Science and Technology of Nuclear Installations

Volume 2016, Article ID 1613989, 8 pages

http://dx.doi.org/10.1155/2016/1613989

## A Calculation Method for the Sloshing Impact Pressure Imposed on the Roof of a Passive Water Storage Tank of AP1000

^{1}School of Nuclear Science and Engineering, North China Electric Power University, Beijing 102206, China^{2}Beijing Key Laboratory of Passive Safety Technology for Nuclear Energy, North China Electric Power University, Beijing 102206, China^{3}China Nuclear Power Engineering Co., Ltd., Beijing 100840, China

Received 18 January 2016; Revised 6 April 2016; Accepted 19 May 2016

Academic Editor: Iztok Tiselj

Copyright © 2016 Daogang Lu 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

There is a large water storage tank installed at the top of containment of AP1000, which can supply the passive cooling. In the extreme condition, sloshing of the free surface in the tank may impact on the roof under long-period earthquake. For the safety assessment of structure, it is necessary to calculate the impact pressure caused by water sloshing. Since the behavior of sloshing impacted on the roof is involved into a strong nonlinear phenomenon, it is a little difficult to calculate such pressure by theoretical or numerical method currently. But it is applicable to calculate the height of sloshing in a tank without roof. In the present paper, a simplified method was proposed to calculate the impact pressure using the sloshing wave height, in which we first marked the position of the height of roof, then produced sloshing in the tank without roof and recorded the maximum wave height, and finally regarded approximately the difference between maximum wave height and roof height as the impact pressure head. We also designed an experiment to verify this method. The experimental result showed that this method overpredicted the impact pressure with a certain error of no more than 35%. By the experiment, we conclude that this method is conservative and applicable for the engineering design.

#### 1. Introduction

As the ultimate heat sink of AP1000 reactor, passive cooling system (PCS) is the key equipment to ensure the safety of nuclear power plant. The large water storage tank, installed at the top of the containment of AP1000, can supply plenty of water for the passive cooling. In the extreme condition, sloshing of the free surface in the tank may impact on the roof and jeopardize structural integrity under long-period earthquake. For the safety assessment of structure, it is necessary to calculate the impact pressure caused by water sloshing.

Since the behavior of sloshing impacted on the roof is involved into a strongly nonlinear phenomenon, calculations of the impact pressure with theoretical or numerical method currently are of difficulties. Ibrahim [1] focused on a 2D tank with simple geometry to solve the linear sloshing problems using analytical methods. A numerical model using finite element technique was presented by Pal et al. [2] to study the linear behavior of cylindrical tanks. Choun and Yun [3] used the velocity potential and the linear water wave theory to decompose the surface wave into multiple forms. There are some complex methods to solve the nonlinear sloshing problems. Li et al. [4] used an improved material point method (MPM) to predict the liquid impact force by a contact algorithm. Liquid sloshing experiments in a partially watered square tank were proposed to validate the results of simulation. Eswaran et al. [5] proposed a numerical method based on volume of fluid (VOF) techniques with arbitrary-Lagrangian-Eulerian (ALE) formulation to analyze baffled and unbaffled tanks with a nonlinear sloshing behavior. However, these researches are usually valid for simple cases with linear or weakly nonlinear liquid sloshing dynamics.

But it is applicable to calculate the height of sloshing in a tank without roof. Fujita et al. [6] utilized the velocity potential theory to analyze the liquid sloshing in the annular region of more intricate coaxial circular cylinders. Formulas about the maximum wave height () at shell wall and the maximum pressure () at the free surface were obtained. More interestingly, the correlation between maximum wave height and maximum pressure was from equation (34) in their research. Virella et al. [7] used the finite element package ABAQUS to investigate the free surface wave amplitude and pressure distribution of tank wall by both linear wave theory and nonlinear wave theory models. Nayak and Biswal [8] used the Galerkin-weighted-residual based finite element method (FEM) to solve Laplace equation with nonlinear boundary conditions. The wave height of nonlinear sloshing was verified to be accurate.

Besides, the impact pressure is an important parameter in the assessment of safety of engineering design. Researchers had conducted large-scale experiments to investigate impact pressure [9–12].

As is mentioned above, the available studies mostly focused on the sloshing characteristics of rectangular tanks with simple geometry. However, considering the special structure of PCCWST, which is a coaxial circular cylinder tank with an inclined bottom, it is difficult in obtaining analytical expressions for the prediction of the natural modes and the liquid motion. Moreover, numerical and analytical methods to precisely describe the sloshing impact pressure are complicated because of the significant nonlinearity phenomena. In the present paper, a simplified method was proposed to calculate the impact pressure using the sloshing wave height. Moreover, an experiment was designed to verify this method.

#### 2. Calculation Method

Sloshing of the water surface in the tank may impact on the roof under long-period earthquake and the prediction of the impact pressure is necessary. Due to the apparent nonlinear behavior caused by complicated sloshing phenomena, a simplified method was proposed to calculate the impact pressure using the sloshing wave height, in which we first marked the position of the height of roof, the solid wide line showed in Figure 1, then produced sloshing in the tank without roof and recorded the maximum wave height which can be shown as the oblique line in Figure 1, and finally regarded approximately the difference between maximum wave height and roof height as the impact pressure head. In this way, the impact pressure can be calculated by the following equation:where is the maximum impact pressure, is the density of water, is the acceleration due to gravity, is the maximum wave height, and is the distance between the static water surface and the roof.