Investigation of the Effects of Annular Baffles on the Seismic Behavior of Fixed-Base Cylindrical Liquid Tanks

Document Type : Original Research

Authors
S. Farahmandpey 1
P. Broumand 2
S. Amiri 2
M. Shekari 3
1 M.Sc. in Water and Hydraulic Structure Engineering at Shiraz University, Shiraz, Iran.
2 Assistant Professor, Department of Civil and Environmental Engineering, Shiraz University, Shiraz, Iran.
3 Assistant Professor, Department of Civil Engineering, Estahban Higher Education Center, Estahban, Iran.
10.22034/23.2.7
Abstract
By studying the literature on liquid storage tanks and their seismic behavior, it is observed that sloshing waves have caused severe damages to the walls and upper parts of these structures. As a remedy, some researchers have provided passive control systems to mitigate the seismic responses; one of these passive systems is annular baffles which are mounted on different heights of the tank wall. In the present study, seismic behavior of the slender and broad fixed-based tanks with baffles of different geometries have been examined; for this purpose, the deformation of the tank shell and baffles in the time and frequency domains are considered. The coupled acoustic-structure formulation based on fluid pressure and structure displacement has been used in the framework of linear finite element method in ABAQUS commercial software. At the interaction surface, fluid pressure and the normal acceleration of the structure interact with each other using the surface-based interaction capability of the ABAQUS software. The liquid is assumed to be compressible, inviscid and irrotational, and seismic loading is applied to the liquid-filled storage tanks' supports. The models are verified by comparison with the results that are reported in the literature in frequency and time domains. A parametric study is performed on Ri/R radius ratio and h/H distance ratio of baffles in the slender and board tank. Results indicated that in the frequency domain, the geometry with ratios (Ri/R=0.3, h/H=0.1 ) of the baffles which has the biggest radial coverage and the smallest distance ratios from the liquid surface, has the highest reduction effect on the frequency of the first convective mode of the slender and broad tanks, equal to 43% and 68%, respectively. Therefore, top-mounted baffles with considerable radial coverage, have higher effects on reducing the frequency of the first convective mode of the tanks. Baffles have fewer effects on the frequency of the first impulsive mode than on the first convective mode. Besides, analyses in the time domain revealed that top-mounted baffles with medium and small radial coverage in the broad tanks caused the increase of the sloshing wave amplitudes by about 68%, at worst cases. Baffles with less effects on the first convective modes were more effective on decreasing the sloshing wave amplitudes. Therefore, satisfactory performance of the baffled liquid tanks may not be obtained by solely relying on the frequency of the first convective mode of the tanks, due to unwanted increase of sloshing amplitudes in the special cases of liquid tank geometry and baffles. According to the results, in the board tanks, top-mounted baffles may amplify the seismic response of the system and thus, considerable attention is required on the use of passive devices in such tanks. Unlike the broad tanks, baffles have satisfactory influences on the seismic behavior of the slender tank. It’s recommended that when the baffles are used as a passive controlling system in a broad tank, all of the tank responses such as base shear, hydrodynamic pressure, and etc. to be considered; since, these responses may increase significantly if top-mounted baffles are used. Analysis in time domain also indicates that the differentiation between the slender and broad tanks in studying the baffles' effects is crucial. In general, using middle-mounted baffles is recommended as an efficient passive system to mitigate the sloshing waves in broad tanks.

