Improved Moving Pulsating Ball Equivalent Model for Large-Amplitude Liquid Slosh

In the process of spacecraft launching, maneuvering, rendezvous, and docking, the liquid fuel may slosh violently due to the action of inertia force and gravity, and the additional sloshing force will have an important impact on the spacecraft. To meet the requirement of high-fidelity real-time simulation of an on-board computer, in this paper, an equivalent dynamic model for large-amplitude liquid sloshing is studied and validated. First, the moving pulsating ball model (MPBM) of liquid large-amplitude sloshing motion is extended to the gravity environment, and the gravity is added to the dynamic equation of the pulsating ball to derive the normal force of the MPBM. At the same time, the equivalent model of the liquid that does not participate in sloshing is introduced, which makes the calculation of the center of mass of the liquid more accurate. The validity of the improved MPBM (IMPBM) in cases of small-amplitude sloshing, large amplitude sloshing and zero momentum maneuvers is verified by three examples. Finally, an experimental platform is designed and built to verify the numerical simulation results. It is shown that the IMPBM can well reflect the reactive force for liquid sloshing in both spherical and nonspherical tanks.