Self-Pressurization and Boil-off Prediction

Liquid hydrogen self-pressurization test article (left); and CFD results (right) [1][2]

This figure shows a ground based self-pressurization test article and associated internal hardware and sensors (left side); and corresponding CFD results for liquid hydrogen (right side). The liquid temperature and flow fields predicted by the CFD model are shown at top right; and pressure response prediction versus test data are at bottom right. This tank was insulated with MLI and tested in a large vacuum chamber.

Why Self-Pressurization Occurs

Self-pressurization occurs naturally in an unvented cryogenic tank as heat leak from the environment:

• Vaporizes some of the liquid over time generating boil-off gas
• Increases the gas temperature resulting in higher ullage pressure
• Increases the bulk liquid temperature resulting in expansion of the liquid and compression of the ullage

In normal gravity this results in the coldest liquid at the tank bottom; saturation temperature at the liquid-gas interface; and the warmest gas at the top of the tank. This characteristic temperature profile in a cryogenic storage vessel is often termed thermal or temperature stratification. In a reduced gravity environment, the tank pressure behavior and thermal stratification is more complex depending on the ullage location, wall heat flux distribution, acceleration vector, and other parameters.

The pressure rise rate of a quiescent cryogenic propellant tank is a function of heat loads (both magnitude and location) and the volumetric fill level. Higher fill levels result in faster pressure rise due to the smaller ullage volume and increased heat flux when more of the tank wall is wetted. Note that periodic mixing of the liquid contents can bring down the saturation temperature at the interface - and the tank pressure along with it - enabling longer passive storage times (i.e., dormancy) before reaching the maximum allowable tank pressure.

Predicting Self-Pressurization

Unlike active pressurization, self-pressurization generally involves much longer time durations. As a result, transient energy exchange among the ullage, liquid, and tank walls becomes a more dominant factor in predicting the tank pressure response. Accurate simulation of the pressure history during self-pressurization requires computational fluid dynamics (CFD) modeling and is particularly influenced by the initial conditions.

Time stepping energy balance models can be used for lower fidelity models and/or as a supplement to CFD models for long simulations once the effects of the initial starting conditions resolve. For example, a lumped-node model can be used to extrapolate the tank pressure conditions for extended durations after a steady state pressure rise is established with a transient CFD model.

Dropping the tank pressure can be done intentionally by mixing the liquid to prolong nonvented storage time or to bring a cryogenic tank toward equilibrium. In these cases, the minimum final tank pressure can be predicted based on the initial liquid temperature profile and the amount of energy added to the liquid due to mixing and condensation. The corresponding saturation pressure (or partial pressures in the case of a binary ullage) can then be iterated upon until convergence is achieved.

Parameters Impacting Self-Pressurization

Key parameters affecting the self-pressurization behavior of a cryogenic propellant tank include:

• Initial tank pressure and volumetric fill level
• Initial tank wall, liquid, and ullage temperature distributions
• Saturation curve of the associated fluid and its thermophysical properties
• Environmental and other heat loads entering the tank (through insulation, structure, feedline, thermal soak back, other penetrations, internal powered components, etc.)
• Time-dependent heat flux distribution along the tank wall
• Thermal radiation from the warm tank wall to the fluid (participating media) and colder tank wall sections
• Induced mixing from internal sources or sloshing
• Other ullage gases in addition to the vapor (and their concentration distribution)

An on-orbit cryogenic propellant tank will be affected by all the above parameters in addition to several other parameters that are unique to reduced gravity:

• Time dependent direction, magnitude, and frequency of the acceleration vector
• Location and shape of the liquid-gas interface
• Transient fluid circulation from surface tension forces, vehicle maneuvers, etc.

Simplified Models for Self-Pressurization

In the last few years several public domain and open source models have been developed and made available [3]. They all make simplifying assumptions to enable lumped-node approaches to estimating transient pressure and temperature response during self-pressurization.

These newer models add to the existing portfolio of codes, many of which were developed at NASA [4]. Together, they provide a lower fidelity (and much lower resource-intensive) approach to predicting self-pressurization compared to CFD modeling.

Since these models don't account for many of the key parameters described above, caution should be exercised in their usage. In particular, the selection of heat transfer coefficients among the various nodes impacts the prediction accuracy and ideally should be "tuned" to experimental results using the configuration being modeled.

Another consideration with their usage is applying accurate heat loads to the fluid. Many models have algorithms to predict environmental heating through insulation such as MLI in a vacuum. However, tank applied systems have degraded performance relative to calorimeter data due to seams, openings, and other degradation factors. In addition, the highest heat loads for many cryogenic tanks comes from solid conduction through various penetrations (e.g., vents, fill/drain lines, access ports, etc.).

References

[1] Cryogenic fluid management of liquid hydrogen, oxygen, and methane: Part 1 - passive technologies, systems, and operations. Moran Innovation LLC, 2024.

[2] Van Dresar et al., NASA TM-105411, 1992; Barsi and Kassemi, Cryogenics, 2008.

[3] Examples include: BoilFast, CryoEvap, HyTank, and EBM.

[4] Examples include: GFSSP, CryoSIM, TankSIM, and CPPPO.

Author Bio

 

Matt Moran is the Managing Member at Moran Innovation LLC, and previous Managing Partner at Isotherm Energy. He's been developing power and propulsion systems for more than 40 years; and first-of-a-kind gas, slush, and liquid hydrogen systems since the mid-1980s. Matt was also the Sector Manager for Energy & Materials in his final position at NASA where he worked for 31 years. He's been a cofounder in seven technology-based startups; and provided R&D, engineering, and innovation consulting to several hundred organizations. Matt has three patents and more than 50 publications including his online Cryogenic Fluid Management guide and Decarbonizing Mobility with Liquid Hydrogen SAE report. He has created and taught liquid hydrogen courses, webinars, and workshops to global audiences.