Towards safer hydrogen refuelling stations: Insights from computational fluid dynamics on LH ₂ leakage

Scaling hydrogen as a key clean energy carrier necessitates a comprehensive understanding of the safety aspects of hydrogen including liquid hydrogen (LH ₂ ). Hence, this study presents a detailed computational fluid mechanics analysis to explore accidental LH ₂ leakage and dispersion in a hydrogen refuelling station under varied conditions which is essential to prevent fire and explosion. The correlated impact of influential parameters including wind direction, wind velocity, leak direction, and leak rate were analysed. The study shows that hydrogen dispersion is significantly impacted by the combined effect of wind direction and surrounding structures. Additionally, the leak rate and leak direction have a significant effect on the development of the flammable cloud volume (FCV), which is critical for estimating the explosion hazards. Increasing wind velocity from 2 to 4 m/s at a constant leak rate of 0.06 kg/s results in an 82% reduction in FCV. The minimum FCV occurs when leak and wind directions oppose at 4 m/s. The most critical situation concerning FCV arises when the leak and wind directions are perpendicular, with a leak rate of 0.06 kg/s and a wind velocity of 2 m/s. These findings can aid in the development of optimised sensing and monitoring systems and operational strategies to reduce the risk of catastrophic fire and explosion consequences.


Introduction
Hydrogen, as the "energy of the future", is a vital component in the global shift towards a cleaner and more sustainable energy landscape.As the global community recognises the urgent need to decarbonise and mitigate the effects of climate change, hydrogen has attracted much attention.The high energy density, efficiency, and environmental benefits granted hydrogen great competitiveness as a key player in the transition away from traditional fossil fuels, particularly in the field of hydrogen-powered fuel cell vehicles, such as buses, trains, boats, and trucks (Aditiya and Aziz, 2021).The realisation of this potential depends on a strong hydrogen refuelling stations (HRSs) network.These stations are crucial for a hydrogen-based transportation infrastructure, providing accessibility and convenience for hydrogen fuel cell vehicles.As the demand for hydrogen increases, the development and safe operation of HRS become pivotal to the success of the emerging hydrogen economy.This necessitates careful safety assessment, given the unique characteristics and potential hazards associated with hydrogen as a fuel (Singh et al., 2015).
The recent investigations on hydrogen-related incidents, including explosions, leakage, near-misses, ruptures, reactions, fire, and explosion incidents, underscore the need for enhanced safety measures in various aspects of the hydrogen industry.With fire explosions accounting for 26% of incidents and explosions close behind at 25%, the potential risks posed by hydrogen infrastructure are apparent.These statistics show the incidence of near-misses and the severe consequences of fire and explosions, highlighting the practical relevance of studying safety protocols in hydrogen refuelling stations (Wen et al., 2022).Recent incidents, such as those documented in (PNNL-29731, 2020), shed more light on specific occurrences, including leaks in LH₂ vent lines and tanks and fires in delivery trucks, demonstrating the real hazards faced within the liquid hydrogen domain.For instance, the explosion incident at the Hydrogen refuelling station in KjØrbo, Norway, attributed to human error during plug installation, serves as a reminder of the necessity for precise operational procedures (Asa et al., 2019;Fuel and Hydrogen, 2024).Similarly, the fire outbreak at an HRS in California in July 2023, although the cause remains under investigation, underscores the need for rigorous safety standards, mainly when dealing with fuel sources like Blue hydrogen produced from natural gas and stored as LH₂ (Buckley, 2023).Moreover, handling a minor incident involving a flame discharge on the LH₂ carrier Suiso Frontier in 2022, attributed to an electrical component failure, highlights the importance of thorough equipment inspection and maintenance to mitigate potential risks (Australian Transport Safety Bureau, 2023, 2024).These recent incidents highlight the urgency for comprehensive safety protocols and risk management strategies within the evolving landscape of hydrogen infrastructure.
Hydrogen is often stored and dispensed at high pressures and in cryogenic states.Compared to compressed gaseous hydrogen (0.03 kg/ L), cryogenic liquid hydrogen (LH₂ has a much higher density (0.07 kg/ L), which makes it ideal for transportation, storage, and quick filling (Niaz et al., 2015).At liquid HRSs, storage tanks are maintained at low temperatures (~20 K).The stored liquid hydrogen is vaporised for dispensing into fuel cell vehicles, either directly at the dispensing unit or through intermediate vaporisation systems (Genovese et al., 2020;Guo et al., 2023;Tang et al., 2020).While diverse storage options are available for various applications, there are limitations and safety concerns with using both high-pressure gaseous hydrogen and cryogenic liquid hydrogen (Moradi and Groth, 2019;Zheng et al., 2013).For gaseous hydrogen, these concerns are linked to local cracks on the tank, burst or localised fire, while the problem with LH₂ is that they have to be continuously consumed to avoid pressure build-up and finally burst (Cirrone et al., 2022).The storage tank materials also become brittle at low temperatures, increasing the risk of tank failure.In both storage options, due to the unique properties of hydrogen, leaks can easily happen due to mechanical failure or human errors.Meanwhile, leaked hydrogen can easily mix with air to form a flammable cloud with a wide flammable range of 4%-75%.If this flammable mixture ignites, an explosion is likely to happen, resulting in overpressure and high temperatures that threaten the safety of nearby equipment and personnel, particularly in HRSs (Abohamzeh et al., 2021).
