Abstract

The sloshing of liquids in microgravity is a relevant problem of applied mechanics with important implications for spacecraft design. A magnetic settling force may be used to avoid the highly non-linear dynamics that characterize these systems. However, this approach is still largely unexplored. This paper presents a quasi-analytical low-gravity sloshing model for magnetic liquids under the action of external inhomogeneous magnetic fields. The problems of free and forced oscillations are solved for axisymmetric geometries and loads by employing a linearized formulation. The model may be of particular interest for the development of magnetic sloshing damping devices in space, whose behavior can be easily predicted and quantified with standard mechanical analogies.

References

References
1.
Reynolds
,
W. C.
, and
Satterlee
,
H. M.
,
1966
, “
The Dynamic Behavior of Liquids in Moving Containers, Ch. 11
,”
NASA Technical Report, SP-106
.
2.
Eswaran
,
M.
, and
Saha
,
U. K.
,
2011
, “
Sloshing of Liquids in Partially Filled Tanks – A Review of Experimental Investigations
,”
Ocean Syst. Eng.
,
1
(
2
), pp.
131
155
. 10.12989/ose.2011.1.2.131
3.
Satterlee
,
H. M.
, and
Reynolds
,
W. C.
,
1964
, “
The Dynamics of Free Liquid Surface in Cylindrical Containers Under Strong Capillary and Weak Gravity Conditions
,”
Stanford University Mechanical Engineering Department, LG-2
.
4.
Dodge
,
F. T.
, and
Garza
,
L. R.
,
1969
, “
Experimental and Theoretical Studies of Liquid Sloshing at Simulated Low Gravities
,”
NASA Technical Report, CR-80471
.
5.
Concus
,
P.
,
Crane
,
G.
, and
Satterlee
,
H.
,
1967
, “
Small Amplitude Lateral Sloshing in a Cylindrical Tank With a Hemispherical Bottom Under Low Gravitational Conditions
,”
NASA Technical Report, CR-54700
.
6.
Concus
,
P.
,
Crane
,
G.
, and
Satterlee
,
H.
,
1969
, “
Small Amplitude Lateral Sloshing in Spheroidal Containers Under Low Gravitational Conditions
,”
NASA Technical Report, CR-72500
.
7.
Salzman
,
J. A.
, and
Masica
,
W. J.
,
1969
, “
Lateral Sloshing in Cylinders Under Low-Gravity Conditions
,”
NASA Technical Report, TN D-5058
.
8.
Dodge
,
F. T.
, and
Garza
,
L. R.
,
1970
, “
Simulated Low-Gravity Sloshing in Spherical, Ellipsoidal, and Cylindrical Tanks
,”
J. Spacecraft Rockets
,
7
(
2
), pp.
204
206
. 10.2514/3.29900
9.
Bauer
,
H. F.
, and
Eidel
,
W.
,
1990
, “
Linear Liquid Oscillations in Cylindrical Container Under Zero-Gravity
,”
Appl. Microgravity Technol.
,
2
(
4
), pp.
212
220
.
10.
Dodge
,
F. T.
,
1971
, “
Further Studies of Propellant Sloshing Under Low-Gravity Conditions
,”
NASA Technical Report, CR-119892
.
11.
Coney
,
T.
, and
Salzman
,
J.
,
1971
, “
Lateral Sloshing in Oblate Spheroidal Tanks Under Reduced- and Normal-Gravity Conditions
,”
NASA Technical Report, TN D-6250
.
12.
Yeh
,
G. C. K.
,
1967
, “
Free and Forced Oscillations of a Liquid in an Axisymmetric Tank at Low-Gravity Environments
,”
ASME J. Appl. Mech.
,
34
(
1
), pp.
23
28
. 10.1115/1.3607644
13.
Concus
,
P.
, and
Crane
,
G. E.
,
1967
, “
Discussion: Free and Forced Oscillations of a Liquid in an Axisymmetric Tank at Low-Gravity Environments
,”
ASME J. Appl. Mech.
,
34
(
4
), pp.
1051
1052
. 10.1115/1.3607829
14.
Chu
,
W.-H.
,
1970
, “
Low-Gravity Fuel Sloshing in An Arbitrary Axisymmetric Rigid Tank
,”
ASME J. Appl. Mech.
,
37
(
3
), pp.
828
837
. 10.1115/1.3408616
15.
Myshkis
,
A.
, and
Wadhwa
,
R.
,
1987
,
Low-Gravity Fluid Mechanics: Mathematical Theory of Capillary Phenomena
, 1st ed.,
Springer
,
Berlin Heidelberg
.
16.
