35 research outputs found
Modeling and simulation of the plasma discharge in a radiofrequency thruster
Mención Internacional en el título de doctorIn the current electric propulsion industry for space applications, two of the main issues are the
lifetime limitation of the mature technologies, Hall effect thrusters and gridded ion thrusters, due to
the erosion of their electrodes; and the search for alternative propellants due to the scarcity of xenon.
Electrodeless thrusters with magnetic nozzles, in particular the helicon plasma thruster and the electron
cyclotron resonance thruster, are disruptive electric propulsion concepts that offer prolonged lifetime
and tolerance for a wide variety of propellants. These thrusters are still under development, and further
research is necessary for them to become competitive in terms of propulsive performances.
This thesis is focused on the modeling and simulation of the plasma discharge in electrodeless
thrusters with two codes. HYPHEN, a two-dimensional axisymmetric hybrid code, is used for full simulations
of the thrusters. This code was extended from Hall effect thrusters to electrodeless thrusters,
within the objective of developing a multi-thruster simulation platform valid for many types of electromagnetic
thrusters. VLASMAN, a one-dimensional kinetic code, is used for simulations of the plasma
expansion along the magnetic nozzles.
The hybrid formulation of HYPHEN offers a good trade-off between computational cost and reliability
of the results for full simulations, with a particle-in-cell model for heavy species and a fluid
model for electrons. The particle model was ready for use from previous works, while the fluid model,
with the basis established, was incomplete from the numerical point of view. The fluid model is solved
on a magnetic field aligned mesh given the anisotropic character of the strongly magnetized electrons.
However, the mesh, for realistic magnetic field topologies, can be highly irregular and the preliminary
numerical algorithms were leading to inaccurate results. Thus, in this thesis, the numerical treatment of
the fluid model is investigated, and solid numerical algorithms are found allowing to solve even complex
magnetic topologies with singular points. Once the electron fluid model is completed, simulations
coupled with the particle model are run for the helicon plasma thruster prototype HPT05M. The simulations
are focused on the plasma transport assuming a known power deposition map from the helicon
antenna. The thruster performances and profiles of plasma magnitudes are studied. The prototype is
partially optimized, in terms of some design parameters, but the thrust efficiencies obtained are within
the state-of-art. The main limitations for a full optimization beyond the state-of-art are identified and
solutions are proposed.
Furthermore, HYPHEN was initially developed to simulate xenon and other atomic propellants.
In this thesis, as many candidates for alternative propellants usually have more complex chemistry, the
code is implemented with the main collisions for diatomic substances. Simulations are run with air
as propellant for HPT05M testing successfully the implementation. The results have allowed also to
evaluate the air-breathing concept in helicon plasma thrusters.
The kinetic formulation of VLASMAN is used for deeper studies of the plasma expansion along
the magnetic nozzles. In the expansion, the plasma becomes very rarefied, and more accurate simulations
than those from HYPHEN are required. Other one-dimensional steady state models were used
in previous works, however they were not able to solve self-consistently a subpopulation of electrons
trapped along the expansion. VLASMAN models the mechanisms responsible for the trapping of electrons,
the transient and collisional processes. Simulations with VLASMAN are run to study the trapped
electrons in terms of the transient history and collisionality. The solution of the subpopulation, and that of the whole plasma, reached in the steady state is found dependent on the transient history. Once the
collisions are added, even if rare, the transient history is erased and the steady state solution becomes
unique. The amount of trapped electrons is found important on the electron cooling and on the balances
of electron momentum and energy. Furthermore, some studies focused on the extraction of results for
implementation in macroscopic models are conducted.En la industria actual de la propulsión eléctrica para aplicaciones espaciales, dos de los principales
problemas son la limitación de la vida útil de las tecnologías maduras, propulsores de efecto Hall y
propulsores iónicos con rejillas, debido a la erosión de sus electrodos; y la búsqueda de propulsantes
alternativos debido a la escasez del xenón. Los propulsores sin electrodos con tobera magnéticas, en
particular el propulsor Helicón y el propulsor cicloelectrónico, son conceptos de propulsión eléctrica
disruptivos que ofrecen una vida útil prolongada y tolerancia a una amplia variedad de propulsantes.
