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Air-Intake Design Investigation for an Air-Breathing
Electric Propulsion System
IEPC-2015-90524/ISTS-2015-b-90524
Presented at Joint Conference of 30th International Symposium on Space Technology and Science,
34th International Electric Propulsion Conference and 6th Nano-satellite Symposium
Hyogo-Kobe, Japan
July 4–10, 2015
Francesco Romano∗, Tilman Binder†, Georg Herdrich‡, Stefanos Fasoulas§
Institute of Space Systems (IRS), University of Stuttgart, Stuttgart, 70569, Germany
and
Tony Sch¨onherr¶
The University of Tokyo, Bunkyo, Tokyo, 113-8656, Japan
An air-breathing electric propulsion system (RAM-EP) ingests the air of the residual
atmosphere through an Air-Intake and uses it as propellant for an electric thruster. Key
component of the system is the Air-Intake, which has the task of collecting atmosphere
particles and directing them into the thruster, accompanied by compression. Studies have
considered different configurations, and have shown the feasibility of the device. Within this
paper an overview of the current Air-Intake designs is given. Results of DSMC simulations,
performed with our in-house code PICLas, are presented and compared to those from the
respective publications. Moreover, the influence of simplifying assumptions, such as free
molecular or hyperthermal flow, is shown. Additionally, a simple analytical model based
on transmittances and the balance of particle flows is derived, applicable for the analysis
and further possible optimization of a generic Air-Intake design. The model is compared
to the results of DSMC simulations and a sensitivity analysis of the basic parameters is
performed. Regarding the assumption of hyperthermal flow, results shows that part of the
particles will interact with the lateral structures of the Air-Intake and therefore will be
scattered loosing their macroscopic velocity. Moreover, the implementation of straws into
the Air-Intake simulations needed particular attention. A deeper investigation over their
single transmittances has been done. Through the balancing model a sensitivity analysis
over their L/R ratio has been performed and results show how a low ratio would lead to
higher densities and collection efficiencies.
∗Ph.D. Student, Institute of Space Systems (IRS), romano@irs.uni-stuttgart.de.
†Ph.D. Student, Institute of Space Systems (IRS), binder@irs.uni-stuttgart.de.
‡Head Plasma Wind Tunnels and Electric Propulsion, Institute of Space Systems (IRS), herdrich@irs.uni-stuttgart.de.
§Head Department of Space Transportation, Institute of Space Systems (IRS), fasoulas@irs.uni-stuttgart.de.
¶Assistant Professor, Dpt. of Aeronautics and Astronautics, schoenherr@al.t.u-tokyo.ac.jp.
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
IEPC-2015-269／ISTS-2015-b-269
IEPC-2015-269／ISTS-2015-b-269
Nomenclature
Ain = Air-Intake Front Surface
Aout = Air-Intake Outlet Surface
Ap = Geomagnetic Index
BM = Balancing Model
DSMC = Direct Simulation Monte Carlo
ECR = Electron Cyclotron Resonance
El. = Element
F= Thrust, Force
F10.7 = Solar Radio Flux at λ=10.7cm
h= Altitude
kB= Boltzmann Constant
L=Length
mp= Particle Mass
˙mthr = Mass Flow to Thruster
navg,ch = Average Number Density in Chamber
nch = Number Density in Chamber
nin = Number Density in Inflow
ntot,in = Total Number Density in Inflow
˙
Naccel = Accelerated Particle Flow
˙
Nin = Incoming Particle Flow
˙
Nthr = Particle Flow to Thruster
˙
Nout = Outlet Particle Flow
pch = Chamber Pressure
pin = Inflow Pressure
R = Radius
Rel. Dev. = Relative Deviation
RAM EP = Air-Breathing Electric Propulsion
S/C = Spacecraft
Tch = Chamber Temperature
Tin = Inflow Temperature
Twall =WallTemperature
vch =VelocityinChamber
vin = Inflow Velocity
vout = Exhaust Velocity
vz=VelocityinzDirection
α= Accommodation Coefficient
Γ = Mass Flux (e.g. by Thermal Effusion)
ηc= Collection Efficiency
ΘClausing = Backflow Transmittance following Clausing’s Assumptions
Θfast = Transmittance for Fast, Unscattered Particles
Θintake1= Transmittance for the Intake in Inflow direction
Θintake2= Transmittance for the Intake in Backflow direction
Θout = Transmittance for the Outflow
Θscattered = Transmittance for Scattered Particles
χ= Aspect Ratio
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I. Introduction
Very low orbits are of great interest for many scientific, civil and military purposes. Recently ESA’s
mission GOCE ended, it provided detailed information of the Earth’s geomagnetic field by orbiting
as low as 229 km using ion thrusters to compensate the drag. The amount of propellant on board is a
limiting lifetime factor for such a mission, in particular if the S/C is orbiting very low around a planet with
atmosphere. The atmosphere is indeed responsible for the drag, which slows down the S/C and reduces its
total mission lifetime. It is also a limiting factor in terms of costs, as more drag to be compensated for a
longer time means an increased amount of propellant to be carried on board, which again increases the total
mass. The lifetime of a S/C orbiting in LEO can be significantly increased by the application of an efficient
propulsion system capable to compensate the drag.
The basic idea of an Air-Breathing Electric Propulsion System, shortened RAM-EP, is to use the air of
the residual atmosphere as propellant and to process it through a device for generating thrust. This will
decrease, ideally nullify, the on board propellant requirement and will generate thrust to partially or fully
compensate the drag. A conceptual scheme of the S/C is shown in Fig. 1.
This paper will focus on the device needed to efficiently collect and drive the atmosphere particles to
Incoming flow
Flight Direction Solar Array
Solar Array
Air-Intake Exhaust
S/C Core
Figure 1: Air-Breathing Electric Propulsion S/C Concept.
the thruster, called the Air-Intake. The investigation on an Air-Intake is part of a Ph.D. program at IRS,
focused on the use of a small inductively heated plasma thruster based on IPG6-S for an Air-Breathing
Electric Propulsion application,14.13 Emphasizing its crucial design, recent studies involved ESA,4BUSEK
Inc.8and JAXA,5,7that proposed and studied different possible design configurations. The outcome of
these studies are sustained by DSMC simulations and experimental activity on ground. In the following,
an overview of these designs is provided, together with results of DSMC simulations, performed with our
in-house code PICLas.10 Additionally, a simple analytical model based on transmittances and the balance of
particle flows is derived, applicable for the analysis and further possible optimization of a generic Air-Intake
design. The model is compared to the results of the DSMC simulations and a sensitivity analysis of the basic
parameters is performed.
II. Assumptions and Considerations
The design of an Air-Intake for an Air-Breathing Electric Propulsion System is a challenge and depends
on many different factors. The requirement is an efficient collection of the particles encountered by the S/C
in order to feed the thruster. The ratio between the collected particle flow ˙
Nthr and the incoming particle
flow ˙
Nin is named Collection Efficiency, see Eq. 1. In order to have a highly efficient device, it is required to
keep ηcas high as possible.
