A detailed analysis of the design and performance of passive baffles for sloshing reduction in microgravity is presented. Sloshing dynamics are investigated for a rectangular container holding a × 15 mm2 volume of liquid with properties similar to a 5 cSt silicone oil. The system response to a pulse-like perturbation is analyzed in terms of the sloshing frequency ω, decay time , and damping ratio , characterizing the decay rate relative to ω. We explore first simple rectangular baffles, parameterized in terms of their length and height, orientation, and position of their center, finding that the vertical centered baffle is optimal for its good performance and simplicity. The analysis is further extended to other designs of higher complexity, including multiple-baffle arrangements, cross-shaped baffles, and free surface baffles. Finally, motivated by the recent work of Peromingo et al. [“Sloshing reduction in microgravity: thermocapillary-based control and passive baffles,” Phys. Fluids 35, 102114 (2023)], we also demonstrate the effectiveness of passive baffles combined with active thermocapillary control. As a whole, the present results suggest a maximum achievable sloshing reduction of approximately 90%.
REFERENCES
1.
Rayleigh
, “
Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density
,” Proc. London Math. Soc.
s1-14
, 170
–177
(1882
).2.
G. I.
Taylor
, “
The instability of liquid surfaces when accelerated in a direction perpendicular to their planes—I
,” Proc. R. Soc. A
201
, 192
–196
(1950
).3.
J. A. F.
Plateau
, Statique Experimentale et Theorique Des Liquides Soumis Aux Seules Forces Moleculaires
(
Gauthier-Villars
, 1873
), Vol.
2
.4.
L.
Rayleigh
, “
XIX. On the instability of cylindrical fluid surfaces
,” London, Edinburgh Dublin Philos. Mag. J. Sci.
34
, 177
–180
(1892
).5.
J. W.
Strutt
, “
VI. On the capillary phenomena of jets
,” Proc. R. Soc. London
29
, 71
–97
(1879
).6.
J.
Porter
,
P.
Salgado Sanchez
,
V.
Shevtsova
, and
V.
Yasnou
, “
A review of fluid instabilities and control strategies with applications in microgravity
,” Math. Modell. Nat. Phenom.
16
, 24
(2021
).7.
P.
Salgado Sánchez
,
V.
Yasnou
,
Y.
Gaponenko
,
A.
Mialdun
,
J.
Porter
, and
V.
Shevtsova
, “
Interfacial phenomena in immiscible liquids subjected to vibrations in microgravity
,” J. Fluid Mech.
865
, 850
–883
(2019
).8.
D. V.
Lyubimov
,
A. A.
Cherepanov
,
T. P.
Lyubimova
, and
B.
Roux
, “
Interface orienting by vibration
,” C. R. l'Académie Sci. Ser. IIB
325
, 391
–396
(1997
).9.
K.
Beyer
,
I.
Gawriljuk
,
M.
Gunther
,
I.
Lukovsky
, and
A.
Timokha
, “
Compressible potential flows with free boundaries. Part I: Vibrocapillary equilibria
,” J. Appl. Math. Mech.
81
, 261
–271
(2001
).10.
I.
Gavrilyuk
,
I.
Lukovsky
, and
A.
Timokha
, “
Two-dimensional variational vibroequilibria and Faraday's drops
,” J. Appl. Math. Phys.
55
, 1015
–1033
(2004
).11.
J.
Fernández
,
P. S.
Sánchez
,
I.
Tinao
,
J.
Porter
, and
J. M.
Ezquerro
, “
The CFVib experiment: Control of fluids in microgravity with vibrations
,” Microgravity Sci. Technol.
29
, 351
–364
(2017
).12.
P.
Salgado Sánchez
,
J.
Fernández
,
I.
Tinao
, and
J.
Porter
, “
Vibroequilibria in microgravity: Comparison of experiments and theory
,” Phys. Rev. E
100
, 063103
(2019
).13.
D. V.
Lyubimov
and
A. A.
Cherepanov
, “
Development of a steady relief at the interface of fluids in a vibrational field
,” Fluid Dyn.
21
, 849
–854
(1986
).14.
R.
Wunenburger
,
P.
Evesque
,
C.
Chabot
,
Y.
Garrabos
,
S.
Fauve
, and
D.
Beysens
, “
Frozen wave induced by high frequency horizontal vibrations on a liquid-gas interface near the critical point
,” Phys. Rev. E
59
, 5440
–5445
(1999
).15.