Estos propulsores aún están en desarrollo y se necesita más investigación para que sean competitivos
en términos de actuaciones propulsivas.
Esta tesis se centra en el modelado y simulación de la descarga de plasma en propulsores sin electrodos
con dos códigos. HYPHEN, un código híbrido axisimétrico bidimensional, se usa para simulaciones
completas de los propulsores. Este código es extendido de los propulsores de efecto Hall
a los propulsores sin electrodos, bajo el objetivo de desarrollar una plataforma de simulación multipropulsor
válido para muchos tipos de propulsores electromagnéticos. VLASMAN, un código cinético
unidimensional, se usa para simulaciones de la expansión del plasma a lo largo de las toberas magnéticas.
La formulación híbrida de HYPHEN ofrece un buen punto intermedio entre el coste computacional
y la fiabilidad de los resultados para simulaciones completas, con un modelo de partículas para
especies pesadas y un modelo fluido para electrones. El modelo de partículas estaba ya listo para su uso
de trabajos anteriores, mientras que el modelo fluido, con la base establecida, estaba incompleto desde
el punto de vista numérico. El modelo fluido se resuelve en una malla alineada con el campo magnético
dado el carácter anisotrópico de los electrones fuertemente magnetizados. Sin embargo, la malla, para
topologías de campos magnéticos realistas, puede ser muy irregular y los algoritmos numéricos preliminares
llevaban a resultados inexactos. En esta tesis, se investiga el tratamiento numérico del modelo
fluido y se encuentran algoritmos numéricos sólidos que permiten resolver incluso topologías magnéticas
complejas con puntos singulares. Una vez que se completa el modelo fluido, se llevan a cabo
simulaciones junto con el modelo de partículas para el prototipo de propulsor Helicón HPT05M. Las
simulaciones se centran en el transporte de plasma asumiendo un mapa conocido de deposición de
potencia de la antena Helicón. Se estudian las actuaciones del propulsor y perfiles de las magnitudes
del plasma. El prototipo se optimiza parcialmente, en términos de algunos parámetros de diseño, pero
las eficiencias de empuje obtenidas están dentro del estado de arte. Se identifican las principales limitaciones
para una optimización total más allá del estado de arte y se proponen soluciones.
Además, HYPHEN se desarrolló inicialmente para simular xenón y otros propulsantes atómicos.
En esta tesis, como muchos candidatos a propulsantes alternativos suelen tener una química más compleja,
el código se implementa con las principales colisiones de sustancias diatómicas. Simulaciones se
llevan a cabo con aire como propulsante para el HPT05M testeando con éxito la implementación. Los
resultados también han permitido evaluar el concepto de air-breathing en los propulsores Helicón.
La formulación cinética de VLASMAN se utiliza para estudiar con mayor profundidad la expansión
del plasma a lo largo de las toberas magnéticas. En la expansión, el plasma se vuelve muy enrarecido
y se requieren simulaciones más precisas que las de HYPHEN. En trabajos anteriores se utilizaron
otros modelos unidimensionales estacionarios, sin embargo, no pudieron resolver de manera autoconsistente una subpoblación de electrones atrapados a lo largo de la expansión. VLASMAN modela
los mecanismos responsables del atrapado de electrones: los procesos transitorios y colisionales.
Simulaciones con VLASMAN se llevan a cabo para estudiar los electrones atrapados en términos del
transitorio y colisionalidad. La solución de la subpoblación, y la de todo el plasma, alcanzada en el
estacionario depende del transitorio. Una vez que se incluyen las colisiones, incluso si son poco frequentes,
se borra el transitorio y la solución estacionaria colapsa en una única. Se descubre que la
cantidad de electrones atrapados es importante en el enfriamiento y en el balance de momento y energía
de los electrones. Además, se realizan algunos estudios enfocados a la extracción de resultados
para su implementación en modelos macroscópicos.This thesis received funding mainly from Airbus Defense and Space, contract number CW240050.