ηc=˙
Nthr
˙
Nin
(1)
A consideration on the need of an Air-Intake should not be avoided. The flow the Air-Intake encounters
will be highly rarefied and, therefore, it is not possible to follow intuition, which is strictly connected to
our experience on Earth where continuum flow sovereigns. For different flow conditions, the presence of an
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
Air-Intake that works perfectly in continuum might worsen and even become counterproductive, providing
to the thruster less particle flow than without an Air-Intake. The incoming particle flow to the intake is
defined by the open front area of the intake Ain and the free stream conditions (e.g. number density nin
and velocity vin)as: ˙
Nin =ninvin Ain (2)
Multiplying the particle flow ˙
Nwith the average particle mass mpresults in the corresponding mass flow
˙m=mp˙
N. With the assumption that the entire collected mass flow ˙mthr is accelerated by the thruster, the
produced thrust can be calculated as in Eq. 3:
F=mp˙
Nthrvout =mpηc˙
Ninvout =(mpnin vinvout )(ηcAin)(3)
Here, vout is the exhaust velocity out of the thruster. A deeper description of the influencing factors for the
flow into the propulsion device will be further described as part of the balancing model in Sec. IV. In the
context of the design of an Air-Intake for an Air-Breathing Electric Propulsion System two important points
have to be considered. On the one hand, for maximizing the thrust, not only the efficiency of the thruster
itself has to be taken care of, but also a sufficient amount of mass flow has to be provided. Eq. 3 suggests that
the area of the intake Ain should be as large as possible to collect the most amount of mass flow, however,
the S/C front area also determines the drag. On the other hand, when considering the feeding system to the
chamber as part of the Air-Intake, the collected gas has also to be fed at a sufficient pressure and, inside an
ionization chamber, the neutral gas should remain as long as possible for an efficient ionization process. For
this, the particles have to be slowed down while increasing pressure. Therefore, a direct flow of free stream
particles into the chamber would not be desired.
III. Air-Intake Review
A. Basic Concepts
The basic concepts for an Air-Intake design are hereby described and shown.
A first logical configuration can be a short cylinder with the cross section of the entire S/C, followed by
a simple entrance cone as shown in Fig. 2a. The cross section cone could converge directly to the size of
the propulsion system or, alternatively, to a feeding system allowing the other S/C subsystems to be placed
behind the Air-Intake.
(a) Air-Intake Simple Cone Concept. (b) Air-Intake By-Pass Concept.
Figure 2: Air-Intake Concepts
However, the approach of using a simple cone is not the best one as the flow is not in the continuum
regime and, thus, dominated by collisions with the walls rather than of inter-particle collisions. This basically
prevents the particles from reaching the end of the cone, which has also been verified through preliminary
Direct Monte Carlo Simulations (DSMC), emphasizing the importance of the right wall model. In case of
diffusive reflections (the most realistic case1), most of the particles will be scattered into a random direction
when hitting the wall. As the solid angle including the cone exit represents for the most reflections only
a very small part of the entire half space, that comprises all possible target directions, nearly all particles
are reflected back into the flight direction. In the case of specular reflection, the situation might be only
improved together with a small cone angle. The basic problem arises that the short cylinder between the
front collection area and the cone does not have only a high transmission probability for the incoming
particles, but also for the flow that is scattered back (the backflow) and, basically, only the particles which
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July 4–10, 2015
were already directed into the projection of the thruster entrance section will enter into it, resulting in a low
collection efficiency ηc.
The performance of the Air-Intake can be improved by providing a design with a high transmission probability
for the incoming flow, and trapping it by a lower transmission probability for the backflow. The key concept
is that the free stream condition has the nature of being a collimated, hyperthermal flow, as the velocity of
the S/C is large compared to the thermal movement of the atmosphere according to the kinetic theory of
gases. Thus, it is less obstructed by lateral structures, such as grids or tubes, than the scattered backflow
is, which has only thermal movement when diffusive reflections at the walls are assumed. Based on this,
a long duct instead of a short one can be better for the collection. According to the study of BUSEK,8
particles will impact at the end of a long duct on the inclined walls gaining random velocity and, due to
the already existing compression, they might be subjected to collisions with the further incoming particles,
creating an even higher compression at the end of the duct. The actual influence of this “collision cascade”
will be analyzed as part of the DSMC simulation in Sec. V. The difference in the transmission for inflow
and scattered backflow might be utilized more efficiently with the introduction of a honeycomb structure of
small straws at the entrance of the Air-Intake.
Another configuration is the by-pass design, see Fig. 2b, which can be additionally combined with the
honeycomb approach. The flow enters from a ring and reaches the inclined surfaces at the end of the duct.
These will act as reflectors/diffusers for the particles which will be then subjected to multiple reflections due
to the presence of the satellite core, as shown in the Fig. 2b. The satellite core provides a sensible position
for most of the other S/C subsystems.
B. Literature Review
From literature review the most detailed Air-Intake studies for Air-Breathing Electric Propulsion applica-
tions are those from ESA,4BUSEK8and JAXA.5
1. ESA
The study from ESA4considers a mechanical Air-Intake as shown in Fig. 3: At the inlet section, a grid is
positioned to stop the incoming particles, a long duct is following to get the required steady pressure level
at the end of the device, where a cone shape finally drives particles into the gridded ion thruster GIT. There
are important considerations about the fact that over a certain length of the Air-Intake, there is no more
improvement in the pressure at the end and, moreover, that a concave or divergent shape at the end does
not improve the flow.
Figure 3: Air-Intake and GIT from ESA.4
2. BUSEK
The BUSEK Inc.8studied the MArs Breathing Hall Effect Thruster (MABHET), a S/C with an Atmosphere-
Breathing Electric Propulsion System. In this design, the Air-Intake is a long tube of 3.7m length and0.6m
diameter, possibly with a honeycomb structure in the front composed of many straws as described in Sec. A.
The Air-Intake is designed as a long tube in order to achieve a higher density region at the back part due to
the presence of an assumed “collision cascade”. A total pressure increment of 100 was observed in DSMC.
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
Examplary designs are shown in Fig. 4a and Fig. 4b.
The design of the Air-Intake led to the following observations:
•A long duct allows a compression zone to form at the back, due to collisions between incoming and
already trapped particles (“collision cascade”);
•Straws fill the inlet, with a certain length, placed in order to block the reflected backflow;
•Main influencing parameter is the ratio of the collisional mean free path to the tube dimension;
•Small inclination of the Air-Intake surfaces will more likely lead to specular reflections at the wall, as
the parallel component of the velocity is still much higher than the perpendicular.
(a) Air-Intake, DSMC results from BUSEK Report.8
(b) Air-Intake, general concept from BUSEK Presentation.9
Figure 4: BUSEK Design
3. Fujita, JAXA
Fujita’s study5considers a by-pass-like design in which the air flow enters through a ring as shown in Fig. 5.
