Figure 1 presents a schematic of the experimental apparatus designed to assess hydrogen safety in varying pipeline geometries. The assembly consists of three primary components: a high-pressure hydrogen tank with an internal diameter of 40 mm, a series of downstream pipes, and a capacious exhaust chamber measuring 500 mm in width. The downstream pipes, delineated in the lower section of the figure, showcase straight sections as well as pipes with 90° and 60° bend angles. These variations are intended to evaluate the impact of different pipe geometries on hydrogen flow and safety characteristics. For the bent pipe scenarios, the inlet section preceding the bend is 120 mm long, while the outlet section extends 240 mm from the bend, both measured along the centerlines, ensuring a consistent evaluation framework across all configurations. The system incorporates a burst disk strategically positioned to ensure the deliberate release of hydrogen upon reaching a pre-determined pressure. Prior to commencing each experiment, a thorough evacuation of air from the hydrogen tank is performed using a vacuum pump, thereby eliminating any potential for air-hydrogen mixing, which could influence the results. The gas compression sequence follows, with hydrogen gradually introduced into the tank until the calibrated burst disk responds to the exceeded pressure threshold, initiating the test sequence. Strategically stationed along the pipes are pressure transducers and light sensors, with the arrangement of sensors including positions at the intrados, extrados, and center of the bends. These sensors are key to capturing real-time data on pressure fluctuations and the propagation of light from hydrogen flames should ignition occur. The precise deployment of these sensors is essential and is triggered by the pressure wave emanating from the initial pressure transducer. More details about the gas compression system, data acquisition system, and sensor information can be found in the references (Duan et al., 2016; Gong et al., 2017).

Figure 4 depicts a comparison between experimental and numerical results of pressure variations observed in a pipe with a 90° bend and a burst pressure of 6.21 MPa. The moment denoted as t ₁ corresponds to when the initial group of shock waves passes the pressure transducer S1, resulting in the expansion waves inside the pipe, which is marked by a pronounced pressure surge. The correspondence between the experimental data and the simulation is quite satisfactory, particularly with respect to the arrival times of the subsequent shock waves, indicated by t ₂, t ₃, and t ₄.

The temporal resolutions for experiments and simulations are 0.1 ms and 0.02 ms, respectively. Additionally, the experimental data has been subjected to a 10-point smoothing average for reducing noise and clarifying the overall trend. Due to these reasons, the simulations are able to depict the dynamics of reflected shocks with more clarity and definition as compared to the experimental data. Therefore, the following analysis are mainly focused on the simulation results.

As depicted in Figure 4, an oscillatory pattern in the pressure waves between times t ₁ and t _1R is indicative of self-ignition having transpired. This is reflected by a narrower variation range in the pressure readings of transducer S2 between t ₂ and t _2R when compared to those of S1, suggesting an increased intensity of ignition at the location of sensor S2. This interpretation is bolstered by the concurrent experimental light sensor data, which reveal a rising trend in the photodiode signals from S1 between t ₁ and t2. From this observation, it may be inferred that the numerical results provide a richer depiction of the pressure wave characteristics, thereby affirming the capability of the numerical method to furnish an in-depth explanation of the ignition mechanism.

The presence of a high-pressure hydrogen discharge into a pipe with a bend is hypothesized to result in the generation of reflected shock waves. These reflections are postulated to account for the elevated pressure readings registered by S1 and S2, markedly surpassing those recorded by transducers S3 and S4. Notably, sensor S2 captures a peak pressure value, approximately thrice the magnitude of the stable propagating shock wave, at time t ₂. Despite the brevity of the oscillatory phase of this reflected pressure, the insights deduced from these limited measurements are corroborated by the experimental findings reported in reference (Uchida et al., 2011). Beyond the 200 µs mark, the intensity of the oscillations at S2 exhibits a discernible decrease, potentially attributable to the forward movement of the ignited flame and the resurgence of dominance by the hydrogen expansion waves.

The pressure of the reflected wave serves as a metric for the vigor of the transverse shock wave. Figure 5 illustrates that a pipe with a 60° bend induces a more intense reflected shock wave. The simulation outputs, which represent an averaged value over 50 µs commencing at the peak pressure point, generally exhibit strong concordance with experimental observations. Variations observed in the high-pressure burst region may be attributable to the real-gas effects or the omission of heat conduction between the gas and the solid boundaries. Furthermore, a smaller bend angle in the pipe leads to a greater deflection in flow, resulting in multiple shock waves reflecting along the upstream direction with augmented intensity.

