Breathing Electric Propulsion System
DEGREE PROJECT IN AEROSPACE ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2020
Intake Design, and Optimization for an Atmosphere- Breathing Electric Propulsion System
Masters Thesis Report
Jesus Espinosa Orozco
KTH ROYAL INSTITUTE OF TECHNOLOGY ELECTRICAL ENGINEERING AND COMPUTER SCIENCE Intake Design, and Optimization for an Atmosphere- Breathing Electric Propulsion System
Masters Thesis Report
Jesus Espinosa Orozco IRS-20-S-066 Stuttgart, Germany 2020
ii Author
Jesus Epinosa Orozco
Examiners
Priv. Doz. Dr.-Ing. Georg Herdrich Institute for Space Systems (IRS), University of Stuttgart, Stuttgart, Germany
Prof. Tomas Karlsson Institute of Space and Plasma Physics, KTH Royal Institute of Technology, Stockholm, Sweden
Supervisors
Francesco Romano, M. Sc. Institute for Space Systems (IRS), University of Stuttgart, Stuttgart, Germany
Nickolay Ivchenko, Associate Professor Institute of Space and Plasma Physics, KTH Royal Institute of Technology, Stockholm, Sweden
iii Abstract
Over the last two decades, Very Low Earth Orbit (VLEO) has gained researchers attention as it provides a significant amount of benefits in the field of earth observation and telecommunications. VLEO provides increased payload performance, improved geospatial accuracy, lower launch mass, simplified end of life disposal, and they reduce space-debris collision risk. However, the utilization of orbits with such low altitudes presents its own set of challenges, denser atmosphere will significantly increase aerodynamic drag, decaying the orbit in a short period of time. Besides increased drag VLEO environment will produce high levels of spacecraft (SC) charging and the presence of atomic oxygen will generate a constant erosion on the surfaces of the SC. An Atmosphere-Breathing Electric Propulsion (ABEP) ingests the residual atmosphere through an intake and uses it as propellant for an electric thruster. Theoretically applicable to any planet with an atmosphere, the system might allow drag compensation for an unlimited time without carrying propellant. In this thesis, different approaches for an intake are introduced, while the modeling, and numerical testing by Direct Simulation Monte Carlo (DSMC) is also presented. The intake is optimized for the RF Helicon-based Plasma Thruster (IPT) developed at IRS and a new concept design takes advantage of new materials properties, for specular surface interactions. Simulation results over different altitudes and conditions used for the verification of the design have been performed achieving a maximum collection efficiency of 94%.
Keywords
Atmospheric Intake, ABEP, Electric Propulsion, Plasma, VLEO
iv Abstrakt
Under de senaste två decennierna har “Very Low Earth Orbit“ VLEO fått stor uppmärksamhet inom forskningsvärlden då det leder till en mängd fördelar inom jordobservation och telekommunikation. VLEO ger ökad nyttolastprestanda, förbättrad geospatial noggrannhet, lägre startmassa, förenklat bortförskaffande och minskning kollisionsrisken för rymdskräp. Användningen av omloppsbanor på så låg höjd medför dessvärre också utmaningar. Den lägre höjden innebär tätare atmosfär och ökar därav det aerodynamiska luftmotståndet avsevärt. Förutom ökad luftmotstånd kommer miljön i VLEO att producera höga nivåer av rymdfarkostladdning och närvaron av atomärt syre leder till en konstant erosion av farkosters ytor. En ABEP leder in den återstående atmosfären genom ett intag och använder den som drivmedel för en elektrisk drivraket. Teoretiskt tillämpbart på alla planeter med en atmosfär, kan systemet tillåta luftmotståndskompensation under obegränsad tid utan något annat drivmedel än den redan befintliga atmosfären. I denna avhandling presenteras olika modeller för ett intag samtidigt som modellering och numerisk testning av DSMC också presenteras. Intaget optimeras för den IPT som utvecklats vid IRS och en ny konceptdesign utnyttjar nya materialegenskaper för speciella ytinteraktioner. Simuleringsresultat över olika höjder och förhållanden som används för verifiering av designen har utförts och resulterat i en maximal insamlingseffektivitet på 94%.
v Übersicht
In den letzten zwei Jahrzenten gewann die tiefe Erdumlaufbahn “Very Low Earth Orbit“ (VLEO) durch die erheblichen Vorteile für Erdbeobachtung und Telekommunikation an Aufmerksamkeit in der Wissenschaft. VLEO ermöglicht eine höhere Nutzlastleistung, verbesserte räumliche Genauigkeit, eine geringere Startmasse, vereinfachte “End-of-Life“ - Entsorgung und verringert das Kollisionsrisiko von Weltraumschrott. Die Nutzung von Umlaufbahnen in diesen geringen Höhen stellt jedoch auch eine Reihe von Herausforderungen dar. Die dichtere Atmosphäre im VLEO erhöht den Luftwiderstand erheblich und verringert die Umlaufbahn in kurzer Zeit. Neben dem erhöhten Luftwiderstand tritt auch hohe Raumschiff- oder Satellitenladung auf und durch atomaren Sauerstoff entsteht konstante Erosion an den Oberflächen. Ein atmosphärenatmender elektrischer Antrieb (ABEP) nimmt die Restatmosphäre über einen Einlass auf und verwendet sie als Treibstoff für ein elektrisches Triebwerk. Theoretisch auf jeden Planeten mit Atmosphäre anwendbar, könnte das System so den Widerstand zeitlich unbefristet ohne Treibstoffverwendung kompensieren. In dieser Arbeit werden verschiedene Ansätze für einen Einlass vorgestellt, und die Modellierung und numerischen Tests durch die “Direct Simulation Monte Carlo“ (DSMC) werden präsentiert. Der Einlass ist für den am IRS entwickelten RF Helicon-basierten Plasma Thruster (IPT) optimiert. Ein neues Konzeptdesign nutzt neue Materialeigenschaften für spiegelartige Oberflächen-Reflektionseigenschaften. Simulationsergebnisse verschiedener Höhen und Konditionen wurden zu der Überprüfung des Entwurfs verwendet, wobei eine maximale Einlassammlungswirkungsgrad von 94% erreicht wurde.
vi Acknowledgements
Throughout the writing of this thesis project I have received highly valuable support and assistance.
I would first like to thank Priv. Doz. Dr.-Ing.Georg Herdrich, the Institute for Space Systems, University of Stuttgart (IRS) and the DISCOVERER project for giving me the opportunity to accomplish this work. I would also like to thank my supervisor, MSc Francesco Romano, whose expertise and feedback were of great help during this project, pushing me to sharpen my critical thinking, and bringing my work to a higher level. In addition, I would also like to thank Dr. Ing. Marcel Pfeiffer for the invaluable insights on the implementation of the “PICLas” tool.
Finally, I would like to thank my supervisor at KTH Dr. Nickolay Ivchenko for his support and facilitation of the required hardware for the development of this project.
vii Acronyms
ABEP Atmosphere-Breathing Electric Propulsion ABIE Air-Breathing Ion Engine AR Aspect Ratio BM Balance Model DSMC Direct Simulation Monte Carlo ECR Electron Cyclotron Resonance EoL End-of-Life EUV Extreme Ultraviolet EP Electric Propulsion EM Electromagnetic FMF Free Molecular Flow GIE Gridded Ion Engine HET Hall-Effect Thruster LEO Low Earth Orbit LIP Lanzhou Institute of Space Technology and Physics LPM Lumped Parameter Model IAG Institute of Aerodynamics and Gasdynamics, University of Stuttgart IPT RF Helicon-based Plasma Thruster IRS Institute for Space Systems, University of Stuttgart RF Radio Frequency RIT Radio Frequency Ion Thruster TPMC Test-Particle Monte Carlo Simulations UV Ultraviolet VLEO Very Low Earth Orbit VKI von Karman Institute for Fluid Dynamics, Aeronautics and Aerospace SC Spacecraft
viii List of Symbols
A m2 Area
Ap - Geomagnetic index D mm Diameter
dp m Particle diameter
3 dv m/s Velocity-space element
3 3 dx m Volume element
CD - Aerodynamic drag coefficient
F 10.7 - Solar radio flux at λSRF = 10.7 cm F N Force
f - Distribution function
h km Orbital Altitude
´23 kb 1.380 649 ˆ 10 J/K Boltzmann constant
Kn - Knudsen number L m Length
Lc m Characteristic length m kg Mass
m˙ mg/s Mass flow rate
n m´3 Particle density
p Pa Pressure
N˙ s´1 Particle flow rate
q m/s Relative Velocity of colliding particles
ix Rin - Particles scattered into a phase-space element
Rout - Particles scattered out of a phase-space element
RC 6371 km Earth’s radius S mm Hexagon short diagonal
T K Temperature t s Time u m/s Average velocity w m/s Thermal velocity v m/s Velocity x m position
π 3.1416 Pi
α ° Incoming flow angle
Ω ° Solid angle between colliding particles
λ m Mean free path
ηc - Collection efficiency
5 2 µC 3.986 ˆ 10 km/s Earht’s gravitational parameter σ m2 Collision cross section
σB - Accommodation coefficient ρ kg/m3 Mass density
x List of Figures
1.1.1 Atmosphere-Breathing Electric Propulsion Systems Concept [1] .... 3 1.1.2 IPT Thruster [2] ...... 3
2.1.1 NRLMSISE-00 Atmospheric Model Data 15/02/2020 at 00:00:00 with F10.7 = 69.5 and Ap = 4.1...... 7 2.2.1 Volume element d3x d3v in phase space from time t Ñ t + dt [3, Ch. 5] 9 2.2.2 Isotropic Maxwell-Boltzmann distribution, showing characteristic velocities. [4] ...... 12 2.2.3 Maxwell interactions between particles [5] ...... 13 2.3.1 General Intake Scheme ...... 15 2.3.2 DSMC of EFD simplified design showing number density [6] ...... 19 2.3.3 Air-Breathing Ion Engine (ABIE) concept [7] ...... 20 2.3.4 ABIE intake design and prototype ...... 21 2.3.5 ESA ABEP proposal with triangular grid intake [8] ...... 21 2.3.6 SITEAL’s RAM-EP proposal with split-ring intake ...... 22 2.3.7 VKI’s RAM-EP proposal with modification on number of slip sections [9] 24 2.3.8 MABHET’s intake proposal [10] ...... 25 2.3.9 TsAGI RAM-EP proposal with square grid intake [11] ...... 26 2.3.10 LIP hybrid intake concept using turbo pumps [12] ...... 27 2.3.11 6U CubeSat with bi-parabolic intake [13] ...... 28
2.3.12 Au, SiO2, and HOPG scattering distributions [14] ...... 29
3.0.1 Methodology Scheme ...... 31 3.4.1 PICLas work flow diagram [15] ...... 34
4.1.1 Intake General Concepts (Red Coloring Indicates Grid Duct Section) . 37 4.1.2 Hexagonal Intake Diagram ...... 38 4.1.3 Parabolic Intake Diagram ...... 38
xi LIST OF FIGURES
4.1.4 Frontal View of the Hexagonal Intake with Multiple Grid Aspect Ratio (AR) 39 4.2.1 Hexagonal Intake with Flow Cutters ...... 40 4.3.1 Cases 15 and 20 Diagram ...... 42 4.3.2 Case 21 Diagram ...... 43 4.3.3 Case 22 Diagram ...... 43 4.3.4 Cases 23 and 24 Diagram ...... 43
4.4.1 ηc and m˙ th of cases 10, 15, and 20 at different different α ...... 48 4.4.3 Case 10 with different accommodation coefficients ...... 50 4.5.1 Pressure Distribution at Chamber Section Case 6 ...... 53 4.5.2 Pressure Distribution of Cases 10 and 19 at 150 km, Pa ...... 55
5.1.1 Optimal Specular Intake Render ...... 58 5.1.2 Optimal Specular Intake Dimensions ...... 58 5.1.3 Parabolic Focus Diagram of Cases 10 and 19 ...... 60 5.1.4 Diffuse Intake Render ...... 61 5.1.5 Diffuse Intake Dimensions ...... 61
A.3.1 Density Distribution of Case 6, m´3 ...... 75 A.3.2 Density Distribution of Case 12, m´3 ...... 75 A.3.3 Density Distribution of Case 15, m´3 ...... 76 A.3.4 Density Distribution of Case 18, m´3 ...... 76 A.3.5 Density Distribution of Case 19, m´3 ...... 77 A.3.6 Density Distribution of Case 20, m´3 ...... 77 A.3.7 Density Distribution of Case 24, m´3 ...... 78 A.4.1 Case 10 α = 5° ...... 78 A.4.2 Case 10 α = 10° ...... 79 A.4.3 Case 10 α = 15° ...... 79 A.4.4 Case 10 α = 20° ...... 79
xii List of Tables
2.1.1 Mass of Atmospheric Species at VLEO ...... 8 2.3.1 Intake Research Proposals ...... 18 2.3.2 Sitael Optimization variables and preliminary mission scenario selection [16] ...... 23
3.4.1 Flow Parameters for intake DSMC Simulations ...... 34 3.4.2 Atmospheric Particles Species Number Density ...... 34 3.4.3 Solar Maximum and Minimum Atmospheric Data ...... 35
4.3.1 Hexagonal Cases Overview ...... 41 4.3.2 Parabolic Cases Overview ...... 42 4.4.1 Hexagonal Cases Results 150km ...... 45 4.4.2 Parabolic Cases Results 150km ...... 46 4.4.3 Case 6, and 12 over different altitudes ...... 47 4.4.4 Case 6 Solar Maximum at 150km ...... 47 4.4.5 Case 6 Flow Misalignment Analysis Results at 150km ...... 47 4.4.6 Case 10, 15, and 20 over different altitudes ...... 48 4.4.7 Case 10 Flow Misalignment Analysis Results at 150km and R = 0.2 .. 50 4.4.8 Case 10 Analysis at 150km ...... 51 4.5.1 Drag vs Thrust Analysis ...... 56
5.1.1 Optimized Specular Intake Performance at Different Altitudes ..... 59 5.1.2 Optimized Specular Intake Performance at Different α ...... 59 5.1.3 Diffuse Intake Performance at Different Altitudes ...... 62
A.1.1 Hexagonal Cases Geometrical Parameters ...... 72 A.1.2 Parabolic Cases Geometrical Parameters ...... 73 A.2.1 Case 10 Verifying Simulations Runs Different Species m˙ at 150km .. 73
xiii LIST OF TABLES
A.2.2 Case 10 Verifying Simulations Runs at 150km ...... 74 A.2.3 Case 10 Multiple Simulation Times at 150km ...... 74
xiv Contents
List of Symbols ix
1 Introduction 1 1.1 Atmosphere-Breathing Electric Propulsion ...... 2 1.2 Problem Statement ...... 4 1.3 Methodology ...... 4 1.4 Outline ...... 5
2 Background 6 2.1 Atmospheric Conditions at Very Low Earth Orbit ...... 6 2.2 Rarefied Gas Flow Physics and Modeling ...... 8 2.2.1 Boltzmann Equation ...... 8 2.2.2 Drifting Maxwellian Distribution ...... 11 2.2.3 Surface Interaction Model ...... 12 2.3 ABEP Intake ...... 14 2.3.1 Basic Concepts ...... 15 2.3.2 Literature Review on Intake Designs ...... 17 2.3.3 Literature Review on Material Selection ...... 28
3 Methods and Tools 30 3.1 Assumptions and Considerations ...... 31 3.2 Mesh Generation ...... 32 3.3 Direct Simulations Monte Carlo ...... 32 3.4 PICLas Tool ...... 33
4 Intake Design and Optimization 36 4.1 Intake Design Considerations ...... 36 4.2 Material Selection ...... 39
xv CONTENTS
4.3 Simulations Cases ...... 40 4.4 Intake Simulation Results ...... 44 4.4.1 Hexagonal Intake ...... 44 4.4.2 Parabolic Intake ...... 45 4.4.3 Design Evaluation ...... 46 4.4.4 Specular Intake Evaluation ...... 49 4.5 Results Analysis ...... 52 4.5.1 Diffuse Intake Analysis ...... 53 4.5.2 Specular Intake Analysis ...... 54
5 Conclusions and Outlook 57 5.1 Conclusion ...... 57 5.2 Outlook ...... 62
References 64
xvi Chapter 1
Introduction
Over the last two decades VLEO has gained researchers attention as it provides a significant amount of benefits in the field of Earth observation and telecommunications. Conceptual studies from different research institutes and governmental agencies have been carried out from CubeSat platforms [13] to full-size platforms [8, 17]. As the orbital altitude is lowered, an increase in the performance of measurement devices is possible with smaller and lighter equipment. VLEO platforms could not only allow higher resolution data for observations and monitoring, but also lighter communication equipment when compared to the higher orbit satellites.