The particles reach the back of the intake hitting a 45◦steep surface, the diffuser/reflector, and are afterwards
reflected on the back of the satellite core and to the thruster’s acceleration grids. Again, such an annular
intake represents a structure with different transmission probabilities for the inflow and the backflow, when
the effective diameter of the open cross section is small compared to the length. An ECR device ionizes the
particles in the part behind the satellite core (the ionization chamber) that are afterwards extracted through
accelerating grids. As difference to the BUSEK design, grids are at the outlet, and the whole thruster is
already included in the design and, therefore, it is not possible to precisely distinguish between Air-Intake
and thruster. In 2012 a new paper from JAXA7dealing with the development of this Air-Intake has been
published. The main design of the Air-Intake is kept with one important modification, that is the addition
of straws inside the ring-shaped inlet region, similarly to the BUSEK design.
From this brief review, the following main points can be summarized:
•A long, annular inlet duct will allow compression at the end of the intake;
•Straws at the entrance section let incoming particles going through, but block the backflow;
•A conical shape at the end of the intake can drive the flow and scatter the particles into the end of the
inlet where they can be driven by other matters to the thruster.
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
Figure 5: Air-Intake from Fujita’s 2004 paper,.5
IV. Balancing Model
A. Introduction
In this Section a simple, analytical model for the evaluation of a generic RAM-EP Air-Intake configuration
is presented. The generic design becomes obvious when comparing the introduced designs, where an intake
section collects the particles with free stream conditions and guides them into the propulsion system. In the
context of this model, the intake section is followed by a chamber section in which it is assumed that all
particles have already gone through wall collisions and, thus, have only a thermal movement with regard to
the wall temperature left. By this, the only particle flows directed out of the chamber are due to thermal
diffusion. One flow back through the intake with its desirably low transmittance probability, and another flow
through the outlet. The representation of the outlet flow strongly depends on the specific configuration. For
the JAXA’s design, it is the flow passing through the thruster grids, increased by the acceleration provided
by them. In general, a feeding system and the thruster itself follows. By balancing these particle flows, the
conditions in the separate sections can be estimated.
B. Assumptions
The basic assumptions for the analytical model are following the nomenclature in Fig. 6:
Twall
Free Stream Condition
pin,n
in,T
in,v
in
Intake Control Volume, Chamber
pch,n
ch,T
ch,v
ch
˙
Nin
Ain
Θintake1,˙
Nintake1
Θintake2,˙
Nintake2
Θout,˙
Nout
(˙
Naccel)
Aout
Figure 6: Balancing Model Scheme.
Ain and Aout are the respective cross sections for the inflow and the outflow representing those of the
chamber section. The parameters of the incoming flow are known: number density nin (or pressure pin),
flow temperature Tin and free stream velocity vin.
Θ is the transmittance into a specific direction through a single structure, indicated in the subscript, and
is the fraction of particles which pass through the exit section against the amount of particles which passed
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
into inflow direction through its start section, as part of them is partially scattered back while crossing the
volume. The transmittance can represent any intake, including a case with straws. This is also used for the
outlet, for the JAXA case with a transmittance for the acceleration grids. For a general design, it represents
the feeding system and thruster.
All in all, three transmittances are to be set: one for the incoming flow, one for the backflow coming from
the chamber (accounting for two values through the intake part), and a third for the flow through the outlet.
Based on these transmittances, the respective particle flows can be defined. ˙
Nintake1is the flow of particles
passing through the intake section from free stream into the chamber section, ˙
Nintake2is the backflow that
goes back to the free stream after having reached the chamber section, and ˙
Nout is the net outflow.
The basic hypotheses of this model are the following:
•Free molecular flow;
•Single species;
•Ideal gas;
•Complete diffusive accommodation, α=1;
•Fixed temperature, Tch =Twall;
•No macroscopic velocity inside the chamber, vch =0m/s.
The general particle flow into the direction of xiis defined as in Eq. 4, where nis the number density,
¯vxiis the averaged flow velocity into xiand Ais the passed area perpendicular to ¯vxi.
˙
Nxi=n¯vxiA(4)
Relying on this equation, the particle flow ˙
Nin into the Air-Intake which can be collected at most is simply
the one using the free stream conditions and the open area.
Regarding the actually collected flow, the following can be written:
˙
Nintake1=˙
NinΘintake1(5)
Based on the for-mentioned hypotheses, the macroscopic velocity of the collected particles will be brought
to zero and a superposed backflow will not influence the inflow as it is a free molecular flow.
Starting from the temperature of the particles inside the chamber, the thermal mass flux Γ, defined in Eq. 6,
according to [1, p.151], can be calculated.
Γ(n, T )xi=nmpkBTch
2π=mpn¯vxi(6)
Therefore, it is possible to apply Γ to determine backflow and outflow in the chamber of the Air-Intake
as following:
˙
Nintake2=Γ(nch,T
ch)
mp
AinΘintake2(7)
˙
Nout =Γ(nch,T
ch)
mp
AoutΘout +˙
Naccel (8)
To this, the continuity equation, see Eq. 9, can be applied which states that the net particle flow through
a control volume, in this case the chamber section, having certain number of outlets and inlets must be zero.
˙
Naccel is the accelerated particle flow which will be actively extracted by the thruster. This value strongly
depends on the operation point of the specific thruster and its respective acceleration process and is, amongst
others, also a function of the ninside the chamber. It is expected that a minimum nis needed inside the
chamber for the thruster ignition. Therefore, the focus is at the situation before ignition, ˙
Naccel =0.
˙
Nintake1=˙
Nintake2+˙
Nout (9)
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
The assumption of a nullified macroscopic velocity in the chamber allows to rewrite Eq. 9 as in Eq. 10:
˙
NinΘintake1=Γ(nch ,T
ch)
mp
(AinΘintake2+Aout Θout) (10)
Therefore Γ can be extracted and, thus, the density nch inside the chamber from Eq. 6 results in:
nch =Γ(nch,T
ch)2π
mpkBTch
(11)
The pressure can be calculated by applying the ideal gas condition as:
pch =nchkBTch (12)
It is therefore possible to analytically calculate the parameters inside the chamber section, when input
conditions and transmittances are given. Based on this, efficiencies for the number particle flow, pressure
and mass flow can be extracted. The approach will be verified through DSMC simulation in Sec. V.
The number density inside the chamber is the value which results together with the other gas properties in a
thermal effusion out of the chamber equal to ˙
Nintake2and the effusion part of ˙
Nout. In a dynamic view, this
values rises until the balance is reached. Considering also the extracted flow ˙
Naccel, it is expected that the
actual nch will decrease after ignition, since the thermal effusion required for mass balance would be smaller.
Collection Efficiency ηcin Eq. 13, pressure ratio in Eq. 14 and number density ratio in Eq. 15 are important
values for the evaluation of an Air-Intake. With regard to Eq. 1, ˙
Nthr can be seen either as ˙
Nintake1or as
˙
Nout. For consistency with the respective publications of the analyzed designs and for a simple comparison
with the DSMC simulations, the latter has been chosen.
