International Conference of Rehabilitation And Retrofitting of Structures Mumbai, Maharashtra, June 19-20, 2019

“ Title of Paper” Eswaran M1, *, G R Reddy2

Abstract

During seismic excitation, the liquid free surfaces in large pool having many internals undergo

complicated motions [1-2]. The typical examples are liquid sodium in pool type fast breeder and

liquid-metal nuclear reactors. These top supported large liquid pools are to be investigated for

liquid sloshing under design basis seismic excitations. In this work, the vibration behavior of top

supported liquid pool under seismic load is studied through two-way fluid-structure interaction

(FSI) analysis. The liquid convective and impulsive pressure, and hoop stress on the tank wall

during liquid oscillation is studied in detail under random excitation.

Introduction

The analysis of the liquid sloshing is very significant in the Nuclear Power Plants structures to

evaluate the dynamic loads bearing capacity [3]. The typical sodium cooled pool type reactor, the

entire radioactive primary sodium circuit components including the core are housed within a

single vessel called main vessel. This stainless steel vessel is around 13 m in diameter which

holds the large pool of liquid sodium weighing about 1,000 tons. The main vessel is supported at

the top by welding to the outer shell of the roof slab and is free to expand downward to

accommodate thermal expansion, i.e.., the roof slab, which forms the top shield, supports the

main vessel. To study the top supported main vessel under seismic load through the two-way FSI

simulation, a 3D cylindrical liquid pool has been taken for analysis as shown in Fig. 1. The water

is taken as fluid and the pool wall made up of structural steel with 5 mm thick. The pool height

and diameter are 2 m and 1.6 m respectively. In order to find the free vibration behavior of this

pool, the frequency analysis is performed through FEM analysis. The first few convective mode

frequencies are estimated as 0.75, 1.3, 1.66, 1.96, 2.26 and 2.54 hz and depicted in Fig. 2.

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1Structural and Seismic Engineering Section, Bhabha Atomic Research Centre & Faculty, Homi Bhabha National Institute, Mumbai, India (*eswaran@barc.gov.in)2Head, Structural and Seismic Engineering Section, Bhabha Atomic Research Centre & Faculty, Homi Bhabha National Institute, Mumbai, India

International Conference of Rehabilitation And Retrofitting of Structures Mumbai, Maharashtra, June 19-20, 2019

Structural steel (Thick=5 mm, height= 2 m,Dia. = 1.6 m)

Mode 1 (0.75 hz) Mode 2 (1.3 hz) Mode 3 (1.66 hz)

Fig.1 Computational domain Fig. 2 Mode shape of liquid

The transient analysis is conducted under 0.75 hz regular excitation. The Fig. 3 shows

circumferential stress on pool side wall and the maximum stress is found as 1.58E6 N/m2. This

stress is the key factor for the elephant boot buckling on tank side wall under transient load. The

slosh height is estimated as shown in Figs. 4 and 5. The maximum slosh height is found as 150

mm under sinusoidal excitation. Displacement (m)

Circumferential stress (Pa)

Displacement (m)Circumferential

stress (Pa)

-200

-100

0

100

200

0 5 10 15 20 25 30

Slos

h he

ight

(mm

)

Time (Sec)

Fig. 3 Circumferential stress of tank side wall at 20.8 sec

Fig. 4 Displacement at 20.8 sec Fig. 5 Slosh height under 0.75 hz

Conclusion

In this work two-way FSI is used to estimate the frequency and liquid loads under regular

excitation. To estimate the liquid loads under seismic load, the random acceleration time history

will be used as input for the further work.

References

[1] Eswaran M and Reddy, G.R. (2015), Liquid sloshing in gravity driven water pool of Advanced Heavy Water Reactor: Pool liquid under design seismic load and slosh control studies, IAEA-INIS, Vol. 46 (28), Ref: 46076128.

[2] Ibrahim, R.A., (2005). Liquid sloshing dynamics: Theory & applications. Cambridge University Press, New York.

[3] Eswaran, M., Reddy, G.R., Singh, R.K., (2015). Effect of higher modes and multi-directional seismic excitations on power plant liquid storage pools. Earthquakes & Structures, 8 (3), 779–799.

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