Heat Leak Estimation

Heat leak estimation for a cryogenic dewar requires identifying all environmental heat loads. Previous posts discussed sizing of the inner vessel and selection of the insulation around it. This post focuses on additional heat transfer from solid conduction paths into the inner vessel.

Heat Leak Sources

As shown above, the H2 Sage™ dewar sizing app automatically calculates heat leak through the insulation based on the conceptual design inputs entered in the insulation tab. This calculation uses the appropriate thermal shape factors for the inner vessel cylindrical section and heads as defined in the inner vessel tab.

However, there are other heat leak sources to consider which are design dependent. Any solid connection to, or penetration through, the inner vessel introduces conduction heat loads to the cryogen. These additional heat leak sources are often greater than the insulation heat leak for small to moderate size dewars, and must be considered even for the largest dewar tanks.

Common additional heat leak sources are provided in the dropdown menu and include:

• Access port (at least one generally located at the top of the dewar, often with a flanged interface and various feedthroughs, and also providing some or all of the structural support for the inner vessel)
• Support strut (usually several providing structural support to the inner vessel from the outer vessel wall)
• Support ring (often used in vacuum-jacketed piping but also in some smaller or lightweight dewars)
• End support (provides structural support at either end of the dewar along the axial midline)
• Fill/drain pipe (for adding or removing cryogen)
• Vent/press pipe (for tank venting and pressurization)
• Wire lead (wires for sensors, powered internals, etc.)
• Tube shape (any other solid conduction source with an inner and outer diameter)

Once the source is selected, the quantity of that source is entered along with several other inputs:

• Diameters: Internal and external diameters, where the internal diameter can be set to zero for solid rods or wires. Thin-walled schedule 10 pipe is common for cryogenic piping if the pressure range is within specifications. In the case of a support ring, the inner diameter is generally in contact with the inner vessel and the outer diameter is against the outer vessel wall.
• Axial length: For most of the sources, the axial length is between the cold and warm boundary temperatures (e.g., pipe length). For a support ring, the axial length is the ring thickness.
• Temperature boundaries: The warm and cold boundary temperatures define the conduction temperature differential. Depending on the heat source, the cold boundary may be at the cryogen temperature or higher (e.g., on the warmer upper vessel wall); and the warm boundary may be ambient temperature or lower (e.g., if a cold box is used).
• Material: Although optional, the solid material type of the source should be entered for documentation.
• Conductivity integral: This is the value of the material's thermal conductivity integrated over the warm and cold temperature range. It can be found using the link to NIST's online calculator, or estimated from the table provided further down the page by subtracting the K value at the cold temperature from the K value at the warm temperature for the appropriate material.
• Series resistance: A value can be added to account for contact resistance or other thermal resistances in series. This would be most common for representing various mounting assemblies for support struts, or the contact resistances at the edges of a support ring.
• Comments: Another optional input for adding additional information about the heat source.

When the add heat leak source button is clicked, the above inputs are used to calculate the heat leak contribution for the specified source.

Heat Leak Summary

The heat leak summary table includes the insulation and all other added heat leak sources by row. Their associated inputs and key calculated values are organized by column. Note that the only editable entry in the table is the comments column. 

A heat leak source can be deleted from the table by checking the box in the first column of any row and choosing the delete icon in the small menu at the upper right of the table. This menu has other options including download of the table in csv format which can be opened in a spreadsheet.

Below the table is a summation of the total heat leak along with a bar chart showing the contribution of each heat leak source. A pie chart is also displayed indicating the percentage breakdown of each heat source. These visuals are helpful for identifying potential design improvements for lowering the overall heat leak.

Environmental heat loads from thermal radiation or convection heat transfer to the inner dewar are generally represented in the insulation heat leak value. Cases or conditions where additional non-conduction heat transfer is significant are not included in the dewar sizing app and would require a separate analysis. A potential example might be a dewar with a low fill level and very warm upper walls.

Dewar Thermal Performance

Normal evaporation rate of the dewar based on the conceptual design and identified heat leak sources is shown below the charts on a mass basis. This value represents the rate of vaporization for the selected cryogen in a saturated state at one atmosphere (1.013 bar) constant pressure (i.e., vented).

The normal vaporization rate as a percentage per day based on total inner vessel volume is also provided. It varies based on on a variety of design parameters, and is indirectly proportional to the dewar size.

For example, the 5000 cbm LH2 tank at NASA KSC has a reported NER of less than 0.05% per day, while much smaller mobile dewars can have an NER two orders of magnitude higher.

This figure of merit is often used (and misused) to characterize a dewar's thermal performance. It is not the boil-off loss per day of a non-venting tank under storage conditions. However, it does provide a metric for comparing the thermal performance of two or more dewar designs. 

Other Bells & Whistles

Toward the bottom of heat leak page is selected reference material on conduction heat transfer, conductivity integrals, and shape factors. A timestamp is also displayed along with an optional text input field for any user notes. These notes are available across all tabs in the dewar sizing app until the session is ended or a new instance is created.

At the top left of the page is a sidebar that can be expanded or hidden and provides a saturation table of pressure versus temperature for the selected cryogen. At the top right of the page is a 3-dot menu with a variety of options and settings. The "About" selection contains links for more details on the app and updates, other H2 Sage™ resources, unit converters, and NIST cryogenic links.

Visit H2sage.com to access the online app and for more detailed information.

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.

Insulation Options Tool

In the previous post I provided some quick start guidelines for using the H2 Sage™ dewar sizing online app for creating a conceptual design of the inner vessel. The next step is to explore insulation options that will be installed around the inner vessel.

Insulation Options

A dropdown menu provides some of the most common insulation options used for liquid hydrogen dewars:

• Multilayer insulation (MLI) is the best performing type of insulation in a vacuum and is frequently used for mobile and stationary dewar tanks of small to moderate size (and vacuum-jacketed piping).
• Perlite has been historically used for large stationary liquid hydrogen dewar tanks.
• Glass bubbles are a newer option for stationary dewar tanks with better performance than perlite.
• Other insulation types can be specified for user-defined configurations, degraded vacuum conditions, or ambient pressure performance.

An annotated plot of the apparent thermal conductivity of various insulation types as a function of cold vacuum pressure is provided to aid in exploring other options. Note that this data is from calorimeter testing which results in better performance than tank-applied insulation systems.

Additional Inputs

Insulation thickness can be specified within a range dictated by the size of the inner vessel. Increasing thickness improves thermal performance but increases overall system mass (i.e., insulation system and outer vessel wall).

Degradation factor takes into account the reduced performance of tank-applied insulation with a value of 1.0 indicating no degradation. Seams, openings for piping and support structures, and other discontinuities in tank-applied MLI affect this factor. A value between 2.0 and 3.0 is recommended for MLI. Other insulation options have different characteristics that may warrant a lower degradation factor.

Warm boundary temperature is the condition at the outer surface of the insulation system (e.g., dewar tank outer vessel wall). This can generally be assumed to be ambient temperature in most scenarios. A lower warm boundary temperature would be used if a vapor-cooled shield, cold wall, or other method is being used to reduce heat leak into the cryogen.

Outputs (Figures of Merit)

Heat flux provides a comparative measure of the thermal performance of different insulation schemes. The total heat leak coming through the insulation for the given tank design will be estimated in a different tab that includes additional heat leak sources.

Areal density is a comparative measure of insulation mass that is particularly important for mobile applications. The insulation system mass will be estimated in a different tab that includes the masses of all the dewar tank structures and components.

Visit H2sage.com to access the online app and for more detailed information about insulation systems including pros and cons of each type.

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.

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 cylindrical 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.