Science and Technology of Nuclear Installations

Volume 2019, Article ID 1418265, 10 pages

https://doi.org/10.1155/2019/1418265

## Investigation of the Equivalent Test Condition for the Seismic Safety Assessment of a Spent Fuel Pool with regard to Sloshing Behavior

Correspondence should be addressed to Choengryul Choi; moc.cetlosle@iohcrc

Received 1 July 2019; Revised 8 October 2019; Accepted 1 November 2019; Published 1 December 2019

Academic Editor: Leon Cizelj

Copyright © 2019 Won Man Park et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Spent fuel pools are used as temporary storage for spent fuel assemblies in nuclear power plants and are filled with coolant which removes the decaying heat from spent fuel assemblies. Sloshing of the coolant can occur if an earthquake occurs in the area. It may produce additional forces on the pool or inner structure and cause overflow of the coolant. It is therefore critical to investigate the phenomenon of sloshing in a seismic assessment of the spent fuel pool. The size of an actual spent fuel pool is excessive for carrying out an experimental study; thus, a scale model is necessary for experimentation. In this study, a scaling law was defined for test conditions using a scale model to understand sloshing behavior, and the results were validated via computational fluid dynamic analysis. Because sloshing is resonant in a fluid and the first mode natural frequency of a fluid is dominant in sloshing behavior, the test condition could be obtained based on the natural frequency of the fluid. In the model, which is scaled with a factor of “,” the scale factors “,” “,” “,” and “” were used for displacement, acceleration, excitation frequency, and excitation time, respectively. Approximately 5% difference in maximum sloshing height between two models was predicted in the only case that 1/8 and 1/4 models (1/8 and 1/4 scaled down from an actual spent fuel pool) were excited with 10 Hz and 7.071 Hz, respectively, but the same sloshing height and pressure were predicted in other cases. The results of this study support the idea that the Froude scaling law can be used when using a scale model for a seismic assessment of spent fuel pools to investigate sloshing behavior.

#### 1. Introduction

Spent fuel pools are facilities in nuclear power plants that act as temporary onsite storage for spent fuel assemblies which have been used in the nuclear reactor. Spent fuel assemblies produce heat from radioactive decay which could result in a critical accident and therefore need to be removed by the coolant within a spent fuel pool. Otherwise, it has been reported that the generation of hydrogen gas caused by the melting of the zircaloy cladding could lead to an explosion in the spent fuel pool [1–3]. Therefore, one of the major concerns about the spent fuel pool is its ability for preventing the loss of coolant and thus maintaining cooling of the radioactive fuel.

When an external force such as a seismic wave shakes a tank or pool which contains fluid, it could lead to sloshing behavior of the fluid. In the case of the spent fuel pool, the sloshing behavior of the coolant causes additional force on the wall of the pool and the racks [4]. This sloshing can also cause overflow of the coolant from the pool, resulting in a reduction in the amount of coolant. For instance, the USNR Commission has reported that decreases in the coolant level by 2.5 ft (1.5 m) was estimated at Units 1 and 3 of the Fukushima Daiichi plant after the Tohoku earthquake (March 11, 2011, Japan) [1]. This overflow, in the authors’ opinion, could be crucial with regard to cooling of the spent fuel assemblies; therefore, it is critical to investigate the sloshing behavior of coolant in an evaluation of the effects seismic occurrences may have on a spent fuel pool.

Sloshing behavior can be investigated using analytical, numerical, and experimental methods [5–8]. The results of experimental studies are used for investigating the sloshing behaviors as well as for validating the results of numerical and analytical studies. However, spent fuel pools are too large to be investigated using a model of actual scale. For example, the size of the spent fuel pool at a particular nuclear power plant in Korea is known to be 10.4 m × 8.6 m × 12.8 m. The use of a scaled-down model and appropriate test conditions for the model are therefore necessary for investigating sloshing behavior in the spent fuel pool.