Hung
,
R. J.
,
Lee
,
C. C.
, and
Leslie
,
F. W.
,
1992
, “
Similarity Rules in Gravity Jitterrelated Spacecraft Liquid Propellant Slosh Waves Excitation
,”
J. Fluids Struct.
,
6
(
4
), pp.
493
522
. 10.1016/0889-9746(92)90028-2
17.
Snyder
,
H.
,
1999
, “
Sloshing in Microgravity
,”
Cryogenics
,
39
(
12
), pp.
1047
1055
. 10.1016/S0011-2275(99)00120-4
18.
Peterson
,
L. D.
,
Crawley
,
E. F.
, and
Hansman
,
R. J.
,
1989
, “
Nonlinear Fluid Slosh Coupled to the Dynamics of a Spacecraft
,”
AIAA J.
,
27
(
9
), pp.
1230
1240
. 10.2514/3.10250
19.
Luppes
,
R.
,
Helder
,
J. A.
, and
Veldman
,
A. E.
,
2006
, “The Numerical Simulation of Liquid Sloshing in Microgravity,”
Computational Fluid Dynamics 2006
,
H.
Deconinck
and
E.
Dick
, eds.,
Springer
,
Berlin, Heidelberg
, pp.
607
612
.
20.
Utsumi
,
M.
,
1988
, “
Liquid Sloshing in an Axisymmetric Container in Low-Gravity Environments
,”
16th International Symposium on Space Technology and Science
,
Sapporo, Japan
,
May 22–27
, Vol.
1
, pp.
815
826
.
21.
Utsumi
,
M.
,
1990
, “
The Meniscus and Sloshing of a Liquid in An Axisymmetric Container At Low-Gravity
,”
JSME Int. J. Ser. 3, Vib., Control Eng., Eng. Ind.
,
33
(
3
), pp.
346
356
.
22.
Utsumi
,
M.
,
1998
, “
Low-Gravity Propellant Slosh Analysis Using Spherical Coordinates
,”
J. Fluids Struct.
,
12
(
1
), pp.
57
83
. 10.1006/jfls.1997.0125
23.
Utsumi
,
M.
,
2004
, “
A Mechanical Model for Low-Gravity Sloshing in An Axisymmetric Tank
,”
ASME J. Appl. Mech.
,
71
(
5
), pp.
724
730
. 10.1115/1.1794700
24.
Dodge
,
F.
,
2000
,
The New Dynamic Behavior of Liquids in Moving Containers
,
Southwest Research Institute
,
San Antonio, TX
.
25.
Chipchark
,
D.
,
1963
, “
Development of Expulsion and Orientation Systems for Advanced Liquid Rocket Propulsion Systems
,”
USAF Technical Report (RTD-TDR-63-1048)
.
26.
Ramachandran
,
N.
,
Leslie
,
F.
,
Peters
,
P.
, and
Sisk
,
R.
,
1998
, “
A Novel Method of Gradient Forming and Fluid Manipulation in Reduced Gravity Environments
,”
36th AIAA Aerospace Sciences Meeting and Exhibit
,
Reno, NV
,
Jan. 12–15
.
27.
Marchetta
,
J. G.
, and
Winter
,
A. P.
,
2010
, “
Simulation of Magnetic Positive Positioning for Space Based Fluid Management Systems
,”
Math. Comput. Modell.
,
51
(
9–10
), pp.
1202
1212
. 10.1016/j.mcm.2010.01.002
28.
Papell
,
S.
,
1963
, “
Low Viscosity Magnetic Fluid Obtained by the Colloidal Suspension of Magnetic Particles
,” U.S. Patent, 3,215,572.
29.
Neuringer
,
J. L.
, and
Rosensweig
,
R. E.
,
1964
, “
Ferrohydrodynamics
,”
Phys. Fluids
,
7
(
12
), pp.
1927
1937
. 10.1063/1.1711103
30.
Rosensweig
,
R.
,
1997
,
Ferrohydrodynamics
,
Dover Publications
,
Mineola, New York
.
31.
Martin
,
J.
, and
Holt
,
J.
,
2000
, “
Magnetically Actuated Propellant Orientation Experiment, Controlling Fluid Motion With Magnetic Fields in a Low-Gravity Environment
,”
NASA Technical Report, TM-2000-210129
.
32.
Marchetta
,
J.
, and
Hochstein
,
J.
,
1999
, “
Fluid Capture by a Permanent Ring Magnet in Reduced Gravity
,”
37th Aerospace Sciences Meeting and Exhibit
,
Reno, NV
,
Jan. 11–14
.
33.
Marchetta
,
J.
, and
Hochstein
,
J.
,
2000
, “
Simulation and Dimensionless Modeling of Magnetically Induced Reorientation
,”
38th Aerospace Sciences Meeting and Exhibit
,
Reno, NV
,
Jan. 10–13
.
