Introduction

Hydrogen energy has the advantages of high calorific value and being clean and pollution-free1, making it one of the important energy carriers for reducing the consumption of fossil energy and achieving the global carbon neutrality goal2,3. Statistics show that the transportation sector is an important source of greenhouse gas emissions, accounting for about one-quarter of global carbon dioxide emissions4, and hydrogen energy is expected to become an important means for the transportation sector to achieve decarbonization5,6. Hydrogen fuel cell buses have the advantages of large hydrogen storage capacity and fixed operating routes7,8,9 and have been promoted and operated in a large number of cities in recent years. However, the use of hydrogen in vehicles also faces many safety issues. Hydrogen has characteristics such as easy diffusion10, wide combustion range11, low ignition energy12, and is prone to cause hydrogen embrittlement of metals13,14. In addition, vibrations, impacts, and corrosion in the vehicle environment can easily lead to hydrogen leakage. In recent years, with the increase in the application of hydrogen energy, hydrogen explosion accidents have occurred frequently, and hydrogen safety has also become one of the key difficulties in the application of hydrogen energy15,16,17,18.

Related works

As the application of hydrogen energy increases, domestic and foreign scholars have also researched hydrogen safety in various scenarios. Hajji et al.19 used Fluent to simulate the diffusion and distribution of hydrogen in garages with different roof shapes and found that the roof shape has a significant impact on the diffusion and distribution of hydrogen, providing important references for related construction. Thawani et al.20 used Fluent to simulate the leakage of hydrogen and methane in small enclosed spaces such as kitchen cabinets. The study found that in a home environment, even a small amount of hydrogen leakage can quickly form a flammable and explosive gas cloud. Therefore, it is crucial to develop effective hydrogen leakage detection and prevention systems. Abbas et al.21 conducted a numerical simulation of hydrogen leakage in enclosed spaces. The study analyzed the concentration distribution of the hydrogen cloud and the change process of the danger area over time under different leakage hole heights, positions, and leakage directions. Li et al.22 studied the diffusion behavior of hydrogen in a closed fuel cell vehicle with obstacles through numerical simulation methods. The study focused on analyzing the impact of obstacles at different positions on hydrogen diffusion, and the results showed that the presence of obstacles affects the vertical and horizontal spread of hydrogen. Yu23 used OpenFOAM to simulate hydrogen leakage under four different window opening conditions at a hydrogen storage pressure of 70 MPa. The simulation considered the impact of environmental wind speed on the distribution of hydrogen in the vehicle and analyzed the distribution of hydrogen concentration and flammable areas. Shen et al.24 conducted leakage experiments on valves to determine the hydrogen leakage flow rate under different pressures and tightening torques and studied the impact of environmental wind on hydrogen leakage and diffusion in fuel cell vehicle piping. The study used the FLACS software to simulate the leakage and diffusion process of hydrogen from the hydrogen system piping and analyzed the impact of wind direction on hydrogen leakage and diffusion. The study found that environmental wind can reduce hydrogen concentration and reduce the range of hydrogen diffusion. Lv25 used the FLACS software to simulate the release of hydrogen in an outdoor parking lot of several hydrogen fuel cell vehicles through a thermally activated pressure relief device (TPRD). The study examined the impact of different leakage diameters, release directions, and parking configurations on the formation of flammable gas clouds and safe distances. Yuan et al.14 used Fluent software to simulate the diffusion process of hydrogen in the cargo hold of a transport ship and analyzed the change patterns of hydrogen concentration under different leakage positions and ventilation conditions. The study found that the leakage position has a significant impact on the distribution of hydrogen diffusion, and increasing ventilation intensity can effectively reduce the range of hydrogen diffusion, providing a reference for the optimal location of hydrogen sensors and a basis for formulating ventilation requirements when transporting hydrogen fuel cell vehicles. Cui et al.26 used numerical simulation methods to simulate the leakage of hydrogen fuel cell vehicles in tunnels, studied the volume of flammable hydrogen clouds under different wind speeds, and ignited the flammable clouds to obtain the range of explosion impact. Ma et al.27 studied the explosion characteristics and disaster effects of hydrogen at hydrogen refueling stations. Through numerical simulation, the study analyzed the propagation pattern of explosion shock waves and the dynamic response process of surrounding structures, and visually and quantitatively assessed the consequences of hydrogen explosions through risk matrices and accident consequence level matrices. Lin et al.28conducted numerical simulation studies on the potential risks of accidental hydrogen fires on offshore hydrogen production platforms. The study analyzed the impact of facility layout, leakage speed, and direction on the consequences of fires, and compared the suppression effects of firewalls of different heights on hydrogen fires. Cui et al.29 developed a CFD numerical model suitable for hydrogen refueling stations in ports, studied the impact of roofs, leakage angles, and wind direction on hydrogen diffusion, and proposed suggestions for the layout of hydrogen detectors based on parametric studies. Li et al.30 studied the diffusion behavior of hydrogen leakage and potential explosion risks at modular hydrogen refueling stations. Through simulation, the study analyzed the impact of ventilation conditions and environmental wind at modular hydrogen refueling stations on the volume and diffusion distance of hydrogen. Currently, research on hydrogen safety mainly focuses on hydrogen leakage at hydrogen refueling stations and the leakage of hydrogen from hydrogen energy vehicles into the environment. There is less research on the leakage of hydrogen into the vehicle interior. When hydrogen leaks into the confined space of the vehicle, it can cause the accumulation of hydrogen, increasing the risk of ignition of the hydrogen cloud.

