⚡ electrical engineering

CFD Model Predictions of Zero Boil‑Off Unvented and Vented Tank Filling in Microgravity

This paper presents 2D and 3D CFD models validated against microgravity tank filling experiments to characterize the relationship between fill rates, geyser flow regimes, and pressure evolution, ultimately demonstrating that stable geysers produce higher peak pressures and that 3D modeling is essential for capturing wobbly geyser behaviors.

Original authors: Rebecca L. Winter, Mohammad Kassemi

Published 2026-07-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Rebecca L. Winter, Mohammad Kassemi

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 you are trying to fill a giant, empty water balloon floating in outer space. On Earth, gravity pulls the water down, so it pools at the bottom. But in space, there is no "down." If you shoot a stream of cold liquid into this floating balloon, it doesn't just settle; it acts like a wild, unpredictable fountain.

This paper is a computer simulation study about exactly that problem: how to fill up a tank of super-cold fuel in space without it exploding or boiling away.

Here is a breakdown of what the researchers found, using simple analogies:

The Big Problem: The "Geyser" Effect

When you shoot cold liquid into a warm, empty tank in space, the liquid doesn't just sit there. It shoots up like a geyser.

The Issue: As the cold liquid hits the warm air inside the tank, the air tries to condense (turn back into liquid), but the liquid also tries to boil. This creates a tug-of-war that changes the pressure inside the tank.
The Danger: If the pressure gets too high too fast, the tank could rupture. If you try to let the gas out (vent it) to save the tank, you lose valuable fuel. The goal is to fill the tank without letting any gas escape (Zero Boil-Off) and without the tank blowing up.

The Four "Dance Moves" of the Liquid

The researchers used a super-computer to watch how the liquid behaves. They found the liquid does four distinct "dance moves" depending on how fast you shoot it in:

The Low Stable Geyser: The liquid shoots up a little bit and stays put, like a calm fountain. It's stable and predictable.
The Wobbly Geyser: The liquid shoots up but starts to lean and sway back and forth like a jellyfish or a drunk dancer. It's still stable, but it's moving around the center.
The Droplet Shedding: The liquid shoots up, but as it gets higher, it breaks apart into individual drops, like a garden hose that's spraying too hard. These drops fly across the tank and hit the other side.
The Full Jet Column: The liquid shoots all the way across the tank in one solid, unbroken stream, like a laser beam of water hitting the opposite wall.

The Surprising Discovery: Slow isn't Always Safe

You might think, "If I fill the tank slowly, the pressure will stay low." The computer models showed this is not always true.

The Analogy: Imagine trying to fill a bucket with a garden hose. If you turn the water on just a tiny trickle (slow speed), the water might shoot up in a straight, stable line that hits the bottom and creates a big splash of heat. This can actually cause a huge spike in pressure right at the start.
The Reality: If you turn the water on a bit faster, the stream might break into droplets. These droplets mix better with the air, cooling it down more efficiently. This can actually result in lower pressure spikes than the slow trickle.
The Lesson: Slowing down the fill rate doesn't guarantee safety; sometimes it makes the pressure spike worse because the liquid behaves differently.

The "Magic Number" (Weber Number)

The researchers found a way to predict which "dance move" the liquid will do using a math concept called the Weber Number.

Think of this like a speed limit sign for the liquid.
If the number is below 1.5, the liquid tends to stay calm (Stable Geyser).
If the number is above 1.7, the liquid tends to go wild (Droplets or Full Jet).
The Gray Area: Between 1.5 and 1.7, it's a toss-up. The liquid might be calm or wild, and the computer couldn't perfectly predict which one it would be just by looking at the speed. This suggests there are other hidden factors at play.

2D vs. 3D: The Flat vs. The Real

The researchers tried to model this in two ways:

2D (Flat): Like looking at a shadow of the tank. It's faster to calculate but misses the "wobbly" dance moves. It thinks the liquid stays perfectly straight, which isn't true in space.
3D (Real): Like looking at the actual tank. This is necessary to see the "wobbly" geyser and the droplets flying around. The 2D model sometimes gave wrong answers about pressure because it couldn't see the liquid swaying.

What About Vents?

They also looked at what happens if you open a valve to let gas out (Vented).

The Result: If you let the gas out, the pressure stays low, and the temperature stays steady. The liquid behaves almost the same as when the tank is sealed, but without the dangerous pressure spikes.
The Catch: If you don't vent, the pressure rises, the temperature changes, and the liquid behaves differently. You can't use a "vented" simulation to predict what happens in a "sealed" tank.

The Vacuum Case

They also simulated filling a tank that was almost a vacuum (empty of air).

The Start: When the liquid first hits the vacuum, it instantly flashes into gas (boils violently), creating a massive cloud.
The Settle: After about 30 seconds, the pressure builds up enough that the liquid stops boiling and starts acting like the normal "geyser" cases described above.

The Bottom Line

To fill a fuel tank in space safely without losing fuel or blowing up the tank, you can't just guess the speed. You have to understand exactly how the liquid will "dance" (geyser, wobble, or break into drops). Sometimes, going slower makes the pressure spike higher, and you need a 3D computer model to see the full picture. The "magic number" (Weber number) helps predict the behavior, but there is still a tricky zone where the liquid is hard to predict.

