the H 2 O 2 liquid concentration, and the downstream orifice size. Operating total pressures inside the flow cell were 0.5 to 1.75 Torr at 22 2 C. The liquid H 2 O 2 /H 2 O mixture was provided by PeroxyChem. As delivered, the concentra- tion of H 2 O 2 was 84% by mass (74% by mol). This solution was further purified up to 90% H 2 O 2 32 Figure 3.1: Experimental set-up including paths for the laser, vapor, dry air, and data. by mass (83% by mol) prior to testing. The liquid H 2 O 2 reservoir was placed in a temperature- controlled water bath to maintain a steady liquid temperature during vacuum evaporation. The pressure was measured both upstream and downstream of the flow cell. Any pressure differential would imply H 2 O 2 decomposition inside the flow cell, which would lead to an increase in pres- sure within the cell. Only conditions resulting in a pressure difference of less than 5% of the total pressure were employed in this study. A dry air purge tent was placed around the entire apparatus to minimize interference from atmospheric H 2 O vapor. Thirty minutes prior to any testing the purge was initiated to displace the H 2 O vapor within the laser path. Despite this precaution not all of the H 2 O vapor was expelled, therefore prior to each test an atmospheric background scan was recorded without any gas in the flow cell to determine the H 2 O vapor background. 3.2 Water Line Cross Section The cross section of the H 2 O line at 1420.015 nm was measured and compared to the Doppler-broadened line strength calculated from the integrated line strength (S) in the HITRAN database [23]. The integrated line strength is related to the Doppler-broadened peak cross section, 0 , by the following equation: 33 0 = p c S (3.1) where is the wavelength, c is the speed of light, and is the most probable molecular thermal velocity. = p 2k B T=M (3.2) where k B is the Boltzmann constant, T is the temperature, and M is the molecular mass. The integrated line strength at 1420.015 nm yields a peak cross section 0 = 4.2610 -20 cm 2 molec -1 based on HITRAN data. Using H 2 O rather than H 2 O 2 in the liquid reservoir, absorption at 1420.015 nm was measured for varying concentrations of H 2 O vapor in the flow cell (obtained by varying liquid temperature). A simple plot of peak absorption versus concentration multiplied by the path length was used to determine the measured peak cross section by using Beer’s Law, Eqn. 1.3. Figure 3.2 shows a plot of the H 2 O absorption at 1420.015 nm as a function of H 2 O va- por concentration. The slope of the data yields a peak cross section of (4.15 0.20)10 -20 cm 2 molec -1 . This value matches the HITRAN calculated cross section noted above which confirms that the measurements are near the Doppler-broadened limit, i.e., collision broadening is insignificant under these conditions. Figure 3.2: Absorption of H 2 O vapor at 1420.015 nm as a function of the concentration of H 2 O vapor in the flow cell at ambient temperature conditions. 34 3.3 Subtracting the Influence of Absorption by Atmospheric Water Vapor The atmospheric H 2 O vapor background was fit with a V oight profile and subtracted from the test data as follows. The V oight profile is a convolution of a Lorentz profile and a Gaussian profile fit. V (x;; ) = Z 1 1 G(x 0 ;)L(xx 0 ; )dx 0 (3.3) where x is the wavelength shift from the peak center, G(x 0 ;) is the centered Gaussian profile and L(xx 0 ; )dx 0 is the centered Lorentzian profile. Figure 3.3 shows a V oight profile fit to the atmospheric H 2 O absorption taken with no vapor inside the flow cell. The V oight profile fit was subtracted from the atmospheric absorption; these residuals are also shown in Figure 3.3. The fact that the residuals are so small compared to the peak demonstrates that the contribution of atmospheric H 2 O vapor absorption can effectively be distinguished from absorption caused by the H 2 O and H 2 O 2 in the flow cell and thus can be eliminated. The spectra of the H 2 O 2 (with the atmospheric H 2 O background removed) at wavelengths from 1419.955 nm to 1420.065 nm and several different pressures is shown in Figure 3.4. It is clear that this region features one significant H 2 O line at 1420.015 nm (i.e., the same fundamental line as shown in Figure 3.3 without the collision broadening experienced at atmospheric pressure) as expected from HITRAN data, plus several distinct lines that are not observed in the absence of H 2 O 2 and thus must be due to absorption by H 2 O 2 . To ascertain whether these lines are Doppler-broadened only or are additionally affected by collision broadening, the experimental data were compared with the theoretical full width at half maximum ( D ) of a Doppler-broadened spectral line at the nominal spatial frequency, 0 , as given by D = r 8k B Tln(2) Mc 2 0 (3.4) For the lines shown in in Figure 3.4, the measured line widths D are 0.024 0.002 cm -1 for the H 2 O peak at 1420.015 nm and 0.017 0.002 cm -1 for the H 2 O 2 peaks. These values are close to the theoretical widths of Doppler-broadened lines in the absence of other broadening mechanisms (Eqn. 3.4) of 0.0211 cm -1 and 0.0154 cm -1 for H 2 O and H 2 O 2 , respectively. This demonstrates that at the low pressures employed in these experiments, broadening is primarily due to Doppler effects and collisional broadening is minimal. 35 Figure 3.3: Absorption spectrum of atmospheric H 2 O vapor absorption in the region of spectral interest at ambient pressure and temperature. The absorption was fit to a Voight profile to allow subtraction of this feature from the data. Figure 3.4: The H 2 O 2 + H 2 O spectrum from 1419.955 nm to 1420.065 nm as a function of H 2 O 2 concentration in the flow cell at ambient temperature. The spectrum has been corrected to remove the atmospheric H 2 O vapor absorption as discussed above. 3.4 Water Diagnostic The vapors flowing into the multipass test cell are a mixture of H 2 O 2 and H 2 O, the relative concentrations of which are not knownapriori. To determine the H 2 O 2 concentration, first the H 2 O concentration was determined by using the known H 2 O absorption coefficient of the 1420.015 nm absorption line of 4.26 x 10 -20 cm 2 molec -1 [23]. From this value, Beer’s law (Eqn. 1.3) can be 36 used to calculate the H 2 O 2 cross section. As seen in Figure 3.4, a small H 2 O 2 absorption peak is present on the right (long-wavelength) shoulder of the H 2 O reference peak. Figure 3.5 shows two Doppler profile fits to this combined spectral feature. The wing of the H 2 O 2 peak does not significantly contribute to the H 2 O lines peak absorption and thus will not significantly interfere with the following procedure to determine the H 2 O 2 cross sections. Figure 3.5: A Doppler profile fit to the H 2 O peak at 1420.015 nm and the small H 2 O 2 peak on the shoulder of that H 2 O peak. With the H 2 O concentrations determined from the spectral feature at 1420.015 nm, it was assumed that the remaining molecules in the flow cell were entirely H 2 O 2 . The H 2 O 2 cross sections at the selected wavelengths were determined by again implementing the Beer’s law (Equation 1.3) as well as the perfect gas law and the partial pressure law to calculate H 2 O 2 molecules per volume, n H 2 O 2 . P H 2 O = n H 2 O N a ~ RT (3.5) P H 2 O 2 =P total P H 2 O (3.6) n H 2 O 2 =N a P H 2 O 2 ~ RT (3.7) H 2 O 2 ; = ln I I 0 n H 2 O 2 L (3.8) where N a is Avogadro’s constant, P H 2 O and P H 2 O2 are the partial pressures of H 2 O and H 2 O 2 , 37 respectively, andP total is the total pressure in the test cell as determined by the pressure sensor. 3.5 Results The cross sections as well at the 95% confidence intervals (based on linear least-square regression) are provided for six H 2 O 2 absorption lines from 1419.958 to 1420.058 nm in Figure 3.6 and Table 3.1. The peak at 1419.988 nm was disregarded because of an apparent doublet behavior. Figure 3.6: Absorption of H 2 O 2 vapor at six measured cross sections as a function of the H 2 O 2 vapor concentration in the flow cell at ambient temperatures. From left to right, then top to bottom the wavelengths shown are 1419.958, 1419.967, 1419.999, 1420.029, 1420.047, and 1420.059 nm. See Table 3.1 for values of the cross sections inferred from these data. 38 Table 3.1: Measured H 2 O 2 cross sections with 95% confidence interval Wavelength (nm) Cross section (cm 2 molec -1 ) 1419.958 (5.26 0.42) x 10 -20 1419.967 (2.05 0.24) x 10 -20 1419.999 (4.99 0.42) x 10 -20 1420.029 (5.22 0.44) x 10 -20 1420.047 (2.61 0.27) x 10 -20 1420.059 (5.36 0.46) x 10 -20 3.6 Summary All six of these lines have distinct peaks and no H 2 O interference, however, “best practice” would be to choose the line with the highest strength while also being far enough from the H 2 O feature to minimize interference. By these criteria the line at 1420.059 nm is recommended as the most advantageous single line for determining H 2 O 2 vapor concentrations at low total pressure. At higher pressures, collisional broadening would need to be considered, however for a low pressure system near the Doppler-broadened limit, these effects would fall within the expected error of the cross section determination. While this study was initiated with the intention to create a diagnostic for a vapor-phase H 2 O 2 space propulsion system, these cross sections could be used for any application that requires H 2 O 2 vapor concentration measurement. NIR lasers are commercially available and relatively easy to operate, making this regime especially enticing forin-situ measurements. CHAPTER 4 REACTION RATES Utilizing the non-invasive H 2 O 2 vapor diagnostic developed in Chapter 3, experimental studies were completed to determine the reaction rates and activation energies associated with H 2 O 2 vapor catalytic decomposition. Previous studies have primarily targeted the kinetics associated with liq- uid catalytic decomposition,i.e., heterogeneous decomposition, and vapor thermal decomposition, i.e., homogeneous decomposition. There has been very few evaluations of H 2 O 2 vapor heteroge- neous decomposition, which is the focus of this work and is a necessary input for detailed catalytic models of liquid and vapor-fed systems. 4.0.1 Literatures Studies of H 2 O 2 Vapor Heterogeneous Reactions The studies that have experimentally investigated vapor heterogeneous reactions have been with relatively inert surfaces (class 1 materials, see summary in Table 4.1). In these studies, the reaction rate constants and activation energies were experimentally determined for the global H 2 O 2 decomposition following Equation 1.5 and 1.6. Table 4.1: Literature H 2 O 2 Vapor Reaction Rate Constants and Activation Energies Study Material Test Condition Rate Constant (s -1 ) Activation Energy (kJ/mol) Gigu` ere and Lui [24] Pyrex R 2 l spherical flask, 350 C, 10 Torr 3 10 -4 41.8 - 50.2 Gigu` ere [61] Aluminum 1 l spherical flask, 96.5 C, 5-6 Torr 1.6 10 -3 50.2 4.0.2 Literatures Studies of H 2 O 2 Liquid Heterogeneous Reactions Albers et al. [62] calculated an H 2 O 2 liquid heterogeneous rate constant of 7.2 10 -2 s -1 and an activation energy of 50.7 kJ/mol for a small monolithic manganese oxide catalyst with a geometric surface area of 2625 m 2 /m 3 . This value matches well with the activation energies found by Orr and Williams [63] for the H 2 O 2 reaction with iron (44.4 - 54.8 kJ/mol). Lin et al. [64] 39 40 investigated the reaction kinetics on relatively inert materials, Teflon TM , glass, stainless steel, and titanium, and found activation energies ranging from 68.2 - 106.3 kJ/mol. 4.1 Experimental Apparatus A diagram of the experimental apparatus is shown in Figure 4.1. Helium, regulated by a flow controller, is bubbled through high concentration (>90% by mass) liquid H 2 O 2 . The vapor mixture is then transported to either an Al 6061 tube containing catalyst or a PTFE bypass tube before continuing into a 163 cm multipass flow cell (radius 2.5 cm, 3 passes). Pressure is measured downstream of the flow cell, ahead of the vacuum pump, with an MKS baratron R (range 1-100 Torr, error 0.25% of reading accuracy). Additional helium is introduced immediately prior to the cell to increase total pressure and decrease the potential for H 2 O 2 decomposition on the cell walls. The helium flow controllers were varied between 0.2 and 4.3 standard cubic centimeters per minute (sccm) to alter the residence time in the catalyst bed and maintain a total pressure between 2.2 - 2.4 Torr, which results in Reynolds numbers, Re, less than 0.35. Hydrogen peroxide concentration entering the catalyst tube varied between 0.005 to 0.03 mol/m 3 , which scales inversely with helium bubbler flow rate. Figure 4.1: Diagram of the reaction rate experimental set-up. 41 4.1.1 Catalysts Three catalyst configurations were investigated with this apparatus: (1) a platinum on alu- mina sphere, (2) a silver mesh, and (3) a platinum mesh. The 0.5% by mass platinum on alumina spheres ranged in diameter from 2.35 to 3.76 mm. Sphere testing was performed with one sphere being placed inside the aluminum tube with a sheet of PTFE mesh downstream to hold its posi- tion. The silver mesh had a nominal aperture of 0.42 mm and a wire diameter of 0.11 mm. The platinum mesh had a nominal aperture of 0.288 mm and a wire diameter of 0.1 mm. Mesh testing was performed with one 6.35 by 6.35 mm mesh installed perpendicular to the flow path. Minor differences in mesh sheet size were documented with precise mass measurements. The platinum on alumina sphere and platinum mesh were purchased from Sigma-Aldrich and the silver mesh from fuelcellmaterials. All catalysts were baked at 500 C for>30 minutes prior to use. 4.1.2 H 2 O 2 diagnostic A Newport near-infrared tunable diode laser, the same used in Chapter 3, was used to scan a wavelength region from 1420.05 to 1420.07 nm. The beam was split with a CaF 2 flat: one beam being directed through the multipass flow cell and into an infrared detector and the other through an equivalent atmospheric path and into a second detector. Incorporating the second detector allowed forin-situ subtraction of atmospheric H 2 O, which would otherwise cause a underlying undesirable broadband signal in the wavelength region of interest. Each experiment was conducted by scanning the wavelength region while the H 2 O 2 vapor mixture passed through the PTFE bypass tube. The scan was then immediately redone with the H 2 O 2 vapor mixture passed through the catalyst tube. This provided a baseline/ initial concentra- tion of H 2 O 2 and a corresponding value after interacting with the catalyst. The H 2 O 2 absorption peak at 1420.059 nm was targeted due to its high relative strength and distance from H 2 O interferers. Beer’s law (Equation 1.3), with the cross section determined in Chapter 3, was used to convert detector signal to H 2 O 2 concentration. Figure 4.2 shows an example of the effects of H 2 O 2 decomposition in the catalyst on the absorbance in the flow cell at 1420.059 nm. 42 Figure 4.2: Absorbance of H 2 O 2 at 1420.059 nm through the bypass tube, 0 , and through the catalyst tube,, for the 2.35 mm platinum on alumina sphere with a 3/1.5 helium flow cell to bubbler ratio. 4.2 Kinetics Following the findings of Gigu` ere and Lui [24], Hoare et al. [65], Hinshelwood and Prichard [66], and Baker and Ouellet [67], the decomposition of H 2 O 2 was treated as a first order reaction. This assumption was further substantiated with the observed behavior presented in Section 4.3. Therefore the reaction rate constant,k, in units of per second could be determined with Equation 1.5, which when differentiated results in ln [H 2 O 2 ] [H 2 O 2 ] 0 =kt (4.1) where [H 2 O 2 ] refers to the gas-phase number density of H 2 O 2 in moles per cubic meter through the catalyst tube, [H 2 O 2 ] 0 is the number density of H 2 O 2 in moles per cubic meter through the bypass, andt is time in seconds. In this case time refers to residence time in the portion of the aluminum tube occupied by catalyst and can be calculated by dividing that volume by the prescribed helium bubbler volumetric flow rate. t = V Q bubbler;He (4.2) This method, and the resulting rate constant, approximates the surface reaction as a gas-phase reaction within the catalyst bed volume. Equation 4.1 also assumes a system with no diffusion or 43 boundary layer effects. A discussion and modification of the rates to incorporate those effects is provided in Section 4.6. In some studies, e.g., the monolithic stirred reactor work of Albers et al. [62], researchers incorporate the catalyst geometry into the reaction rate constant with the goal of normalizing their relation and allowing its use outside of their specific application. In this study, this will be referred to as the engineering rate constant,ERC, and is also provided for all of the tests: ERC =k V SA (4.3) whereERC has units of meters per second, V is the catalyst bed volume, and SA is the surface area of the catalyst. Equations for the catalyst surface area and catalyst bed volume for each configuration can be found in Appendix B. Temperature dependence was characterized using the Arrhenius relation shown in Equation 1.6. Due to the limited temperature range of this study, it was assumed that the activation energy, E a , and pre-exponential factor,A 0 , are constant. 