Study of propellant sloshing with passive mitigation in the stability of a micro- launch vehicle

Abstract This work presents stability analyzes results for a micro-launch vehicle (Micro-LV) considering the effects of sloshing. A conceptual Two-Stage to Orbit (TSTO) Micro-LV utilizing liquid propulsion with LOX and RP-1 is developed. Its mission objective is to deploy a payload of 100 kg into 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 relating the pitch angle ∅ y and the engine gimbal angle, β E y are determined for open-loop stability analyses considering a proportional-derivative (PD) attitude controller. It is observed that at a FR of 90%, the RP-1 tank exhibits instability because its sloshing mass is situated between the center of percussion (CP) and the center of gravity (CG) of the Micro-LV, in the area referred as the danger zone. 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 the vehicle’s stability is analyzed.