Simulation Analysis of the Leakage and Diffusion Risk of a Hydrogen Storage System in Hydrogen Aircraft

Abstract

Hydrogen is an alternative energy source for the aviation industry due to its renewability and cleanliness, although this novel application needs to be reassessed for the potential leakage risk. For this reason, we take a small hydrogen-powered aircraft as the research object and investigate hydrogen diffusion behavior in the cabin after 35 MPa onboard hydrogen storage system leakage. Firstly, the effectiveness of the numerical simulation model is verified. Secondly, the numerical simulation model is utilized to simulate the changes in hydrogen mole fraction in the cabin under various scenario conditions (different leakage diameters, directions, and environment parameters). Finally, we investigate the impact of ventilation. Forced ventilation could significantly reduce the hydrogen mole fraction in the cabin in a short time. However, forced ventilation also promotes the diffusion of residual hydrogen in the cabin, resulting in a large proportion of the volume having a hydrogen mole fraction greater than 0.04, but it can significantly reduce the proportion of high hydrogen mole fraction (>0.1 or >0.2) regions.

1. Introduction

With the development of civil aviation, issues related to aviation energy and emissions have become increasingly urgent. Hydrogen energy, as a green and environmentally friendly source, has once again attracted people’s attention. Hydrogen is considered a strategic energy for achieving zero-carbon emissions and sustainable development in the future. Hydrogen-powered aircraft are one of the key forms for realizing carbon peak and carbon neutrality (“dual carbon” goals) in the aviation sector [1,2]. Hydrogen-powered aircraft, which use compressed hydrogen as fuel, offer higher fuel efficiency compared to traditional engine aircraft, with no carbon oxides in the exhaust gases; the only byproduct of hydrogen combustion is water [3]. By the year 2050, when hydrogen fuel cells are estimated to be mature enough to completely replace kerosene-based engines, the forthcoming hybrid-electric aircraft promise no NO_x and CO₂ direct emissions [4]. Those aircraft are expected to be an economically and sustainably viable form of carbon free flight [5].

Hydrogen, as a green energy source, has broad prospects for development. However, as an alternative aviation fuel, hydrogen possesses characteristics that pose significant safety concerns, i.e., it is highly flammable (with a wide flammable range, from 4% to 75% in air), explosive (with a minimum ignition energy of 0.019 mJ at 1 atm), and prone to leakage (due to its small molecular size) [6]. Moreover, hydrogen can weaken materials through hydrogen embrittlement [7], presenting major challenges for the storage and transportation of high-pressure hydrogen. Unlike conventional fuel systems, hydrogen storage systems in aircraft require stricter standards for structural integrity, sealing, and material properties, and also introduce new safety requirements.

In small hydrogen-powered aircraft, high-pressure hydrogen tanks with a simpler structure and more mature technology than liquid hydrogen storage devices are usually utilized for hydrogen storage. The extensive piping and valves between the engine and the hydrogen storage tank make the system susceptible to hydrogen leaks, which can lead to fires, explosions, and other cascade risks, severely risk flight safety. Therefore, the impact of the introduction of hydrogen on aircraft safety needs to be considered. When assessing the safety of hydrogen aircraft, the issues of hydrogen leakage cannot be ignored. Fault tree analysis, Bayesian networks and other security analysis methods have become security analysis methods of newly configuration [8,9,10,11].

