Multi-body modeling for fluid sloshing dynamics investigation in fast spinning rockets
Creators: name: BUCCI, Lorenzo
name: LAVAGNA, Michele
Publisher: name: Proceedings of the 7th European Conference for Aeronautics and Space Sciences. Milano, Italy, 3-6 july 2017
Year: 2017
Subjects: NUMERICAL MODELING

description: Fuel sloshing dynamics inside space vehicles is a broad topic, still quite open to investigation for modelling, verification and validation. The behaviour of liquids in tanks, subject to a certain spectrum of external accelerations, is hard to predict, no matter the vehicle is either a launcher or a spacecraft. A step over in complexity is added whenever spinning vehicles are considered, as centrifugal actions may play an important role in defining the fluid shape inside the tank; furthermore, if the fluid dissipates energy, the vehicle might lose attitude stability, thus overcoming the benefit of spin stabilization. The numerical modelling of the phenomenon may be faced with different level of accuracy and, therefore, of complexity, even preserving the meaningfulness of the attainable results. The present research investigated the sloshing effects in highly spinning rockets. In particular, also in the light of a possible experimental test to validate the model and characterize this complex phenomenon, a scenario involving a small sounding rocket with a liquid or hybrid propulsion system, hence carrying a significant liquid propellant mass with respect to the overall mass, spun up to enhance the flight stability, was investigated. The liquid mass may undergo sloshing vibrations, coupled with the spin frequency, and affect both the attitude and the trajectory of the rocket. The analysis was performed by exploiting a PoliMi-DAER multi-body numerical tool. The fluid carried on board is modelled with a lumped parameter method, as a set of rigid bodies connected by different types of joints, springs and non-linear dampers. First, the shape of the fluid is obtained with analytical approximations, and its overall inertia properties are estimated. Then, the sloshing modes shapes and natural frequencies are modelled exploiting different configurations embedded in the Simulink-based software, allowing swirling, tangential and longitudinal motion of the fluid mass. Since the sloshing modes themselves were unknown at the beginning of the study, the analysis served as a preliminary investigation on the topic, to investigate the effect of sloshing in a fast-spinning vehicle. Several cases were investigated, corresponding to different tank filling ratios, and different kinematic and dynamic conditions; although preliminary, the numerical results suggest that the high spin rate might trigger an unstable swirling of the fuel, if one of the natural swirling frequency is below the spin frequency. The modelling of the viscous damping is a crucial part, still partially open, of the study. According to the parameters, the viscosity may reveal beneficial in damping the undesired sloshing behaviour, but could also be a source of energy dissipation which leads towards an overall unstable dynamics of the vehicle. The paper presents the adopted model and its implementation and critically discusses the obtained results as potential drivers to the propulsion unit and mission profile design.