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A Study on Hall Effect Thruster Exhaust Plume Simulation

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A Study on Hall Effect Thruster Exhaust Plume Simulation DEGREE PROJECT IN ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2019 A study on Hall Effect Thruster exhaust plume simulation ANDRIUS ŠUKYS KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE ROYAL INSTITUTE OF TECHNOLOGY EF233X DEGREE PROJECT IN SPACE TECHNOLOGY A study on Hall Effect Thruster exhaust plume simulation Author: Supervisors: Andrius ŠUKYS Nickolay IVCHENKO Dejan PETKOW Examiner: Tomas KARLSSON A thesis submitted in fulfillment of the requirements for the degree of master’s in aerospace engineering in the Department of Space and Plasma Physics School of Electrical Engineering and Computer Science December, 2019 Contents List of FiguresIV List of TablesV NomenclatureVI Abstract XIV Abstrakt/SammanfattningXV Acknowledgement XVI Author’s contribution XVII 1 Introduction1 1.1 Hall Effect Thruster......................1 1.1.1 Working principle..................2 1.2 Motivation...........................3 1.3 Objective............................4 1.4 Limitations...........................4 1.5 Outline.............................4 2 Theoretical Background5 2.1 Tsiolkovsky equation.....................5 2.2 Plasma Characteristics....................7 2.2.1 Debye length.....................7 2.2.2 Larmor radius.....................8 2.2.3 Magnetization.....................9 2.2.4 Gyro frequency.................... 11 2.2.5 Plasma frequency................... 11 I CONTENTS 2.3 Field equations........................ 12 2.3.1 Maxwell‘s equations................. 12 2.4 Dilute gas assumption.................... 13 2.4.1 Mean free path perspective............. 14 2.5 Particle-particle interactions................. 14 2.5.1 Elastic collisions................... 14 2.5.2 Inelastic collisions.................. 16 2.6 Particle-surface interactions................. 18 2.6.1 Neutralization..................... 18 2.6.2 Reflection/Scattering................. 19 2.6.3 Secondary electron emission............ 19 2.6.4 Sputtering....................... 19 3 Electric Propulsion 22 3.1 Types.............................. 22 3.1.1 Electrothermal thrusters............... 23 3.1.2 Electromagnetic thrusters.............. 23 3.1.3 Electrostatic thrusters................ 24 3.2 Spacecraft-plume interaction................ 25 3.2.1 Physical interactions................. 25 3.2.2 Mechanical interactions............... 26 4 Hall Effect Thruster (HET) 27 4.1 Types.............................. 27 4.1.1 Stationary Plasma Thruster (SPT).......... 27 4.1.2 Thruster with Anode Layer (TAL)......... 29 4.1.3 External discharge Hall thruster (XPT)....... 30 4.1.4 Magnetically Shielded................ 31 4.1.5 Cylindrical Hall Thruster.............. 32 4.2 Thruster Performance..................... 34 4.2.1 Anode efficiency................... 35 4.3 Thruster lifetime........................ 35 4.3.1 Erosion rate...................... 35 4.4 Neutralizer........................... 36 4.4.1 Working principle.................. 36 4.4.2 Neutralizer cathode KN-3B............. 38 4.5 SPT-100B............................ 38 5 Set-Up, Simulation and Results 41 5.1 VSTRAP............................ 41 II CONTENTS 5.1.1 Boundary Element Method............. 42 5.1.2 Fast Multipole Method................ 42 5.1.3 Direct Simulation Monte Carlo........... 42 5.1.4 Fokker Planck..................... 43 5.1.5 Particle Pusher.................... 43 5.1.6 Particle Wall Interaction............... 45 5.2 Inflow Conditions....................... 46 5.2.1 Exit Inflow....................... 46 5.2.2 Cathode Inflow.................... 50 5.3 Potential Simulation..................... 51 5.3.1 Geometry....................... 51 5.3.2 Boundary Conditions................ 53 5.3.3 Results......................... 55 5.4 DSMC Simulation....................... 57 5.4.1 Geometry....................... 57 5.4.2 Simulation parameters................ 58 5.4.3 Simulation....................... 59 5.4.4 DSMC Validation................... 60 5.5 Plasma Simulation...................... 64 5.5.1 Far field versus Near field.............. 64 5.5.2 Boundary Conditions................ 64 5.5.3 Inflow and simulation parameters......... 65 5.5.4 Simulation time.................... 66 6 Discussion 68 6.1 Outlook............................. 69 6.1.1 Simulation....................... 69 6.1.2 Hardware....................... 70 6.1.3 Software........................ 70 7 Conclusion 72 Bibliography 74 III List of Figures 1.1 Hall Effect thruster operating on Xenon [1].........2 2.1 Sketch for Tsiolkovsky equation derivation (adapted from [2])................................6 2.2 Positively charged particle moving in a uniform vertical magnetic field [3]........................9 4.1 Schematic of SPT [3]...................... 