Present study

Fluent software is a computational fluid dynamics (CFD) tool developed by ANSYS, mainly used for simulating fluid flow, heat transfer, chemical reactions, combustion, mass transfer, etc., and has been used by many researchers for simulation studies of hydrogen leakage and explosion. This paper uses Fluent software to simulate the leakage of hydrogen into the passenger cabin of hydrogen fuel cell buses and the explosion scenario after leakage. The study focuses on analyzing the laws of hydrogen diffusion and distribution under different leakage positions and different leakage flow rates, as well as the range of harm under different ignition source positions and ignition moments. This study aims to analyze the accidental leakage during the use of hydrogen fuel cell buses, to provide references for the formation of emergency rescue plans, effectively reduce casualties, and the research results also have a guiding role in the prediction of potential explosion accidents and risk assessment. This article innovatively investigates hydrogen leakage and explosion dynamics within the confined space of a fuel cell bus, a relatively unexplored area in hydrogen safety research. The simulation will couple comprehensive CFD with realistic scenarios related to leakage and ignition cases, thus providing comprehensive insight into the behavior of hydrogen in real environmental vehicle conditions. The research program provided recommendations on how to pragmatically improve safety and enhance hydrogen-powered transport systems.

Numerical simulation of hydrogen gas leakage

Geometric model

A geometric model was established based on a certain fuel cell bus available on the market, and a study was conducted on the accidental leakage of hydrogen into the passenger cabin of the vehicle31. The dimensions of the bus are 9.0 m × 2.5 m × 3 m, with six hydrogen storage cylinders of 35 MPa on the roof, and a hydrogen storage volume of 0.84 m³. The dimensions of the computational domain are 37 m × 26.5 m × 17 m. The simplified model is shown in Fig. 1. This paper takes into account the influence of seats and other factors, retaining typical features such as the seats inside the vehicle.

Fig. 1
Fig. 1
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Proposed geometric model.

Mesh generation

The computational domain mesh was generated using ICEM, and the entire model utilized hexahedral grids, as shown in Fig. 2. To ensure the accuracy of the model, the same set of grids was used for both hydrogen leakage and explosion numerical simulations. Therefore, during the grid independence verification, both the accuracy of the hydrogen diffusion simulation and the hydrogen explosion simulation were considered32. The grids near the vehicle and inside the vehicle were divided using cells of sizes 0.04 m, 0.05 m, 0.06 m, and 0.07 m, while larger grid sizes were used in areas further away from the vehicle to reduce the number of grids.

Fig. 2
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Computational domain mesh.

The grid independence was verified for these four sets of grids by numerically calculating the hydrogen concentration at the monitoring points inside the vehicle, as shown in Fig. 3 (a). The trend of hydrogen concentration at the monitoring points was the same, with the relative error in hydrogen concentration being below 1%. A simulation of the hydrogen explosion scenario was conducted, and the overpressure values at the monitoring points were obtained. Comparisons were made at the monitoring points outside the vehicle, and a maximum error of 5% was considered acceptable for grid independence. As shown in Fig. 3 (b), the relative error between the 0.05 m grid size and the 0.04 m grid size was 2.13%. Therefore, considering both computational accuracy and cost, a grid size of 0.05 m was chosen, with a total of 9.6 million grids.

Fig. 3
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Grid independence verification; (a) Hydrogen diffusion validation; (b) Hydrogen explosion validation.

Boundary conditions and simulation schemes

This chapter’s numerical simulation primarily considers the diffusion distribution of hydrogen under different leak source locations and different leak rates. The rear of the vehicle is where the fuel cell system pipelines are arranged, and there is also a maintenance hatch at the back of the bus leading to the fuel cell compartment. Therefore, the leak source inside the vehicle is chosen at the rear of the vehicle. A total of seven different simulation scenarios are set up, and the specific simulation schemes are shown in Table 1.

The determination of the leak flow rate is calculated using Eq. (1).

The Abel-Noble state equation is33:

$$\:{{\uprho\:}}_{1}=\frac{{\text{p}}_{1}}{\text{b}{\text{p}}_{1}+{\text{R}}_{{\text{H}}_{2}}{\text{T}}_{1}}$$
(1)

In which ​\(\:{{\uprho\:}}_{1}\) represents the initial hydrogen density, in kg/m³; \(\:{\text{p}}_{1}\) denotes the initial pressure, in Pa; b is the co-volume constant, 7.69 × 10− 3m3/kg, and RH2 is the gas constant for (\(\:{\text{R}}_{\text{H}2}=4.12\:\text{N}\text{m}/\text{g}\text{m}\:\text{K}\)); \(\:{\text{R}}_{{\text{H}}_{2}}\) is the gas constant for hydrogen, taken as 4.124 × 103 \(\:\text{J}/\text{k}\text{g}\:\text{K}\); \(\:{\text{T}}_{1}\) is the initial temperature, in K.