Considering the potential hazards and research costs, some researchers take a CFD approach to investigate hydrogen leakage and diffusion risk. José Antonio Salva et al. [12] analyzed the hydrogen leakage diffusion inside a fuel cell vehicle, with the leakage point set at the rear of the vehicle. The study found that installing ventilation devices inside the vehicle can significantly reduce the hydrogen concentration, thereby effectively lowering the risk of hydrogen accumulation and explosion. Wang et al. [13] used numerical simulation to perform transient and steady state analyses of hydrogen leakage diffusion in a hydrogen production container and quantified the consequences of hydrogen leakage using the TNT equivalent method. The study showed that, after a hydrogen leak, the arc-shaped dome structure of the hydrogen production room would preferentially accumulate flammable gas clouds, and ventilation windows should be placed at the top of the space. At critical ventilation flow rates, the damage radius could be reduced. Cui et al. [14] used numerical simulations to study the effects of leakage angle, ambient wind, and roof shape on hydrogen leakage diffusion in hydrogen refueling stations. The study found that hydrogen tends to accumulate on the underside of the roof, and a hydrogen detector placement scheme based on the simulation results achieved an alarm success rate of 83.33%. Lv et al. [15] used numerical simulations to investigate the hydrogen leakage diffusion and explosion characteristics of fuel cell vehicles in a parking lot when a thermal actuated pressure relief device (TPRD) was activated. The study showed that larger leakage diameters result in a wider and more concentrated hydrogen–air mixture cloud, and that ventilation significantly reduces the volume and concentration of the mixture cloud. Song et al. [16] used CFD methods to study hydrogen leakage inside hydrogen fuel cell vehicles (HFCVs), discussing the effects of different leakage locations, leakage rates, and ventilation conditions. The study found that different leakage conditions lead to different hydrogen concentration distributions within the vehicle, and proper placement of ventilation outlets can rapidly expel hydrogen, reducing the concentration inside the vehicle. Li et al. [17] used CFD methods to study the impact of obstacle positions on hydrogen leakage diffusion behavior in fuel cell buses. The study found that the distance between obstacles and the leakage source significantly affects hydrogen diffusion, with vertically placed obstacles promoting vertical diffusion and hindering horizontal transport, thus limiting the distribution of flammable zones within the vehicle. Mao et al. [18] studied the diffusion process of hydrogen between compartments in a fuel cell ship and numerically simulated the hydrogen explosion process caused by different ignition sources. The study found that the thermal radiation and overpressure damage from hydrogen explosions posed serious threats to the ship and its occupants, with the bow compartment being the least affected area and suitable as an ideal temporary refuge. Xu et al. [19] used numerical simulation methods to study the ventilation strategy of hydrogen–blended natural gas (HBNG) and recommended the installation of a safety interlock device to quickly shut down the pipeline in the event of a leak. Zhang et al. [20] developed a simplified model to study the leakage and diffusion of hydrogen gas in a rectangular space under natural ventilation. Kim et al. [21] used numerical simulation to study the effect of ship motion on hydrogen diffusion in enclosed areas. Lee et al. [22] developed a two-dimensional axisymmetric model using numerical simulation to study the temperature changes in hydrogen tanks under different pressure and temperature conditions during charging. Based on the numerical results, a regression equation was used to predict the maximum temperature of the tank. Yassin et al. [23] validated a CFD simulation package using different experimental results and showed good consistency; hence, this package can be used to simulate actual hydrogen leakage. Han et al. [24] numerically investigated the hydrogen concentration distribution through a hole with a size of less than 1 mm, and it satisfied the hyperbolic decay characteristics and fitted the experiment well. Zhang et al. [25] conducted a series of open space large-scale liquid hydrogen release experiments, comparing the diffusion of hydrogen in the atmosphere under different release apertures and ground materials. Xu et al. [26] used experimental and numerical simulation methods to study the diffusion of hydrogen mixed with natural gas in a sealed kitchen (using a mixture of nitrogen and helium as substitutes), and investigated the effects of parameters, such as explosion peak pressure, explosion overpressure, and explosion flame temperature.

Based on the above literature, the numerical simulation method is commonly used to investigate hydrogen leakage and diffusion characteristics in hydrogen refueling stations, fuel cell vehicles, etc. The ventilation will accelerate the diffusion of hydrogen and reduce the risk of hydrogen accumulation. However, there is currently insufficient risk analysis for hydrogen leakage and diffusion in the hydrogen storage systems of hydrogen aircraft.

This study takes a four-seater hydrogen-powered aircraft as the research object and investigates hydrogen leakage and diffusion characteristics in the hydrogen aircraft using the numerical simulation method. The study analyzes the development of hydrogen diffusion and the hydrogen mole fraction range under different leakage scenarios in the aircraft and investigates the impact of ventilation wind velocity in order to provide some references for the design of hydrogen aircraft ventilation systems and the risk analysis of hydrogen leakage in hydrogen aircraft. This will promote the application of hydrogen energy in the aviation industry.

The main contributions of this study are as follows:

• Simplification of the supercritical hydrogen leakage process using the ideal gas law and “virtual nozzle method”. Then, we perform an analysis of the hydrogen leakage and diffusion characteristics in a hydrogen aircraft using the validated numerical simulation method.
• Investigating the hydrogen mole fraction in aircraft under different ventilation conditions and analyzing the hydrogen evacuation efficiency under different ventilation conditions.

2. Methodology

2.1. Basic Assumptions

Before the simulation, the following assumptions are made:

• Hydrogen, air, and their mixtures are considered compressible gases, and the variable for density satisfies the ideal gas law.
• The leaked hydrogen does not undergo chemical reactions with the air inside the cabin.
• During the continuous leakage process, the hydrogen concentration at the leak orifice is 100%, and the mass flow rate remains constant.
• The shape of the hydrogen leak orifice is assumed to be a circular hole.

2.2. Governing Equations

Hydrogen leakage and diffusion follows the equation of continuity, the equation of the conservation of momentum, and the equation of the conservation of energy. Since the chemical reaction of hydrogen is not considered, the species transport equations without chemical reaction are adopted.

The continuity equation is as follows:

$${\displaystyle \frac{\partial \rho }{\partial t}}+{\displaystyle \frac{\partial (\rho u_i)}{\partial x_i}}=0$$

(1)

where $\rho$ is the density of the gas; $u_i$ is the velocity vector.

The momentum equation is as follows:

$${\displaystyle \frac{\partial (\rho u_i)}{\partial t}}+{\displaystyle \frac{\partial (\rho u_i{u}_j)}{\partial x_j}}=-{\displaystyle \frac{\partial p}{\partial x_i}}+{\displaystyle \frac{\partial T_{ij}}{\partial x_j}}+\rho g_i$$

(2)

where $p$ is pressure, $T_{ij}$ is the partial stress tensor, $T_{ij}=\left[\mu \left({\displaystyle \frac{\partial u_i}{\partial x_j}}+{\displaystyle \frac{\partial u_j}{\partial x_i}}\right)\right]-{\displaystyle \frac{2}{3}}\mu {\displaystyle \frac{\partial u_l}{\partial x_l}}{\delta }_{ij}$, $\mu$ is viscosity, ${\delta }_{ij}$ is the Kronecker symbol, and $g_i$ is the gravity.