ηc=˙
Nout
˙
Nin
=Γ(nch,T
ch)
mp
AoutΘout
˙
Nin
=Θintake1AoutΘout
AinΘintake2+Aout Θout
(13)
pch
pin
=mp˙
NinΘintake1
AinΘintake2+Aout Θout 2π
mpkBTch
Tch
Tinnin
(14)
nch
nin
=mp˙
NinΘintake1
AinΘintake2+Aout Θout 2π
mpkBTch
1
nin
(15)
V. Air-Intake Simulations
In this section, the DSMC simulations performed with our in-house code PICLas are presented. The
consideration of a honeycomb structure of small straws at the entrance required an elaborate modelling
approach which is additionally described.
A. PICLas
PICLas, developed at the IRS and the Institute of Aerodynamics and Gas Dynamics (IAG) of the University
of Stuttgart,10 was employed for the following simulations. The code is a coupled, three-dimensional particle
method based on unstructured, hexahedral meshes and includes, besides general routines for particle tracking
and particle-wall collisions, a Direct Simulation Monte Carlo (DSMC)1as well as a particle-in-cell method,
with additional modules for Low Diffusion and Fokker-Planck models.11
In the context of this paper, only the DSMC part was used. A pairing scheme including the Natural-Sample-
Size method with the variable hard sphere model was applied for inter-particle collisions. Internal degrees of
freedom of molecules were taken into account while neglecting chemical reactions because of the relatively low
temperatures in all simulations. By switching the pairing scheme off (corresponding to collision probabilities
of zero) and, thus, using only the tracking, wall collisions and analysis routines, also ideal, free molecular
flows were simulated.
In general, symmetry was exploited by simulating only one quarter of the domain. Diffusive reflection with
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
full accommodation was assumed at walls, whereas specular reflection for the planes of symmetry. All
other boundaries were open with a defined transparence (i.e., crossing particles are deleted with the given
probability, otherwise reflected) with an optional inflow from a virtual buffer layer filled with particles of a
Maxwell-Boltzmann distribution corresponding to the respective inlet condition.
B. DSMC Simulations of the Reference Cases
1. JAXA Air-Intake
Based on the Fujita’s 2004 study,5DSMC simulations have been performed for comparison with their
paper results and to verify the balancing model. The input values are the same as reported in the paper5
(atmospheric model MSISE-90), as well as the geometrical data. In particular, two different geometric
configurations are considered, with a form factor of χ=10.0 for a short intake optimized for low altitudes,
and χ=20.0 for a longer intake optimized for higher altitudes. The form factor χ, see Fig. 7, is defined as in
Eq. 16. Two altitudes have been simulated, 140km and 180 km, the highest with both geometries (χ=10.0
and χ=20.0) and the lowest with a different outlet transmittance, given by the acceleration grids of the
assumed thruster (Θout =0.1andΘ
out =0.2).5
χ=L1
R2−R1
(16)
Figure 7: Air-Intake Geometry,.5
Additionally to the MSISE-90, the NRLMSISE-00 atmosphere model was used for comparison. It is
the most advanced regarding the composition of the atmosphere at low altitudes.12 The differences of
the two models are, in our simulations, the inclusion of additional species ( He and Ar at 140 km, also
Nat180km),alowerTin and a slightly lower ntot. Input parameters for the model have been set for
01/01/2014 at hour =1.50, lat. 55.00, long. 45.00 in average solar and geomagnetic activity defined by
F10.7=F10.7avg = 140 and Ap = 15. In Tab. A1 of the Appendix the input parameters are shown.
Concerning the short Air-Intake, χ=10.0 at 140 km using NRLMSISE-00 model, DSMC simulations have
been run also with the hypothesis of an ideal free molecular flow, that means considering only collisions
between particles and walls. By this, the contribution, if there is any, of inter-particle collisions inside the
chamber can be evaluated.
The results of our simulations are compared to the Fujita’s from 2004 in Tab. 1 in terms of the averaged
value of the total number density ninside the region behind the satellite core. Results have, except for
the χ= 10 case at 180 km, a deviation of less than 10% from the reference values. Therefore the results
are, at least, in the same range and verify the general simulation set-up. The main reason of the deviations
is assumed to be the ambiguity of a defined chamber pressure. Furthermore, not all assumptions of the
reference are known.
A more elaborate presentation and discussion of the results is given in Sec. VI.
2. BUSEK Air-Intake Simulation
Based on the BUSEK design,8DSMC simulations have been performed to cover a wider range of Air-Intake
configurations. The considered design is supposed to operate in a low Mars orbit and is a 3.7m long tube
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
Table 1: Fujita’s 2004 Air-Intake DSMC Results Comparison
hχΘout nch ,from
5navg,ch , PICLas Rel. Dev. Note
km - - m−3m−3%-
140 10.0 0.1 7.24 ×1018 7.77 ×1018 +7.32
140 10.0 0.2 4.82 ×1018 4.95 ×1018 +2.70
”” ” ” 4.40 ×1018 −8.71 NRLMSISE-00
180 10.0 0.2 1.11 ×1018 9.32 ×1017 −16.04
180 20.0 0.2 1.37 ×1018 1.237 ×1018 −9.71
”” ” ” 1.01 ×1018 −26.28 NRLMSISE-00
Table 2: BUSEK Air-Intake DSMC Results Comparison
ηc,from
8ηc, PICLas Rel. Dev. Note
%%% -
28 23 −17.9 With Collisions
<19 17 - No Collisions
” 20 - With Straws, With Collisions
<19 15 - With Straws, No Collisions
with a 0.6 m diameter terminating with a conical surface converging on a 0.14 m diameter exit to fed the Hall-
Thruster. As complete data is not available, nhas been extracted from a given plot showing the compression
efficiency ηcat different products of number densities and intake diameter. A value of ntot =5.3×1017 m−3
was used for the simulated intake diameter of 0.6 m. Remaining flow condition are set to vin =3.5km/sand
Tin = 250K, the latter represents a common value for the temperature of the upper Mars atmosphere.6As
simplifying assumption only CO2was considered (that is present ∼96%) and the internal degrees of freedom
of the particles were neglected.
The main physical principle pointed out by BUSEK is the pushing of the incoming particles on the already
trapped particles by inter-particle collisions. To quantify this effect, those collisions have been switched off
for comparison, analogously to the JAXA cases. The main results from the simulations are briefly presented
in Tab. 2 and compared to the available data from BUSEK,8that is an ηcof ∼28% for the simulated point
and ∼19% for the lowest included nwhich is, therefore, interpretable as an upper limit for the simulations
assuming free molecular flow. The results are here also in the same range as those from the reference which
verifies the general system set-up, but emphasizes the availability lack of the exact reference assumptions.
In Tab. 2 there also already simulations with included straws, these will be further described in Sec. VI.
