3DOF-rigid-pendulum analogy for nonlinear liquid slosh in spherical propellant tanks

The problems of large-amplitude lateral sloshing, rotary sloshing and liquid rotation-starting in liquid-filled spacecraft remain of great concern to aerospace engineers. A composite 3DOF-rigid-pendulum model is proposed in this paper for nonlinear liquid slosh in spherical propellant tanks. The primary modes of liquid behavior in moving tanks, including the overall rigid motion, the liquid spinning motion, the lateral sloshing and the rotary sloshing, can be approximately described by using this equivalent mechanical model (EMM). First, the liquid sloshing dynamics equations are derived via the Lagrangian approach. Next, by giving three different simulation cases and comparing the forces generated by the EMM with that generated by the actual liquid, the equivalency of the mechanics is validated. Finally, the primary nonlinear effects of liquid in partially-filled tanks, which has been recognized in published experimental researches, are investigated by the proposed EMM. Additionally, the drifting phenomena, which indicate symmetry breaking, are displayed in the non-planar motion of the 3DOF-rigid-pendulum under unidirectional lateral motion of moving tanks.