4.3 Experiment: Reaction of H 2 O 2 on Platinum and Silver Surfaces at Am- bient Temperatures Experimental conditions were varied by changing the helium bubbler flow rate between 0.2 and 3.5 sccm. An overall helium system flow rate of 4.5 sccm was maintained by compensating with the flow of helium directly into the flow cell. 4.3.1 Baseline Prior to running experiments with catalytic materials, a test series was conducted with no catalyst within the aluminum tube. It was focused on the temperature and flow rate regime of interest: ambient temperature (21 1 C) and bubbler flow rates of 0.2-3.5 sccm. An average background destruction of 10.4% was found. For all of the evaluated catalysts, this known destruction was accounted for by adding 0.104 [H 2 O 2 ] 0 , the number density of the H 2 O 2 flowing through the bypass, to [H 2 O 2 ], the number density of the H 2 O 2 flowing through the catalyst. 44 4.3.2 Platinum on Alumina Spheres Four catalyst spheres measuring 2.35, 3.05, 3.43, and 3.76 mm in diameter and weighing 0.009, 0.013, 0.022, 0.030 grams, respectively, were tested in this study. As expected, increasing residence times and catalyst diameters led to higher percentages of H 2 O 2 destruction. Figure 4.3 shows this behavior. Figure 4.3: Destruction of H 2 O 2 on platinum on alumina spheres for varying residence times and catalyst sizes. Using the method described in Section 4.2 the reaction rates for each of the catalyst diam- eters were determined. Figure 4.4 shows the natural log of the ratio of final over initial H 2 O 2 concentration by residence time. The resulting slope is the rate constant. In order to account for the difference in diameter of the 4 spheres, the rate constants were divided by their respective sur- face area over volume, as shown in Equation 4.3. The rate constants in per second and the ERC in meters per second as well as the 95% confidence intervals (based on linear least-square regression) are shown in Table 4.2. 45 Figure 4.4: Rate constant determination for different platinum on alumina sphere catalyst sizes. Table 4.2: Platinum on Alumina Sphere Reaction Rate Constants Catalyst Diameter (mm) Rate Constant (s -1 ) ERC (m/s) 2.35 33 6:6 0:073 0:015 3.05 55 14 0:094 0:023 3.43 70 23 0:107 0:035 3.76 118 23 0:165 0:033 4.3.3 Silver Mesh Three experimental series were performed with silver mesh. While all the meshes were ap- proximately 6.35 by 6.35 mm, small deviations were captured by weighing each sample. Catalyst A, B, and C weighed 0.022 g, 0.017 g, and 0.016 g, respectively. Room temperature experiments with Catalyst A and B showed poisoning of the catalyst through the test series, where performance decreased with repeated tests. This decreasing decom- position over the test series is documented in Table 4.3. These tests were performed for varied residence times with similar results. However when the temperature of the catalyst was raised to 40 C for Catalyst A and 60 C for Catalyst B, the mesh appeared to re-condition through repeated tests, as shown in Table 4.4. Once it had been conditioned in the H 2 O 2 flow, it maintained that level of destruction, even after 46 returning to room temperature. The third silver mesh, Catalyst C, was tested only at 80 C and all tests maintained high decomposition percentages throughout the series (baseline destruction at elevated temperatures was assumed to be the same as determined for ambient). Table 4.3: Poisoning of Silver Mesh at Room Temperature Catalyst A Catalyst B Test H 2 O 2 Destruction (%) Test H 2 O 2 Destruction (%) 1 30.7 1 77.0 2 23.2 2 56.1 3 18.7 3 33.6 4 24.6 4 19.9 5 17.6 5 35.2 6 22.8 6 33.1 - - 7 23.3 - - 8 23.7 Note: Percentages prior to baseline adjustment Table 4.4: Conditioning of Silver Mesh at Elevated Temperatures Catalyst A Catalyst B Test Temp. ( C) H 2 O 2 Destruction (%) Test Temp. ( C) H 2 O 2 Destruction (%) 1 23 22.8 1 22 23.7 2 40 41.0 2 40 52.1 3 40 83.4 3 40 58.0 4 40 91.8 4 40 50.6 5 40 90.8 5 60 64.5 6 40 93.9 6 60 78.8 7 40 91.8 7 60 91.6 8 30 85.4 8 60 90.5 9 22 85.0 9 22 89.4 10 25 91.4 10 22 93.3 11 26 90.5 11 22 88.5 Note: Percentages prior to baseline adjustment 47 Once conditioned, the average rate constant and ERC of the silver mesh was found to be 398 125 s -1 and 0.15 0.047 m/s, respectively, for these samples. See Figure 4.5 for the test data used in this average. The silver mesh ERC is very similar to that calculated for the platinum spheres. However due to the high decomposition, which seemed relatively independent of residence time in the regime of this study, approximately 75.6% (after baseline adjustment), the actual rate constant could be higher. Additional testing with lower residence times or less catalyst would be required to get a more accurate value and develop linear relations like those established for the platinum on alumina spheres. Figure 4.5: H 2 O 2 destruction for conditioned silver mesh catalysts. 4.3.4 Platinum Mesh Two experimental series were performed with platinum mesh. While the meshes were ap- proximately 6.35 by 6.35 mm, Catalyst A and B weighed 0.027 g and 0.032 g, respectively. Flow rate and catalyst temperature was varied, however destruction remained relatively con- stant for all conditions (baseline destruction at elevated temperatures was assumed to be the same as determined for ambient). Figure 4.6 shows the limited performance witnessed during the test series. The rate constant was calculated as 26.8 3.2 s -1 and the ERC as (7.4 0.88) 10 -3 m/s. Note that limited reaction on platinum wire was also witnessed by Bramanti et al. [68] in room temperature testing with liquid H 2 O 2 . 48 Figure 4.6: Minimal destruction of H 2 O 2 on platinum catalyst even at elevated temperatures. 4.4 Experiment: Reaction of H 2 O 2 on Platinum on Alumina Spheres at El- evated Temperatures Due to the high decomposition of H 2 O 2 vapor on one sheet of silver mesh and the minimal reaction on platinum mesh, rigorous temperature studies were only conducted with the platinum on alumina spheres; silver and platinum mesh temperature variations in Section 4.3 were only exploratory (baseline destruction at elevated temperatures was not characterized). Two catalyst diameters were considered in this study, 2.35 and 3.05 mm, at a helium flow rate of 0.5 sccm, which corresponds to a residence time of 12.8 and 16.7 ms, respectfully. An additional experimental series was conducted with the 2.35 mm catalyst at 0.2 sccm, corresponding to a residence time of 31.7 ms. Catalyst temperatures were varied from 21 - 120 C. 4.4.1 Baseline A new baseline destruction test series was performed for these tests due to changes in the set-up and temperature range. These changes included: (1) the use of a new Al catalyst tube, (2) the addition of a PTFE centering rod in the catalyst tube, and (3) the increased temperature range from 21 - 120 C. The fractional destruction in the tube without a catalyst followed the relation B = 0:114T 25:6 (4.4) whereB is the fractional destruction andT is the catalyst temperature in kelvins. This baseline 49 destruction was accounted for with the same method as was used for the ambient temperature studies, by addingB [H 2 O 2 ] 0 to [H 2 O 2 ]. 4.4.2 Determination of Arrhenius Constants Figure 4.7 shows the rate constant as a function of temperature for the different catalyst diameters and flow rates. The activation energies and pre-exponential factors extracted from the data are provided in Table 4.5. Figure 4.7: Temperature dependence for different platinum on alumina sphere sizes and helium flow rates. Table 4.5: Platinum on Alumina Sphere Activation Energies and Pre-exponential Factors Catalyst Diameter (mm) Flow rate (sccm) E a (J/mol) A 0 (s -1 ) 2.35 0.2 597 32.4 2.35 0.5 32.4 43.8 3.05 0.5 460 53.1 4.5 Role of Diffusion The calculated activation energies for all of the platinum on alumina sphere temperature studies were less than 600 J/mol, indicating little to no temperature sensitivity from 21 - 120 C, 50 similarly to what was witnessed with the platinum mesh. This lack of temperature influence sug- gests that the reaction could be diffusion-controlled in this regime. In order to compare the exper- imental values found here with theory, two extreme cases were evaluated: (1) H 2 O 2 consumption in a spherical infinite diffusion system and (2) H 2 O 2 consumption in a 1D convection-diffusion system. For a spherical infinite system, the H 2 O 2 consumption can be modeled as _ n = Dx 1 Mr SA (4.5) where _ n is the molar consumption rate of H 2 O 2 in moles per second, SA is the catalyst surface area, is the H 2 O 2 density in the stream, D is the diffusion coefficient, x 1 is the H 2 O 2 mole fraction in the stream,M is the H 2 O 2 molar mass, andr is the catalyst radius. The H 2 O 2 mole fraction in the stream, x 1 , was found by multiplying the mole fraction of H 2 O 2 in the flow cell by the ratio of prescribed helium flow, _ V He;total = _ V He;bubbler . The diffusion coefficient was taken from CHEMKIN [69]. For a 1D convection-diffusion system, the H 2 O 2 consumption can be modeled as _ n = Dx 1 M A ? (4.6) = D u (4.7) where is the diffusion coefficient andA ? is the catalyst area perpendicular to the flow. Table 4.6 shows the ratio of theoretical to experimental consumption rates for the four cata- lyst diameters, specifically for the case with 0.5 sccm of helium flow through the bubbler, 4 sccm helium directly into the flow tube, and at ambient temperatures. Table 4.6: Ratio of Theoretical to Experimental H 2 O 2 Consumption Catalyst Diameter (mm) Spherical Infinite Diffusion 1D Convection-Diffusion 2.35 1:7 10 3 3:8 3.05 1:7 10 3 4:8 3.43 1:6 10 3 5:0 3.76 2:2 10 3 7:1 The experimental consumption rates are much closer to the 1D convection-diffusion values. 51 This is most likely due to the constrained flow of the tube where most of the H 2 O 2 vapor encounters the catalyst at the front face. In order to better represent the boundary conditions of the experiment, an axisymmetric multiphysics model of the catalyst tube with the 3.05 mm platinum on alumina sphere was devel- oped in COMSOL. The fluid flow was modeled using the steady state, compressible form of the Navier-Stokes equations for a Newtonian fluid: Equation 4.8 (continuity) and 4.9 (conservation of momentum). The transport of chemical species through diffusion and convection is solved with the mass conservation relation, Equation 4.11. r (u) = 0 (4.8) (ur)u =r [rhoI +K] + F (4.9) K =(ru + (ru) T ) 2 3 (ru)I (4.10) rJ i +urc i =R i (4.11) J i =D i rc i (4.12) where is the density, u is the mass averaged velocity vector, F is the volume force vector, K is the viscous stress vector, is the dynamic viscosity, c i is the concentration of the species, R i is the reaction rate expression for the species, J i is the mass flux vector, andD i is the diffusion coefficient. The decomposition of H 2 O 2 was handled as a fast irreversible reaction at the sphere surface. The rate limiting species, H 2 O 2 , was set to zero at the boundary and the species participating in the reaction, H 2 O 2 , H 2 O, and O 2 , were re-set according to their stoichiometric coefficients, -1, 1, and 0.5, respectively. The model parameters were set based on the experimental results at the 0.5 sccm helium bubbler flow rate condition; these parameters can be seen in Table 4.7. The H 2 O 2 concentration and velocity in the catalyst tube are shown in Figure 4.8. The results indicate that in a diffusion-controlled reaction where the entire surface of the sphere is reactive, almost all of the H 2 O 2 would be destroyed. The experimental results for this condition 52 Table 4.7: COMSOL Model Parameters Flow Velocity 0.184 m/s H 2 O 2 Concentration Upstream 0.0166 mol/m 3 H 2 O Concentration Upstream 0.00996 mol/m 3 Pressure Downstream 2.27 Torr Temperature 21 C had<60% H 2 O 2 destruction. While this might indicate that the experiment is not well-described as a diffusion-controlled reaction, additional, more detailed, modeling of the sphere surface would be required to substantiate that claim. The catalyst spheres used in the experiments were only 0.5% platinum by mass. Therefore only a small percentage of the sphere surface is covered with platinum and will participate in the reaction. A model with a sphere containing reactive and non-reactive regions could provide deeper insight. 53 Figure 4.8: COMSOL diffusion-controlled model: flow velocity (left), H 2 O 2 concentration (right). 4.6 Modification of Reaction Rates to Account for Diffusion and Boundary Conditions The reaction rates reported in Section 4.3 assume a batch reactor-style system with no dif- fusion or boundary conditions. In order to determine reaction rate constants that account for those contributing factors, a COMSOL model was created for each of the three catalyst materials, using the parameters in Table 4.7. In this model, instead of assuming a fast reaction at the catalyst sur- face, a finite rate constant was defined, applied to the catalyst bed volume, and iterated on until the model H 2 O 2 destruction matched that of the experiment. No surface interactions were considered, instead, the reaction proceeded in the gas phase when it entered the region of the tube containing catalyst. The reaction was assumed to be first order, following Equation 1.5. The flow velocity and the H 2 O 2 concentrations for each of the three catalysts can be seen in 54 Figure 4.9. The H 2 O 2 destruction based on the experimental results at the 0.5 sccm helium bubbler flow rate as well as the corresponding rate constants and ERCs are provided in Table 4.8. Figure 4.9: COMSOL gas only finite reaction rate model: (1) flow velocity, (2) H 2 O 2 concentration for 3.05 mm platinum on alumina sphere, (3) H 2 O 2 concentration for silver mesh (4) H 2 O 2 concentration for platinum mesh. Table 4.8: COMSOL Reaction Rate Constants and ERCs for 0.5 sccm Helium Bubbler Flow Rate Catalyst Material/Size Percentage Destruction k (s -1 ) ERC (m/s) 3.05 mm Platinum on Alumina Sphere 56.5 1.74 3.0 10 -3 Silver Mesh 73.7 10.7 4.0 10 -3 Platinum Mesh 25.3 1.42 3.9 10 -4 55 4.7 Summary The surface area and temperature dependence of the H 2 O 2 reaction on a catalytic surface was determined. Silver mesh, while highly effective at elevated temperatures, proved to have issues with poisoning in H 2 O 2 flow at room temperature. Unlike silver, platinum mesh did not appear to be a good catalyst over the temperature and flow rate range explored in this study. Potentially a more aggressive pre-treatment would have raised the performance. The experimental ERCs found here for H 2 O 2 vapor heterogeneous decomposition on catalytic surfaces are several orders of magnitude higher than the ERCs found by Gigu` ere and Lui [24] on Pyrex R and Gigu` ere [61] on pure aluminum, as was expected when comparing catalytic and inert surface reactions. They are also higher than ERCs published for liquid H 2 O 2 decomposition on manganese oxide [62]. Table 4.9 shows these literature ERCs (based on the published surface areas and volumes) compared to the ERC calculated for the 3.05 mm platinum on alumina sphere (Table 4.8). Table 4.9: Experimental Engineering Reaction Rates (ERCs) Compared with Literature Source Prop. State Material ERC (m/s) This Study (Rate accounting for Diffusion and Boundary Effects) Vapor Platinum on Alumina Sphere 3.0 10 -3 Gigu` ere and Lui [24] Vapor Pyrex R 7.8 10 -6 Gigu` ere [61] Vapor Aluminum 3.3 10 -5 Albers et al. [62] Liquid Manganese Oxide Monolith 2.7 10 -5 The temperature studies of H 2 O 2 vapor reacting with platinum on alumina spheres revealed an extremely low activation energy, unlike the literature studies of vapor on inert materials [24, 61] and liquid on catalytic materials [62, 63]. This indicates that the reaction is temperature- independent within the scope of this study, specifically at ultra-low Reynolds numbers (<0.35) and catalyst temperatures from ambient to 120 C. To better understand the conditions, a theo- retical analysis of a spherical infinite diffusion system and a 1D convective-diffusion system was completed. A simplified reaction model was also developed in COMSOL, a multiphysics finite el- ement software, but it was determined that a more detailed surface geometry would be required to determine if the temperature-independent nature of the experiment is due to a diffusion-controlled process. CHAPTER 5 PERFORMANCE OPTIMIZATION Prototype 1 proved that a low pressure, vacuum-evaporated H 2 O 2 vapor would decompose on a catalyst and produce high temperature gas useful for propulsion. It also provided information on the required vapor mole fraction and catalyst temperature to initiate rapid reaction. The objective of the two follow-on prototypes was improved performance. This was executed by: (1) testing catalyst configurations, (2) incorporating high-compatibility materials, and (3) minimizing heat transfer from the catalyst chamber to the main thruster body. The performance was evaluated by measuring catalyst temperatures, system pressures, and thrust (for the final design). 