From the equations of mass conservation and energy conservation, it is further derivable through Eq. (2):

$$\:{\left(\frac{{{\uprho\:}}_{1}}{1-\text{b}{{\uprho\:}}_{1}}\right)}^{{\upkappa\:}-1}={\left(\frac{{{\uprho\:}}_{3}}{1-\text{b}{{\uprho\:}}_{3}}\right)}^{{\upkappa\:}-1}[1+\frac{{\upkappa\:}-1}{2{(1-\text{b}{{\uprho\:}}_{3})}^{2}}]$$
(2)
$$\:\frac{{\text{T}}_{1}}{{\text{T}}_{3}}=1+\frac{{\upkappa\:}-1}{2{\left(1-\text{b}{{\uprho\:}}_{3}\right)}^{2}}$$
(3)

The density of hydrogen at the actual leak outlet is according to Eq. (4):

$$\:{{\uprho\:}}_{3}=\frac{{\text{p}}_{3}}{\text{b}{\text{p}}_{3}+{\text{R}}_{{\text{H}}_{2}}{\text{T}}_{3}}$$
(4)

The adiabatic index κ is taken as 1.4; \(\:{{\uprho\:}}_{3}\) is the density of hydrogen at the actual leak outlet, in kg/m³; \(\:{\text{T}}_{3}\) shows the temperature at the actual leak outlet, in K; \(\:{\text{p}}_{3}\) depicts the pressure at the actual leak outlet, in Pa.

The leakage velocity of hydrogen at the actual leak outlet is according to Eq. (5):

$$\:{\text{u}}_{3}=\sqrt{\frac{{\upkappa\:}{\text{p}}_{3}}{{{\uprho\:}}_{3}\left(1-\text{b}{{\uprho\:}}_{3}\right)}}$$
(5)

The leakage rate of hydrogen is according to Eq. (6):

$$\:\text{Q}=\text{A}{{\uprho\:}}_{3}{\text{u}}_{3}$$
(6)

The leakage velocity (\(\:{\text{u}}_{3}\)) at the actual leak outlet is in meters per second (m/s); Q represents the mass leakage rate in kilograms per second (kg/s); A is the area of the leak outlet in square meters (m2).

Fuel cell vehicles operate in complex environments characterized by long pipelines and multiple connections. Factors such as vibration and impacts during vehicle operation may lead to leaks in the hydrogen storage system, yet accurately determining hydrogen flow rates remains highly challenging34. According to an analysis of 120 hydrogen safety incidents by Yang et al.35, leaks caused by failures in pipelines, fittings, and valves accounted for the highest proportion (32.28%). However, publicly available experimental data on hydrogen leakage from pipe fittings in fuel cell vehicles remains limited. Therefore, this study calculated hydrogen leakage flow rates for five scenarios by determining leakage rates from high-pressure (35 MPa) and low-pressure (1 MPa) pipelines under varying leak aperture sizes. The leakage flow rates under different pressures and leak diameters were derived using Eqs. (1)–(6) presented in this paper. Calculations were performed for both 35 MPa high-pressure pipelines and 1 MPa low-pressure pipelines across multiple leak apertures; partial calculation results are presented in Table 1.

Table 1 Hydrogen fuel cell bus leakage condition.
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At lower leakage flow rates, the hydrogen volume fraction remains relatively low, posing a relatively minor hazard. However, such leaks are difficult to detect. With well-implemented safety monitoring measures, they generally do not lead to serious accidents. Drawing from previous research on hydrogen leakage, this study established a hydrogen leakage flow rate range of 0.0043 kg/s to 0.048 kg/s. The selected leakage location inside the vehicle was the rear section of the bus, where the hydrogen fuel cell system is installed and where maintenance access points connect to the passenger cabin. Considering that seating arrangements and location are the primary factors affecting hydrogen diffusion in the rear section of the vehicle, this study identified the influencing factors for different leakage locations discussed in the paper.

The walls and seats near the leak source can affect the diffusion of hydrogen36. Therefore, three different typical locations are considered in the simulation scenarios3, which are located at the rear wall of the vehicle, under the rear seats, and in the middle of the vehicle. The direction of the leak is horizontal, to study the diffusion of hydrogen under different leak locations, denoted as Case 1, Case 6, and Case 7.

When the location of the hydrogen leak is at the rear wall of the vehicle, the diffusion of hydrogen under five different leakage rates (0.0043 kg/s, 0.0104 kg/s, 0.0169 kg/s, 0.0240 kg/s, 0.0349 kg/s) is discussed, namely Case 1, Case 2, Case 3, Case 4, and Case 5. The simulation scenarios are shown in Table 2.

Table 2 Simulation scenarios.
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This paper uses ANSYS Fluent to perform transient three-dimensional flow field numerical simulations of the fluid domain37. The standard k-ε turbulence model is used to simulate the turbulent structure of the gas, and the full buoyancy effect is considered. The mixture material selected is a “hydrogen-air” mixture38. The main components of the “hydrogen-air” mixture include hydrogen, oxygen, nitrogen, and water vapor. The mixture gas state equation uses the ideal gas equation, and the viscosity uses the ideal gas mixing rule. A pressure-based solver is chosen, with the SIMPLE algorithm for pressure-velocity coupling, and the convection terms in the momentum and energy equations are both second-order upwind difference schemes. The calculation is considered to have converged when the residuals of the continuity, momentum, and energy equations are less than 1 × 10− 4. The simulation considers the effects of gravity and buoyancy on the diffusion of hydrogen, with gravity directed along the negative Z-axis, and the acceleration due to gravity is set at 9.81 m/s2.