Ensuring the integrity of different modules in an HRS such as storage systems, pipelines, and dispensers is crucial to prevent leaks and the associated safety risks such as fire and explosion.Experimental studies provide insights towards leaked hydrogen and its subsequent dispersion, flame, and explosion behaviours (Liu et al., 2023).Nevertheless, experiments are often conducted on a small scale due to safety concerns, and the findings from an experimental setup are also often restricted to that particular scenario.There is a need to obtain a detailed physical understanding of a hydrogen leakage scenario, especially at an industrial or urban scale (Jäkel et al., 2014).With accurate data obtained from experiments, validated numerical simulations could help better understand hydrogen behaviour, safety measures, and potential hazards.Several studies applied computational fluid dynamics (CFD) simulations, to understand the impact of different operational and environmental parameters, shedding some light on requirements for safe handling of hydrogen (Shibani et al., 2022).Other techniques such as probabilistic risk analysis have been also developed for safety assessments of HRS.
The key focus of the previous studies has been on safety assessment relevant to handling gaseous hydrogen due to its common application in HRS.Different aspects, including leakage, fire, and explosion have been extensively studied.Schefer et al. (2011) investigated interactions between hydrogen jet fire and wall barriers as a way of mitigating the hazards.Later, Tsunemi et al. (2019) conducted quantitative risk assessments in an HRS, and they found that setting proper separation distances and barriers eliminates the fatal risks to workers and consumers in HRS.In addition, Kown et al. (Kwon et al., 2022) performed a quantitative risk assessment of gaseous HRS using Hy-KoRAM and Phast/Safeti.By cross analysing the impact and risks, they were able to produce reliable recommendations for further development of an HRS.Liu et al. (2023) established a full-scale numerical model for a mobile HRS and analysed the hydrogen diffusion behaviour after leakage, and the potential risk of explosion using numerical simulations.Different ventilation conditions for the mobile HRS with ambient wind were investigated.A minimum safe distance of 313 m was determined in hydrogen explosion scenarios.Wang et al. (2023) proposed a dynamic risk assessment method based on Dynamic Bayesian Network (DBN) for LH₂ leakage in HRS.They identified that human factors and corrosion are the two most significant hazard sources.
While gaseous hydrogen storage is the common choice for refuelling stations, there are some recent interests in the application of cryogenic liquid hydrogen in HRSs (He et al., 2021).This is due to the advantages that cryogenic hydrogen offers.Cryogenic hydrogen has a significantly higher energy density than high-pressure gaseous hydrogen, allowing for more efficient storage in smaller volumes.LH₂ is also considered cost-effective for high-demand or mid-range distance transportation.Handling high-pressure gaseous hydrogen can be more complex and poses safety concerns due to the need for specialised infrastructure (Cui et al., 2023).Storing hydrogen at low pressures simplifies transportation and reduces safety risks associated with gaseous hydrogen (Guo et al., 2023;Lu et al., 2023).
In recent years, several investigations have focused on enhancing the safety of HRSs by examining the behaviour of hydrogen releases across various scenarios (Niaz et al., 2015;Singh et al., 2015).Modelling HRSs using CFD simulations demonstrated that the dispersion properties of hydrogen leaks are significantly affected by the leak angle, wind direction, arrangement of components, temperature, and humidity (Qian et al., 2020a;Sun et al., 2022;Yuan et al., 2022).Mohammadpour and Salehi (2024) developed an accurate numerical model to study cryogenic hydrogen release from circular and high aspect ratio nozzles using OpenFOAM.The outcomes, closely aligning with experimental data, suggested potential applications for expansive facilities, underscored by comparable hydrogen mass fractions and temperature decay rates between circular and high aspect ratio nozzles.Tian et al. (2023) developed a new model for liquid hydrogen on heavy-duty trucks.The model investigated situations when the pressure-reducing valve was damaged, leading to a leak and fire.The research is beneficial for designing standards for LH₂ storage and transportation.Baraldi et al. (2009) utilised CFD simulations for a liquid HRS, where an assumed leakage accident occurred during refuelling.Various wind directions were evaluated for mitigated scenarios, revealing that the role of wind in reducing the size of flammable clouds, crucial for minimising overpressures in the event of an explosion, is not consistently positive and depends on both the wind direction and the structures of the HRS.
As mentioned, understanding LH₂ leakage and the development of the flammable cloud in HRSs is critical to prevent its accumulation in concentrations that could lead to ignition and consequently fire and explosion (Baraldi et al., 2009;Qian et al., 2020b;Shao et al., 2018).However, despite previous studies on HRSs safety, some concerns persist, necessitating further exploration, particularly for the application of LH₂ in HRSs.The research priorities workshop at Québec concluded that accident physics of liquid/cryogenic hydrogen behaviour is the top priority for further investigation and analysis.Under accident scenarios for liquid/cryogenic hydrogen, there is a lack of studies on the impact of complex geometries on dispersion and consequently explosion (Keller et al., 2022).
The focus of this study is to assess the correlated impact of the environmental and operational parameters on the development of flammable hydrogen clouds during the accidental release of LH 2 in an HRS.While previous studies have touched upon individual aspects of hydrogen dispersion, this research uniquely integrates multiple critical parameters, including the wind direction, wind velocity, leak direction, and leak rate to provide a holistic understanding of flammable cloud dynamics.By considering these factors together, the study aims to understand the dynamics of flammable cloud formation comprehensively.The present research utilises advanced computational simulations to analyse the effects of these parameters on flammable clouds' behaviour and dispersion patterns.The interplay between these factors is pivotal in assessing the dynamics of hydrogen dispersion and the resultant flammable cloud expansion within the flammable range of 4%-75%.This study is beneficial to design effective sensing systems for early detection of hydrogen in HRSs.It also contributes to developing safety regulations and standards and emergency responses for adopting LH₂ in HRSs, ensuring wider acceptance of hydrogen energy with reduced risks.