5.1 Prototype 2: Focus on Catalyst and Chamber Construction Three catalyst materials and two catalyst chamber designs were investigated in this study using the Prototype 2 design, with a focus on maximizing catalyst temperature. The same cata- lyst materials investigated in Chapter 4 were considered here: silver mesh, platinum mesh, and platinum on alumina spheres. The MACOR R catalyst chamber design used in Prototype 1 and a thin-walled SS 316 design were both tested with comparable catalyst loadings. 5.1.1 Design and Construction In order to meet long-term compatibility requirements, all thruster wetting materials were carefully selected for Prototype 2. The plastic pressure sensors and valves used in Prototype 1 showed signs of deterioration after extended testing and therefore were replaced for this iteration. The two valves selected for this design were made of SS 304 with an orifice size of 1 mm. Some internal parts within the valve were made with SS 430, which has lower compatibility with H 2 O 2 and therefore had to be monitored for adverse reaction. TE Connectivity pressure sensors were used to measure tank pressure upstream of the valves. One for ambient conditions (range of 0 - 100 psi) and the other for higher resolution at operating conditions (range of 0 - 5 psi). The error band of these sensors is3% span and they use a SS 316L diaphragm as the sensing element with a Viton R o-ring seal. The valves and sensors were chosen based on their overall size and compatibility. For one variant of the design, the pressure was also taken downstream of the catalyst ahead of the nozzle. This was done with a Honeywell TruStability TM pressure sensor with a 0 - 1 56 57 psi range (error 0.25% span). Due to its location, downstream of the catalyst, the materials did not have to be highly compatible with H 2 O 2 . Therefore a sensor was chosen with a tighter range and smaller size. Heaters and temperature sensors were placed on the outside of the tank and manifold to maintain desired liquid temperatures during testing. The CAD model and engineering unit can be seen in Figure 5.1. The tank and manifold were constructed of Al 6061. All temperature readings on the thruster, including those on and in the nozzles were taken with Omega type K thermocouples (range -200 C - 1250 C, error greater of 2.2 C or 0.5%). Figure 5.1: Hydrogen peroxide vapor thruster Prototype 2: test unit (left), CAD model (right). The two catalyst chambers/nozzles tested were (1) a thin-walled SS 316 design where tem- perature was measured along the exterior of the nozzle and (2) a MACOR R rectangular cuboid with the capability to take 3 interior temperature measurements and 1 pressure measurement down- stream of the catalyst. Both nozzles featured the same interior converging diverging (CV) design and mounting as Prototype 1, details provided in Section 2.2.1. These will be referred to as the SSCD nozzle and the MCD nozzle for the remainder of this thesis. The MCD nozzle is imple- mented in Figure 5.1. A close up of the SSCD and MCD nozzles is shown in Figure 5.2. The H 2 O 2 solution used is this study was procured from PeroxyChem at a 92% H 2 O 2 by mass (86% by mol). 58 Figure 5.2: Prototype 2: SSCD nozzle (left), MCD nozzle (right). 5.1.2 Experimental Results Tests were performed varying the following elements: nozzle construction, tank temperature, catalyst material, and catalyst length. The majority of tests were performed in the SSCD nozzle with temperature measurements on the exterior of the nozzle. Tests performed with the MCD nozzle gave chamber pressure and local catalyst temperature data, since the thermocouples were embedded in the catalyst. For all nozzle constructions, catalyst materials, and catalyst lengths, the tank temperature was varied from 60 C to 80 C. The standard catalyst length was 7 sheets (approximately 0.77 mm in length for the silver and 0.42 mm in length for the platinum). These sheets were compacted on a perforated SS sheet, which was used to increase the structural integrity of the bed. Due to the placement of the catalyst within the nozzle, the temperature measurement at the throat is considered the catalyst temperature. The other measurement were taken at chamber locations upstream of the catalyst. Figure 5.3 shows the catalyst chamber temperature for the SSCD nozzle with 7 sheets of silver, varying the tank temperature. Higher tank temperatures led to higher vapor pressure, as can be seen in Figure 5.4. Dotted lines bound the steady state region, from 80 to 160 seconds. Table 5.1 shows the average steady state catalyst temperature (with its respective range) for the varying catalysts and configurations tested in the SSCD nozzle. Silver mesh had the highest temperatures, with 7 sheets and 3 sheets having similar values. In order to get a better understanding of what was happening in the catalyst bed, the MCD nozzle was used in experiments to collect direct interior measurements of temperature and pressure. Temperature was taken at 3 locations within the catalyst bed: (1) under the first mesh sheet (top), (2) under the fourth sheet (middle), and (3) on the SS perforated sheet at the bottom of the bed (bottom). Figure 5.5 gives an example of these measurements for a 60 C tank temperature test run. The average catalyst temperature for each test is shown in Figure 5.6 and shows an average 59 Figure 5.3: Catalyst temperatures for the tests using the SSCD nozzle and 7 sheets silver mesh at tank temperatures of 60 C, 70 C, and 80 C. Figure 5.4: Tank pressures for tests using the SSCD nozzle and 7 sheets silver mesh at tank temperatures of 60 C, 70 C, and 80 C. steady state temperature approximately 22 - 24% higher than the temperature from outside of the SSCD nozzle for the same catalyst and configuration. The pressure downstream of the catalyst is shown in Figure 5.7. This reveals that the pressure drop in the system is approximately 35 - 45% of tank pressure. Table 5.2 lists the average catalyst temperatures and pressures for the MCD nozzle with 7 sheets of silver mesh. Experimental relations from Scatchard et al. [51], Equation 2.2, were used to determine the vapor concentration at varying temperatures and liquid concentrations. Figure 5.8 shows a plot of 60 Table 5.1: SSCD Nozzle Average Catalyst Temperatures for Different Catalyst Materials and Configurations 3 Sheets 7 Sheets 14 Sheets Spheres 60 C Tank Temperature Silver 1392 C 1352 C 98 C - Platinum 1244 C 1312 C - 1143 C 70 C Tank Temperature Silver 1821 C 1814 C 1301 C - Platinum 1692 C 1763 C - 1543 C 80 C Tank Temperature Silver 2311 C 2364 C 1701 C - Platinum 2202 C 224 C - 2033 C Figure 5.5: Top, middle, and bottom catalyst temperatures in the MCD nozzle with 7 sheets silver mesh and a tank temperature of 60 C. Table 5.2: MCD Nozzle Average Catalyst Temperatures and Chamber Pressures for 7 Silver Sheets Tank Temperature ( C) 80 70 60 Average Catalyst Temperature ( C) 3056 2395 1746 Catalyst Chamber Pressure (Torr) 45.10.7 27.70.3 16.40.4 61 Figure 5.6: Catalyst temperatures for the tests with the MCD nozzle and 7 sheets silver mesh at tank temperatures of 60 C, 70 C, and 80 C. Figure 5.7: Catalyst chamber pressures for tests with the MCD nozzle and 7 sheets silver mesh at tank temperatures of 60 C, 70 C, and 80 C. vapor concentration with increasing temperature with the steady state tank pressures plotted for all of the test runs. As would be expected, the test data indicates that the liquid concentration was decreasing from the initial 92% by mass (86% by mol) delivered from PeroxyChem over the period of the test campaign. To compare the experimental results with the theoretical performance, the adiabatic temper- atures for a vapor H 2 O 2 decomposition considering an 86% and 92% by mass (77% and 86% by mol) liquid were calculated using a chemical equilibrium code based on STANJAN [48], i.e., the 62 Figure 5.8: Vapor pressure relation developed by Scatchard et al. [51] compared to experimental data. same method that was used in Chapter 2.1. Figure 5.9 shows the theoretical and experimental catalyst temperature values for all of the tests. Note that the highest performing test is only 29% of the adiabatic value (assuming 86% by mass H 2 O 2 ). Figure 5.9: Adiabatic temperature compared with experimental values for catalyst temperature. 5.1.3 Heat Transfer Analysis using Finite Element Modeling In order to further understand what factors were driving the experimental temperatures, a COMSOL model focused on conductive, convective, and radiative heat transfer was created. To 63 reduce computational time and complexity, chemical reaction and fluid flow were initially ignored. Instead the vapor was considered stagnant and a specified heat flux was applied to the catalyst. The system geometry was also simplified to allow for larger grid element sizes. The COMSOL model is shown in Figure 5.10. Figure 5.10: COMSOL geometry featuring MCD catalyst chamber: full model (left), sectioned at plane (right). Local temperatures are calculated by solving the heat balance equation: C p T t +u trans rT +r (q +q r ) =T dS dt +Q (5.1) where is the density, C p is the specific heat capacity, T is the absolute temperature, u trans is the velocity vector of translational motion,q is the heat flux by conduction,q r is the heat flux by radiation, is the coefficient of thermal expansion,S is the second Piola-Kirchhoff stress tensor, and Q contains additional heat sources (e.g., the catalyst heat flux). For conduction and convection q =krT , where k is the thermal conductivity. For ra- diation q = (Ge b (T )) on the side of the boundary, where is the surface emissivity, G is the irradiation, ande b (T ) is the blackbody hemispherical total emissive power. Besides through radiation, heat was allowed to transfer out of the system via convection from the nozzle exit: nq = 0, wheren represents the normal direction. While parameters such as set tank temperature and chamber pressure were easy to draw from the experimental data, other inputs had to be pulled from literature or theory. Material emissivities, 64 , for aluminum, SS 316, and MACOR R were assumed to be 0.3, 0.6, and 0.9 respectively. The catalyst heat flux was determined using the change in enthalpy (assuming product gases at adiabatic temperature! tank temperature) multiplied by the mass flow rate (assuming product gases at adiabatic temperature upstream of the nozzle) for the 92% H 2 O 2 by mass case. The resulting flux was 2.03 W, 3.47 W, and 5.65 W for 60 C, 70 C, and 80 C, respectively. 5.1.3.1 Modeling Results The average steady state catalyst temperatures for the MCD and SSCD nozzles at tank tem- peratures of 60 C, 70 C, and 80 C is shown in Table 5.3. Figure 5.11 shows the local tempera- tures inside the two systems, sectioned on the same plane as Figure 5.10. The model temperatures are lower than the experimental values; this result was expected due to the model’s assumption of a perfect thermal connection between all of the thruster components. However, the model does show the same correlation as the experiments for tank temperature and catalyst heat flux to average catalyst temperature. Table 5.3: COMSOL Model Average Catalyst Temperatures Tank Temperature ( C) 80 70 60 MCD Nozzle Catalyst Temperature ( C) 199 142 101 SSCD Nozzle Catalyst Temperature ( C) 224 163 116 Heat loss paths, specifically conduction to the manifold and radiation, were isolated and eliminated individually for both the MCD and SSCD nozzle configurations. The average catalyst temperature at a tank temperature of 80 C for (1) the complete model as characterized in Table 5.3, (2) a model with no conduction to the manifold/tank, and (3) a model with no radiation is provided in Table 5.4. The models indicate that conduction to the manifold and tank is the primary driver of catalyst temperature in these designs, with radiation playing a minimal role. 65 Figure 5.11: COMSOL model slice temperature for 80 C tank temperature (location at plane indicated in Figure 5.10): MCD nozzle (left), SSCD nozzle (right). Table 5.4: COMSOL Model Average Catalyst Temperatures for Various Heat Transfer Conditions at a Tank Temperature of 80 C Heat Transfer Assumption Complete No Conduction to Manifold No Radiation MCD Nozzle Catalyst Temperature ( C) 199 369 206 SSCD Nozzle Catalyst Temperature ( C) 224 527 233 5.1.4 Summary In this study, 2 catalyst chamber configurations and 3 catalyst materials were evaluated, with silver mesh resulted in the highest catalyst chamber temperatures. This outcome matches well with what was found in the ambient reaction rate studies of Chapter 4. A 35% - 45% system pressure drop limited catalyst chamber pressures, and therefore thrust level and performance. Also, upon disassembly of the thruster, corrosion was evident in the valve flow path, which would have de- creased the H 2 O 2 concentration upstream of the catalyst bed. Between these two loss mechanisms and the heat transfer from the catalyst chamber to the manifold, several design improvements are evident. Thermal modeling in COMSOL allowed for visualization of heat transfer through the system. 66 The models revealed that minimizing the heat transfer from the nozzle to manifold could increase average catalyst temperatures by up to 135%. 5.2 Prototype 3: Focus on Robust Components and Minimal Pressure Drop for Thrust Measurement While Prototype 2 provided valuable information about catalyst configurations, it also ex- posed issues with the pressure drop, heat transfer, and valve corrosion. A third design iteration was implemented to target those areas and improve system performance. Direct measurement of force produced by the prototype was measuring utilizing a torsional pendulum thrust stand. For this test series only the silver mesh catalyst was used, specifically the 7 sheet configura- tion. This catalyst proved the most favorable both in practical thruster tests (e.g., Prototype 2), as well as in the reaction rate experiments of Chapter 3. The hydrogen peroxide used was 941% by mass, measured with a MISCO refractometer. 5.2.1 Design and Construction Prototype 3 can be seen in Figure 5.12. In this iteration two major changes were made to the manifold design. First, the flow path between the tank and nozzle was increased from 1.8 mm to 5.3 mm. Second, the two valves were replaced with one all aluminum valve with Viton R seals and a 1.32 mm orifice. These design changes addressed two of the major concerns from the previous iteration: pressure drop and corrosion. 5.2.1.1 Catalyst Chamber/ Nozzle Two different nozzle mounting configurations were tested in this series: (1) the 3 screw, Kalrez R o-ring variant that was used in Prototype 1 and 2 and (2) a 6 screw, Vespel R spacer variant intended to improve thermal isolation and seal integrity. These will be referred to as the o-ring and spacer variant for the remainder of this thesis. The spacer design prevents the nozzle from direct contact with the aluminum manifold, using the Vespel’s low thermal conductivity (0.35 W/m/ C at 40 C, compared to stainless steel’s 16 W/m/ C) to limit heat transfer. The spacer de- sign also utilizes a symmetric screw pattern to decrease the potential for thermal cycle induced loosening. Figure 5.13 shows the manifold, o-ring/seal, and nozzle for both of the variants, specif- ically showing the difference in the sealing, screw holes, and isolation. 