Study on the Predictive Evaluation Method for Liquid Surface Shape and Flow Velocity in Nonlinear Sloshing Based on Simplified Equations

Abstract

Abstract When cylindrical tanks installed in the ground, such as oil tanks and liquid storage tanks, receive strong seismic waves, including the long-period component, motion of the liquid surface inside the tank called sloshing may occur. If large-amplitude sloshing occurs and the waves collide with the tank roof, it may lead to accidents such as damage of the tank roof or outflow of internal liquid of the tank. Also, there is a possibility that the internal components in the tank may be damaged due to the fluid force generated by the flow of the sloshing. In order to evaluate the load acting on the tank roof, it is considered that the liquid surface shape and the liquid surface velocity are required as input parameters. In order to evaluate the load acting on the internal component in the tank, the flow velocity generated by sloshing is required as an input parameter. If the sloshing wave height is small, these values can be calculated based on the linear potential theory. However, when the sloshing wave height increases, the sloshing becomes nonlinear, and the difference between the nonlinear sloshing behavior and the linear sloshing behavior. Therefore, the method of evaluating nonlinear sloshing behavior is necessary to evaluate the design load of tank under the large sloshing wave height condition. In this paper, new methods of evaluating nonlinear sloshing behavior are proposed for the first-order sloshing mode of a cylindrical tank, which can evaluate the maximum nonlinear sloshing wave height, the nonlinear liquid surface shape, the liquid surface velocity, and the flow velocity. Proposed methods, which consist of simplified equations, are expected to be applied to a new sloshing load evaluation method in primary design.1