The initial gauge pressure is set at 0 Pa, and the temperature is 297 K. The hydrogen leak outlet is a mass inlet, and the car windows are considered as internal surfaces when open and as wall surfaces when closed. The vehicle body, seats, and floor are set as no-slip stationary wall surfaces, and the computational domain boundary is a free boundary outlet. The specific boundary condition settings are shown in Table 3.

Table 3 Model boundary conditions.
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Numerical simulation of hydrogen explosion

Boundary conditions and simulation schemes

Once a flammable hydrogen cloud is ignited, it can cause a severe explosion39. Therefore, simulating the distribution of overpressure and high temperature after hydrogen ignition and explosion can provide a reference for emergency plans40. The explosion simulation of hydrogen used the partially premixed combustion model in Fluent. To accurately detect the pressure and temperature distribution inside and outside the vehicle, 18 monitoring points were established, as shown in Fig. 4. Among them, points 6 to 11 are located on the side of the vehicle, points 12 to 17 are on the front of the vehicle, and points 6 to 11 are on the rear of the vehicle. The first five monitoring points on each side are 0.5 m apart, and the last monitoring point is 5 m away from the fifth monitoring point.

Fig. 4
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Schematic diagram of monitoring point location.

There are significant differences in the concentration and distribution of hydrogen at different times after leakage. Therefore, the ignition of combustible hydrogen inside the vehicle at 10s, 20s, 30s, 40s, and 50s after leakage is simulated to analyze the impact of different leakage durations on the pressure and temperature distribution inside the vehicle and outside. Under the Case 3 30s condition, the influence of the ignition source position on the pressure and temperature distribution was analyzed, considering three positions: the front, middle, and rear of the vehicle.

Table 4 shows the initial settings before the explosion solution using Fluent. Due to the large number of settings, only key attention items are briefly described here, and those that are default and consistent with the previous hydrogen leakage simulation are not repeated.

Table 4 Initialization settings for solving the explosion process.
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Boundary conditions and simulation schemes

Computational simulations using this model were performed for the experiment conducted by William et al.41, with comparisons of hydrogen concentration at heights of 0.38 m and 1.52 m. William et al. constructed a full-scale garage measuring 6.1 m × 6.1 m × 3.05 m internally. Two openings of 0.2 m × 0.2 m were located on the right wall at a height of 2.3 m. In this experiment, hydrogen entered the garage through a rectangular vent measuring 0.305 m × 0.305 m × 0.15 m. Under standard conditions, the hydrogen mass flow rate was 83.3 g/min. The model was meshed using ICEM software, as illustrated in Fig. 5. Figure 6presents a comparison between simulation results and experimental data. During the leakage process, the simulation results showed good agreement with experimental measurements, though the simulated hydrogen concentration remained slightly higher than experimental values throughout the leakage period. This discrepancy may be attributed to external air infiltration through gaps between the door and walls during the experiment, as air ingress through these gaps was also monitored in the experimental setup.

Fig. 5
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William’s garage mesh model.

Fig. 6
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Comparison of hydrogen concentrations at monitoring sites.

To validate the effectiveness of the selected numerical method in capturing the transient flow field of hydrogen explosions, this study adopts Bauwens’ large-scale hydrogen explosion venting experiment42 as the research subject. A physical model with dimensions identical to the experimental setup was established, as shown in Fig. 7. The left panel displays the experimental configuration, while the right panel illustrates the established discretized finite element model. Simulation conditions were configured to match experimental parameters. Figure 8 presents the experimental and simulated overpressure curves at identical locations within the explosion chamber. As observed in Fig. 7.

Fig. 7
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Floor plan and finite element model of the experimental setup.

Fig. 8
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Comparison of overpressure results.

Results and discussion

Diffusion distribution patterns

A volume fraction of 1% is the maximum allowable hydrogen concentration inside the vehicle. Figure 9 illustrates the development process of the 1% concentration isosurface. It can be observed that during the upward diffusion process, the 1% volume fraction isosurface takes 2 s to spread from the leak outlet to the top. As shown in Figs. 3 and 8, the 1% volume fraction isosurface appears spherical, with the diameter of the spherical structure increasing over time. When the 1% volume fraction isosurface reaches the top, the 1% hydrogen concentration isosurface then begins to gradually advance.

Fig. 9
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1% concentration isosurface diffusion process.

To quantitatively analyze the vertical and lateral flow of hydrogen43, six concentration collection lines were established on the middle cross-section of the vehicle, as shown in Fig. 10. The six concentration collection lines are respectively 1.5 m, 3 m, 4.5 m, 6 m, 7.5 m, and 8.3 m away from the leak source.

Fig. 10
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Data acquisition lines inside the vehicle.

As shown in Fig. 11, at 22 s, the initial front of the hydrogen reaches the front wall of the vehicle and begins to roll downward. Before this, the vertical concentration distribution of hydrogen, as depicted in Fig. 10 (at 10s and 15s), exhibits a distinct concentration gradient in the vertical direction within the vehicle. When the initial front of the hydrogen begins to pass through the top of the vehicle for the second time, a layer of constant hydrogen concentration starts to appear in the vertical direction. After the initial front of the hydrogen has completely passed through the top of the vehicle for the second time, there is no longer significant lateral diffusion. At this point, the hydrogen mixture primarily shows an increase in the thickness and concentration value of the constant concentration layer.

