Study of propellant sloshing in the stability of a microlaunch vehicle with passive mitigation.

Abstract

This work analyzes the stability of a micro-launch vehicle (Micro-LV) considering the effects of sloshing during the ascent phase of flight in the atmosphere with the burn of the first stage. A conceptual Two-Stage to Orbit (TSTO) Micro-LV utilizing liquid propulsion with LOX and RP-1 is implemented as a benchmark for stability analyses. Its mission objective is to deploy a payload of 100 kg into a low Earth orbit (LEO) at an altitude of 300 km. Linearized equations of motion for rigid and flexible bodies, along with engine inertia effects and sloshing, are considered and arranged in a state-space formulation. Transfer functions between the pitch angle  and the gimbal angle of the engine  are determined for open-loop stability analyses considering a proportional-derivative (PD) attitude controller. Root locus techniques are employed to identify regions located in the right half-plane (RHP) associated with sloshing frequencies, which characterize instability. Due to propellant consumption throughout the flight, stability analyses are conducted for various fill ratios (FR) ranging from 0% to 100% of the tanks, in increments of 10%. It is observed that at a fill ratio of 90%, the RP-1 tank exhibits instability because the sloshing mass is situated between the center of percussion (CP) and the center of gravity (CG) of the LV, in the area referred by some authors as the danger zone. It was noted that flexibility slightly dampened the effects of sloshing, but not significantly. Additionally, the coupling between the tanks concerning the variation of damping from one tank to another was investigated. A solution for the passive mitigation of sloshing instability is implemented by introducing ring baffles with a minimum damping requirement of 0.15%, and its effect on vehicle stability is analyzed.