Lateral and Axisymmetric Ferrofluid Oscillations in a Cylindrical Tank in Microgravity

Full text

Lateral and axisymmetric ferrofluid oscillations in a cylindrical
tank in microgravity
Álvaro Romero-Calvo ∗
Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, CO, United States
Antonio J. García-Salcedo†, Francesco Garrone‡, Inés Rivoalen§, and Filippo Maggi¶
Department of Aerospace Science and Technology, Politecnico di Milano, Milan, Italy
I. Introduction
Magnetic polarization forces are becoming increasingly popular in space technology as a means of controlling
multiphase flows in reduced gravity environments. Applications include mass transfer [
1
–
5
], spacecraft propulsion
[
6
–
8
], thermomagnetic convection [
9
,
10
], phase separation [
11
], sample holding [
12
], or diamagnetically-enhanced
electrolysis [
13
], among others. The polarization force can be induced on natural liquids and magnetically-enhanced
substances, which are classified as diamagnetic, paramagnetic, or ferromagnetic. Although the dia/paramagnetic force is
so weak that terrestrial applications are almost nonexistent, in microgravity even the slightest disturbance can determine
the behavior of a fluid system [
14
]. The same force acting on a highly-susceptible ferrofluid can be dominant both on
Earth and in space [15].
The simulation of low-gravity multiphase flows subject to inhomogeneous polarization forces is severely complicated
by the coupling between fluid and magnetic problems and the presence of strong capillary forces [
16
]. However, some
of the most important space applications can still be addressed by means of efficient quasi-analytical tools. Following
the track of classical low-gravity fluid mechanics research [
17
,
18
], recent works have focused on the study of the
equilibrium, stability, and free surface oscillations of inviscid magnetic liquid interfaces [
19
]. The latter is of particular
importance for the development of novel magnetic liquid sloshing control devices, which have been recently proposed to
complement or substitute traditional capillary propellant management devices [
16
]. The final goal of such systems is to
transform a highly unpredictable propellant sloshing problem into a simple and reliable superposition of analogous
linear oscillators.
Even though low-gravity liquid sloshing and its interactions with spacecraft dynamics continue to be very active
fields of research [
20
–
26
] and a number of publications have explored the magnetic positioning of liquid oxygen and
low-susceptibility ferrofluids in microgravity [
27
–
35
], the study of highly susceptible ferrofluids for space applications
∗
Graduate Research Assistant, Department of Aerospace Engineering Sciences, University of Colorado Boulder,
alvaro.romerocalvo@
colorado.edu, AIAA Student Member.
†Graduated student, Department of Aerospace Science and Technology, Politecnico di Milano.
‡Graduated student, Department of Aerospace Science and Technology, Politecnico di Milano.
§Graduated student, Department of Aerospace Science and Technology, Politecnico di Milano.
¶Associate Professor, Department of Aerospace Science and Technology, Politecnico di Milano, AIAA Senior Member.
Accepted Manuscript
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is still in its infancy. The accurate determination of the modal shapes and frequencies of oscillating ferrofluid surfaces
in low-gravity is, however, critical for magnetic sloshing control devices. In order to cover this fundamental gap, the
European Space Agency (ESA) Drop Your Thesis! 2017 [
36
,
37
] experiment studied the axisymmetric oscillations
of water-based ferrofluids in cylindrical tanks when subjected to an inhomogeneous magnetic field in microgravity.
The results show that the theoretical model presented in Ref.
19
overestimates the axisymmetric magnetic frequency
response, pointing to the existence of unaccounted physical effects such as viscous damping or a complex magnetic
influence on the contact line hysteresis process [
38
]. Lateral oscillations, which have an intrinsic technical value as main
sources of attitude disturbances, remained unexplored. The United Nations Office for Outer Space Affairs (UNOOSA)
DropTES 2019 StELIUM experiment, whose design is described in Refs. [
39
–
41
], was subsequently launched at the
drop tower of the Center of Applied Space Technology and Microgravity (ZARM) to complement the analysis initiated
in Ref. 38 with the lateral sloshing case.
This technical note presents the final results of the UNOOSA DropTES 2019 StELIUM experiment and addresses the
influence of the magnetic field generated by a circular coil on the fundamental axisymmetric and lateral frequencies of an
oscillating ferrofluid located in a cylindrical tank in microgravity. Predictions from the aforementioned quasi-analytical
free surface oscillations model are compared with the experiments under different regimes. The framework of analysis
introduced in Ref.
