Dynamic characteristics of liquid sloshing in cylindrical tanks filled with porous media

Abstract

The dynamic characteristics of liquid sloshing in cylindrical tanks filled with porous media are analyzed in this paper. As the tank is subjected to the small external excitations, the flow is assumed to be in Darcy's flow regime, and then the porous medium can provide damping effect linearly proportional to the fluid velocity. Based on the pore flow theory, the linear equivalent mechanical model with the damping effect due to porous medium is established. This equivalent model consists of a rigidly fixed mass and infinite sets of mass-damping-spring systems, which can exert the same total dynamic force as the linearized actual fluid field. The equivalent system can explain the dynamic characteristics of each modal response of sloshing in a cylindrical porous-medium tank. Therefore it is more convenient to analyze the sloshing behavior from the structural dynamic analysis point of view. By this model, the natural frequency and damping ratio of the cylindrical porous-medium tank are revealed. Both parameters are related to the tank dimensions, porosity and permeability of the porous medium.