# A Thermodynamic Model for Cryogenic Liquid Hydrogen Fuel Tanks
## 4 Analysis of Cryogenic Fuel Tanks
### Analysis Results  
The transient analysis was performed with respect to the analysis conditions. The analysis was conducted for three cases: (1) storage without fuel emission after fuel charging, (2) fuel consumption immediately after fuel charging, and (3) 30 min delay before fuel consumption after refueling. The first case was a scenario in which fuel was stored without fuel emission after fuel charging. The total mass of hydrogen inside the tank remained constant, as shown in Figure 5a, because hydrogen was not discharged to the outside. The dotted line represents  
Figure 4: Geometry of cryogenic liquid fuel tank. the total mass of hydrogen inside the tank, the blue solid line represents the mass of liquid hydrogen, and the red solid line shows the mass of gaseous hydrogen. The mass of liquid hydrogen decreased over time because it was vaporized by heat transferred from the outside of the tank. The mass of gaseous hydrogen was increased by the mass of vaporized liquid hydrogen. The temperature of gaseous hydrogen rose due to heat transfer from the outside, as displayed in Figure 4(b). The pressure in the tank increased rapidly, as shown in Figure 4(c), because the specific volume of the vaporized hydrogen was much larger than that of liquid hydrogen. The pressure was 7.62 MPa when the storage time reached 30 min, and 12.0 MPa when the storage time reached 1 h.  
The second case reflected a scenario of fuel consumption immediately after fuel charging. In this case, the total mass of hydrogen inside the tank was constantly reduced, as shown in Figure 5(a), because hydrogen was discharged to the outside at a constant fuel consumption rate. The change in the mass of liquid hydrogen in the tank displayed behavior similar to that seen in case 1. The mass of gaseous hydrogen increased at the  
Figure 5: Analysis results for cryogenic fuel tank without fuel consumption. beginning, and then decreased. This was because the amount of heat transferred to the liquid hydrogen gradually decreased. When the amount of liquid hydrogen was reduced, the heat transfer area of the liquid hydrogen was decreased, and thus, the amount of vaporization eventually decreased. The gaseous temperature was higher than that of case 1, as shown in Figure 5(b), because the mass of hydrogen in the gas region was reduced (i.e., the density of the gas region was reduced) due to fuel consumption. However, the tank pressure was increased initially and then gradually decreased, as represented in Figure 5(c), as gaseous hydrogen was continuously discharged to the outside. The pressure reached a maximum of 2.30 MPa at about 37 min. The final cases (case 3) represented scenarios of 5 min (case 3a), 10 min (case 3b), and 30 min (case 3c) delays before fuel consumption after fuel charging. In these cases, the initial 5, 10, and 30 min after charging showed the same behavior as in case 1 when there was no fuel emission. After that, as fuel consumption started, differences appeared in the mass, temperature, and pressure behavior. As shown in Figure 6(a), the mass of  
Figure 6: Analysis results for cryogenic fuel tank with fuel consumption. gaseous hydrogen in cases 3a and 3b increased as fuel consumption began. On the contrary, in case 3c, it gradually reduced. This was because the evaporation of liquid hydrogen occurred consistently regardless of delayed time, and the amount of evaporation decreased as time passes. Figure 7: Analysis results for cryogenic fuel tank with delay time before fuel consumption. The temperature of the gaseous hydrogen slightly decreased as fuel consumption began, but it is soon rose again, as represented in Figure 7b. As the fuel was discharged out of the tank, the internal gas expanded and the temperature dropped, but it appeared to have increased due to heat inflow. The temperature increased rapidly from about 77 min onwards, at which point the liquid hydrogen was fully evaporated.