19
is summarized in Sec. II, followed by a description of the experimental methods in Sec. III and the
discussion of results in Sec IV.
Fig. 1 Geometry of the system under study.
2
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II. Magnetic free surface oscillations model
The system under study, represented in Fig. 1, consists of an upright cylindrical tank with radius
𝑎
that contains a
volume
𝑉
of a water-based ferrofluid in microgravity. The liquid is incompressible and Newtonian, and has density
𝜌
,
surface tension
𝜎
, and static wall contact angle
𝜃𝑐
. The free space is filled by air at pressure
𝑝𝑔
. In microgravity, a coil
located at the base of the vessel generates an inhomogeneous axisymmetric magnetic field
𝑯
that interacts with the
magnetic fluid with magnetization
𝑀
(
𝐻
), with
𝐻
and
𝑀
being the modules of their corresponding vector fields. In
Fig. 1,
𝑠
is a curvilinear coordinate along the meniscus with origin in the vertex
𝑂
, and the local vertical coordinates
are given by
𝑤
(fluid surface - vertex),
𝑓
(meniscus - vertex) and
ℎ
(fluid surface - meniscus). The dynamic (
𝑆
) and
static (
𝑆0
) fluid surfaces meet the wall
𝑊
of the vessel at the contact lines
𝐶
and
𝐶0
, respectively. The set of cylindrical
coordinates {𝑟, 𝜃 , 𝑧}, centered at the vertex of the meniscus, is considered in the analysis.
The oscillations of free liquid surfaces in microgravity have traditionally been studied through modal analysis [
42
,
43
]
and then validated using microgravity experiments [
44
–
52
] already since the development of the first non-magnetic
low-gravity free surface oscillation model by Satterlee and Reynolds in 1964 [
53
]. One of the main reasons for adopting
this approach is the complete analogy between the modal decomposition process and the superposition of linear
spring-mass-damper systems employed to model liquid sloshing [
14
,
18
,
54
,
55
]. The framework here presented for
magnetic liquids, summarized from Ref.
19
, is not an exception. It assumes an inviscid, potential, isothermal, and
magnetically dilluted flow to which the ferrohydrodynamic Bernoulli equation [
56
] is applied. After linearizing the
equations of motion around the meniscus, the variational principle
(1a)
𝐽
=
∬𝑆0"H2
𝑅
1 + 𝐹2
𝑅3/2
+
1
𝑅2
H2
𝜃
1 + 𝐹2
𝑅1/2
+
𝐵𝑜
+
𝐵𝑜mag
(
𝑅
)
H2−
Ω
2
Φ
H#𝑅𝑑𝑅 𝑑𝜃 −
Ω
2∬𝑊
Φ
𝐺𝑅𝑑𝑅𝑑𝜃 −
Γ
Z𝐶0"H2
1 + 𝐹2
𝑅3/2#𝑅=1
d
𝜃
=
extremum
is obtained, subjected to
∇2Φ= 0 in 𝑉 , (1b)
H=Φ𝑍−𝐹𝑅Φ𝑅on 𝑆0,(1c)
𝐺=Φ𝑍−𝑊𝑅Φ𝑅on 𝑊, (1d)
H𝑅=ΓHon 𝐶0,(1e)
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where the subindices denote the partial derivatives. The magnetic Bond number is defined as
𝐵𝑜mag (𝑅) = −𝜇0𝑎2
𝜎𝑀𝜕𝐻
𝜕𝑧 + M𝑛
𝜕M𝑛
𝜕𝑧 𝐹(𝑅)
,(2)
and describes the ratio between magnetic and surface tension forces. The dimensionless cylindrical coordinates
𝑅
=
𝑟/𝑎
,
𝑍
=
𝑧/𝑎
, vertical coordinates
𝐹
=
𝑓 /𝑎
,
𝜙
(
𝑅, 𝜃 , 𝑍, 𝑡
) =
p𝑔0𝑎3
Φ(
𝑅, 𝜃, 𝑍
)
sin
(
𝜔𝑡
),
ℎ
(
𝑅, 𝜃 , 𝑡
) =
p𝑎𝑔0/𝜔2H
(
𝑅, 𝜃
)
cos
(
𝜔𝑡
),
circular frequency Ω
2
=
𝜌𝑎3𝜔2/𝜎
, and hysteresis parameter Γ=
𝑎𝛾
are employed with
𝑔0
= 9
.
