Dynamics of liquid-filled spacecraft

A method is presented for simulating coupled liquid-solid dynamics. An important example of a coupled liquid-solid system is a satellite carrying fuel. The dynamics of the satellite and the onboard fuel influence each other, which may lead to satellite motion that is uncontrollable. For better understanding of the complex dynamics of coupled systems, a numerical model is developed. The model consists of two parts. The first part that solves the liquid motion is only briefly discussed here. The focus in this paper is on the way in which the dynamics of the liquid and the solid body are coupled. For this, the governing equations are presented in which terms appear that represent the force and torque on the solid body due to the sloshing liquid. The governing equations are rewritten such that the discrete approximation of these equations can be integrated in a stable manner for arbitrary liquid/solid mass ratios. Results are presented demonstrating the stability of the present model. A grid-refinement study and a time-step analysis are performed. Finally, the flat-spin motion of a satellite, partially filled with liquid, that flew in 1992 as part of the Wet Satellite Model experiment is studied. Results from the simulation are compared with the actual flight data.