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Research Papers: Fluid-Structure Interaction

Transient Sloshing in Partially Filled Laterally Excited Horizontal Elliptical Vessels With T-Shaped Baffles

[+] Author and Article Information
Wenyuan Wang

School of Hydraulic Engineering, Faculty of Infrastructure Engineering,
Dalian University of Technology,
Dalian 116024, China;
State Key Laboratory of Coastal and Offshore Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: wangwenyuan@dlut.edu.cn

Guolei Tang

Associate Professor
School of Hydraulic Engineering,
Faculty of Infrastructure Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: tangguolei@dlut.edu.cn

Xiangqun Song

Professor
School of Hydraulic Engineering,
Faculty of Infrastructure Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: sxqun@126.com

Yong Zhou

School of Hydraulic Engineering,
Faculty of Infrastructure Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: yongzhou2021@foxmail.com

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received March 10, 2016; final manuscript received July 5, 2016; published online September 27, 2016. Assoc. Editor: Tomomichi Nakamura.

J. Pressure Vessel Technol 139(2), 021302 (Sep 27, 2016) (13 pages) Paper No: PVT-16-1041; doi: 10.1115/1.4034148 History: Received March 10, 2016; Revised July 05, 2016

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.

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Figures

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Fig. 1

Problem geometries (a) horizontal cylinder of arbitrary cross section under transverse or longitudinal excitation, (b) a surface-piercing vertical baffle, (c) a bottom-mounted vertical baffle, and (d) combination form

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Fig. 2

The coordinate definition of SBFEM

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Fig. 3

Schematic of baffled half-full elliptical containers with (a) a surface-piercing vertical baffle and (b) a bottom-mounted vertical baffle

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Fig. 4

SBFEM mesh of baffled half-full elliptical containers with (a) a surface-piercing vertical baffle and (b) a bottom-mounted vertical baffle

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Fig. 5

El Centro earthquake

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Fig. 6

Time histories of sloshing force between SBFEM and FEM

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Fig. 7

The discretization for the FE analysis and the SBFE analysis. (a) FEM mesh and (b) SBFEM mesh.

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Fig. 8

Sloshing frequencies of two-dimensional horizontal cylinder antisymmetric modes comparison with experimental data

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Fig. 9

Meshes of schematic of baffled elliptical containers in SBFEM. (a) A surface-piercing vertical baffle, (b) a bottom-mounted vertical baffle, and (c) combination form baffle.

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Fig. 10

The variation in the first two normalized antisymmetric sloshing masses with the vertical length L2 of the baffle. (a) First mode and (b) second mode.

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Fig. 11

Time histories of sloshing force for different vertical length with h=0.8536a and L2/h=0.5 under El Centro ground motion excitation

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Fig. 12

Time histories of sloshing force with h=0.8536a under El Centro ground motion excitation. (a) Bottom-mounted baffle and (b) surface-piercing baffle.

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Fig. 13

Time histories of sloshing force for different ratio b/a with h=0.8536a and L2/h=0.5 under El Centro ground motion excitation. (a) Bottom-mounted baffle and (b) surface-piercing baffle.

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Fig. 14

The variation in the first two normalized antisymmetric sloshing masses with the horizontal length L2 of the bottom-mounted baffle. (a) First mode and (b) second mode.

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Fig. 15

The variation in the first two normalized antisymmetric sloshing masses with the horizontal length L2 of the surface-piercing baffle. (a) First mode and (b) second mode.

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Fig. 16

The variation in the first two normalized antisymmetric sloshing masses with the horizontal length L2 of the combination form baffle. (a) First mode and (b) second mode.

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Fig. 17

Time histories of sloshing force with h=0.8536a under El Centro ground motion excitation

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Fig. 18

Schematic of baffled elliptical containers. (a) Surface-piercing vertical baffle, (b) bottom-mounted vertical baffle, and (c) combination form baffle.

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Fig. 19

The first four normalized antisymmetric sloshing masses versus the angle θ of the Y-shaped bottom-mounted baffle. (a) First mode and (b) second mode.

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Fig. 20

The first two normalized antisymmetric sloshing masses versus the angle θ of the Y-shaped surface-piercing baffles. (a) First mode and (b) second mode.

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Fig. 21

The first two normalized antisymmetric sloshing masses versus the angle θ of the Y-shaped combination form baffle. (a) First mode and (b) second mode.

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Fig. 22

Time histories of sloshing force for different the angle θ of the Y-shaped baffle under El Centro ground motion excitation

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