A structural analysis, sizing optimization, and weight prediction study was performed by Collier Research Corporation and NASA Glenn on a spherical cryogenic hydrogen tank. The tank consisted of an inner and outer wall separated by a vacuum for thermal insulation purposes.

HyperSizer®, a commercial automated structural analysis and sizing software package was used to design the lightest feasible tank for a given overall size and thermomechanical loading environment. Weight trade studies were completed for different panel concepts and metallic and composite material systems. Extensive failure analyses were performed for each combination of dimensional variables, materials, and layups to establish the structural integrity of tank designs. Detailed stress and strain fields were computed from operational temperature changes and pressure loads. The inner tank wall is sized by the resulting biaxial tensile stresses which cause it to be strength driven, and leads to an optimum panel concept that need not be stiffened. Conversely, the outer tank wall is sized by a biaxial compressive stress field, induced by the pressure differential between atmospheric pressure and the vacuum between the tanks, thereby causing the design to be stability driven and thus stiffened to prevent buckling. Induced thermal stresses become a major sizing driver when a composite or hybrid composite/metallic material systems are used for the inner tank wall for purposes such as liners to contain the fuel and reduce hydrogen permeation.

NASA is investing in technology development efforts and alternate fuel foundation technologies that will greatly reduce or even eliminate environmentally harmful emissions. Because of this, liquid hydrogen (LH2) has emerged as a propellant to supply the fuel needs for future aircraft due to its high energy per unit mass. Durable, lightweight cryogenic propellant storage and feed systems are required to enable the development of hydrogenfueled aircraft.

Current preliminary mission requirements that are pushing the long-flight-duration hydrogen aircraft development include 14-day (336- hr) flight duration with a payload capacity that is sufficient to accommodate the instrumentation required for the various missions. It is precisely these types of aircraft with relatively long flight durations on the order of days that provide the greatest engineering challenges to develop long-term and lightweight hydrogen storage systems, since boiloff of the cryogenic fluid can become a significant problem. For example, space shuttle operation accepts a loss rate (boiloff) of approximately 1.6 percent of LH2 by weight per hour, whereas for long flight duration aircraft applications an acceptable rate of boiloff of LH2 would be on the order of 0.1 percent by weight per hour. Consequently, the need for reduced weight in combination with good insulating properties for long-term storage provides a new challenge for cryogenic tank design.

These new designs provide an opportunity to apply advanced materials and structural concepts in an effort to reduce the overall weight of the tank and keep the volume at an acceptable and practical level. Although, the design of a cryogenic LH2 storage tank, coupled with the use of LH2 as aircraft fuel, involves many challenges, the most dominate structural ones include geometry, temperature, permeation, hydrogen embrittlement, and safety factors as reviewed recently by Mital et al.

In the present study we revisited prior work and performed preliminary material and structural trade studies on a doubled-walled, vacuum jacketed, spherical cryogenic tank concept; wherein the following was analyzed for the sizing of both inner and outer tanks:

1. Increased factors of safeties
2. Reduced strain allowables to prevent leakage are imposed
3. Multiple failure criteria
4. Metallic inner tank liner materials are introduced
5. Additional materials are utilized

HyperSizer is a structural analysis and sizing software tool developed by the Collier Research Corp. that
automates the types of structural analyses that a typical aerospace stress engineer performs using closed-form, empirical based, and state-of-the-art numerical solutions. HyperSizer contains specialized aerospace structures knowledge and methods and provides a computational framework for performing non-FEA based analyses.

However, the HyperSizer software seamlessly links with NASTRAN finite element models as well, so that loads can be extracted automatically, and then used to size a section of the structure, including the effects of stiffeners.

If needed, HyperSizer can then update the NASTRAN model with new properties based on the sizing results of the section. The HyperSizer approach is to perform comprehensive failure analysis for all specified load cases and structural locations. These failure analyses are either not possible or not practical to perform with FEA. HyperSizer analyses are very rapid as panel concepts are analyzed without the need to discretely mesh with finite elements the shape of the stiffeners or their spacing. This permits tremendous flexibility and rapid turn around of trades with different panel concepts all from the same coarsely meshed global structural representation. Consequently, HyperSizer can find the lightest structural weight for a given set of candidate materials and panel concepts while ensuring that all potential failure modes are prevented from occurring during the sizing optimization.

Typical HyperSizer analyses consist of the following seven steps:

1. Use finite element mesh to define structural geometry
2. Assign material directionalities
3. Apply boundary conditions
4. Apply load cases
5. Select material and panel concept constraints
6. Define failure criteria, limit and ultimate factors of safety, and buckling factors
7. Perform sizing analysis – where margins of safety are calculated throughout the structure

Figure 4. FEA eigenvalue determination of appropriate buckling span for the outer wall. The left
mode shape is for a stiffened panel that shows 7” half modes. The right mode shape is for an
unstiffened panel and shows 6” modes.

Note, although higher factors of safety and lower strain allowables were imposed in this study as compared with previous work, the final overall hybrid tank system weight (composed of an Al 2024 inner tank and Gr/Ep outer tank) was approximately 60 lbs lighter. This decrease in weight is mainly attributable to the fact that no minimum gage thickness was imposed in this study; with the result being a three times thinner inner tank wall thickness as compared to previous work. Clearly then weight growth is to be expected, due to minimum gage thickness either for manufacturing limitations or for hydrogen permeation requirements, as well as closeout details and items such as weld fillets, brackets, clips, etc. The final choice regarding which tank design would be selected will most likely be determined by manufacturing and inspectability costs and requirements.

For more information on this project, please click here to download this Collier Research published paper:

"Spherical Cryogenic Hydrogen Tank Preliminary Design Trade Studies",48th AIAA/ASME/ASCE/ AHS/ASC Structures, Structural Dynamics & Materials Conference, Honolulu, HI, April 2007.