A Comparative Study on 3d Sloshing Dynamics for Negative-G Acceleration
This study validates and compares the accuracy, performance, and computational cost of five OpenFOAM flow models (including laminar, LES, and k-ω SST) in simulating 3D negative-g sloshing dynamics within a domed circular cylinder tank under various fill ratios, excitation forces, and internal pressures to assess their capability in predicting sloshing forces, center of mass locations, and propellant discontinuities.
Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
Imagine a spacecraft traveling through the vacuum of space, carrying a tank filled with liquid fuel. Unlike a car on a road, this vehicle cannot rely on gravity to keep the fuel settled at the bottom of its tank. When the rocket fires its engines, the fuel sloshes around, but when the engines cut off or the vehicle maneuvers sharply, the fuel can fly in any direction. If the rocket suddenly accelerates in a way that pushes the fuel away from the outlet at the bottom of the tank, the engine might starve for fuel and shut down. This is a critical problem for mission safety. Engineers need to predict exactly how this liquid will behave inside a moving container, how much force it will hit the walls with, and precisely when the flow of fuel might stop. To do this, they use powerful computer simulations that act like digital wind tunnels, but for liquids inside a tank.
A team of researchers at Istanbul Technical University set out to test how well different computer models could predict this chaotic behavior. They focused on a specific, dangerous scenario: a sudden negative acceleration, where the rocket pushes the fuel away from the drain at the bottom of the tank. They used a virtual tank shaped like a cylinder with rounded ends, filled with a liquid similar to hydrazine, a common rocket propellant. The researchers ran simulations using five different mathematical approaches to describe the flow. Some models treated the liquid as perfectly smooth and calm, while others tried to account for the tiny, chaotic swirls and turbulence that happen in real fluids. They also tested how the pressure inside the tank, ranging from a vacuum to extremely high pressures of 600 bars, might change the way the fuel moves.
The researchers discovered that while all the computer models agreed on the basic movement of the fuel when it was pushed straight down, they disagreed significantly when it came to the side-to-side motion. When the fuel hit the top of the tank and splashed back down, it created complex, high-speed swirls moving in directions perpendicular to the main flow. The simpler models, which assumed the liquid moved smoothly, failed to capture these violent side-to-side movements and often predicted the forces on the tank walls incorrectly. The more advanced models, which accounted for turbulence, were much better at predicting these sudden, sharp changes in force. However, these advanced models required significantly more computing power and time to run.
A key finding of the study was that increasing the pressure inside the tank did not calm the sloshing down as one might expect. Even at very high pressures, the fuel continued to move violently, and the duration of time the fuel was disconnected from the drain remained the same. The simulations showed that after about 3.85 seconds of negative acceleration, the fuel mass would lift away from the bottom of the tank, cutting off the flow to the engine. This timing was consistent across all the models, regardless of the pressure level or the complexity of the math used. The researchers also found that the shape of the tank's rounded ceiling played a major role in creating these chaotic side currents, generating short-lived but powerful eddies that the simpler models missed.
Ultimately, the study suggests that for designing safe spacecraft, engineers cannot rely on the simplest computer models if they need to predict the exact forces and moments acting on the vehicle during severe maneuvers. While the simple models are faster and cheaper to run, they miss the critical, nonlinear spikes in force that occur in the lateral directions. The more complex models provide a clearer picture of these dangerous dynamics, even though they demand more computational resources. The work confirms that to ensure a rocket engine never runs dry during a critical maneuver, simulations must be detailed enough to capture the chaotic, swirling nature of the fuel as it bounces off the tank walls, rather than assuming it moves in a smooth, predictable line.
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