34.
Marchetta
,
J.
,
Hochstein
,
J.
,
Sauter
,
D.
, and
Simmons
,
B.
,
2002
, “
Modeling and Prediction of Magnetic Storage and Reorientation of Lox in Reduced Gravity
,”
40th AIAA Aerospace Sciences Meeting and Exhibit
,
Reno, NV
,
Jan. 14–17
.
35.
Ohno
,
K.
,
Shimoda
,
M.
, and
Sawada
,
T.
,
2008
, “
Optimal Design of a Tuned Liquid Damper Using a Magnetic Fluid With One Electromagnet
,”
J. Phys.: Condens. Matter
,
20
(
20
), p.
204146
. 10.1088/0953-8984/20/20/204146
36.
Ohno
,
K.
,
Suzuki
,
H.
, and
Sawada
,
T.
,
2011
, “
Analysis of Liquid Sloshing of a Tuned Magnetic Fluid Damper for Single and Coaxial Cylindrical Containers
,”
J. Magn. Magn. Mater.
,
323
(
10
), pp.
1389
1393
. 10.1016/j.jmmm.2010.11.052
37.
Ohaba
,
M.
, and
Sudo
,
S.
,
1995
, “
Liquid Surface Behavior of a Magnetic Liquid in a Container Subjected to Magnetic Field and Vertical Vibration
,”
J. Magn. Magn. Mater.
,
149
(
1-2
), pp.
38
41
. 10.1016/0304-8853(95)00332-0
38.
Sudo
,
S.
,
Nishiyama
,
H.
,
Katagiri
,
K.
, and
Tani
,
J.
,
1999
, “
Interactions of Magnetic Field and the Magnetic Fluid Surface
,”
J. Intell. Mater. Syst. Struct.
,
10
(
6
), pp.
498
504
. 10.1106/N3PX-57EL-F43B-L4AO
39.
Kaneko
,
S.
,
Ishiyama
,
T.
, and
Sawada
,
T.
,
2013
, “
Effect of An Applied Magnetic Field on Sloshing Pressure in a Magnetic Fluid
,”
J. Phys. Conf. Ser.
,
412
(
1
), p.
012018
. 10.1088/1742-6596/412/1/012018
40.
Ishiyama
,
T.
,
Kaneko
,
S.
,
Takemoto
,
S.
, and
Sawada
,
T.
,
2014
, “
Relation Between Dynamic Pressure and Displacement of Free Surface in Two-Layer Sloshing Between a Magnetic Fluid and Silicone Oil
,”
Materials Science Forum
,
792
, pp.
33
38
. https://doi.org/10.4028/www.scientific.net/MSF.792.33
41.
Sawada
,
T.
,
Ohira
,
Y.
, and
Houda
,
H.
,
2002
, “
Sloshing Motion of a Magnetic Fluid in a Cylindrical Container Due to Horizontal Oscillation
,”
Energy Convers. Manage.
,
43
(
3
), pp.
299
308
. 10.1016/S0196-8904(01)00103-0
42.
Dodge
,
F. T.
, and
Garza
,
L. R.
,
1972
, “
Free-Surface Vibrations of a Magnetic Liquid
,”
J. Eng. Ind.
,
94
(
1
), pp.
103
108
. 10.1115/1.3428097
43.
Lamb
,
H.
,
1895
,
Hydrodynamics
,
University Press
,
Cambridge
.
44.
Sawada
,
T.
,
Kikura
,
H.
, and
Tanahashi
,
T.
,
1999
, “
Kinematic Characteristics of Magnetic Fluid Sloshing in a Rectangular Container Subject to Non-Uniform Magnetic Fields
,”
Exp. Fluids
,
26
(
3
), pp.
215
221
. 10.1007/s003480050282
45.
Hildebrand
,
F.
,
1965
,
Methods of Applied Mathematics
, 2nd ed.,
Prentice-Hall
,
Englewood Cliffs, NJ
.
46.
Dodge
,
F.
, and
Garza
,
L.
,
1967
, “
Experimental and Theoretical Studies of Liquid Sloshing At Simulated Low Gravity
,”
ASME J. Appl. Mech.
,
34
(
3
), pp.
555
562
. 10.1115/1.3607743
47.
Heidt
,
H.
,
Puig-Suari
,
J.
,
Moore
,
A. S.
,
Nakasuka
,
S.
, and
Twiggs
,
R. J.
,
2000
, “
CubeSat: A New Generation of Picosatellite for Education and Industry Low-Cost Space Experimentation
,”
Proceedings of the AIAA/USU Conference on Small Satellites
,
Logan, UT
.
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