Axisymmetric simulation codes for hall effect thrusters and plasma plumes

Mención Internacional en el título de doctorThe development of reliable and versatile plasma discharges simulation codes is becoming of central importance, given the rapidly evolving electric propulsion landscape. These tools are essential for facilitating and complementing the design of new prototypes, signiffcantly reducing development time and costs. Moreover, they can provide a deeper insight on already proven technologies, revealing optimization opportunities so as to improve the thruster performance and lifetime, and predicting the operational parameters at different regimes of interest. This Thesis is devoted to the numerical study of different plasma discharges and, in particular, the Hall effect thruster (HET) discharge. With special focus on particle-based modeling, two simulation codes have been developed. The first one, named HYPHEN, is a new two-dimensional axisymmetric hybrid, particle-in-cell (PIC)/fluid multi-thruster simulation platform. Its versatile PIC-based module for heavy species supports the simulation of inner active surfaces, mixed specular-diffuse neutral-wall reflection, and chargeexchange (CEX) collisions, thus extending the code capabilities and enabling the simulation of axisymmetric plasma plumes. Moreover, it features a new population control which monitors independently every heavy species and limits the statistical noise at a low computational cost. Furthermore, an improved version of the HET electron fluid module for the isotropic electron pressure case is presented. Three major studies have been carried out with this code. First, the simulation of an ion thruster plasma plume has permitted to benchmark HYPHEN against the 3D plasma plume code EP2PLUS. Second, an investigation on the neutral-wall interaction effects on an unmagnetized plasma discharge in a surface-dominated cylindrical channel with isothermal electrons has been performed. The discharge ignition requires different propellant injection mass ows in the diffuse and specular neutral-wall reflection cases. Third, preliminary simulations of a SPT-100 HET have been carried out to demonstrate the code capabilities and reveal its limitations. Consistent results have been obtained for different cathode locations in the near plume region and various electron turbulent transport parameter profiles. The second code corresponds to a new version of the one-dimensional radial particle model of a HET discharge, originally developed by F. Taccogna. The major improvements are an ionization controlled discharge algorithm, which enables sustaining a steady-state discharge, and an extended volumetric weighting algorithm which provides a more accurate macroscopic description of the low populated species, such as the wall-emitted secondary electrons. The radial dynamics of both the primary and secondary electron populations have been analyzed in detail, assessing the temperature anisotropy ratio of their velocity distribution functions and the asymmetries introduced by cylindrical geometry effects in the macroscopic laws of interest, thus aiming at a future improvement of the plasma-wall interaction module implemented in HYPHEN.El desarrollo de códigos fiables y versátiles para la simulación de descargas de plasma es cada vez más importante dada la rápida evolución de la propulsión espacial eléctrica. Estas herramientas son esenciales para facilitar y complementar el diseño de nuevos prototipos, reduciendo significativamente los tiempos y costes de desarrollo. Además, pueden ampliar la comprensión de las tecnologías ya establecidas, revelar vías de optimización del propulsor que permitan mejorar su rendimiento y vida útil, y predecir los parámetros de operación del mismo en diferentes regímenes de interés. Esta Tesis está dedicada al estudio numérico de diferentes descargas de plasma y, en particular, de descargas HET. Se han desarrollado dos códigos de simulación, con especial énfasis en los modelos de partículas. El primero de ellos, llamado HYPHEN, es una nueva plataforma de simulación multi-propulsor, híbrida PIC/fluida y axisimétrica. Su módulo PIC para especies pesadas permite la simulación de superficies activas inmersas en el plasma, procesos de reflexión especular-difuso de neutros en pared y colisiones CEX, extendiendo por tanto las capacidades del código y permitiendo la simulación de plumas de plasma axisimétricas. Además, incluye un nuevo control de población que monitoriza a cada especie pesada por separado limitando el ruido estadístico y el coste computacional. Por otra parte, se presenta una versión mejorada del modelo fluido de electrones isótropos para HET. Tres estudios principales se han llevado a cabo con este código. En primer lugar, la simulación de la pluma de plasma de un motor iónico ha permitido validar HYPHEN con el código de plumas 3D EP2PLUS. Por otro lado, se ha investigado el efecto de la interacción del gas neutro con la pared en una descarga no magnetizada con electrones isotermos en un canal cilíndrico esbelto. La ignición de la descarga requiere inyectar diferentes gastos másicos de propulsante en los casos de reflexión difusa y especular. En tercer lugar, se han realizado simulaciones preliminares de un motor HET de tipo SPT- 100 con el objeto de demostrar las capacidades del código y revelar sus limitaciones, obteniendo resultados consistentes para diferentes posiciones del cátodo en la región de la pluma cercana, y perfies del parámetro de turbulencia de electrones. El segundo código representa una nueva versión del modelo radial de partículas de una descarga HET desarrollado originalmente por F. Taccogna. Las principales mejoras consisten en un algoritmo de control de la descarga a través de la ionización, que permite obtener una descarga estacionaria, y un algoritmo de pesado volumétrico extendido, que proporciona una descripción macroscópica más precisa de las especies poco pobladas, como los electrones secundarios emitidos desde las paredes del motor. Para posibilitar una futura mejora del módulo de HYPHEN de interacción plasma-pared, se han analizado en detalle la dinámica radial de los electrones primarios y secundarios, la anisotropía de temperatura de sus funciones de distribución de velocidad, y las asimetrías cilíndricas en las leyes macroscópicas de interés.Programa Oficial 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 Virgili.Presidente: Iván Calvo Rubio.- Secretario: Gonzalo Sánchez Arriaga.- Vocal: Daniela Pedrin