The last year of thesis was supported by the HIPATIA project of HORIZON 2020 (European Commission),
grant number GA870542.Programa de Doctorado en Mecánica de Fluidos por la Universidad Carlos III de Madrid; la Universidad de Jaén; la Universidad de Zaragoza; la Universidad Nacional de Educación a Distancia; la Universidad Politécnica de Madrid y la Universidad Rovira i VirgiliPresidente: Ricardo Albertoni.- Secretario: José Miguel Reynolds Barredo.- Vocal: Justin Littl
Fluid modeling and simulation of the electron population in Hall Effect Thrusters with complex magnetic topologies
Mención Internacional en el título de doctorLa propulsión eléctrica es una tecnología consolidada, utilizada por vehículos espaciales para llevar
a cabo maniobras no atmosféricas. Este tipo de motores cohete ha estado presente en numerosas
aplicaciones en las últimas décadas y sus usos van desde el mantenimiento de la posición orbital
de satélites comerciales a transferencias interplanetarias en misiones de exploración. La mayor
ventaja de los numerosos tipos de propulsores eléctricos es su capacidad de proporcionar un determinado
impulso a un coste de propelente reducido, en comparación con otros tipos de propulsión.
El desarrollo de los motores de plasma, la clase más común de propulsor eléctrico, se ha visto
impedido en mayor medida que los cohetes químicos, por ejemplo, debido a la complejidad de la
interacción de los fenómenos físicos y a dificultades asociadas con las campañas experimentales.
En las últimas dos décadas se ha introducido el uso de simulaciones numéricas para ayudar a
la caracterización de estos aparatos. A pesar de que el diseño asistido por ordenador juega aún
un papel muy reducido, el incremento de recursos computacionales y la creciente exactitud de
los modelos físicos han permitido a estas simulaciones describir numerosos mecanismos físicos,
explorar el espacio de diseño de estos aparatos y complementar los ensayos experimentales.
Esta tesis está centrada en el estudio numérico de la población de electrones en descargas de
plasma poco colisionales, bajo la influencia de campos eléctricos y magnéticos. El trabajo realizado
ha contribuido al desarrollo de una nueva herramienta de simulación híbrida, cuasi-neutra, bidimensional
y axisimétrica, denominada HYPHEN; su naturaleza híbrida se debe al tratamiento
por separado de las especies pesadas, descritas a través de un conocido método de partículas, y de
la población de electrones, descrita como un fluido. Una de nuestras mayores contribuciones es la
introducciÃsn de un modelo anisotrÃspico de dos temperaturas, que permite capturar los efectos
de la falta de uniformidad del campo magnético sobre el transporte de electornes. Esta función
abre el camino para la caracterización de nuevos propulsores electromagnéticos. Actualemente,
el código está orientado hacia la simulación de las regiones del canal y de la pluma cercana en
motores de efecto Hall, en los que se enfoca esta tesis. Parte del trabajo se ha dedicado a dotar al
código de las capacidades necesarias para la simulación de topologías magnéticas complejas.
El presente documento detalla la motivación detrás de HYPHEN, su metodología de diseño y
la influencia de trabajos previos. Se ha prestado una especial atención al modelo fluido propuesto,
detallando el uso de una malla alineada con el campo magnético para el tratamiento numérico de
la población confinada de electrones, para la cual se han utilizado diversos métodos ad-hoc de discretización
temporal y espacial. Varios modelos auxiliares también se han descrito, con el objetivo
de caracterizar la respuesta de la capa límite del plasma y de los distintos procesos colisionales en
el seno del mismo. Se presenta también el estudio de los aspectos numéricos del modelo fluido,
incluyendo la sensibilidad a condiciones iniciales, a los valores del paso temporal, el refinamiento
de la malla, etc. Finalmente, HYPHEN se ha testeado para la configuración de un conocido motor
Hall. Los resultados demuestran que las propiedades físicas y las actuaciones obtenidas son comparables
con resultados provenientes de estudios experimentales. Bajo este contexto, se ha llevado a
cabo un estudio paramétrico para determinar la dependencia de la respuesta del motor con algunos
de los parámetros más relevantes del modelo, tales como el transporte anómalo de electrones o la
fracción de termalización de la capa límite, y con los diferentes modelos colisionales.Electric propulsion is an established technology used for non-atmospheric spacecraft maneuvering.
This type of rockets have been present in numerous applications in the last decades, and their
uses range from station keeping of commercial satellites to interplanetary transfers in deep space
exploration missions. While electric propulsion thrusters are multi-faceted, presenting numerous
and distinct types, their best selling point is the capability to deliver a given impulse at much
lower propellant cost, in comparison to other types of propulsion.