Problem description
The HRS layout incorporates a high-pressure cascade storage and a gas compressor for ongoing replenishment (25 kg/h flow rate, 94.4 MPa outlet pressure).The cascade storage consists of different units, each with usually 5 pressure vessels, meeting refuelling needs and minimising the compressor's flow rate.Here, following previous works (Ehrhart, 2019;Ehrhart et al., 2021), we have simplified the components.Fig. 1 shows a schematic view of the HRS which is established based on the specifications given in the NFPA 2 code (NFPA 2, 2020).The reader is referred to Sandia's report for further details on the NFPA 2 requirements (Hecht, 2018;Ehrhart et al., 2020).The LH₂ storage tank is located at the site of the HRS, enclosed in three directions by 3 m high walls (Ehrhart et al., 2020).Further information on dimensions is provided in Table 1.
The current study focuses on the combined effects of wind direction and its intensity which play a significant role in determining the dispersion of leaked hydrogen (Baraldi et al., 2009;Giannissi et al., 2014;Pu et al., 2019;Tang et al., 2020;Yuan et al., 2022).The wind velocities of 2 and 4 m/s are applied in both north and west directions, spanning wind directions parallel, perpendicular, and opposing the leak direction.The selected values represent the most comment wind velocity in New South Wales in Australia as reported by the Bureau of Meteorology: Australia's official weather forecasts (Bureau of Meteorology, 2010).The ambient temperature is kept constant at 290 K (Australian Government Bureau of Meteorology, 2020) obtained from the average annual temperature in New South Wales in Australia.Consistent with previous studies (Caponi et al., 2021;James et al., 2014), the leak rate is considered as 0.05 and 0.06 kg/s.The case study is performed for the three different directions of hydrogen leak: in the positive horizontal direction (x⁺), negative horizontal direction (x⁻), and vertically downward direction (z⁻) which are marked in Fig. 1.The horizontal releases are at the same height of 1.72 m, slightly higher than the bottom of the cylinder.However, the vertical leak is at the bottom of the storage cylinder and has a height of 1.25 m.The leak positions are selected by considering the obstacles around the liquid hydrogen storage tank to study the effects of the obstacle in the dispersion of the flammable cloud.Various combinations of parameters are investigated to understand the correlated impacts of these parameters on the liquid hydrogen dispersion.Table 2 provides further details on the parameters for different cases.