The average speed of the shock wave can be determined from the timing of detections by the pressure transducers and their intervening distances, as demonstrated in Figure 6. The velocity of the incident shock wave diminishes as it navigates through the bend. This attenuation is due to the cumulative effect of expansion waves produced when preceding waves collide with the walls, which reduces both the pressure and the momentum of the incident shock wave. Notably, in certain scenarios, the mean velocity of the shock wave actually increases after negotiating the corner. This acceleration is attributed to the more pronounced effects of reflections from subsequent shock waves and the interaction between shocks and vortices, which eclipse the dampening influence of expansion waves stemming from auto-ignition phenomena within the bends.

The phenomenon of spontaneous ignition during high-pressure hydrogen release into straight pipes has been the subject of extensive investigation. The summarized understanding of the process involves a shock wave that travels into the ambient air, heating it through compression. The highest temperatures are typically observed within the boundary layer, where a decrease in velocity and a significant magnitude of vorticity prevail. Under critical conditions, this setup triggers spontaneous ignition, facilitated by turbulent mixing and the thermal effects of shock waves, as detailed in references (Uchida et al., 2011; Bragin et al., 2013; Lee et al., 2015). Figure 7 provides insights into the self-ignition process, showcasing the temporal evolution of temperature and hydroxyl (OH) mass fractions. Generally, the shock wave is followed by a contact surface which separates the cold hydrogen and the heated mixture, as depicted. The thickness of the heated air layer, demarcated by the isoline f _H = 0, expands progressively over time. If the shock-vortex interaction in strong enough, chemical reaction will propagate in the direction from the wall to the pipe center as the contact surface propagates downstream. Given the thorough analysis of ignition mechanisms in straight sections, our investigation is primarily concerned with the variation in physical phenomena occurring within the bent regions of the pipe.

In scenarios involving a straight pipe with a burst pressure of 2.18 MPa, neither experimental observations nor simulations indicate the onset of ignition. However, the presence of flames was registered by light sensors S3 and S4 under identical conditions in pipes with 90° and 60° bends. To explain the discrepancies observed in these configurations, simulations with burst pressure of 2.18 MPa were conducted.

Figures 8, 9 presents temperature variations over time in the 90°- and 60°-pipes respectively. The figures start from 95 µs, this initial time step, the pressure wave front has collided with the wall and reflected, forming a localized high-temperature and pressure zone around the bend that is not yet conducive to ignition. Isolines of stoichiometric mixture fraction (f _H = 0.029) and mixture/air contact surface (f _H = 0) are also shown in Figure 8. At this moment the reflected shocks are about to colliding with following mixtures which could be distinguished by isoline f _H = 0. By 100 µs, the clearly defined boundaries of the reflected shock begin to deform and exhibit a wrinkled texture, indicating the heating of the mixture and the formation of small vortices in close proximity to the stoichiometric line induced by the collision process. The resulting vortices enhance turbulent mixing and promote heat transfer. Consequently, spontaneous ignition is observed at 102 µs within a region adjacent to and slightly richer than the stoichiometric line. Disturbance in the vicinity of isoline of f _H = 0 is weak, and most vortices are observed in the rich mixture (except in the boundary layers), which means that the chemical reaction rate is very limited. However, with the contact between the first group of shocks and the inner wall surface, the heated air and mixture will be further heated due to compression and deceleration. Then reflected waves will be generated continuously and interact with subsequent pressure waves, as seen in the figures from time 100–140 µs. Within this interval, the air trailing strong shock fronts is substantially heated, creating conducive conditions for hydrogen reactions. The air behind strong shocks is readily heated for the hydrogen to react. Enlarged figures of ignition region from 102 to 115 µs are also shown in Figure 8. It is found that shock interactions with chemistry can create mixing and reacting regions such as a vortex ring in the bent area. Therefore, spontaneous ignition can be initiated and developed more easily.

Figure 9 depicts the spontaneous ignition process within the 60° pipe. The hot, reflected shocks colliding with compressed mixtures result in higher temperatures and more reactive mixtures, potentially decreasing ignition delay and facilitating ignition. Nevertheless, two ignition regions exist in 60° pipe. Ignition dynamics of the lower one are comparable to those observed in 90° pipe, albeit with a delayed ignition onset and an accelerated growth rate, as evidenced by the magnified details in the lower portion of Figure 9. The reason is attributed to that the reflected pressure wave interaction is stronger due to more violent deceleration. For pressure waves passing the intrados (point 1 showed in Figure 1) in both pipes, wave diffraction is observed continuously which resulting in considerable vortex. Moreover, the diffraction will collide with the reflected, heated air from 95 µs which leads to self-sustained ignition in the higher region. Compared to the case in 90° pipe, the same diffraction pressure wave fails in ignition. The reason maybe that the colliding in 60° pipe is more strenuous and the reflected air is more compressed and heated. One proof is that the heated air region downstream is thinner in 60° pipe.

