Similarity rules in gravity jitter-related spacecraft liquid propellant slosh waves excitation

The dynamical behavior of fluids, in particular the effect of surface tension on partially filled rotating fluids in a full-scale prototype Gravity Probe-B Spacecraft propellant tank and various 10 percent 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. 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.