81
𝑚/𝑠2
being the
gravitational acceleration at ground level,
𝜙
the dimensional perturbed velocity potential, and
𝜔
the dimensional circular
frequency.
𝐺
is a function defined by Eq. 1d that accounts for the non-penetration wall boundary condition and that
arises naturally after reducing a volume integral in the original form of Eq. 1a to a surface integral using Green’s
theorem, as described in Ref.
43
. The hysteresis parameter Γin Eq. 1e can be regarded as the dynamic equivalent of the
static contact angle
𝜃𝑐
, and describes how the dynamic surface interacts with the walls of the container. The limiting
cases Γ= 0 and Γ
→ ∞
lead to the free-edge and stuck-edge conditions, respectively. In other words, Γdescribes how
freely the contact line
𝐶
slides over the walls of the tank, and has consequently a large influence on the shape of the
eigenmodes and their associated eigenfrequencies [38].
The system described by Eqs. 1a-e is solved in two steps. First, the axisymmetric meniscus
𝐹
(
𝑅
)is computed with an
iterative algorithm that accounts for the fluid-magnetic coupling. The algorithm solves the meniscus balance equations
(derived in Ref.
19
) for a given magnetic field, and then the magnetic field is recomputed in Comsol Multiphysics
employing the new interface. The process is repeated until the vertex of the meniscus converges with an error of
±
0
.
1
mm. In a second step, Eqs. 1a-e are transformed into an eigenvalue problem by using Ritz’s method with a set of
admissible functions that enforce the boundary conditions given by Eqs. 1b-e. The process relies on the previously
computed axisymmetric meniscus
𝐹
(
𝑅
)and
𝐵𝑜mag
(
𝑅
)number, and takes the geometry and magnetic environment, the
physical properties of the liquid (
𝜌
,
𝜎
,
𝑀
(
𝐻
)), and the wall boundary conditions (
𝜃𝑐
,Γ) as inputs. The solution of the
eigenvalue problem is the eigenvalue
𝜔𝑛
and eigenmode
ℎ(𝑛)
for the axisymmetric or lateral mode
𝑛
. Further details on
the formulation and operation of this method can be found in Ref.
19
. Its implementation is fully equivalent (excluding
liquid and geometrical properties) to that described in Ref. 38.
III. Materials and methods
A. Experimental setup
The experimental setup of StELIUM, depicted in Fig. 2, is designed to operate in a 9.3 s catapult launch at ZARM’s
drop tower [
57
]. The system, that is thoroughly described in Ref.
39
, is subdivided into two identical assemblies that
contain a cylindrical Plexiglas container, a surrounding electromagnetic coil, and an horizontal linear slider that imposes
a lateral oscillation to the fluid in the middle of the flight. This oscillation induces a lateral sloshing wave that is
4
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Detection system
Container assembly
Drop tower capsule
ZARM’s drop tower
953 mm
200 mm
Fig. 2 Experimental setup (not in scale).
complemented with the axisymmetric wave induced by the initial launch acceleration. A restoring polarization force is
applied to the ferrofluid during this process by operating the coils with constant current intensities
𝐼
ranging from 0 to
20 A. The 20 A level generates an inhomogeneous magnetic force distribution with characteristic meniscus magnetic
Bond number and accelerations values of ∼35 and ∼0.71 m/s2, respectively.
The evolution of the free surface is captured by a custom device located on top of each container. A laser line
is pointed at the surface of the ferrofluid while a camera records its projection. The deformation of the line is then
correlated with the height of the surface, and the 3D liquid surface profile is extracted. The system is able to compute the
axisymmetric meniscus, from which the apparent contact angles
𝜃𝑐
are derived, and the evolution of the axisymmetric
and lateral waves along the direction of excitation. A modal projection is subsequently applied to compute the hysteresis
parameter Γfrom the lateral waves, while a Fast Fourier Transform of the movement of the laser line is employed to
extract the modal frequencies. Γis here assumed to be the same for axisymmetric and lateral modes. This assumption is
motivated by the difficulty in extracting Γin the axisymmetric case, where magnetic and non-magnetic modal shapes
are very similar [
38
]. Further details on the design and operation of the detection system can be found in Refs. [
40
,
41
].
B. Liquid properties
The liquid tank has 11 cm diameter and 20 cm height, and is filled up by a 1:5 volume solution of the Ferrotec
EMG-700 water-based ferrofluid. Oil-based options are discarded to avoid the visualization issues reported in previous
works [
27
]. The ferrofluid has a density of 1058 kg/m
3
, surface tension of 55
.