D.
Gligor
,
P.
Salgado Sánchez
,
J.
Porter
, and
V.
Shevtsova
, “
Influence of gravity on the frozen wave instability in immiscible liquids
,” Phys. Rev. Fluids
5
, 084001
(2020
).16.
M.
Troitiño
,
P.
Salgado Sánchez
,
J.
Porter
, and
D.
Gligor
, “
Symmetry breaking in large columnar frozen wave patterns in weightlessness
,” Microgravity Sci. Technol.
32
, 907
(2020
).17.
K.
Kumar
and
L. S.
Tuckerman
, “
Parametric instability of the interface between two fluids
,” J. Fluid Mech.
279
, 49
–68
(1994
).18.
V.
Shevtsova
,
Y. A.
Gaponenko
,
V.
Yasnou
,
A.
Mialdun
, and
A.
Nepomnyashchy
, “
Two-scale wave patterns on a periodically excited miscible liquid-liquid interface
,” J. Fluid Mech.
795
, 409
–422
(2016
).19.
E.
Labrador
,
P.
Salgado Sanchez
,
J.
Porter
, and
V.
Shevtsova
, “
Secondary faraday waves in microgravity
,” J. Phys.: Conf. Ser.
2090
, 012088
(2021
).20.
I.
Torres
,
P.
Salgado Sanchez
, and
J.
Porter
, “
Faraday waves in alternating multi-layer systems in microgravity
,” AIP Conf. Ser.
2872
, 040007
(2023
).21.
M. M.
Weislogel
and
H. D.
Ross
, “
Surface settling in partially filled containers upon step reduction in gravity
,” NASA Technical Momrandum No. 103641 (
NASA
, 1990
).22.
R.
Ibrahim
, “
Liquid sloshing dynamics with aerospace applications
,” in Proceedings of the 9th ASAT Conference
(Military Technical College, Kobry El-Kobbah, Cairo, Egypt, 2001
), p. 155
.23.
H. N.
Abramson
, “
The dynamic behavior of liquids in moving containers, with applications to space vehicle technology
,” Report No. NASA SP-106 (
NASA
, 1966
).24.
S.
Ahmed
,
H.
Xin
,
M.
Faheem
, and
B.
Qiu
, “
Sloshing assessment of oil tanks in Keiyo petrochemical industrial complex under long-period seismic ground motion
,” Agriculture
12
, 379
(2022
).25.
F.
Cheli
,
V.
D'Alessandro
,
A.
Premoli
, and
E.
Sabbioni
, “
Simulation of sloshing in tank trucks
,” Int. J. Heavy Veh. Syst.
20
, 1
–18
(2013
).26.
A.
Bourdelle
,
J.-M.
Biannic
,
H.
Evain
,
C.
Pittet
,
S.
Moreno
, and
L.
Burlion
, “
Modeling and control of propellant slosh dynamics in observation spacecraft with actuator saturations
,” in 8th European Conference for Aeronautics and Aerospace Science (EUCASS)
(2019
).27.
H.
Ueda
,
F.
Yamazaki
, and
W.
Liu
, “
Sloshing assessment of oil tanks in Keiyo petrochemical industrial complex under long-period seismic ground motion
,” J. Jpn. Assoc. Earthquake Eng.
16
, 1
–14
(2016
).28.
29.
R.
Ibrahim
,
V.
Pilipchuk
, and
T.
Ikeda
, “
Recent advances in liquid sloshing dynamics
,” Appl. Mech. Rev.
54
, 133
–199
(2001
).30.
H.
Snyder
, “
Sloshing in microgravity
,” Cryogenics
39
, 1047
–1055
(1999
).31.
M.
Utsumi
, “
Slosh damping caused by friction work due to contact angle hysteresis
,” AIAA J.
55
, 265
(2017
).32.
H. M. R.
Belakroum
,
M.
Kadja
, and
C.
Maalouf
, “
An efficient passive technique for reducing sloshing in rectangular tanks partially filled with liquid
,” Mech. Res. Commun.
37
, 341
–346
(2010
).33.
E.
Demirel
and
M. M.
Aral
, “
Liquid sloshing damping in an accelerated tank using a novel slot-baffle design
,” Water
10
, 1565
(2018
).34.
J.
Wang
,
C.
Wang
, and
J.
Liu
, “
Sloshing reduction in a pitching circular cylindrical container by multiple rigid annular baffles
,” Ocean Eng.