Governing equations
The numerical analysis of the project utilises FLACS-CFD (V22.1 r2), engaging the Reynolds-averaged Navier-Stokes (RANS) equations.The solver applies a second-order scheme in space and a first/second-order scheme in time.FLACS-CFD employs the distributed porosity concept to precisely represent complicated geometries on relatively coarse computational meshes.This method allows large objects and walls to be represented on-grid, while smaller objects use sub-grid interpretation.In numerical analysis, the porosity field indicates local blocking and limi-  tation, enabling sub-grid objects to influence flow resistance, turbulence generation, and flame folding.Cryogenic liquid hydrogen release involves complex phase changes (i.e.condensation, evaporation and freezing) at the discharged point.However, simplified models can be adopted when the focus is on the far field.Following previous studies (Alfarizi et al., 2023;Gexcon AS, 2023;Papanikolaou et al., 2012;Yuan et al., 2022), a pseudo-source model is adopted for simulating liquid hydrogen release which simplifies complex heat and mass transfer at the discharge points.More details on the release model are given below.The governing equations for fluid flow include the conservation of the mass, momentum, energy, and fuel mass fraction expressed as.
where ρ stands for density, p for pressure, t for time, and u for velocity.x denotes general coordinates, whereas subscripts i and j symbolise the notation for the directions.In the continuity equation, ṁ represents the mass flow rate, and V shows the control volume followed by the momentum equation where g signifies the acceleration due to gravity, whereas in the energy equation h stands for enthalpy and Q for energy source terms.Y fuel stands for the fuel mass fraction, and R fuel refers to the fuel reaction rate.F o,i and F w,i indicate the resistance offered by the subgrid obstructions and walls to the flow.β v and β j are the cell volume and surface porosities, respectively.The wall friction, F w,i , can be expressed as where τ w,i is the shear stress due to walls and expressed as follows.
where E + is a wall function constant and assumed as 11.
The turbulence model solves the transport equations for kinetic energy, k, and dissipation rate, ε, which are given as (Liu et al., 2023) where σ i,j is a stress tensor, P k and P ε are the production rates of k and ε, respectively.μ eff is the effective viscosity, and C 2e , σ k , σ h , and σ ε are model constants.
The pseudo-source model is based on the conversation of mass and momentum.The primary action requires utilising Bernoulli's equation to calculate the outlet mass flow rate (m o ) of LH₂, considering storage pressure (P o ), ambient pressure (P atm ), the density of LH₂ in the storage tank (ρ o ), outlet area (A), and flow coefficient (C) as shown in Eq. ( 10).The flow coefficient is typically set to 0.62 (Yuan et al., 2022).
Bernoulli's equation is applied to calculate the outlet mass flow rate of LH₂ and outlet velocity, where the flash mass fraction and isenthalpic expansion are estimated from the National Institute of Standards and Technology (NIST) equation of state and calculated as (Giannissi and Venetsanos, 2018) where h o signifies the enthalpy of saturated liquid at storage pressure.h g and h l are the enthalpy of saturated liquid and saturated gas at ambient pressure, respectively.x shows a flash mass fraction, and v o is the exit velocity.ρ g and ρ l denote the saturated gas and saturated liquid density, respectively.The air condensation can be disregarded due to the insignificant effect of the LH₂ jet on the far-field flow which is the focus of this study.Therefore, the mandatory amount of air aiding the evaporation of remaining LH₂ can be calculated from Equation ( 13) provided by Yuan et al. (2022), supporting that air phase changes are negligible for horizontal jet releases of LH₂.
In Eq. ( 13), γ is the latent heat of vaporisation of LH₂, m air is the amount of air required to evaporate the remaining LH₂, and C p is the specific heat of air at constant pressure.T ∞ and T sat are ambient and saturation temperatures.It is worth noting that several studies have examined the potential impact of air condensation during LH₂ releases.Sun et al. (2022) found that the flammable volume of LH₂ is unaffected by air condensation.Similarly, Ichard et al. (2012) observed no significant changes in dispersion when experiments resembled one of cases conducted by Health and Safety Laboratory (HSL), a horizontal LH₂ release at a height of 850 mm.Giannissi and Venetsanos (2018) also confirmed that hydrogen dispersion remains unaffected by air condensation.
The moment of conservation is considered to calculate the velocity and area of the pseudo-source plume near the outlet.
where v i is the velocity of the pseudo source, A i is the area of the pseudo source, and ρ air is the air density.Assuming instantaneous evaporation by the warmth of surrounding air, the momentum conservation principles are utilised to express the velocity and area of the pseudo-source plume near the outlet.This behaviour aligns with previous investigations, indicating that the initial plume's cold temperature causes it to move downward before heat exchange with the ground.The proposed model's consistency with experimental results suggests its applicability for simulating LH₂ release into the ambient environment (Ichard et al., 2012;Yuan et al., 2022).In summary, the present investigation is performed based on some critical assumptions: (i) liquid hydrogen released into the atmosphere transitions to a gaseous state at a boiling temperature of 20 K, (ii) the analysis disregarded details of phase change in multiphase scenarios as it focused on the far-field dynamics, (iii) it also overlooked humidity levels and condensation effects.Employing the Homogeneous Equilibrium Model (HEM), the study assumes local thermal and kinematic equilibrium between phases, with instantaneous transport, and categorises phases based solely on their volume or mass fractions (Yuan et al., 2022;Ichard et al., 2012;Hansen, 2020).Considering the mentioned assumptions, there are some limitations to the current study.Particularly the current model cannot provide details of the flow near the release point, however, it is expected this does not affect the far field as demonstrated in the previous studies.

Numerical setup
The pressure-velocity coupling in this research utilises the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm.Timesteps in transient simulations are controlled and adapted using the Courant-Friedrichs-Lewy (CFL) number.The timestep extent in the present analysis adjusts between 10 − 4 and 10 − 3 s depending on the specific cases.For modelling turbulence, the standard k-ε model is employed to simulate the turbulent flow characteristics.The ideal gas equation of state is also incorporated into the model.
For modelling atmospheric boundary layer flow (wind), profiles for velocity (wind speed and direction), temperature, and turbulence parameters are incorporated into the inlet boundaries (Gexcon AS, 2023).The wind conditions are set with a speed of 2 and 4 m/s at the reference height of 10 m while the wind build-up time is 5 s.The Pasquill class for the investigation is neutral.The boundary condition for non-wind boundaries is considered as nozzle, while the rest is specified as the wind boundary.For simple modelling of the leak, a pseudo-source model is adopted, assuming that gaseous hydrogen is released at its boiling point of 20 K, consistent with the previous studies (Ichard et al., 2012;Yuan et al., 2022).
A cartesian mesh is adopted while refinements are conducted near the leakage point and obstacles.Details of the validation case and the mesh study are given in Section 3.3.For the studied HRS, the mesh study is also conducted, demonstrating a mesh with 859,000 cells is suitable for simulations.The minimum cell sizes are 0.6 m, 0.025 m, and 0.025 m, in X, Y and Z directions, respectively.