6mN/m, a viscosity of 1.448 mPa
·
s,
employs an anionic surfactant, and contains a 1.16% vol concentration of 10 nm magnetic nanoparticles. The
magnetization curve of the solution, that determines its magnetic response, was measured with a MicroSense EZ-9
Vibrating Sample Magnetometer, resulting in an initial magnetic susceptibility 𝜒= 0.39 and saturation magnetization
5
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Table 1 Experimental results for contact angle, fundamental oscillation frequency and damping ratios for
axisymmetric and lateral waves, and lateral hysteresis parameter
I
[A]
𝜃𝑐
[deg]
Γ
[-]
𝜔𝑎,1
[rad/s]
𝜉𝑎,1
[-]
𝜔𝑙,1
[rad/s]
𝜉𝑙,1
[-]
Upper
0 60.52 16.75 4.52 0.19 2.58 0.21
10 59.87 7.23 5.82 0.15 3.62 0.16
15 62.36 7.11 7.05 0.14 4.60 0.12
20 65.67 4.41 7.60 0.13 5.30 0.11
Lower
0 47.52 15.27 3.62 0.23 2.21 0.22
10 53.07 4.88 5.41 0.16 3.36 0.17
15 58.15 5.44 5.98 0.17 4.18 0.15
20 * * * * 4.90 *
*
Not available due to a malfunction of the primary detection
system.
𝑀𝑠= 4160 ±100 A/m. The curve is fitted with a function of the form
𝑀(𝐻) = 2
𝜋[𝜅1arctan (𝜅3𝐻)+𝜅2arctan (𝜅4𝐻)] ,(3)
where 𝜅1= 1120.25 A/m, 𝜅2= 3103.56 A/m, 𝜅3= 8.49 ·10−6m/A, and 𝜅4= 1.94 ·10−4m/A.
IV. Results and discussion
Estimations for the fundamental axisymmetric and lateral frequencies
𝜔𝑎/𝑙
, fundamental damping ratios
𝜉𝑎/𝑙
,
contact angle
𝜃𝑐
, and lateral hysteresis parameter Γare obtained after analyzing the laser line projection as described
in Sec. III.A. Results are shown in Table 1 as a function of current intensity
𝐼
for upper and lower containers. Data
for the lower container at the 20 A drop is recovered from a time-of-flight sensor. Even though they share the same
geometry and a very similar magnetic environment, each container has significantly different values of
𝜃𝑐
(two-sample
t-test
𝑡
(5) = 3
.
07,
𝑝
= 0
.
03), revealing dissimilar wettability conditions. An analogous bias is observed with Γ, although
in this case it is not statistically significant (
𝑡
(3) = 0
.
90,
𝑝
= 0
.
43). These effects may be attributed to the potentially
uneven application of the hydrophobic treatment over the internal walls of the tanks and to the large sensitivity of water
to surface contamination [58, 59].
Microgravity facilities are expensive to operate and their access is generally limited. Having only 4 launch
opportunities, the StELIUM team decided to favor the derivation of statistical trends rather than statistical repetitions.
The comparative analysis between individual data points shall thus be treated with care since data dispersion may impair
accuracy. Nevertheless, there seems to be a strong dependence between Γand
𝐼
when switching between non-magnetic
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Lower:
Upper: Experimental
Experimental
Interpolated Γ, θ
Interpolated Γ, θ
Mean Γ, θ
Mean Γ, θ
Free edge
Free edge
Stuck edge
Stuck edge
Axisymmetric Freq. [rad/s]
4
6
8
10
Coils current intensity [A]
0 5 10 15 20
Lateral Freq. [rad/s]
2
3
4
5
6
Coils current intensity [A]
0 5 10 15 20
Fig. 3 Axisymmetric (left) and lateral (right) fundamental frequencies as a function of the coils current
intensity.
(
𝐼
= 0 A) and magnetic (
𝐼
= 10 A) regimes. A 56.3% and 68.0% drop in Γis observed for upper and lower containers,
respectively, suggesting the existence of a shift from surface-tension-dominated to magnetic-force-dominated regimes.
To the best knowledge of the authors, this effect has not been reported before and should be confirmed by future studies.
In spite of the aforementioned limitations, solid statistical conclusions can be drawn through the application of
appropriate statistics to the variables of interest, as discussed in Ref.