Sloshing has been investigated in the seismic assessment of nuclear power plants as well as in marine and ocean engineering because of its importance in fluid dynamics. Faltinsen introduced a mathematical model for estimating sloshing motion in a rectangular tank [5]. Various numerical models have been developed by Frandsen, Wu et al., Chen et al., and Okamoto and Kawahara and used for investigating sloshing motion in various excitation conditions [6, 9–11]. Goudarzi and Sabbagh-Yazdi investigated the sloshing behavior of a spent fuel pool for a seismic safety assessment via experiments using scale models and computer simulation [12]. Zhao et al. Mitra and Sinhamahapatra developed a pressure-based finite element technique and analyzed the sloshing dynamics of a partially filled rigid container with bottom-mounted submerged components [13]. Kim et al. investigated sloshing-induced pressure in tanks of different scales by using an experimental method to investigate the pressure applied on the tanks of liquid natural gas (LNG) carriers under conditions of the movement of the ship [14]. Merino et al. analyzed the motion of a submerged rack, on which sloshing behavior can affect, in a spent fuel pool as a response to seismic movement using scale models via experimental methods and computer simulation in the assessment of a spent fuel pool [15].

In case that an actual scale model is too big or too small, the use of a scaled-down or -up model instead is very common in the mechanical engineering field [12, 14–16]. An actual “spent fuel pool,” which is the interest of this study, is not only too big but also too heavy to be used as experimental equipment. Therefore, for predicting and investigating the sloshing behavior of the coolant in a spent fuel pool, it is necessary to develop a scaled-down model and experimental conditions for it. Here, the methods to develop a scaled model and test conditions are important factors determining the accuracy and validity of the experiments. In this study, the test conditions were calculated to investigate sloshing behavior in a scaled-down model which has the same shape but is different in size to an actual pool. The conditions were validated via computer simulation by using computational fluid dynamics. The developed testing condition was compared to the testing condition using dimensionless numbers. Moreover, the sloshing behavior of the coolant in a spent fuel pool was evaluated under beyond-design-earthquake (BDE) conditions.

#### 2. Materials and Methods

##### 2.1. Test Condition for the Sloshing Behavior of the Coolant in the Scale Model

It has previously been observed that the first natural frequency and mode are dominant in the sloshing motion of a fluid in a tank or pool [17, 18]. The first natural frequency of a fluid can be calculated via the following [5]:where , , , , and are the nth natural frequency (rad/s) of the fluid, gravity, depth of fluid, width of a tank or pool, and wave number, respectively.

When *n* is 0, is calculated as 0.999 and it becomes 1.000 when *n* is greater than or same to 1. Therefore, we can assume that the square root of the natural frequency is inversely proportional to and is directly proportional to the scale factor :

Therefore, the square root of the natural frequency is inversely proportional to the scale factor :

Because the sloshing behavior of the fluid resonates with external excitation, it is to be expected that the external excitation of the scaled-down model iswhere and are the excitation frequency (rad/s) for the actual size and the scaled-down model, respectively.

Based on the linear theory introduced by Faltinsen, the sloshing height () of a two-dimensional rectangular tank at location and time can be calculated as follows:where and are the impulsive and convective components of sloshing, calculated from the following equations [9, 12]:where and are the amplitudes of excitation and gravity, respectively. Parameters in equations (7) and (8), , , , and , are defined according to equations (1), (2), (9), and (10):

Because both and are directly proportional to amplitude and is directly proportional to the scale factor, is directly proportional to the scale factor .

Thus, the excitation frequency (), amplitude (), and excitation time () of the scaled-down model are as follows:

If it is assumed that if sine-wave external excitation is applied, the displacements of the actual scale model () and the scaled-down model () are calculated as follows:

If external excitation is applied using acceleration, the acceleration of the real scale model () and the scaled-down model () are calculated as follows:

The amplitude of the excitation acceleration for the scaled-down model is therefore the same as that of the actual scale model, but the duration of the excitation time in the scaled-down model should be changed by considering the scale factor given in equation (13).

##### 2.2. CFD (Computational Fluid Dynamics) Analysis of the Sloshing Behaviors

The length, width, and height of the spent fuel pool at the Korean nuclear power plant considered in this study are approximately 10.4 m, 8.6 m, and 12.8 m, respectively. The level of the coolant reaches approximately 12.2 m in the pool. Two-dimensional computer fluid dynamic models with scale factors of 1/4 and 1/8 were developed using the commercial CFD software Ansys/Fluent (Ansys Inc., Canonsburg, PA, US) (Figure 1). However, the height of the pool was enlarged as high as twice the water level to avoid overflow of the water, because we could not obtain the sloshing height in case that the sloshing motion exceeds the given analysis domain. Thus, the length and height of the pool and the water level of the 1/8 and 1/4 scale models were assumed to be 1.3 m, 3.0 m, and 1.525 m (for the 1/8 scale model) and 2.6 m, 6.0 m, and 3.050 m (for the 1/4 scale model), respectively.