Axisymmetric Finite Element Analysis for Sloshing Response of Floating Roofs in Cylindrical Storage Tanks Shoichi YOSHIDA*3,Kazuyoshi SEKINE and Tsuka

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Axisymmetric Finite Element Analysis for Sloshing Response of Floating Roofs in Cylindrical Storage Tanks Shoichi YOSHIDA*3,Kazuyoshi SEKINE and Tsukasa MITSUTA *3 Center for Risk Management and Safety Sciences, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama-shi, Kanagawa, 240-8501 Japan The floating roofs are widely used to prevent evaporation of content in the large oil storage tanks. The 2003 Tokachi-Oki earthquake caused severe damage to the floating roofs due to liquid sloshing. The structural integrity of the floating roofs for the sloshing is urgent issue to establish for the petrochemical and oil refining industries. This paper presents the axisymmetric finite element analysis for the sloshing response of floating roofs in cylindrical storage tanks. The hydrodynamic coupling of fluid and floating roof under seismic excitation is taken into consideration in the analysis. It is assumed that the fluid is incompressible and inviscid, and the roof is linear elastic while the sidewall and the bottom are rigid. The theory for the finite element analysis in which the behavior of the fluid is formulated in terms of dynamic pressure as the Eulerian approach is developed. The basic vibration characteristics of the floating roof, such as natural frequencies and vibration modes, can be obtained from the analysis. These give engineers important information on the floating roof design. Key Words : Sloshing, Coupled Vibration, Seismic Motion, Finite Element Method, Structural Analysis, Floating Roof, Cylindrical Storage Tank E-mail : s-yoshi@ynu.ac.jp

Fig.1 Analytical model of floating roof tank Fig.2 Axisymmric fluid element

1294 Nodes. 74 Shell elements. 1200 Fluid elements Table1 Circular plate model Fig.5 Mesh division Table3 Numerical examples Table2 Natural period Fig.4 Analytical model of single deck floating roof

Fig.7 Dynamic pressure mode at z=h Table4 Natural period (a) 1st, 2nd and 3rd modes Fig.8 (b) 4th and 5th modes Dynamic pressure mode on roof surface Fig.6 Vibration mode

Fig.10 Input acceleration wave (a) 1st mode (b) 2nd mode Fig.11 Displacement response at r=40000mm Fig.9 (c) 3rd mode Bending stress mode of deck plate

Fig.13 Radial bending stress Fig.14 Pontoon cross section Fig.12 Displacement

Fig.15 Bending moment response of pontoon (1)Hazardous Materials and Safety Techniques Association, Report on Damages of Oil Storage Tanks in Kushiro, Tomakomai and Tomakomai-Tobu Industrial Area(in Japanese), Safety & Tomorrow, No.95(2004), pp.23-39. (2)Sogabe, K. and Sibata, H., Response Analysis on Sloshing of Liquid in a Cylindrical Storage-I, Basic Equation and Response to Sinusoidal Input(in Japanese), Seisan-Kenkyu, Vol.26, No.3(1974), pp.119-122. (3)Nakagawa, K., On the Vibration of an Elevated Water Tank-II, Technical Reports of Osaka University, Vol.5, No.170 (1956), pp.317-336. (4)Kondo, H., Analysis of Rigid Body Motion of Floating Roofs(in Japanese), Proceedings of Spring Annual Meeting, Japan Society of Mechanical Engineers, No.840-3(1984), pp.185-187. (5)Sakai,F., Nishimura, M. and Ogawa, H., Sloshing Behavior of Floating-Roof Oil Storage Tanks, Computers & Structures, Vol.19, No.1-2(1984),pp183-192. (6)Matsui, T., Sloshing in a Cylindrical Liquid Storage Tank with Floating Roof under Earthquake Excitation : Analytical Solution(in Japanese), Transactions of Architectural Institute of Japan, Journal of Structural and Construction Engineering, No.594(2005),pp.167-173. (7)Matsui, T., Sloshing in a Cylindrical Liquid Storage Tank with a Single-Deck Type Floating Roof under Seismic Excitation(in Japanese), Transactions of Architectural Institute of Japan, Journal of Structural and Construction Engineering, No.607(2006), pp.101-108. (8)Matsui, T., Sloshing in a Cylindrical Liquid Storage Tank with a Single-Deck Type Floating Roof under Seismic Excitation, Solution Based on Dry-Mode Expansion for Coupled Deck-Pontoon System(in Japanese), Transactions of Architectural Institute of Japan, Journal of Structural and Construction Engineering, No. 612(2007), pp.87-94. (9)Miura, M., Kikuchi, T., Yonekawa, F. and Hitomi, M, Sloshing Simulation of Floating Roofs(in Japanese), Idemitsu Technical Report, Vo1.47, No.3(2004), pp.276-284. (10)Nishiguchi, H., Ito, M., Honobe H. and Kanoh, T., Sloshing Action Analysis and Safety Evaluation of the Oil Tank by the Long Period Earthquake Motion(in Japanese), Journal of Thermal & Nuclear Power Engineering Society, Vol.58, No.581(2005), pp89-94. (11)Nishi, H., Yamada, M., Zama, S., Hirokawa, Y., Sekine, K., Minowa, C. and Mikoshiba, T., Experimental Study on Sloshing Behavior of Floating Roofs by using Small-Scale Cylindrical Tank(in Japanese), Journal of High Pressure Institute ofjapan, Vol.45. No.3(2007), pp.118-126. (12)Cacciatore, RI, HantzlV, B.F. and Gustafsson, LM., Evaluation of Storage Tank Floating Roofs for Stress and Stability due to Earthquake Induced Liquid Sloshing, Proceedings of Pressure Vessels & Piping Conference, American Society of Mechanical Engineers, PVP2007-26283(2007). (13)Zienkiewicz, O.C. and Taylor, RL., The Finite Element Method, 4th Edition, Vol.2, McGraw-Hill (1991), pp.199-202. (14)Wilson, E.L. and Khalvati, M., Finite Elements for the Dynamic Analysis of Fluid-Solid Systems, International Journal for Numerical Methods in Engineering, Vo1.19 (1983), pp.1657-1668. (15)Ohtsubo, H. and Kubbta, A., Coupled Systems (in Japanese), Baihu-kan(1991), pp.5-29. (16)Hazardous Materials and Safety Techniques Association, Report of the Committee on Screening Criterion of Floating Roofs of Oil Storage Tanks (in Japanese), Safety & Tomorrow, No.99(2005), pp.66-79. (17)Yoshida, S. and Kitamura, K., Elastic Buckling of Pontoons of Single Deck Floating Roofs subjected to Circumferential Bending Load (in Japanease), Journal of High Pressure Institute ofjapan, Vol.45. No.3(2007), pp.144-153.

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