The VLEO orbits are commonly understood as orbits with a mean altitude below 450 km [18]. These orbits provide increased payload performance, improved geospatial accuracy, lower launch mass, simplified End-of-Life (EoL) disposal, and they reduce space-debris collision risk. However the utilization of orbits with such low altitudes presents its own set of challenges, denser atmosphere will significantly increase aerodynamic drag, decaying the orbit in a short period of time. Besides increased drag VLEO environment will produce high levels of Spacecraft (SC) charging and the presence of atomic oxygen will generate a constant erosion of the surfaces of the SC [19].
This masters thesis project is a continuation of the initial ABEP intake design, started in 2015 at IRS [6]. An initial assessment of the existing designs by JAXA and Busek Inc. was performed [20], where an analytical model was created and validated through DSMC. The intake was further optimized performing a sensitivity analysis of the different length over radius ratios (L/R) for the inlet grid structure, and the grid geometry.
1 CHAPTER 1. INTRODUCTION
The results were validated with a simplified model simulated on DSMC and provided the initial design constrains for this project. In 2017 the DISCOVERER project was initiated, aiming to redesign Earth observation satellite platforms by combining new aerodynamic materials, aerodynamic control and introducing ABEP systems for drag- compensation [19].
1.1 Atmosphere-Breathing Electric Propulsion
An ABEP system enables thrust generation in an atmospheric environment without the need of on-board propellant. By collecting and compressing the residual atmospheric particles found at low altitudes, an ABEP system can provide the required propellant mass flow so the on-board thruster is able to overcome the drag force experienced by the SC. Replacing on-board propellant with residual atmospheric particles provides the possibility of long-term missions at VLEO, and increases the payload capabilities as no propellant tank is required. In order to collect sufficient particles an ABEP system must keep an orbital altitude below 250 km, as the atmosphere above might be too rarefied to allow collection by a typical sized SC [19]. A circular orbit is selected for this thesis work, defining the orbital velocity of the SC as
… µC vSC (h) = (1.1) RC + h where µC is the gravitational parameter of the Earth and it is equal to 15 2 3.986 ˆ 10 km/s and RC = 6371 km corresponds to the Earth’s radius. For altitudes (h) corresponding to VLEO the orbital velocity is approximately 7.8 km/s. This section will provides the key concepts of an ABEP system, while introducing the need of an optimized intake for optimal operation of the system. The idea of an ABEP system is to ingest the residual atmosphere of the planet, and use it as propellant for an electric propulsion thruster. The system can be divided in two main sections: the intake or atmosphere collector and the electric thruster, as seen in figure 1.1.1.
2 CHAPTER 1. INTRODUCTION
Figure 1.1.1: Atmosphere-Breathing Electric Propulsion Systems Concept [1]
Several options for Electric Propulsion (EP) thrusters have been investigated over the years [10, 21–24]. While continuous long term operation of the most common EP system, such as Hall-Effect thruster (HET) and radio frequency ion thruster (RIT) have been experimentally verified. They experience significant degradation as surfaces are in direct contact with oxygen [25]. This thesis will use the IPT [2], developed by IRS for the DISCOVERER project. This novel contactless radio frequency (RF) thruster solves the issue of the thruster erosion as there is no component immersed in the plasma, which is contained and accelerated by electromagnetic (EM) fields.
(a) IPT Rendering (b) IPT Assembly 09/2019
Figure 1.1.2: IPT Thruster [2]
The IPT is the latest iteration of a contactless plasma thruster developed at IRS. The thruster main components are the propellant injector or gas inlet, the discharge channel which is encased by the birdcage antenna, this in turn is enclosed by a brass RF shield that isolates the plasma outer environment from the EM fields created by the
3 CHAPTER 1. INTRODUCTION antenna, and shelters it from external influences. An external solenoid is installed to generate a static magnetic field along the axis, thus creating the boundary condition for the formation of helicon waves into the plasma, improving ionization in the discharge channel. Finally, the structure is made of brass which helps minimizing Eddie currents due to the RF fields, while also reducing interactions with the magnetic field fields [1,2]. The thruster can be seen in figure 1.1.2.
To provide the IPT with the necessary particle mass flow for the optimal operation an optimized intake needs to be developed. This component of the ABEP system will collect atmospheric particles, compress them and feed them to the thruster inlet. A more detailed explanation of the intake is presented in section 2.3.
1.2 Problem Statement
As mentioned before, one of the main constrains of an ABEP system is its capability of efficiently collecting enough residual atmosphere to sustain the EP thruster ignition and continuous operation. While in principle this might appear to have a straightforward solution by just funneling the particles, the rarefied gas flow makes this simplistic approach not possible. Particles will be scattered when interacting the intake walls, this will generate an outwards flow, known as back-flow. The back-flow will significantly decrease the effective amount of collected particles supplied to the thruster.
The aim of this thesis project is to develop an intake design which maximizes the collection efficiency by minimizing the back-flow. The intake design must generate the necessary mass flow and pressure required by the IPT optimal continuous operation on VLEO environment. An analysis on material selection, size, and shape definition will optimize for the design for the operation with the IPT to achieve maximum collection efficiency. The design will be validated by simulating the atmospheric conditions with the DSMC module of the in-house software “PICLas”.
1.3 Methodology
In the development of this project the following methodology was implemented. An understanding of the flow physics models for Free Molecular Flow (FMF) was done. This was followed by a deep investigation on a state of the art of different Intake design
4 CHAPTER 1. INTRODUCTION proposed by research institutes all over the globe. The investigated designs provided the initial parameter for the intake design, such as: duct geometries, grid lengths and other geometrical definitions. The designs were developed on CAD software and exported for constructing meshed approximations of the complex geometries for flow dynamics simulations. After the mesh was constructed each design was simulated with the DSMC module from in-house software “PICLas”, the results were visualised and processed using Paraview software. The geometrical parameters of the intake were then modified in an iterative process to optimize its performance according to the IPT requirements.
1.4 Outline
Chapter 1 offers an introduction to ABEP systems, the methodology followed in the development thesis project, as well as the aim of project.
Chapter 2 provides the reader with the theoretical background of this project. Starting by addressing atmospheric conditions at VLEO, and offering the theory behind the modeling of the flow dynamics in this region. A introduction to the ABEP intake is then provided, followed by a state of the art review on previous intake design and material selection.
Chapter 3 present the different assumptions made on the realization of the thesis work, as well as the different methods used for the result generation.
Chapter 4 starts with the design process for the intake, followed the presentation of the different designs. The simulations results are shown here in different plots and tables. This chapter concludes with the in-dept analysis for the different selected design, and selects the optimal configuration for the IPT.
In Chapter 5 conclusions are presented, together with an outlook for future work on validation and prototype development the intake for ABEP system.
5 Chapter 2
Background
This section provides the theoretical base and concepts for the development of an optimal intake for an ABEP system. Atmosphere conditions at VLEO are further described and rarefied gas flow physics modeling is introduced. The probabilistic model description of this region of the Earth’s atmosphere is then later discussed, and surface interaction models are described, which provide the basis for DSMC. Later on the concept of an intake is presented, providing the state of the art investigation for designs and materials selection.
2.1 Atmospheric Conditions at Very Low Earth Orbit
VLEO is generally referred as orbital altitudes below 450 km [26, 27], here it will be constrained to altitudes between 150 - 250 km [28]. The lower limit is constrained by aerodynamic drag, which increases exponentially below the altitude of 150 km, and cannot be compensated by ABEP systems due to infeasible power requirements [28]. While the upper limit of 250 km is set as the atmosphere above might be too rarefied to allow collection by a typical sized SC [19]. This region of the atmosphere is conformed by the thermosphere, which begins at h « 80 km - 90 km and extends to about 500 km [29]. Embedded within the thermosphere, the ionosphere consists of weakly ionized plasma that has strong dynamic and electrodynamic interactions with the neutral gases of the thermosphere. This plasma is created by solar Extreme Ultraviolet (EUV) radiation at wavelengths shorter than 103 nm [30]. It presents a strong variation
6 CHAPTER 2. BACKGROUND due to solar emissions, increasing in thickness and moving closer to the Earth during daylight and retracting over night. The thermosphere is the rarefied region of the atmosphere where the temperature increases dramatically with altitude. The main composition of the lower section is primarily molecular nitrogen N2 and oxygen O2, in the upper regions O2 dissociates by the absorption of solar Ultraviolet (UV) radiation at wavelengths between 130 and 175 nm, creating atomic oxygen O which becomes the dominant gas [30]. Both the thermosphere and ionosphere are strongly influenced by the absorption of solar UV radiation. In the polar regions, the thermosphere and ionosphere are affected by auroral processes, a result from the interaction between the solar wind and the Earth’s magnetic field. In addition they are influenced by dynamic processes propagating upwards from the lower atmosphere, such as: gravity waves, tides, planetary waves, pressure gradients, and scattering processes. The combined effect of the various forces give rise to the great variability existing in the thermosphere-ionosphere system [29,30]. Although several atmospheric models have been developed over the years, only the NRLMSISE-00 is used in this thesis, since it accurately accommodates for the lower thermosphere atmospheric conditions, and has been previously used for work on ABEP systems [23,28]. Figure 2.1.1 shows the averaged particle densities, and neutral temperature ( Tin ) at VLEO for an equatorial orbit. The latitude is fixed to 0° while longitudes are averaged over 0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°, and 360°.
Figure 2.1.1: NRLMSISE-00 Atmospheric Model Data 15/02/2020 at 00:00:00 with F10.7 = 69.5 and Ap = 4.1.
7 CHAPTER 2. BACKGROUND
The data was extracted from the NASA Community Coordinated Modeling Center [31] for the date 15/02/2020 at 00:00:00 with a recorded F10.7 = 69.5 which corresponds to the solar radio flux at a wavelength of 10.7 cm, and the geomagnetic index was recorded at Ap = 4.1. The date was selected as it offered the latest data updated solar activity data for NASA Community Coordinated Modeling Center at the beginning of this project. Additionally, table 2.1.1 shows the different particle masses for the species found at VLEO.