Particle modeling of radial electron dynamics in a controlled discharge of a Hall thruster

Special issue on plasma-surface InteractionsAn improved radial particle-in-cell model of an annular Hall effect thruster discharge with secondary-electron emission from the walls and a radial magnetic field is presented. New algorithms are implemented: first, to adjust the mean neutral density to the desired mean plasma density; second, to avoid the refreshing of axially accelerated particles; and third, to correctly weigh low-density populations (such as secondary electrons). The high-energy tails of the velocity distribution functions of primary and secondary electrons from each wall are largely depleted, leading to temperature anisotropies for each species. The secondary-electron populations are found to be partially recollected by the walls and partially transferred to the primary population. The replenishment ratio of the primary high-energy tail is determined based on the sheath potential fall. Significant asymmetries at the inner and outer walls are found for the collected currents, the mean impact energy, and the wall and sheath potentials. Radial profiles in the plasma bulk are asymmetric too, due to a combination of the geometric expansion, the magnetic mirror effect, and the centrifugal force (emanating from the E x B drift). The temperature anisotropy and non-uniformity, and the centrifugal force modify the classical Boltzmann relation on electrons along the magnetic lines.The work at UC3M was supported by the CHEOPS project, funded by the European Union’s Horizon 2020 Research and Innovation Programme, under Grant Agreement 730135. Additional support came from Spain’s National Research and Development Plan (Project ESP2016-75887). F T was sup-ported by the Apulia Space Project (grant PON03PE_00067_6)

Influence of Reynolds number on theoretical models for trailing vortices

We conduct direct numerical simulations for a NACA0012 airfoil at Reynolds numbers (Re) ranging from 300 to 7000 to determine the wake behavior behind this wing profile. We characterize the structure of the wing-tip vortex, finding a reasonable agreement with experimental results at Re=7000. In addition, we model the trailing vortex theoretically, thus obtaining the parameters for Batchelor’s and Moore and Saffman’s models. We compare the results of the best fitting for the axial vorticity and the azimuthal velocity, finding only small discrepancies. The main contribution of this research work is to study the evolution of these theoretical parameters as function of the Reynolds number. We observe that the wake becomes unstable at Re ≈1200, in agreement with previous results. These instabilities in the wake behind the wing produce a change in the trend of theoretical parameters (keywords: vortex dynamics, trailing vortices, theoretical models).Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Hybrid 3D model for the interaction of plasma thruster plumes with nearby objects

This paper presents a hybrid particle-in-cell (PIC) fluid approach to model the interaction of a plasma plume with a spacecraft and/or any nearby object. Ions and neutrals are modeled with a PIC approach, while electrons are treated as a fluid. After a first iteration of the code, the domain is split into quasineutral and non-neutral regions, based on non-neutrality criteria, such as the relative charge density and the Debye length-to-cell size ratio. At the material boundaries of the former quasineutral region, a dedicated algorithm ensures that the Bohm condition is met. In the latter non-neutral regions, the electron density and electric potential are obtained by solving the coupled electron momentum balance and Poisson equations. Boundary conditions for both the electric current and potential are finally obtained with a plasma sheath sub-code and an equivalent circuit model. The hybrid code is validated by applying it to a typical plasma plume-spacecraft interaction scenario, and the physics and capabilities of the model are finally discussed.The research leading to the results of this paper was initiated within the LEOSWEEP project (“Improving Low Earth Orbit Security With Enhanced Electric Propulsion”), funded by the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement N.607457. Additional funding to complete it has been received by Spain’s R&D National Plan, under grant ESP2016-75887