67 Figure 5.12: Hydrogen peroxide vapor thruster Prototype 3: test unit (left), CAD model (right). Figure 5.13: Prototype 3 mounting configurations: o-ring (left), spacer (right). Thrust measurements were made with both mounting configurations. For the o-ring variant, measurements were made for both the MCD and the SSCD nozzles; images of both of these noz- zles can be seen in Figure 5.2. For the spacer variant, measurements were made for a SSCD nozzle and a SS converging only nozzle, which will be referenced as the SSCO nozzle. All interior dimen- sions and wall thicknesses were designed to be the same for the spacer and o-ring configurations, however due to the complex machining required for the small nozzles some minor variations in throat and exit diameter are noted in Table 5.5. Id. A, B, etc. will be used to reference the various builds. Models of the nozzles used in the spacer variant can be seen in Figure 5.14. 68 Figure 5.14: Spacer variant nozzles: SSCD (left), SSCO (right). Table 5.5: Measured Nozzle Throat and Exit Diameters Id. Nozzle Characteristic Throat Diameter (mm) Exit Diameter (mm) A O-ring MCD 0.7 0.013 4.6 0.1 B O-ring SSCD 0.6 0.013 6.0 0.1 C Spacer SSCD 0.72 0.013 5.5 0.1 D Spacer SSCO 1 0.67 0.013 - E Spacer SSCO 2 0.67 0.013 - 5.2.2 Thrust Measurement Setup Thrust measurements were made with a torsional pendulum thrust stand consisting of an aluminum arm balanced on a frictionless pivot with a calibrated spring constant. The thruster was placed on one side of the arm; for balance, counterweights were placed on the other side. When the thruster was fired, the arm displacement was measured with an optical displacement meter. Thrust was then calculated using the measured displacement and the spring constant, F T = k L (5.2) whereF T is thrust, is the deflection of the arm, k is the spring constant, andL is the moment arm. The spring constant was experimentally determined using calibration electrodes to exert a known electrostatic force on the test stand. This calibration was performed with the thruster mounted and the stand leveled and balanced, once at the beginning of a test day and again at the end. Figure 5.15 shows an image of the Prototype 3 thruster on the thrust stand. Further details on the design and calibration of the specific thrust stand used in this study can be found in Hsu 69 Schouten et al. [70]. Figure 5.15: Prototype 3 thruster on torsional pendulum thrust stand. 5.2.3 Results Thrust, catalyst temperature, tank temperature, and tank pressure were measured (catalyst chamber pressure was also measured for the MCD nozzle cases). Both the o-ring and the spacer mounting configurations were tested. All H 2 O 2 test series were completed at tank temperatures of 60 C, 70 C, and 80 C for varying run times (1, 5, and 10 minutes). The two spacer variant nozzles were also tested with water (H 2 O) as the propellant for a direct comparison of performance. Water tests were performed at 30 C, 40 C, 50 C, and 60 C for the same run times. Data for all of the test runs are provided in Appendix D. A separate test series was completed for all of the mounting configurations, nozzles, and propellants to experimentally determine mass flow through the system. Mass flow rate relations and data provided in Appendix E. 5.2.3.1 O-ring Variant Two nozzles, the MCD and SSCD, were tested with the same o-ring mounting configuration as Prototype 2. MCD Nozzle [Id. A] For each of the three tank temperatures of interest (60 C, 70 C, and 80 C) a series including six 1 minute tests, three 5 minute tests, and one 10 minute test was performed. The series was 70 then completed with an additional test at 80 C until all of the propellant was expelled. Catalyst temperature measurements were taken at 3 locations along the centerline of the catalyst chamber in the MCD nozzle: (1) under the first sheet of silver mesh (top), (2) under the fourth sheet (middle), and (3) under the final sheet (bottom), same as was done for the Prototype 2 test series. These catalyst temperatures are shown for a 80 C tank temperature test run featuring three 1 minute tests and two 5 minute tests in Figure 5.16. The average catalyst temperature was taken as the mean of these measurements. Figure 5.17 shows the tank pressure and chamber pressure for that same test run. Table 5.6 lists the steady state tank pressure, steady state pressure drop to the catalyst chamber, and max average catalyst temperature for all of the MCD nozzle tests. The system pressure drop is approximately 5% of the tank pressure, which is a substantial improvement over the previous iteration. Figure 5.16: Top, middle, and bottom catalyst temperatures in the O-ring MCD nozzle with 7 sheets silver mesh and a tank temperature of 80 C during a thrust measurement test series. Table 5.6: Steady State Tank and Chamber Pressures and Maximum Average Catalyst Temperature for O-ring MCD Nozzle Tests Tank Temperature ( C) Steady State Tank Pressure (Torr) System Pressure Drop (Torr) Max Average Catalyst Temperature ( C) 60 21.0 (-2.6 +3.4) 0.9 (-0.3 +0.4) 241 (-2.6 +4.4) 70 34.2 (-3.5 +4.7) 1.6 (- 0.2 +0.2) 317 (-5.8 +9.0) 80 51.2 (-5.4 +7.3) 2.8 (-0.6 +0.7) 387 (-6.0 +6.1) 71 Figure 5.17: Tank and catalyst chamber pressure in the Spacer MCD nozzle with 7 sheets silver mesh and a tank temperature of 80 C during a thrust measurement test series. Thrust and average catalyst temperature for all of the tests are shown in Figures 5.18 and 5.19, respectively. Variation in the thrust level at a specific tank temperature is due to vacuum distillation of the liquid propellant throughout the test series. Distillation decreased the vapor pressure and therefore the thrust. Figure 5.18: Measured thrust for all O-ring MCD nozzle thrust measurement test runs. 72 Figure 5.19: Average catalyst temperature for all O-ring MCD nozzle thrust measurement test runs. Due to the nature of the thrust measurement test series (i.e., the entire series was completed with one propellant load), mass flow measurements were not possible. Therefore an additional test series was performed with the same nozzle configuration and more targeted test runs to experimen- tally determine the relationship between tank pressure, propellant load, and mass flow rate. For each test a known quantity of propellant was loaded, the tank was set to either 60 C, 70 C, or 80 C, and the test was run until the propellant was fully expelled. Figure 5.20 shows the mass flow relationship with tank pressure. This linear fit was used to determine the I sp of each test performed on the thrust stand. The average thrust and I sp for each tank temperature and length are shown in Table 5.7. Details for each test are provided in Appendix D. Using the mass flow rate relation and run times, the overall propellant usage was calculated to be 10.5 ml. This value is within 1% of the measured loaded value. 73 Figure 5.20: O-ring MCD nozzle mass flow rate calculated from known propellant load and test run length. Table 5.7: Thrust and I sp for O-ring MCD Nozzle Tests Test Steady State Thrust (mN) Steady State I sp (s) 60 C, 1 min 0.75 (-0.02 +0.02) 55.9 (-7.6 +6.8) 60 C, 5 min 0.71 (-0.01 +0.02) 54.7 (-4.2 +7.6) 60 C, 10 min 0.73 62.9 70 C, 1 min 1.35 (-0.07 +0.05) 61.1 (-4.5 +4.3) 70 C, 5 min 1.23 (-0.02 +0.03) 59.6 (-2.7 +4.8) 70 C, 10 min 1.25 64.9 80 C, 1 min 2.13 (-0.08 +0.11) 63.5 (-2.5 +2.6) 80 C, 5 min 1.94 (-0.03 +0.03) 62.0 (-2.0 +3.4) 80 C, 10 min 1.88 64.9 80 C, 11 min 1.81 63.0 SSCD Nozzle [Id. B] The test series performed on the MCD nozzle was repeated for the SSCD nozzle: same tank temperatures (60 C, 70 C, and 80 C) and run times (1, 5, and 10 minutes). The catalyst chamber temperature measurement was taken on the outside of the SS body at the throat. Due to higher temperatures at the o-ring in this design, leakage between the manifold and nozzle prevented a fully successful test series. Figure 5.21 shows an example of a leak in the middle of a test run, where the catalyst temperature drops off immediately with the thrust following shortly after. Any 74 test with this behavior was eliminated from the aggregated data of Table 5.8. Figure 5.23 and 5.22 show the catalyst temperatures and thrust levels for all of the test runs without apparent leaks. However, major variations in temperature and thrust at the same tank temperature suggests small leaks might have been prevalent throughout the series. Figure 5.21: Evidence of leak between manifold and catalyst chamber in 80 C tank temperature run of O-ring SSCD nozzle. Table 5.8: H 2 O 2 Steady State Tank Pressures, Maximum Average Catalyst Temperature, Steady State Thrust, and Steady State I sp for O-Ring SSCD Nozzle Tests Tank Temp. ( C) Tank Press. (Torr) Max Cat. Temp. ( C) Thrust (mN) I sp (s) 60 21.9 (-2.2 +2.8) 195 (-11.1 +11.7) 0.57 (-0.05 +0.07) 58.2 (-9.1 +6.3) 70 36.2 (-6.0 +4.1) 255 (-22.4 +28.7) 1.07 (-0.13 +0.13) 66.2 (-6.5 +5.0) 80 62.1 (-3.1 +4.4) 327 (-17.9 +25.4) 1.88 (-0.11 +0.22) 67.4 (-3.6 +3.5) 75 Figure 5.22: Measured thrust for all O-ring SSCD nozzle thrust measurement test runs. Figure 5.23: Catalyst temperature for all O-ring SSCD nozzle thrust measurement test runs. 5.2.3.2 Spacer Variant Two nozzles, the SSCD and the SSCO, were tested with the spacer mounting configuration. These nozzles were tested both with H 2 O 2 as well as with H 2 O to get a direct comparison of performance. In the H 2 O tests, the silver catalyst was removed. SSCD Nozzle [Id. C] For each of the 60 C, 70 C, and 80 C tank temperatures, three 1 minute, two 5 minute and one 10 minute tests were performed with H 2 O 2 as the propellant. Due to H 2 O’s higher vapor pressure, H 2 O test runs were performed at 30 C, 40 C, 50 C, and 60 C. Temperature was measured on the outside of the SS catalyst chamber in 2 locations (1) 76 immediately upstream of the converging nozzle section and (2) at the throat. In both nozzles using the spacer mounting variant, temperature was measured using a type K thermocouple with a SS sheath. An image is shown in Figure 5.24. Temperature measurements for both thermocouples are shown for an H 2 O 2 , 60 C tank temperature test series in Figure 5.25. Chamber temperatures for the water tests are not shown, since they match the tank temperature within 1 C. Figure 5.24: Thermocouple placement on Spacer SSCD nozzle. Figure 5.25: Temperature measured at the bottom of the catalyst chamber and throat for a 60 C tank experiment series on the Spacer SSCD nozzle running H 2 O 2 . Thermocouple placement shown in Figure 5.24. Thrust and catalyst temperatures for the H 2 O 2 tests are shown in Figure 5.26 and 5.28, re- spectively. Catalyst temperature is taken as the throat temperature measurement, for congruity with previous tests. The average steady state tank pressure, maximum catalyst temperatures, steady state 77 thrust, and steady state I sp for each of the tank temperatures are provided in Table 5.9. Evidence of minor catalyst chamber leaking can be seen in the catalyst temperature and thrust during the 80 C tests. Thrust measurements for the H 2 O tests can be seen in Figure 5.27, with temperatures, pres- sures, thrust, and I sp provided in Table 5.10. The system heaters and thermocouple feedback loop were designed for the lower evaporation rate associated with H 2 O 2 . This resulted in more tank temperature variation and therefore tank pressure variation with the H 2 O tests. This presents itself as a slight wobble in the thrust measurement. Small irregularities in the water evaporation also appear in the pressure and thrust measurements, potentially due to lack of adequate nucleation sites. Figure 5.26: Measured thrust for all H 2 O 2 Spacer SSCD nozzle thrust measurement test runs. Table 5.9: H 2 O 2 Steady State Tank Pressures, Maximum Average Catalyst Temperature, Steady State Thrust, and Steady State I sp for Spacer SSCD Nozzle Tests Tank Temp. ( C) Tank Press. (Torr) Max Cat. Temp. ( C) Thrust (mN) I sp (s) 60 25.0 (-1.7 +1.3) 263 (-18.3 +7.7) 1.17 (-0.05 +0.05) 71.7 (-1.1 +2.1) 70 43.1 (-2.6 +2.6) 336 (-2.0 +1.1) 2.07 (-0.13 +0.16) 73.3 (-0.6 +1.5) 80 69.4 (-6.5 +5.3) 388 (-36.8 +9.8) 3.27 (-0.43 +0.32) 71.9 (-2.9 +1.6) 78 Figure 5.27: Measured thrust for all H 2 O Spacer SSCD nozzle thrust measurement test runs. Figure 5.28: Catalyst temperature for all H 2 O 2 Spacer SSCD nozzle thrust measurement test runs. Table 5.10: H 2 O Steady State Tank Pressures, Maximum Average Catalyst Temperature, Steady State Thrust, and Steady State I sp for Spacer SSCD Nozzle Tests Tank Temp. ( C) Tank Press. (Torr) Max Cat. Temp. ( C) Thrust (mN) I sp (s) 30 29.6 (-0.5 +1.3) 30 (-0.3 +0.3) 1.31 (-0.03 +0.05) 48.6 (-1.0 +1.7) 40 54.0 (-2.0 +1.8) 40 (-0.7 +0.6) 2.45 (-0.10 +0.09) 50.1 (-0.2 +0.3) 50 87.8 (-6.8 +4.9) 50 (-0.5 +0.2) 4.13 (-0.40 +0.36) 51.8 (-1.1 +1.6) 60 136.7 (-1.6 +1.6) 59 (-0.1 +0.1) 6.73 (-0.29 +0.29) 54.3 (-1.7 +1.7) 79 SSCO Nozzle [Id. D and E] The H 2 O 2 and H 2 O tests performed on the spacer SSCD nozzle were repeated with a SSCO nozzle. Due to the lack of a diverging section, temperature could only be taken on the bottom exterior of the catalyst chamber. However, as was shown in Figure 5.25, this temperature closely matches that of the throat. For the SSCD test series, both the H 2 O 2 and H 2 O tests were performed with the same nozzle build (Id. C, catalyst removed for water tests). In this test series, with the SSCO configuration, the H 2 O 2 tests and H 2 O tests were performed with different nozzle builds, Id. D and Id. E, respectively. While they have the same measured throat diameter, as detailed in Table 5.5, there appeared to be a burr in the flow path of the nozzle used in the water test series, which decreased the mass flow rate for that test series. Thrust for the H 2 O 2 and H 2 O tests are shown in Figure 5.29 and Figure 5.30, respectively. The catalyst temperatures for the H 2 O 2 test are shown in Figure 5.31. Averaged data are provided in Table 5.11 and Table 5.12. For the H 2 O 2 tests, leaks between the catalyst chamber and manifold are evident during the 80 tank test series; this shows up in both the thrust measurement and in the catalyst temperatures. Both the H 2 O 2 and H 2 O thrust measurements show some variance in tank temperature/pressure/thrust. Improper heater placement/control resulted in more dramatic swings in tank temperature. Also the H 2 O SSCO tests show small irregular pops in pressure and thrust, as was seen in the previous H 2 O SSCD test series. Figure 5.29: Measured thrust for all H 2 O 2 Spacer SSCO nozzle thrust measurement test runs. 80 Figure 5.30: Measured thrust for all H 2 O Spacer SSCO nozzle thrust measurement test runs. Figure 5.31: Catalyst temperature for all H 2 O 2 Spacer SSCO nozzle thrust measurement test runs. Table 5.11: H 2 O 2 Steady State Tank Pressures, Maximum Average Catalyst Temperature, Steady State Thrust, and Steady State I sp for Spacer SSCO Nozzle Tests Tank Temp. ( C) Tank Press. (Torr) Max Cat. Temp. ( C) Thrust (mN) I sp (s) 60 25.7 (-1.0 +0.9) 232 (-5.6 +4.0) 1.01 (-0.02 +0.02) 68.7 (-2.1 +2.3) 70 42.9 (-2.6 +1.4) 309 (-5.9 +5.4) 1.74 (-0.09 +0.05) 70.7 (-0.9 +0.5) 80 66.9 (-4.8 +4.2) 345 (-42.8 +29.7) 2.63 (-0.26 +0.18) 68.5 (-1.9 +1.7) 81 Table 5.12: H 2 O Steady State Tank Pressures, Maximum Average Catalyst Temperature, Steady State Thrust, and Steady State I sp for Spacer SSCO Nozzle Tests Tank Temp. ( C) Tank Press. (Torr) Max Cat. Temp. ( C) Thrust (mN) I sp (s) 30 30.7 (-0.3 +0.9) 30 (-0.2 +0.2) 0.86 (-0.03 +0.02) 52.6 (-1.2 +1.6) 40 55.5 (-1.4 +1.6) 40 (-0.3 +0.7) 1.56 (-0.05 +0.05) 53.0 (-0.5 +0.4) 50 92.0 (-3.1 +3.1) 49 (-0.3 +0.5) 2.53 (-0.08 +0.11) 51.9 (-0.6 +0.5) 60 139.0 (-8.2 +6.4) 58 (-0.5 +0.7) 3.89 (-0.24 +0.18) 52.8 (-0.5 +0.6) 5.2.4 Analysis Several factors influence the thrust and overall system performance. In order to directly compare the different configurations, thrust and I sp for all of the cases were normalized to the o- ring MCD nozzle mass flow rate at the 60 C, 70 C, and 80 C (corresponding to 30 C, 40 C, and 50 C for H 2 O). This adjustment compensated for the different throat diameters. Additionally, a disparity between the mass flow rate relations developed during a separate experimental series and the thrust measurement experimental series was corrected (discussion and data provided in Appendix F). A direct comparison of the thrust and I sp for all of the Prototype 3 designs and propellants is provided in Figure 5.32 and Figure 5.33, respectively. The spacer variant SSCD nozzle operating with H 2 O 2 propellant demonstrated the highest thrust and I sp , approximately 60% higher than the same nozzle operating on H 2 O. Figure 5.32: Average normalized thrust for all Prototype 3 thrust measurement tests. 