Table 2.1.1: Mass of Atmospheric Species at VLEO
N2 O O2 He Ar H N
10´26 kg 10´26 kg 10´26 kg 10´27 kg 10´26 kg 10´27 kg 10´26 kg 4.652 2.657 5.314 6.646 6.634 1.67 2.326
2.2 Rarefied Gas Flow Physics and Modeling
Traditional flow physics use the continuum model to describe the flow behaviour. Continuum assumes a regular distribution of the mass function with no empty space, allowing macroscopic properties to be defined, as long as there are sufficient molecular density within the smallest considerable volume of the flow. To determine if the flow lays in the continuum regime, the degree of rarefaction of gas particles needs to be defined by the dimensionless Knudsen number Kn = λ/Lc. This quantity is the ratio of the mean free path λ, and the characteristic length Lc. Continuum is valid for Kn < 0.01, while Kn > 10 defines FMF where the particles do not interact with each other, but only with surfaces and walls. The regions between 0.01 < Kn < 0.1 and 0.1 < Kn < 10 are known as slip flow and transitional flow regime respectively [32].
The thermosphere is conformed by rarefied gas, where λ is greater than Lc. As mentioned before this areas conditions greatly vary depending on the numerous forces it is exposed to, meaning its properties and Kn are highly volatile. To properly describe the behaviour of the particles in this region a statistical approach shall be used.
2.2.1 Boltzmann Equation
To describe the state of the gas statistically, a distribution function in phase space f(x, v, t) needs to be defined, such that f d3x d3v is the average number of particles
8 CHAPTER 2. BACKGROUND contained in a volume element d3x about x and a velocity-space element d3v about v at time t. This approach is shown in figure 2.2.1, where f ě 0 and f Ñ 0 as the velocity ( vx,y,z ) goes to infinity. This will guarantee that a finite number of particles have a finite energy [33].
Figure 2.2.1: Volume element d3x d3v in phase space from time t Ñ t + dt [3, Ch. 5]
Bulk properties such as particle density n, mass density ρ, and average velocity u within the volume element can be derived form the distribution function f(x, v, t) by
ż 8 n(x, t) = f(x, v, t) d3v (2.1) ´8
ρ(x, t) = m n(x, t) (2.2)
ż 8 u(x, t) = n´1 f(x, v, t) v d3v = |v| (2.3) ´8 where m is the mass of a single particle and v = w + u. w corresponds to the thermal velocity of the particle [33]. In order to describe f(x, v, t) when t Ñ t + dt, two main assumptions need to be made: the mean inter-molecular distance δ is much greater than the effective particle diameter dp, allowing only binary collisions in a single gas component, and collisions are instantaneous. Knowing the distribution function and following this assumptions, the Boltzmann transport equation can be derived from the
Liouville’s theorem [34], where F is the external force vector, ∇ is the gradient, and ∇v is the gradient in velocity space
( ) Bf F Df + v ¨ ∇f + ¨ ∇vf = (2.4) Bt m Dt coll
9 CHAPTER 2. BACKGROUND
When particles experience a collision their velocities are changed. This change in velocity will happen such that dv1 wont be centered around v1, but rather in a different v0 centered around v0 with v0 ‰ v. Additionally, particles which previously were not contained in the original element dv may end up in dv due to collisions, making 0 ( ) Df f(x, v, t) no longer invariant. The collision term Dt coll will accounts for this particles. It will provide the net rate at which particles are entering the phase-space element, and can be formulated by
( ) Df = Rin ´ Rout (2.5) Dt coll where Rin and Rout corresponds to the particles scattered in-to and out-of the phase- space element [33]. This ratio is defined by the double integral
ż ż ( ) 8 4π 1 1 3 Df (f1f2 ´ f1f2)q ¨ σ(Ω)dΩd v2 = (2.6) ´8 0 Dt coll where q is the relative velocity of the colliding particles, σ is the collision cross- section, and Ω the solid angle. The ’ superscript stands for after collisions and the subscript 1 and 2 define the colliding particle pair. Given the complexity of Eq. 2.6, analytical solutions for Eq. 2.4 are extremely complicated to derive, fortunately two different scenarios can lead to a more achievable solutions [34]. If FMF is assumed the collision term can be neglected, this is often found in diluted gases on space, f(x, v, t) only changes in case of collisions with surfaces, otherwise it remains constant. Furthermore, the lack of an external force to the particle flow simplifies Eq. 2.4 to
Bf + v ¨ ∇f = 0 (2.7) Bt
The second scenario is found when the mean free path λm is way smaller than characteristic length Lc. If λm << Lc inter-molecular collisions are very frequent, making Rin = Rout. This corresponds to each inter-molecular collision scattering a particle out of the phase-space element being counteracted by a particle entering the volume. This second particle is subjected to the same process in a different phase-space element. This process will reach thermodynamic equilibrium as scattered particles are counteracted and provide a solution to Eq. 2.4 in the form of
10 CHAPTER 2. BACKGROUND
1 1 f(v1) ¨ f(v2) = f(v1) ¨ f(v2) (2.8)
2.2.2 Drifting Maxwellian Distribution
An equilibrium distribution of a gas flowing with a constant bulk speed u gives the solution to Eq. 2.8 in the form of the drifting Maxwellian distribution of an ideal gas [34], also known as Maxwell-Boltzman distribution
( ) ( ) m 3/2 m ¨ w2 f(w) = n ¨ ¨ ´ (2.9) 2π kb T 2 kb T
´23 where kb = 1.380 649 ˆ 10 J/K is the Boltzmann constant, m and T corresponds to the particle mass, and temperature respectively and n is the number density. In an equilibrium state the particle interactions do not affect their distribution with time and space. In a undisturbed non-equilibrium state every distribution of an uniform and closed system will converge over time towards the drifting maxwellian distribution. f(w) correspond to a probability and it will be normalized such that
ż 8 f(w) d3w = 1 (2.10) ´8
Considering the bulk velocity u = 0, f(w) becomes an isotropic distribution, isotropy leads to d3w = 4π w2 dw in spherical coordinates. Furthermore g(w) can be defined as the function of the scalar magnitude of w [35, Ch. 7]. The probability distribution g(w) travelling with a scalar (positive) velocity in the interval w Ñ w + dw is defined by
( ) ( ) m 3/2 m w2 g(w) = 4πn w2 exp ´ (2.11) 2π kb T 2 kb T
It can be noted that increasing the temperature will shift the peak of the distribution of higher thermal velocities. Also particle mass and temperature are directly dependent, meaning that heavier particles distributions will behave as low temperature distributions and vice versa. The characteristic velocities of the distribution Eq. 2.11 can then be derived following the assumption of zero bulk velocity [4]:
( )1/2 2 kb T • The probable thermal velocity: vth = m ( )1/2 8 kb T • The mean thermal velocity: w¯ = πm = 1.128vth
11 CHAPTER 2. BACKGROUND √ ( )1/2 2 3 kb T • The mean square thermal velocity: w¯ = m = 1.1225vth 1 2 3 • The average kinetic energy: 2 mw¯ = 2 kb T • The random flux, defined as the flux of particles traversing a surface in a single nw¯ direction: nw¯ i = 4
The plot of Eq. 2.11 displaying the most relevant characteristic velocities can be seen in figure 2.2.2.
Figure 2.2.2: Isotropic Maxwell-Boltzmann distribution, showing characteristic velocities. [4]
Given that w = [wx, wy, wz], it is required to know how the distribution function behaves in every possible velocity direction. By integrating Eq. 2.11 over w∥ and wK, and keeping u = 0, g(w) becomes
( ) ( ) 1/2 2 m 2 m wk g(wk) = n w exp ´ (2.12) 2π kb T 2 kb T which is a one-dimensional Maxwellian density distribution function in the direction of kˆ = [x, y, z]. Each of the velocity components will follow a Gaussian distribution with an average value equal to 0, resulting in no transnational motion of the system [4,35].
2.2.3 Surface Interaction Model
The last section provided the solution for rarefied flow by assuming FMF, but this will not be a valid approach for solving f(x, v, t) when collisions with surfaces occur. To accommodate this the boundary conditions for the velocity distribution function at the solid surfaces need to be specified. Thus, it is required to know how incident
12 CHAPTER 2. BACKGROUND molecules interact with a surface. In general, particles can undergo three basic types of interactions with a surface. Particles can either be absorbed, scattered, or undergo a chemical reaction. Accurate modeling of these processes is highly complex due to the lack of sufficient knowledge of surface properties, such as surface finish, cleanliness, adsorbed gas layers, etc. Several approaches to model these interactions have been investigated [32,36,37], but this master thesis work focuses only on the Maxwell Model, as this model is implemented on the gas-surface interaction module in “PICLas”. The Maxwell Model assumes collisions with surfaces are instantaneous and local and it has been previously implemented in ABEP simulations [6,20,38].
Maxwell Model
The Maxwell Model suggests a simplified approach by using only two types of interactions: specular and diffuse reflection. Figure 2.2.3 illustrates both types of interactions between particles and walls, here the velocity vector of the particles are represented by the black arrows, while grey arrows show the resulting pressure force vectors acting on the surface.
Figure 2.2.3: Maxwell interactions between particles [5]
Specular reflection can be seen as mirror-like reflection, particles rebound elastically when hitting the surface providing no energy exchange. The angle of reflection equals the incident angle θr = θi, and the tangential component of particle velocity vt remains constant. Only the normal velocity component vn will be affected, as it will suffer a 1 complete inversion vt Ñ ´vt. Specular reflation occurs mainly in three scenarios [39]:
• Smooth metal surfaces that have been outgassed through exposure to high
13 CHAPTER 2. BACKGROUND
vacuum and temperatures. • The ratio of the gas molecular weights and surface molecules is small in comparison to unity. • The translational energy of the gas molecules relative to the surface is larger than several eV.
In diffuse reflection, the velocity of reflected molecules v1 is independent of incident velocity. Particles will reach thermal equilibrium and be reflected according to a half- range Maxwellian distribution corresponding to the wall temperature Twall and particle velocity. Purely diffuse reflections typically occur in microscopically rough surfaces and low-speed flows at common temperatures.
The Maxwell model defines a parameter to represent the fraction between diffuse reflection (σB), and specular reflection (1 ´ σB). This parameter is called the tangential momentum or accommodation coefficient, and it is highly dependent on the surface material properties [39]. The accommodation coefficient can be implemented in both the momentum and energy equations [40] which results in
1 1 vt ´ vt Tt ´ Tt σB = = (2.13) vt ´ vt´wall Tt ´ Twall
For realistic FMF and most surface materials, a full accommodation of diffuse reflections σB = 1 provides good simulation results on surface interactions [32, Ch. 5,pp. 118]. However, investigations on new materials [14] suggest that perfect specular or near specular reflection can be archived in FMF.
2.3 ABEP Intake
The main differentiator from ABEP system to other propulsion systems is its capability of collecting residual atmosphere and use it as propellant by the EP thruster. The intake funnels particles from an inlet area (Ain) to the thruster discharge channel entrance
(Aout). An optimal intake design must generate the necessary density and pressure required by the propulsion system for its optimal continuous operation while keeping an acceptable collection efficiency. Figure 2.3.1 shows a general schematic of an intake with its different sections, the grid section represents the inlet duct geometry, the chamber section focuses the collected particles to the IPT thruster discharge channel.
14 CHAPTER 2. BACKGROUND
In this section, the basic concepts of the intake are discussed, along with a review on the state-of-the-art for intake designs, and material selection.
Figure 2.3.1: General Intake Scheme
2.3.1 Basic Concepts
Different particle species will have their specific collection efficiency, and as VLEO composition is highly variable the task to efficiently collect each species becomes more challenging. The main parameter evaluating an intake design is the collection efficiency which is defined to be
N˙ (h) η (h) = outi (2.14) ci ˙ Nini (h)
˙ ˙ where Nout is the collected particle flow and Nin is the incoming particle flow, the subscript i refers to each different particle species i = [1,Ns], the total collection efficiency of an intake at a given altitude is then defined by
ÿNs ηc(h) = ηci(h) (2.15) i=1
˙ The incoming particle flow Nini (h) is derived from the open frontal area of the intake
Ain and free stream conditions: number density nini , and bulk velocity vini . The free stream conditions at VLEO are known to be rarefied, and given that the relative velocity between the SC and the atmosphere is 7.8 km/s, the particle flow can be
15 CHAPTER 2. BACKGROUND treated as hyperthermal. This means that the incoming flow is collimated1 and at high speed [12]. This assumption is valid at sufficiently low temperatures when the random thermal motion of the incoming particles is negligible compared to the speed of the SC. It allows to treat the incoming flow as a collimated beam entering the intake with a single free stream bulk velocity vin(h) [40], which is equal the orbital speed of the SC, so that
ÿNs ÿNs ˙ ˙ Nin(h) = Ain nini (h) vin(h) = Nini (h) (2.16) i=1 i=1 here the relative velocity of the particles vin(h) is perpendicular to the intake area Ain defining vin(h) as
… µC vin(h) = vSC (h) = « 7836m/s (2.17) RC + h
The total particle flow accelerated by the thruster is defined by
ÿNs ˙ Nout(h) = Ain ηini (h) nini (h) vthi (h) (2.18) i=1
By applying the ideal gas assumption, the pressure at the intake chamber is given by
ÿNs
pch = nchi kb Tch (2.19) i=1 where Tch and nch correspond to the temperature and number density in the intake chamber section. The total mass flow can be obtained by
ÿNs ˙ m˙ th(h) = mpi Nouti (h) (2.20) i=1
where mpi is each species particle mass. Following the assumption that the entire collected mass flow (m˙ th) is accelerated by the thruster, the magnitude of resultant thrust force is calculated by
1accurately parallel, with no divergence, and will not disperse with distance
16 CHAPTER 2. BACKGROUND
ÿNs
Fth(h) =m ˙ th(h) vout = ηci (h) nini (h) vin(h) mpi Ain vout (2.21) i=1 where vout is the is the exhaust velocity out of the thruster. EP thrusters can theoretically approach vout values of 100 km/s for heavy propellant such as Xe atoms, and 1000 km/s for light propellants such as He [41]. However, modern RIT and HET operate with vout in the ranges of 20-50 km/s and 10-60 km/s [42,43]. The general description of drag force is
1 F = C n v2 A (2.22) Drag 2 D SC SCt
where ASCt = Ain + ASCbody is total frontal area of the SC, n is the flow density, vSC is the SC orbital velocity, and CD corresponds to the aerodynamic drag coefficient, which is approximately 2.2 for 1U CubeSat at 350 km [27]. This value is considered conservative as the GOCE spacecraft [44] measured CD up to 3.7 - 4.0, but given that the 1U CubeSat model approaches more to the expected SC size, CD = 2.2 is implemented. Complete drag compensation occurs when Fth = FDrag . As seen from Eq. 2.21 and 2.22, just increasing the intake inlet area is not a feasible solution for an optimal intake, as ASCt will also increment, generating a higher FDrag.