The energy equation is as follows:

$${\displaystyle \frac{\partial \left(\rho E\right)}{\partial t}}+{\displaystyle \frac{\partial \left[u_i\left(\rho E+p\right)\right]}{\partial x_i}}={\displaystyle \frac{\partial }{\partial x_j}}\left[\left({\lambda }_{eff}+{\displaystyle \frac{cp{\mu }_t}{{\mathrm{Pr}}_t}}\right){\displaystyle \frac{\partial T}{\partial x_j}}+u_i{T}_{ij}^{eff}\right]$$

(3)

where $E$ is the total energy of the gas; ${\lambda }_{eff}$ is the effective heat transfer conductivity; $c_p$ is the specific heat capacity at constant pressure; ${\mu }_t$ is the turbulent viscosity; ${\mathrm{Pr}}_t$ is the turbulent Prandtl number; $T$ is temperature; $T_{ij}^{eff}$ is the effective partial stress tensor.

The species transport equation is as follows:

$${\displaystyle \frac{\partial \left(\rho w_i\right)}{\partial t}}+{\displaystyle \frac{\partial }{\partial x_i}}(\rho u_i{w}_i)={\displaystyle \frac{\partial }{\partial x_i}}\left[\left(\rho D_i+{\displaystyle \frac{{\mu }_t}{S{c}_t}}\right){\displaystyle \frac{\partial w_i}{\partial x_i}}\right]$$

(4)

where $w_i$ is the mass fraction of species $i$, $u_{\mathrm{i}}$ is the velocity vector, ${\mu }_t$ is the turbulent dynamic, $S{c}_t$ is the turbulent Schmidt number, and $D_i$ is the molecular diffusivity of the species $i$.

The equations can be solved by direct numerical simulation (DNS), but this requires a lot of computational resources. Turbulence occurs during the mixing of hydrogen with air. To simulate the turbulence and balance the computation efficiency, a turbulence model is selected to solve this problem. The Reynolds averaged Navier–Stokes equations (RANS) method addresses the problem of the high computational resource requirement of the direct numerical simulation method by using the mean and fluctuating velocity fields instead of the real velocity field. The $\kappa -\epsilon$ turbulence model can accurately model high Reynolds number hydrogen mixing and leakage flows [27]. Therefore, the $\kappa -\epsilon$ turbulence model is selected for this numerical simulation.

2.3. Virtual Nozzle Method

Before conducting the study on hydrogen leakage and diffusion, it is necessary to determine the flow state of hydrogen at the leak orifice. When the leakage conditions satisfy Equation (5), the hydrogen gas is supercritical jet. Equation (5) is as follows:

$${\displaystyle \frac{p_0}{p_t}}\le {\left({\displaystyle \frac{2}{k+1}}\right)}^{{\displaystyle \frac{k}{k-1}}}$$

(5)

where $p_0$ is the ambient pressure; $p_t$ is the pressure inside the hydrogen storage tank; $k=1.4$ is the specific heat ratio of hydrogen.

From the above calculations, it can be determined that when the hydrogen storage pressure reaches 35 MPa, the pressure exceeds the critical pressure of hydrogen. At the leakage orifice of the hydrogen storage tank, the flow is characterized as a high pressure underexpanded jet. This type of jet undergoes rapid expansion and compression outside the orifice, forming a shockwave structure called a Mach disk.

For numerical simulations, the complexity of the underexpanded jet flow field near the orifice poses significant challenges to the convergence of the calculations. Additionally, the small scale of the orifice requires a very fine computational mesh, which substantially increases the computational costs [28]. A common approach to address this issue is to use a “virtual nozzle model” for simplification. The virtual nozzle is a hypothetical leak source, assuming that the mass flow rate through the actual leakage orifice and the virtual nozzle are the same, and the pressure at the virtual nozzle is equal to the ambient pressure. This is just to simplify the calculation process, and such a location with the thermodynamic coefficients may not exist in the actual physical environment, but it will lead to the same diffusion phenomenon.

Based on some assumptions, the diameter of the virtual nozzle, the velocity of the gas flow, and other thermodynamic state parameters after the shockwave are calculated. These results are then used as boundary conditions in numerical simulations for subsequent solutions, avoiding the complex shockwave structures of the underexpanded hydrogen jet while maintaining some accuracy of hydrogen concentration. This significantly simplifies the numerical simulation process for supercritical underexpanded hydrogen jets.

Many researchers have proposed various virtual nozzle methods based on different assumptions, like Birch in 1984 [29], Birch in 1987 [30], Ewan in 1986 [31], and Yuceil in 2002 [32]. Li et al. [28] compared the results of these models with experimental results and found that the model proposed by Birch in 1987 [30] is sufficiently accurate.