82 Figure 5.33: Average normalized I sp for all Prototype 3 thrust measurement tests. 5.2.4.1 Comparison with Theoretical Nozzle A chemical equilibrium code based on STANJAN [48] was used to compute the isentropic mass flow rate, thrust, and vacuum specific impulse for comparison with the spacer variant nozzle experimental values; results are shown in Table 5.13. Throat Reynolds number,Re t , and Knudsen number,Kn t , were also computed using Equations 5.3, 5.4, and 5.5. The input parameters of the analyses were the average measured tank pressures and average maximum catalyst chamber tem- peratures. The analysis assumed complete decomposition and isentropic expansion of the products by a specified exit-to-throat area ratio. From the pressure, velocity, and density at the throat (de- fined as the location where the local sound speed is equal to the local velocity,i.e., a Mach number of unity) and the exit were calculated. These calculations assume continuum flow and no boundary layer effects. Re t = u t d t t (5.3) = k B T 0 p 2d 2 P 0 (5.4) Kn t = d t (5.5) whereu t is the throat flow speed,d t is the throat diameter, t is the throat kinematic viscosity, is the gas mean free path,k B is the Boltzmann constant,T 0 is the stagnation temperature or catalyst temperature, d is the average molecular diameter, and p 0 is the stagnation pressure or chamber pressure. The mass flow rate ratio, which is often referred to as discharge coefficient, C D , appears 83 Table 5.13: Comparison of the Spacer Variant Nozzle Experimental Mass Flow Rate, Thrust, and I sp with that of an Isentropic Nozzle in Continuum Flow Nozzle Type/ Id. Prop. Tank Temp. ( C) Re t Kn t _ m (Ex./Th.) Thrust (Ex./Th.) I sp (Ex./Th.) SSCD/ C H 2 O 2 60 171 0.0084 0.77 0.51 0.67 SSCD/ C H 2 O 2 70 245 0.0059 0.83 0.53 0.64 SSCD/ C H 2 O 2 80 344 0.0042 0.87 0.52 0.60 SSCO/ D H 2 O 2 60 176 0.0082 0.78 0.70 0.90 SSCO/ D H 2 O 2 70 240 0.0060 0.83 0.73 0.87 SSCO/ D H 2 O 2 80 343 0.0042 0.86 0.70 0.82 SSCD/ C H 2 O 30 553 0.0026 0.97 0.49 0.51 SSCD/ C H 2 O 40 955 0.0015 0.99 0.51 0.51 SSCD/ C H 2 O 50 1479 0.00098 1.00 0.52 0.52 SSCO/ E H 2 O 30 533 0.0027 0.64 0.5 0.78 SSCO/ E H 2 O 40 915 0.0016 0.65 0.50 0.77 SSCO/ E H 2 O 50 1441 0.0010 0.66 0.49 0.74 directly correlated with Reynolds number. Higher Reynolds number leads to a C D approaching unity. Note the SSCO nozzle with H 2 O as the propellant is disregarded in this analysis. Post- testing a large burr was found in the throat region, which would have a dramatic effect on flow characteristics, specifically mass flow rate. This relationship between Re and C D has been established by other researchers and the experimental values determined here match relatively well with the relation developed by Kuluva et al. [71] (Equation 5.6). Experimental H 2 O 2 C D values were within 5% of those found via the equation, with the H 2 OC D values within 11%. C D = r c + 0:05r t r c + 0:75r t 0:019 " 1 r c + 0:10r t r t 0:21 1 Re 0:5 f( ) # (5.6) f( ) 0:97 + 0:86 (5.7) wherer c is the radius of the chamber,r t is the radius of the throat, and is the specific heat ratio. The discrepancy in the theoretical and experimental thrust and I sp is not completely explained by the differences in mass flow rates, especially for the nozzles with a diverging section. However 84 with aRe< 1000 for a majority of the tests, viscosity losses are a known dominate factor in nozzle performance. Inefficiencies arise from the adverse interaction of the subsonic boundary layer near the wall with the supersonic flow at the core. For low Reynolds numbers the viscous boundary layer can occupy almost all of the diverging section. Bruccoleri et al. [72] found nozzle efficiencies of around 75% forRe > 1500, but that dropped to approximately 60% forRe 400, and 40% for Re < 200. Murch et al. [73] also found that the inviscid core/ boundary layer interaction was an important effect that scaled with Reynolds number. Kim [74] studied the viscous and divergence losses for nozzles with Reynolds numbers ranging from 270 to 1150 using a full Navier Stokes code. Results showed large viscous boundary layers, which dominate an increasing portion of the exit plane with increasing nozzle length. In addition to viscous losses, divergence losses also decrease performance with respect to theory. The SSCD design features an especially large nozzle angle,, of 67 . Thrust loss due to divergence is typically treated by F conic;appox = _ mu e + (p e p a )A e (5.8) = 1 + cos 2 (5.9) whereF conic;appox is the theoretical thrust approximation for a conical nozzle with a nozzle angle of. Incorporating this into the isentropic theoretical calculations for the SSCD nozzle deceases the potential thrust by approximately 30%. The converging only designs, SSCO, would also expe- rience divergence losses due to flow expansion at the exit plane. Due to the low Reynolds numbers and Knudsen numbers bordering the transitional flow regime (0.01 < Kn < 100), theoretical calculations of mass flow rate, thrust, and I sp in a free molecular flow were also completed: F T;FM = p 0 A t 2 (5.10) I sp;FM = r 2 k B M T 0 1 g (5.11) _ m FM = F T;FM I sp;FM g (5.12) whereF T;FM is the free molecular thrust,A t is the throat area,M is the molecular mass, andg is 85 the gravitational constant. Ratios of the experimental mass flow, thrust, and I sp to that of free molecular flow theory are provided in Table 5.14. Based on the lack of difference in thrust and I sp ratios with Knudsen number, all the experiments performed in this study appear to fall in the continuum regime. In the free molecular or transitional regime, higher Knudsen numbers would have ratios approaching unity. Table 5.14: Comparison of the Spacer Variant Nozzle Experimental Mass Flow Rate, Thrust, and I sp with that of an Isentropic Nozzle in Free Molecular Flow Nozzle Type/ Id. Prop. Tank Temp. ( C) Re t Kn t _ m (Ex./Th.) Thrust (Ex./Th.) I sp (Ex./Th.) SSCD/ C H 2 O 2 60 171 0.0084 1.24 1.72 1.39 SSCD/ C H 2 O 2 70 245 0.0059 1.32 1.77 1.34 SSCD/ C H 2 O 2 80 344 0.0042 1.37 1.74 1.26 SSCO/ D H 2 O 2 60 176 0.0082 1.24 1.67 1.35 SSCO/ D H 2 O 2 70 240 0.0060 1.33 1.73 1.30 SSCO/ D H 2 O 2 80 343 0.0042 1.37 1.67 1.22 SSCD/ C H 2 O 30 553 0.0026 1.54 1.63 1.06 SSCD/ C H 2 O 40 955 0.0015 1.57 1.67 1.07 SSCD/ C H 2 O 50 1479 0.00098 1.59 1.73 1.09 SSCO/ E H 2 O 30 533 0.0027 1.02 1.19 1.16 SSCO/ E H 2 O 40 915 0.0016 1.04 1.20 1.15 SSCO/ E H 2 O 50 1441 0.0010 1.06 1.17 1.11 5.2.5 Comparison with Theoretical Catalyst Temperature Average catalyst temperatures for all of the Prototype 2 and 3 nozzles, with H 2 O 2 as the propellant, are shown in Figure 5.34. When comparing the Prototype 2 nozzles to that of their equivalent Prototype 3 nozzles, there is an improvement of approximately 30 - 40% depending on the tank temperature. However even the maximum temperature seen in these tests still falls well below the adiabatic temperatures shown in Figure 5.9. 86 Figure 5.34: Average catalyst temperatures for all Prototype 2 and 3 thrust measurement tests. 5.2.5.1 Heat Transfer Analysis using Finite Element Modeling COMSOL was used to model the two mounting configurations and their respective nozzles using the same equations and assumptions as Section 5.1.3. Due Prototype 3’s lower system pres- sure drop (i.e., higher chamber pressure) and higher liquid H 2 O 2 concentration (i.e., higher vapor H 2 O 2 concentration), the heat flux values used to model the decomposition process were slightly higher than the Prototype 2 values at 2.65 W, 4.32 W, and 6.47 W for tank temperatures of 60 C, 70 C, and 80 C, respectively. Table 5.15 compares the average catalyst temperatures for the Prototype 2 nozzles and those of Prototype 3, both the o-ring and spacer variants. Images of the Prototype 3 COMSOL models sectioned along the centerline are shown in Figures 5.35 and 5.36. Overall the model trends for each nozzle style are reflected in the experimental values shown in Figure 5.34. Measured and modeled temperatures increased for the MCD nozzle from Prototype 2 to Prototype 3. Measured and modeled temperatures also increased for the SSCD nozzle from Prototype 2 to the o-ring variant of Prototype 3 to the space variant of Prototype 3. One deviation was with the spacer SSCO nozzle; the model predicted that the catalyst temperatures would be higher than the spacer SSCD nozzle, which was not realized in the thrust measurement experimental series. 87 Table 5.15: COMSOL Catalyst Temperatures for Prototype 2 and 3 Prototype 2 Prototype 3 O-Ring O-Ring Spacer Tank Temp. MCD Nozzle SSCD Nozzle MCD Nozzle SSCD Nozzle SSCD Nozzle SSCO Nozzle 60 C 101 C 116 C 115 C 132 C 197 C 227 C 70 C 142 C 163 C 161 C 184 C 281 C 320 C 80 C 199 C 224 C 217 C 243 C 375 C 421 C Figure 5.35: Kalrez R O-Ring variant COMSOL model slice temperature for 80 C tank temperature: MCD nozzle (left), SSCD nozzle (right). 88 Figure 5.36: Vespel R Spacer variant COMSOL model slice temperature for 80 C tank temperature: SSCD nozzle (left), SSCO nozzle (right). 5.3 Summary The development and test of Prototype 2 allowed for the investigation of 3 different catalyst materials and the identification of the highest performing material and bed length: 7 sheets of silver mesh with an aperture of 0.42 mm and a wire diameter of 0.11 mm. Measured catalyst temper- atures were approximately 30% of their adiabatic temperature, assuming full decomposition. A finite element model of the system heat transfer was developed to identify and help inform design modifications. The model showed that conduction from the nozzle to the manifold was the primary heat loss path. Minimizing that loss could improve catalyst temperatures by up to 135%. While valuable data was collected in the Prototype 2 series, high system pressure drop and mild valve corrosion spurred the design of Prototype 3. In Prototype 3, the flow path diameter was increased and the valves were replaced with a more compatible, larger orifice option. Using a torsional pendulum thrust stand, thrust measurements were made with the Prototype 3 design with four different nozzle configurations: (1) a MACOR R converging diverging nozzle with a Viton R o-ring seal, (2) a stainless steel converging diverging nozzle with a Viton R o-ring seal, (3) a stainless steel converging diverging nozzle with a Vespel R spacer seal, and (4) a stainless steel converging only nozzle with a Vespel R spacer seal. The last two nozzle configurations were tested with both H 2 O 2 and H 2 O as the propellant, for a direct comparison of performance. Testing revealed that the Spacer SSCD nozzle with H 2 O 2 was the highest performer in terms of both thrust 89 and specific impulse. It outperformed its H 2 O counterpart by 60%. Comparison of the experimental thrust results with a theoretical isentropic, inviscid nozzle showed the dramatic impact of the low Reynolds number viscous boundary layer (Re H 2 O 2 < 350, Re H 2 O < 1500). Thrust and I sp ratios (experimental/theoretical) varied from 0.49 - 0.73 and 0.51 - 0.9, respectively. A 30 - 40% increase in catalyst temperature was realized between the Prototype 2 and 3 configuration, which showed the benefit of the larger manifold flow area and the additional thermal isolation. A heat transfer model of the Prototype 3 design was compared to that of Prototype 2; the models matched the experimental trends. CHAPTER 6 CATALYTIC THERMAL TRANSPIRATION Thrust level in an H 2 O 2 vapor thruster is controlled by changing the propellant concentration or the propellant temperature. This can be limiting if higher thrust levels are desirable. Another option to increase thrust is to increase the pressure within the catalyst chamber utilizing a micropump. However, due to enhanced friction losses, manufacturing tolerances, sealing, and other issues as- sociated with miniaturization [75], micropumps with moving parts are relatively inefficient at con- verting electrical power to pumping power. For gas phase, low Reynolds number systems, thermal transpiration can be used instead of a “traditional” micropump to provide pressurization without any moving parts or fluids. Thermal transpiration causes a pressure gradient to exist when (1) a temperature gradient is present, and (2) the mean free path of the gas is on the order of the perpendicular system dimension, i.e., the diameter of a membrane pore or tube. The gas then flows in the direction of increasing temperature. An illustration of this can be seen in Figure 1.4. The phenomenon of thermal transpiration was first explained by Reynolds in 1879 [76] and investigated theoretically by Maxwell [77]. A pumping device utilizing the thermal transpiration effect is sometimes referred to as a “Knudsen compressor” after Martin Knudsen, who is credited as the first to produce a staged compressor comprised of a series of differentially heated and cooled capillaries [37]. Since then several researchers [38, 78–83] have investigated thermal transpiration pumps utilizing electrical power to generated the required temperature differential. Recently, Wang et al. [43] demonstrated the first thermal transpiration pump utilizing com- bustion, instead of electrical power, to generate the required temperature differential. This resulted in a self-pressurizing, self-sustaining combustor with no moving parts or electrical requirements. Specifically, they used a propane/air reaction on a platinum catalyst at ambient pressures. In this study, a thermal transpiration membrane will be incorporated into the catalyst chamber of the H 2 O 2 vapor thruster. The necessary heat is generated from the H 2 O 2 decomposition on a silver catalyst at pressures ranging from 20 - 50 Torr. 90 91 6.0.1 Theoretical Performance An important factor in the analysis of the thermal transpiration phenomenon is the degree of rarefaction within the system, which is determined by the local Knudsen number, Kn. The Knudsen number is the ratio of the mean free path () of the gas to a characteristic length of interest. A system that has aKn> 100 is said to be in free molecular flow, where molecule-wall interactions dominate over molecule-molecule interactions. AKn< 0.01 indicates a system in continuum flow where molecule-molecule interactions dominate. In continuum flow the characteristic length is too large (much greater than the gas mean free path) for thermal transpiration. The region where the Knudsen number is between 0.01 and 100 is considered the transition flow regime. This regime presents the ideal balance of pressure increase and flow velocity, leading to minimization of a device’s volume per unit of upflow and significant reductions in energy usage and device size. In 2002, Muntz et al. [83] published a theoretical model that applies in this transitional flow regime. Those equations are presented in this section. In order to determine whether the system is within the transitional flow regime, the mean free path and Knudsen number need to be calculated: = k B T avg p 2d 2 P 1 (6.1) Kn = L r (6.2) wherek B is the Boltzmann constant,T avg is the average temperature,d is the molecular diameter, P 1 is the initial pressure, andL r is the characteristic length. The maximum pressure gain can be calculated using Equation 6.3. The flow coefficients,Q T andQ P , are extracted from published data by Sone et al. [84] (see Table 6.1). P max P avg;max = T T avg Q T Q P (6.3) P max = P 1 1 1 2 T Tavg Q T Q P (6.4) P =P max (6.5) Equation 6.4 provides the maximum pressure differential, which assumes a flow rate of 92 Table 6.1: Thermal Transpiration Flow Coefficients Kn Q T Q P 1128.4 0.7467 1.4996 112.84 0.7179 1.4764 56.419 0.696 1.4604 45.135 0.6867 1.454 33.851 0.6729 1.4449 28.209 0.663 1.4387 22.568 0.6495 1.4306 11.284 0.5975 1.404 5.642 0.5294 1.3817 2.257 0.4171 1.3867 1.128 0.3217 1.4584 0.5642 0.2272 1.6577 0.2257 0.1222 2.3482 0.1128 0.0686 3.5636 0.0846 0.053 4.386 0.0564 0.0363 6.0403 Reference: [84] zero. Therefore the true change in pressure is determined using Equation 6.5, where is the flow/pressure coefficient. A=1 corresponds to zero upflow, but maximum pressure increase and a =0 corresponds to a maximum upflow, but zero pressure increase. For this study p will be iterated on until the mass flow calculated in the isentropic nozzle equation, Eqn. G.11, matches that of the Muntz mass flow given in Eqn. 6.6, _ m =p avg fA 2 k B m T avg ( 1 2 ) L r L x T T avg Q T (1) (6.6) wheref is the fraction of open area in the membrane,m is a single molecule’s mass, andL x is the membrane thickness. 