Equivalent mechanical model for liquid sloshing during draining

For a spacecraft draining liquid fuel during a continuous thruster maneuver, a brief equivalent method is proposed to model the time-varying properties of liquid sloshing for dynamics and control design. The sloshing liquid during draining is equivalent to a set of mechanical model with variable parameters. The model parameters for sample filling ratios are determined by an efficient finite element method according to equivalent principles, while the parameters for other filling ratios are obtained by piecewise linear interpolation. Using the proposed model, forces and torques acted on a Cassini shaped tank by the inside liquid during draining are investigated undergoing several typical motions. Verifications and comparative studies are done with Computational Fluid Dynamics simulations, which confirm the accuracy of the brief model while the sloshing amplitude is small and the flow rate is low.