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https://doi.org/10.1007/s12217-021-09894-4

ORIGINAL ARTICLE

Axisymmetric Ferrofluid Oscillations inaCylindrical Tank

inMicrogravity

ÁlvaroRomero‑Calvo1 · MiguelÁngelHerrada2· TimH.J.Hermans3· LidiaParrillaBenítez2·

GabrielCano‑Gómez4· ElenaCastro‑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

C′

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 ofAerospace Engineering Sciences, University

ofColorado 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, Sevilla41092, Spain

3 Astrodynamics andSpace Missions, Delft University

ofTechnology, Delft, TheNetherlands

4 Departamento de Física Aplicada III, Universidad de Sevilla,

Avenida de los Descubrimientos s/n, Sevilla41092, Spain

/ Published online: 23 July 2021

Microgravity Science and Technology (2021) 33: 50

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