THE RAREFIED GAS ELECTRO JET (RGEJ) MICRO-THRUSTER FOR PROPULSION OF SMALL SATELLITES By ARIEL BLANCO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2017 © 2017 Ariel Blanco To my family, friends, and mentors ACKNOWLEDGMENTS I thank my parents and maternal grandmother for their continuous support and encouragement, for teaching me to persevere and value the pursuit of knowledge. I am extremely thankful to my friends and lab colleagues who have helped me so much, not only academically but also by giving me moral support and solidarity. Finally, yet importantly, it is a genuine pleasure to express my deep sense of thanks and gratitude to all my mentors, especially my advisor, Dr. Subrata Roy. Without his guidance, mentoring, and support, this study would not have been completed. 4 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................. 4 LIST OF TABLES ............................................................................................................ 8 LIST OF FIGURES ........................................................................................................ 10 ABSTRACT ................................................................................................................... 12 CHAPTER 1 INTRODUCTION .................................................................................................... 14 The Rarefied Gas Electro Jet (RGEJ) Design and Motivation ................................ 18 Performance Parameters ........................................................................................ 25 2 MICROPROPULSION TECHNOLOGIES ............................................................... 29 Introduction to Micro-propulsion Devices ................................................................ 29 Chemical Propulsion Devices for Small Satellites ................................................... 29 Cold Gas Thrusters .......................................................................................... 30 Mono Propellant Thrusters ............................................................................... 31 Bipropellant Thrusters ...................................................................................... 33 Electric Propulsion Devices for Small Satellites ...................................................... 34 Electrothermal Thrusters .................................................................................. 34 Free molecule micro-resistojet (FMMR) ...................................................... 35 Low-power DC arcjets ................................................................................. 37 Microcavity discharge thrusters ................................................................... 38 Micro-plasma thruster (MPT) ...................................................................... 39 Electrostatic Thrusters ...................................................................................... 40 Miniature ion engines .................................................................................. 41 Miniature hall thrusters ................................................................................ 43 Colloidal and field emission electric propulsion (FEEP) thrusters ............... 46 Electromagnetic Thrusters ................................................................................ 49 Conclusion of Micro-propulsion Technologies Survey ............................................ 50 3 GAS DISCHARGE PHYSICS ................................................................................. 52 Electrical Breakdown of Gases ............................................................................... 53 Dark Discharge ................................................................................................. 54 Glow Discharge ................................................................................................ 56 Arc Discharge ................................................................................................... 57 Qualitative Characteristics of DC Glow Discharge .................................................. 57 Paschen’s law ......................................................................................................... 62 5 Sputtering ............................................................................................................... 64 4 GOVERNING EQUATIONS .................................................................................... 66 Hydrodynamic Plasma Model ................................................................................. 66 Boltzmann Equation ......................................................................................... 66 Distribution Function Moments Equation .......................................................... 68 Continuity Equation .......................................................................................... 70 Momentum Equation ........................................................................................ 72 Energy Equation ............................................................................................... 74 Drift-Diffusion Approximation ............................................................................ 76 Maxwell’s Equations ......................................................................................... 81 Transport Properties ......................................................................................... 84 Boundary Conditions ........................................................................................ 87 Open surface boundary ............................................................................... 88 Anode boundary .......................................................................................... 89 Cathode boundary ...................................................................................... 90 Dielectric wall .............................................................................................. 90 Plasma Electrostatic Force and Electrothermal Heating Source ...................... 91 Rarefied Gas Equations .......................................................................................... 92 Heat Transfer Governing Equations ....................................................................... 97 Thermal Radiation Heat Transfer ..................................................................... 97 View Factor Formulas ...................................................................................... 98 Conduction Heat Transfer .............................................................................. 100 Conduction Heat Transfer Boundary Conditions ............................................ 101 5 NUMERICAL MODEL ........................................................................................... 102 The Ionized Gas Module ....................................................................................... 103 The Rarefied Gas Module ..................................................................................... 107 Galerkin Weak Statement ............................................................................... 108 Finite Element Basis Function ........................................................................ 110 Bilinear Basis .................................................................................................. 112 Newton-Raphson Scheme.............................................................................. 115 Decoupled Heat Transfer Codes .......................................................................... 117 Conduction Numerical Code ........................................................................... 117 Thermal Radiation Heat Transfer Numerical Code ......................................... 117 6 BENCHMARKING AND VALIDATION .................................................................. 119 Ionized Gas Module (IGM) .................................................................................... 119 Verification and Grid Convergence Study of the IGM ..................................... 119 Validation of the IGM ...................................................................................... 122 Rarefied Gas Module (RGM) ................................................................................ 125 Verification of the RGM using plane Poiseuille flow ....................................... 125 Benchmarking/Validation of the RGM ............................................................ 129 6 7 CASES STUDIED ................................................................................................. 132 Geometry and Grid ............................................................................................... 132 Cold gas thruster and constant thermal heating source thrusters’ results and comparison ........................................................................................................ 134 RGEJ thruster performance .................................................................................. 145 RGEJ thruster discharge characteristics ............................................................... 156 Thermal analysis ................................................................................................... 159 8 SUMMARY ..........................................................................................................