## 2 Overall Analysis Approach and Implemented Methods
### Data and Assumptions on LH\({}_{2}\) Technology
#### 2.1.2 L\({}_{2}\) Storage  
The most relevant change introduced by the LH\({}_{2}\) propulsion is the need for a new kind of tank. A hydrogen tank should guarantee thermal insulation and pressurisation in order to preserve the storage state of the hydrogen. Furthermore, in the case of tank cracks or failures, a proper level of pressurisation is needed to prevent oxygen from entering the tank, which can lead to explosive mixtures ([25, 33]). The hydrogen storage state is an important point of discussion, since it influences the hydrogen density and the tank structural design; the main options are the three blue areas highlighted in Figure 2, taken from [34]. Most of the studies ([14, 16, 18, 19, 20, 22, 24, 25, 26, 29, 31, 32, 34, 35]) concern tanks at storage states close to region 1 (see Figure 2), where the hydrogen is in a saturated liquid form (LH\({}_{2}\)), the pressure varies between 0.1 and 0.4 MPa and temperatures are lower than 30 K. In region 3, gaseous hydrogen (H\({}_{2}\)) is stored at a higher density (+33%) but the storage pressure is considerably higher (50-100 MPa), which leads to heavier tanks and safety issues, since the pressure rises faster under incoming heat flux [24]. Storage solutions in region 2 exhibit the lowest density, hence larger tanks which are difficult to integrate with the aircraft. For the reasons above, in this work the hydrogen is considered stored in a state close to the region 1. In such state, both liquid and gaseous phases are present (biphasic saturated state), hence, LH\({}_{2}\) cannot fill the total internal volume of the tank. Liquid and gaseous saturated phases are at equilibrium and show the same temperature and the same pressure; therefore, they constitute a saturated liquid-gas mixture. In saturation state, the gas law is no more valid, and pressure and temperature of the mixture show a bijective relation  
Figure 2: Storage density of hydrogen for different pressure and temperature conditions ([34]). not dependent on other variables (Figure 3). For the purposes of this work, the physical properties of the two phases were taken from [36] and used in the form of lookup tables for data interpolation. Since the heat flux directed from the external environment towards the tank causes a pressure raise ([31]), tanks need a venting valve which avoids the internal pressure overcoming the maximum design pressure. The venting of H2 represents a loss of fuel and leads to a reduction in the aircraft flight range; therefore, an insulation system is required to minimise the heat exchange and thus the pressure increase. For any assigned reference internal pressure, the internal volume cannot be completely filled with LH2, because in the case of pressure rise there would not be H2 to be vented and pressure could not be lowered. Anyway, when considering a partial filling, it must be verified that the stored LH2 does not expand (Figure 3b) to the maximum capacity of the tank when it reaches the venting pressure. For the reasons above, the authors of [24; 25; 26] studied pressure levels and filling volumes in order to have a reasonable fuel density, while considering a minimum pressure to avoid contamination. The heat flux across the tank walls depends on three main thermal exchange stages: convection and radiation with the external environment, conduction across the tank insulant and structures, and the heat exchange inside the fluid ([24; 25]). There are different ways to guarantee the insulation of the tank; the simplest is to use a thick layer of insulating material ([14; 16]), such as closed cells foams; other methods use open cell foams and a mylar liner ([24; 25]) or a double-walled tank, with vacuum between the walls and multi-layer insulation on each side of the vacuum jacket, in order to prevent thermal exchange by radiation ([34]). In this work, simple closed cell insulation foams are considered.