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Axisymmetric Ferrofluid Oscillations in a Cylindrical Tank in Microgravity

DOI:10.1007/s12217-021-09894-4
Authors:
Álvaro Romero-Calvo at Georgia Institute of Technology
Álvaro Romero-Calvo
Ma Herrada at Universidad de Sevilla
Ma Herrada
Tim H. J. Hermans at Utrecht University
Tim H. J. Hermans
  • Utrecht University
Lidia Parrilla Benítez
Lidia Parrilla Benítez
Lidia Parrilla Benítez
  • This person is not on ResearchGate, or hasn't claimed this research yet.
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Abstract and Figures

The sloshing of liquids in low-gravity entails several technical challenges for spacecraft designers due to its effects on the dynamics and operation of space vehicles. Magnetic settling forces may be employed to position a susceptible liquid and address these issues. Although proposed in the early 1960s, this approach remains largely unexplored. In this paper, the equilibrium meniscus and axisymmetric oscillations of a ferrofluid solution in a cylindrical tank are studied for the first time while subject to a static inhomogeneous magnetic field in microgravity. Coupled fluid-magnetic simulations from a recently developed inviscid magnetic sloshing model are compared with measurements collected at ZARM's drop tower during the ESA Drop Your Thesis! 2017 campaign. The importance of the fluid-magnetic interaction is explored by means of an alternative uncoupled framework for diluted magnetic solutions. The coupled model shows a better agreement with experimental results in the determination of the magnetic deformation trend of the meniscus, but the uncoupled framework gives a better prediction of the magnetic frequency response which finds no theoretical justification. Although larger datasets are required to perform a robust point-by-point validation, these results hint at the existence of unmodeled physical effects in the system.
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https://doi.org/10.1007/s12217-021-09894-4
ORIGINAL ARTICLE
Axisymmetric Ferrofluid Oscillations inaCylindrical Tank
inMicrogravity
ÁlvaroRomero‑Calvo1 · MiguelÁngelHerrada2· TimH.J.Hermans3· LidiaParrillaBenítez2·
GabrielCano‑Gómez4· ElenaCastro‑Hernández2
Received: 6 October 2020 / Accepted: 30 May 2021
© The Author(s), under exclusive licence to Springer Nature B.V. 2021
Abstract
The sloshing of liquids in low-gravity entails several technical challenges for spacecraft designers due to its effects on the
dynamics and operation of space vehicles. Magnetic settling forces may be employed to position a susceptible liquid and
address these issues. Although proposed in the early 1960s, this approach remains largely unexplored. In this paper, the
equilibrium meniscus and axisymmetric oscillations of a ferrofluid solution in a cylindrical tank are studied for the first time
while subject to a static inhomogeneous magnetic field in microgravity. Coupled fluid-magnetic simulations from a recently
developed inviscid magnetic sloshing model are compared with measurements collected at ZARM’s drop tower during the
ESA Drop Your Thesis! 2017 campaign. The importance of the fluid-magnetic interaction is explored by means of an alterna-
tive uncoupled framework for diluted magnetic solutions. The coupled model shows a better agreement with experimental
results in the determination of the magnetic deformation trend of the meniscus, but the uncoupled framework gives a better
prediction of the magnetic frequency response which finds no theoretical justification. Although larger datasets are required
to perform a robust point-by-point validation, these results hint at the existence of unmodeled physical effects in the system.
Keywords Liquid sloshing· Microgravity· Ferrofluids· Space propulsion· Magnetic Positive Positioning
Nomenclature
𝛼
Laser inclination
𝐀
Magnetic vector potential
𝐀d
Dipole term of the magnetic vector potential
a Container radius
𝛽
Tilting angle of the visual line with respect to
the axis of the camera
𝐁
Magnetic flux density
Bo Bond number
Bomag
Magnetic Bond number
𝜒
Magnetic susceptibility
C Dynamic contour
Meniscus contour
Δ𝜔−3dB
Peak width at -3 dB in frequency spectrum
dp
In-plane laser displacement
dV
Vertical laser displacement
𝜂
Geometric variable for magnetic vector
potential
E(x) Elliptic integral of second kind
F Dimensionless f
f Relative height between meniscus and vertex
f′
Relative height between meniscus contour
and vertex
FOV Field Of View of the camera
Γ
Dimensionless
𝛾
𝛾
Surface hysteresis parameter
G Wall boundary condition function
g Inertial acceleration
g0
Gravity acceleration at ground level
H
Dimensionless h
𝐇
Magnetic field
𝐇0
Applied magnetic field
h Relative height between meniscus and
dynamic liquid surface
* Álvaro Romero-Calvo
alvaro.romerocalvo@colorado.edu
1 Department ofAerospace Engineering Sciences, University
ofColorado Boulder, CO, USA
2 Área de Mecánica de Fluidos, Dep. Ingeniería Aeroespacial y
Mecánica de Fluidos, Universidad de Sevilla, Avenida de los
Descubrimientos s/n, Sevilla41092, Spain
3 Astrodynamics andSpace Missions, Delft University
ofTechnology, Delft, TheNetherlands
4 Departamento de Física Aplicada III, Universidad de Sevilla,
Avenida de los Descubrimientos s/n, Sevilla41092, Spain
/ Published online: 23 July 2021
Microgravity Science and Technology (2021) 33: 50
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... The validation of this feature is complicated by the fact that previous experiments were mostly concerned with the equilibrium and dynamic evolution of ferrofluid interfaces rather than their modal response. An exception is the European Space Agency (ESA) Drop Your Thesis! 2017 The Ferros project, that studied the axisymmetric sloshing of water-based ferrofluids when subjected to an inhomogeneous magnetic field in microgravity [39][40][41]. Although the axisymmetric and lateral sloshing of ferrofluids were also studied during the United Nations Office for Outer Space Affairs (UNOOSA) DropTES 2019 experiment StELIUM [42][43][44], statistical significance was not achieved for the axisymmetric modes [45]. ...
