A numerical model based on the boundary element method is proposed for the sloshing of a flowing liquid in a three-dimensional tank. Assuming a mean flow in the tank in addition to a perturbation flow, the nonlinear boundary conditions of the liquid free-surface are linearized. Using the boundary element method along with the modal analysis technique a reduced order model is obtained which is used to calculate the fundamental sloshing frequencies and modes in the tank with an inlet and outlet. The obtained results for a test case are compared with the literature data to validate the proposed model. The results are in a very good agreement with analytical results and show an acceptable comparison with experimental data. Then a rectangular tank is provided for further studies and the effects of flow inlet position and velocity on the sloshing frequencies and modes are investigated.

References

References
1.
Ibrahim
,
R.
,
2005
,
Liquid Sloshing Dynamics: Theory and Applications
,
Cambridge University Press
,
Cambridge, UK
.
2.
Okamoto
,
K. M. H.
, and
Fukaya
,
M.
,
1993
, “
Flow Pattern and Self-Induced Oscillation in a Thin Rectangular Tank With Free Surface
,”
J. Fac. Eng., Univ. Tokyo
,
42
(
2
), pp.
123
142
.
3.
Okamoto
,
K. S. S. M. H.
,
2004
, “
Analysis on the Self-Induced Sloshing Using Particle Image Velocimetry
,” Nuclear Engineering Research Laboratory.
4.
Madarame
,
H.
,
1999
, “
Self-Induced Oscillation of Upward Round Jet Impinging on Free Surface (2nd Report, Energy Supply Mechanism)
,”
Nihon Kikai Gakkai Ronbunshu, B Hen/Trans. Jpn. Soc. Mech. Eng., Part B
,
65
(
635
), pp.
2286
2292
.10.1299/kikaib.65.2286
5.
Madarame
,
H.
,
Okamoto
,
K.
, and
Lida
,
M.
,
2002
, “
Self-Induced Sloshing Caused by an Upward Round Jet Impinging on the Free Surface
,”
J. Fluids Struct.
,
16
(
3
), pp.
417
433
.10.1006/jfls.2000.0428
6.
Iguchi
,
D.
,
Ueda
,
Y.
,
Ohmi
,
T.
, and
Iguchi
,
M.
,
2008
, “
Self-Induced Rotary Sloshing Caused by an Upward off-Centered Jet in a Cylindrical Container
,”
Mater. Trans.
,
49
(
8
), pp.
1874
1879
.10.2320/matertrans.MRA2008038
7.
Nakamura
,
H.
,
Kaminaga
,
F.
, and
Matsumura
,
K.
,
2001
, “
Self-Induced Oscillation of Free Surface Caused by Free Jet (Classification of Surface Oscillation and Control Factor of Oscillation Mode)
,”
Nihon Kikai Gakkai Ronbunshu, B Hen/ Trans. Jpn. Soc. Mech. Eng., Part B
,
67
(
659
), pp.
1704
1711
.10.1299/kikaib.67.1704
8.
Iida
,
M.
,
2000
, “
Numerical Analysis of Self-Induced Free Surface Flow Oscillation by Fluid Dynamics Computer Code SPLASH-ALE
,”
Nucl. Eng. Des.
,
200
(
1
), pp.
127
138
.10.1016/S0029-5493(99)00333-7
9.
Saeki
,
S.
,
Madarame
,
H.
,
Okamoto
,
K.
, and
Tanaka
,
N.
,
1999
, “
Study on Growth Mechanism of Self-Induced Sloshing, Using Numerical Simulation (2nd Report, Oscillation Energy Transformation System)
,”
Nihon Kikai Gakkai Ronbunshu, B Hen/Trans. Jpn. Soc. Mech. Eng., Part B
,
65
(
635
), pp.
2263
2269
.10.1299/kikaib.65.2263
10.
Saeki
,
S.
,
Madarame
,
H.
, and
Okamoto
,
K.
,
1999
, “
Growth Mechanism of Self-Induced Sloshing Caused by Horizontal Plane Jet
,”
Proceedings of the 1999 3rd ASME/JSME Joint Fluids Engineering Conference
,
FEDSM’99
, San Francisco, CA, July 18–23.
11.
Saeki
,
S.
,
Madarame
,
H.
, and
Okamoto
,
K.
,
2001
, “
Self-Induced Sloshing Excited by a Horizontally Injected Plane Jet
,”
J. Fluid Mech.
,
448
, pp.
81
114
.10.1017/S0022112001004153
12.
Baba
,
M.
,
Madarame
,
H.
, and
Okamoto
,
K.
,
1999
, “
Self-Induced Sloshing Caused by Plunging Jet
,” Nihon Kikai Gakkai Ronbunshu,
B Hen/Trans. Jpn. Soc. Mech. Eng., Part B
,
65
(
635
), pp.
2278
2285
.10.1299/kikaib.65.2278
13.
Nagakura
,
H.
, and
Kaneko
,
S.
,
2000
, “
Self-Excited Sloshing Due to the Fluid Discharge Over a Flexible Plate Weir
,”
J. Pressure Vessel Technol.
,
122
(
2
), pp.
192
197
.10.1115/1.556170
14.
Kaneko
,
S.
,
Nagakura
,
H.
, and
Nakano
,
R.
,
1999
, “
Analytical Model for Self-Excited Vibration of an Overflow Flexible Plate Weir
,”
J. Pressure Vessel Technol.
,
121
(
3
), pp.
296
303
.10.1115/1.2883706
15.
Hara
,
F.
,
1990
, “
Experimental Study on Sloshing Characteristics of a Flowing Liquid in a Tank
,”
JSME Int. J.
,
33
(
3
), pp.
330
338
.10.1299/jsmec1988.33.330
16.
Hara
,
F.
,
1989
, “
Experimental Study on Sloshing Characteristics of a Flowing Liquid in a Tank
,” American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP, Vol. 157, pp.
133
141
.
17.
Macidda
,
T.
,
Kaneko
,
S.
,
Niina
,
S.
, and
Watanabe
,
T.
,
1997
, “
Nonlinear Response of Sloshing With Steady Circulating Flow
,” Asia-Pacific Vibration Conference’97, Kyongju, Korea, Nov. 9–13.
18.
Firouz-Abadi
,
R. D.
,
Haddadpour
,
H.
,
Noorain
,
M. A.
, and
Ghasemi
,
M.
,
2008
, “
A 3D BEM Model for Liquid Sloshing in Baffled Tanks
,”
Int. J. Numer. Methods Eng.
,
76
(
9
), pp.
1419
1433
.10.1002/nme.2363
19.
Firouz-Abadi
,
R. D.
,
Haddadpour
,
H.
, and
Ghasemi
,
M.
,
2009
, “
Reduced Order Modeling of Liquid Sloshing in 3D Tanks Using Boundary Element Method
,”
Eng. Anal. Boundary Elem.
,
33
(
6
), pp.
750
761
.10.1016/j.enganabound.2009.01.005
20.
Nagashima
,
T.
,
2009
, “
Sloshing Analysis of a Liquid Storage Container Using Level Set X-FEM
,”
Commun. Numer. Methods Eng.
,
25
(
4
), pp.
357
379
.10.1002/cnm.1122
You do not currently have access to this content.