Keywords

Subjects

[1]. Rawat, A., V.A. Matsagar, and A.K. Nagpal, Numerical Study of Base-Isolated Cylindrical Liquid Storage Tanks Using Coupled Acoustic-Structural Approach. Soil Dynamics and Earthquake Engineering, 2019. 119: p. 196-219.
[2]. Rawat, A., et al., Earthquake Induced Sloshing and Hydrodynamic Pressures in Rigid Liquid Storage Tanks Analyzed by Coupled Acoustic-Structural and Euler-Lagrange Methods. Thin-Walled Structures, 2019. 134: p. 333-346.
[3]. Jadhav, M.B. and R.S. Jangid, Response of Base-Isolated Liquid Storage Tanks. Shock and Vibration, 2004. 11: p. 276030.
[4]. Housner, H., The Dynamic Behavior of Water Tank. Bulletin of the Seismological Society of America, 1963. 53: p. 381-389.
[5]. Housner, G., Dynamic Pressures on Accelerated Fluid Containers. Bulletin of the Seismological Society of America, 1957. 47: p. 15-35.
[6]. Zienkiewicz, O.C. and R.E. Newton, Coupled vibrations of a structure submerged in a compressible fluid. Proceedings of the International Symposium on Finite Element Techniques, Stuttgart, 1969.
[7]. Haroun Medhat, A. and W. Housner George, Seismic Design of Liquid Storage Tanks. Journal of the Technical Councils of ASCE, 1981. 107(1): p. 191-207.
[8]. Ohayon, R. and H. Morand, Mechanical and Numerical Modelling of Fluid-Structure Vibration Instabilities of Liquid Propelled Launch Vehicle. Chaos, Solitons & Fractals, 1995. 5(9): p. 1705-1724.
[9]. Malhotra, P.K., T. Wenk, and M. Wieland, Simple Procedure for Seismic Analysis of Liquid-Storage Tanks. Structural Engineering International, 2000. 10(3): p. 197-201.
[10]. Shahverdiani, K., A. Rahai, and F. Khoshnoudian, Sloshing in Concrete Cylindrical Tanks Subjected to Earthquake. Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics, 2010. 163(4): p. 261-269.
[11]. Gedikli, A. and M.E. Ergüven, Seismic Analysis of a Liquid Storage Tank With a Baffle. Journal of Sound and Vibration, 1999. 223(1): p. 141-155.
[12]. Wang, W., et al., Liquid Sloshing in Partly-Filled Laterally-Excited Cylindrical Tanks Equipped with Multi Baffles. Applied Ocean Research, 2016. 59: p. 543-563.
[13]. Cho, J.R., H.W. Lee, and K.W. Kim, Free Vibration Analysis of Baffled Liquid-Storage Tanks by the Structural-Acoustic Finite Element Formulation. Journal of Sound and Vibration, 2002. 258(5): p. 847-866.
[14]. Biswal, K.C., S.K. Bhattacharyya, and P.K. Sinha, Free-Vibration Analysis of Liquid-Filled Tank with Baffles. Journal of Sound and Vibration, 2003. 259(1): p. 177-192.
[15]. Goudarzi, M., S.-R. Sabbagh-Yazdi, and W. Marx, Investigation of Sloshing Damping in Baffled Rectangular Tanks Subjected to the Dynamic Excitation. Bulletin of Earthquake Engineering, 2010. 8: p. 1055-1072.
[16]. Shekari, M.R., A.A. Hekmatzadeh, and S.M. Amiri, On the Nonlinear Dynamic Analysis of Base-Isolated Three-Dimensional Rectangular Thin-Walled Steel Tanks Equipped with Vertical Baffle. Thin-Walled Structures, 2019. 138: p. 79-94.
[17]. Sigrist, J.-F., Structural Dynamics with Fluid-Structure Interaction, in Fluid‐Structure Interaction. 2015. p. 225-280.
[18]. Zienkiewicz, O.C. and B. Nath, Earthquake Hydrodynamic Pressures on Arch Dams - an Electric Analogue Solution. Proceedings of the Institution of Civil Engineers, 1963. 25(2): p. 165-176.
[19]. Hilber, H.M., T.J.R. Hughes, and R.L. Taylor, Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics. Earthquake Engineering & Structural Dynamics, 1977. 5(3): p. 283-292.
[20]. Biswal, K.C., S.K. Bhattacharyya, and P.K. Sinha, Dynamic Response Analysis of a Liquid-Filled Cylindrical Tank with Annular Baffle. Journal of Sound and Vibration, 2004. 274(1): p. 13-37.
[21]. Eurocode 8: Design Provisions of Earthquake Resistance of Structures Part 4: Silos, Tanks, and Pipelines. European Committee for Standardization, Brussels, 1998.
[22]. Sun, Y., D. Zhou, and J. Wang, An Equivalent Mechanical Model for Fluid Sloshing in a Rigid Cylindrical Tank Equipped with a Rigid Annular Baffle. Applied Mathematical Modelling, 2019. 72.
[23]. Khaji, N. and M.H. Arab, Seismic Analysis of Baffled Liquid Storage Tanks Using Boundary Element Method. Modares Civil Engineering Journal, 2012. 12(2): p. 11-22.
Modares Civil Engineering journal
Volume 23, Issue 2
May and June 2023
Pages 107-122