2.3.2 Literature Review on Intake Designs
In this section, a detailed review of the current intake design is presented. Although several research teams have approached the possibility of developing an ABEP system for different platforms and thrusters, [13, 22–24, 45], here only proposals that included a dedicated intake design study will be presented. Table 2.3.1, shows an overview of the design that are going to be discussed.
17 CHAPTER 2. BACKGROUND
Table 2.3.1: Intake Research Proposals
Project Intake Type Author Ref. EFD ABEP Intake Tube collector with honeycomb grid IRS. [6,20] intake structure to reduce back-flow. Optimized for the discharge channel of IPG6-S plasma source. ABIE, Air Breathing Intake composed of individual ducts JAXA [7,17, Ion Engine with ECR that form long and narrow passages, 46,47] ionization and a reflector which dams up the flow and reflects partly in mirror direction. RAM-EP RAM-EP: Generic collector with grid ESA [8,9,16] RAM-HET system formed by triangles to damp SITAEL AETHER, incoming velocity and prevent back- VKI Air-Breathing Electric flow. Thruster RAM-HET: Continuation on ESA initial design by SITAEL, intake design was changed to a coaxial split-ring intake with constant aspect ratio division followed by conical collector, and separate ionization chamber to ensure mass flow to thruster. AETHER VKI: Optimization by implementing different number of divisions and aspect ratios between each coaxial cylinder. Proposal of machine learning algorithm for further intake optimization. MABHET, Martian Long and slender tube collector with Busek [10] Atmosphere honeycomb duct grid intake structure Co. Inc. Breathing Hall-Effect to reduce back-flow. Thruster (HET) Air-breathing Ion Square grided intake, with conical TsAGI [11] engine accumulator (collector), and ionization chamber. Design and analysis Hybrid system: passive multi-hole LIP [12] of vacuum air-intake plate followed by active compression device used in by turbo pump system collector. air-breathing electric propulsion Design of an Introduction of a parabolic University [13] Air-Breathing Electric collector using specular gas - surface of Col- Thruster for CubeSat interactions. orado Applications
18 CHAPTER 2. BACKGROUND
IRS: EFD ABEP Intake
The EFD is the fist approach of IRS for the design of ABEP intake, it was optimized for the discharge channel size of the IPG6-S plasma source (test-bed for thruster development). For this work and initial assessment for different duct geometries were conducted theoretically implementing the Balance Model (BM)[20] and the calculated transmittance probabilities for different duct geometries [38], their results were later corroborated with the DSMC of a full-scale rectangular grid intake. During their research, it was found that cylindrical and hexagonal duct geometries were the ones having the highest collection efficiencies, with a ηc « 0.4 for realistic scenarios. The most relevant conclusion of this work is the definition of three geometrical relations for an optimal intake design. The first one being the area ratio of Ain/Aout < 100 as a higher ratios will lead to a decrease in the gain of the m˙ th. Secondly, it was presented that ”medium” AR in the grid geometry will lead high inflow transmissions while keeping low back-flow transmissions. Finally, it was found that for the collector AR a value of 10.667 will lead to an increase of 5% in the intake’s efficiency. These results were tested by DSMC under Mars atmospheric conditions. A simplification of the design was made to a squared shaped grid intake and can be seen in figure 2.3.2, with an approximate total length of 0.454 m, a frontal area of 0.005 38 m2, and a duct radius of
2.5 mm. The optimized design obtained a ηc « 0.34.
Figure 2.3.2: DSMC of EFD simplified design showing number density [6]
19 CHAPTER 2. BACKGROUND
JAXA: ABIE
JAXA introduced the concept of ABIE [17] back in 2003. Since then different research teams have made substantial research on the development of the project [7, 46–48]. The system is composed of an intake, a discharge chamber where the collected atmosphere is ionized actively by an Electron Cyclotron Resonance (ECR) ion engine. A grid configuration is used for ion beam acceleration and an external neutralizer is implemented. The concept can be seen in figure 2.3.4, the main differentiator with other development on ABEP intakes is that the intake is located around the SC body instead of upfront.
Figure 2.3.3: ABIE concept [7]
The air intake design can be seen in figure 2.3.4a, it consists of a collimator section, which is composed of several slender ducts that form narrow and long passages. And a reflector section, where particles impact the surface and are directed to the ionization area. Figure 2.3.4b shows the latest development on the ABIE intake, which was experimentally tested with a N2 and atomic oxygen using a laser detonation beam source to simulate VLEO environment [48]. The intake prototype consisted of 796 ducts with 0.15 mm thickness and a diameter of 4.5 mm. Two tube lengths were tested in the study, 20 mm and 67 mm. Although the test set-up could not provide a continuous particle flow for the intake, the experiment showed that both lengths archived a nearly identical pressure of around 0.1333 Pa. Suggesting that the difference in length of the collimator does affect the incoming N2 molecular flow. In contrast, it was also found that
20 CHAPTER 2. BACKGROUND
the longer option (67 mm) performs better by preventing the back-flow of N2 molecules and maintaining the high pressure for a longer period (30 ms versus < 5 ms).
(a) Render showing collimator ducts [7] (b) Test prototype [48]
Figure 2.3.4: ABIE intake design and prototype
ESA: RAM-EP Gridded Ion Engine (GIE) RIT-10
In 2007 an ESA study on an ABEP concept design and mission profile was published [8]. The schematic of the intake concept can be seen in figure 2.3.5. The intake consisted of a collector cylinder with a frontal area of 0.6 m2 and the grid system used to stop the particles at the entrance of the collector to increase the pressure and reduce the back-flow.
Figure 2.3.5: ESA ABEP proposal with triangular grid intake [8]
Different collector length and varying collector configurations (concave, straight, and divergent) were tested under DSMC simulations. Results showed an optimal length of 1 m with a pressure of 1 ˆ 10´3 Pa, while the collector configuration yielded no significant results.
21 CHAPTER 2. BACKGROUND
SITAEL S.p.A: RRM-EP Double stage HET
Based on the ESA study from 2007 [8], the Italian company SITAEL S.p.A started their development of an ABEP system in 2015 and since then they have conducted substantial research on the field [16, 49–52]. The design consists of a passive split- ring intake, an intake-to-thruster collector interface, and a double stage HET, in which the first stage enhances the ionization of the collected particles by plasma confinement and ion magnetization and the second stage electrostatically accelerates the plasma. An overview of the design can be seen in figure 2.3.6a
(a) Internal view of the split-ring intake [51] (b) Frontal scheme of split-ring intake [49]
Figure 2.3.6: SITEAL’s RAM-EP proposal with split-ring intake
The intake concept is a cylindrical multi-ducts channel with constant duct cross-section. The developed prototype has a 3 split-ring configuration, and the schematic showing the frontal view is shown in figure 2.3.6b. The design has a duct aspect ratio2 equal to 6 and an area ratio3 in the range of 0.15 - 0.3. This ratios generate compression ratio of around 95 - 140 and a collection efficiency ηc « 0.28 - 0.32. The prototype is optimized for a 200 km orbital altitude.
In their latest publication [16], the intake was re-optimized under pattern-search optimization algorithm for several variables. The constrains are given by their previous work on intake design and the VEGA launcher system. The results yielded in the selection of an orbital altitude of 195 km for a preliminary mission scenario. The optimization variables followed by the selected scenario can be seen in table 2.3.2, all selected values as marked as approximated as are extracted from the plots presented in the article. 2Duct aspect ratio, defined as the ratio between the length and the square-root of the cross-section area of each inlet duct [52]. 3Area ratio, defined as the ratio between the thruster outlet area and the intake inlet area [52].
22 CHAPTER 2. BACKGROUND
Table 2.3.2: Sitael Optimization variables and preliminary mission scenario selection [16]
Variable Range Selection Orbit altitude 140 - 250 km 195 km Ionization stage inlet area 0 - 0.10 m2 « 0.08 m2 Ionization stage length 0 - 5.00 m « 0.55 m Intake total inlet area 0 - 3.00 m2 « 0.45 m2 Intake length 0 - 5.00 m « 0.65 m Number of intake ducts 0 - 300 « 140 Total thruster operating voltage 0 - 600 V « 600 V Voltage utilization ratio4 0 - 1.00 « 0.85
Although their results seem promising and a mission scenario was presented for the 195 km orbit. Validation under simulation or experimental results is expected to corroborate the results of the optimization algorithm.
SITAEL & von Karman Institute for Fluid Dynamics, Aeronautics and Aerospace (VKI): AETHER
VKI joined SITAEL RAM-HET concept on 2019, and the project was renamed AETHER. In their study, the BM was implemented and transmission probabilities for different duct geometries were calculated, these topics are furthered discussed in Chapter 3. In their study a new parameter was introduced, the reduced thruster transmissivity defined as ϕ2˚ = Aout/Ainϕ2, which represents the transmissivity of the thruster referred to the intake’s frontal area. Their results found that a large ϕ2˚ is required to archive high collection efficiency ηc. The efficiency of the ABEP system is highly related to the capability of the intake to provide a sufficient collection efficiency
ηc, such that the EP system can operate at its optimal and deliver the expected specific impulse. After these results, an Lumped Parameter Model (LPM) sensitivity analysis was used to investigate the relative contribution of the VLEO environment on the propulsion system’s performance. The LPM results suggested that all geometric parameters of the intake design play a key role in the ABEP system performance. Regarding the intake performance, it is only sensitive to the aspect ratio of the ducts, as the effective ram area ratio designated by Ain/Aout does provide significant effects. 4Voltage utilization ratio, the fraction of discharge voltage applied to the acceleration stage.
23 CHAPTER 2. BACKGROUND
However, ϕ2˚ and the collection area Ain play a substantial role. It was found that efficient thermal design of the intake brings the possibility of modifying the compression performance without affecting the collection efficiency. On the other hand, the variation on the thruster specific impulse does not affect intake’s performance, as ϕ2˚ was found to be the dominant parameter.
(a) 2D and 3D view of 11 section intake (b) Parametric view of 4 section intake
Figure 2.3.7: VKI’s RAM-EP proposal with modification on number of slip sections [9]
To further verify their results simulation on DSMC were conducted, the 2-dimensional schematic of the design used on the simulation can be seen in figure 2.3.7a, while the 3-D model was used for investigating chemical reactions in the gas phase. In their 2-D simulations, the effect of the Knudsen variation was investigated and it was found that the performance maximum degradation is about 3% for Kn « 15 and 11% for Kn « 10. The 3-D model was used to assess the misalignment angle effect on the incoming flow and the accommodation coefficient assumption. Their results suggested that introducing specular reflections increases the collection efficiency and decreases the density ratio. While the misalignment angle has a significant impact on ηc and density ratio, at 5° the collection efficiency decreases by 10 ´ 20%, and at 10° more than 40% degradation was shown.
After identifying all the key aspects affecting the intake performance a differential evolution optimization algorithm was developed for multi-objective optimization. This method is going to be used to optimize the design seen in figure 2.3.7b, for a sun- synchronous orbit at 200 km. The design presents four coaxial cylinders with three, four, five, and six-channel separations of the same length.
24 CHAPTER 2. BACKGROUND
Busek Co. Inc. MABHET, Martian Atmosphere-Breathing HET
The USA company Busek Co. Inc developed MABHET in 2012, the study performed a feasibility study of an ABEP dedicated for the martian atmosphere. The SC concept can be seen in figure 2.3.8a. Although Mars atmosphere is formed primarily of CO2, the conditions for the ABEP systems remain the same, as at the selected orbital altitudes (120 - 180 km) particle flow is rarefied and thermalized as well. The intake schematic can be seen in figure 2.3.8b, it consists of a 3.7 m long tube with a 0.6 m diameter. The intake also includes a honeycomb structure of ducts at the entrances which proved to increase the performance.
