The transient sloshing in laterally excited horizontal elliptical containers with T-shaped baffles is first investigated by using a novel semi-analytical scaled boundary finite-element method (SBFEM). The proposed method combines the advantages of the finite-element and the boundary element methods (BEMs) with unique properties of its own, in which a new coordinate system including the circumferential local coordinate and the radial coordinate has been established. Only the boundary of the computational domain needs to be discretized in the circumferential direction as the same as the BEM and the solution in the radial direction is analytical. Assuming ideal, irrotational flow and small-amplitude free-surface elevation, the formulations (using a new variational principle formulation) and solutions of SBFEM equations for an eigenvalue problem under zero external excitation (free sloshing problem) are derived in detail. Subsequently, based on an appropriate decomposition of the container-fluid motion, and considering the eigenvalues and eigenmodes of the above eigenvalue problem, an efficient methodology is proposed for externally induced sloshing through the calculation of the corresponding sloshing masses and liquid motion. Several numerical examples are presented to demonstrate the simplicity, versatility, and applicability of the SBFEM during the simulation of sloshing problems of complex containers, and excellent agreement with the other methods is observed. Meanwhile, three T-shaped baffle configurations are considered including surface-piercing baffle, bottom-mounted baffle and their combination form, and Y-shaped configuration evolved from that of T-shaped baffle has been taken into consideration as well. The liquid fill level, arrangement and length of those baffles affecting the sloshing masses, and liquid motion are investigated in detail. The results also show that the present method can easily solve the singularity problems analytically by choosing the scaling center at the tip of the baffles and allows for the simulation of complex sloshing phenomena using far less number of degrees-of-freedom.

References

References
1.
Ibrahim
,
R. A.
,
2005
,
Liquid Sloshing Dynamics
,
Cambridge University Press
,
Cambridge, UK
.
2.
Armenio
,
V.
, and
La Rocca
,
M.
,
1996
, “
On the Analysis of Sloshing of Water in Rectangular Containers Numerical Study and Experimental Validation
,”
Ocean Eng.
,
23
(
8
), pp.
705
739
.
3.
Goudarzi
,
M. A.
, and
Sabbagh-Yazdi
,
S. R.
,
2012
, “
Analytical and Experimental Evaluation on the Effectiveness of Upper Mounted Baffles With Respect to Commonly Used Baffles
,”
Ocean Eng.
,
42
, pp.
205
217
.
4.
Akyldz
,
H.
,
Erdem
,
U. N.
, and
Aksoy
,
H.
,
2013
, “
An Experimental Investigation of the Effects of the Ring Baffles on Liquid Sloshing in a Rigid Cylindrical Tank
,”
Ocean Eng.
,
59
, pp.
190
197
.
5.
Gavrilyuk
,
I.
,
Lukovsky
,
I.
,
Trotsenko
,
Y.
, and
Timokha
,
A.
,
2006
, “
Sloshing in a Vertical Circular Cylindrical Tank With an Annular Baffle—Part 1: Linear Fundamental Solutions
,”
J. Eng. Math.
,
54
(
1
), pp.
71
88
.
6.
Toumi
,
M.
,
Bouazara
,
M.
, and
Richard
,
M. J.
,
2008
, “
Analytical and Numerical Analysis of the Liquid Longitudinal Sloshing Impact on a Partially Filled Tank-Vehicle With and Without Baffles
,”
Int. J. Veh. Syst. Modell. Test.
,
3
(
3
), pp.
229
249
.
7.
Chantasiriwan
,
S.
,
2009
, “
Modal Analysis of Free Vibration of Liquid in Rigid Container by the Method of Fundamental Solutions
,”
Eng. Anal. Boundary Elem.
,
33
(
5
), pp.
726
730
.
8.
Hasheminejad
,
S. M.
, and
Aghabeigi
,
M.
,
2011
, “
Transient Sloshing in Half-Full Horizontal Elliptical Tanks Under Lateral Excitation
,”
J. Sound Vib.
,
330
(
14
), pp.
3507
3525
.
9.
Hasheminejad
,
S. M.
, and
Aghabeigi
,
M.
,
2012
, “
Sloshing Characteristics in Half-Full Horizontal Elliptical Tanks With Vertical Baffles
,”
Appl. Math. Modell.
,
36
(
1
), pp.
57
71
.
10.
Wu
,
C. H.
,
Faltinsen
,
O. M.
, and
Chen
,
B. F.
,
2012
, “
Numerical Study of Sloshing Liquid in Tanks With Baffles by Time-Independent Finite Difference and Fictitious Cell Method
,”
Comput. Fluids
,
63
, pp.
9
26
.
11.