Considering computational resources and efficiency, this research adopts the Birch 1987 model to simplify the underexpanded hydrogen jet. Referred to as the Birch model in the following text. As shown in Figure 1, the hydrogen is in a stagnation state inside the tank at level 1. It is in a high-pressure underexpanded state at the leakage orifice at level 2 (the speed here is the local speed of sound). From level 2 to level 3, the hydrogen jet undergoes expansion and compression. At level 3, which is the assumed virtual nozzle, the hydrogen has completed its expansion and the pressure has returned to the ambient pressure. The Birch model [30] assumes that the gas satisfies the ideal gas law. Based on the analysis of isentropic expansion, the flow parameters at the hydrogen leakage orifice (level 2) can be calculated as follows:

$$p_1=p_0{\left({\displaystyle \frac{2}{k+1}}\right)}^{{\displaystyle \frac{k}{k-1}}}$$

(6)

$$T_1=T_0\left({\displaystyle \frac{2}{k+1}}\right)$$

(7)

$${\rho }_1={\displaystyle \frac{p_{1}M}{R_A{T}_1}}$$

(8)

$$u_1=\sqrt{{\displaystyle \frac{k{R}_A{T}_1}{M_{H_2}}}}$$

(9)

where $p$ is pressure; $T$ is temperature; $\rho$ is hydrogen density; $u$ is flow velocity; subscripts 0 and 1 represent the stagnation state inside the tank and the actual leakage orifice, respectively; $k$ is the specific heat ratio of hydrogen; $M$ is the molar mass of hydrogen, $M_{H_2}=2\mathrm{g}/\mathrm{mol}$; $R_A$ is the gas constant, $R_A=8.31\mathrm{J}/(K\cdot \mathrm{mol})$.

Considering the relationship between level 2 and level 3, ignoring the entraining effect and gas fraction, the mass conservation equation, momentum conservation equation, and cross-sectional area expression are calculated as follows:

$${\rho }_2{u}_2{A}_2={\rho }_1{u}_1{A}_1$$

(10)

$${\rho }_2{u}_2^2{A}_2={\rho }_1{u}_1^2{A}_1+(p_1-p_2)A_1$$

(11)

$$A_1={\displaystyle \frac{1}{4}}\pi D_1^2$$

(12)

$$A_2={\displaystyle \frac{1}{4}}\pi D_2^2$$

(13)

The simplified method assumes that the mass flow rates at level 2 and level 3 are the same, where the flow rate at level 3 is as follows:

$$Q=u_2{A}_2{\rho }_2$$

(14)

where $Q$ is the mass flow rate at the virtual nozzle; ${\rho }_2$ is the density of hydrogen at ambient pressure and temperature; $A_1$ and $A_2$ are the cross sectional areas at the actual leakage orifice and the virtual nozzle, respectively; $p_2$ is the ambient pressure; $D_1$ and $D_2$ are the diameters of the actual leakage orifice and the virtual nozzle, respectively. Using the above equations, $u_2$, $D_2$, and $Q$ can be calculated, and these values can be used as boundary conditions for the numerical simulation.

3. Simulation Method Validation

To verify the correctness of the hydrogen leakage modeling method described earlier, we conducted two verification tests on the leakage and diffusion of hydrogen gas and compared the numerical simulation results with the hydrogen leakage experiment data from references [28,33], respectively. For the leakage, a case with a stagnation pressure of 1 MPa and a leakage orifice diameter of 1 mm was selected [28]. The calculated virtual nozzle diameter was 1.89 mm, and the flow velocity was 1905 m/s.

The mesh was refined at the inlet. A structured grid was adopted, and due to the symmetry of the hydrogen jet, a two-dimensional axisymmetric model was adopted to save computational resources and improve computational efficiency, as shown in Figure 2.

The calculation was performed using a pressure based steady solver with an implicit algorithm. The $\kappa -\epsilon$ turbulence model was chosen for the simulation, and the SIMPLE algorithm was used for pressure–velocity coupling. The convection terms were discretized using the second-order upwind scheme. The ambient temperature was set to 300 K, and the pressure outlet was set to one standard atmosphere. The hydrogen leaked vertically, and the effect of gravity was considered, with the gravity acceleration set to 9.8 m/s² in the direction opposite to the jet. The contour of hydrogen mole fraction was shown in Figure 3 and numerical simulation results were compared with the experimental results, as shown in Figure 4.

In Figure 4, z represents the distance along the centerline from the leakage orifice, de is the diameter of the leakage orifice, and Ycl is the mole fraction of hydrogen along the centerline. As can be seen from the figure, the numerical simulation results for the mole fraction of hydrogen along the jet centerline are in good agreement with the experimental results, and both show a consistent trend. This indicates that the virtual nozzle model and numerical simulation method described earlier can simplify the process of high-pressure hydrogen leakage and effectively predict the mole fraction along the hydrogen jet.

Furthermore, we used the experiment data of Pitts et al. [33] for numerical validation of hydrogen leakage and diffusion in an enclosed environment. Pitts et al. conducted experiments in a garage with dimensions of 6.1 m × 6.1 m × 3.05 m. Hydrogen gas was released through a rectangular box with dimensions of 0.305 m × 0.305 m × 0.15 m at the center of the garage floor, with a flow rate of 994 L/min. There was a garage door in the middle of the front wall, measuring 2.4 m × 2.1 m. There were two observation windows on the right wall with a length of 0.2 m and height of 2.3 m, and two skylights on the top of the garage for lighting, with a length of 0.3 m, located above the sensor array and hydrogen leak point. Select hydrogen concentration data from four sensors with the coordinates (3.05, 5.49, 1.14), (3.05, 5.49, 1.52), (3.05, 5.49, 1.9), and (3.05, 5.49, 2.59), labeled as M1, M2, M3, and M4, respectively, are shown in Figure 5a. A comparison between experimental data and numerical simulation results of hydrogen concentration near each sensor point is shown in Figure 5b. It can be seen that the numerical simulation results are slightly lower than the experimental data, and this trend is consistent during the leakage. In general, the method of numerical simulation described in the previous section can predict the hydrogen leakage and diffusion behavior, and the results are credible.

