Study on Occurrence Condition of Extremely Large Sloshing Load in Cylindrical Tanks

Abstract During an earthquake, if the seismic waves include frequency components close to the natural sloshing frequency of a cylindrical tank, sloshing will occur inside the tank. When high amplitude sloshing occurs, the liquid surface collides with the roof of the tank. In the tank design, it is important to evaluate the sloshing load acting on the roof. In our previous studies, we identified through our test results that an extremely large sloshing load on the roof may occur even if the excitation amplitude is small. In addition, we also identified through our CFD analysis that a slightly deformed liquid surface causes the extremely large sloshing load. In detail, a very weak collision with the roof initially causes the slightly deformed liquid surface, which subsequently entraps air between the liquid surface and the roof during the next collision. The moment the air is completely entrapped between the roof and the liquid surface, the extremely large sloshing load occurs impulsively. Focusing on the fact that the very weak collision serves the starting point of the slightly deformed liquid surface, we have formulated the condition for the occurrence of the extremely large sloshing load. This formulation is based on our test results and the simplified nonlinear sloshing model proposed in our previous studies. The proposed occurrence condition formula can numerically predict whether an extremely large sloshing load occurs. In parallel with the above study, we examined a method to reduce the calculation time of CFD analysis by replacing seismic wave excitation with equivalent sinusoidal wave excitation comprising several waves. However, in some cases, an extremely large sloshing load occurred only under either seismic wave excitation or sinusoidal wave excitation, and they were not equivalent. Therefore, we have addressed this issue by utilizing the previously mentioned occurrence condition formula, which takes into account the extremely large sloshing load in the proposed method that replaces seismic wave excitation with equivalent sinusoidal wave excitation.