Akyildiz
,
H.
,
2012
, “
A Numerical Study of the Effects of the Vertical Baffle on Liquid Sloshing in Two-Dimensional Rectangular Tank
,”
J. Sound Vib.
,
331
(
1
), pp.
41
52
.
12.
Liu
,
D. M.
, and
Lin
,
P. Z.
,
2009
, “
Three-Dimensional Liquid Sloshing in a Tank With Baffles
,”
Ocean Eng.
,
36
(
2
), pp.
202
212
.
13.
Cao
,
X. Y.
,
Ming
,
F. R.
, and
Zhang
,
A. M.
,
2014
, “
Sloshing in a Rectangular Tank Based on SPH Simulation
,”
Appl. Ocean Res.
,
47
, pp.
241
254
.
14.
Biswal
,
K. C.
,
Bhattacharyya
,
S. K.
, and
Sinha
,
P. K.
,
2003
, “
Free-Vibration Analysis of Liquid-Filled Tank With Baffles
,”
J. Sound Vib.
,
259
(
1
), pp.
177
192
.
15.
Biswal
,
K. C.
,
Bhattacharyya
,
S. K.
, and
Sinha
,
P. K.
,
2006
, “
Non-Linear Sloshing in Partially Liquid Filled Containers With Baffles
,”
Int. J. Numer. Methods Eng.
,
68
(
3
), pp.
317
337
.
16.
Belakroum
,
R.
,
Kadja
,
M.
,
Mai
,
T. H.
, and
Maalouf
,
C.
,
2010
, “
An Efficient Passive Technique for Reducing Sloshing in Rectangular Tanks Partially Filled With Liquid
,”
Mech. Res. Commun.
,
37
(
3
), pp.
341
346
.
17.
Hosseini
,
M.
, and
Farshadmanesh
,
P.
,
2011
, “
The Effects of Multiple Vertical Baffles on Sloshing Phenomenon in Rectangular Tanks
,”
WIT Transactions on the Built Environment
, Vol.
120
, WIT Press, Billerica, MA, pp.
287
298
.
18.
Lu
,
L.
,
Jiang
,
S. C.
,
Zhao
,
M.
, and
Tang
,
G. Q.
,
2015
, “
Two-Dimensional Viscous Numerical Simulation of Liquid Sloshing in Rectangular Tank With/Without Baffles and Comparison With Potential Flow Solutions
,”
Ocean Eng.
,
108
(
1
), pp.
662
677
.
19.
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
.
20.
Sygulski
,
R.
,
2011
, “
Boundary Element Analysis of Liquid Sloshing in Baffled Tanks
,”
Eng. Anal. Boundary Elem.
,
35
(
8
), pp.
978
983
.
21.
Ebrahimian
,
M.
,
Noorian
,
M. A.
, and
Haddadpour
,
H.
,
2013
, “
A Successive Boundary Element Model for Investigation of Sloshing Frequencies in Axisymmetric Multi Baffled Containers
,”
Eng. Anal. Boundary Elem.
,
37
(
2
), pp.
383
392
.
22.
Kolaei
,
A.
,
Rakheja
,
S.
, and
Richard
,
M. J.
,
2015
, “
A Coupled Multimodal and Boundary-Element Method for Analysis of Anti-Slosh Effectiveness of Partial Baffles in a Partly-Filled Container
,”
Comput. Fluids
,
107
, pp.
43
58
.
23.
Wang
,
W. Y.
,
Guo
,
Z. J.
,
Peng
,
Y.
, and
Zhang
,
Q.
,
2016
, “
A Numerical Study of the Effects of the T-Shaped Baffles on Liquid Sloshing in Horizontal Elliptical Tanks
,”
Ocean Eng.
,
111
(
1
), pp.
543
568
.
24.
Wolf
,
J. P.
, and
Song
,
C. M.
,
1996
,
Finite-Element Modelling of Unbounded Media
,
Wiley
,
Chichester, UK
.
25.
Song
,
C. M.
, and
Wolf
,
J. P.
,
2002
, “
Semi-Analytical Representation of Stress Singularities as Occurring in Cracks in Anisotropic Multi-Materials With the Scaled Boundary Finite-Element Method
,”
Comput. Struct.
,
80
(
2
), pp.
183
197
.
26.
Li
,
C.
,
Ooi
,
E. T.
,
Song
,
C. M.
, and
Natarajan
,
S.
,
2015
, “
SBFEM for Fracture Analysis of Piezoelectric Composites Under Thermal Load
,”
Int. J. Solids Struct.
,
52
, pp.
114
129
.
27.
Lehmann
,
L.
,
Langer
,
S.
, and
Clasen
,
D.