4. Simulation Modeling of Hydrogen Storage System

4.1. Physical Model

Based on a new-designed four-seater hydrogen internal combustion aircraft, the physical model of the aircraft was established, with a length of 6 m, a width of 1 m, and a height of 1.1 m (6 m × 1 m × 1.1 m). The aircraft carries two carbon fiber winding hydrogen storage tanks, which are located at the rear of the fuselage, and the pressure of the hydrogen in the tanks is 35 MPa. The structure inside the aircraft is complex, including various pipelines and brackets, which makes it difficult to make mesh division for CFD. Therefore, we simplified it on this basis by keeping the two main hydrogen tanks, four seats, and a partition separating the tank storage compartment from the passenger compartment, with a thickness of 5 cm, which is closed on a daily basis and can be opened for daily inspection and maintenance of the aircraft’s hydrogen system, with a gap of 3.5 cm around the edge of the partition to simulate the diffusion of hydrogen through the gap to the front of the aircraft cabin due to poor sealing failure, as shown in Figure 6.

In the hydrogen aircraft, the hydrogen-related systems include the hydrogen storage system and the hydrogen delivery system. A common architecture for these systems in hydrogen aircraft is illustrated in Figure 7.

Due to the properties of hydrogen, leaks can potentially occur at various points within these systems. For the hydrogen storage system, the inner liner of the hydrogen storage tank is typically made of plastic or aluminum, and the outer layer is wound with carbon fiber composite materials [34]. These tanks are designed to withstand high pressure, high temperature, and impact, and their reliability has been increasing with technological advancements, making hydrogen leakage less likely. However, the interfaces between the storage tank and the piping, due to different thermal expansion coefficients, poor assembly, high pressure, and the alternating loads experienced during aircraft take-off and landing, can become loose, leading to hydrogen leakage. Therefore, in this study, the hydrogen leakage is assumed to occur at the front of the No. 2 storage tank, specifically at the connection point of the hydrogen supply pipe in front of the tank’s opening. The leakage direction is normal to the leak surface. The dimension of hydrogen-powered aircraft is shown in Figure 8a and the potential leakage point is drawn in Figure 8b.

4.2. Ventilation Scheme

Oscillating heat pipe (OHP) is the preferred heat dissipation technology for aerospace equipment [35]. To prevent the accumulation of hydrogen in the cabin, appropriate measures must be taken to manage the leaked hydrogen. Wang et al. [13] have shown that a proper designed ventilation layout, combined with forced ventilation measures and sufficient ventilation rates, can significantly reduce the concentration of leaked hydrogen within hydrogen-related facilities, thereby preventing the hydrogen concentration from reaching a dangerous level. Hajji et al. [36] conducted a study on hydrogen leakage and ventilation layouts in residential garages. Their research indicated that rectangular or square shaped vents are more effective than circular or triangular ones. However, rectangular or square openings can lead to stress concentrations at the corners, which may affect the structural fatigue life.

Therefore, we set up a ventilation layout on the roof and floor of the aircraft to investigate the effect of the ventilation on the hydrogen mole fraction in the cabin after a 35 MPa hydrogen leakage. The ventilation layout consisted of eight 10 cm-diameter holes on the roof of the aircraft and four 20 cm-diameter holes on the floor of the aircraft, which were symmetrically distributed along the aircraft’s roll axis, with passive air outlets on the roof of the cabin and active air intakes in the floor of the cabin, seen in Figure 9. The vents in the floor were numbered 1, 2, 3, and 4 to distinguish them from one another. During the forced ventilation scenario, the air inlet velocity was set to 20 m/s and 50 m/s, separately.

4.3. Mesh Division and Independence Verification

A hexahedral mesh was used to divide the space in the cabin, and the mesh of the model is shown in Figure 10. The mesh division is closely related to the accuracy of the numerical simulation results, so it is necessary to perform the mesh-independence verification, considering four mesh configurations with the number of cells from 4.1 × 10⁵ to 2.2 × 10⁶, as shown in Figure 11. It can be seen that, when the number of cells reaches 1.2 × 10⁶, the difference in hydrogen mole fraction in the cabin is less than 2%. Finally, the mesh size at the hydrogen leakage point is set to 0.5 mm, at the air inlet and outlet, it is set to 5 mm, and the number of cells is 1,688,832.

4.4. Time Step Independence Verification

As the hydrogen leakage diffusion process in the cabin is a transient process, must be understood using transient calculations. When carrying out a transient numerical simulation, the size of the time step will have a great impact on the calculation results. In order to ensure the accuracy and efficiency of the calculation, it is necessary to perform the independence test of the time step, select the time steps of 0.001 s, 0.01 s, and 0.1 s for the test, and the results are as shown in Figure 12. Finally, the time-step was set to 0.01 s.

4.5. Selection of Planes and Monitoring Points

The hydrogen mole fraction field inside the cabin is three-dimensional, with a total of three planes selected on three coordinate axes that are perpendicular to each other, seen in Figure 13. Among them, plane-1 is an x–y plane; z = 1 m, plane-2 is an x–z plane; y = 0.5 m, and plane-3 is a y–z plane; x = 1.66 m, which is the plane at the leakage point. In addition, six points were selected in the front, middle, and rear of the cabin to ensure that different parts and heights of the cabin have monitoring points. The coordinates of these points are shown in

Table 1. Monitoring point coordinates.