29 4.2 Schematic of TAL [3]...................... 30 4.3 External discharge thruster [4]................ 31 4.4 Magnetically shielded HET thruster [5]........... 32 4.5 CHT with cusp magnetic field design [6].......... 33 4.6 HETs with cusp magnetic field design............ 33 4.7 Nested channel Hall Thruster X3 [7]............. 34 4.8 Hollow cathode geometry [3]................. 36 4.9 SPT-100B thruster........................ 39 5.1 Illustration of specular scattering............... 45 5.2 Simulation domain...................... 53 5.3 Boundary conditions..................... 54 5.4 Potential distribution inside the channel.......... 55 5.5 Potential distribution inside the domain........... 56 5.6 Comparison of potentials with [8].............. 56 5.7 Simulation Domain...................... 57 5.8 Particle number evolution towards the steady-state... 60 5.9 Mean particle collision per iteration............ 61 5.10 Direct plots at steady-state.................. 62 5.11 Derived plots at steady-state................. 63 5.12 BCs for plasma simulation.................. 65 IV List of Tables 2.1 Fitting parameters for CEX cross sections [9]........ 17 2.2 Fitting parameters for secondary electron yield data [3].. 20 2.3 Material model fitting coefficients for sputtering yield [10]. 21 3.1 Comparison of electric thrusters............... 25 4.1 Cathode neutralizer KN-3 parameters............ 38 4.2 HET SPT-100B operational properties............ 40 4.3 Dimmensions of SPT-100B................... 40 5.1 Inflow conditions....................... 51 5.2 Boundary Conditions..................... 54 5.3 Boundary Conditions..................... 65 5.4 Hardware estimations.................... 67 V Nomenclature Note: All quantities and equations are in SI units, unless stated other- wise Physical Constants −12 −1 0 Vacuum permittivity 8;854 · 10 F m −7 −1 µ0 Vacuum permeability 4π · 10 H m −1 c0 Speed of light 299 792 458 m s e Elementary charge 1;602 · 10−19 C g Gravitational Constant 6;673 · 10−11 N m2 kg−2 h Plank Constant 6;626 · 10−34 J s −23 2 −2 −1 kB Boltzmann constant 1;381 · 10 m kg s K −31 me Electron mass 9;109 · 10 kg −25 mi Xenon ion mass 2;180 · 10 kg 23 −1 NA Avogadro number 6;022 · 10 mol VI NOMENCLATURE Acronyms and Abbreviations AFRL Air Force Research Laboratory AR Aerojet Rocketdyne BC Boundary Condition BEM Boundary Element Method CEX Charge-Exchange CHT Cylindrical Hall Thruster CPU Central Processing Unit CP Chemical Propulsion CSP Cross Section Pre-processor DSMC Direct Simulation Monte Carlo EDB Experimental Design Bureau EMI Electromagnetic Interference EP Electric Propulsion FMM Fast Multipole Method FP Fokker Planck GPU Graphics Processing Unit GRC Glenn Research Center HET Hall Effect Thruster JPL Jet Propulsion Laboratory LeRC Lewis Research Center MEX Momentum-Exchange MPDT Magnetoplasmadynamic Thruster MS Magnetic Shielding NASA The National Aeronautics and Space Administra- tion NHT Nested channel Hall Thruster PPT Pulsed Plasma Thruster PP Particle Pusher VII NOMENCLATURE PWI Particle Wall Interaction SEE Secondary Electron Emission SPT Stationary Plasma Thruster STEX Space Technology Experiment TAL Thruster with Anode Layer UM University of Michigan VSTRAP Versatile Software Tool for Rarefied Plasmas WRT With Respect To XHT External discharge Hall Thruster VIII NOMENCLATURE Variables χ Angle of electron deflection ∆F Force increment ∆mP Change of propellant ∆pp Change of particle momentum ∆v Change of velocity or velocity increment δ Mean distance between particles δMe Electron magnetization parameter δMi Ion magnetization parameter δM Magnetization parameter ∆W Work function m_ a Anode mass flow m_ c Cathode mass flow m_ P Propellant mass flow m_ Xe+ Xenon single charged ion mass flow from anode m_ Xe2+ Xenon double charged ion mass flow from anode m_ Xea Xenon neutral gas mass flow from anode m_ Xec Xenon neutral gas mass flow from cathode _ Np Particle flow in particles per second _ Ne Electron particle flow from anode _ NXe+ Xenon single charged ion particle flow from anode _ NXe2+ Xenon double charged ion particle flow from anode _ NXea Xenon neutral gas particle flow from anode _ NXec Xenon neutral gas particle flow from cathode η+ Fraction of singly charged ions η2+ Fraction of doubly charged ions ηa Anode efficiency ηT Total thruster efficiency IX NOMENCLATURE Γ(x) Gamma function κ Angle of collision λDe Debye length r Short-hand notation for a differentiation called Nabla, del or gradient σCEX CEX collision cross-section B Magnetic field vector j plasma current density in vector form v Velocity vector A Richardson coefficient a; b Fitting coefficients for CEX or secondary electron yield Aco Area of the cathode orifice Aex Area of the thruster exit Ako Area of the keeper orifice a(t) Acceleration function b0, b1, b2, b3 and k Material
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