(b) Scheme of intake
(a) Rendered parametric and frontal views
Figure 2.3.8: MABHET’s intake proposal [10]
The selection of a long tube came from the idea that particles are pushed towards the end of the tube and new incoming particles will impact this volume further increasing the pressure and density in that area. Where the thruster inlet is going to be located, this phenomenon is identified as ”collision cascade”. The intake was analysed under DSMC software, which resulted in the intake length for a 100 ˆ compression factor and collection efficiencies ηc « 0.2 ´ 0.4 [10].
TsAGI: ABEP, Air-breathing Ion engine
Another study started in 2015 [22] and further developed in 2017 [11] presents a similar engine design as SITAEL. Composed of an intake channel section, an accumulator, an ionization stage, and the plasma acceleration system. In the optimization process, the maximum value of molecular concentration at the input of ionization was defined by two parameters: B which is determined by the molecule deceleration rate, and ϕ defined by the inlet channel geometrical shape and the velocity ratio in the incoming flow.
25 CHAPTER 2. BACKGROUND
The optimization process was conducted for three duct geometries: truncated cone or confuser, cylindrical channel, and square cross-section channel. Their results suggest the use of a square cross-section channel formed by a honeycomb structure, as it provides compactness, adjustable wet area, and could the spacecraft drag since it is possible to hide its lateral surface behind the input cross-section of the intake [11]. The design for a prototype can be seen in figure 2.3.9, the paper suggests more research is being done for the intake optimization and testing but until now no updates have been given.
Figure 2.3.9: TsAGI RAM-EP proposal with square grid intake [11]
Lanzhou Institute of Space Technology and Physics (LIP)
In 2015, the Chinese research institute LIP published a study for the development of an ABEP system. Their proposal differs from the majority of known systems as it involves an active method of compression, a pair of turbo-molecular pumps. The design is conformed of coaxial cylinders with different stages as seen in figure 2.3.10. The front a 500 mm multi-hole plate will passively compress the molecular flow. The plate has a porosity5 of 0.95 and the cross-section of every hole in the plate is square. The flow then encounters a ”Big turbo” made of a few rotors and stators of a turbo-molecular pump and the followed by the ”Small turbo”, which is a small hybrid turbo-molecular pump and a miniature scroll pump in a series configuration. The design was optimized under Test-Particle Monte Carlo Simulations (TPMC) software for some parameters such as: the length between the blade root and the axis of the turbo rroot = 250 mm, and the axial distances from the turbo to the multi-hole plate L1 = 37.5 mm and the small
5Assumed to be the ratio between efficient frontal area and total frontal area of the plate.
26 CHAPTER 2. BACKGROUND
turbo-molecular pump L2 = 37.5 mm, the inlet radius of the small turbo-molecular pump ra = 62.5 mm.
Figure 2.3.10: LIP hybrid intake concept using turbo pumps [12]
The thickness of the multi-hole plate Lt was assumed to be negligible when compared with other lengths of the design, also the collisions between molecules in the multi-hole plate were ignored for the simulations. A low-speed case with 5 stages turbo and a high-speed case with 3 stages turbo were simulated for altitudes between 150 - 240 km.
The collection efficiency for the high speed case were ηc = 0.5647 - 0.5785 and and for the low speed case ηc = 0.4167 - 0.4260. The results show that the collected gas can already be compressed significantly and reach atmospheric pressures by the implementation of only the ”small turbo” and the scroll pump. This solution will an added weight of 5.7 kg for a small turbo-molecular pump and a 0.84 kg for the miniature scroll pump. Besides the weight, the pump system will require a total power consumption on the range of 27.1 - 150.3 W. Although the study strongly suggests that the pump system is suitable and somehow required for an efficient ABEP system, the added weight and power requirements may prove to be insufficient. As more research has been done by passive compression systems, the requirement of an extra compression system is not clear. Also, to ensure mission feasibility the pump system should have a backup system, as it is a high priority component of the SC, which will lead to a higher weight.
27 CHAPTER 2. BACKGROUND
University of Colorado
In 2018, the University of Colorado developed a new intake design using the optical proprieties of a parabola [53]. Following the assumption that clean satellite surfaces will reflect incoming particles nearly specularly, three different geometries were tested for capture efficiency: cone, pyramid and parabola. The later resulting in almost 100% capture efficiency which is affected by the dimension of the parabola. The 6U CAD prototype can be seen in figure 2.3.11, where two 10 cm long intakes are included. The shapes were simulated on MolFlow+ software a “test-particle MonteCarlo” algorithm for rarefied gas flow modeling [13].
Figure 2.3.11: 6U CubeSat with bi-parabolic intake [13]
2.3.3 Literature Review on Material Selection
In this section, a detailed review of the material selection for the ABEP intake is presented, crucial step in the development of an atmospheric intake. The selected material and surface finish will provide the building block for the intake, as it will define the gas - surface interactions which rule the flow behaviour at FMF. Moreover, such material must be resistant to the continuous erosion found at VLEO.
Different metals, alloys, and polymers have been suggested as plausible candidates for space applications, but experimental testing at VLEO conditions has prove to be challenging as oxygen (O) concentration factor is strongly limited by the thermal cycling processes and recombination reactions [54, 55]. It is found that glasses and ceramics organic materials will not react with O, organic materials will experience different degrees of erosion depending on specific environmental conditions [56]. Metals such as copper, gold, stainless steel, tantalum, molybdenum, aluminium, alloys, etc. were further investigated on experimental set ups at the International Space Station (ISS) [57]. It is found that oxide will appear on the surface all metals changing the optical properties drastically. Aluminium will face considerable corrosion with a
28 CHAPTER 2. BACKGROUND maximum material loss of 300 μm per year [55]. Titanium, titanium nitride, copper and molybdenum have been further investigated under exposure to ion mixture of nitrogen- oxygen [58]. It is found that coating the surface with oxides and nitrides results in an increased resistance to corrosion, as atoms of the tested material are not expelled from the surface. The investigation found that nitrogen or oxygen atoms (found in the oxides and nitrides) are expelled from the surface, but they are also immediately replaced by new atoms from the gas medium creating a protective film [59]. Although resistance to corrosion for a typical mission duration has been achieved surface properties of these material can not be precisely determined. Surface topology will change considerably during the mission life time, making diffuse scattering the more realistic gas - surface interaction.
However, specular or near specular scattering can be obtained for certain materials. gold (Au), of highly oriented pyrolytic graphite (HOPG), silicon dioxide (SO2) are further investigated by the Department of Chemistry and Biochemistry, Montana
State University [14]. Experimental results using a hyperthermal beam of O and O2 characterized the scattering dynamics of these materials. The results can be seen in figure 2.3.12, it is concluded that both SiO2 and HOPG offer interesting properties for gas surface interactions, but HOPG offers almost a perfect specular scattering [14]. Which makes HOPG an ideal candidate for the development of an atmospheric intake that can take advantage of optical properties.
Figure 2.3.12: Au, SiO2, and HOPG scattering distributions [14]
29 Chapter 3
Methods and Tools
In this section, the methodology followed in the development of this thesis project is going to be introduced. Figure 3.0.1 represents the sequence of the different methods implemented on the development of this master’s project. Each method derivation is described in detail under its specific section. Furthermore, an initial assumption and consideration section gives a general overview of the hypothesis used in these methods.
30 CHAPTER 3. METHODS AND TOOLS
Research Question How to increase the particle density and pressure for an ABEP system that operates at VLEO?
Theoretical Background
Hypothesis The development of an intake could provide the required mass flow while reducing the back flow of particles increasing the overall performance of the ABEP system
State-of-the-art Investigation
Material Selection (Surface Interactions) Intake Design
Feedback and Optimization Geometric CAD Modeling & Parameters Mesh Generation
Result Analysis
3D Direct MonteCarlo Simulations
Conclusions Approve / Reject Hypothesis
Figure 3.0.1: Methodology Scheme
3.1 Assumptions and Considerations
In this section, the assumptions that were used when implementing the different models, and simulations are presented.
While developing the simulations it is assumed that the temperature of the chamber is equal to the one of the wall and that all particles have gone already through wall
31 CHAPTER 3. METHODS AND TOOLS collisions and, have lost all the kinetic energy in this process, setting the chamber velocity equal to 0 m/s. Therefore the flowfields inside the chamber can be treated as free-molecular or hyperthermal flow. This approach was introduced in [32, Ch. 7], and it states that collisionless plasma flowfields can be formed by the superimposition of different classes of molecules, which can be separate streams with independent temperatures, but with a relative velocity between them or a surface. Thus it can be assumed that particles in the chamber section will only have a thermal movement with respect to the chamber wall temperature.
3.2 Mesh Generation
The simulation of flow dynamics and its interactions with complex geometries can only be achieved by dividing the desired domain into simpler elements that can be used as discrete local approximations of the complete model. The mesh uses simpler geometries: triangles, prisms, tetrahedrons, or hexahedrals to accommodate the complex geometry and flow volume conditions. The mesh will directly influence the accuracy, convergence, and speed of the simulation. The software used in this project for the meshing process is HEXPRESS 9.1, and the consideration followed in the meshing process is the following:
• No negative cells • No concave nor twisted cells • Double Symmetry over X and Y planes • Optimize to minimum number of cells for FMF simulation.
3.3 Direct Simulations Monte Carlo
As mentioned in section 2.2, flows with high Knudsen numbers cannot be treated with classic continuum methods, as represented usually by the Navier–Stokes equations. Instead, the Boltzmann equation needs to be solved, this has proven to be a complex and highly time-consuming therefore probabilistic approximations are the more feasible approach, see section 2.2.2. The DSMC method takes advantage of this approach to generate simulations of a large number of real molecules in a probabilistic simulation to solve the Boltzmann equation, with the fundamental assumption that the molecular
32 CHAPTER 3. METHODS AND TOOLS movement and collision phases can be decoupled over time periods that are smaller than the mean collision time. The methods discretize the real particle domain into a global distribution function, each particle is then tracked inside the computational domain. After each time step ∆t boundaries are generated and particles are moved according to the equations of motion and their t ´ ∆t parameters (position and velocity), the process is repeated for each particle until they exit the computational domain. While moving, each particle will experience intermolecular collisions or collisions with surfaces or boundaries, this will lead them to exchange momentum or undergo chemical reactions. These processes can be implemented into a DSMC simulation through different probabilistic models thanks to the individual treatment of particles and their decoupling from the movement. Simulation results for the macroscopic properties such as density, temperature, and velocity of the gas flow are obtained by sampling all over the particles after the flow has become stationary.
3.4 PICLas Tool
The “PICLas” software is developed by IRS and Institute of Aerodynamics and Gasdynamics, University of Stuttgart (IAG). The code is a three-dimensional, parallelized simulation framework with DSMC and Particle-in-Cell, and other particle methods that can be coupled for the simulation of non-conventional flow and collisional plasma flows. The working scheme of the software can be seen in figure 3.4.1. For the scope of this project, only the DSMC block plus the ”Gas-Surface Interaction” module were included in the compilation of the software, as FMF conditions can be simulated with this set-up. Additionally, “PICLas” allows the definition of specular and diffuse reflection to the surface boundary conditions. The variable “R” which represents the momentum accommodation is utilized to decide whether a diffuse (R > X) or specular reflection (R < X) occurs upon particle impact, where X = [0, 1) is a random number [60].
33 CHAPTER 3. METHODS AND TOOLS
Figure 3.4.1: PICLas work flow diagram [15]
The flow parameters use in the DSMC can be seen in table 3.4.1, while the atmospheric particle data is presented in table 3.4.2.
Table 3.4.1: Flow Parameters for intake DSMC Simulations
h Tin Twall vSC nin,total
km K K m/s 1/m3 150 582.0 300 7818.2 4.131E+16 180 666.1 ” 7800.3 1.042E+16 200 690.7 ” 7788.5 4.967E+15 220 703.9 ” 7776.6 2.560E+15 250 713.4 ” 7759.0 1.045E+15
Table 3.4.2: Atmospheric Particles Species Number Density
h N2 O O2 He Ar H N
km 1/m3 1/m3 1/m3 1/m3 1/m3 1/m3 1/m3 150 2.504E+16 1.406E+16 2.139E+15 1.252E+13 4.604E+12 1.163E+13 1.419E12
180 4.913E+15 5.111E+15 3.600E+14 9.278E+12 4.723E+12 6.751E+11 2.360E+13
200 1.901E+15 2.908E+15 1.271E+14 7.954E+12 1.244E+12 5.427E+11 2.182E+13
220 7.732E+14 1.716E+15 4.675E+13 6.918E+12 3.523E+11 4.839E+11 1.649E+13
250 2.121E+14 8.067E+14 1.089E+13 5.688E+12 5.775E+10 4.412E+11 9.348E+12
34 CHAPTER 3. METHODS AND TOOLS
For selected concepts two additional scenarios to account for solar maximum and minimum were simulated. Table 3.4.3 shows the flow parameter for the two extra scenarios. The date 01/04/2014 represents solar maximum with F10.7 = 149.4 and Ap = 4.8. The 01/12/2019 accounts for solar minimum with F10.7 = 68.5 and Ap = 3.3. These dates are based on 24th and 25th Solar Cycle [61], the data is extracted from the NASA Community Coordinated Modeling Center [31] following the same procedure utilized in section 2.1.
