Pulsed Fusion Space Propulsion: Computational Ideal Magneto-Hydro Dynamics of a Magnetic Flux Compression Reaction Chamber
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Pulsed Fusion Space Propulsion: Computational Ideal Magneto-Hydro Dynamics of a Magnetic Flux Compression Reaction Chamber G. Romanelli Master of Science Thesis Space Systems Engineering PULSED FUSION SPACE PROPULSION: COMPUTATIONAL IDEAL MAGNETO-HYDRO DYNAMICS OFA MAGNETIC FLUX COMPRESSION REACTION CHAMBER by Gherardo ROMANELLI to obtain the degree of Master of Science at the Delft University of Technology, to be defended publicly on Friday February 26, 2016 at 10:00 AM. Student number: 4299876 Thesis committee: Dr. A. Cervone, TU Delft, supervisor Prof. Dr. E. K. A. Gill, TU Delft Dr. Ir. E. Mooij, TU Delft Prof. A. Mignone, Politecnico di Torino An electronic version of this thesis is available at http://repository.tudelft.nl/. To boldly go where no one has gone before. James T. Kirk ACKNOWLEDGEMENTS First of all I would like to thank my supervisor Dr. A. Cervone who has always sup- ported me despite my “quite exotic” interests. He left me completely autonomous in shaping my thesis project, and still, was always there every time I needed help. Then, I would of course like to thank Prof. A. Mignone who decided to give his contribute to this seemingly crazy project of mine. His advice arrived just in time to give an happy ending to this story. Il ringraziamento più grande, però, va di certo alla mia famiglia. Alla mia mamma e a mio babbo, perché hanno sempre avuto fiducia in me e non hanno mai chiesto ragioni o spiegazioni alle mie scelte. Ai miei nonni, perché se di punto in bianco, un giorno di novembre ho deciso di intraprendere questa lunga strada verso l’Olanda, l’ho potuto fare anche per merito loro. A tutti gli altri, perché erano sempre li a fare il tifo per me. Poi ci sono i miei cari vecchi amici di Arezzo. Con alcuni ci siamo incontrati “solo” 12 anni fa, con altri anche un po’ prima, e nonostante io sia scappato lontano, loro sono ancora li ogni volta che ne ho bisogno. Un altro saluto va ai colleghi/amici di Pisa, perché anche se abbiamo condiviso un periodo breve, è stato comunque un capitolo fondamentale. Finally, there is Delft where I met new people, new chal- lenges, new feelings, and a new life. Lucky me that I also had some good friends to share the adventure with. iii ABSTARACT Verifying the working principle of a magnetic flux compression reaction chamber might be crucial for the development of pulsed fusion propulsion: a system that has been projected to possibly revolutionise manned space exploration. For that purpose, an exhaustive computational Magneto-Hydrodynamics (MHD) analysis is a necessary step. This master thesis investigated the possibility of using PLUTO1 to estimate the ideal-MHD of a multi-coil parabolic reaction chamber. PLUTO is a freely-distributed and modular code for computational astrophysics that, although not originally pro- grammed for engineering applications, has demonstrated great adaptation capabil- ities: implementing the boundary conditions to effectively emulate a magnetic flux compression reaction chamber has eventually been possible. Besides, the attained results are in accordance with theoretical projections and previous numerical analy- ses. However, the outcomes pointed out that ideal-MHD could be an over-simplified model: relativistic conditions, that are not properly reproduced by the ideal-MHD equations, have been identified in several locations of the computational domain. In addition, some aspects of the real system physics have yet to be thoroughly in- vestigated as well as mathematically described. Therefore, further investigations are required. According to this research, no other computational analyses of a multi-coil parabolic reaction chamber (i.e. the latest and most promising magnetic flux com- pression reaction chamber concept) have been found in the literature. Therefore, the results hereby reported contribute to the body of knowledge of plasma physics and nuclear fusion applied to space propulsion. In particular: The objective of this master’s thesis project is to contribute to the development of a magnetic flux compression reaction chamber for space propulsion applications, by completing the first computational ideal-MHD analysis of the plasma expansion in a multi-coil parabolic chamber Besides, completing such a project has answered to the following research questions: • How is the thrust generated in a magnetic flux compression reaction chamber? – What is the theoretical background at support of the projected working principle of a reaction chamber? – What is the latest and most promising reaction chamber concept? • How have the so far projected performance been derived? 