38
. Figure 3 shows the fundamental axisymmetric
and lateral free surface oscillation frequencies as a function of current intensity. Experimental values, whose error
bands are derived by identifying the FFT resolution with the
±
3
𝜎
Gaussian interval, are superposed with free edge
(Γ= 0) and stuck edge (Γ
→ ∞
) estimations from the model described in Sec. II using mean contact angle values of
62.15°
and
52.91°
for upper and lower containers, respectively. The use of mean contact angle values is motivated by
the absence of a significant linear correlation between
𝐼
and
𝜃𝑐
for upper (
𝑟
(2) = 0
.
79,
𝑝
= 0
.
21) and lower (
𝑟
(1) = 0
.
99,
𝑝
= 0
.
10) containers
∗
. From a technical perspective, reducing the number of inputs simplifies the characterization and
simulation of the system. The free edge condition is associated with the lowest free surface frequency, while the stuck
edge case sets the maximum possible value. Although experimental lateral frequencies fall withing those boundaries,
the same does not seem to happen in the axisymmetric case.
Two more theoretical predictions are superposed in Fig. 3: a first one that considers a linear interpolation of the
contact angle
𝜃𝑐
and hysteresis Γvalues reported in Table 1, and a second that assumes average
𝜃𝑐
and magnetic Γ
(upper: 6.25, lower: 5.16) results. Both curves are practically identical, exemplifying the small effect of the contact angle
variability, but diverge by
∼
0.2 rad/s for
𝐼
= 0. This effect is attributed to the large increase of Γin the non-magnetic case.
The most remarkable feature of these predictions is, however, the excellent agreement with experimental results observed
for the lateral frequencies. While the interpolation of Γand
𝜃𝑐
results in an adjusted coefficient of determination
∗
However, previous works [
60
–
62
] have reported a dependence between the apparent contact angle and the applied magnetic field of ferrofluid
droplets, an effect that should be explored with larger datasets for the setup employed in this work.
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𝑅2
adj
= 0
.
983 (with 3 explanatory variables, Γ,
𝜃𝑐
, and
𝐼
) and a mean-squared error of
𝑀𝑆𝐸
= 0
.
01 rad/s, the use of
averaged values returns
𝑅2
adj
= 0
.
976 with a single explanatory variable
𝐼
and an
𝑀𝑆𝐸
= 0
.
02 rad/s. Both models lead
to normally distributed residuals according to the Saphiro-Wilk test (
𝑝
= 0
.
075,
𝑊
= 0
.
84 and
𝑝
= 0
.
49,
𝑊
= 0
.
93 for
the fitted and averaged models, respectively). Interestingly, if the frequencies are computed with a restoring inertial
acceleration equivalent to the mean magnetic acceleration at the interface (which, for
𝐼
= 20 A, is
∼
0.71 m/s
2
), the
deviation at 20 A is just
∼
0.3 rad/s for both the free and stuck lateral cases. The reasons are that (i)
𝐵𝑜mag
(
𝑅
)remains
almost constant along the meniscus for this setup [
38
], and (ii) the meniscus profile is only slightly deformed by the
magnetic field. In other words, when these two conditions apply, the frequencies can be roughly estimated by assuming
a low-gravity interface subject to an equivalent inertial acceleration.
Results for lateral oscillations are in sharp contrast with the axisymmetric case, where the free-edge model
(
𝑅2
adj
= 0
.
873) performs much better than the rest (e.g. the averaged alternative,
𝑅2
adj
= 0
.
486). This is consistent with
the analysis reported in Ref.
38
, that assumes the free-edge condition, and with the fact that the Γvalues are derived
from the shape of the lateral sloshing waves. The magnetic response of the model (i.e. its current-frequency slope)
cannot be robustly assessed because, unlike in Ref.
38
, the small sample size prevents any meaningful comparison.
Furthermore, an
𝑅2
adj
coefficient of just 0.873 is far from acceptable for confirming or denying the conclusions of said
reference, where the analytical framework in Sec. II is shown to overestimate the axisymmetric free surface oscillation
frequencies. This effect is attributed to unmodeled physical effects, like the potential coupling between Γand
𝐼
reported
in Tab. 1, that may be addressed in a future work.