Table 3.4.3: Solar Maximum and Minimum Atmospheric Data
Solar N2 O O2 He Ar H N Tin Activity 1/m3 1/m3 1/m3 1/m3 1/m3 1/m3 1/m3 K Max 3.04E+16 2.03E+16 1.74E+15 1.93E+13 5.17E+13 5.35E+11 2.25E+13 688 Min 2.66E+16 1.44E+16 2.00E+15 1.31E+13 4.65E+13 1.36E+12 1.04E+13 585
To successfully run the simulation a specific environment on a Linux machine needed to be constructed. Additionally, the simulated geometries needed to be transformed into a mesh with the correct format (.h5). The different environments used for this master’s thesis project as well as the software versions are presented in the following box. Simulation Environment Operating system Windows 10 Home Version 10.0.18362 4 CPUs - RAM: 6Gb Orace VM - VirtualBox 6.1: Linux - Ubuntu 16.04LTS - 3.5Gb Linux Server - Ubuntu 16.04LTS - 8 CPUs - RAM: 15Gb CAD & Mesh software Autodesk Inventor 2018 - MS Windows x86-64 HEXPRESS 9.1 - MS Windows x86-64: version 2.345.2.3 HOPR - Ubuntu 16: version 1 Build tools cmake - Ubuntu 16: version 3.17.0 OPENMPI - Ubuntu 16: version 2.15 HDF5 - Ubuntu 16: version 1.10.3 DSMC Software PICLas - Ubuntu 16: version 1.6.0
35 Chapter 4
Intake Design and Optimization
In this section, the design of the intake is introduced. An initial investigation for the general dimensions is conducted, to assess different intake’s lengths, inlet diameters, and grid dimensions. The results provide an initial assessment of existing intake performance. Two general concepts are designed, the grid hexagonal intake, and the specular parabolic intake. These concepts are further investigated to develop and optimize the intake design. Optimized designs are then characterized under different flow conditions and material properties.
4.1 Intake Design Considerations
The intake’s main design constraints are defined by early IPT testing, which drives the input propellant flow rate in the range of 1 - 0.1 mg/s for Ar corresponding to an estimated pressure in the discharge channel of pch « 1 - 7 Pa. Additionally, the IPT has a discharge channel of 37 mm inner diameter, hence the outlet diameter of the intake should be fixed to this value. Previous investigations conducted by IRS describe the behavior of different geometries in FMF. In these studies, it is concluded that the hexagonal geometries are the most adequate for an intake grid geometry because they present lower back-flow transmission probabilities for single and multiple ducts [38]. Several sensibility analysis are performed for optimal AR of the duct grid geometry and the results are verified by DSMC [6,20]. Knowing this, hexagonal grid geometry is implemented in different intake designs for 3D optimization. The two general concepts can be seen in figure 4.1.1.
36 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
A A B B
SECTION B-B SECTION A-A
(a) Hexagonal Intake (b) Parabolic Intake
Figure 4.1.1: Intake General Concepts (Red Coloring Indicates Grid Duct Section)
The aspect ratio is defined by
{ L R = S for the hexagonal intake AR = 2 (4.1) R D R = 2 for the parabolic intake where S is the hexagonal duct short diagonal, and D is the diameter. The different variables for the hexagonal and parabolic intake can be seen in figures 4.1.2 - 4.1.3.
The hexagonal intake investigates how different grid AR on diffuse surface properties affect the overall ηc. The hexagonal intake outer geometry is developed to maximize
37 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION the packing ratio of the grid and facilitate simulations. In contrast, the parabolic intake seen in figure 4.1.1b, maximizes ηc by taking advantage of specular scattering surface properties.
R_Grid
e
k
a
t
n
I
_
R
e
k
a t S_Grid
n
I
_
S
D
DETAIL D SCALE 3 : 1
L_Grid
e
k
a
t
n
I
_
L
Chamber Angle
Figure 4.1.2: Hexagonal Intake Diagram
D_IPT
D_Intake L_Intake
Figure 4.1.3: Parabolic Intake Diagram
Furthermore, for the hexagonal intake concept two grid variations are considered: constant and variable grid AR. A schematic showing the variable grid AR can be seen in figure 4.1.4.
38 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
"Large" AR "Small" AR
Figure 4.1.4: Frontal View of the Hexagonal Intake with Multiple Grid AR
4.2 Material Selection
The main design driver of the intake comes from the material selection. Previous investigations on intake design are based on titanium, titanium alloys or other metals that can withstand the degradation on VLEO. These metals offer a significant resistance to corrosion, but are bound to diffuse scattering in gas - surface interactions. The hexagonal intake is designed around this type of interaction and uses long hexagonal ducts to reduce the back-flow from the intake.
Alternatively, the specular parabolic intake is designed around the specific material properties of Highly Oriented Pyrolytic Graphite (HOPG), and Silicon Dioxide (SO2), which offer specular or near specular surface interaction with rarefied gases. This intake design evolves around the optical properties of a parabolic shaped geometry.
To fully evaluate the advantages of HOPG, and SO2 both general concepts are simulated under perfect specular scattering. Additionally, the hexagonal intake design is retrofitted with a set of fins or flow cutters at the back of the collector. The design is simulated with different combinations of specular and diffuse properties, its configuration can be seen in figure 4.2.1.
39 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
6x Flow Cutters or "Fins" C
SECTION C-C C
Figure 4.2.1: Hexagonal Intake with Flow Cutters
4.3 Simulations Cases
In the simulations each case refers to a specific intake geometry. Case 1 is a single square shaped volume which is simulated for all altitudes and inflow angles to verify correct definition of the simulation parameters. Therefore results for case 1 are not presented. The simulations are divided in the two general geometries presented in figure 4.1.1. An overview of the hexagonal intake cases is presented in table 4.3.1, where “Simple” indicates constant AR hexagonal grid. Case 2 and 3 only differ on the chamber angle, 60° for case 2 and 45° for case 3. All remaining hexagonal intake cases have a chamber angle of 45°. Case 6 investigates the implementations of two different AR for the duct grid geometry, presented in figure 4.1.4.
40 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
Table 4.3.1: Hexagonal Cases Overview
Type Intake AR Grid AR Area Ratio Case 1 Flow Check - - - Case 2 Hexagonal Simple 1.00 8.00 3.00 Case 3 Hexagonal Simple ” 8.00 ” Case 4 Hexagonal Simple ” 10.00 ” Case 5 Hexagonal Simple ” 25.00 ” Case 6 Hexagonal Multi AR ” 8.00 / 11.20 ” Case 7 Hexagonal Simple ” 4.00 ” Case 8 Hexagonal Simple 10.67 5.00 2.24 Case 9 Hexagonal Simple 4.00 20.00 2.16 Case 11 Hexagonal Simple 4.00 10.00 2.16 Case 12 Hexagonal Simple 2.12 11.67 2.16 Case 13 Hexagonal Simple 4.00 24.00 2.16 Case 14 Hexagonal Simple 2.88 21.25 3.00 Case 16 Hexagonal Simple 2.50 10.00 8.00 Case 17 Hexagonal Simple Fins 2.50 10.00 8.00
An overview of the parabolic cases is presented in table 4.3.2, where “Extended” investigates the possibility of larger area ratios to increase m˙ th. In cases 10, 18, and 19 the different geometric parameters affect the focus of the parabola. In cases 15 and 20 the hexagonal duct grid geometry is included as seen in figure 4.3.1.
41 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
Table 4.3.2: Parabolic Cases Overview
Type Intake AR Grid AR Area Ratio Case 10 Parabolic 3.85 - 4.27 Case 15 Parabolic with Grid 3.85 15.00 4.27 Case 18 Parabolic 2.00 - 6.18 Case 19 Parabolic 2.19 - 4.83 Case 20 Parabolic with Grid 3.85 5.00 4.27 Case 21 Parabolic Extended 3.14 - 9.15 Case 22 Parabolic Extended 2.47 - 8.95 Case 23 Parabolic Extended 2.23 - 9.15 Case 24 Parabolic Extended 1.98 - 9.15
The grid section in case 15 and 20 is simulated under diffuse and specular surface interactions, and different incoming flow angles (α).
Figure 4.3.1: Cases 15 and 20 Diagram
Diagrams of the “Extended” cases can be seen in Figures 4.3.2 to 4.3.4. Case 21 increases the inlet area by adding a second parabola at the front, while in case 22 a cone is included.
42 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
Figure 4.3.2: Case 21 Diagram
Figure 4.3.3: Case 22 Diagram
In cases 23 and 24 a the conical section is added to the back of the parabolic geometry, seen in figure 4.3.4. This conical section is simulated under specular and diffuse surface interactions. The cone section has an angle of 30° for case 23 and 45° for case 24.
Figure 4.3.4: Cases 23 and 24 Diagram
43 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
4.4 Intake Simulation Results
In total 23 cases are simulated, in appendix A.1.1 and A.1.2 the geometrical parameters for all the cases are presented, where D is the inlet diameter and a corresponds to the rate of change of the parabola in the form of y = a x2. To optimize the highly time consuming simulation process, all cases where initially run at 150 km altitude, later the most promising designs are tested in different altitudes, surface properties and flow conditions to fully evaluate their performance.
4.4.1 Hexagonal Intake
The results for the hexagonal cases can be seen in 4.4.1. While these concepts are based on diffuse scattering σB = 1, some cases are also simulated with specular scattering on specific boundary conditions. These hybrid cases are represented by
“SP”, where the specified boundary condition is simulated with σB = 0.
44 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
Table 4.4.1: Hexagonal Cases Results 150km
2 2 ˙ ˙ AIntake m Fill Ratio Ain m Nin 1/s Nout 1/s ηc m˙ mg/s Case 2 0.008 50.6% 0.004 1.31E+18 1.99E+17 0.152 0.0093
Case 3 0.008 50.6% 0.004 1.31E+18 2.44E+17 0.187 0.0114
Case 4 0.008 44.4% 0.003 1.15E+18 1.47E+17 0.128 0.0068
Case 5 0.008 50.6% 0.004 1.31E+18 4.15E+17 0.317 0.0193
Case 6 0.008 51.8% 0.004 1.34E+18 6.14E+17 0.458 0.0240
Case 7 0.008 50.6% 0.004 1.31E+18 2.21E+17 0.169 0.0085
Case 8 0.004 69.0% 0.003 9.93E+17 1.38E+17 0.139 0.0064
Case 9 0.004 87.9% 0.003 1.18E+18 3.40E+17 0.288 0.0148
Case 9 0.004 87.9% 0.003 1.18E+18 3.22E+17 0.272 0.0140 SP: Chamber
Case 9 0.004 87.9% 0.003 1.18E+18 3.47E+17 0.294 0.0151 SP: Chamber, Intake
Case 9 0.004 87.9% 0.003 1.18E+18 4.38E+17 0.371 0.0189 SP: All
Case 11 0.004 87.9% 0.003 1.18E+18 4.75E+17 0.402 0.0207
Case12 0.004 92.6% 0.004 1.24E+18 5.43E+17 0.437 0.0212
Case 13 0.004 83.3% 0.003 1.12E+18 5.14E+15 0.005 0.0002
Case 14 0.008 88.5% 0.007 2.29E+18 3.94E+17 0.172 0.0172
Case 16 0.057 79.2% 0.045 1.46E+19 2.61E+17 0.018 0.0103
Case 16 0.057 79.2% 0.045 1.46E+19 2.84E+17 0.020 0.0109 SP: All
Case 17 0.057 79.2% 0.045 1.46E+19 3.01E+17 0.021 0.0118
Case 17 0.057 79.2% 0.045 1.46E+19 2.25E+17 0.015 0.0088 SP: Fins, Chamber
Case 17 0.057 79.2% 0.045 1.46E+19 2.54E+17 0.017 0.0098 SP: Fins, Chamber, Intake
Case 17 0.057 79.2% 0.045 1.46E+19 2.79E+17 0.019 0.0109 SP: Fins
4.4.2 Parabolic Intake
The results for the parabolic cases can be found in table 4.4.2. These cases are based on specular scattering σB = 0, but to investigate hybrid surface interaction some cases are also simulated with specular and diffuse scattering. These cases are differentiated
45 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
with “DF”, where the specified boundary condition is simulated with σB = 1.
Table 4.4.2: Parabolic Cases Results 150km
2 2 ˙ ˙ AIntake m Fill Ratio Ain m Nin 1/s Nout 1/s ηc m˙ mg/s Case 10 0.019 100.0% 0.019 6.33E+18 5.97E+18 0.943 0.232
Case 15 0.019 88.5% 0.017 5.61E+18 4.97E+18 0.887 0.193
Case 15 0.019 88.5% 0.017 5.61E+18 2.46E+18 0.439 0.098 DF: Grid
Case 18 0.041 100.0% 0.041 1.33E+19 7.83E+18 0.591 0.309
Case 19 0.025 100.0% 0.025 8.11E+18 7.15E+18 0.882 0.279
Case 20 0.019 88.5% 0.017 5.61E+18 4.79E+18 0.854 0.186
Case 21 0.090 100.0% 0.090 2.91E+19 5.90E+18 0.203 0.229
Case 22 0.086 100.0% 0.086 2.78E+19 4.69E+18 0.169 0.182
Case 23 0.090 100.0% 0.090 2.91E+19 8.26E+18 0.284 0.327
Case 23 0.090 100.0% 0.090 2.91E+19 5.80E+18 0.199 0.229 DF: Chamber
Case 24 0.090 100.0% 0.090 2.91E+19 9.71E+18 0.334 0.384
Case 24 0.090 100.0% 0.090 2.91E+19 7.28E+18 0.250 0.287 DF: Chamber
4.4.3 Design Evaluation
From intake results cases 6, 10, 12, 15 and 20 are further investigated as they offered the best performance among the hexagonal and parabolic concepts. Case 6 and 12 are simulated at different altitudes, the results can be seen in table 4.4.3.