C. Consideration of Straws inside the Air-Intake
JAXA7and BUSEK9presented an Air-Intake with a honeycomb straw structure inside the inlet. The
function of the straws, as already explained, is to minimize the backflow and, therefore, increase pressure
and density at the end of the Air-Intake and ηc. The main assumption for the straws, in both studies, is that
the incoming flow, as result of being hyperthermal, is well collimated and no interaction between particles
and straw walls will arise. That means the particles will keep their macroscopic velocity until they scatter
at the surfaces of the end of the Air-Intake.
1. Implementation in DSMC
Due to the high computational resources required for the actual inclusion of an honeycomb straw structure
into the DSMC domain, a simplifying modeling approach has been used within the simulations.
For this, single straws have been simulated, represented by simple cylinders open at both sides with an in-
coming flow along the direction of the axis. To simulate the Air-Intake completely with straws, the velocity
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
distribution at the outlet of a single straw has been extracted and used as input for the Air-Intake simulation
itself. The velocity distributions show two main peaks, one corresponding to the high, macroscopic velocity
of particles that went through the straw without wall collisions, and another for the particles scattered along
the inner wall, with a macroscopic velocity of zero. The number of fast and of scattered particles are ex-
tracted from the simulations and the respective transmittances, Θfast and Θscattered, used for the following
Air-Intake simulations were included.
As there will be also a backflow from the downstream part of the intake through the straw, a transmit-
tance for this flow is needed. The corresponding problem is an already well-known subject of gas kinetics,
mostly connected to the work of Clausing2who dealt with free molecular flow through cylinders in terms of
transmission probability. The Clausing Factor, referred as ΘClausing, depends only on the L/R ratio of the
respective cylinder and is valid under the following assumptions:
•Ideal free molecular flow;
•vin =0;
•Tin =Twall;
•fully diffusive reflections at the walls, α=0.
Precise solutions of the Clausing equations were calculated by Cole3for discrete L/R ratios. These solutions
were used, rather than the long tube approximation, in which the Clausing factor is approximated as in
Eq. 17, due to the significant error the latter produces in the range of our interest (L/R < 100), as shown
in Fig. 8. For example, the relative error is ∼40% for L/R = 10 and still of 5% for L/R = 100.
ΘClausing =8
3
R
L(17)
L/R, -
10-1 10010110210 3
Transmittance, -
10-3
10-2
10-1
100
Transmittance vs. L/R
Clausing Equation vs. Long Tube Approximation
Clausing Equation
Long Tube Approximation
Figure 8: Comparison of Precise Clausing Factors Against Long Tube Approximation.
2. Verification of the Approach
To verify the applicability of the for-mentioned approach for the inclusion of straws into the Air-Intakes
simulation, additional DSMC simulations have been performed for a geometry including only the annular
intake section of Fujita’s Air-Intake, by which, the required transmittances could be extracted for a simulation
including only the part after the satellite core. This has been chosen as the effective diameter of the ring
open cross section is small compared to the length, similarly as for a single straw and, thus, it shows a similar
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
compression ability. Furthermore, the general approach can be demonstrated in the following.
The intake section to be modeled is simulated with open boundaries at both ends, i.e., all particles crossing
these areas are deleted. However, their velocities during the crossing are saved, which enables the evaluation
of the velocity distribution. This probability density function of directed velocity,however, does not represent
the function inside a given volume, as every particle crossing an outlet was saved and, therefore, fast particles
were preferred against slow velocities which could have started also from a larger distance. The velocity
distribution at the end is assumed to be Bi-Maxwellian, including the fast, unscattered particles with vin
and Tin on the one hand, and the scattered particles with Twall on the other hand. Based on this, the only
values to be extracted are the flow rates of fast and scattered particles that flow into the domain. These are
the corresponding transmittances Θfast and Θscatter ed multiplied by the incoming particle flow. An accepted
error is based on the fact that particles with a large lateral velocity will be scattered inside the cylinder with
a higher probability and, thus, the outflow is not supposed to follow an ideal, Gaussian distribution into
those corresponding directions.
Fig. 9 shows the corresponding data for the simulated case including both inlet and outlet section. A,Band
Care the areas given by the integrals over the individual distributions, respectively of the scattered backflow
A, the scattered flow Band the fast/unscattered flow C. As the sum of all 3 areas (A+B+C) represents
Nin,Θ
fast is calculated as C/(A+B+C)andΘ
scattered as B/(A+B+C). The same was conducted for
an inflow without macroscopic velocity, giving only the areas Aand Band a ΘC lausing of B/(A+B). These
three transmittances, shown in Tab. 3, were applied as input to the simulation including only the chamber
section as mentioned above. Results showed no significant difference to the simulation including both intake
and chamber section, as it will be shown in Sec. VI. Therefore, the extraction of the approach has been
verified and can be applied for the straw implementation.
vz, m/s
-4000 -2000 0 2000 4000 6000 8000 10000 12000
f(vz), -
C
B
A
Figure 9: Extracted Velocity Distribution, Fujita’s design inflow including only the Annular Intake Section.
Table 3: Annular Intake Section Transmittances.
El. ΘClausing ,(A)Θ
scattered,(B)Θ
fast,(C)
O 0.212 0.289 0.392
N20.212 0.276 0.466
O20.212 0.253 0.512
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
3. JAXA Straws
In 2012 a new paper from JAXA7dealt with the improvement of Fujita’s design, in particular a model for
laboratory testing was developed with the addition of straws in a honeycomb structure, and tested with an
atomic oxygen flux generator. Since the geometry of this particular Air-Intake is not available, its straws
with a L/R = 20 have been applied to the Fujita’s design for the altitude of 140 km, χ= 10. The atmospheric
model applied is the NRLMSISE-00. The transmittances extracted from our simulations are summarized for
each species in Tab. 4.
Table 4: JAXA Straw Transmittances Results.
Element Θfast Θscattered ΘClausing
Ar 0.381 0.293 0.109
He 0.064 0.288 0.109
N20.307 0.315 0.109
O 0.204 0.334 0.109
O20.333 0.308 0.109
4. BUSEK Straws
In the BUSEK presentation on MABHET,9straws are mentioned to be used in the Air-Intake for the fore-
mentioned reasons. Detailed information on their geometry is not available and, therefore, a rough estimation
from the schemes in the report8and in the presentation9was done. The estimated values provide an aspect
ratio of L/R ∼35. The extracted transmittances are presented in Tab. 5.
Table 5: BUSEK Straw Transmittances Results.
Element Θfast Θscattered ΘClausing
CO20.100 0.306 0.067
VI. Simulation Results and discussion
In this section, the results of the Air-Intake simulations for both Fujita/JAXA and BUSEK cases, also
with the inclusion of straws, are presented and discussed. Averaged, macroscopic values inside discrete cells
are extracted for the total number density nand velocity vzinto inflow direction zfrom lines along the
Air-Intake, as it is shown in Fig. 10 together with contours of total nfor the JAXA intake with MSISE-90
model, χ=10.0andΘ
out =0.2 at 140 km (“chamber” illustrates the averaging volume for the calculation
of nch). For the BUSEK cases, center lines have been extracted.