To gain insights into the ignition mechanism and flame structure from a statistical perspective, scatter plots correlating temperature and mixture fraction at varying temporal stages are illustrated in Figure 10. The scatter data represented in Figure 10 was gained from comprehensive spatial sampling across the entire domain, ranging from the burst disk to the end of the pipe. The equilibrium temperature—computed based on a standard condition of 298 K and 1 atm—is delineated via red dashed lines. Initially, an uptick in temperature is observed within fuel-lean mixtures, followed by the temperature peak transitioning towards richer mixtures. This shift significantly demonstrates that ignition preferentially initiates under hot or stoichiometric conditions, featuring a shorter ignition delay. This phenomenon is different from premixed flame where auto-ignition starts from fuel-lean area (Echekki and Chen, 2003). Temperature reaches maximum in stoichiometric mixture fraction, and then decreases to a stable value from f _H approximately equal to 0.1. This finding suggests that self-ignition transpires within a notably confined range of mixture fractions, with the most reactive mixtures situated close to stoichiometry. The relationship between mixture fraction and ignition propensity is corroborated by the data presented in Figure 7, which outlines the temperature profiles, and Figure 10, which details the ignition occurrences across different mixture fractions. The alignment of data between these figures provides a cross-validation for the conclusion that stoichiometric mixtures are the most reactive and, therefore, the most likely to undergo self-ignition under conducive conditions. According to temperature ranges and distributions, it can be concluded that reactions in 60°-pipe are more intensive than in 90°-pipe. Furthermore, extensive non-reacting but heated mixtures for all cases imply that flame propagation even detonation is promising.

Figure 11 presents numerical results of temperature profiles in a 90° pipe subjected to a burst pressure of 6.40 MPa, examining the influence of bend geometry on the downstream flame structure. Illustrated alongside are the stoichiometric mixture fraction (f _H = 0.029) marked by a blue solid line and the boundary demarcating the mixture from the air (f _H = 0) indicated by a red solid line. Given the elevated burst pressure, ignition can occur almost instantaneously in the reactive region near the boundary layer, resulting in flame formation as the flow traverses the bend. At 56 µs, flame sustainability is compromised along the upper wall due to flame-shock diffraction; nonetheless, at 64 µs, the reflected shock waves intensify, creating a region of extremely high temperature. Consequently, any prior extinction is overcome, with re-ignition being consistently observed between 66 and 74 µs. This sequence of events leads to significant shock heating and the emergence of a self-sustaining flame that propagates through the remainder of the tube. Once again, the most reactive area is identified as being slightly rich in mixture. It is evident that flames develop more extensively in bent pipes compared to straight ones. As previously mentioned, vortices generated near the boundary layer after navigating the bend contribute to the widespread distribution of reaction zones. In contrast, in a straight pipe, the heated area is considerably broader, leading to a less turbulent mix and a more confined reaction space, as indicated by the OH profile in the lower graph of Figure 7. The presence of bends appears to enhance turbulent mixing, promoting reactions throughout the downstream regions. It is thus deduced that the flame propagating along the boundary layer is a result of turbulence-induced reactions.

Figure 12 presents the pressure profiles along the intrados (point 1 indicated in Figure 1), extrados (point 2), and the centerline (point 3) for three distinct types of pipes. The profiles are examined at the specific moment when the pressure wave reaches the pipe outlet, providing a snapshot of the pressure loads. As seen in Figure 2, the pressure typically exhibits high oscillations. To enhance the clarity of the graphical representation, a smoothing process has been applied to the sample data. In the straight pipe, the pressure readings do not display significant variation across different points on the pipe wall. Conversely, in the bent pipes, the pressure prior to the bend is notably higher, attributed to the effect of reflected waves. The calculated average pressures between sensors S1 and S2, as well as S3 and S2, reveal that the pressure drop escalates with decreasing bend angle. The pressure profiles clearly demonstrate that the pressure loads in the bent pipe sections are greater compared to the corresponding straight tube sections near the corner in the experiments involving bends.

It is observed that the reactions within a 60° bend are significantly more intense than those in a 90° bend. This increased intensity is attributed to greater deceleration and subsequent compression of the gas mixture at sharper angles, which can enhance the likelihood of flame acceleration and possibly lead to detonation in confined spaces. In light of these insights, it is recommended the following practical measures for the design and safety of hydrogen storage and transport systems:

1) Minimize Sharp Bends: Where possible, design pipelines to avoid sharp bends. The usage of gentler curves helps to minimize abrupt decelerations and compressions that can escalate reaction intensities.