93 6.0.1.1 Effects of Thermal Transpiration Membrane Pore Radius To show the theoretical effects of integrating a thermal transpiration pump upstream of the catalyst, the relations were applied to an idealized H 2 O 2 vapor thruster operating in a perfect vac- uum. The throat diameter was set to 0.79 mm, exit diameter 4.80 mm, and tank temperature 60 C, same as was postulated in Section 2.1. The catalyst chamber pressure was taken to be the vapor pressure of the propellant at the prescribed temperature. The propulsion cycle analysis assumes steady flow with constant-pressure decomposition of the vapor followed by isentropic expansion (Equation G.11). The thermal transpiration device was assumed to be a microfilter/membrane with a porosity (open area) of 50%, membrane thickness of 675 m, and membrane area of 10 cm 2 . The membrane pore radius was varied from 0.1 to 1.0m. The corresponding Knudsen number spanned from 3 to 35, well within the transitional regime. The effects on pressure and mass flow and therefore thrust are shown in Figures 6.1 and 6.2. Theoretical specific impulse is not effected, since catalyst temperatures are assumed the same. Mass flow rate follows the trend of pressure. Therefore the ratio of thrust to mass flow rate does not change in theI sp relation: I sp = F T _ mg (6.7) whereF T is thrust, _ m is mass flow rate, andg is the gravitational constant. Figure 6.1: Chamber pressure and mass flow with a transpiration phase for a tank temperature of 60 C. The mass flow rate and pressure without the membrane is 1.14 10 -6 kg/s and 20.9 torr, respectively, for all pore sizes. 94 Figure 6.2: Thrust with and without a transpiration phase for a tank temperature of 60 C. 6.0.1.2 Effects of Tank Temperature Using the same thruster and membrane characteristics provided in Section 6.0.1.1, the ef- fect of changing the tank temperature and therefore mass flow rate, chamber pressure, and catalyst temperature was investigated by locking the membrane pore size at 0.7m and varying the tank temperature from 60 C to 80 C. The corresponding Knudsen number is well within the transi- tional regime (1<Kn< 5). The effects on pressure and mass flow and therefore thrust are shown in Figures 6.3 and 6.4. Figure 6.3: Chamber pressure and mass flow with and without a transpiration phase for a pore diameter of 0.7m. 95 Figure 6.4: Thrust with and without a transpiration phase for a pore diameter of 0.7m. 6.1 Experiment The Prototype 3 o-ring variant MCD nozzle (as seen in Figures 5.2 and 5.12) was modified slightly for the initial thermal transpiration test series. For improved sealing: (1) the o-ring groove was moved from the MCD nozzle to the manifold and (2) an additional screw was used to connect the MCD nozzle to the manifold. For pressure measurement immediately upstream of the thermal transpiration membrane an additional TE Connectivity 0 - 5 psi pressure sensor was incorporated into the manifold, downstream of the valve. The test unit and CAD model are shown in Figure 6.5. The thermal transpiration membrane was introduced to the chamber as shown in Figure 6.6. It was sandwiched between two washers to prevent flow bypass and to stabilize the membrane. The perforated sheet downstream of the catalyst was used for structural integrity of the catalyst bed and the sheet upstream of the membrane allowed for compression and thermal contact with the manifold. This was done by using a variable length aluminum tube, where the length was varied by the amount it was screwed into the manifold. The tube screwed into the manifold is visible in the model of Figure 6.5. Temperature was taken along the centerline: (1) on the perforated sheet upstream of the membrane, (2) in-between the membrane and the catalyst, and (3) on the perforated sheet downstream of the catalyst. 96 Figure 6.5: Hydrogen peroxide vapor thruster for thermal transpiration studies: test unit (left), CAD model with transparent manifold (right). Figure 6.6: Catalyst chamber with integrated thermal transpiration membrane. Temperature measurement locations indicated with numbers. 6.1.1 Catalyst and Membrane The catalyst used in these experiments was the same as was used in Prototype 3: 7 sheets of silver mesh with a nominal aperture of 0.42 mm and a wire diameter of 0.11 mm. This proved to be the most successful catalyst configuration tested (highest measured catalyst temperatures). Two thermal transpiration membranes were tested in this series and are detailed in Table 6.2. They are both Whatman glass microfiber binder-free filters, primarily used for cell harvesting, liquid scintillation counting, and pollution monitoring. However due to their inert materials and 97 small pore size, they are excellent fit for this application. Table 6.2: Thermal Transpiration Membrane Attributes Id. Pore Diameter (m) Thickness(m) A 0.7 420 B 1.0 675 6.2 Results Due to the limited membrane area possible within the Prototype 3 design (0.2 cm 2 ), thermal transpiration was not witnessed in this initial test series. The smaller membrane (when compared to the theoretical analysis in Section 6.0.1) resulted in an effective membrane flow area dramatically smaller than that of the nozzle throat. Therefore even assuming a zero pressure rise ( = 0), the thermal transpiration flow rate dictated by Equation 6.6 was less than the isentropic nozzle mass flow rate. This can be seen in the experimental data when comparing the mass flow rate with and without a membrane; see Table 6.3. However, the experiments did provide valuable information on realistic temperature differ- entials that could be maintained within the catalyst chamber. They also showed that the transpira- tion membrane implementation was effective. The system demonstrated minimal to no membrane bypass flow, low upstream pressure drop, and high temperature gradients. Catalyst chamber tem- peratures and pressures for tank temperatures of 60 C, 70 C, and 80 C are shown for three cases: (1) no membrane, (2) membrane A, and (3) membrane B (Figures 6.7 - 6.12). Membrane A rup- tured during the 80 C tank test. This can be seen in Figures 6.9 and 6.10 by the increase in catalyst chamber pressure and catalyst temperatures near the beginning of the run. Table 6.3: Mass Flow Rate with and without Transpiration Membrane for Tank Temperatures of 60 C Membrane Id. Tank Temp. ( C) Tank Press. (Torr) Cat Chamber Press. (Torr) Mass Flow Rate (kg/s) - 60 18.3 15.9 1.31 10 -6 A 60 18.1 5.6 4.27 10 -7 B 60 18.1 4.7 3.95 10 -7 98 Figure 6.7: Catalyst chamber temperatures for thermal transpiration experiment set-up with no membrane installed: thermocouple 1 = solid line, 2 = dashed line, and 3 = dotted line (number based on Figure 6.6). Figure 6.8: System pressures for thermal transpiration experiment with no membrane installed: tank pressure = solid line, upstream of catalyst chamber = dashed line, and downstream of silver catalyst = dotted line. For the tests with no membrane, vast temperatures differentials were maintained between the upstream perforated sheet and the top of the catalyst. This indicates that the manifold thermal grounding tube was working as desired,i.e., maintaining the temperature near that of the manifold. The temperature drop through the catalyst can be associated with heat loss to the walls as well as local behavior on the catalyst mesh; this behavior has been prevalent throughout this work during direct catalyst temperature measurements within the MCD nozzle. 99 Figure 6.9: Catalyst chamber temperatures for thermal transpiration experiment with membrane A installed: thermocouple 1 = solid line, 2 = dashed line, and 3 = dotted line (number based on Figure 6.6). Figure 6.10: System pressures for thermal transpiration experiment with membrane A installed: tank pressure = solid line, upstream of catalyst chamber = dashed line, and downstream of silver catalyst = dotted line. Temperature differentials still exist in the tests series with membranes A and B, but over- all catalyst temperatures are lower. For tank temperatures at or below 60 C, both catalyst tem- peratures (thermocouples 2 and 3, Figure 6.6) are in close alignment. However, at higher tank temperatures and flow rates, the top catalyst temperature rises dramatically and the differential between the two measurements increases (maximum T> 500 C). The addition of the low ther- mal conductivity membrane further decreased the temperature of the upstream perforated sheet by 100 Figure 6.11: Catalyst chamber temperatures for thermal transpiration experiment with membrane B installed: thermocouple 1 = solid line, 2 = dashed line, and 3 = dotted line (number based on Figure 6.6). Figure 6.12: System pressures for thermal transpiration experiment with membrane B installed: tank pressure = solid line, upstream of catalyst chamber = dashed line, and downstream of silver catalyst = dotted line. approximately 40%, contributing to a higher potential transpiration membrane temperature differ- ential. Pressures upstream and downstream of the catalyst chamber (which contains the membrane and silver catalyst), as well as all of the chamber temperatures are provided in Table 6.4. To predict the potential thrust gains for a system properly sized for thermal transpiration, the experimental temperature differentials and system pressures found in this test series were incorpo- rated into the theoretical model using the larger membrane area of 10 cm 2 . Pressure, mass flow 101 Table 6.4: Catalyst Chamber Temperatures with and without a Membrane Mem. Id. Tank Temp. ( C) Upstream Press. (torr) Cat. Chamber Press. (torr) Mem. Top Temp. ( C) Cat. Top Temp. ( C) Mem. Bot. Temp. ( C) - 60 16.8 15.9 102 576 244 - 70 30.5 29.3 125 725 336 - 80 49.3 47.9 150 817 409 A 30 3.2 1.2 30 37 39 A 40 6.3 2.1 40 60 63 A 50 12.1 4.0 52 115 115 A 60 20.3 6.3 64 155 151 A 70 34.3 10.4 76 465 200 A 80 48.8 29.7 94 850 332 B 30 1.6 1.3 30 49 52 B 40 5.6 2.2 40 73 77 B 50 10.9 3.5 50 101 107 B 60 19.7 5.7 60 133 142 B 70 33.2 9.2 72 5o7 189 B 80 48.8 29.7 83 683 239 rate, and thrust gains can be seen in Figures 6.13 and 6.14. 102 Figure 6.13: Chamber pressure and mass flow with and without a transpiration phase for a pore diameter of 0.7m. Figure 6.14: Thrust with and without a transpiration phase. Higher pressures lead to higher thrust. 6.3 Summary The first incorporation of a thermal transpiration membrane into an H 2 O 2 vapor thruster was presented and shows the potential to increase thrust. Theoretical models of an adiabatic, isentropic system show a 62% increase in thrust with the addition of a transpiring membrane (pore diameter: 0.7m, thickness: 420m, porosity: 50%, area: 10 cm 2 ). Due to the smaller membrane area in the experimental set-up (0.2 cm 2 ), thermal transpiration 103 pumping was not possible in the initial test series. Instead the series focused on experimental design: minimal system pressure drop, no membrane bypass flow, and high membrane temperature differentials. Tests with and without a micropore membrane were performed. Tests containing the membrane showed large pressure drops due to the low effective flow area (50 - 70%). Experimental temperature differentials and upstream pressure measurements were incorpo- rated into the theoretical model to give a more realistic expectation of pressure and thrust gains for an adequately-sized membrane. For a 60 C tank temperature and a membrane area of 10 cm 2 (the area used in the adiabatic calculation), a 26% increase in thrust was predicted. While in an adiabatic theoretical system there is no specific impulse gain associated with thermal transpira- tion, in a real thruster higher mass flow rates will result in a favorable increases in _ q gen = _ q loss (heat generated over heat loss). More heat retained in the chamber and therefore higher catalyst temper- atures would lead to higher specific impulses. Due to limited volume within the catalyst chamber a balance between decreasing throat area and increasing membrane area would be necessary to optimizing a thermal transpiration propulsion system. CHAPTER 7 CONCLUSIONS 7.1 Thesis Summary The objective of this thesis was to understand and evaluate the use of hydrogen peroxide vapor in low thrust propulsion applications, specifically for small satellites. Theoretical and ex- perimental methods were used to (1) investigate and prove that a monopropellant vapor would decompose and produce enough heat for propulsion at low pressures, (2) characterize the reaction of H 2 O 2 vapor on a catalytic surface to improve catalyst bed design and modeling, and (3) opti- mize the H 2 O 2 vapor thruster design, determine the performance, and investigate potential future improvements. To enable these investigations, a novel non-invasive diagnostic for determining the concentration of H 2 O 2 vapor was also developed. Ultimately, the findings presented in this thesis prove that low pressure, vacuum-evaporated monopropellant vapor can provide unique benefits for small satellite propulsion. However consideration must be given for the particular conditions of low Reynolds number flow, specifically how it affects heat transfer and boundary layer develop- ment. Three overarching conclusions can be extracted from this work. First, monopropellant H 2 O 2 vapor does outperform water vapor. This outcome was expected from typical combustion and nozzle relations, specifically adiabatic, isentropic, inviscid equations. However, these simplifying assumptions do not hold when working in the low pressure, low mass flow regime. In Chapter 5, H 2 O 2 vapor and steam were compared directly using the exact same thruster body and nozzle. Even at lower Reynolds numbers, H 2 O 2 vapor demonstrated a 60% higher thrust and specific impulse. Second, heat transfer and subsonic boundary layer flow dramatically affect the performance of an H 2 O 2 vapor propulsion system. With less than 10 W of energy being generated in the cata- lyst chamber, losses to the thruster body become especially critical and an adiabatic assumption no longer applies. Lower catalyst temperatures decrease the performance of the nozzle as was seen in the experimental studies detailed in Chapters 2 and 5. Finite element modeling was used to inves- tigate potential design iterations, specifically targeted at improved thermal isolation. These models revealed multiple avenues to increased catalyst temperatures and therefore performance. The low pressure associated with a vacuum-evaporated system results in low Reynolds number flow through the nozzle throat and diverging sections. With Reynolds numbers< 400, large subsonic boundary 104 105 layer flows (in some cases making up>50% of the exit area) cause dramatic inefficiencies. This was witnessed in the thrust measurements presented in Chapter 5, for both H 2 O 2 and H 2 O. To im- prove performance, focus on low Reynolds number nozzle design would be necessary to decrease the subsonic region near the wall. Third, H 2 O 2 vapor reacts rapidly, even at ambient conditions. This proved to be both a benefit and a burden. In terms of catalyst design, a rapid reaction at ambient conditions meant that a catalyst bed heater was not required, whereas a heater is necessary for a majority of other monopropellants, including other green propellants such as ADN and HAN. It also allowed for a relatively short catalyst bed and a plethora of catalyst bed material options, this was seen in Chapters 4 and 5. However, due to this ease of reaction, it was difficult to determine the actual concentration of the H 2 O 2 vapor at any point in time. It could decompose on relatively inert surfaces, including stainless steel, aluminum, and even glass after extended exposure. This spurred the creation of the H 2 O 2 vapor diagnostic in Chapter 3. It also imposed strict material requirements on the thruster and made it difficult to know the exact concentration of H 2 O 2 vapor entering the catalyst chamber. The actual reaction rate was investigated in Chapter 4 and showed a temperature- independent, fast catalytic reaction (when compared to liquid) at temperatures from ambient to 120 C. 7.2 Future Directions From the work presented in this thesis, there are a multitude of potential future research avenues. Fortunately, the methods and lessons learned here provide a solid foundation for tackling these open questions. H 2 O 2 Vapor Reaction Mechanism In Chapter 4, the decomposition of H 2 O 2 vapor on silver mesh, platinum mesh, and plat- inum on alumina spheres was observed using NIR laser absorption. Using those observations, a gas-phase approximation of the global reaction rates was presented. Difficulty in characterizing the surface of the catalyst as well as limitations in the experimental temperatures and flow rates prevented a more detailed reaction mechanism analysis. The use of a more uniform catalyst in a more capable experimental apparatus could allow for the hypothesis and experimental backing of a new H 2 O 2 vapor reaction model, including the H 2 O 2 vapor sticking coefficient. Further Performance Improvements to the H 2 O 2 Vapor Thruster Design As was presented in Section 7.1, several options for improved performance of the H 2 O 2 vapor 106 thruster are available, but could not be explored within this thesis. More effective thermal isolation of the catalyst chamber from the body could dramatically increase the catalyst temperatures and therefore the overall performance. Redesigning the nozzle for low Reynolds number flow could also increase performance by minimizing the subsonic boundary layer. Investigation of other Monopropellants with Vacuum-Evaporated Propellant Delivery Hydrogen peroxide is not the only propellant that can work in a vacuum-evaporated mono- propellant thruster design. In Chapter 2, several other potential propellants were introduced, in- cluding isopropyl nitrate and nitromethane. While these propellants were not investigated in this thesis, they have excellent potential in this type of design. Integration of Thermal Transpiration Membrane in Gas-Phase Propulsion Systems Chapter 6 introduced the concept of integrating a thermal transpiration membrane into a vapor propulsion system. However, within this thesis, actual demonstration of pumping was not possible. By following the model laid out in Chapter 6, the realization of passively increasing the catalyst chamber pressure and therefore increasing the thrust with no moving parts is possible. 