# A Thermodynamic Model for Cryogenic Liquid Hydrogen Fuel Tanks
## 1 Introduction  
The development of eco-friendly fuels and renewable energies is attracting attention worldwide due to international interest and agreements to reduce carbon emissions in order to solve the global warming problem. In addition, as fossil fuels are currently the main global fuel source, they are expected to be depleted in the future, and thus it is necessary to reduce dependence on fossil fuels and to secure and develop new energy sources. There are many fuels that can replace fossil fuels, such as natural gas, biofuels [1; 2], and synthetic fuels, but these fuels generate CO\({}_{2}\) during combustion because they are also composed of carbon. Ammonia is a fuel that does not produce CO\({}_{2}\)[3; 4], but ammonia is highly toxic and has a pungent odor. Hydrogen is another fuel that does not generate CO\({}_{2}\), and unlike ammonia, hydrogen is an odorless, colorless, and tasteless gas. Since hydrogen has the advantage of having a higher specific energy than other fuels, it can be used in the transportation field. The specific energy of hydrogen is 120 MJ/kg, which is 2.8 times greater than that of fossil fuels (43.2 MJ/kg) [5; 6]. Due to this advantage, hydrogen-oxygen was used as a propellent in the second stage of Saturn IB (S-IVB) in 1966 in the field of space launching [7], and launch vehicles using hydrogen are still being developed [8; 9; 10; 11]. In the field of aviation, zero-carbon-emission future vehicles using hydrogen as fuel are being developed [12; 13]. Airbus aims to develop zero-emission commercial aircraft that use hydrogen as a power source by 2035, and the company has proposed threeconcepts for such an aircraft [14]. As such, a lot of research and development is being conducted surrounding the use of hydrogen as a fuel in the transportation field. However, since hydrogen has a very low density at room temperature and atmospheric pressure, it has the disadvantage of requiring a lot of storage space to store an equivalent amount of energy as conventional fossil fuels [6; 13; 15]. For this reason, hydrogen requires storage methods different from fossil fuel storage methods. Therefore, research into hydrogen tanks for storing and supplying hydrogen as a fuel is required in order to use hydrogen as a power source. The hydrogen fuel tank design method used depends on the type of hydrogen storage required. There are two methods of storing hydrogen: compressing it at high pressure, and liquefying it at a cryogenic temperature. Storing hydrogen gas at high pressure has the advantage of enabling it to be stored at room temperature. Gaseous hydrogen is usually stored at a pressure of 35 MPa (350 bar) [16] or 70 Mpa (700 bar) [17]. When compressed at high pressure, the density of hydrogen increases from 0.0852 kg/m\({}^{3}\) at room temperature and atmospheric pressure to 23.995 kg/m\({}^{3}\) at 35 Mpa and 40.172 kg/m\({}^{3}\) at 70 Mpa. In order to store hydrogen gas at high pressure, the tank requires the application of structural design techniques that enable it to withstand the high pressure [18; 19]. Thus, a disadvantage of high-pressure hydrogen tanks is that the weight of these tanks increases because they must withstand a very high pressure. Hydrogen can be liquefied when cooled to cryogenic temperatures and stored in a liquid state. The liquefaction temperature of hydrogen is \(-\)252.78 \({}^{\circ}\)C (20.37 K) at atmospheric pressure. Liquid hydrogen tanks require insulated designs [20; 21] to prevent loss to vaporization since liquid hydrogen is vaporized into a gas by external heat inflow. However, no matter how excellent the insulation performance of the tank is, liquid hydrogen is vaporized by heat inflow. When liquid hydrogen is vaporized, its specific volume expands approximately 53 times from 0.0141 m\({}^{3}\)/kg to 0.7507 m\({}^{3}\)/kg at atmospheric pressure. The internal pressure of the tank increases when liquid hydrogen is vaporized inside the tank [22; 23].