,
2006
, “
Scaled Boundary Finite Element Method for Acoustic
,”
J. Comput. Acoust.
,
14
(
4
), pp.
489
506
.
28.
Liu
,
J.
, and
Lin
,
G.
,
2012
, “
A Scaled Boundary Finite Element Method Applied to Electrostatic Problems
,”
Eng. Anal. Boundary Elem.
,
36
(
12
), pp.
1721
1732
.
29.
Bazyar
,
M. H.
, and
Talebi
,
A.
,
2015
, “
Transient Seepage Analysis in Zoned Anisotropic Soils Based on the Scaled Boundary Finite-Element Method
,”
Int. J. Numer. Anal. Methods Geomech.
,
39
(
1
), pp.
1
22
.
30.
Wang
,
X.
,
Jin
,
F.
,
Prempramote
,
S.
, and
Song
,
C. M.
,
2011
, “
Time-Domain Analysis of Gravity Dam-Reservoir Interaction Using High-Order Doubly Asymptotic Open Boundary
,”
Comput. Struct.
,
89
, pp.
668
680
.
31.
Lin
,
G.
,
Wang
,
Y.
, and
Hu
,
Z. Q.
,
2012
, “
An Efficient Approach for Frequency-Domain and Time-Domain Hydrodynamic Analysis of Dam-Reservoir Systems
,”
Earthquake Eng. Struct. Dyn.
,
41
(
13
), pp.
1725
1749
.
32.
Lin
,
G.
,
Liu
,
J.
,
Li
,
J. B.
, and
Fang
,
H. Y.
,
2011
, “
Scaled Boundary Finite Element Approach for Waveguide Eigenvalue Problem
,”
IET Microwaves, Antennas Propag.
,
12
(
5
), pp.
1508
1515
.
33.
Liu
,
J.
,
Lin
,
G.
,
Li
,
J. B.
, and
Zhong
,
H.
,
2012
, “
Analysis of Quadruple Corner-Cut Ridged Square Waveguide Using a Scaled Boundary Finite Element Method
,”
Appl. Math. Modell.
,
36
(
10
), pp.
4797
4809
.
34.
Bazyar
,
M. H.
, and
Talebi
,
A.
,
2015
, “
A Scaled Boundary Finite-Element Solution to Non-Homogeneous Anisotropic Heat Conduction Problems
,”
Appl. Math. Modell.
,
39
(
23–24
), pp.
7583
7599
.
35.
Gravenkamp
,
H.
,
Birk
,
C.
, and
Song
,
C. M.
,
2015
, “
Simulation of Elastic Guided Waves Interacting With Defects in Arbitrarily Long Structures Using the Scaled Boundary Finite Element Method
,”
J. Comput. Phys.
,
295
(
15
), pp.
38
455
.
36.
Syed
,
N. M.
, and
Maheshwari
,
B. K.
,
2015
, “
Improvement in the Computational Efficiency of the Coupled FEM-SBFEM Approach for 3D Seismic SSI Analysis in the Time Domain
,”
Comput. Geotech.
,
67
, pp.
204
212
.
37.
Tao
,
L. B.
,
Song
,
H.
, and
Chakrabarti
,
S.
,
2009
, “
Scaled Boundary FEM Model for Interaction of Short-Crested Waves With a Concentric Porous Cylindrical Structure
,”
J. Waterw., Port, Coastal, Ocean Eng.
,
135
(
5
), pp.
200
212
.
38.
Liu
,
J.
,
Lin
,
G.
, and
Li
,
J. B.
,
2012
, “
Short-Crested Waves Interaction With a Concentric Cylindrical Structure With Double-Layered Perforated Walls
,”
Ocean Eng.
,
40
, pp.
76
90
.
39.
Deeks
,
A. J.
, and
Cheng
,
L.
,
2003
, “
Potential Flow Around Obstacles Using the Scaled Boundary Finite-Element Method
,”
Int. J. Numer. Methods Fluids
,
41
(
7
), pp.
721
741
.
40.
Spyros
,
A. K.
,
Dimitris
,
P.
, and
Manolis
,
A. P.
,
2009
, “
Finite Element Analysis of Externally-Induced Sloshing in Horizontal-Cylindrical and Axisymmetric Liquid Vessels
,”
ASME J. Pressure Vessel Technol.
,
131
(5), p.
051301
.
41.
McCarty
,
J. L.
, and
Stephens
,
D.
,
1960
, “
Investigation of the Natural Frequencies of Fluids in Spherical and Cylindrical Tanks
,” National Aeronautics and Space Administration, Langley Research Center, Langley, VA, Report No. NASA TN D-252.
You do not currently have access to this content.