Similarity rules in gravity jitterrelated spacecraft liquid propellant slosh waves excitation

Abstract

The dynamical behavior of fluids, in particular the effect of surface tension on partially filled rotating fluids (cryogenic liquid helium and helium vapor) in a full-scale prototype Gravity Probe-B Spacecraft propellant tank and various 10% subscale containers with identical values of similarity parameters such as Bond number, dynamical capillary number, rotational Reynolds number, and Weber number, as well as imposed gravity jitters have been investigated. It is shown that the Bond number can be used to simulate the wave characteristics of slosh wave excitation, whereas the Weber number can be used to simulate the wave amplitude of slosh-mode excitation. This is because the slosh-wave excitation is mainly governed by the interaction of gravity (gravity jitters) and surface tension (interface between liquid and vapor fluids) forces, which is characterized by the Bond number; whereas the amplitude of slosh-wave excitation is dominated by the interaction between dynamical (centrifugal) and surface tension forces, which is characterized by the Weber number. In this study, perturbation of fluid stress distribution on the outer walls of the rotating container, caused by the excitation of slosh waves and their associated large amplitude disturbances on the liquid-vapor interface, have also been investigated. It is shown that a dynamical capillary number can be used to simulate the induced perturbation of the fluid stress distribution exerted on the wall. This distribution is governed by the interaction between surface tension (slosh-wave excitation along the liquid-vapor interface) and viscous (fluid stress exerted on the wall) forces.