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Research Papers: Fluid-Structure Interaction

Finite Element Analysis of Externally-Induced Sloshing in Horizontal-Cylindrical and Axisymmetric Liquid Vessels

[+] Author and Article Information
Spyros A. Karamanos1

Department of Mechanical Engineering, University of Thessaly, 38334 Volos, Greeceskara@mie.uth.gr

Dimitris Papaprokopiou, Manolis A. Platyrrachos

Department of Mechanical Engineering, University of Thessaly, 38334 Volos, Greece

1

Corresponding author.

J. Pressure Vessel Technol 131(5), 051301 (Jul 24, 2009) (11 pages) doi:10.1115/1.3148183 History: Received April 12, 2008; Revised February 08, 2009; Published July 24, 2009

Motivated by the earthquake response of industrial pressure vessels, the present paper investigates externally-induced sloshing in horizontal-cylindrical and axisymmetric liquid containers. Assuming ideal and irrotational flow, small-amplitude free-surface elevation, and considering appropriate trigonometric functions for the sloshing potential, a two-dimensional eigenvalue problem is obtained for zero external excitation, which is solved through a variational (Galerkin) formulation that uses triangular finite elements. Subsequently, based on an appropriate decomposition of the container-fluid motion, and considering the eigenmodes of the corresponding eigenvalue problem, an efficient methodology is proposed for externally-induced sloshing through the calculation of the corresponding sloshing (or convective) masses. Numerical results are obtained for sloshing frequencies and masses in horizontal circular cylindrical, spherical, and conical vessels. It is shown that, in those cases, consideration of only the first sloshing mass is adequate to represent the dynamic behavior of the liquid container quite accurately. For the case of a horizontal cylinder subjected to longitudinal external excitation, its equivalence with an appropriate rectangular container is demonstrated. The numerical results are in very good comparison with available semi-analytical or numerical solutions and available experimental data.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Liquid vessel under horizontal external excitation (along the x̂-axis)

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Figure 2

Horizontal cylinder of arbitrary cross section under transverse or longitudinal excitation

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Figure 3

Axisymmetric liquid container with arbitrary meridian shape

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Figure 4

Horizontal-cylindrical, spherical, and conical liquid vessel with 45 deg semivertex angle

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Figure 5

Typical finite element meshes with triangular elements for horizontal cylinder and for sphere (h=H/R=1.2)

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Figure 6

Sloshing frequencies of two-dimensional horizontal cylinder (antisymmetric modes); comparison with experimental data (30)

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Figure 7

Convective and impulsive masses for horizontal cylinder under transverse excitation

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Figure 8

(a) El Centro earthquake; (b) response of a 70% full cylinder (h=1.4) subjected to El Centro earthquake (NM=4); and (c) response of a 70% full cylinder (h=1.4) subjected to El Centro earthquake (NM=1)

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Figure 9

Sloshing frequencies of two three-dimensional horizontal cylinders with L/R=5.8 and L/R=3.5; comparison between numerical finite element results, experimental data (30), and predictions from equivalent rectangular container using Eq. 97

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Figure 10

Equivalent rectangle concept for horizontal cylinders under longitudinal excitation

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Figure 11

Sloshing frequencies in spherical vessel with respect to liquid depth; comparison with experimental data (30)

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Figure 12

Convective and impulsive masses in spherical vessels with respect to liquid depth

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