Technical Summary: CFD Model Predictions of Zero Boil‑Off Unvented and Vented Tank Filling in Microgravity

Problem Statement
The safe and efficient storage and transfer of cryogenic liquid fuels in microgravity is a critical challenge for NASA's future long-duration space missions. In-orbit refueling is essential for missions to the Moon and Mars, yet the lack of gravity complicates fluid management. A primary concern is the pressure rise within a tank during filling, which can result from heat leaks or the filling process itself, potentially leading to pipe rupture or fuel self-ignition. While venting the tank prevents pressure buildup, it reduces transfer efficiency. Consequently, "no-vent" (unvented) filling is a preferred but complex operational mode that requires a deep understanding of two-phase flow, heat transfer, and phase change dynamics in microgravity. This study addresses the need for predictive models to understand the transient pressure evolution and liquid-gas interface behaviors (specifically "geyser" formation) during unvented and vented tank filling in microgravity.

Methodology
The authors employed a multi-faceted modeling approach combining thermodynamic analysis and Computational Fluid Dynamics (CFD):

Thermodynamic Model: A zero-dimensional (0D) homogeneous thermodynamic model was developed to predict the final steady-state pressure. This model assumes fluid homogeneity at saturation temperature and pressure, solving mass and energy conservation equations to establish a theoretical limit for the system.
CFD Models: Two-phase CFD simulations were conducted using ANSYS Fluent with the Volume of Fluid (VOF) scheme, explicit formulation, and sharp interface tracking.
- Dimensions: Both 2D axisymmetric and 3D parametric models were utilized.
- Fluid: Perfluoro-n-pentane (PNP) was used as a simulant fluid, with properties derived from the DIPPR database at 253.18 K.
- Conditions: Simulations covered filling rates of 1.0–1.65 mL/s in a cylindrical tank (0.094 m height, 0.03 m radius) under microgravity conditions ( $9.81 \times 10^{-6}$ m/s²).
- Scenarios: The study examined unvented (no-vent) and vented (side and top) configurations, various inlet velocity profiles (flat plug flow and parabolic Poiseuille flow), and different initial tank conditions (empty, partially prefilled, and near-vacuum).
- Validation: Mesh independence and time-step studies were performed to ensure solution accuracy. The CFD results were validated against previous experimental data from drop tower studies (e.g., Symons et al., Govindan and Dreyer).

Key Contributions and Results

Geyser Behavior Classification: The 3D CFD models identified four distinct geyser behaviors based on inlet velocity and flow profile:
1. Low Stable Geyser: A small liquid mound with steady growth.
2. Wobbly Geyser: A stable but erratically leaning/bending liquid column.
3. Droplet Shedding: An unstable regime where the liquid column pinches off into droplets.
4. Full Jet Column: An unstable regime where the liquid reaches the opposite tank wall without breaking.
  The study found that 2D axisymmetric models could not capture the "wobbly geyser" behavior due to its asymmetric nature, often predicting non-physical necking instead.
Pressure Evolution and Transient Peaks: A significant finding is the relationship between geyser stability and transient pressure. Contrary to the assumption that lower fill rates always yield lower pressures, the models showed that stable geyser cases (low and wobbly) produced higher transient pressure peaks than unstable cases. This is attributed to the smaller interfacial surface area in stable geysers, which reduces the efficiency of vapor condensation. Unstable geysers (droplet shedding/jets) provide larger surface areas, facilitating rapid condensation and mitigating pressure spikes.
Weber Number Threshold: The study confirmed that the Weber number (adjusted for inlet velocity profile) effectively predicts the transition between stable and unstable regimes. A critical threshold between 1.5 and 1.7 was identified, consistent with previous experimental findings. However, the authors noted inconsistencies within this range, suggesting that the Weber number alone may not fully distinguish between low stable and wobbly geysers, implying other parameters may influence stability.
Thermodynamic vs. CFD Agreement: While the 0D thermodynamic model successfully predicted the final steady-state pressure (converging to the thermodynamic limit), it failed to capture the early transient pressure overshoots observed in the CFD models. The thermodynamic model also incorrectly suggested that lower fill rates would always result in lower early pressures, missing the nuance of geyser-induced pressure spikes.
Vented vs. Unvented and Initial Conditions:
- Vented Filling: Geyser shapes in vented cases were nearly identical to unvented cases, though venting prevented pressure rise and temperature increase. Side vents resulted in isothermal conditions, while top vents allowed some temperature rise due to partial obstruction by liquid.
- Initial Conditions: Partially prefilled tanks showed reduced temperature rises compared to empty tanks. Near-vacuum filling exhibited an initial flash evaporation phase, but after approximately 30 seconds, the geyser behavior converged to resemble the standard filling cases.
- Gravity Effects: Comparisons between microgravity and zero-gravity (0g) showed no discernible differences in geyser behavior, validating the use of drop tower (0g) data for predicting low Earth orbit and deep space mission performance.

Significance
The paper claims that understanding specific geyser behaviors is crucial for accurately predicting the transient pressure evolution in unvented tank filling, a factor often overlooked by simplified thermodynamic models. The research highlights that reducing fill rates is not a universally effective strategy for preventing over-pressurization, as it may inadvertently transition the system into a stable geyser regime with higher pressure peaks. By validating CFD models against experimental data and establishing the limitations of 2D axisymmetric approximations for asymmetric flows, the study provides a more robust framework for designing cryogenic fluid management systems for future space missions. The work underscores the necessity of capturing detailed two-phase flow physics to ensure the safety and efficiency of in-orbit refueling operations.