Dynamic Characteristics of Liquid Motion in Partially Filled Tanks of a Spinning Spacecraft

This paper presents a boundary-layer model to predict dynamic characteristics of liquid motion in partially filled tanks of a spinning spacecraft. The solution is obtained by solving three boundary-value problems: an inviscid fluid problem, a boundary-layer problem, and a viscous correction problem. The boundary-layer solution is obtained analytically, and the solutions to inviscid and viscous correction problems are obtained by using finite element methods. The model has been used to predict liquid natural frequencies, mode shapes, damping ratios, and nutation time constants for a spinning spacecraft. The results show that liquid motion in general will contain significant circulatory motion due to Coriolis forces except in the first azimuth and first elevation modes. Therefore, only these two modes can be represented accurately by equivalent pendulum models. The analytical results predict a sharp drop in nutation time constants for certain spacecraft inertia ratios and tank fill fractions. This phenomenon was also present during on-orbit liquid slosh tests and ground air-bearing tests.