Monitor Point	Coordinates
Point-1	(1, 0.5, 1) m
Point-2	(1, 0.5, 0.3) m
Point-3	(1.8, 0.5, 1) m
Point-4	(1.8, 0.5, 0.3) m
Point-5	(3, 0.5, 0.9) m
Point-6	(3, 0.5, 0.5) m

.

4.6. Numerical Simulation Settings

The simulation was performed using a transient solver, with the species transport equations used to calculate the mixture of hydrogen and air in the cabin over a period of 10 s after the leakage. The pressure velocity coupling was handled using the coupled algorithm, and the convection terms were discretized using the second-order upwind scheme. The effect of buoyancy was considered, with the gravity acceleration set to 9.8 m/s², directed vertically downward. The $\kappa -\epsilon$ turbulence model was chosen with the standard wall function. The air inlet was set as the velocity inlet boundary condition, and the outlet was set as the pressure outlet boundary condition. The hydrogen leakage pressure was 35 MPa.

5. Simulation Results and Analysis

5.1. Hydrogen Leakage and Diffusion Under Natural Ventilation

The geometry inside the cabin is complex, and hydrogen leakage and diffusion inside the cabin are affected by multiple factors. This is because the flammable range of hydrogen is large and the mole fraction of hydrogen at different locations varies greatly. Therefore, the volume-weighted average hydrogen mole fraction inside the cabin was selected as the evaluation index to investigate the relationship between different leakage conditions and the hydrogen mole fraction inside the cabin.

5.1.1. Effect of Leakage Diameter

The leakage diameters were set to 1 mm, 1.5 mm, and 2 mm and the diameters of the virtual nozzles were set to 11.33 mm, 16.12 mm, and 21.5 mm, respectively. The leakage direction was the z+ direction, as shown in Figure 8. The relationship between the hydrogen mole fraction in the cabin and the leakage diameter is shown in Figure 14.

From Figure 14, as the leakage diameter increases, the hydrogen mole fraction in the cabin will rapidly increase at the same time. After 10 s of leakage, when the leakage diameter is 2 mm, the mole fraction of hydrogen in the cabin is 2.6 times that of 1 mm. The high-pressure hydrogen leakage with a large diameter has a huge impact on the mole fraction of hydrogen in the cabin. Therefore, in the safety design of hydrogen storage systems for hydrogen aircraft, the occurrence of large-diameter leakage should be avoided as much as possible.

5.1.2. Effect of Leakage Direction

The location and direction of hydrogen leakage have a significant impact on the diffusion of hydrogen in the cabin. Based on the four potential leakage directions shown in Figure 8, the leakage diameter of hydrogen was set to 1 mm, and the diameter of the virtual nozzle was set to 11.33 mm. The relationship between the hydrogen mole fraction in the cabin and the leakage location was calculated, as shown in Figure 15.

The hydrogen leakage vertically upwards will quickly impact the ceiling and spread around. However, due to buoyancy effects, leaks in horizontal and vertical downwards directions will not only spread horizontally but will also move upwards after being obstructed by the storage tank and the side walls of the cabin. This leads to a larger overall diffusion range than leaks in the vertical upwards direction, as seen in Figure 15. To further illustrate this situation visually, a volume rendering of the hydrogen mole fraction in the cabin after 1 s the leakage was drawn, as shown in Figure 16.

When the hydrogen leak occurs in the y-direction, the hydrogen is obstructed by No. 1 tank, resulting in a large-scale horizontal diffusion. At the same time, under the effect of buoyancy, it diffuses upwards. When the hydrogen leak occurs in the z-direction, the hydrogen flow hits the cabin floor, weakening the gas kinetic energy. However, due to the influence of buoyancy and hydrogen mole fraction gradient, the hydrogen diffuses outwards and upwards. These diffusion model all form a large range of hydrogen mole fractions in the cabin, but there is not significant difference in the values of the hydrogen mole fraction inside the cabin.

5.1.3. Effect of Environment Temperature and Pressure

As the flight altitude changes, the ambient temperature and pressure inside the cabin of an aircraft without cabin pressurization will also vary. In order to investigate the effects of temperature and pressure on hydrogen leakage and diffusion, the hydrogen leakage diameter was set to 1 mm, with ambient temperatures of 280 K, 290 K, and 300 K and ambient pressures of 101,325 Pa, 84,560 Pa, and 67,230 Pa, respectively. The diameter of virtual nozzle and flow velocity were calculated as shown in

Table 2. Hydrogen thermodynamic parameters and virtual nozzle results.

Temperature (K)	Pressure (Pa)	Density (kg/m3)	Diameter (mm)	Velocity (m/s)	Mass Flow Rate (kg/s)
280	67,230	0.058	13.85	1994	0.017414
280	84,560	0.073	12.35	1994	0.017392
280	101,325	0.087	11.31	1993	0.017411
290	101,325	0.084	11.31	2028	0.017017
300	101,325	0.081	11.33	2063	0.016838

, and we used the CoolProp 6.8.0 [37] library to calculate the density of hydrogen. The relationship between the hydrogen mole fraction in the cabin and temperature and pressure is shown in Figure 17.