A. JAXA Air-Intake
Fig. A1a in the appendix, shows vzand nalong the intake for the reference cases at 140 km. nincreases
when getting closer to the chamber while the vzdecreases, which is also expected as the part of scattered
particles increases. Higher density and lower velocity are shown in the case with a lower transmittance of
the outlet grid, indicating a higher compression. In the plot the result including only the chamber section
for the modeling of the velocity distribution is also shown, and very good agreement is visible, therefore,
verifying the extraction approach of the velocity distribution.
Fig. A1b shows the results for the Air-Intake at 180 km with both atmospheric models and both χ. Red and
black lines are using the same atmospheric model but a different χ, the short Air-Intake optimized for 140km
provides indeed a smaller nwhile keeping the velocity higher than in the case with the long Air-Intake of
χ=20.0. The slightly lower nof the NRLMSISE-00 model compared to the MSISE-90, produces the lower
nin the Air-Intake of the same size, the different Tin probably influences the shape of the curve itself. Tab. 6
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
Figure 10: JAXA intake with MSISE-90 model, χ=10.0andΘ
out =0.2 at 140 km.
shows the results of the simulations performed with the NRLMSISE-00 model, illustrating the influence of
inter-particle collisions and straws inside the intake. In particular, the extracted average number density
over the chamber volume navg,ch is shown. Starting from this value the pressure and density ratio are derived
and, moreover, ηcis also included. The line plots of the Air-Intake are shown in Fig. A2 in the Appendix.
Results indicate that the use of straws, in this particular geometric configuration, will provide less nin the
chamber, thus, density and pressure ratio and, therefore, also ηcwill be lower. In particular, from Fig. A2,
the nprofile shows an higher value at the entrance, which decreases towards the chamber. The opposite
behavior is obtained without straws which shows the additional compression by the straws but, as a matter
of fact, only at the inflow part of the intake. Lower performance of the Air-Intake means that the presence of
straws is counterproductive for this particular geometry. Regarding the effect of the inter-particle collisions
in the case without straws, both simulations have very similar results which shows the good approximation
of an ideal free molecular flow for this specific case. With collisions, a slightly lower nis achieved inside the
chamber, possibly due to the fact that the particles represent an obstacle for the incoming flow.
Table 6: DSMC Results for JAXA’s design: Influence of inter-particle collisions and straws inside the intake.
hχΘout nav g,ch ηcpch/pin nch /nin Note
km - - m−3-- -
140 10.0 0.2 4.40 ×1018 0.49 29.4 56.9 NRLMSISE-00, With Collisions
”” ”4.64 ×1018 0.50 31.0 60.0 NRLMSISE-00, Without Collisions
”” ”3.61 ×1018 0.40 24.1 46.7 NRLMSISE-00, Straws, With Collisions
B. BUSEK
Fig. A3 in the Appendix shows nalong the center line (zaxis) of the BUSEK Air-Intake design. The rapidly
decreasing nat the end of the intake is due to the assumption of a completely open outlet8with no backflow.
In the real case, the thruster systems would follow, creating also a backflow. The DSMC results of the
simulations without straws (black and blue lines) show that nsignificantly increases and reaches a region of
nearly constant state at the back, if collisions are taken into account. When collisions are neglected, that
region is missing and, instead, an almost linear increase of nalong the Air-Intake occurs with a maximum
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July 4–10, 2015
less than the maximum value of the case with collisions. This shows that the assumed cascade effect actually
exists, in which incoming particles collides with the trapped particles and form a region of higher pressure at
the back of the Air-Intake. Concerning the application of straws to this design, Fig. A3 shows a slightly lower
n, but based on the higher nin the front part it is evident that particles are actually trapped inside the Air-
Intake. Conspicuous is the existence of a region of lower nin front of the honeycomb outlet with increasing n
into both direction for the collisional case, while, without collisions, nis monotonically decreasing, similar to
the JAXA case with straws. This can be explained by the collisions of incoming particles with the trapped
ones, representing an obstacle in the case with collisions. This can be also seen in Fig. A4 that shows the
velocity along the zaxis. In the cases with collisions, there is a jump in the velocity at the entrance - the
particles already inside are pushed into the intake.
All in all, results show that colliding particles will actually create a region of higher nat the back of the
Air-Intake, and that this principle can be used to generate a region of higher constant ninside the Air-
Intake. However, an actual improvement by the existence of straw cannot be observed which motivated a
more detailed analysis of their influence.
VII. Application of the Balancing Model and Straw Sensitivity Analysis
A. Comparison of the Balancing Model with DSMC
In the following, the Balancing Model is verified for exemplary cases analyzed by DSMC. They were:
1. Fujits’s design, MSISE-90 model, χ=10.0andΘ
out =0.2 at 140 km, with collisions;
2. Fujita’s design with NRLMSISE-00 model and straws, with collisions;
3. BUSEK design without straws (with and without collisions);
4. BUSEK design with straws (with and without collisions).
Same inflow conditions as for the DSMC simulations were used. As the transmittances are different for each
species, the balancing model was applied for each species and the resulting nand ˙
Nare added together
for calculating the total values. The cases with straws represent an intake section including two separate
parts - the straws and the remaining intake without straws. Therefore, Eq. 18 is applied for combining two
transmittances ΘAand ΘBto a single value ΘAB,withAfor the straw values and Bfor the values of the
remaining free intake (a ring for the Fujita/JAXA and tube for the BUSEK case).
ΘAB =Θ
AΘB+
N
n=0
ΘA(1 −ΘB)(1 −ΘA,Clausing )[(1 −ΘA,C lausing)(1 −ΘB ,Clausing )]nΘB,Clausing (18)
Similar to the straw implementation in DSMC, transmittances were divided into ΘAB,scattered and ΘAB ,f ast,
their sum was used for the transmittances inside the balance model. The values were taken from DSMC
simulations (ΘBfor the JAXA cases from calculations of only the intake ring) or, where applicable, as known
Clausing Factors. The transmittances are summarized in Tab. A2 in the Appendix.
As Tab. 7 shows, results agree very well with DSMC results in terms of nch and ηc. Compared to the DSMC
simulations assuming free molecular flow (corresponding to the same conditions as for the Balancing model),
the relative error is less than 10%, in the Fujita/JAXA case with straws even nearly exact for nch and −1.3%
regarding ηc. For the BUSEK case, the values are also compared to the simulations without collisions and
are still in the same range. Regarding the increased discrepancy when compared to DSMC with collisions,
this is because their effect is that the incoming particles literally push the already trapped particles further
into the Air-Intake, therefore increasing ηcand n. In the Balancing Model, this cannot be taken into account,
as it assumes free molecular flow.
The Balancing Model seems to be a very good approximation for the DSMC results and it also confirms the
reduction of ηcwhen including straws inside the intake section. However, most of the used transmittances
have to be calculated by DSMC at first and, thus, this does not represent a general approach for evaluating
any arbitrary configuration. For this, the transmittances need to be calculated directly from a given geometry.