171
, 241
–249
(2019
).35.
H.
Kim
,
N.
Parthasarathy
,
Y.-H.
Choi
, and
Y.-W.
Lee
, “
Reduction of sloshing effects in a rectangular tank through an air-trapping mechanism—A numerical study
,” J. Mech. Sci. Technol.
32
, 1049
–1056
(2018
).36.
H.
Kim
,
N.
Parthasarathy
,
Y.-H.
Choi
, and
Y.-W.
Lee
, “
Numerical estimation on applying air-trapping mechanism to suppress sloshing loads in a prismatic tank
,” J. Mech. Sci. Technol.
34
, 2895
(2020
).37.
Y.
Xie
and
X.
Zhao
, “
Sloshing suppression with active controlled baffles through deep reinforcement learning–expert demonstrations–behavior cloning process
,” Phys. Fluids
33
, 017115
(2021
).38.
A.
Romero-Calvo
,
A.
Garcia-Salcedo
,
F.
Garrone
,
I.
Rivoalen
,
G.
Cano-Gomez
,
E.
Castro-Hernandez
,
M.
Herrada
, and
F.
Maggi
, “
StELIUM: A student experiment to investigate the sloshing of magnetic liquids in microgravity
,” Acta Astronaut.
173
, 344
–355
(2020
).39.
A.
Romero-Calvo
,
F.
Maggi
, and
H.
Schaub
, “
Magnetic positive positioning: Toward the application in space propulsion
,” Acta Astronaut.
187
, 348
–361
(2021
).40.
A.
Romero-Calvo
,
V.
Urbansky
,
V.
Yudintsev
,
H.
Schaub
, and
V.
Truchlyakov
, “
Novel propellant settling strategies for liquid rocket engine restart in microgravity
,” Acta Astronaut.
202
, 214
–228
(2023
).41.
A.
Romero-Calvo
,
G.
Cano-Gomez
, and
H.
Schaub
, “
Diamagnetically enhanced electrolysis and phase separation in low gravity
,” J. Spacecr. Rockets
59
, 59
–72
(2022
).42.
D.
Gligor
,
P.
Salgado Sánchez
,
J.
Porter
, and
I.
Tinao
, “
Thermocapillary-driven dynamics of a free surface in microgravity: Response to steady and oscillatory thermal excitation
,” Phys. Fluids
34
, 042116
(2022
).43.
D.
Gligor
,
P.
Salgado Sánchez
,
J.
Porter
, and
J. M.
Ezquerro Navarro
, “
Thermocapillary-driven dynamics of a free surface in microgravity: Control of sloshing
,” Phys. Fluids
34
, 072109
(2022
).44.
P.
Salgado Sánchez
,
U.
Martinez
,
D.
Gligor
,
I.
Torres
,
J.
Plaza
, and
J. M.
Ezquerro
, “
The “thermocapillary-based control of a free surface in microgravity” experiment
,” Acta Astronaut.
205
, 57
–67
(2023
).45.
C.
Peromingo
,
D.
Gligor
,
P.
Salgado Sánchez
,
A.
Bello
, and
K.
Olfe
, “
Sloshing reduction in microgravity: Thermocapillary-based control and passive baffles
,” Phys. Fluids
35
, 102114
(2023
).46.
D.
Schwabe
and
A.
Scharmann
, “
Some evidence for the existence and magnitude of a critical Marangoni number for the onset of oscillatory flow in crystal growth melts
,” J. Cryst. Growth
46
, 125
–131
(1979
).47.
S. Z.
Shuja
,
B. S.
Yilbas
, and
O.
Momin
, “
Laser repetitive pulse heating and melt pool formation at the surface
,” J. Mech. Sci. Technol.
25
, 479
–487
(2011
).48.
F. J.
Higuera
, “
Liquid-fuel thermocapillary flow induced by a spreading flame
,” J. Fluid Mech.
473
, 349
–377
(2002
).49.
S.
Madruga
and
C.
Mendoza
, “
Heat transfer performance and melting dynamic of a phase change material subjected to thermocapillary effects
,” Int. J. Heat Mass Transfer
109
, 501
–510
(2017
).50.
J. M.
Ezquerro
,
A.
Bello
,
P.
Salgado Sánchez
,
A.
Laverón-Simavilla
, and
V.