At 10 s, the initial front of the hydrogen reaches the position of Line 1, from which it can be estimated that the thickness of the initial front of the hydrogen mixture is approximately 0.9 m. At 15 s, the initial front of the hydrogen completely passes through Line 2, at which point the hydrogen mixture at Line 2 forms a single layer with a thickness of about 0.65 m. At 32 s, the initial front of the hydrogen mixture passes through Collection Lines 5 and 6, at which time the thickness of the hydrogen mixture at Lines 5 and 6, after the initial front has passed through the top of the vehicle for the second time, is about 1.05 m.

Fig. 11
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Hydrogen concentration distribution along data collection lines.

Figure 12 is a streamlined map of hydrogen gas diffusing in space. From the streamlined map, it can be seen that the vortex center formed by the airflow inside the vehicle gradually moves upward from the leak and then moves along the top of the vehicle44. Eventually, a circulation is formed in the upper part of the passenger cabin, which is also the reason why hydrogen gas forms a vertically constant concentration layer.

Fig. 12
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Streamlines of hydrogen diffusion in space.

Diffusion distribution patterns at different leak locations

To compare the diffusion and distribution of hydrogen under different leak locations45, the hydrogen concentration contour plots for the first 20 s were compared, as shown in Fig. 13. The red areas in the contour plots represent parts where the hydrogen concentration exceeds 1%. Through Fig. 13, it can be observed that when the leak location is at the rear of the vehicle close to the vehicle wall, the 1% hydrogen isosurface spreads upward in a circular shape, reaching the top of the vehicle in about 2 s. When the leak location is in the middle of the vehicle, the 1% hydrogen isosurface spreads in a cylindrical shape, due to the horizontal direction of the hydrogen leak, which reduces the resistance to hydrogen diffusion, hence it no longer spreads in a circular arc, and the 1% isosurface spreads to the top of the vehicle in about 1 s. When the hydrogen leak is located under the seat, the leaking hydrogen impacts the seat and begins to envelop it before continuing to spread upward. After reaching above the seat, the hydrogen mixture converges into a single hydrogen plume that rises to the top of the vehicle. The 1% hydrogen isosurface reaches the top of the vehicle in about 3 s. The obstruction of the seat delays the time it takes for hydrogen to reach the top of the vehicle, so it is possible to consider adding hydrogen detection points under the seats to quickly monitor the leaking hydrogen.

Using the moment when hydrogen contacted the roof as the start timing point and its arrival at the front wall as the end timing point, the lateral diffusion velocity of the 1% hydrogen-air mixture isosurface is calculated. The average lateral diffusion velocities for Cases 1 and 7 were determined to be 0.47 m/s and 0.41 m/s, respectively.

Fig. 13
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The distribution of hydrogen under different leakage locations.

Figure 14 shows the variation in hydrogen concentration at four monitoring points. Under the three schemes, the hydrogen concentration at the monitoring points is within the flammable range (4%-75%). The concentration levels displayed by the four monitoring points are in the order of Case 1 > Case 6 > Case 7. When the leak source is located at the rear of the vehicle (Case 1), the hydrogen concentration at the monitoring points is the highest. At 200 s, the concentration values at the rear of the vehicle (point 1, point 2) are 0.223, which falls within the concentration corresponding to the minimum ignition energy (0.22–0.26). At this time, there is a significant risk of ignition for the hydrogen at the rear of the vehicle.

Fig. 14
Fig. 14
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The concentration of hydrogen at the monitoring point.

Figure 15 compares flow streamline patterns under three leakage locations, revealing consistent gas flow behavior where the vortex core ascends before extending toward vortex sidewalls. However, unlike Case 6 where symmetric vortices form on both sides of the leak point, Case 1 exhibits predominantly unidirectional flow constrained by the rear vehicle wall—a confinement effect corroborated by Fig. 13 showing restricted hydrogen diffusion leading to elevated concentration in Case 1. Concurrently, seat obstructions accelerate hydrogen-air mixing, thereby reducing local concentration. Figure 16 reveals that Case 7 exhibits the largest volume of hydrogen-air mixture. This finding corroborates that the seats accelerate the mixing of hydrogen with air, resulting in the formation of a large-volume, low-concentration mixture within the vehicle. Conversely, Case 1 yields the smallest mixture volume. Due to the wall effect, Case 1 leads to the formation of a small-volume, high-concentration hydrogen mixture inside the vehicle compartment.

Fig. 15
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Flow trajectories in space under three different operating conditions.

Fig. 16
Fig. 16
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Volume of combustible hydrogen gas cloud.

Figure 17 shows the vertical concentration distribution of hydrogen at lines 5 and 6, 200 s into three different scenarios. It can be observed that under Case 1 conditions, the concentration of the hydrogen concentration constant layer is the highest, and the concentration within this layer is above the lower explosion limit of hydrogen, posing a greater risk upon ignition compared to Cases 5 and 6. Under Case 6 conditions, the thickness of the hydrogen concentration constant layer is the greatest; however, the concentration within this layer is the lowest, approximately 0.15. Therefore, at the same hydrogen leak flow rate, Case 1 is the most dangerous scenario.