46 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
Table 4.4.3: Case 6, and 12 over different altitudes
h km Nin 1/s Nout 1/s ηc m˙ mg/s 150 1.34E+18 6.11E+17 0.4565 0.0240 180 3.37E+17 1.49E+17 0.4431 0.0053 Case 6 200 1.60E+17 7.14E+16 0.4450 0.0023 220 8.26E+16 3.51E+16 0.4254 0.0011 250 3.36E+16 1.40E+16 0.4157 0.0004
150 1.24E+18 5.43E+17 0.4367 0.0212 180 3.13E+17 1.42E+17 0.4530 0.0050 Case 12 200 1.49E+17 6.62E+16 0.4442 0.0022 220 7.67E+16 3.43E+16 0.4471 0.0011 250 3.12E+16 1.31E+16 0.4203 0.0004
Furthermore, case 6 is investigated at solar maximum and different (α), the results are shown in table 4.4.4, and table 4.4.5.
Table 4.4.4: Case 6 Solar Maximum at 150km
Geometry Collisions Nin 1/s Nout 1/s ηc m˙ mg/s no 1.70E+18 7.52E+17 0.4414 0.0285 Case 6 yes 1.70E+18 7.54E+17 0.4429 0.0286
Table 4.4.5: Case 6 Flow Misalignment Analysis Results at 150km
Geometry α ° Nout 1/s ηc m˙ mg/s 0 6.11E+17 0.456 0.0240 5 5.07E+17 0.378 0.0198 Case 6 10 3.62E+17 0.270 0.0140 15 2.60E+17 0.194 0.0099 20 2.01E+17 0.150 0.0077
Cases 10, 15 and 20 are also investigated for different α at 150 km. The selection of cases 15 and 20 investigates if a frontal grid duct section could aid on these scenarios. The collection efficiency as well as the output mass flow for these cases at different incoming flow angles can be seen in figure 4.4.1.
47 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
Figure 4.4.1: ηc and m˙ th of cases 10, 15, and 20 at different different α
Moreover case 10, 15, and 20 are simulated at different orbital altitudes, the results can be seen in table 4.4.6.
Table 4.4.6: Case 10, 15, and 20 over different altitudes
h km Nin 1/s Nout 1/s ηc m˙ th mg/s 150 6.33E+18 5.97E+18 0.943 0.2320 180 1.59E+18 1.49E+18 0.934 0.0522 Case 10 200 7.58E+17 7.06E+17 0.930 0.0231 220 3.90E+17 3.62E+17 0.926 0.0110 250 1.59E+17 1.47E+17 0.922 0.0041
150 5.61E+18 4.97E+18 0.887 0.1930 180 1.41E+18 1.25E+18 0.884 0.0437 Case 15 200 6.72E+17 5.92E+17 0.882 0.0193 220 3.46E+17 3.04E+17 0.879 0.0092
150 5.61E+18 4.79E+18 0.854 0.1860 180 1.41E+18 1.20E+18 0.851 0.0421 Case 20 200 6.72E+17 5.71E+17 0.850 0.0186 220 3.46E+17 2.91E+17 0.842 0.0089
48 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
4.4.4 Specular Intake Evaluation
Case 10 is found to have the best performance among all intake concepts, so further simulations are performed to explore this design. To evaluate the statistical stability of the results, case 10 is simulated a total of 8 times under identical conditions at 150 km and α = 0°. The results can be seen in appendix A.2.1 and A.2.2. It is found that all simulation runs reach the same results, keeping a consistent ηc = 0.943. Figure4.4.2 shows different plots of the evaluated parameters, figure 4.4.2a displays the total particle density. Figure 4.4.2c presents the total velocity magnitude, where the arrows indicate flow direction. In figure 4.4.2b the kinetic temperature of the particles can be observed, and figure 4.4.2d shows the results for particle density flow (N˙ ).
(a) Total number density, m´3 (b) Total kinetic temperature, K
(c) Total velocity, m/s (d) N˙ , 1/s
Figure 4.4.2: Case 10 Parabolic Specular Intake Simulation Results
The variation of the accommodation coefficient is also investigated by modifying the
“R” parameter on “PICLas” parameter file. Although an exact relation form σB to “R” cannot be derived, the “R” parameter is utilized to decide whether a diffuse or specular reflection occurs upon particle impact. It is assumed that by having R = 0.1 there is a
49 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
10% probability for diffuse reflection upon particle impact, thus the surface is assumed to have 90% specular surface properties. Perfect specular reflection is defined by letting R = 0.0. The results of different “R” values at different orbital altitudes can be seen in figure 4.4.3.
Figure 4.4.3: Case 10 with different accommodation coefficients
After investigating on the impact of the accommodation coefficient variation thought the “R” parameter, it is considered that a 80% specular material (R = 0.2), could represent a more realistic scenario to match previous investigations on material scattering dynamics [14], as perfect specular reflection is an idealized scenario. Therefore different α are simulated again with R = 0.2, the results can be seen in table 4.4.7.
Table 4.4.7: Case 10 Flow Misalignment Analysis Results at 150km and R = 0.2
Geometry α ° Nout 1/s ηc m˙ th mg/s 0 4.64E+18 0.732 0.180 5 4.59E+18 0.724 0.179 Case 10 10 4.15E+18 0.655 0.163 15 2.43E+18 0.384 0.095 20 6.57E+17 0.104 0.025
Additionally, Case 10 is simulated at solar maximum and solar minimum conditions. In both scenarios collisions and 80% specular material are also simulated to investigate
50 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION how different input densities and simulation conditions affect the performance of the design. The results can be seen in table 4.4.8, where “Ideal” indicates that perfect specular surface interactions (R = 0.0) are used in the simulation.
Table 4.4.8: Case 10 Analysis at 150km
Geometry Case Specification Collisions Nout 1/s ηc m˙ th mg/s Ideal no 5.97E+18 0.943 0.232 Ideal yes 5.97E+18 0.942 0.229 R = 0.2 no 4.64E+18 0.732 0.180 R = 0.2 yes 4.63E+18 0.731 0.178 Ideal, Solar Maximum no 7.54E+18 0.937 0.284 Ideal, Solar Maximum yes 7.54E+18 0.937 0.284 Case 10 R = 0.2, Solar Maximum no 5.85E+18 0.728 0.220 R = 0.2, Solar Maximum yes 5.84E+18 0.725 0.220 Ideal, Solar Minimum no 6.23E+18 0.943 0.242 Ideal, Solar Minimum yes 6.23E+18 0.943 0.242 R = 0.2, Solar Minimum no 4.84E+18 0.733 0.188 R = 0.2, Solar Minimum yes 4.83E+18 0.731 0.188
Finally, to corroborate that the mesh simulation accounts for the bow shock generating at the front of the intake, a new mesh which includes the flow in front and outside of the intake is constructed. This mesh is simulated at 150 km and solar maximum conditions, plots of the results can be seen in figure 4.4.4
51 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
(a) Bow Shock Mesh n, m´3 (b) Intake mesh n, m´3
(c) Bow Shock Mesh v, m/s (d) Intake mesh v, m/s
Figure 4.4.4: Case 10 bow shock analysis with R = 0.2 and collision enabled at 150 km Solar Maximum
4.5 Results Analysis
After the analysis of the results presented in tables 4.4.1 - 4.4.2, it is decided that the cases: 6, 12, 10, and 19 are going to be further investigated as they offer best intake performance. Although cases 18 and 24 provide the highest values for m˙ th, their ηc is lower than the one from the selected cases. Case 19 offered both a high m˙ th « 0.28 mg/s , and competitive ηc « 0.88, but it is not investigated on different h, “R” nor α due to its close resemblance to case 10, and time constrains on the project. Nevertheless the 150 km results of case 19 are used for the analysis in this section. In appendix A.2 plots of the different densities profiles for cases: 6, 12, 15, 18, 19, 20, and 24 can be observed.
52 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
4.5.1 Diffuse Intake Analysis
The hexagonal intake concepts are developed around diffuse surface properties, from these concepts cases 6 and 12 offer the most promising results for developing a diffuse intake. Such intake can be developed with materials already used in space applications, such as polymers, stainless steel and other alloys which have proven resistance to O degradation [55]. Ideally oxide or nitride coated titanium could offer great protection against corrosion [59], ensuring the intake’s optimal performance throughout the satellite life cycle. Both cases present ηc > 0.40, which is consistent at the different simulated altitudes, and although the m˙ is bellow the requirement of the IPT, it can be expected to be increased as higher input density will yield to larger m˙ without affecting ηc. This scenario is plausible due to the high volatility of the VLEO 17 3 region, where ntotal can approach 10 1/m at 150 km [50]. It is important to mention that although a representation of solar maximum, and minimum are performed, the solar activity in these cycles is found to be low in comparison to other historical data [62], which provides low input density. The main differentiator of both designs is the achieved chamber pressure. Case 12 generates a pch « 0.02 Pa which is two orders of magnitude below the estimated pch for the operation of the IPT. Although this value is expected to be increased with a higher input particle density, and the IPT requirements are based on preliminary tests, it is unlikely that pch > 0.1 Pa, which is the expected minimum for the IPT operations. Also, it is found that case 12, present low pressure regions in the chamber section, which would affect the intake efficiency and m˙ th. In contrast, Case 6 provides an almost homogeneous pch « 0.27 Pa which is expected to increase with higher input density, figure 4.5.1 present the plot of the pressure distribution at the chamber of Case 6.
Figure 4.5.1: Pressure Distribution at Chamber Section Case 6
53 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
4.5.2 Specular Intake Analysis
The parabolic concepts designed around specular scattering offer the highest ηc, with case 10 having a maximum of ηc « 0.94. Case 10 is simulated in several scenarios to corroborate these results. Different simulation times, verifying runs, solar maximum- minimum, bow shock analysis and orbital altitudes keep the ηc > 0.90, while also showing a consistent m˙ th « 0.23 mg/s at 150 km which makes it the ideal candidate for the optimal intake. This is further ratified by the analysis of the different α results seen in figure 4.4.1, where cases 15 and 20 are thought to improve the performance in these scenario, but failed to do so and experience a larger decrease of ηc. It can also be observed that case 10 maintained a almost constant ηc until α « 10°, further increase in α has large impact on the ηc. The step from α = 10 ÝÑ 11° decreases ηc by almost 10%, this reduction continues until 20° where ηc « 0.13. This behaviour makes
α > 15° critical scenarios where not only ηc < 0.6, but also m˙ th > 0.1 mg/s can not be assured. In appendix A.4 the plots of v and n at different α of case 10 can be observed. The results consider perfect specular gas-surface interactions, but the scattering dynamics of HOPG and SiO2 are not ideal. To address this issue simulations modifying the accommodation coefficient through the “R” parameter are performed. Figure 4.4.3 displays the result of these simulations over different altitudes. Although a specific relation of the “R” parameter to the scattering dynamics cannot yet be concluded, the result suggest an almost linear decrease of ηc as “R” is increased. These results are of importance as they show the influence of an accurate definition of the surface properties. This phenomena is further investigated by performing different simulations of the intake with a R = 0.2, results shown in tables 4.4.7 and 4.4.8 show that 80% specular material still performs within the estimated requirements of the IPT. In figure 4.5.2 the pressure distribution of case 10 and 19 is presented. It can be observed that the parabolic shape has a different pressure distribution as the one seen in the hexagonal intakes. This is expected as collection is based on optical properties of the parabola. In figure 4.5.2a it can be seen that case 10 achieves a pch « 0.3 Pa at the center area of the discharge channel, this value can be increased by a higher input density. In contrast, case 19 seen in figure 4.5.2b achieves a larger pressure, reaching over 1 Pa in the central region while also having a greater larger pressure region.
54 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
(a) Case 10 (b) Case 19
Figure 4.5.2: Pressure Distribution of Cases 10 and 19 at 150 km, Pa
Finally, to asses the performance on an ABEP system level a thrust vs drag analysis is performed. Table 4.5.1 shows the results in the analysis of thrust vs drag. Assuming that the intake frontal area represents the SC cross-section, and using Eq. 2.22 and Eq. 2.21 and a thruster efficiency of 20% [63]. The expected exhaust velocity is calculated by setting 1 = FDrag/Fthrust. This is done as no experimental data for vth is yet generated for the IPT.
55 CHAPTER 4. INTAKE DESIGN AND OPTIMIZATION
Table 4.5.1: Drag vs Thrust Analysis
Case h km FDrag mN vout km/s 150 2.104 45.44 180 0.478 45.72 Case 10 200 0.211 45.82 220 0.101 45.93 250 0.038 46.05 150 0.859 179.17 180 0.195 183.26 Case 6 200 0.086 183.28 220 0.041 191.25 250 0.015 199.20 150 2.104 58.48 180 0.478 58.74 Case 10 R = 0.2 200 0.211 59.06 220 0.101 58.99 250 0.038 59.71 Case 10 Smax 150 2.278 49.20 Case 19 150 2.693 48.18
It can be observed that the low m˙ th on case 6 would require high exhaust velocities, which are three times larger than the operational vth of modern thrusters [42]. Case 10 in full specular and 80% specular configuration, as well as case 19 generate more realistic vth, which are in the range of modern thrusters [42], making them the best options for an VLEO mission.