Lapuerta
, “
The thermocapillary effects in phase change materials in microgravity experiment: Design, preparation and execution of a parabolic flight experiment
,” Acta Astronaut.
162
, 185
–196
(2019
).51.
J. M.
Ezquerro
,
P.
Salgado Sánchez
,
A.
Bello
,
J.
Rodríguez
,
V.
Lapuerta
, and
A. Laverón
Simavilla
, “
Experimental evidence of thermocapillarity in phase change materials in microgravity: Measuring the effect of Marangoni convection in solid/liquid phase transitions
,” Int. Commun. Heat Mass Transfer
113
, 104529
(2020
).52.
S.
Madruga
and
C.
Mendoza
, “
Enhancement of heat transfer rate on phase change materials with thermocapillary flows
,” Eur. Phys. J. Spec. Top.
226
, 1169
–1176
(2017
).53.
A.
Borshchak Kachalov
,
P.
Salgado Sánchez
,
J.
Porter
, and
J. M.
Ezquerro
, “
The combined effect of natural and thermocapillary convection on the melting of phase change materials in rectangular containers
,” Int. J. Heat Mass Transfer
168
, 120864
(2021
).54.
P.
Salgado Sanchez
,
J. M.
Ezquerro
,
J.
Fernandez
, and
J.
Rodriguez
, “
Thermocapillary effects during the melting of phase change materials in microgravity: Heat transport enhancement
,” Int. J. Heat Mass Transfer
163
, 120478
(2020
).55.
P.
Salgado Sanchez
,
J. M.
Ezquerro
,
J.
Fernandez
, and
J.
Rodriguez
, “
Thermocapillary effects during the melting of Phase Change Materials in microgravity: Steady and oscillatory flow regimes
,” J. Fluid Mech.
908
, A20
(2021
).56.
R.
Varas
,
P.
Salgado Sánchez
,
J.
Porter
,
J.
Ezquerro
, and
V.
Lapuerta
, “
Thermocapillary effects during the melting in microgravity of phase change materials with a liquid bridge geometry
,” Int. J. Heat Mass Transfer
178
, 121586
(2021
).57.
N.
Martínez
,
P.
Salgado Sanchez
,
J.
Porter
, and
J. M.
Ezquerro
, “
Effect of surface heat exchange on phase change materials melting with thermocapillary flow in microgravity
,” Phys. Fluids
33
, 083611
(2021
).58.
A.
Borshchak Kachalov
,
P.
Salgado Sánchez
,
U.
Martínez
,
J.
Fernández
, and
J. M.
Ezquerro
, “
Optimization of thermocapillary-driven melting in trapezoidal and triangular geometry in microgravity
,” Int. J. Heat Mass Transfer
185
, 122427
(2022
).59.
N.
Garcia-Acosta
,
P.
Salgado Sanchez
,
J.
Jimenez
,
U.
Martinez
, and
J. M.
Ezquerro
, “
Thermocapillary–enhanced melting of different phase–change materials in microgravity
,” Microgravity Sci. Technol.
34
, 92
(2022
).60.
N.
Martínez Figueira
,
P.
Salgado Sanchez
,
A.
Bello
,
K.
Olfe
, and
J.
Rodriguez
, “
Effect of surface heat exchange on phase change materials melting with thermocapillary flow in microgravity
,” Phys. Fluids
35
, 084115
(2023
).61.
R.
Varas
,
U.
Martinez
,
K.
Olfe
,
P.
Salgado Sanchez
,
J.
Porter
, and
J. M.
Ezquerro
, “
Effects of thermocapillary and natural convection during the melting of phase change materials with a liquid bridge geometry
,” Microgracity Sci. Technol.
35
, 17
(2023
).62.
B.
Seta
,
D.
Dubert
,
F.
Gavalda
,
J.
Massons
,
M.
Bou-Ali
,
X.
Ruiz
, and
V.
Shevtsova
, “
Effect of heat transfer through an interface on convective melting dynamics of phase change materials
,” J. Fluid Mech.
966
, A46
(2023
).63.
A.
Borshchak Kachalov
,
R.
Garcia-Roco
,
P.
Salgado Sanchez
,
K.
Olfe
, and
A.
Bello
, “
Thermocapillary effects during the melting of phase change materials subjected to lateral heat flux in microgravity
,” Int. J. Heat Mass Transfer
218
, 124806
(2024
).64.
P.
Salgado Sanchez
,
J. M.
Ezquerro
,
J.