Fig. 17
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The vertical distribution of hydrogen concentration at different leakage locations.

Figure 18 compares the thickness of combustible hydrogen inside the vehicle at 200 s. Under Case 1 conditions, the thickness of combustible hydrogen is the smallest, approximately 0.8 m; under Case 6 conditions, the thickness of combustible hydrogen is about 0.85 m; under Case 7 conditions, the thickness of combustible hydrogen is about 1.07 m, which is a 34% increase compared to Case 1.

Fig. 18
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Comparison of the thickness of combustible hydrogen clouds.

Distribution of hydrogen at different leak rates

Figure 19 shows the distribution of hydrogen under different leak rates. It can be observed that, under different leak rates, the diffusion pattern of hydrogen within the vehicle is essentially similar. However, the higher the leak rate of hydrogen, the greater the distance the 1% hydrogen isosurface spreads at the same moment. The lateral propagation speed of the 1% hydrogen concentration isosurface was calculated using contact with the vehicle’s upper wall as the initiation timing point and arrival at the front wall as the termination point, yielding average lateral diffusion velocities of 0.47 m/s (Case 1), 0.66 m/s (Case 2), 0.78 m/s (Case 3), 0.88 m/s (Case 4), and 0.97 m/s (Case 5).

Fig. 19
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The distribution of hydrogen under different leakage flow rates.

Figure 20 shows the variation of hydrogen concentration at the monitoring point inside the vehicle after the leakage occurs. The data from the monitoring point indicates that the concentration of hydrogen inside the vehicle is greatly affected by the leakage flow rate, with the concentration of hydrogen increasing as both the leakage flow rate and the leakage time increase. However, different leakage flow rates all reached a stable state within 200 s after the leakage occurred, with the hydrogen concentration at the monitoring point exceeding the LEL (Lower Explosive Limit) standard. Among them, the leakage flow rate of 0.0104 kg/s, when the concentration at the monitoring point is stable, is closest to the optimal ignition ratio of hydrogen to air (0.295). Therefore, theoretically, under this leakage flow rate condition, if hydrogen is ignited, it could be more destructive.

Fig. 20
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The concentration of hydrogen at the monitoring point.

Figure 21 illustrates the distribution of hydrogen concentration along data acquisition line 5 when the distribution of hydrogen in the vehicle reaches a stable state at 200 s. The greater the leakage flow rate of hydrogen, the higher the concentration of the hydrogen-gas mixture in the constant concentration layer. However, the thickness of the hydrogen concentration constant layer is almost equal, approximately 0.55 m. This is because the stratified circulation formed at the top of the vehicle is mainly determined by the leakage position and spatial distribution, and the stratified circulation determines the thickness of the hydrogen concentration constant layer.

Fig. 21
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Vertical distribution of hydrogen under different leakage flow rates.

Figure 22 presents the flammable hydrogen cloud thickness formed inside the vehicle at 200 s under varying leakage flow rates, along with the correlation between cloud thickness and leakage rate. The analysis reveals that the thickness of flammable hydrogen-air mixtures increases with higher leakage rates, yet this growth occurs at a diminishing rate as leakage intensifies. Notably, the interface of the flammable hydrogen cloud remains nearly parallel to the ground across all scenarios.

Fig. 22
Fig. 22
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Flammable hydrogen cloud thickness.

Hydrogen explosion

The calculation results of hydrogen leakage in Chap. 2 show that in Case 3, the range span of hydrogen concentration at the monitoring point is quite significant. Therefore, this chapter uses this working condition as the initial condition for the study of hydrogen explosions. Simulations were conducted for different ignition times and ignition positions46, and the distribution of overpressure and temperature after ignition was analyzed.

Different ignition positions

Figure 23 compares the magnitude of overpressure inside the vehicle at different ignition moments. When the ignition source is located at the rear or the middle of the vehicle, the overpressure inside the vehicle is almost equal; when the ignition source is located at the front of the vehicle, the overpressure inside the vehicle is the smallest, and the maximum overpressure drops below 20,000 Pa (causing minor injuries to humans)32. This is because the ignition position is close to the front window, which serves as a pressure relief.

Fig. 23
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In the case of different ignition source locations, the pressure inside the vehicle.

Figure 24 shows the pressure change curves at the side monitoring points of the vehicle under different ignition positions. The maximum overpressure at the monitoring points can be used to estimate the location of the secondary explosion; when igniting at the rear, the secondary explosion is close to monitoring point 8 (1.5 m away from the vehicle), with an overpressure of 9,570 Pa, and the overpressure peak occurs at approximately 0.138 s; when igniting in the middle, the secondary explosion is close to monitoring point 7 (1 m away from the vehicle), with an overpressure of 8,611 Pa, and the overpressure peak occurs at approximately 0.085 s; when igniting at the front of the vehicle, the secondary explosion is close to monitoring point 6 (0.5 m away from the vehicle), with an overpressure of 4,192 Pa, and the overpressure peak occurs at approximately 0.073 s. As the ignition position gets closer to the front window, the time of the secondary explosion gradually shortens, the overpressure value of the secondary explosion also gradually decreases, and the explosion location is closer to the vehicle. This is because the closer the ignition position is to the front window, the less hydrogen gas mixture is expelled from the vehicle during the explosion, and the time for the flame to propagate from the ignition position to the window is shorter.