7.3 Final Thoughts The ideas explored in this thesis were sparked by the evolution of satellites in recent years. Small satellites allow for more participants, more access, and ultimately more advances in space research. 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APPENDIX A Nomenclature Roman Symbols A 0 Pre-exponential factor C D Discharge coefficient C F Thrust coefficient C p Specific heat capacity c* Characteristic velocity d Diameter e b Blackbody emissive power F T Thrust f Fraction of open area G Irradiation g Gravitational constant J Mass flux K Viscous stress Kn Knudsen number _ m Mass flow rate Q T , Q P Thermal transpiration flow coefficients q Heat flux Re Reynolds number Greek Symbols Coefficient of thermal expansion, nozzle angle Number of sites per unit area Activity coefficient, Specific heat ratio Emissivity Fraction of occupied sites, Deflection Flow/pressure coefficient Wavelength, Mean free path 114 BIBLIOGRAPHY 115 Molecular thermal velocity Frequency, Kinematic viscosity Density Absorption cross section Chemical Formulas ADN Ammonium dinitramide C 3 H 7 NO 3 Isopropyl nitrate CaF 2 Calcium fluoride CH 3 NO 2 Nitromethane H 2 O Water H 2 O 2 Hydrogen peroxide HAN Hydroxylammonium nitrate N 2 H 4 Hydrazine O 2 Oxygen Pt Platinum Acronyms and Abbreviations Al Aluminum CAD Computer Aided Design CO Converging only CV Converging diverging ECAPS Ecological Advanced Propulsion Systems EPA Environmental Protection Agency ERC Engineering Rate Constant FEEP Field-Emission Electric Propulsion FM Free Molecular GPS Global Positioning System GWU George Washington University HITRAN High-resolution transmission molecular absorption database M MACOR R NASA National Aeronautics and Space Administration BIBLIOGRAPHY 116 NIR Near infrared OCSD Optical Communications and Sensors Demonstration PTFE Polytetrafluoroethylene PVC Polyvinylchloride SCAPE Self Contained Atmospheric Protection Ensemble SFL Space Flight Laboratory SS Stainless Steel sscm Standard cubic centimeters SSTL Surrey Satellite Technology Ltd. TNO Netherlands Organization for Applied Scientific Research APPENDIX B Volume and Surface Area for Reaction Rate Calculations Catalyst bed volume is a subjective value when considering small quantities of catalysts. For this study catalyst bed volume was considered the tube volume that contained catalyst material. Therefore for the platinum on alumina spheres, the volume,V catbed;sphere , was considered V catbed;sphere = 4 d 2 tube d sphere (B.1) whered tube is the inner diameter of the tube andd sphere is the diameter of the catalyst sphere. The catalyst volume of the mesh accounted for (1) the mesh perpendicular to the flow and (2) the additional mesh lining the sidewall. V catbed;mesh = 4 d 2 tube 2d wire + L wire d tube 2 (B.2) whereL wire is the length of the wire in the mesh. The surface area used in Equation 4.3 is treated as the exposed area of catalyst. Therefore for the spherical catalyst this is SA cat;sphere =d 2 sphere (B.3) For the mesh the surface area is the total area of all the wires contained in the mesh (inter- ference with other wires is ignored). SA cat;mesh =n wires d wire L wire + d 2 wire 2 (B.4) wheren wires is the number of wires contained in the mesh. 117 APPENDIX C Prototype 2 Experimental Data Average catalyst temperatures, tank pressures, and catalyst chamber pressures (when available) are provided for all of the test runs of the Prototype 2 design. Averages are taken from 80 - 160 seconds into the test run. Errors provided are the minimum and maximum deviation from that average. Table C.1: Prototype 2, SSCD nozzle, 7 Sheets Silver Mesh Catalyst Tank Temp. ( C) Catalyst Temp. ( C) Tank Press. (Torr) 60 135.9 (-1.4 +0.5) 29.0 (-3.5 +3.5) 60 134.6 (-1.4 +0.7) 28.6 (-3.1 +3.3) 70 183.0 (-1.3 +0.3) 46.0 (-3.0 +3.8) 70 180.8 (-1.3 +0.4) 47.6 (-3.5 +3.9) 70 179.2 (-1.7 +0.8) 46.6 (-3.5 +3.3) 80 239.0 (-1.5 +0.6) 74.8 (-4.2 +4.0) 80 236.0 (-1.9 +0.7) 76.2 (-3.4 +4.1) 80 233.8 (-1.4 +0.7) 75.3 (-4.2 +4.3) Table C.2: Prototype 2, SSCD nozzle, 3 Sheets Silver Mesh Catalyst Tank Temp. ( C) Catalyst Temp. ( C) Tank Press. (Torr) 60 139.2 (-1.7 +0.7) 28.5 (-0.4 +0.3) 70 182.5 (-1.4 +0.6) 46.2 (-0.2 +0.2) 80 231.3 (-1.4 +0.4) 74.4 (-0.8 +0.4) 118 BIBLIOGRAPHY 119 Table C.3: Prototype 2, SSCD nozzle, 14 Sheets Silver Mesh Catalyst Tank Temp. ( C) Catalyst Temp. ( C) Tank Press. (Torr) 60 98.2 (-0.3 +0.1) 28.2 (-0.2 +0.2) 70 130.4 (-1.0 +0.5) 46.7 (-0.4 +0.2) 80 169.7 (-1.1 +0.4) 74.5 (-0.4 +0.3) Table C.4: Prototype 2, SSCD nozzle, 7 Sheets Platinum Mesh Catalyst Tank Temp. ( C) Catalyst Temp. ( C) Tank Press. (Torr) 60 130.2 (-1.8 +0.8) 29.3 (-0.2 +0.3) 60 130.9 (-0.7 +0.3) 29.0 (-0.2 +0.1) 70 176.8 (-1.9 +0.6) 47.7 (-0.5 +0.2) 70 175.2 (-2.1 +0.9) 47.9 (-0.3 +0.2) 80 223.6 (-1.4 +0.8) 74.7 (-1.3 +0.9) Table C.5: Prototype 2, SSCD nozzle, 3 Sheets Platinum Mesh Catalyst Tank Temp. ( C) Catalyst Temp. ( C) Tank Press. (Torr) 60 123.6 (-3.9 +1.5) 29.2 (-0.2 +0.2) 70 168.6 (-2.0 +0.9) 46.6 (-0.3 +0.2) 80 219.9 (-1.5 +0.4) 73.7 (-1.5 +1.3) Table C.6: Prototype 2, SSCD nozzle, Platinum Sphere Catalyst Tank Temp. ( C) Catalyst Temp. ( C) Tank Press. (Torr) 60 113.7 (-2.9 +1.5) 30.8 (-0.3 +0.4) 70 154.3 (-3.2 +1.6) 49.7 (-0.3 +0.1) 80 202.7 (-2.5 +0.9) 78.7 (-1.2 +0.7) BIBLIOGRAPHY 120 Table C.7: Prototype 2, MCD nozzle, 7 Sheets Silver Mesh Catalyst Tank Temp. ( C) Catalyst Temp. ( C) Tank Press. (Torr) Catalyst Chamber Press. (Torr) 60 175.7 (-2.0 +2.1) 27.3 (-2.2 +2.1) 16.3 (-0.4 +0.4) 60 174.5 (-2.4 +2.5) 27.8 (-1.8 +1.8) 16.3 (-0.3 +0.3) 60 172.4 (-4.6 +3.7) 27.5 (-2.0 +2.3) 16.5 (-0.5 +0.5) 70 237.2 (-3.6 +2.7) 43.7 (-2.0 +1.9) 27.5 (-0.3 +0.4) 70 239.2 (-2.4 +1.9) 44.4 (-1.9 +2.7) 27.7 (-0.5 +0.4) 70 240.2 (-1.8 +0.9) 44.4 (-3.1 +1.8) 27.9 (-0.4 +0.4) 80 307.5 (-4.0 +3.7) 69.5 (-3.2 +2.9) 45.0 (-0.7 +0.7) 80 306.4 (-3.2 +3.0) 70.5 (-2.6 +2.6) 45.3 (-0.7 +0.7) 80 302.2 (-3.2 +3.0) 69.7 (-3.2 +3.4) 45.0 (-0.7 +0.8) APPENDIX D Prototype 3 Thrust Measurement Experimental Data Thrust measurements with calibration error and I sp values (with thrust measurement calibration error propagated) are shown for the MCD and SSCD nozzles in Table D.1 and D.2, respectively. Calibration was performed at the beginning and end of a test day. Thrust is reported as the mean of the average steady state thrust using those two calibrations (with error reported as the maximum deviation from that based on the two calibrations). Differences in calibration could be attributed to differences in thruster body temperature; typically the first calibration was at 60 C and the last at 80 C. An example of thrust using the two different calibrations is provided in Figure D.1. Figure D.1: Thrust for a 80 C tank test run using calibration 1 (taken at the beginning of the test day) and calibration 2 (taken at the end of the test day). The average of the steady state mean was reported as the thrust value. 121 BIBLIOGRAPHY 122 D.1 Kalrez R O-ring Variant Table D.1: H 2 O 2 Propellant: O-ring Variant, MCD Nozzle Test Steady State Values Tank Temp. ( C) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) Avg. Cat. Chamber Press. (Torr) Steady State Thrust (mN) Steady State I sp (s) 60 60.8 246 24.5 23.1 0.74 (+/-0.02) 48.4 (+/-1.1) 60 60.9 245 23.7 22.5 0.73 (+/-0.02) 49.5 (+/-1.0) 60 60.9 239 23.1 22.0 0.72 (+/-0.02) 49.9 (+/-1.0) 60 300.6 240 22.2 21.1 0.70 (+/-0.01) 50.5 (+/-1.1) 60 300.6 239 21.7 20.7 0.70 (+/-0.01) 51.3 (+/-1.1) 71 60.9 326 39.0 37.3 1.40 (+/-0.03) 57.2 (+/-1.2) 70 60.8 325 36.1 34.4 1.28 (+/-0.03) 56.6 (+/-1.2) 70 60.8 325 37.1 35.4 1.33 (+/-0.03) 57.3 (+/-1.2) 70 300.9 315 34.3 32.5 1.22 (+/-0.03) 56.9 (+/-1.2) 70 300.9 313 33.5 31.8 1.21 (+/-0.03) 57.5 (+/-1.2) 80 61.0 393 58.5 55.9 2.23 (+/-0.05) 60.9 (+/-1.3) 80 60.7 391 54.8 52.3 2.10 (+/-0.04) 61.1 (+/-1.3) 80 60.6 391 55.8 53.0 2.13 (+/-0.04) 61.0 (+/-1.3) 80 300.9 383 51.9 48.8 1.97 (+/-0.04) 60.5 (+/-1.3) 80 300.8 381 50.7 47.5 1.91 (+/-0.04) 60.0 (+/-1.3) 70 60.6 313 33.7 32.2 1.37 (+/-0.04) 65.0 (+/-2.0) Continued on next page BIBLIOGRAPHY 123 Table D.1 – continued from previous page Tank Temp. ( C) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) Avg. Cat. Chamber Press. (Torr) Steady State Thrust (mN) Steady State I sp (s) 70 59.6 315 33.5 32.0 1.37 (+/-0.04) 65.5 (+/-2.0) 70 61.0 314 33.2 31.7 1.35 (+/-0.04) 65.1 (+/-2.0) 70 300.7 311 31.3 29.8 1.26 (+/-0.04) 64.4 (+/-2.0) 70 600.8 311 30.7 28.9 1.25 (+/-0.04) 64.9 (+/-2.0) 60 60.9 241 19.5 18.9 0.77 (+/-0.02) 62.7 (+/-1.9) 60 61.1 240 19.1 18.5 0.75 (+/-0.02) 62.6 (+/-1.9) 60 60.6 242 19.4 18.7 0.76 (+/-0.02) 62.5 (+/-1.9) 60 300.6 241 18.7 18.0 0.73 (+/-0.02) 62.4 (+/-1.9) 60 600.8 240 18.4 17.7 0.73 (+/-0.02) 62.9 (+/-1.9) 80 60.8 390 52.2 50.0 2.16 (+/-0.07) 66.0 (+/-2.0) 80 60.6 389 50.4 48.0 2.08 (+/-0.06) 66.1 (+/-2.0) 80 60.8 389 49.8 47.3 2.05 (+/-0.06) 65.7 (+/-2.0) 80 301.8 381 47.4 44.4 1.94 (+/-0.06) 65.4 (+/-2.0) 80 600.1 381 46.2 42.8 1.88 (+/-0.06) 64.9 (+/-2.0) 80 681.1 384 45.9 42.4 1.81 (+/-0.06) 63.0 (+/-1.9) BIBLIOGRAPHY 124 Table D.2: H 2 O 2 Propellant: O-ring Variant, SSCD Nozzle Test Steady State Values Tank Temp. ( C) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) Steady State Thrust (mN) Steady State I sp (s) 60 60.7 188 24.7 0.54 (+/- 0.00) 49.1 (+/- 0.1) 60 60.4 188 23.6 0.53 (+/- 0.00) 50.1 (+/- 0.1) 60 60.7 184 23.2 0.52 (+/- 0.00) 50.2 (+/- 0.1) 60 300.7 189 22.9 0.51 (+/- 0.00) 50.0 (+/- 0.1) 60 300.4 190 22.8 0.53 (+/- 0.00) 51.9 (+/- 0.1) 71 60.6 261 40.2 1.09 (+/- 0.00) 60.7 (+/- 0.2) 70 60.7 260 38.5 1.03 (+/- 0.00) 59.7 (+/- 0.2) 70 60.7 251 37.0 0.99 (+/- 0.00) 59.9 (+/- 0.2) 70 300.6 255 36.2 0.97 (+/- 0.00) 60.0 (+/- 0.2) 70 300.9 256 36.4 0.98 (+/- 0.00) 60.4 (+/- 0.2) 80 61.5 322 61.2 1.81 (+/- 0.00) 66.0 (+/- 0.2) 80 61.1 321 59.0 1.77 (+/- 0.00) 67.0 (+/- 0.2) 80 60.7 341 62.4 1.78 (+/- 0.00) 63.8 (+/- 0.0) 80 60.6 353 61.0 1.78 (+/- 0.00) 65.1 (+/- 0.0) 80 60.8 352 60.7 1.78 (+/- 0.00) 65.5 (+/- 0.0) 70 61.3 264 38.6 1.12 (+/- 0.00) 64.7 (+/- 0.0) 70 61.5 266 37.6 1.12 (+/- 0.00) 66.4 (+/- 0.0) 70 61.1 269 37.4 1.11 (+/- 0.00) 66.5 (+/- 0.0) Continued on next page BIBLIOGRAPHY 125 Table D.2 – continued from previous page Tank Temp. ( C) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) Steady State Thrust (mN) Steady State I sp (s) 70 304.5 282 36.7 1.09 (+/- 0.00) 66.6 (+/- 0.0) 70 602.3 283 36.1 1.09 (+/- 0.00) 67.2 (+/- 0.0) 70 601.3 284 35.6 1.07 (+/- 0.00) 66.8 (+/- 0.0) 60 60.7 193 22.0 0.63 (+/- 0.00) 64.5 (+/- 0.0) 60 60.5 197 21.5 0.62 (+/- 0.00) 64.4 (+/- 0.0) 60 60.3 196 21.2 0.61 (+/- 0.00) 64.1 (+/- 0.0) 60 300.9 207 20.7 0.59 (+/- 0.00) 63.8 (+/- 0.0) 60 600.7 204 20.2 0.58 (+/- 0.00) 63.7 (+/- 0.0) 60 600.6 203 19.9 0.57 (+/- 0.00) 63.5 (+/- 0.0) 60 600.7 203 19.7 0.56 (+/- 0.00) 63.4 (+/- 0.0) 80 60.7 311 66.5 2.10 (+/- 0.06) 70.4 (+/- 2.0) 80 61.0 309 63.6 2.01 (+/- 0.06) 70.8 (+/- 2.0) 80 60.9 309 62.4 1.98 (+/- 0.05) 70.9 (+/- 2.0) 70 61.1 238 37.7 1.20 (+/- 0.03) 71.2 (+/- 2.0) 70 61.2 237 36.8 1.17 (+/- 0.03) 71.0 (+/- 2.0) 70 61.1 237 36.5 1.16 (+/- 0.03) 71.1 (+/- 2.0) 70 300.8 240 34.9 1.10 (+/- 0.03) 70.6 (+/- 2.0) 70 301.1 235 31.6 0.99 (+/- 0.03) 69.8 (+/- 1.9) Continued on next page BIBLIOGRAPHY 126 Table D.2 – continued from previous page Tank Temp. ( C) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) Steady State Thrust (mN) Steady State I sp (s) 70 600.9 238 32.7 1.02 (+/- 0.03) 69.9 (+/- 1.9) 70 600.7 233 30.2 0.94 (+/- 0.03) 69.2 (+/- 1.9) D.2 Vespel R Spacer Variant Table D.3: H 2 O 2 Propellant: Spacer Variant, SSCD Nozzle Test Steady State Values Tank Temp. ( C) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) Steady State Thrust (mN) Steady State I sp (s) 60 60.6 245 26.3 1.22 (+/- 0.02) 70.7 (+/- 1.4) 60 60.6 263 26.0 1.20 (+/- 0.02) 70.6 (+/- 1.4) 60 60.5 263 25.5 1.18 (+/- 0.02) 70.9 (+/- 1.4) 60 300.5 271 24.7 1.15 (+/- 0.02) 71.4 (+/- 1.4) 60 300.5 269 24.2 1.15 (+/- 0.02) 72.8 (+/- 1.5) 60 600.5 268 23.3 1.13 (+/- 0.02) 73.9 (+/- 1.5) 70 60.5 337 45.6 2.23 (+/- 0.05) 74.7 (+/- 1.5) 71 60.4 337 45.7 2.19 (+/- 0.04) 73.3 (+/- 1.5) Continued on next page BIBLIOGRAPHY 127 Table D.3 – continued from previous page Tank Temp. ( C) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) Steady State Thrust (mN) Steady State I sp (s) 70 60.4 337 44.3 2.11 (+/- 0.04) 72.7 (+/- 1.5) 70 300.5 336 41.6 1.99 (+/- 0.04) 72.9 (+/- 1.5) 70 300.5 334 40.8 1.95 (+/- 0.04) 73.1 (+/- 1.5) 70 600.5 335 40.5 1.93 (+/- 0.04) 72.9 (+/- 1.5) 80 60.5 351 74.7 3.59 (+/- 0.07) 73.4 (+/- 1.5) 80 60.4 397 73.2 3.51 (+/- 0.07) 73.3 (+/- 1.5) 80 60.4 397 71.0 3.40 (+/- 0.07) 73.1 (+/- 1.5) 80 300.5 397 68.1 3.25 (+/- 0.07) 72.9 (+/- 1.5) 80 300.5 395 66.5 3.02 (+/- 0.06) 69.4 (+/- 1.4) 80 405.2 388 62.9 2.84 (+/- 0.06) 68.9 (+/- 1.4) Table D.4: H 2 O Propellant: Spacer Variant, SSCD Nozzle Test Steady State Values Tank Temp. ( C) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) Steady State Thrust (mN) Steady State I sp (s) 30 60.5 30 29.7 1.28 (+/- 0.04) 47.5 (+/- 1.6) 30 60.5 30 29.1 1.27 (+/- 0.04) 48.2 (+/- 1.6) Continued on next page BIBLIOGRAPHY 128 Table D.4 – continued from previous page Tank Temp. ( C) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) Steady State Thrust (mN) Steady State I sp (s) 31 60.4 30 30.9 1.35 (+/- 0.05) 48.2 (+/- 1.6) 30 300.6 30 29.2 1.29 (+/- 0.04) 48.7 (+/- 1.6) 30 600.5 30 29.2 1.33 (+/- 0.04) 50.3 (+/- 1.7) 40 60.5 40 55.8 2.53 (+/- 0.08) 49.9 (+/- 1.7) 39 60.5 40 53.3 2.44 (+/- 0.08) 50.4 (+/- 1.7) 41 60.7 40 55.7 2.54 (+/- 0.09) 50.3 (+/- 1.7) 40 300.8 39 52.9 2.40 (+/- 0.08) 50.0 (+/- 1.7) 40 600.5 40 52.0 2.35 (+/- 0.08) 49.9 (+/- 1.7) 49 60.5 50 90.2 4.24 (+/- 0.14) 51.8 (+/- 1.7) 50 60.5 49 92.7 4.48 (+/- 0.15) 53.3 (+/- 1.8) 50 60.5 50 92.3 4.33 (+/- 0.14) 51.8 (+/- 1.7) 48 300.6 50 82.7 3.84 (+/- 0.13) 51.2 (+/- 1.7) 48 600.6 50 80.9 3.72 (+/- 0.12) 50.7 (+/- 1.7) 57 60.5 59 138.3 7.03 (+/- 0.24) 56.0 (+/- 1.9) 57 44.2 59 135.1 6.44 (+/- 0.22) 52.6 (+/- 1.8) BIBLIOGRAPHY 129 Table D.5: H 2 O 2 Propellant: Spacer Variant, SSCO Nozzle Test Steady State Values Tank Temp. ( C) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) Steady State Thrust (mN) Steady State I sp (s) 60 60.5 231 26.3 1.01 (+/- 0.04) 66.7 (+/- 2.6) 60 61.3 232 26.6 1.03 (+/- 0.04) 67.5 (+/- 2.6) 60 61.3 227 25.8 1.00 (+/- 0.04) 67.4 (+/- 2.6) 60 301.1 233 25.5 1.01 (+/- 0.04) 68.8 (+/- 2.7) 60 301.0 234 25.4 1.04 (+/- 0.04) 71.1 (+/- 2.8) 60 601.1 236 24.7 1.01 (+/- 0.04) 70.9 (+/- 2.8) 70 61.3 303 43.7 1.76 (+/- 0.07) 70.1 (+/- 