When Propellant Controls the Spin: Two-Phase Fluid Dynamics and Their Impact on Spacecraft Rotational Stability

Internal fluid rotation and slosh in spacecraft tanks produce time-varying torques and changes in effective inertia that directly affect a satellite’s rotational dynamics. For small tanks or low fluid mass fractions, these effects can be treated as perturbations, approximated by simple slosh modes, or even considered negligible noise. However, when tanks are large relative to the vehicle’s structural mass, the fluid’s inertia and unsteady torques can alter the rotational equilibrium and its stability. This work examines how rotating internal fluid motion affects spacecraft attitude stability, with particular attention to the minimal axis instability phenomenon, in which a body containing a cavity filled with a two-phase fluid shift from rotating about its axis of minimum inertia to rotating about its axis of maximum inertia as the fluid dissipates energy, and the consequences of that behaviour for rotation-sensitive missions. The objective is to establish a connection between viscous boundary-layer dissipation mechanisms, the minimal axis instability phenomenon, and the relative time scale, which also depends on the fill level.