Model validation and verification
The Health and Safety Laboratory (HSL) in the UK conducted a series of LH₂ leak experiments, and the results of Test 7 are employed for the model validation in the present study (Royle and Willoughby, 2014).The experiment was performed on a concrete pad of 32 m diameter, and liquid hydrogen was released horizontally from a storage tank with a mass flow rate of 0.07 kg/s, 0.86 m above the ground.The leak orifice diameter was measured as 26.3 mm, and the tank pressure was 2 bars.A wind velocity of 2.9 m/s and ambient temperature of 284.5 K was measured during the experiment.The flow of LH₂ traversed a 20-m insulated pipe and a 1.6-m non-insulated pipe before being released into the ambient atmosphere.This setup facilitates the significant evaporation of large quantities of LH₂ within the pipes.Therefore, a mixture of gas and liquid hydrogen is expected at the release point.Previous works studied the impact of a flash mass fraction and concluded that a mass fraction of 0.6 provided reasonable agreement with the measurement which is adopted in this study (Ichard et al., 2012;Yuan et al., 2022).
In the experiment, various sensors (tc1 to tc30) are located along the wind direction at different distances from the release point and different heights from the ground.The sensor layout is illustrated in Fig. 2 and within this figure, the location of the identified leak is marked in red at a height of 0.86 m.The data from sensors tc11, tc8, tc2, tc5, and tc14 are employed here for the model validation which are located 0.75 m m from the ground.
A mesh sensitivity analysis is initially conducted for the validation case by monitoring the temperature at tc11, positioned at a height of 0.75 m and a distance of 1.5 m from the leak source.tc11 is chosen for its proximity to the release point, with the height of 0.75 m closely matching the release height of 0.86 m.Fig. 3 shows the temperature evolution for three distinct mesh sizes: 552,000, 825,000, and 1,677,000.At a steady state condition, it is observed that the results verify the marginal impact of the mesh size on the prediction of the temperature by increasing the mesh size from 825,000 to 1,677,000.Therefore, the mesh configuration with 825,000 cells is utilised for all further cases within this study to save computational resources while obtaining an accurate simulation result.
Fig. 4 shows the temperature contours during the development stage in the XZ plane, spanning from 1.5 s to 3 s.It shows characteristics of low-temperature (consequently dense) gas behaviour, distinguishing it from the typical dispersion and dissipation observed in releases of hydrogen gas at the standard temperature.As can be seen, the denser gas touches down to the ground approximately 6 m away from the source leak which is different from the normal buoyant behaviour of light gases.This observation aligns with findings from prior investigations (Hansen, 2020).The phenomenon can be attributed to the low temperature of the initial discharge.In addition, there is no heat exchange with the ground before the release makes contact, contributing to its initial density compared to the surrounding ambient air, causing it to slide down.This behaviour is also observed in both experiments and other numerical works (Hansen, 2020;Sun et al., 2022), confirming the current model successfully captures the jet behaviour.
The present results are compared with measurements and previous CFD data in Fig. 5 (Ichard et al., 2012;Yuan et al., 2022).The results present temperatures at tc 2, 5, 8, 11, and 14 which are at 0.75 m above the ground along the leak direction (Royle and Willoughby, 2014).Notably, a satisfactory level of agreement is observed between the present results, the experimental data, and the findings from previous  numerical studies shown in Fig. 5.The deviation at different horizontal distances varies between 10.5 and 24%.The maximum deviation is observed near the leak point at a distance of 1.5 m.This discrepancy could be due to the high gradients of temperature near the leak caused by the temperature difference between the released hydrogen (20 K) and the surrounding atmosphere (290 K).Nevertheless, the agreement is reasonable, confirming the accuracy of the current model which is adopted for modelling the HRS.

Results and discussion
In this section, we investigate the impacts of various parameters, including wind direction and velocity as well as the leak rate and its direction.This section discusses the development of the flammable cloud volume (FCV) and its extension under different conditions.FCV is defined as the volume of the region with the hydrogen concentration corresponding to the flammability range from 4% to 75%.