The damping ratios reported in Table 1 are computed by means of the half-power bandwidth method as
𝜉𝑎/𝑙 =1
2
Δ𝜔−3𝑑𝐵
𝜔𝑎/𝑙
,(4)
where Δ
𝜔−3𝑑𝐵
is the frequency peak width between the -3 dB points on the FFT spectrum. The division by
𝜔𝑎/𝑙
justifies
the decrease of
𝜉𝑎/𝑙
with
𝐼
. Most importantly, the excellent agreement between inviscid theoretical and experimental
lateral frequencies confirms the negligible impact of fluid viscosity and magnetically-induced viscosity [
56
,
63
] on the
sloshing problem for the system under study.
From a technical perspective, this analysis shows that, given an educated estimate of
𝜃𝑐
and Γand an appropriate
characterization of the geometric and magnetic environments, the inviscid model first introduced in Ref.
19
and
summarized in Sec. II is able to predict the lateral sloshing parameters of a highly-susceptible low-viscosity magnetic
liquid in microgravity. This is important for future space applications involving magnetic positive positioning or
magnetic liquid sloshing [
16
] since lateral oscillations represent the largest fuel-induced attitude control disturbance.
Furthermore, the results confirm the importance of coupling the magnetic and fluid problems for the study of the
dynamics of highly susceptible ferrofluids: if the simplified uncoupled model introduced in Ref.
38
was considered
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instead, the frequencies at 20 A would be underestimated by 1.37 rad/s and 0.74 rad/s for the axisymmetric and lateral
cases, respectively, falling well beyond the error bands. The excellent agreement between experimental results and
the averaged model, that operates employing a global estimation of
𝜃𝑐
and Γ, makes basic science discussions on
the dependence of such parameters on the applied magnetic field less relevant for most applications, at least for the
configuration here considered. The same can be said about axisymmetric oscillations, which have a weaker impact on
the spacecraft dynamics [14, 18].
V. Conclusions
The final results of the UNOOSA DropTES StELIUM experiment, that studies the axisymmetric and lateral
oscillations of a ferrofluid solution in a series of drop tower experiments, validate the quasi-analytical magnetic sloshing
model presented in Ref.
19
for the study of lateral oscillations. The small dependence of the contact angle and hysteresis
parameter with the applied magnetic field is shown to have an almost negligible impact on the frequency response of the
system under study, which simplifies the development of magnetic sloshing control devices. Although the presence
of unmodeled physical effects reported in Ref.
38
for the axisymmetric free surface oscillations problem cannot be
confirmed due to the small sample size, existing results indicate that the axisymmetric frequencies follow a free-edge
behavior rather than the measured lateral hysteresis parameter. The results highlight the importance of accounting for
the fluid-magnetic coupling in applications involving highly susceptible ferrofluids.
Competing Interests
The authors declare no competing interests.
Funding Sources
This work was supported by the United Nations Office for Outer Space Affairs (UNOOSA), the Center of Applied
Space Technology and Microgravity (ZARM) and the German Space Agency (DLR) in the framework of the UNOOSA
DropTES Programme 2019. Further financial and academic support was obtained from Ferrotec Corporation, Politecnico
di Milano, the University of Seville, the European Space Agency (ESA) and the European Low Gravity Research
Association (ELGRA). A.R.C. acknowledges the financial support offered by the La Caixa Foundation (ID 100010434),
under agreement LCF/BQ/AA18/11680099.
Acknowledgments
We acknowledge the financial, technical, and academic support offered by UNOOSA, DLR, ZARM, Ferrotec
Corporation, Politecnico di Milano, and the University of Seville. We also thank ESA and ELGRA for financing
the presentation of this work at the 70th International Astronautical Congress (IAC) and the 26th ELGRA Biennial
9
Accepted Manuscript
The final version of this paper can be found in https://doi.org/10.2514/1.J061351

Symposium and General Assembly. We are in debt with ZARM’s drop tower engineers Jan Siemer and Fred Oetken,
ZARM’s point of contact Dr Thorben Könemann and UNOOSA’s point of contact Ayami Kojima for their endless
support. We would like to thank the technicians Giovanni Colombo, Alberto Verga and the PhD student Riccardo Bisin
from the Space Propulsion Laboratory (SPLab) of Politecnico di Milano for their academic and technical assistance, as
well as the rest of members of this research group for contributing to the creation of an extraordinary professional and
human environment. Finally, we acknowledge the support offered by Prof. Elena Castro-Hernández, Prof. Gabriel
Cano-Gómez, and Prof. Miguel Herrada in the early stages of the StELIUM project.
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