Equivalent Dynamic of Liquid Sloshing Coupled with Mass Transfer During On-Orbit Refueling

During an on-orbit refueling mission, the liquid fuel partially filling in the tanks will slosh and produce coupled motion with the servicer-to-client transfer, which may bring dangers to the spacecraft and even lead to attitude divergence. To effectively simulate the motion and the inertia of liquid fuel in a cylindrical tank during refueling, equivalent dynamic modeling of liquid fuel sloshing coupled with mass transfer is developed in this paper. A spring-mass-damper model with time-varying elastic and damping coefficients is implemented in the axial direction to equal the motion of the liquid mass center, while a pendulum model with time-varying pendulum length is adopted in the radial direction. An equivalent liquid elliptical cylinder is developed to approximate the inertia of dispersed liquid while sloshing. A series of computational fluid dynamics simulations are carried out to observe the liquid behaviors in the fuel tanks and to verify the proposed equivalent dynamic model. Finally, three-dimensional sloshing is theoretically and numerically analyzed.