Fig. 24
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Overpressure on the side of the vehicle under different ignition source positions.

Fig. 25
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Explosion flame temperature cloud map.

Figure 25 is a cloud map of the flame temperature after a hydrogen explosion inside the vehicle, where it takes 0.3 s for the ignition source to appear and the flame to spread throughout the vehicle. It is observed that after the hydrogen is ignited, the flame rapidly develops around, some combustible gases are squeezed out of the vehicle and ignited, forming a fireball outside the vehicle. The flame inside the vehicle continues to propagate towards the front of the vehicle. At 0.1 s, as shown in Fig. 25, it is found that the flame inside the vehicle exhibits faster propagation on both sides and slower in the middle, which may be due to the rear seats accelerating the spread of the hydrogen flame. In some studies, it has also been found that obstacles can accelerate the propagation speed of hydrogen flames24. Therefore, the flame inside the vehicle shows faster propagation on both sides and slower in the middle. At 0.14 s, the flame develops to the outside of the vehicle through the front window, at which time a large amount of hydrogen-gas mixture outside the vehicle is ignited, forming a jet flame in front of the vehicle’s front window. By 0.3 s, the jet flame outside the vehicle is significantly reduced, and the interior of the vehicle is also completely covered by flames.

Figure 26 shows the maximum distance of high-temperature impact under three different ignition positions. It can be compared and found that when the ignition source appears at the rear of the vehicle, the flame propagation distance (\(\:\text{T}>1300\:\text{K}\)), the distance causing severe human injury (\(\:\text{T}>453\:\text{K})\), and the critical injury distance47(\(\:\text{T}>391\:\text{K}\)) are all the greatest; when the ignition source is in the middle of the vehicle, it is the next, and when the ignition source is at the front of the vehicle, it is the smallest. Figure 26(b) compares the maximum horizontal cross-sectional area of the largest volume of flame formed outside the vehicle during the explosion process. After comparison, it is found that when the ignition source is in the middle position of the vehicle, the flame area, the area causing severe human injury, and the area causing critical human injury formed outside the vehicle are the largest. This indicates that when the ignition source is in the middle of the vehicle, the dangerous area formed outside is the largest; when the ignition source is at the rear of the vehicle, the dangerous distance caused by the jet flame is the greatest.

Fig. 26
Fig. 26
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The extent of injury under different ignition source positions. (a) The farthest distance affected by the flame; (b) The area of the flame outside the vehicle.

Different ignition times

For the mixed gas that leaks at the rear of the carriage, ignition is carried out at 10 s, 20 s, 30 s, 40 s, and 50 s moments, respectively, to compare and analyze the overpressure and flame distribution in the vehicle under different ignition times. Figure 27 shows the overpressure change curve of monitoring point 4 inside the vehicle after ignition at different moments. Observation results show that, overall, the overpressure inside the vehicle first increases and then decreases with the increase of ignition time. The overpressure inside the vehicle reaches its peak when ignited at the 40th second. The overpressure increases rapidly before 30s and slows down between 30s and 40s, and after 40s, the hydrogen concentration at the monitoring points inside the vehicle is already far higher than the optimal concentration for hydrogen combustion, so the overpressure inside the vehicle begins to gradually decrease after 40s.

Fig. 27
Fig. 27
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Overpressure inside the vehicle under different ignition moments.

Figure 28 shows the pressure change curve of the side monitoring points of the vehicle at different ignition times. Unlike the overpressure inside the vehicle, the external peak pressure always increases with the increase of ignition time. This is because as the leakage time increases, the amount of hydrogen expelled outside the vehicle during the explosion also increases. At 10 s, there is almost no external explosion outside the vehicle, because the volume of combustible hydrogen inside the vehicle at this time is small, and only a small amount of hydrogen is expelled outside, which is not enough to trigger a secondary explosion outside the vehicle. Under different ignition times, the maximum overpressure of the secondary explosion always appears at the position of monitoring point 8. As the ignition time increases, the pressure difference between monitoring point 8 and monitoring point 9 gradually decreases, indicating that the later the ignition time, the farther the position of the secondary explosion, but the impact is smaller (< 0.25 m).

Fig. 28
Fig. 28
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Overpressure on the side of the vehicle under different ignition moments.

Figure 29 illustrates the distances of the flame, severe human injury temperature, and critical human injury temperature at different ignition moments. Observations and comparisons reveal that as the ignition moment increases, the distance of harm caused by the hydrogen explosion gradually increases; however, the rate of increase in the harm distance decreases as the ignition time gets later. Taking the distance causing severe human injury as an example, when ignited at 20 s, the distance increased by 2.89 m compared to 10 s, with a growth rate of 54.32%; when ignited at 30 s, the distance increased by 1.80 m compared to 20 s, with a growth rate of 21.92%; when ignited at 40 s, the distance increased by 0.24 m compared to 30 s, with a growth rate of 2.40%. The growth of the harm distance outside the vehicle follows a similar pattern to the overpressure inside the vehicle, indicating that the harm distance outside the vehicle may be significantly related to the overpressure inside the vehicle. The greater the overpressure inside the vehicle, the farther the distance the hydrogen-gas mixture is propelled. However, when comparing ignition at 50 s with 40 s, an increase in the harm distance is still observed, despite a decrease in the overpressure inside the vehicle from 40 s to 50 s, as shown in the figure. This suggests that as the time of the ignition source increases, the amount of hydrogen expelled outside the vehicle also increases, which can lead to an enhancement of the secondary explosion overpressure of the hydrogen-gas mixture outside the vehicle, increasing the dangerous distance outside.

