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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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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan

July 4–10, 2015

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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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan

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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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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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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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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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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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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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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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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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan

July 4–10, 2015

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.)

21

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, 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.

22

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

23

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.

24

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.

25

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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Joint Conference of 30th ISTS, 34th IEPC and 6th NSAT, Hyogo-Kobe, Japan

July 4–10, 2015