Porter
,
J.
Fernandez
,
J.
Rodriguez
,
I.
Tinao
,
V.
Lapuerta
,
A.
Laveron-Simavilla
,
X.
Ruiz
,
F.
Gavalda
,
M. M.
Mounir Bou-Ali
, and
J.
Ortiz
, “
The effect of thermocapillary convection on PCM melting in microgravity: Results and expectations
,” in Proceeding of the 72th International Astronautical Conference (IAC)
(2020
).65.
P.
Salgado Sanchez
,
J. M.
Ezquerro
,
D.
Gligor
,
U.
Martinez
,
J.
Fernandez
, and
I.
Tinao
, “
The “effect of Marangoni convection on heat transfer in phase change materials” experiment, from a student project to the international space station
,” in Proceedings of the 4th Symposium on Space Education Activities
(Universitat Politècnica de Catalunya, 2022
), pp. 1
–6
.66.
J.
Porter
,
A.
Laveron-Simavilla
,
M. M.
Bou-Ali
,
X.
Ruiz
,
F.
Gavalda
,
J. M.
Ezquerro
,
P.
Salgado Sanchez
,
U.
Martínez
,
D.
Gligor
,
I.
Tinao
,
J.
Gomez
,
J.
Fernandez
,
J.
Rodríguez
,
A.
Borshchak Kachalov
,
V.
Lapuerta
,
B.
Seta
,
J.
Massons
,
D.
Dubert
,
A.
Sanjuan
,
V.
Shevtsova
, and
L.
García-Fernandez
, “
The “effect of Marangoni convection on heat transfer in phase change materials” experiment
,” Acta Astronaut.
210
, 212
–223
(2023
).67.
68.
COMSOL
, COMSOL Multiphysics Reference Manual
(
COMSOL
, 2017
).69.
M.
Lappa
, “
Coalescence and non-coalescence phenomena in multi-material problems and dispersed multiphase flows: Part 2—A critical review of CFD approaches
,” Fluid Dyn. Mater. Process.
1
, 213
–234
(2005
).70.
P.
Salgado Sánchez
,
Y.
Gaponenko
,
V.
Yasnou
,
A.
Mialdun
,
J.
Porter
, and
V.
Shevtsova
, “
Effect of initial interface orientation on patterns produced by vibrational forcing in microgravity
,” J. Fluid Mech.
884
, A38
(2020
).71.
Y. A.
Gaponenko
,
M. M.
Torregrosa
,
V.
Yasnou
,
A.
Mialdun
, and
V.
Shevtsova
, “
Interfacial pattern selection in miscible liquids under vibration
,” Soft Matter
11
, 8221
–8224
(2015
).72.
I.
Harari
and
T. J. R.
Hughes
, “
What are C and h?: Inequalities for the analysis and design of finite element methods
,” Comput. Methods Appl. Mech. Eng.
97
, 157
–192
(1992
).73.
R.
Codina
, “
A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation
,” Comput. Methods Appl. Mech. Eng.
110
, 325
–342
(1993
).74.
D.
Liu
and
P.
Lin
, “
Three-dimensional liquid sloshing in a tank with baffles
,” Ocean Eng.
36
, 202
–212
(2009
).75.
G. R.
Fowles
and
G. L.
Cassiday
, Analytic Mechanics
(
Saunders College Publishing
, 1986
).76.
N.
Ahmad
,
M.
Varshney
, and
M.
Farooqi
, “
Design and CFD analysis of baffles of fuel tanker trucks for normal and grade highway conditions
,” Int. J. Forensic Eng. Manage.
1
, 76
(2020
).77.
X.
Zheng
,
X.
Li
,
Y.
Ren
,
Y.
Wang
, and
J.
Ma
, “
Effects of transverse baffle design on reducing liquid sloshing in partially filled tank vehicles
,” Math. Probl. Eng.
2013
, 1
–13
.78.
T. B.
Benjamin
and
F. J.
Ursell
, “
The stability of the plane free surface of a liquid in vertical periodic motion
,” Proc. R. Soc. London A
225
, 505
–515
(1954
).79.
M. A.
Goudarzi
,
S. R.
Sabbagh-Yazdi
, and
W.
Marx
, “
Investigation of sloshing damping in baffled rectangular tanks subjected to the dynamic excitation
,” Bull. Earthquake Eng.
8
, 1055
–1072
(2010
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
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