Combined effects of leak direction and wind direction
Depending on wind direction and HRS layout, wind can either enhance flammable cloud dispersion and reduce overpressures during explosions or trap the cloud and increase concentrations and turbulence (Baraldi et al., 2009).In addition, the leak direction may lead to the maximum diffusion distance or high hydrogen concentration based on its position (Sun et al., 2022).This section comprehensively discusses the combined effects of leak and wind directions to provide a more insightful understanding of predicting hydrogen dispersion.
Fig. 6 shows the effect of the wind direction on the size of FCV under different leak directions.In Cases 1, 2, and 3, the wind direction aligns with the positive X direction (north), while Cases 4, 5, and 6 are oriented in the positive Y direction (west).When the leak is towards the ground (z⁻) in Cases 3 and 6, the FCV size is significantly smaller, as obstacles block the wind and reduce its intensity.Furthermore, when the leak is in proximity to an obstacle and directed toward it, the space between the obstacle and the tank constrains the maximum potential volume of the cloud, limiting its development and dispersion.For example, Case 1 exhibits the most substantial FCV due to the greater space available for dispersion in the X⁺ direction (extending 4.6 m to the next obstacle).
Among cases shown in Fig. 6, Case 1 exhibits the highest FCV at 47.5 m 3 since wind and leak are aligned, assisting with the extension of the cloud (Shao et al., 2018;Silgado-Correa et al., 2020).On the other hand, the minimum FCV is observed in Case 6 with 2.32 m 3 due to the leak in a vertically downward direction in the presence of the westerly wind.For Cases 2, 3, 4, and 5, the magnitudes for flammable volume are 13.7,Temporal evolution of FCV t 1 , t 2 , and t 3 = 40 s t 1 and t 2 correspond to the time when the FCV reaches 30% and 60% of its maximum value in each scenario, respectively.The leak direction is x⁺.
At the constant leak rate, when the leak direction is towards x⁺ and z⁻, the quasi-steady-state flammable cloud size is larger under the wind in the north direction compared to the west direction, as shown in Fig. 6 (a) and (c).However, a different trend is evident in Fig. 6 (b) when the leak is towards the x⁻ direction.This phenomenon is due to the cloud's interaction with the surrounding structures, particularly, when the leak encounters the side wall adjacent to the LH₂ tank.It is carried along the wall by the wind velocity in that direction.This contributes to the dispersion of the flammable cloud over a significant area.This phenomenon is further elucidated in Figs.7 and 8.
The evolution of the flammable profile and its interaction with the surrounding walls are presented in Fig. 7 for Cases 1 and 4 at time instances t 1 , t 2 , and t 3 .t 1 and t 2 are selected in the development period and they correspond to the time when the FCV reaches 30% and 60% of its maximum value in each scenario, respectively.t 3 = 40s and it represents the quasi-steady-state stage.Similar results are presented in Fig. 8 for Cases 2 and 5 for a leak in the negative X direction, positioned 3.3 m away from the border wall.It is evident that in both Cases 1 and 4, the flammable cloud remains confined within the envelope formed by the three boundary walls when the wind is in the north and west directions.However, it is apparent that when the wind aligns with the north direction, the flammable cloud is facilitated to disperse farther before being obstructed by structures, leading to its accumulation against the structures.The cloud shows a rapid increase within the first 10 s and continues to change.The wind facilitates the dispersion of the cloud towards the envelope before it hits the opposite side wall, scattering along its surface.Notably, Case 4 achieves steady-state dispersion much faster than Case 1. Considering the influence of the wind, Case 4 reaches its maximum volume within the envelope.Examining the steady-state progression, it is evident that the cloud encounters the first large obstacle in its path, directed by the wind as it moves around the object.Fig. 8. Temporal evolution of FCV t 1 , t 2 , and t 3 = 40 s t 1 and t 2 correspond to the time when the FCV reaches 30% and 60% of its maximum value in each scenario, respectively.The leak direction is x⁻.
However, when the wind direction is perpendicular to the leak, dispersion is less extensive, allowing obstacles to further diminish and divert the release (Case 4).
The analysis of Case 2 and Case 5 (Fig. 8) shows that following the interaction of the hydrogen cloud with the wall and exposure to wind influence, the flammable volume of the cloud diverges.In Case 2, the wind in the north direction is obstructed by the side wall 2.18 m away from the hydrogen storage tank, causing a slight deviation in the leak direction.Upon reaching a steady state and moving beyond the boundary walls, a noticeable change in the FCV is observed.The developed cloud volume is 13.7 and 22.52 m 3 for Case 2 and Case 5, respectively.On the other hand, in Case 5 the wind moves the leaked gas along the side wall, causing a collision, and drags it towards the back wall which may lead to hazardous situations (Ehrhart et al., 2021).
Based on NFPA 2, the portable LH₂ container with a capacity below 150 L, when situated within a building, must maintain a minimum distance of 6.1 m from all categories of flammable or combustible liquids.For a large LH₂ system (280,000 L), the separation distance is larger which is computed based on the maximum pipe size and maximum operating pressures.According to the guideline, the required distances are 48 m for Group 1-Air intakes (for compressors), 1.5 m between LH₂ containers for Group 3, and 23 m for all classes of flammable and combustible liquids.Considering these regulations and examining the trends for FCVs in Case 5, it emphasises that caution must be taken.The storage area includes an evaporator near the LH₂ tank (3.2 m), a chiller at 7.0 m, and a hydrogen compressor located 5.69 m away.Despite this, a flammable cloud has spread to about 15 m.
To further explore the impact of the wind, Fig. 9 shows the velocity profiles for Cases 1 and 4 at 40 s.In Fig. 9 (a), the velocity in Case 1 encounters obstruction primarily from the boundary side wall.As a result, the impact of the wind within the vicinity of the fuel storage area is minimal.The obstruction limits the wind's capacity to affect the immediate surroundings of the storage area.However, in Fig. 9 (b), the wind direction in Case 4 originates from the front of the storage area.Notably, higher velocities (up to 4 m/s) are observed around the obstacles.The presence of higher wind velocities facilitates the dispersion of this cloud around the liquid and gaseous hydrogen storage area, justifying the observed trend in Fig. 7.

