Dynamic Characteristics of Liquid Motion in Partially Filled Tanks of 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: inviscid, the boundary layer, and viscous correction. This boundary layer solution is obtained analytically, and the inviscid and viscous correction solutions are obtained by using finite element methods. This model has been used to predict liquid natural frequencies, mode shapes, damping ratios, and nutation time constants for the INTELSAT VI spacecraft. The analytical results were compared with experimental results and are in good agreement. 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 inertia ratios and tank fill fractions. This phenomenon, known as anomalous resonance, was also present during INTELSAT IV in-orbit liquid slosh tests and ground air bearing tests for INTELSAT IV and VI.