Analysis of Two-Dimensional Nonlinear Sloshing in a Rectangular Tank by Using a Concentrated Mass Model

Major problems can occur when liquid sloshes in a tank, such as occurs in liquid storage tanks during an earthquake, and this is an important engineering problem to address. To analyze this phenomenon, semi-analytical methods such as the perturbation method, the multimodal method, and the finiteelement method are generally used. However, semi-analytical methods involve quite complicated equations, and the finite-element method involves many degrees of freedom when the tank is large. In this paper, a nonlinear numerical model with relatively few degrees of freedom is established for vertical and horizontal two-dimensional nonlinear sloshing in a rectangular tank excited horizontally. The model comprises concentrated masses of liquid connected by nonlinear springs and dampers. The connecting springs have characteristics based on the static and dynamic pressures of the liquid. In addition, a method is proposed for reducing the number of degrees of freedom in the two-dimensional model. The natural frequencies, modes, and frequency responses are then compared among the concentrated-mass model, theoretical calculations, and experimental results. Good agreement was achieved among them, thus demonstrating the validity of the model.

Study on the Predictive Evaluation Method of Load Acting on the Roof and Internal Components of Cylindrical Tanks by Nonlinear Sloshing

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 free liquid surface inside the tank called sloshing may occur. If high-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. Therefore, it is important to predict the wave height of sloshing generated by earthquake motions. Sloshing is a type of vibration of free liquid surface, and if the sloshing wave height is small, it can be approximated with a linear vibration model. In this case, the velocity-response-spectrum method using velocity potential can estimate the sloshing wave height under earthquake motions. However, if the sloshing wave height increases, the sloshing becomes nonlinear, and necessary to evaluate the wave height using other methods such as numerical analysis. Design earthquake magnitude levels in Japan tend to increase in recent years, long-period components of earthquake wave which act on the sloshing wave height also increase instead of introducing seismic isolation mechanisms. To evaluate load acting on the internal components of cylindrical tanks by nonlinear sloshing, there are few applications which quantitatively evaluated the crest impact load of nonlinear sloshing. In order to evaluate the load acting on the internal components of cylindrical tanks, the range of applicability of the fluid flow analysis method which validated the analysis accuracy of impact load acting on the roof in a simple cylindrical tank in the past study (PVP2019-93442) is extended to cylindrical tanks with internal components.

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

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