Effects of the leak rate
Fig. 10 investigates the effect of the leak rate, comparing cases with a leak rate of 0.06 kg/s with cases with a leak rate of 0.05 kg/s.For the presented results, the wind is in the north direction.Fig. 10 (a), (b), and (c) show the results for the gas leak in the x + direction (Cases 1 and 7), the x⁻ direction (Cases 2 and 8), and the z − direction (Cases 3 and 9), respectively.In all scenarios, as expected, a higher leakage rate results in a larger FCV at least at the early stages.Interestingly, when the wind a leak direction align (Cases 1 and 7), the impact of the leakage rate becomes small, and the FCV reaches 47 m 3 in both cases.This might be due to the development of flammable clouds beyond the domain boundaries.In Cases 2 and 8, the side wall blocks the development of the leaked gas, leading to a smaller FCV compared to Cases 1 and 7. When the gas releases in x⁻, reducing the leakage rate results in a 73% reduction in the cloud size while this is 90% when leakage is toward the ground (Cases 3 and 9) which could be due to the minimal influence of the wind.
To further study the impact of leakage rates, Fig. 11 illustrates the results of different leakage flow rates of 0.02, 0.03, 0.05, and 0.06 kg/s corresponding to Cases C17, C18, C7, and C1.The wind velocity is 4 m/s in "North" direction while hydrogen leaks in "x⁺" direction.As the leak rate decreases, the steady-state FCV decreases initially, however, the results show that the FCV values are very close for leak rates of 0.05 and 0.06 kg/s, indicating a minimal difference between the two rates.This observation suggests that further reductions in leak rate may not significantly impact FCV beyond a certain threshold, highlighting the importance of carefully managing and monitoring hydrogen leaks to optimise safety measures.

Effects of wind velocity
The impact of the wind velocity, specifically 2 and 4 m/s, on the FCV is further investigated at the leak rate of 0.06 kg/s with a consistent leak direction (x⁺).Table 3 compares each pair of cases under the same test conditions at the two different wind velocities.The wind velocity magnitudes for Case 1 and Case 13 are 4 and 2 m/s, respectively, indicating that when the leak and wind both are in the same direction, a difference of 30% is achieved.However, by increasing the wind velocity a notable reduction of 82% in the FCV is evident in Cases 2 and 14 where the wind and leak become in opposing directions.Furthermore, the minimum FCV size (13.7 m 3 ) is achieved in Case 2, consistent with the results demonstrated in Fig. 8. Cases 4,5,11,and 12 show the results for the westerly wind (perpendicular to the leakage direction).A percentage difference of 44 between Case 4 and Case 11 is achieved by increasing the wind velocity while it is 73.45% for Cases 5 and 12.In perpendicular scenarios, increasing the wind speed is more effective for x⁻ leakage cases.In the x⁻ leakage cases, the jet is initially extended toward the side wall and then it continues its extension in the opposite direction toward the HRS's units.At 2 m/s, the wind is not strong enough to dilute the dispersed hydrogen, and hence, the released hydrogen is trapped between boundary walls, increasing the size of FCV, reaching 84.80 m 3 in Case 12. Increasing the wind to 4 m/s helps with the gas dispersion and hence there is a significant reduction in FCV size (Case 5).
Fig. 12 presents four scenarios where there is a leak in the "x⁺" direction and wind blowing from the "North" direction.The wind velocities for each scenario are as follows: C15 is simulated at 1 m/s, C13 at 2 m/s, C1 at 4 m/s, and C16 at 5 m/s.It is evident that decreasing the wind velocity increases the volume of the flammable cloud.This indicates a greater spread of hydrogen over a larger area, emphasising the inverse relationship between wind velocity and the spread of hydrogen.

Extension of the flammable cloud
While the size of the flammable cloud volume is a good indicator to assess the potential hazards, it is important to also understand the extension of the flammable cloud toward different units in HRS which is explored in this section.This is critical since the flammable cloud has a complex shape.Fig. 13 demonstrates the development of the flammable cloud in x (toward the HRS's units and convenience store), y (toward dispensing units and back walls), and z directions for all cases presented in this study.The colour code represents the direction of the leak, with purple showing the leak in x⁺, yellow representing the leak in x⁻, and green signifying the leak in z⁻ directions.As shown in Fig. 13 (a), the x⁺ leakage cases exhibit the largest development in the x-direction (toward critical units in HRS).Specifically, Case 1, when the leakage aligns with the wind, demonstrates a magnitude of 12.0 m.In this case, the wind has a negative impact, and it does not help with reducing the risk of leakage.Comparing Case 1 and 13 shows even though the FCV is larger in Case 13 (Table 3), its extension is less in the x direction.This confirms the complex interaction between the wind and FCV.When considering the x⁻ leakage cases, the maximum value is achieved by Case 14 with a wind velocity of 2 m/s.The z⁻ leakages cases show a relatively small size with Case 3 attaining the maximum value when the wind is in the north direction.
As depicted in Fig. 13 (b), for x⁺ leakage cases, Case 13 exhibits the maximum magnitude of 16.55 m which is higher than Case 1, justifying its larger FCV.Among x⁻ leakage cases, the Y-extension of the FCV is large for Cases 5, 10, and 12 when the wind direction is parallel to the

