Proposed Benchmark Problems for Validation of Low-G Slosh Models

Propellant slosh is a concern for ultra-stable pointing platforms such as the Nancy Grace Roman Space Telescope, and for spacecraft with stringent maneuvering requirements like OSIRIS-REx, Artemis, and robotic servicing vehicles. Modeling slosh well in the spacecraft design is important for retiring risk to mission performance and safety.
The ideal slosh model would be accurate over all flight regimes, computationally cheap, and backed by ample experimental experience. As might be expected, practical considerations impose constraints, and compromises must be made. Experimental data for low-g dynamics is qualitative and limited, due to the challenges of providing a low-g environment and instrumenting fluid.
Computational Fluid Dynamics (CFD) is more practical than experiment for supporting control system design, but is still quite expensive in time and computing resources. An economical technique is to model slosh as a pendulum suspended within the spacecraft body. The commonly-seen torsion pendulum assumes an acceleration field, so is of questionable suitability for the low-g regime. A more suitable choice for low-g is a translational pendulum. Both types of pendulum are computationally cheap, but of limited accuracy. Multiple pendulums may be superposed to model multiple modes of motion, but some phenomena remain difficult to model well.
The high-g and low-g dynamic regimes pose distinct problems in modeling fluid dynamics. In high-g, the gravity and momentum forces dominate. Low-g dynamics are dominated by momentum and surface tension forces. The transition between low-g and high-g also has its own distinct transient phenomena, such as geysering, breakaway, and bubble formation. These transient phenomena are challenging to capture using pendulum models.
Consider CFD and pendulum models to be the two ends of the fidelity-vs-cost spectrum. We are investigating Smoothed Particle Hydrodynamics (SPH) as a fluid model that, by selecting the number of particles, could be tuned to balance accuracy against computational cost as desired. It still needs backing by CFD to select some model parameters. In addition, the trade between complexity and accuracy needs to be understood. For example, how many particles are required for bubble formation to be adequately modeled? Over what ranges of excitation may slosh motion be modeled as a linear system?
The benchmark problems presented here are intended to provide a common basis for anyone pursuing low-to-medium fidelity slosh models to ground their models in