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July 4–10, 2015
Table 7: Results Balancing Model, BM , vs. DSMC Results
Case nDSMC
ch ηDSMC
cnBM
ch ηBM
cErr. nch Err. ηc
m−3% m−3%%%
JAXA 4.95 ×1018 48 5.34 ×1018 51 +7.9 +5.8
JAXA with straws 3.61 ×1018 40 3.61 ×1018 40 0.0 -1.3
BUSEK (without collisions) ∼6.1×1019 17 6.43 ×1019 18 +5.4 +4.7
BUSEK (with collisions) ∼7.5×1019 23 ””-14.3 -21.4
BUSEK with straws (without collisions) ∼6.5×1019 15 5.93 ×1019 17 -8.8 +7.8
BUSEK with straws (with collisions) ∼6.5×1019 20 ””-8.8 -16.7
B. Straw Sensitivity Analysis
DSMC simulations on various straw geometries with macroscopic vin >0 have shown that a certain fraction
of the particles does not collide with the walls and leaves the straw with inflow condition, while the remaining
part is scattered, and has only a thermal movement corresponding to Twall left. As this problem is not covered
by the well-known Clausing’s assumptions and equations, it is of interest to get a wider idea of how straw
geometries and flow conditions influence the respective transmittances. Therefore, a sensitivity analysis was
performed by DSMC simulations varying the following parameters:
•Tin and Twall;
•incoming flow velocity, vin ;
•particle mass mp, different species;
•Land R.
The results of the sensitivity analysis are shown in Tab. A3 in the Appendix. By comparing Cases 1 and
3, both having the same L/R ratio but different radii, it is expected that for the same ratio, the same Θ’s
follow. Additionally, Cases 1 and 2 show that if the ratio Twall/mpis kept constant, the transmittances do
not change. Cases 4 and 5, and 10 and 11 illustrate that Twall does not have any influence and Cases 7 and
8 that Θ’s do not change for a constant vinR/L. All in all, it can be assumed that in the considered range
of parameters, the driving non-dimensional value is Xfrom Eq. 19.
X=kBTin
mp
vin
L
R(19)
The ratio of the square-root and vin can be interpreted as the one of the lateral, thermal velocity to the
axial, macroscopic velocity. Plotting all points of Tab. A3 in terms of Θ(X) results in Fig. 11. It can be seen
that the transmittances correlate well by the use of the polynomial fits given in Eq. 20 for the scattered part
and Eq. 21 for the fast part. Based on this, different values of L/R can now be analyzed both for JAXA
and BUSEK cases. L/R values with ΘClausing given by Cole3were used, in particular the Xrange was kept
the same as for the correlation. The length is kept constant (corresponding to different straw radii) which
enables the use of the same transmittances for the remaining intake part without straws (B from Eq. 18).
Θ(X)scattered =Θ
2=0.041447835X3−0.2850944924X2+0.5808664686X−0.031410537 (20)
Θ(X)fast =Θ
1=−0.0532264802X3+0.405367838X2−1.0704252233X+1.0533360985 (21)
In Fig. 11 represents Θ3the total inflow transmittance, while the Clausing factor ΘClausing represents
the backflow transmittance. The former depends on both the geometry (L/R) and the inflow conditions
(Tin,mpand vin ), but the latter only on L/R. By merging both dependencies to the single value X,
Θ3is now dependent on solely Xand ΘClausing additionally on the geometry or the inflow conditions.
Therefore, ΘClausing is shown for a set of three different inflow conditions representing most of the range of
the sensitivity analysis and, thus, the considered RAM-EP cases. Fig. 11 shows that, independently from
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
the actual flow condition, Θ3decreases always slower than ΘClausing for low L/R ratios, but faster for large
ratios. Therefore, it is preferable to choose a design with low L/R ratios, as an high transmittance for the
inflow, together with a low transmittance for the backflow is desired. Moreover, it can be seen that for a
fixed X,Θ
Clausing increases with Tin and decreases with mpand vin , while Θ3remains constant. By this,
it can be assumed that, e.g., lighter species are collected less efficiently than heavier ones, as it is also shown
in Fig. A5. Fig. A5, A6, A7, and A8 in the Appendix show the resulting dependence of nch and ηcfrom
L/R for the separate species of the JAXA case and three different intake lengths for the BUSEK case. They
show that, for the considered range of parameters, the Air-Intake is supposed to be most efficient for small
L/R, corresponding to a simple grid. To verify this conclusion, DSMC simulations for shorter geometries
should be performed which would additionally include the influence of inter-particle collisions.
Figure 11: Generalized Cylinder Transmittances
VIII. Conclusion
This paper focused on the Air-Intake which collects and drives the atmosphere particles to the thruster,
in an air-breathing electric propulsion system. Recent studies have been reviewed, in particular the focus
has been on the Fujita’s design, its improvement from JAXA and the BUSEK design. Their early results
have been verified through our DSMC code.
Moreover, the introduction of straws and the influence of inter-particle collisions inside the Air-Intake, that
could improve the collection efficiencies, have been analyzed. In order to simulate the presence of straws, a
method of extraction of the velocity distribution at the end of a single straw to be inserted as input condition
for the Air-Intake has been verified and applied.
A sensitivity analysis on the straws in terms of various input parameter has been performed and showed
the dependency of the transmittances results. The velocity distribution shows that the particles will always
interact with the straw and, therefore, only a part of the flow will reach the end with a macroscopic velocity
while the rest will be only moving due to thermal diffusion.
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
In particular for the Fujita’s design, the introduction of the straws of JAXA studies has shown a decrease
collection efficiency ηcand a smaller total number density nch inside the chamber than in the case without.
The application of a newer atmospheric model showed slightly lower atmospheric nand lower Tin.
Regarding the BUSEK study, the principle of a collision cascade at the end of a long tube shaped Air-Intake
that generates a compression has been verified. In particular a cushion of almost constant nis present in
front of the end of the Air-Intake and its length is increased by the addition of straws, although with a
decrease of n.
A balancing model based on separated particle flows and transmittances has been introduced and compared
with the DSMC results which have shown a good approximation in the results, however it must be sustained
by the calculation of transmittances a priori. With this model a sensitivity analysis over the L/R ratio of
the straws has been performed and applied to Fujita’s and BUSEK Air-Intakes.
This was additionally sustained by the development of a correlation between geometry/flow data and the
respective transmittance. Ideally, it should be as high as possible for the inflow, and as low as possible for
the backflow in an Air-Intake. The results show indeed, that a lower L/R ratio is preferable as it provides
higher ηcand nch. It suggests that a grid, rather than a honeycomb structure of straws at the front of the
Air-Intake, shall be used to form a higher performance Air-Intake.
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
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Appendix
Table A1: Inflow Conditions for Fujita/JAXA cases.
hn
tot,in Tin vin nN2nO2nOnAr nHe nNAtm. Model
×1016 ×1016 ×1015 ×1016 ×1013 ×1013 ×1012
km m−3Kkm/sm
−3m−3m−3m−3m−3m−3-
140 8.73 682.07.82 5.68 3.84 2.67 - - - MSISE-90
”7.73 580.57.82 4.36 3.79 2.98 8.68 0.29 - NRLMSISE-00
180 1.75 968.07.80 0.90 0.47 0.80 - - - MSISE-90
”1.38 731.47.80 0.53 0.29 0.815 0.45 4.12 9.30 NRLMSISE-00
Table A2: Balancing Model Results.