The maturation of plasma thrusters, the most common type of electric propulsion devices, has
faced more limitations than chemical rockets, for example, due to the complexity of the physical
interactions at play, and the difficulties associated with experimental campaigns. Over the past
two decades, numerical simulations were introduced as a novel tool in the characterization of these
devices. While true computer-aided-design is not yet a reality, the increment of computational
resources and the heightened fidelity of the physical models have allowed to describe numerous
physical mechanisms, explore the design space of these devices and complement experimental
testing.
This thesis focuses on the numerical study of the electron population in weakly collisional
plasma discharges, under the influence of applied magnetic and electric fields. The work has been
a primary contribution in the development of a new, quasi-neutral, two-dimensional, axisymmetric,
hybrid simulation tool, called HYPHEN. Its hybrid nature responds to the different treatment of
the heavy species populations, described through a well known discrete-particle approach, and the
electron population, described as a fluid. One of our main contributions has been the introduction
of a two-temperature anisotropic approach, which allows capturing of the magnetic non-uniformity
effects over electron transport; this feature paves the way for the characterization of some novel
electromagnetic propulsion technologies. Presently, the code is oriented to the simulation of the
channel and near-plume regions in Hall effect thrusters, which have been the main focal point of
the thesis. Dedicated efforts have been directed to providing the capabilities for the simulation of
the plasma under complex magnetic field topologies.
The manuscript details the motivation and design methodology behind HYPHEN, as well as
the influence of previous work. Special attention has been given to the particularities of the
proposed fluid model; this includes the use of a magnetic field aligned mesh for the numerical
treatment of the electron population under magnetic confinement, for which ad-hoc spatial and
temporal discretization methods have been proposed. Additional ancillary physical models have
also been developed, characterizing the response of plasma boundary layers and the various collisional
processes in the plasma. The numerical aspects of the model have been investigated,
including the sensitivity to initial conditions, time-step values, mesh refinement, etc. Finally,
HYPHEN has been tested in the context of a representative Hall-thruster configuration. The
results were found to be in line with experimentally reported thruster performances and plasma
discharge quantities. Additionally, a parametric investigation has been carried out in order to
investigate the dependency of the thruster response with the most relevant model parameters,
such as the anomalous electron transport or the boundary layer thermalization fraction, and the
different collisional models.This work has been partially supported by the CHEOPS project, that received funding from
the European Union’s Horizon 2020 research and innovation program, under grant agreement No.
730135. Additional support came from Project ESP2016-75887, funded by the National research
and development program of Spain.Programa Oficial de Doctorado en Plasmas y Fusión NuclearPresidente: José Javier Honrubia Checa.- Secretario: Mario Merino Martínez.- Vocal: Paul-Quentin Elia
Numerical Particle-In-Cell studies of Hall thrusters using unstructured grids
In a few decades, space has become a crucial part of our modern society. With the imminent deployment of mega satellite constellations, their number will increase dramatically. These future satellites will be mainly equipped with electric propulsion systems, and in particular Hall thrusters. However, the processes governing the plasma physics within Hall thrusters remain poorly understood, which forces manufacturers to carry out costly and laborious experimental campaigns to certify the finished product. To overcome this difficulty, numerical simulations are essential. They can be based on a Particle-In-Cell (PIC) method, well adapted to the physics of this type of plasma. Indeed, these plasmas present kinetic effects that cannot be accurately described by fluid methods. Due to the cost of PIC simulations and the complex phenomena involved, existing codes in the literature remain limited to academic configurations based on structured meshes. In an effort to overcome these challenges, the AVIP PIC code is developed at CERFACS as a predictive tool capable of modeling industrial configurations. To do this, AVIP PIC works with unstructured meshes, which no other code in the community can currently do. This innovation comes at the cost of a considerable complexity of the code and a substantial optimization work was first done in previous work. Because of its innovative character, the first objective of this thesis was to systematically validate AVIP PIC. Thus, AVIP PIC was first used to participate successfully in an international benchmark on a 2D configuration in the axial-azimuthal plane. During this work, all groups obtained close results with 5% difference at most on the main plasma parameters profiles. An azimuthal plasma oscillation, the electron drift instability, was also observed by all participants with