Modeling Torsional Stiffness and Damping of Liquid Slosh in Spacecraft Diaphragm Tanks

Abstract

This study presents a pendulum-based empirical model of liquid slosh in spacecraft diaphragm tanks. Diaphragm torsional stiffness and effective damping are predicted within a range of lateral excitation frequency typical of launch or on-orbit operations. A pendulum-analog model with two primary slosh modes is extracted from diaphragm tank slosh data corresponding to steady-state triaxial force measurements at the support points of the tank under sinusoidal excitation. The approach leads to repeatable and accurate determination of pendulum model parameters. A gradient-based algorithm and a procedure for setting initial conditions for optimal parameter estimation are proposed to predict the liquid slosh forces and torques acting on the tank as frequency response functions of apparent mass and apparent mass moment. The pendulum models were assessed by comparing model-predicted force/torques with measurements, showing good agreement (1–5% prediction error in the time domain) under most test conditions (fill level, excitation amplitude, and frequency). An empirical model of the stiffness and damping is also proposed for the tested range of operational conditions. Because of the nonlinear nature of liquid slosh behavior in a diaphragm tank, both the stiffness and damping are local values for a given set of test conditions.