By examining the distribution and magnitude of explosion pressure and temperature at different times, it can be concluded that the high temperatures resulting from hydrogen explosions are the primary source of harm. Figure 29(b) shows the areas of the flame outside the vehicle, the area of severe human injury temperature, and the area of critical human injury temperature at different ignition moments; as the ignition moment increases, the area of harm caused by the hydrogen explosion also gradually increases.

Fig. 29
Fig. 29
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The extent of injury under different ignition times. (a) The farthest distance is affected by the flame. (b) The area of the flame outside the vehicle.

Findings and practical implications

The study highlights critical findings on hydrogen leakage and explosion dynamics in fuel cell buses. Hydrogen leakage creates a stratified concentration layer at the cabin’s top, with the highest concentrations observed near the rear wall of the vehicle. With increasing leakage rates, hydrogen diffuses more quickly, and its concentration rises. Ignition causes a very sudden rise in internal pressure and creates secondary explosions outside the vehicle. Compared to overpressure effects, thermal hazards extend far away. The furthest distance of flame propagation is 10.88 m for the case of rear ignition and corresponds to the furthest thermal hazard zone. For overpressure, with a peak value of 40 s after leakage, it decreases afterward. The explosion effects outside increase with increasing leakage time. Under-seat leaks reduce diffusion, while the resultant layers of hydrogen concentrations are thicker. Conclusion: These findings constitute a solid ground for promoting safety in hydrogen-powered buses through better sensor placement optimization, ventilation strategies, and explosion mitigation protocols.

This study gives recommendations that are applicable to ensure safety and operational reliability in hydrogen fuel cell buses. Key deductions indicate that there should be strategic positioning of hydrogen sensors in accident-prone areas, such as the back part of the vehicle due to accumulation, among other places. Moreover, cabin ventilation systems should be improved to decrease the flammable levels of hydrogen and prevent hazardous stratified airflow patterns. Ignition timing and location also provide important source term data for emergency response planning, including the formulation of evacuation plans, the establishment of safe standoff distances, and the design of explosion mitigation methods. The results are expected to provide useful input on the design and construction of bus structures to resist over-pressurization and flame propagation and, consequently, to minimize the consequences of a potential explosion. These will be coupled with the ability of stakeholders to better assure the safety of hydrogen-powered buses, building public confidence and allowing hydrogen to assume its full role as a clean, sustainable transportation fuel.

Conclusions

This paper established a finite element model for hydrogen leakage and explosion in a hydrogen fuel cell bus using the CFD analysis software Fluent. A detailed analysis of the diffusion process of hydrogen leakage into the vehicle was conducted, and the situation where the combustible gas was ignited after hydrogen leakage to form an explosion accident was simulated, obtaining the safety distance under relevant conditions. The study concludes that after hydrogen diffusion stabilizes, stratified airflow forms a constant-concentration hydrogen layer at the top of the vehicle. Leakage location significantly impacts hydrogen behavior: leakage at the rear of the vehicle results in higher hydrogen concentration but smaller combustible volume, whereas leakage under the rear seats produces lower concentrations but larger combustible volume and thicker concentration layers. Higher leakage flow rates lead to increased hydrogen concentrations, faster lateral diffusion, and thicker single-layer mixtures, though the stabilized layer thickness remains consistent. Upon ignition, thermal hazards extend farther than overpressure effects. Rear and center ignition sources generate the highest internal overpressure, which initially increases with ignition timing but decreases after peaking, while external secondary explosion overpressure continues to intensify with prolonged leakage.

Recommendations and future perspectives

Based on the simulation results in the text, two recommendations are proposed to enable early detection of hydrogen leakage and reduce hydrogen accumulation:

Seat structures impede hydrogen diffusion toward the vehicle roof, prolonging the dispersion time. Therefore, hydrogen concentration sensors should be installed beneath the seats to rapidly detect leaks. Additionally, leveraging the diffusion patterns of hydrogen within the cabin, a continuous array of concentration sensors should be deployed along the vehicle’s lateral and vertical axes. By analyzing the response sequence of lateral sensors, the phase of hydrogen diffusion can be determined. Similarly, the spatial distribution data from vertical sensors can quantify the thickness of the hydrogen cloud layer, enabling assessment of potential explosion hazards.

The volumetric expansion of leaked hydrogen occurs primarily during the lateral diffusion phase. To disrupt this process, ventilation outlets should be integrated into the vehicle roof. These outlets will expedite hydrogen discharge, block lateral diffusion pathways at the top, and effectively reduce hydrogen accumulation near the roof.

During the research process related to this work, to reduce the amount of calculation and increase the quality of the mesh, the model of the vehicle was simplified, and the ignition position was also idealized. Geometrical detailing of the vehicle and realistic ambient conditions are future subjects of further studies. Other possibilities concern further analysis of variations in the placement of the ignition sources and variations concerning external conditions, such as wind or temperature. Above all, more advanced safety systems and explosion-mitigating materials could be studied.