Straw Ring/Tube
Case Θscattered Θfast ΘC lausing Θscattered Θfast ΘClausing Θintake1Θintak e2
Fujita/JAXA, O 1110.289 0.392 0.212 0.681 0.212
”, N21110.276 0.466 0.212 0.742 0.212
”, O21110.253 0.512 0.212 0.765 0.212
Fujita/JAXA, O 0.330 0.200 0.109 0.255 0.472 0.222 0.401 0.078
”, N20.330 0.200 0.109 0.255 0.472 0.222 0.488 0.078
”, O20.310 0.330 0.109 0.202 0.597 0.222 0.500 0.078
”, He 0.290 0.064 0.109 0.243 0.265 0.222 0.256 0.078
”, Ar 0.290 0.38 0.109 0.182 0.642 0.222 0.533 0.078
BUSEK 1110.265 0.447 0.162 0.712 0.162
”0.307 0.099 0.067 0.240 0.507 0.181 0.315 0.049
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Table A3: Extracted Straws Transmittances from DSMC Simulations.
Case L/R vin Twall Tin mp/El. Θfast Θscattered Note
No. -km/sK K ×10−26 kg --
110 7.80 300 300 2.66/O0.613 0.192 R=R1
210 7.80 600 600 5.31/2×O0.613 0.192
310 7.80 300 300 2.66/O0.616 0.192 R=R1/2
410 7.80 150 150 2.66/O0.722 0.139
510 7.80 600 150 2.66/O0.721 0.139
610 15.60 300 300 2.66/O0.803 0.099
710 3.90 300 300 2.66/O0.326 0.311
820 7.80 300 300 2.66/O0.325 0.311
920 7.80 300 300 2.66/O0.324 0.311 nin ≈n140 km, Collisions
10 10 7.80 600 600 2.66/O0.475 0.256
11 10 7.80 150 600 2.66/O0.474 0.256
12 14.89 7.80 300 300 2.66/O0.450 0.265
13 4.44 7.80 300 300 2.66/O0.825 0.088
14 60.63 7.80 300 300 2.66/O∼0.05 ∼0.25
15 34.48 7.80 300 300 2.66/O0.141 0.323
16 34.48 3.50 300 250 7.31/CO20.100 0.306
17 20 7.82 300 580.5 6.34/Ar 0.380 0.293
18 20 7.82 300 580.5 0.665/He 0.063 0.281
19 20 3.91 300 1451.25 6.65/10 ×He 0.063 0.281
20 20 7.82 300 580.5 4.65/N20.307 0.315
21 20 7.82 300 580.5 2.66/O0.204 0.334
22 20 7.82 300 580.5 5.31/O20.333 0.308
(If not mentioned, inter-particle collisions are switched off, assuming free molecular flow.)
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z, m
0 0.2 0.4 0.6 0.8 1 1.2
vz, m/s
0
100
200
Fujita Air-Intake 140 km, χ=10.0, MSISE-90, v z and n along a line
vz, ΘOut =0.2
n, ΘOut =0.2
vz, ΘOut =0.1
n, ΘOut =0.1
vz, Chamber , ΘOut =0.2
nz, Chamber, ΘOut =0.2
n, m -3
×10 18
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
(a) Air-Intake, DSMC results at 140km for JAXA Design, MSISE-90.
z/L, -
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
vz, m/s
0
20
40
60
80
100
Fujita Air-Intake 180 km, ΘOut =0.2, v z and n along a line
n, m -3
×10 18
0
0.5
1
1.5
2
vz, χ=10
n, χ=10
vz, χ=20
n, χ=20
vz, χ=20, NRLMSISE-00
nz, χ=20, NRLMSISE-00
(b) Air-Intake, DSMC results at 180km for JAXA Design, MSISE-90, NRLMSISE-00
Figure A1: Air-Intake, JAXA results, MSISE-90 and NRLMSISE-00.
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
z, m
0 0.2 0.4 0.6 0.8 1 1.2
vz, m/s
0
100
200
Fujita Air-Intake 140 km, χ=10.0, ΘOut =0.2, NRLMSISE-00, v z and n along a line
vz
n
vz, without collisions
n, without collisions
vz, straws
nz, straws
n, m -3
×10 18
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
Figure A2: Air-Intake, DSMC results, JAXA Design with straws NRLMSISE-00.
z, m
00.5 11.5 22.5 33.5 4
n,m -3
×10 19
0
1
2
3
4
5
6
7
8BUSEK Air-Intake Mars, n along the center line
with collisions
without collisions
straws with collisions
straws without collisions
Figure A3: Density Along Center Line, BUSEK Design
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
z,m
00.5 11.5 22.5 33.5 4
vz,m/s
0
20
40
60
80
100
120
140
160
180
BUSEK Air-Intake Mars, v z along the center line
with collisions
without collisions
straws with collisions
straws without collisions
Figure A4: Velocity Along Center Line, BUSEK Design
L/R,-
6 8 10 12 14 16 18 20
ηc,-
20
25
30
35
40
45
50
55
60
65
70 Collection Efficiency, JAXA Air-Intake, χ=10.0 over L/R straw ratio
O
N2
O2
He
Ar
Figure A5: Balancing model applied to the JAXA Design, Collection Efficiency over L/R.
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
L/R,-
6 8 10 12 14 16 18 20
nch/n in , -
10
20
30
40
50
60
70
80
90
100
110
nch/n in ratio, JAXA Air-Intake, χ=10.0 over L/R straw ratio
O
N2
O2
He
Ar
Figure A6: Balancing model applied to the JAXA Design, Number Density Ratio over L/R.
L/Rstraw ,-
0 5 10 15 20 25 30 35 40
ηc,-
10
15
20
25
30
35
40
45 Collection Efficiency, BUSEK Design, over L/R straw ratio
Ltube,after straw =3.2 m
Ltube,after straw =1.5 m
Ltube,after straw =6.0 m
Figure A7: Balancing model applied to the BUSEK Design, Collection Efficiency over L/R.
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
L/Rstraw ,-
0 5 10 15 20 25 30 35 40
nch/n in , -
100
120
140
160
180
200
220
240
260
280
300
nch/n in ratio, BUSEK Design, over L/R straw ratio
Ltube,after straw =3.2 m
Ltube,after straw =1.5 m
Ltube,after straw =6.0 m
Figure A8: Balancing model applied to the BUSEK Design, Number Density Ratio over L/R.
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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan
July 4–10, 2015
Acknowledgments
F. Romano gratefully thanks the Landesgraduiertenf¨orderung of the University of Stuttgart for the finan-
cial support; the authors acknowledge Mr. Yasuyoshi Hisamoto for the fruitful exchange of data regarding
the japanese studies.
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