Modeling the Effects of Liquid-to-Gas Density Ratio on Slosh Dynamics

Mechanical models are commonly used in Guidance, Navigation and Controls (GN&C) system-level models to represent propellant slosh forces on launch vehicles and spacecraft. The slosh model parameters are typically predicted using semi-empirical analytical methods that are based on experimental data for high liquid-to-gas density ratios (such as water and air at standard sea level conditions). Model parameter calculations typically neglect any contribution to slosh dynamics from the gas phase. However, some cryogenic propellant systems operate in conditions where the density ratio can be orders of magnitude smaller. Analytical and computational modeling was used in this effort to investigate the effects of liquid-to-gas density ratio on slosh dynamics. No experimental data nor previous studies are available at this time that quantify the effect of liquid-to-gas density ratio on slosh dynamics. However, in a recent CFD study, results showed that density ratio can have a significant effect on slosh model parameters. In this study, a dual pendulum slosh model was created that distinctly represents both liquid and gas phase dynamics. Solution of the model, which invokes the Euler-Lagrange equations of motion, demonstrates that slosh frequency is a combination of liquid slosh frequency and gas phase slosh frequency. Additionally, it shows that slosh mass is reduced due to the opposing motion of the gas phase with respect to that of the liquid phase. The slosh model parameter trends were verified using Computational Fluid Dynamics (CFD) analysis results for various liquid-to-gas density ratios, tanks, and fill levels.