1http://plutocode.ph.unito.it/ v viA BSTRACT – Which were the assumptions taken to estimate the performance of the rocket? – Can the same assumptions be confirmed by a more detailed plasma physics? – How much do the simplifications and assumptions taken affect the re- sults of the estimation? • Can the same performance be reproduced by a more extensive computational analysis? – What is the plasma physics model that better reproduces the dynamics in a magnetic flux compression reaction chamber? – What are the available codes that can be used to perform the computa- tional analysis? – What are the assumptions/simplification that can be taken to attain an efficient (i.e. in a reasonable amount of time) and still effective analysis? – Can the computational analysis be performed on a commercial laptop? CONTENTS List of Figures xi List of Tables xv Abbreviations xvii Physical Constants xix List of Symbols xxi 1 Introduction1 1.1 Magnetic Flux Compression Reaction Chamber...............4 1.2 Research Contributions.............................7 1.3 Thesis Outline...................................8 2 Plasma Dynamics: Physical Description 11 2.1 Plasma: the 4th state of matter.............................. 11 2.2 Classical Electromagnetism........................... 12 2.2.1 Maxwell’s equations........................... 14 2.2.2 Single-Particle Dynamics........................ 15 2.3 Plasma Fluid Theory............................... 15 2.3.1 Zeroth Moment.............................. 16 2.3.2 First Moment............................... 16 2.3.3 Second Moment.............................. 16 2.3.4 Single-Fluid Theory............................ 17 2.4 Ideal-MHD..................................... 20 2.4.1 Collisionless Plasma........................... 21 2.4.2 High-Conductivity Plasma....................... 21 2.4.3 Non-Relativistic Plasma Wave Velocity................ 22 3 Magnetic Flux Compression Reaction Chamber: Operation 25 3.1 Working principle................................. 25 3.1.1 Seed Magnetic Field Generation.................... 26 3.1.2 Magnetic Field Compression and Momentum Transfer...... 29 3.2 Previous Concept Designs............................ 32 3.2.1 Project Daedalus............................. 32 3.2.2 Vehicle for Interplanetary Space Transport Applications (VISTA) 33 3.2.3 Human Outer Planet Exploration (HOPE).............. 34 vii viii CONTENTS 4 Magnetic Flux Compression Reaction Chamber: Elementary Analysis 39 4.1 System Energy Balance.............................. 40 4.1.1 Estimated Performance......................... 45 4.2 Simplified Analytical Model........................... 46 4.2.1 Initial Magnetic Flux Derivation.................... 53 4.3 Analytical Model Validation........................... 57 4.3.1 Initial Conditions............................. 57 4.3.2 Integration Problem........................... 59 4.3.3 Results................................... 60 4.3.4 Final Remarks............................... 60 5 Magnetic Flux Compression Reaction Chamber: Computational Code Selection 63 5.1 Selection of the Computational Code..................... 63 5.2 PLUTO........................................ 65 5.2.1 Computational Domain and Solving Strategy............ 66 5.2.2 Defining Initial Conditions....................... 69 5.3 Previous Numerical Analysis.......................... 70 5.3.1 Computational Problem Set-Up.................... 71 6 Magnetic Flux Compression Reaction Chamber: Computational Analysis 75 6.1 Final Set-Up.................................... 75 6.1.1 Computational Domain......................... 76 6.1.2 Plasma Pellet and Seed Magnetic Field Definition......... 76 6.1.3 Boundary Conditions.......................... 78 6.1.4 Ambient Conditions........................... 83 6.1.5 Entropy Switch.............................. 86 6.1.6 Runtime Analysis............................. 87 6.2 Validation...................................... 89 6.3 Results........................................ 91 6.3.1 Simplified analytical model verification............... 97 7 Conclusions 101 7.1 Research Contributions............................. 104 7.2 Recommended Future Work........................... 105 A MATLAB script 107 A.1 Arrays Definition................................. 107 A.2 Integration Problem............................... 108 B PLUTO 111 B.1 pluto.ini....................................... 111 B.2 definitions.c.................................... 112 B.3 init.c......................................... 113 B.4 userdefoutput.c.................................. 119 CONTENTS ix B.5 ct.c.......................................... 120 Bibliography 123 LISTOF FIGURES 1.1 Thrust, specific impulse (Isp ), and input power of nowadays available space propulsion systems [1].........................2 1.2 Comparison between the section of a de Laval nozzle a), and of a mag- netic nozzle b) [2]................................3 1.3 Artistic impression of a Fusion Driven