Using CFD Techniques to Predict Slosh Force Frequency and Damping Rate

Resonant effects and energy dissipation due to sloshing fuel inside propellant tanks are problems that arise in the initial design of any spacecraft or launch vehicle. A faster and more reliable method for calculating these effects during the design stages is needed. Using Computational Fluid Dynamics (CFD) techniques, a model of these fuel tanks can be created and used to predict important parameters such as resonant slosh frequency and damping rate. This initial study addresses the case of free surface slosh. Future studies will focus on creating models for tanks fitted with propellant management devices (PMD) such as diaphragms and baffles. I. Introduction: During the initial stages of spacecraft and launch vehicle design, it is important to account for the forces created by the sloshing propellant in the fuel tanks. The variable conditions under which these propellant tanks operate make analytical models rather difficult to construct. There exists some very good predictive tools for bare tanks of certain geometries, but the addition of baffles, diaphragms, bladders and other slosh control devices invalidates the results obtained by these tools. A strong desire exists to perform large scale Monte Carlo statistical analyses on spacecraft and launch vehicle dynamic behavior in order to account for these variable conditions. A five or ten thousand case Monte Carlo study requires a simplified slosh model that can run rapidly in order to compute in a reasonable amount of time. Using a primary CFD model to determine parameters for a simplified mechanical analog slosh model holds great promise in terms of increasing accuracy and saving time, money, and effort on physical ground testing. For this reason, this study will focus on a more modern approach that uses computational fluid dynamics techniques to help model the liquid propellant slosh. In three axis stabilized spacecraft, coupling between the spacecraft or upper stage flight control system and an unanticipated slosh resonance can result in disaster as seen in the Space X Falcon 1 mission launched in 2007. Unforeseen slosh resonances can result in excessive attitude control fuel usage, pointing or attitude control issues that may violate mission requirements. For this reason it is important to fully understand the slosh dynamics of propellants in fuel tanks. In the case of spin stabilized spacecraft, any sloshing motion of the fuel will cause a loss of kinetic energy of the spacecraft. Since the stabilization of these particular vehicles is dependant on their spin, a loss of rotational kinetic energy could prove to be disastrous for the spacecraft and the payload 1 . Any transverse rates present during