In Figure 17, as the ambient temperature decreases, the hydrogen mole fraction in the cabin decreases, but it is not significant. However, as the ambient pressure decreases, the hydrogen mole fraction in the cabin increases significantly.

According to Fick’s first law Equation (15), the diffusion rate of hydrogen is influenced by the diffusion coefficient and concentration gradient. The relationship between the diffusion coefficient and environmental pressure and temperature can be known roughly in Equation (16). As the environmental temperature increases, the gas density decreases and the buoyancy decreases, suppressing the vertical movement, but this increases the horizontal diffusion behavior of hydrogen. In general, there is not significant difference in hydrogen mole fraction in cabin. When the environmental pressure decreases, the diffusion coefficient increases, thereby accelerating the diffusion of hydrogen. Meanwhile, the smaller molecular mass of hydrogen gas amplifies its diffusion behavior at low temperatures and pressures. Equation (15) is as follows:

$$J=-D{\displaystyle \frac{\partial C}{\partial x}}$$

(15)

$$D\propto {\displaystyle \frac{T^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{P}}\sqrt{{\displaystyle \frac{1}{{\mu }_{H_2}}}+{\displaystyle \frac{1}{{\mu }_{\mathrm{air}}}}}$$

(16)

where $J$ is the diffusion flux; $D$ is the diffusion coefficient; ${\displaystyle \frac{\partial C}{\partial x}}$ is the concentration gradient; $T$ is temperature; $P$ is pressure; ${\mu }_{H_2}$ and ${\mu }_{\mathrm{air}}$ are the molecular mass of hydrogen and air, respectively.

5.2. Effect of Ventilation on Hydrogen Mole Fraction

In order to investigate the effect of different ventilation conditions on the hydrogen mole fraction in the cabin, numerical simulations were conducted on the hydrogen mole fraction field in the cabin under different ventilation conditions. The leakage diameter was 1 mm, the virtual nozzle diameter was 11.33 mm, and the velocity of flow was 2063 m/s. Transient calculations were performed for a duration of 10 s. The setting of the simulation conditions is shown in the

Table 3. Ventilation wind velocity setting.

	Ventilation Conditions Setting
	Vent-1	Vent-2	Vent-3	Vent-4
Case-1	20 m/s	20 m/s	0	0
Case-2	0	0	20 m/s	20 m/s
Case-3	20 m/s	20 m/s	20 m/s	20 m/s
Case-4	50 m/s	50 m/s	0	0
Case-5	0	0	50 m/s	50 m/s
Case-6	50 m/s	50 m/s	50 m/s	50 m/s

. The vent number can be seen in Figure 9.

Figure 18 shows the hydrogen mole fraction contour on three planes of the cabin under different ventilation conditions, where the wind velocity of Case-1, Case-2, and Case-3 was 20 m/s and the wind velocity of Case-4, Case-5, and Case-6 was 50 m/s, respectively. It can be seen that the overall hydrogen mole fraction in the cabin decreases under forced ventilation, i.e., the increase in wind velocity is beneficial for the evacuation of hydrogen, while the areas with higher hydrogen mole fractions in the cabin are concentrated near the leakage point along the hydrogen jet, around the corner near the partition, and tend to diffuse along the cabin walls.

Hydrogen mole fraction samples were taken from the monitoring points mentioned earlier, and the variation in the hydrogen mole fraction at the monitoring points in the cabin with leakage time under Case-1 to Case-6 conditions was obtained, as shown in Figure 19.

From Figure 19, it can be seen that as the wind velocity increases, the hydrogen mole fraction in the cabin gradually decreases. When the wind velocity is 20 m/s, the combined ventilation effectiveness of opening vents 1–4 is significantly better than opening vents 1 and 2 or 3 and 4 separately. When vents 1 and 2 are opened, the hydrogen mole fraction at most monitoring points is lower than in the scenario in which vents 3 and 4 are opened. Furthermore, when the wind velocity is 50 m/s, the hydrogen mole fraction in the cabin is relatively low (below 0.1 mole fraction of hydrogen) under all conditions. The combination ventilation of vents 1–4 is used to keep the hydrogen mole fraction in the middle and rear of the cabin below 0.02. However, due to the faster wind velocity in the cabin, the remaining hydrogen is blown through the gap in the partition and diffuses towards the front of the cabin, causing the hydrogen mole fraction at the monitoring points in the front of the cabin to increase.

The hydrogen evacuation efficiency inside the cabin is defined as follows:

$$\epsilon ={\displaystyle \frac{C_e}{C_p}}$$

(17)

where $C_e$ is the mole fraction of hydrogen at the air outlet, $C_p$ is the arithmetic average hydrogen mole fraction at 6 monitoring points, and the higher of value $\epsilon$ indicates a higher hydrogen evacuation efficiency for monitoring points.

