Rarefied Gas Flows and Dynamic Plasma Phenomena in Electric Propulsion Systems

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• Publisher: Cuvillier Verlag
• Year: 2021
• Print ISBN: 9783736973244
• eBook ISBN: 9783736963245
• Edition: 1

Zu den aktuellen Entwicklungen in der Raumfahrtindustrie zählen das stetig wachsende Interesse an miniaturisierten Satelliten sowie der immer häufigere Einsatz elektrischer Antriebssysteme zu allgemeinen Lage- und Bahnregelungszwecken. Die Entwicklung miniaturisierter Satelliten erfordert ihrerseits den Einsatz von Antriebssystemen, die sehr kleine und präzise zu steuernde Schubkräfte erzeugen. Vor diesem Hintergrund stellen elektrische Triebwerke eine attraktive Option dar, die Antriebsanforderungen von Satelliten sowohl in herkömmlichen als auch in miniaturisierten Größen langfristig zu erfüllen. Bei miniaturisierten Satelliten sind die Schubanforderungen oft mit niedrigen Treibstoff-Massenstromwerten und verhältnismäßig kleinen geometrischen charakteristischen Längen verbunden. Dies kann zu verdünnten Gaszuständen innerhalb der Triebwerksdüsen führen. Wegen der hohen Komplexität der Plasmaphänomene innerhalb elektrischer Triebwerke sowie der typischerweise hohen Rechenanforderungen, die mit der Plasmamodellierung einhergehen, werden elektrische Antriebssysteme oft auf Basis empirischer Modelle und experimenteller Daten entwickelt. Der Fokus der vorliegenden Arbeit liegt auf den oben beschriebenen Herausforderungen und den dazugehörigen Forschungsfeldern: der Untersuchung verdünnter Gaszustände in transsonischen Strömungen sowie der Entwicklung numerischer Modellierungsansätze zur Beschreibung des Plasmaverhaltens innerhalb elektrischer Antriebssysteme.New trends regarding fundamental design approaches of orbital spacecraft have been developing in the space industry in recent years. They include an increased interest in miniaturized satellites as well as a general rise in the use of electric propulsion systems for orbit and attitude control. The successful implementation of miniaturized satellites requires the use of propulsion devices able to provide small and precise thrust and impulse levels. One technical solution able to meet the requirements of both standard-sized as well as miniaturized spacecraft involves the use of highly efficient and precise electric propulsion systems. In the particular case of miniaturized satellites, the propulsion requirements are often associated with low propellant mass flow rates and small characteristic geometrical lengths, potentially leading to the appearance of rarefied conditions inside the nozzles of the propulsion devices. Because of the high complexity of the plasma phenomena taking place inside such systems and the usually very high computational requirements associated with their numerical modelling, electric propulsion systems for space applications are usually designed based on empirical models and experimental data. The present work focuses on two key aspects outlined above: rarefied gas conditions in transonic micronozzle flows as well as the numerical modelling of plasma phenomena inside electric propulsion systems.

Table of contents

• Chapter 1 Introduction
• 1.1 Motivation
• 1.2 Basic setup
• 1.3 Goals and thesis outline
• Chapter 2 Theoretical Principles
• 2.1 Knudsen number and flow regimes
• 2.2 Lagrangian and Eulerian specification of the flowfield
• 2.3 Conservation of mass
• 2.4 Conservation of momentum
• 2.5 Conservation of energy
• 2.6 Ideal gas
• 2.7 The Laval nozzle
• 2.8 Fundamentals of plasma
• 2.8.1 Physical properties of plasma
• 2.9 Kinetic theory of gases
• 2.9.1 Fundamental concepts
• 2.9.2 Velocity distribution function and macroscopic properties
• 2.9.3 Maxwell distribution
• 2.9.4 Boltzmann equation
• 2.10 Summary
• Chapter 3 Computational Methods
• 3.1 Methods based on transport equations
• 3.1.1 Finite Difference Method
• 3.1.2 Finite Volume Method
• 3.1.3 Methods for unsteady problems
• 3.1.4 Solution algorithms for the Navier-Stokes equations
• 3.2 Direct Simulation Monte Carlo (DSMC)
• 3.2.1 Molecular transport
• 3.2.2 Molecular collisions
• 3.2.3 Implementation of boundary conditions
• 3.2.4 Macroscopic properties
• 3.3 Particle-In-Cell Method (PIC)
• 3.3.1 Particle motion - Lorentz solver
• 3.3.2 Field equations - Maxwell solver
• 3.3.3 Particle and force weighting
• 3.4 Summary
• Chapter 4 Transonic Gas Flows AcrossMultiple Flow Regimes
• 4.1 State of the art and previous studies
• 4.2 Experimental setup
• 4.2.1 Vacuum and measurement systems
• 4.2.2 Arcjet thruster and Laval nozzle
• 4.2.3 Experimental series
• 4.3 Numerical setup
• 4.3.1 Solved equations and numerical solver
• 4.3.2 Numerical mesh and boundary conditions
• 4.3.3 Numerical setup for DSMC simulations
• 4.4 Results and discussion
• 4.4.1 Experimental results
• 4.4.2 Navier-Stokes simulations
• 4.4.3 DSMC results
• 4.4.4 Comparison between Navier-Stokes and experimental results
• 4.4.5 Knudsen-dependent correcting function for the dimensionlesspressure drop
• 4.4.6 Molar mass dependency of the Knudsen function coefficients
• 4.4.7 Thrust and specific impulse
• 4.5 Summary
• Chapter 5 Development of a Kinetic PlasmaModel for Electric PropulsionSystems
• 5.1 Electric propulsion systems for spacecraft
• 5.2 State of the art and previous works
• 5.2.1 Resistojets
• 5.2.2 Arcjet thrusters
• 5.2.3 Ion thrusters
• 5.2.4 Hall thrusters
• 5.3 Development of a kinetic plasma model
• 5.3.1 General modelling concept
• 5.3.2 Basis DSMC solver
• 5.3.3 Implementation of PIC algorithm
• 5.3.4 Coulomb collisions with the MCC algorithm
• 5.3.5 Electron-neutral collisions
• 5.3.6 Recombination
• 5.3.7 Boundary conditions in dsmcPlasmaFoam
• 5.3.8 Numerical aspects
• 5.3.9 Global model implementation in OpenFOAM
• 5.4 Summary
• Chapter 6 Validation of dsmcPlasmaFoam
• 6.1 Maxwell solver
• 6.2 Lorentz solver
• 6.2.1 Solver behaviour without implementation of the Leapfrog algorithm
• 6.2.2 Solver behaviour with implemented Leapfrog algorithm
• 6.3 Particle and force weighting
• 6.4 Coulomb collisions
• 6.5 Electron-neutral collisions
• 6.6 Summary
• Chapter 7 Conclusion
• 7.2 Conclusion and outlook
• Appendix AMathematical Theorems
• A.1 Divergence theorem
• A.2 Reynolds transport theorem
• Appendix BSource Code dsmcPlasmaFoam
• B.1 Maxwell solver
• B.2 Lorentz solver
• B.3 Cumulative Coulomb collisions
• B.4 Electron-Neutral collisions
• B.5 Dynamic particle weighting
• Bibliography
• 7.1 Summary