Numerical Modeling of Liquid Propellant Mass Transfer with Sloshing during On-Orbit Refueling

Over a couple of decades, an On-Orbit Refueling (OOR) application has been continuously developed to prolong the life span of the satellite whose end of life (EOL) has reached. It can reduce the cost of space applications by extending the life span of large satellites like communication satellites, which have been used for critical missions. During the OOR mission, the liquid propellant like unsymmetrical dimethyl hydrazine (UDMH) is partially filled in a propellant tank, which can slosh and produce non-cooperative couple motion between the chaser-target satellite, which results in non-cooperative activity and leads to divergence in a coupled attitude of the satellite. A non-linear dynamic modeling of the liquid propellant mass transfer with sloshing was developed in this paper to simulate the on-orbit non-cooperative and inertial movement of the liquid propellant in the cylindrical propellant tank during refueling after proximity and docking of the chaser-target satellite, a fuel injector connected with the target satellite are modeled by using the time-varying spring mass damper system in the in-track motion of satellites, which is coequal to the motion of the propellant mass center, Whereas, time-varying pendulum model is used in the radial direction of the coupled satellite. During sloshing, a coequal propellant elliptical cylinder is developed to model the inertia of dispersed liquid propellants. Multiple scenarios of on-orbit propagation of coupled satellites are designed to provide the orbital disturbance to the propellant tank. In contrast, computational fluid dynamics simulations were carried out to observe the liquid propellant dynamics behavior in micro-gravity in the propellant tanks and to verify the proposed non-linear dynamics model, as CFD simulation has no limitation on gravitational acceleration and can be applied to realistic flight sloshing tank models. A three-dimensional on-orbit sloshing behavior of the liquid propellant in micro-gravity is analyzed theoretically and numerically using the CFD. This paper provides the results of the propellant phase contour of the chaser and target spacecraft along the axial and radial direction throughout the refueling time. Various plots of propellant mass center (MC) and moment of inertia were sketched from the OpenFOAM CFD and compared with the results of a proposed coequal dynamic model. It was found that the suggested dynamic modeling accurately determines the sloshing behaviors along with the mass transfer motion during the onorbit refueling with fewer computation resources, and deviation in the sloshing parameters between the methods is less than ten percent.