56 Chapter 5
Conclusions and Outlook
5.1 Conclusion
After the investigation of different geometries, based on diffuse and specular gas- surface interactions an optimal intake for operation with the IPT has been successfully developed. Case 10 is selected as the optimal Specular Parabolic Intake, the design is chosen as it offers the best performance with a ηc = 0.94 and a m˙ th « 0.23 mg/s , while keeping vout « 45 km/s at VLEO altitudes. The selected design provides sufficient m˙ th to achieve full drag compensation at orbital altitudes from 150 - 250 km. Although it falls under the estimated value for IPT discharge channel pressure, it has been experimentally shown that RF Helicon Thrusters can operate at 0.266 Pa [63]. An isometric view of the specular intake final design render can be seen in figure 5.1.1. In figure 5.1.2 a detailed technical drawing of the optimized specular intake can be seen.
57 CHAPTER 5. CONCLUSIONS AND OUTLOOK
Figure 5.1.1: Optimal Specular Intake Render
HOPG or SiO2 Surface Coating 1.00 mm
DETAIL E Ismoteric View SCALE 2 : 1
304.48 mm 37.00 mm
m
m
0
0 E
.
7
3
IPT Discharge Channel 162.00 mm Lateral View Fontal View
Figure 5.1.2: Optimal Specular Intake Dimensions
58 CHAPTER 5. CONCLUSIONS AND OUTLOOK
The selection derives form the simulation and analysis of different geometries at different flow conditions, such as: flow misalignment (α), altitude (h), accommodation coefficient (σB), and solar cycle. These simulations provide insights in the importance of accurate modeling of the surface interactions. It is shown that this phenomena rules the definition of the intake’s geometry, meaning that a small difference scattering dynamics could lead to different geometry being the optimal design. In table 5.1.1 the intake’s performance is presented for different VLEO orbital altitudes, while table 5.1.2 shows the performance at different α and 150 km.
Table 5.1.1: Optimized Specular Intake Performance at Different Altitudes
2 ˙ ˙ h km Ain m Nin 1/s Nout 1/s ηc m˙ th mg/s vout km/s
150 0.019 6.33E+18 5.97E+18 0.943 0.232 45.4
180 ” 1.59E+18 1.49E+18 0.934 0.052 45.7
200 ” 7.58E+17 7.06E+17 0.930 0.023 45.8
220 ” 3.90E+17 3.62E+17 0.926 0.011 45.9
250 ” 1.59E+17 1.47E+17 0.922 0.004 46.0
Table 5.1.2: Optimized Specular Intake Performance at Different α
˙ ˙ h km α, ° Nin 1/s Nout 1/s ηc m˙ th mg/s
150 0 6.33E+18 5.97E+18 0.943 0.232
” 5 ” 5.98E+18 0.944 0.233
” 10 ” 5.69E+18 0.899 0.223
” 11 ” 5.30E+18 0.836 0.208
” 12 ” 5.07E+18 0.801 0.199
” 13 ” 4.64E+18 0.733 0.182
” 14 ” 4.07E+18 0.642 0.160
” 15 ” 3.447E+18 0.548 0.136
” 20 ” 8.45E+17 0.133 0.031
59 CHAPTER 5. CONCLUSIONS AND OUTLOOK
It is important to mention that even though case 10 has been selected as the optimal intake, further studies and experimental results in pressure profile accepted by the IPT need to be performed. This could switch the optimal design form case 10 to 19, which has a lower ηc = 0.88, but offers a higher pressure distribution on the outlet section of the intake. The difference in the pressure distributions comes from the focus of the parabola being shifted forwards as seen in figure 5.1.3.
Focus Focus
Case 10 Case 19
Figure 5.1.3: Parabolic Focus Diagram of Cases 10 and 19
Additionally, during the result analysis it was brought to attention that the selected solar activity data for the nominal simulation case is right in the middle of the solar minimum of solar cycle 24 - 25. The cycle 25 is expected to be a weak cycle [64], but average solar activity is still going to increase. The specular parabolic intake design is therefore a robust result as it performs optimally in this “worst” case scenario. The intake performance will benefit from higher solar activity as the input density will increase, providing larger m˙ th while maintaining ηc. The diffuse intake (Case 6) requires large values exhaust velocity due to the low mass flow, but this could change as the design could benefit greatly from more accurate studies in drag coefficients and experimental results on the IPT efficiency. In figure 5.1.4 a isometric view render of the diffuse intake is shown, while in figure 5.1.5 a detailed technical drawing of the diffuse intake can be seen.
60 CHAPTER 5. CONCLUSIONS AND OUTLOOK
Figure 5.1.4: Diffuse Intake Render
Material: Oxide or Nitride coated Ti 6AI-4V
3.50 mm
2.50 mm
DETAIL C SCALE 2 : 1
85.16 mm
55.50 mm Isometric View 1.00 mm 14.00 mm
45.0
m
m
m
m
m
5
m
0
4
0
.
3
.
8
1
7
.
3
3 8 C
9
IPT Discharge Channel Lateral View Frontal View
Figure 5.1.5: Diffuse Intake Dimensions
Finally, table 5.1.3 shows the diffuse intake performance at different orbital
61 CHAPTER 5. CONCLUSIONS AND OUTLOOK altitudes.
Table 5.1.3: Diffuse Intake Performance at Different Altitudes
2 ˙ ˙ h km Ain m Nin 1/s Nout 1/s ηc m˙ th mg/s vout km/s
150 0.008 1.340E+18 6.11E+17 0.456 0.0240 179.17
180 ” 3.37E+17 1.49E+17 0.443 0.0053 183.26
200 ” 1.60E+17 7.14E+16 0.445 0.0023 183.28
220 ” 8.26E+16 3.51E+16 0.424 0.0011 191.25
250 ” 3.36E+16 1.40E+16 0.416 0.0004 199.20
5.2 Outlook
Although the performance of the intake is characterized under DSMC in different scenarios at VLEO, the design could benefit from simulation offering an average solar activity case. In addition, further investigations to match the exact behaviour of the scattering dynamic of HOPG and SiO2 should be carried out. Investigations on the drag coefficient and geometry of the SC should also be carried out, as new research in O resistant and drag-reducing materials is being done [65]. This would provide more realistic results on the intake performance. More important, an experimental analysis should be carried out to finalize the verification of the intake design. A prototype should be constructed with SiO2 and HOPG and tested in VLEO environment. The Rarefied Orbital Aerodynamics Research facility (ROAR) at Manchester University could be used for experimentally validating the design under atomic oxygen flow. Furthermore, to facilitate the intake design further studies on understating rarefied flow physics should be carried out, generating an analytical model of the FMF flow and scattering dynamics will drastically reduce the time needed to design and optimize an intake. This comes of relevance as each thruster will have specific requirements which will affect the intake performance, so a tailored intake must be design for each thruster. Providing an initial overview of intake performance will cut down the number of geometries simulated to find an optimal design. Thanks to the advantages on Earth observation and telecommunications of VLEO over Low Earth Orbit (LEO)[26], it is likely that in the near future a technological
62 CHAPTER 5. CONCLUSIONS AND OUTLOOK demonstration could be carried out for ABEP verification. A GOCE-like mission [44] should be carried out, where high resolution data from Earth’s magnetic field can be acquired and mapping of the Earth’s geoid with extremely high accuracy could be performed. The small platform which is equipped with ABEP, would serve as technological demonstration for the ABEP system, while providing valuable data for better understating the Earth’s environment.
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70 Appendix - Contents
List of Symbols ix
A Appendix 72 A.1 Geometrical Parameters ...... 72 A.2 Case 10 Verification Results ...... 73 A.3 Density Profiles ...... 75 A.4 Case 10 Different Incoming Flow Angles (α) ...... 78
71 Appendix A
Appendix
A.1 Geometrical Parameters
Table A.1.1: Hexagonal Cases Geometrical Parameters
Case S Intake mm Thickness mm L Intake mm L Grid mm S Grid mm Chamber Angle ° 2 111.00 1.0 55.50 10.00 2.5 - 3 111.00 1.0 55.50 10.00 2.5 60 4 111.00 1.0 55.50 8.00 2.0 45 5 111.00 1.0 55.50 31.25 2.5 45 6 111.00 1.0 55.50 14.0 3.5 45 7 111.00 1.0 55.50 5.00 2.5 45 8 82.80 0.5 441.60 6.25 2.5 45 9 80.00 0.5 160.00 80.00 8.0 45 11 80.00 0.5 160.00 40.00 8.0 45 12 80.00 0.5 85.00 70.00 12.0 45 13 80.00 0.5 160.00 60.00 5.0 45 14 111.00 0.5 160.00 85.00 8.0 45 16 296.00 1.0 370.00 40.00 8.0 45 17 296.00 1.0 370.00 40.00 8.0 45
72 APPENDIX A. APPENDIX
Table A.1.2: Parabolic Cases Geometrical Parameters
Case D Intake mm Thickness mm L Intake mm L Grid mm S Grid a Chamber Angle ° 10 158.00 0.5 304.50 - - 0.025 - 15 158.00 0.5 304.50 60.00 8.0 0.025 - 18 228.56 0.5 228.56 - - 0.027 - 19 178.74 0.5 196.20 - - 0.020 - 20 158.00 0.5 304.50 20.00 8.0 0.025 - 21 338.66 0.5 578.00 - - 0.004 / 0.025 - 22 331.20 0.5 427.00 - - 0.025 - 23 338.67 0.5 378.00 - - 0.004 30 24 338.67 0.5 333.00 - - 0.004 45
A.2 Case 10 Verification Results
Table A.2.1: Case 10 Verifying Simulations Runs Different Species m˙ at 150km
Check Spec1m˙ mg/s Spec2 m˙ mg/s Spec3 m˙ mg/s Spec4 m˙ mg/s Spec5 m˙ mg/s Spec6 m˙ mg/s Spec7 m˙ mg/s 1 1.70E-07 1.66E-08 4.54E-08 2.56803E-11 8.11E-12 1.98E-12 7.43E-13
2 1.70E-07 1.66E-08 4.54E-08 2.56803E-11 8.11E-12 1.98E-12 7.43E-13
3 1.70E-07 1.66E-08 4.54E-08 2.56803E-11 8.11E-12 1.98E-12 7.43E-13
4 1.70E-07 1.66E-08 4.54E-08 2.56803E-11 8.11E-12 1.98E-12 7.43E-13
5 1.70E-07 1.66E-08 4.54E-08 2.56803E-11 8.11E-12 1.98E-12 7.43E-13
6 1.70E-07 1.66E-08 4.54E-08 2.56803E-11 8.11E-12 1.98E-12 7.43E-13
7 1.70E-07 1.66E-08 4.54E-08 2.56803E-11 8.11E-12 1.98E-12 7.43E-13
8 1.70E-07 1.66E-08 4.54E-08 2.56803E-11 8.11E-12 1.98E-12 7.43E-13
73 APPENDIX A. APPENDIX
Table A.2.2: Case 10 Verifying Simulations Runs at 150km
Check Nout 1/s ηc m˙ total mg/s 1 5.97E+18 0.943 2.32E-01
2 5.97E+18 0.943 2.32E-01
3 5.97E+18 0.943 2.32E-01
4 5.97E+18 0.943 2.32E-01
5 5.97E+18 0.943 2.32E-01
6 5.97E+18 0.943 2.32E-01
7 5.97E+18 0.943 2.32E-01
8 5.97E+18 0.943 2.32E-01
Table A.2.3: Case 10 Multiple Simulation Times at 150km
Tend Nout 1/s ηc m˙ mg/s 1.50E-3 5.97E+18 0.9423 2.31E-01
1.75E-3 5.97E+18 0.9425 2.31E-01
2.00E-3 5.97E+18 0.9426 2.32E-01
2.25E-3 5.97E+18 0.9425 2.31E-01
2.50E-3 5.97E+18 0.9425 2.32E-01
2.75E-3 5.97E+18 0.9423 2.31E-01
3.00E-3 5.97E+18 0.9423 2.31E-01
74 APPENDIX A. APPENDIX
A.3 Density Profiles
Figure A.3.1: Density Distribution of Case 6, m´3
Figure A.3.2: Density Distribution of Case 12, m´3
75 APPENDIX A. APPENDIX
Figure A.3.3: Density Distribution of Case 15, m´3
Figure A.3.4: Density Distribution of Case 18, m´3
76 APPENDIX A. APPENDIX
Figure A.3.5: Density Distribution of Case 19, m´3
Figure A.3.6: Density Distribution of Case 20, m´3
77 APPENDIX A. APPENDIX
Figure A.3.7: Density Distribution of Case 24, m´3
A.4 Case 10 Different Incoming Flow Angles (α)
(a) Density Distribution, m´3 (b) Velocity Distribution, m/s
Figure A.4.1: Case 10 α = 5°
78 APPENDIX A. APPENDIX
(a) Density Distribution, m´3 (b) Velocity Distribution, m/s
Figure A.4.2: Case 10 α = 10°
(a) Density Distribution, m´3 (b) Velocity Distribution, m/s
Figure A.4.3: Case 10 α = 15°
(a) Density Distribution, m´3 (b) Velocity Distribution, m/s
Figure A.4.4: Case 10 α = 20°
79 TRITA-EECS-EX-2020:922
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