Gaseous hydrogen tank computation

Tank volume calculation

The tank inner volume is calculated based on the hydrogen mass specified by user (\(m_{H2}\)) and the ideal gas assumption. Thus, the ideal gas constant (\(R\)), the storage temperature (\(T\)), and the storage pressure (\(P\)) are applied in this calculation.

\[V_{inner} = \frac{Z*m_{H2}*R*T}{P}\]

The hydrogen gas compressibility factor (\(Z\)) is expressed as:

\[Z = 0.99704 + 6.4149*10^{-9}*P\]

Tank geometry calculation

Tank diameter calculation

The gaseous hydrogen tank’s outer diameter (\(D_{outer}\)) is defined based on its installation location. For an internal installation, it is set as a fraction of the maximum fuselage height to ensure proper fit. For an external installation, the outer diameter is fixed at 20% of the maximum fuselage height to minimize drag.

\[\begin{split}D_{outer} = \begin{cases} 0.9 \cdot \max(H_{fuselage}) & \text{if inside fuselage} \\ 0.2 \cdot \max(H_{fuselage}) & \text{if outside fuselage} \end{cases}\end{split}\]

Then the inner diameter calculation is based on the hoop stress of a cylindrical tank calculation provided by [CK02]

\[t_{wall} = \frac {R_{in} * SF*P}{\sigma_{wall}}\]

With the tank outer diameter calculated in advance, the tank inner diameter (\(D_{inner}\)) is derived with the following equation:

\[D_{inner} = \frac{\sigma_{wall} * D_{outer}}{\sigma_{wall}+ SF*P}\]

Where \(SF\) represent the safety factor of the tank, \(P\) is the tank storage pressure, and \(\sigma_{wall}\) is the tank wall material yield stress.

Tank length calculation

With the assumption that the shape of the tank is cylindrical with hemispherical cap at both end, the length of the tank can be expressed as:

\[L = \frac {V_{inner} - V_{cap}} {A_{cross}} + D_{outer}\]

Where \(V_{inner}\) denotes the inner volume, as calculated in the tank capacity section, \(V_{cap}\) represents the inner volume of the two hemispherical caps, while \(A_{cross}\) refers to the tank’s inner cross-sectional area.

\[\begin{split}V_{cap} = \frac{\pi D_{inner}^3}{6} \\ A_{cross} = \frac{\pi D_{inner}^2}{4}\end{split}\]

Component Computation Structure

The following two links are the N2 diagrams representing the performance and sizing computation in gaseous hydrogen tank component.

Gaseous hydrogen tank performance N2 diagram
Gaseous hydrogen tank sizing N2 diagram