2.7) 70 61.2 308 44.2 1.80 (+/- 0.07) 70.9 (+/- 2.8) 70 61.0 306 44.4 1.78 (+/- 0.07) 69.9 (+/- 2.7) 70 301.1 311 43.0 1.75 (+/- 0.07) 71.1 (+/- 2.8) 70 301.2 310 42.0 1.72 (+/- 0.07) 71.2 (+/- 2.8) 70 600.9 314 40.4 1.65 (+/- 0.06) 71.3 (+/- 2.8) 79 61.4 364 66.8 2.65 (+/- 0.10) 69.2 (+/- 2.7) 81 61.0 326 71.1 2.81 (+/- 0.11) 68.9 (+/- 2.7) 80 61.4 370 67.3 2.69 (+/- 0.10) 69.5 (+/- 2.7) 80 60.8 370 69.1 2.71 (+/- 0.11) 68.3 (+/- 2.7) 80 300.9 375 67.3 2.71 (+/- 0.11) 70.2 (+/- 2.7) 80 301.2 311 64.5 2.46 (+/- 0.10) 66.6 (+/- 2.6) Continued on next page BIBLIOGRAPHY 130 Table D.5 – continued from previous page Tank Temp. ( C) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) Steady State Thrust (mN) Steady State I sp (s) 80 507.1 303 62.0 2.37 (+/- 0.09) 66.6 (+/- 2.6) Table D.6: H 2 O Propellant: Spacer Variant, SSCO Nozzle Test Steady State Values Tank Temp. ( C) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) Steady State Thrust (mN) Steady State I sp (s) 30 60.5 30 30.5 0.83 (+/- 0.03) 51.5 (+/- 1.6) 30 60.7 30 30.5 0.84 (+/- 0.03) 52.1 (+/- 1.6) 30 60.5 30 31.6 0.87 (+/- 0.03) 52.2 (+/- 1.6) 30 300.6 30 30.6 0.86 (+/- 0.03) 53.1 (+/- 1.6) 30 600.6 30 30.4 0.87 (+/- 0.03) 54.2 (+/- 1.7) 40 60.7 40 56.5 1.58 (+/- 0.05) 52.7 (+/- 1.6) 40 60.5 39 55.0 1.55 (+/- 0.05) 53.3 (+/- 1.6) 40 60.5 40 57.1 1.61 (+/- 0.05) 53.1 (+/- 1.6) 40 299.8 39 54.9 1.55 (+/- 0.05) 53.3 (+/- 1.7) 40 600.5 39 54.1 1.50 (+/- 0.05) 52.4 (+/- 1.6) 49 60.5 50 92.9 2.54 (+/- 0.08) 51.6 (+/- 1.6) Continued on next page BIBLIOGRAPHY 131 Table D.6 – continued from previous page Tank Temp. ( C) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) Steady State Thrust (mN) Steady State I sp (s) 50 60.6 49 95.1 2.64 (+/- 0.08) 52.4 (+/- 1.6) 50 60.5 49 93.1 2.53 (+/- 0.08) 51.3 (+/- 1.6) 50 300.7 49 90.0 2.49 (+/- 0.08) 52.2 (+/- 1.6) 50 600.6 50 88.9 2.45 (+/- 0.08) 52.0 (+/- 1.6) 58 60.5 59 142.9 3.96 (+/- 0.12) 52.3 (+/- 1.6) 59 60.6 58 143.8 4.07 (+/- 0.13) 53.4 (+/- 1.7) 60 60.6 58 145.4 4.02 (+/- 0.12) 52.2 (+/- 1.6) 58 300.6 59 130.8 3.65 (+/- 0.11) 52.6 (+/- 1.6) 58 600.6 58 132.1 3.73 (+/- 0.12) 53.3 (+/- 1.6) APPENDIX E Prototype 3 Mass Flow Rate Experimental Data To experimentally determine the mass flow rate through the different nozzles with the different propellants, a series of tests at varying temperatures and propellant loads were run from start until all of the propellant was expelled. With those data, a mass flow rate relation for each of the nozzles and propellant pairings was determined. Mass flow rate relations were of the form _ m =a _ m P (E.1) where _ m was the mass flow rate in grams per second,P was the tank pressure in torrs,a _ m was the calculated mass flow rate coefficient in grams torrs per second. Table E.1 provides the mass flow rate coefficient as well as the coefficient of determination, R 2 , for all of the nozzle/propellant pairings. Nozzles are labeled following their identification letter from Table 5.5. The table also provides the reference to the data figures and tables. Table E.1: H 2 O 2 Propellant: O-ring Variant, MCD Nozzle Mass Flow Rate Test Series Nozzle Id. Propellant a _ m (g Torr/s) R 2 Figure Table A H 2 O 2 6.39 10 -5 0.981 5.20 E.2 B H 2 O 2 4.56 10 -5 0.966 E.1 E.3 C H 2 O 2 6.68 10 -5 0.979 E.2 E.4 C H 2 O 9.25 10 -5 0.986 E.3 E.5 D H 2 O 2 5.85 10 -5 0.986 E.4 E.6 E H 2 O 5.40 10 -5 0.984 E.5 E.7 E.1 Kalrez R O-ring Variant 132 BIBLIOGRAPHY 133 Figure E.1: H 2 O 2 Propellant: O-ring Variant, SSCD nozzle mass flow rate calculated from known propellant load and test run length. Table E.2: H 2 O 2 Propellant: O-ring Variant, MCD Nozzle Mass Flow Rate Test Series Tank Temp. ( C) Prop. Load (ml) Run Time (s) Max Cat. Temp. ( C) Avg. Tank Press. (Torr) Avg. Cat. Chamber Press. (Torr) 60 1.0 1156.7 212 18.8 16.2 60 1.5 1719.2 215 18.4 16.1 60 0.8 1037.5 217 18.9 16.1 70 0.8 602.2 293 31.5 27.6 70 1.5 1013.4 296 31.0 27.9 79 1.5 559.3 398 52.7 49.8 80 2.6 1055.8 405 53.3 50.0 79 0.8 318.5 415 53.8 50.4 70 2.6 1639.3 336 33.3 30.8 60 2.6 2846.8 242 18.9 17.0 70 2.6 1762.0 315 30.7 28.2 70 1.5 956.6 320 30.6 28.5 80 5.2 2355.4 388 48.3 44.8 60 1.5 1597.8 245 18.6 17.0 BIBLIOGRAPHY 134 Table E.3: H 2 O 2 Propellant: O-ring Variant, SSCD Nozzle Mass Flow Rate Test Series Tank Temp. ( C) Prop. Load (ml) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) 80 1.5 812.7 349 52.1 70 1.5 1271.5 226 32.5 60 1.5 2020.2 170 18.8 80 2.6 1560.5 296 50.2 70 2.6 2402.7 229 32.3 80 0.8 461.8 285 52.5 60 0.8 1334.9 171 18.5 70 1.5 1305.7 226 31.1 60 0.8 1345.1 201 18.6 70 2.6 2414.8 269 31.6 80 0.8 480.9 314 53.7 BIBLIOGRAPHY 135 E.2 Vespel R Spacer Variant Figure E.2: H 2 O 2 spacer SSCD nozzle mass flow rate calculated from known propellant load and test run length. Figure E.3: H 2 O spacer SSCD nozzle mass flow rate calculated from known propellant load and test run length. BIBLIOGRAPHY 136 Figure E.4: H 2 O 2 spacer SSCO nozzle mass flow rate calculated from known propellant load and test run length. Figure E.5: H 2 O spacer SSCO nozzle mass flow rate calculated from known propellant load and test run length. BIBLIOGRAPHY 137 Table E.4: H 2 O 2 Propellant: O-ring Variant, SSCD Nozzle Mass Flow Rate Test Series Tank Temp. ( C) Prop. Load (ml) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) 60 1.5 1151.6 222 25.7 70 1.5 714.9 289 41.4 70 0.8 398.6 293 44.6 60 0.8 660.1 222 25.4 80 1.5 405.5 308 69.7 80 0.8 232.4 301 72.0 70 2.6 1258.4 259 42.3 Table E.5: H 2 O Propellant: O-ring Variant, SSCD Nozzle Mass Flow Rate Test Series Tank Temp. ( C) Prop. Load (ml) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) 40 1.5 303.8 38 50.8 30 1.5 518.2 29 29.9 30 0.8 305.3 29 29.7 40 0.8 173.8 38 51.7 48 1.5 193.2 47 77.2 48 2.6 355.9 47 76.9 30 1.5 505.6 29 30.1 Table E.6: H 2 O 2 Propellant: O-ring Variant, SSCO Nozzle Mass Flow Rate Test Series Tank Temp. ( C) Prop. Load (ml) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) 80 0.8 268.9 352 67.3 70 0.8 528.2 281 37.6 60 0.8 864.5 223 22.5 70 1.5 867.0 291 37.9 60 1.5 1469.5 226 22.2 80 2.6 1043.0 313 60.6 80 1.5 540.3 350 62.0 BIBLIOGRAPHY 138 Table E.7: H 2 O Propellant: O-ring Variant, SSCO Nozzle Mass Flow Rate Test Series Tank Temp. ( C) Prop. Load (ml) Run Time (s) Max Catalyst Temp. ( C) Avg. Tank Press. (Torr) 58 0.8 117.0 57 132.2 57 1.5 196.4 57 131.1 40 1.5 456.8 39 54.5 30 0.8 500.5 30 31.2 30 1.5 815.8 30 31.5 40 0.8 287.9 39 55.7 40 2.6 855.9 39 55.5 APPENDIX F Prototype 3 Thrust Measurement Mass Flow Rate Correction Mass flow rates relations for all of the nozzles and propellant combinations were determined by a separate series of experiments, as was detailed in Section 5.2.3.1; data provided in Appendix E. Using this mass flow rate relation with the measured tank pressures and run times from the thrust measurement experiments, the overall propellant load can be calculated. For the o-ring MCD experiments, this calculated value was within 1% of the actual loaded value. For all of the SS nozzles (excluding the o-ring SSCD - total run time was not captured for that nozzle), the error between the calculated and actual propellant load values were larger, up to 10% (calculated and loaded values provided in Table F.1). This discrepancy was accounted for by modifying the thrust measurement mass flow values by the ratio of actual propellant load to calculated propellant load. The mass flow experiments were performed in a small vacuum chamber with a higher am- bient pressure when compared to the chamber used in the thrust measurement experiments. Dif- ferences in radiative and convective heat losses as well as boundary layer conditions could have contributed to the differences in mass flow. Specifically for the H 2 O 2 tests, the maximum cata- lyst temperatures in the smaller chamber were lower than the catalyst temperatures taken for the same nozzle and tank temperature in the larger chamber. Viscosity increases with temperature and therefore the boundary layer would be larger in the thrust measurement experiments, potentially decreasing the effective nozzle area. Table F.1: Loaded vs. Calculated Propellant Volume Nozzle Id. Mounting Config. Nozzle Type Prop. Loaded Prop. (ml) Calculated Prop. (ml) A O-ring MCD H 2 O 2 10.4 10.5 B O-ring SSCD H 2 O 2 10.4 Unknown C Spacer SSCD H 2 O 2 7.6 8.4 C Spacer SSCD H 2 O 17.5 18.1 D Spacer SSCO H 2 O 2 7.2 7.8 E Spacer SSCO H 2 O 17.5 18.4 139 APPENDIX G Isentropic Nozzle Relations Isentropic, inviscid, one-dimensional relations from Sutton and Biblarz [11] were used to balance mass flow rate and pressure rise in the theoretical evaluation of thermal transpiration in a thruster application. The characteristic velocity (c ? ) can be determined with the chamber temperature and the product gas ratio of specific heats: c ? = s RT c + 1 2 +1 2( 1) (G.1) whereT c is the combustion chamber temperature, is the specific heat ratio of the exhaust gases andR is their gas constant (which is a function of the molecular weight). Assuming frozen flow, the throat temperature (T t ), pressure (P t ), density ( t ), and velocity (u t ) are given by the following equations: T t =T c 2 + 1 (G.2) P t =P c 2 + 1 1 (G.3) t = P t RT t (G.4) u t = p RT t (G.5) whereP c is the chamber pressure. Mach number (M e ), temperature (T e ), and density ( e ) at the nozzle exit can be determined by the following equations: M e = v u u t 2 1 " P c P e 1 1 # (G.6) T e = T c 1 + 1 2 M 2 e (G.7) 140 BIBLIOGRAPHY 141 e = P e RT e (G.8) whereP e is the exhaust pressure. Using isentropic nozzle relations, the exit/throat area ratio ( Ae At ) and thrust coefficient (C F ) can be calculated. A e A t = 1 M e 2 + 1 1 + 1 2 M 2 e +1 2( 1) (G.9) C F = v u u t 2 + 1 +1 1 2 1 " 1 p e p c 1 # + p e p a p c A e A t (G.10) whereP a is ambient pressure. Mass flow rate ( _ m), exit velocity (u e ), and throat area (A t ) can be computed with the follow- ing equations: _ m = P c A t c ? (G.11) u e =C F c ? (G.12) A t = F C F P c (G.13) Finally thrust and specific impulse can be calculated. F T = _ mu e + (P e P a )A e (G.14) I sp = F T _ mg (G.15) whereg is the gravitational constant.

Abstract (if available)

Abstract Propulsion is a critical capability for artificial satellites, allowing for constellation management, extended mission durations, and orbit reconfiguration. However due to volume and power constraints as well as safety requirements, only a limited number of CubeSats have launched with on-board propulsion systems. With the recent trend towards smaller satellites but more plentiful constellations, new propulsion concepts need to be developed and executed to enable these smaller platforms to perform more broad missions. ❧ This body of work details the development of the first vacuum-evaporated monopropellant propulsion system. The iterative design and optimization process is documented for three working prototypes, all specifically designed to meet small satellite volume and power limitations. Hydrogen peroxide (H₂O₂) was chosen as the monopropellant of study and its vapor properties and decomposition reaction was examined extensively to understand the behavior within the thruster body and specifically the catalyst chamber. ❧ Theoretical studies showed the H₂O₂ vapor thruster concept had the potential to provide the highest vacuum specific impulse of any H₂O₂ system (>200 s), while retaining the advantages of small size and simple construction typical of liquid monopropellant systems. For a nominally-sized thruster, the theoretical thrust could be varied from 0.5 to 8 mN simply by changing the temperature of the tank in which the liquid H₂O₂ is stored. The first prototype found that when vapor was allowed to flow over the catalyst its temperature increases slowly at first then rapidly when the vapor H₂O₂ mole fraction exceeded approximately 0.5 and a catalyst temperature of about 130℃ was reached. An analysis of the equilibrium state on the catalyst indicated that this temperature corresponded to the condition where the surface coverage shifts from predominantly H₂O to a significant fraction of open platinum sites where H₂O₂ could adsorb and react. ❧ To better understand the behavior of the H₂O₂ vapor within the propulsion system, an H₂O₂ vapor concentration diagnostic was developed using near-infrared laser absorption. The spectral features of low pressure H₂O₂ vapor were examined near the Doppler-broadened limit. An advantageous portion of the spectra near 1420 nm containing several distinct H₂O₂ peaks and one well-known water (H₂O) peak (for calibration) was identified and the cross-sections of these peaks determined. Specifically the peak at 1420.06 nm was recommended as the most advantageous single line for determining H₂O₂ concentration due to its high strength and distance from interfering absorbers. ❧ The cross section values were then employed to measure vapor-phase concentrations of H₂O₂ upstream and downstream of several known catalyst materials, specifically silver mesh, platinum mesh, and platinum on alumina spheres. Using those data, the global reaction rates were determined as a function of catalyst surface area, residence time, and temperatures from ambient to 120℃. The kinetics, approximated as a gas-phase reaction, were found to be first order. Silver mesh showcased the highest reaction rate, with a rate constant of 10.7 s⁻¹ and an average destruction of 76%. ❧ The same catalyst materials were also investigated in the second thruster prototype. Silver mesh led to the highest catalyst temperatures (>236℃), specifically when 3 - 7 sheets were compacted into the chamber. Sheet numbers outside this range resulted in lower temperatures. Heat transfer proved to be the primary concern in the system, with substantial effects on catalyst temperature and overall system performance. Finite element modeling was used to identify heat paths in the design and make improvements to decrease catalyst chamber heat loss. ❧ Thrust measurements were conducted for the third and final prototype design, which featured the lowest pressure drop and most compatible valve and sensor package (when compared to the prior prototypes). Depending on the thruster design and tank temperature, thrust varied from 0.5 mN to 2.5 mN and specific impulse varied from 55 s to 80 s. Comparison of experimental results to theory revealed substantial thrust losses, most likely due to a large subsonic boundary layer that forms at low Reynolds numbers. Comparisons of the H₂O₂ vapor system to a steam variant using the same thruster body and nozzle, revealed a 60% better performance by the H₂O₂ vapor. Improvements in catalyst temperature and nozzle design were suggested to further increase that performance differential. ❧ Lastly, the potential integration of a thermal transpiration pump into the catalyst chamber was explored. The third H₂O₂ vapor thruster prototype was modified slightly to allow for pressure measurement directly upstream and downstream of the catalyst chamber. A microfiber membrane, pore diameter < 1 μm, was added to the chamber ahead of the catalyst. A combination of theoretical and experimental studies show a potential 30 - 60% increase in thrust and mass flow rate by incorporating the thermal transpiration pump.

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University of Southern California Dissertations and Theses

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Creator Rhodes, Brandie LeNae (author)

Core Title Hydrogen peroxide vapor for small satellite propulsion

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Astronautical Engineering

Publication Date 06/28/2021

Defense Date 05/24/2019

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag absorption spectroscopy,catalyst, silver catalyst,COMSOL,CubeSat,finite element analysis,finite element model,flight unit,green propellant,heat transfer,hydrogen peroxide,laser diagnostic,millinewton,monopropellant,nozzle,OAI-PMH Harvest,patent,platinum catalyst,propulsion,prototype,reaction kinetics,satellite,thermal transpiration,thrust measurement,vacuum evaporation,water thruster

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Language English

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Advisor Ronney, Paul (committee chair), Erwin, Dan (committee member), Reisman, Garrett (committee member)

Creator Email brandie.l.rhodes@gmail.com,brandrhodes@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-178881

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Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

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