extremely similar characteristics. This instability due to kinetic effects, most probably plays a fundamental role in the anomalous transport of electrons within the engine. Based on this first success, we then used this case to explore and parameterize an active particle control algorithm. By preventing the number of particles from increasing too much, this tool reduces the computational cost and will be very useful in future simulations. Still, in the perspective of code validation, we then studied a simplified 2D configuration in the radial- azimuthal plane of the engine. Indeed, taking into account the presence of the walls can considerably modify the simulated physics of the engine. In particular, we have highlighted a radial-azimuthal instability, also called modified two-stream instability, which is coupled to the electron drift instability mentioned above. A benchmark work, conducted by CERFACS with six international groups, confirmed this result with an excellent agreement, despite the great diversity of the codes involved. Capitalizing on our experience in 2D, we then developed a 3D simulation based on the same geometrical elements and plasma conditions than in the two previous cases. During this study the 3D electron drift instability was identified as well as a possible signature of the radial- azimuth instability. The comparison with the previous 2D configurations seems to show that the 2D simulations tend to create a hotter and denser plasma, which affects the oscillatory phenomena. The general structure of the plasma remains nevertheless similar. Finally tools for the analysis of the code performance have been developed which will prove to be valuable for the development of more advanced 3D configurations
Modeling of magnetized expanding plasmas
In fusion reactors, the walls are exposed to very high particle and energy fluxes. To study the problem of wall erosion and hydrogen retention in these conditions, the Magnum-PSI experiment at the FOM Institute of Plasma Physics is set up. The plasma source for Magnum-PSI is a cascaded arc, where a strong magnetic field is applied to obtain the desired conditions. The focus of this thesis is the development of a numerical model for studying the plasma creation in the source and the consecutive magnetized expansion. To describe the behavior of the different species in the range of conditions in the plasma – from gas to fully ionized, from non-magnetized to strongly magnetized – a multicomponent diffusion description is needed. Numerical techniques are developed to successfully apply multicomponent diffusion to magnetized expanding plasmas. Multi-component diffusion results in a system of coupled continuity equations for all species. In addition this coupled system is subject to mass and charge conservation constraints. To deal with the coupling between the species a new finite volume discretization method is introduced to discretize the system of continuity equations. For numerical stability, mass and charge constraints are not explicitly applied. Instead, all species mass fractions are treated as independent unknowns and mass and charge constraints are a result of the continuity equations, the boundary conditions, the diffusion algorithm and the new discretization scheme. With this method, mass and charge constraints can be satisfied exactly, although they are not explicitly applied. To verify the suitability of the method, simulations of both magnetized and nonmagnetized expansions have been performed. The simulations are able to reproduce important characteristics of magnetic confinement. Results show that in the magnetized case, the plasma production cannot be modeled by considering the source alone, since plasma production extends into the expansion region
Detailed Numerical Simulation of Multi-Dimensional Plasma Assisted Combustion
Interaction between flames and plasmas are the guiding thread of this work. Nanosecond Repetitively Pulsed (NRP) discharges are non-thermal plasmas which have shown interesting features for combustion control. They can interact with flames not only through heat, but also chemically by producing active species. In this work, fully-coupled plasma assited combustion simulations are targeted. To achieve this goal, plasma discharge capabilities are built in the low temperature plasma code, AVIP. The corresponding numerical methods, as well as validation cases regarding each set of equations, are first presented. To simulate plasma discharges, the coupled drift-diffusion equations and the Poisson equation are considered. AVIP is coupled to the AVBP code which solves the reactive Navier-Stokes equations to describe combustion phenomena. In a second part, we start by constructing and validating a fully-detailed chemistry for methane-air mixtures in zero-dimensional reactors before reducing it for multi dimensional simulations. The multi-dimensional streamer simulation capabilities of the code are then assessed using simple chemistries. All the validated parts of the code come together in a fully detailed simulation of ignition using NRP discharges. We finish by discussing phenomenological models built upon the knowledge that we gained from fully-detailed simulations. In a last part, finally, attempt to solve the Poisson and generalized Poisson equations using neural networks, which have a potential for speedup compared to classical linear solvers, is carried out