Parametric study of the radial plasma-wall interaction in a Hall thruster

An investigation on the influence of relevant parameters on an annular Hall effect thruster plasma discharge is performed using a radial particle-in-cell simulation code with secondary electron emission from the walls and prescribed axial electric and radial magnetic fields. A simulation with true-secondary electrons only is taken as reference. First, the near-wall conductivity effects on the magnetized secondary electrons are illustrated by doubling the , allowing a further code validation. Second, when secondary backscattered electrons are included, the enhanced secondary emission yields lower sheath potential drops and primary electron temperature. Moreover, the dominant backscattered electrons increase the average secondary electrons emission energy, greatly affecting its temperature anisotropy ratio and increasing the replenishment level of the wall collectable tails of the primary electrons velocity distribution function. Third, the effect of the true-secondary electrons emission energy on the potential profile is shown to be negligible, the latter being mainly set by the dominant magnetic mirror effect. Finally, a planar case featuring symmetric plasma profiles permits to confirm the validity of the large cylindrical asymmetries present in the reference case, induced by the combined effects of the geometric expansion, the magnetic mirror and the centrifugal force (due to the drift). A smaller deviation of the primary electron momentum equation from the Boltzmann relation along the magnetic lines is still found in the planar case, induced by the parallel temperature non-uniformity.The UC3M researchers have been supported by the PROMETEO-CM project, Grant number Y2018/NMT-4750 (Comunidad de Madrid/FEDER/FSE). Additional funding for A Domínguez-Vázquez came from Project ESP2016-75887 (Spain's National Research and Development Plan - MINECO/FEDER) F Taccogna has been supported by the italian Ministero dell'Istruzione, dell'Università e della Ricerca (MIUR) under the CLOSE project (grant ARS01_00141)

Simulations of driven breathing modes of a magnetically shielded Hall thruster

The operation of a 5 kW-class magnetically shielded Hall effect thruster with sinusoidal modulation of the discharge voltage is investigated through simulations with a 2D axisymmetric hybrid (particle-in-cell/fluid) code. The dynamic response of the thruster for different modulation amplitudes and frequencies is presented and discussed. The analysis of partial efficiencies contributing to thrust efficiency allows identifying counteracting effects limiting net gains in performance figures. Voltage modulation enhances the amplitude of plasma oscillations and can effectively control their frequency when the modulation frequency is close to that of the natural breathing mode (BM) of the thruster. The 2D plasma solution reveals that the dynamics of the ionization cycle are governed by the electron temperature response, enabling a driven BM at the modulation frequency. For modulation frequencies far from the natural BM one, voltage modulation fails to control the plasma production via the electron temperature, and the natural BM of the thruster is recovered. High order dynamic mode decomposition applied to the 2D plasma solution permits analyzing the complex spatio-temporal behavior of the plasma discharge oscillations, revealing the main characteristics of natural and externally driven modes.This work has been supported mainly by the EDDA project, funded by the European Union's Horizon 2020 Research and Innovation Program, under Grant Agreement Number 870470. Its completion has been possible thanks to ESPEOS project, funded by the Agencia Estatal de Investigación (Spanish National Research Agency), under Grant No. PID2019-108034RB-I00/AEI/10.13039/501100011033

Radial Line Slot Antenna Design with Groove Gap Waveguide Feed for Monopulse Radar Systems

Radial line slot arrays (RLSAs) are well suited to be used in monopulse radar systems. The excitation of the sum and difference patterns can be achieved by the design of simple feeds as shown in this paper. In this work, a feed system based on the use of a cavity made in groove gap waveguide technology (GGW) is presented. The design is made at 24 GHz but can be easily scaled to higher frequencies as the technology is contact-less and fully made in metal. A good isolation between the sum and difference ports together with a good matching of the two of them is obtained. The radiation patterns of the manufactured antenna are also in good agreement with the simulated ones.This work was supported in part by the Spanish Government, Ministry of Economy, National Program of Research, Development and Innovation under the projects TEC2016-79700-C2-2-R and TEC2017-85529-C3-1-R and by the Madrid Regional Government under the project SPADERADAR “Space Debris Radar” (S2013/ICE-3000) and the FPI grant with reference BES-2015-07523

