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.
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.
To quantitatively analyze the vertical and lateral flow of hydrogen, 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.
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.
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 vehicle. 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.
To compare the diffusion and distribution of hydrogen under different leak locations, 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.
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.
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.
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.
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.
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).
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.
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.
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.
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 positions, and the distribution of overpressure and temperature after ignition was analyzed.
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). This is because the ignition position is close to the front window, which serves as a pressure relief.
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.
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 flames. 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 (), the distance causing severe human injury (, and the critical injury distance() 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.
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.
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).
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.
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.