LH2 Dewar Sizing: Inner Vessel Capacity

One of the initial activities in the conceptual design of a liquid hydrogen (LH2) system is sizing the storage dewar. I've created an online interactive tool available at h2sage.com to demonstrate how to do it. Below are some general usage guidelines for the first step of determining the inner vessel capacity 

Liquid Conditions

Calculations should be performed using parahydrogen properties for an LH2 dewar. The selected storage pressure is the long term storage condition expected and is generally below 5 bar. This should not be confused with the much higher maximum expected operating pressure (MEOP) which will be used later for stress calculations and mass estimates.

Nitrogen is often used for check-out testing and cold shocking, so this fluid option is also provided. The tool can be used to size a liquid nitrogen (LN2) dewar for these purposes. In addition, the mass of nitrogen can be calculated to help mitigate overloading of an LH2 dewar during checkout (e.g., only partially fill the LH2 dewar with LN2 if it is not structurally designed for greater density load).

The storage pressure is used to evaluate the saturation liquid temperature and density. If the dewar is loaded at a lower saturation condition, the bulk liquid will slowly warm up to the new saturation temperature. If it is loaded at a higher saturation condition, the liquid will quickly flash to the new saturation temperature.

Volume Adjustments

Using saturation conditions at the selected storage pressure ensures that the liquid will not expand beyond the maximum volumetric fill level. The fill level must allow for some amount of ullage for pressure control, with 90% being a common value for stationary dewars. Aerospace vehicles and other mobility applications sometimes use fill levels as high as 95%.

Minimum residual liquid volume accounts for the amount of LH2 that always remains in the tank during operation. Complete draining of an LH2 dewar is usually avoided unless it is being taken out of service for maintenance or repair. Maintaining a minimum residual amount of liquid in the dewar mitigates the need for a full chilldown from ambient temperatures and the associated vaporization losses.

Tank internals include components that take up some of the internal volume such as level probes, vent/drain lines, mixers, etc. It is difficult to estimate these volumes during the conceptual sizing phase, so a percentage of the overall internal volume is used as input.

Inner Vessel Geometry

Inner vessel shapes currently supported in the tool are a sphere, oblate spheroid, or cylinder with hemispherical or elliptical (2:1) heads. Diameter and cylindrical length can be varied to investigate the effect on the overall form, dimensions, and usable liquid mass.

The choice of head type depends upon the application. Hemispherical heads are the strongest and require half the wall thickness as the cylindrical section for the same material properties. However, they are more costly to fabricate with metals and result in the longest vessel for a fixed volume requirement.

Metal elliptical heads are less costly to fabricate and result in a shorter vessel length relative hemispherical heads for the same internal volume. The most common type has a minor radius that is half of the major radius (i.e., 2:1). They are not as strong as hemispherical heads resulting in a thickness about equal to the cylindrical section for the same material properties.

Flanged and dished (F&D) heads are another common type that incorporate a short transition section, a small radius knuckle section, and a dish-shaped main section (sometimes referred to as torispherical). These types of heads come in various configurations and are the least costly to fabricate for metal, but require thicker walls than hemispherical or 2:1 elliptical heads.

F&D heads are not currently supported in the tool because of the many variations possible. For initial inner vessel sizing, 2:1 elliptical heads can be selected since their volume and resulting overall vessel length are similar, then updated with detailed F&D head specifications if desired.

Results and Outputs

The primary output of the tool is the mass of usable liquid for the resulting inner vessel conceptual design. This value takes into account the liquid conditions, volumetric adjustments, and inner vessel geometry selected by the user.

An additional output is a three dimensional rendering of the inner vessel that can be manipulated to review the overall geometry. A full screen mode is also available, and any selected viewing perspective can be downloaded as an image file.

At the bottom of the main screen is a text area for user inputs that are retained until the browser tab is refreshed or closed. The date, user name, scenario information, and results from previous runs can be documented in this area for later printing or saving (see below).

Finally, the three dots menu at the top right provide several more utilities:

• Rerun the app tool (this retains all input data)
• Settings for light or dark themes; and wide mode display option
• Print a hardcopy or save as a pdf file
• Record a screencast during tool interaction

Additional features planned for the dewar sizing tool include insulation options, heat loads, mass estimates, and an overall concept design summary that includes dimensions of the outer vessel.

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.