... From a technical perspective, the ESA Drop Your Thesis! 2017 experiment The Ferros was conceived to test new magnetic propellant management devices for in-space propulsion [41]. Propellant sloshing is one of the paramount lowgravity fluid dynamic problems due to its inherent complexity and impact on the operation of space vehicles [46][47][48]. ...
... A quasi-analytical model was recently introduced to study the equilibrium and modal response of ferrofluid interfaces in microgravity [22]. The model has been shown to offer an excellent estimation of the lateral modal frequencies in the aforementioned UNOOSA DropTES 2019 campaign [45], but over-predicted the axisymmetric sloshing frequencies of the ESA Drop Your Thesis! 2017 experiment [41]. An additional (technical) motivation for this work is thus to shed light on this disagreement and develop a tool that provides the equilibrium, global stability, modal response, and time-dependent evolution of the capillary ferrohydrodynamic interfaces that may find application in space propulsion. ...
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... 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. ...
... Γ is here assumed to be the same for axisymmetric and lateral modes. This assumption is motivated by the difficulty in extracting Γ in 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. ...
... 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 Two more theoretical predictions are superposed in Fig. 3: a first one that considers a linear interpolation of the contact angle and hysteresis Γ values reported in Table 1, and a second that assumes average 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 = 0. ...
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... Subsequent publications by Marchetta and coworkers presented refined numerical models and results of technical relevance for the development of liquid oxygen magnetic positioning devices [46][47][48][49][50][51][52][53][54]. Recent works have also explored the free surface oscillations of ferrofluids in microgravity, which may be relevant for slosh control and the development of novel PMDs [55][56][57][58][59][60]. A comprehensive review of the field can be found in Ref. 28. Significant advances have been made in the modeling and fundamental understanding of MP 2 devices during the last two decades. ...
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... In order to verify the implementation of Sec. 7.4.5, the numerical approach introduced in Ref. 108 to simulate the nonlinear dynamics and linear stability of capillary fluid systems is adopted in Ref. 316 to study a ferrofluid surface in a cylindrical tank taking the magnetic Bond number and the meniscus profile ...
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The commercialization of the sub-orbital environment, the ambition to make humans a multi-planetary species, and the urgent need for sustainable space operations are driving the development of a new generation of space systems. The use of electromagnetic forces (and electromagnetism, in general) is proposed in this dissertation to enable mid-distance, contactless actuation and sensing for space technology development. Following this paradigm, two applications are explored: electron-based touchless spacecraft potential sensing, and low-gravity magnetohydrodynamics. The electron-based touchless potential sensing method was recently introduced to characterize the electrostatic state of non-cooperative objects in GEO and deep space. Applications span from arcing prevention to space debris removal. Although the fundamentals of this approach were studied in previous works, several open questions remained regarding the effect of complex geometries and differential charging on the sensing process. Such questions are here addressed with efficient numerical tools and vacuum chamber experiments, providing key insights into the behavior of realistic spacecraft formations. In addition, new active photoelectron-based sensing strategies are proposed that overcome some of the challenges of previous implementations. The concept of low-gravity magnetohydrodynamics is also introduced as a way to actuate low-gravity fluid mechanics systems using magnetic forces. The theoretical foundations of the field are established from the analytical, numerical, and experimental perspectives with particular attention to the equilibrium, stability, and modal response of gas-liquid interfaces. Specific features of bubbles and droplets are also explored. Finally, the use of magnetic polarization and Lorentz forces in low-gravity fluid systems is discussed together with some of their applications, which include phase separation, magnetic positive positioning, and low-gravity electrolysis. The development of such technologies is initiated with support from microgravity research campaigns at ZARM's drop tower and Blue Origin's New Shepard suborbital rocket.
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... [35][36][37][38][39][40][41][42][43] Recent works have also explored the free surface oscillations of ferrofluids in microgravity, which may be relevant for slosh control and the development of novel propellant management devices (PMDs). [44][45][46][47][48][49] A comprehensive review of the field can be found in Ref. 19. ...
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