Lumped Parameter Model for Liquid Sloshing in a Cylindrical Tank Equipped with Multiple Annular Baffles

A lumped parameter model for liquid sloshing in a rigid circular cylindrical tank with multiple rigid baffles under horizontal excitation is developed to represent continuous fluid. The subdomain method for liquid sloshing is implemented to divide the fluid domain into simple subdomains with continuous boundary conditions. The exact results of the convective velocity potential are obtained based on the continuity condition of pressure and velocity at the interfaces of liquid subdomains. By generating the same shear and moment as analytical solutions, an equivalent lumped parameter model with masses and springs is identified. The formulations of the lumped parameters in the model are analytically derived, including the convective and impulsive masses as well as their locations connected to the wall. Comparisons between the present results and available solutions confirm the feasibility and validity of the model. Detailed sloshing responses of liquid in the tank with multiple baffles are analyzed with regard to the dimensionless liquid heights, baffle positions, and sizes, respectively. The lumped parameter model can be simply assembled to make the dynamic analysis of complex fluid-structure systems with acceptable precision and a small amount of calculation.