The figure of hydrogen evacuation efficiency over time under different ventilation conditions was obtained, as shown in Figure 20. From Figure 20a, it can be seen that when the wind velocity is 20 m/s, the hydrogen evacuation efficiency in the early stage is around 3, and the hydrogen evacuation efficiency of separately opening vents 1 and 2 is higher than that of separately opening vents 3 and 4, but this gradually decreases as the leakage process continues. When opening vents 1–4, the hydrogen evacuation efficiency first increases and then decrease, but the efficiency drops to around 1.5 at 10 s. It can be seen from Figure 20b that when the wind speed is increased to 50 m/s, the hydrogen evacuation efficiency of opening vents 1–4 in the early stage of leakage is around 8, higher than the 20 m/s wind velocity, and it will rapidly decrease to 3 in a short period of time. However, the hydrogen evacuation efficiency of separately opening vents 1 and 2 is lower than that of separately opening vents 3 and 4 from 1 s to 10 s. In addition, the efficiency of opening vents 1–4 is lower than opening 3 and 4 after 3 s. Due to the high diffusivity of hydrogen gas, forced ventilation during the initial stage of leakage can effectively reduce the mole fraction of hydrogen in the cabin in a short period of time. Therefore, the initial hydrogen evacuation efficiency is high. However, as hydrogen evacuation continues, forced ventilation not only evacuates the hydrogen but also causes residual hydrogen gas in the cabin to diffuse, making it difficult to evacuate.

It can be seen that forced ventilation evacuates most of the hydrogen in the cabin, although residual hydrogen is difficult to evacuate. The hydrogen mole fraction in the cabin will reach dynamic stability, and the hydrogen evacuation efficiency also tends to stabilize after a period of forced ventilation. We calculated the volume proportion of different hydrogen mole fraction ranges in the cabin. Figure 21 shows the changes in the volume proportion of different hydrogen mole fraction ranges in the cabin over time under different ventilation conditions.

From Figure 21, it can be seen that forced ventilation reduces the hydrogen mole fraction inside the cabin by evacuating it to the outside, while also promoting the diffusion of residual hydrogen inside the cabin. In Case-1 and Case-4, the hydrogen mole fraction in most of the cabin spaces reaches 0.04 or above at t = 10 s after the leak. In Case-2 and Case-3, approximately 60% of the space inside the cabin has a hydrogen mole fraction of 0.04 or above at t = 10 s after the leak. In Case-5, approximately 15% of the cabin space reached a hydrogen mole fraction of 0.04 or above at t = 10 s after the leak, but the space above 0.1 and 0.2 hydrogen mole fraction increased compared to Case-4. Under Case-6, the spaces with hydrogen mole fractions above 0.1 and 0.2 in the cabin are the lowest under all ventilation conditions, but the spaces with a hydrogen mole fraction of 0.04 or above reached around 50% at t = 10 s after the leak.

Forced ventilation can evacuate most of the hydrogen in the cabin, but, due to the low flammable concentration and strong diffusion of hydrogen gas, a small amount of hydrogen gas from the leakage point can cause the hydrogen mole fraction in a large area of space to reach above the lower flammable limit (LFL) which is 0.04 in a relatively enclosed space, like the cabin. This makes it difficult to maintain the hydrogen mole fraction in most of the cabin below 0.04 through forced ventilation. Therefore, the failure state of hydrogen leakage should be considered in the early design of hydrogen storage systems for hydrogen-powered aircraft, and safety design methods should be used to satisfy the airworthiness and safety of the entire aircraft.

6. Discussion

This study established a three-dimensional numerical simulation model of the target hydrogen-powered aircraft and investigates the hydrogen diffusion process in the cabin after supercritical hydrogen leakage occurs in the onboard hydrogen storage system through numerical simulation. We analyzed the changes in the hydrogen mole fraction in the cabin under different ventilation conditions and the volume proportion of different hydrogen mole fraction ranges in the cabin space. Based on the numerical simulation results, the following conclusions can be drawn:

• The cabin of the hydrogen aircraft is a small and relatively enclosed space, and the hydrogen mole fraction can quickly reach relatively high levels (4–75%, flammable range) when a leakage occurs. The hydrogen diffuses rapidly and spreads over a wide area, and it can be detected in the front, middle, and rear of the cabin a short time after the leak occurs.
• The diameter of hydrogen leakage has a significant impact on the hydrogen mole fraction range in the cabin, and large-scale hydrogen leakage can increase the hydrogen mole fraction range in the cabin rapidly. Due to the complex internal structure of the cabin, the hydrogen storage tanks, cabin partition, and cabin wall will block the diffusion of hydrogen. Therefore, different directions of hydrogen leakage will lead to different hydrogen diffusion behaviors and propagation paths. However, the overall high concentration range is distributed in the middle of the cabin, near potential leakage points. As the ambient temperature increases and the ambient pressure decreases, it will promote the diffusion behavior of hydrogen in the cabin. Compared to plain areas, hydrogen diffusion behavior is more significant in low-temperature and high-altitude regions.
• Forced ventilation can quickly and effectively reduce the hydrogen mole fraction in the cabin in a short period of time, but it also promotes the diffusion of residual hydrogen in the cabin. Under different ventilation conditions, the range of the hydrogen mole fraction greater than 0.04 in the cabin varies, with a maximum of 96.3% (Case-1) and a minimum of 15.5% (Case-5). However, with the increase in wind velocity, the high hydrogen mole fraction areas (>0.1 or >0.2) all decrease.
• Hydrogen can quickly diffuse into the cockpit through the gaps between the partition and the wall. It is necessary to strictly separate the hydrogen storage tank compartment from the cockpit in the front and confirm its sealing during subsequent maintenance inspections, as there are a large number of electronic devices in the cockpit, which will be relatively far away from the risk of explosion.

In future work, a quantitative risk assessment is worth considering on the basis of this study.