Table 3
The effect of the wind velocity on the FCV size at the leak rate of 0.06 kg/s with the same leak direction (x⁺).leak whereas the magnitude reduces for Cases 2, 8, and 14 when the wind direction is perpendicular.This demonstrates how wind assists with diluting the released gas and reducing the extension of the FCV.It is also interesting that Case 3 with the gas release toward the ground shows a high value since the wind is toward the north.Based on Fig. 13 (c), it is also evident that for z⁻ leaks, the distance covered by flammable cloud is notably limited, reaching a maximum value in Case 11 with 6.6 m for x⁺ release, Case 12 with 4.45 m, and Case 3 with 2.5 m.Considering FCV for all cases in Fig. 13 (d), the highest FCV does not always correspond to maximum extension in all three directions.Conversely, the minimal volume does not ensure safety, as it may extend hazardously in specific directions.For instance, Case 12 demonstrates the highest FCV of 84.83 m 3 , while its dimensions in the X, Y, and Z directions do not surpass those of other cases.This is due to the complete shape of the flammable cloud.In a regime dominated by momentum and buoyancy, the flammable gas cloud profile ascends as part of the continuous diffusion process (Qian et al., 2020a) (Qian et al., 2020b).Furthermore, a lower source height tends to concentrate the hydrogen cloud closer to the ground, whereas a higher source height helps to distance the flammable clouds from the ground (Sun et al., 2022).
The outcomes of this study help to enhance the safety of large-scale hydrogen facilities.A detailed understanding of how the correlated impact of wind direction and leakage direction assists with the development of emergency responses.It also assists with the optimum design of the sensing system and sensors' location for timely detection of hydrogen leakage, preventing catastrophic fire and explosion consequences.

Conclusion
This work studied the dynamics of liquid hydrogen release and dispersion within hydrogen refuelling stations (HRS) and highlighted the crucial role of facility layout and design in risk mitigation.Detailed computational simulations were conducted to anlyse the significant influences of parameters including wind direction, leak direction, leak rate, and wind velocity on flammable cloud dynamics and dispersion.We investigated different scenarios while envorimentla and operational parameters varied including wind direction (north and west), leak direction (x+, x-, and z-), leak rate (0.02-0.06 kg/s), and wind velocity (1-5 m/s).In total, 18 scenarios were comprehensively examined under the weather conditions in NSW, Australia in the present research.
It was found that lower flow rates correspond to a decrease in the steady state flameable cloud volum (FCV), thereby reducing the risk of ignition and explosion.Fruther, we found as wind velocity increased, the steady state FCV diminished, supporting the observation that higher velocities facilitated the rapid dispersion of hydrogen, consequently reducing the risk of flammable hydrogen accumulation in a given area.This minimised the potential danger associated with hydrogen ignition and explosion.
The numerical results highlighted the significant impact of wind direction alignment and leak direction on flammable cloud dynamics and dispersion, particularly before encountering obstacles.This study also demonstrated how obstacles, such as walls and structures, alter the flammable cloud's dispersion with wind, notably reducing FCV when the cloud encounters obstacles.Understanding the collaborative effects of leak rate and wind velocity is crucial for safety assessments.It was highlighted increasing wind velocity from 2 to 4 m/s at a constant leak rate of 0.06 kg/s resulted in an 82% reduction in FCV.However, achieving maximum FCV did not necessarily correlate with maximum cloud dimensions in the X, Y, and Z directions.The outcomes confirmed that when wind and leak are aligned, the steady state of FCV reduceed with an increase in the velocity.This is also true for cases where leaks were perpendicular and opposite to the wind.Thus, the higher the wind velocity, the quicker the dispersion will be, creating safer surroundings and suggesting a well-ventilated area.The study emphasises the need for a comprehensive approach to safety assessments, considering multiple factors for designing safer hydrogen storage facilities, adjusting separation distances, and formulating effective hazard mitigation strategies.This study has established a comprehensive set of data which could be employed for explosion analysis in future work.For further detailed

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1.The model layout for a liquid HRS.

Fig. 5 .
Fig. 5. Validation of the present numerical model in HSL test 7.

Fig. 6 .
Fig. 6.Effect of wind directions on FCV, a) Leak x⁺, b) Leak x⁻, c) Leak z⁻.The orange and blue solid lines show the results for North-direction and West-direction wind, respectively.(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 11 .
Fig. 11.Effect of the leak rate on the steady-state FCV.

Fig. 12 .
Fig. 12.Effect of the wind velocity on the steady-state FCV.

Fig. 13 .
Fig. 13.Extension of the flammable cloud in the X, Y and Z directions and steady-state FCV: the purple, orange, and green colours represent cases with the leak in the x⁺, x⁻, and z⁻ directions, respectively.(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Table 1
Dimensions of components within the liquid HRS.

Table 2
Different test conditions in the present research.