On heavy particle-wall interaction in axisymmetric plasma discharges

The effects of heavy particle-wall interaction on a cylindrical plasma source discharge are investigated, through hybrid particle-in-cell/fluid simulations. The bulk plasma is considered quasineutral with isothermal electrons, and with no secondary electron emission from the walls. The neutral gas wall reflection model is shown to play a major role in determining the conditions for a self-sustained and stationary plasma discharge. A hysteresis cycle on the injection mass flow rate is found when neutrals deviate from a purely diffuse reflection at the walls, with the mass utilization efficiency changing up to 20% between purely specular and diffuse scenarios. However, as the ratio of ionization mean free path to macroscopic length is decreased, the neutral-wall reflection model becomes irrelevant. Finally, even small deviations from unity of the ion energy accommodation coefficient at the walls are seen to have a major impact on both the ion and neutral distribution functions, and ultimately the mass utilization efficiency. This behavior stresses out the importance of a precise experimental determination of this parameter for accurate simulations.This paper has been funded mainly by Comunidad de Madrid/FEDER/FSE, through the PROMETEO-CM project, Grant No. Y2018/NMT-4750. Additional support came from the ESPEOS project, funded by the Agencia Estatal de Investigación (Spanish National Research Agency), under Grant No. PID2019-108034RB-I00/AEI/10.13039/501100011033

Axisymmetric plasma plume characterization with 2D and 3D particle codes

The expansion of a rarefied axisymmetric plume emitted by a plasma thruster is analyzed and compared with a 3D Cartesian-type and a 2D cylindrical-type simulation code, both based on a particle-in-cell formulation for the heavy species and a simple Boltzmann-type model for the electrons. The first part of the paper discusses the 2D code numerical challenges in the moving of particles, their generation within the cells, and the weighting to the nodes, caused by the radial non-uniformity and the singular and boundary character of the symmetry axis. The second part benchmarks the 2D code against the 3D one for a high-energy, unmagnetized plume with three major species populations (injected neutrals, singly-charged and doubly-charged ions) and three minor species populations (constituted by particles coming from collisional processes, such as the charge-exchange reactions). The excellent agreement found in the results proves that both plume codes are capable of simulating, with a reasonable noise level, heavy particle populations differing by several orders of magnitude in number density. For simulations with a comparable level of accuracy, the 2D code presents a ten-fold gain in computational cost, although the symmetry axis remains its weakest point, due to particle depletion there and the related weighting noise

Fatigue behaviour of PBF additive manufactured TI6AL4V alloy after shot and laser peening

Article number 106536Additive manufacturing (AM) of metallic parts is a relatively new manufacturing procedure. Many industry sectors, such as the aerospace or automotive sectors, have started to apply this technology to produce some elements, thus reducing costs and weight. Several metallic alloys have been employed for AM. Due to the high strength-to-density ratio, Ti6Al4V alloy is probably the alloy most used for AM in the aerospace industry. This alloy usually shows good static strength properties. However, the presence of internal defects and the surface roughness result in a fatigue strength that is clearly lower than that of materials produced by traditional pro cesses. Moreover, the scatter of the fatigue results is generally higher than in the case of wrought pieces. Different treatments have been proposed to improve the fatigue behavior by reducing internal defects and roughness or generating a favorable residual stress field. In this work, selected surface treatments were considered to improve the fatigue strength of AM parts, including shot and laser peening as well as a combination of shot peening plus chemical assisted surface enhancement (CASE®). Three groups of specimens, each with one of the surface treatments, were fatigue tested to compare the results produced by these treatments. The residual stresses, roughness and hardness produced by the treatments were analyzed. After testing, the fracture surfaces were also analyzed to better understand the fatigue process of the different groups of specimens. The results indicate that laser peening produced the best results, followed by shot peening plus CASE and shot peening. In all three cases, the fatigue strength was much higher than that of the reference group without surface treatment. It was also observed that all failures initiated from an interior defect in the shot peening plus CASE group, four out of six failures in the laser peened group, but only one failure in the case of shot peened group and none in the reference group. Failures of specimens with initiation from internal defects started from defects located deeper than the compressive residual stress layer produced by the treatments