Calculation and Verification of Pendulum Length for Equivalent Pendulum Model of Liquid Lateral Sloshing in Horizontal Cylindrical Tanks

Abstract Aiming at the problem that the pendulum length of the equivalent pendulum model for liquid sloshing is difficult to determine, leading to the inaccurate calculation of liquid sloshing frequency, this paper takes the lateral sloshing mode of Newtonian fluid in horizontal cylindrical tanks as the research object. Based on the axis of rotation theorem, Newton’s law of viscosity and the equivalent principle of resultant moment, a calculation model for the pendulum length of the equivalent pendulum model for liquid sloshing is derived. On this basis, the feasibility and effectiveness of the proposed calculation method for the pendulum length of the equivalent pendulum model are verified through three methods: liquid sloshing dynamics theory, sub-scale liquid tank truck experiment and numerical simulation using Fluent software. The results show that when the liquid in the horizontal cylindrical tank sloshes laterally, the resultant force action point of the shear force inside the liquid is approximately located at 1/3 of the liquid height, and the pendulum length of the equivalent pendulum model is the distance from the tank center to this resultant force action point. The research results have strong reference value for further analyzing the equivalent mechanical model of liquid sloshing and exploring the liquid-solid coupling nonlinear dynamic characteristics of liquid transport vehicles.