Safe Design of a Hydrogen-Powered Ship: CFD Simulation on Hydrogen Leakage in the Fuel Cell Room

: Adopting proton exchange membrane fuel cells fuelled by hydrogen presents a promising solution for the shipping industry’s deep decarbonisation. However, the potential safety risks associated with hydrogen leakage pose a signiﬁcant challenge to the development of hydrogen-powered ships. This study examines the safe design principles and leakage risks of the hydrogen gas supply system of China’s ﬁrst newbuilt hydrogen-powered ship. This study utilises the computational ﬂuid dynamics tool FLACS to analyse the hydrogen dispersion behaviour and concentration distributions in the hydrogen fuel cell room based on the ship’s parameters. This study predicts the ﬂammable gas cloud and time points when gas monitoring points ﬁrst reach the hydrogen volume concentrations of 0.8% and 1.6% in various leakage scenarios, including four different diameters (1, 3, 5, and 10 mm) and ﬁve different directions. This study’s ﬁndings indicate that smaller hydrogen pipeline diameters contribute to increased hydrogen safety. Speciﬁcally, in the hydrogen fuel cell room, a single-point leakage in a hydrogen pipeline with an inner diameter not exceeding 3 mm eliminates the possibility of ﬂammable gas cloud explosions. Following a 10 mm leakage diameter, the hydrogen concentration in nearly all room positions reaches 4.0% within 6 s of leakage. While the leakage diameter does not impact the location of the monitoring point that ﬁrst activates the hydrogen leak alarm and triggers an emergency hydrogen supply shutdown, the presence of obstructions near hydrogen detectors and the leakage direction can affect it. These insights provide guidance on the optimal locations for hydrogen detectors in the fuel cell room and the pipeline diameters on hydrogen gas supply systems, which can facilitate the safe design of hydrogen-powered ships.


Introduction
The International Maritime Organization (IMO) has set a decarbonisation strategy aimed at reducing the carbon intensity of all ships by at least 40% by 2030 and cutting total GHG emissions from global shipping by 50% (compared to 2008 levels) by 2050 [1,2].To this end, various actions based on clean energy technologies should be implemented [3][4][5].Hydrogen's emission-free properties make it a promising alternative fuel for the shipping industry [6,7].Among various hydrogen energy technologies, proton exchange membrane fuel cells (PEMFC) are promising due to their high energy efficiency and zero emissions [8][9][10][11][12][13].
Numerous research projects across Europe, North America, and Asia have yielded significant results in the marine fuel cell (FC) field, including developing industrialised marine FCs and practical demonstration projects [14,15].Recent research efforts have focused on assessing the feasibility and reliability of ship power systems utilising FCs [16][17][18][19], energy management for FC-powered ships [20,21], and optimising ship power system design related to FCs, including hybrid systems [22][23][24][25][26].These studies have examined various aspects of FC technology for use on ships, providing valuable insights for developing hydrogen-FC-powered ships.However, relatively little research has focused on hydrogen safety for FC ships.Hydrogen is highly hazardous due to its extreme flammability and explosiveness [27][28][29][30].Previous research has identified several factors that impede the development and use of hydrogen FCs on ships, including inadequate risk management to mitigate the risks of leakage and the formation of flammable gas clouds (FGC) [31,32], as well as insufficient international regulations and standards for hydrogen supply chains [33].The risk of hydrogen FGC explosions is anticipated to rise significantly in enclosed or confined spaces, including hydrogen gas supply systems (HGSS) located in the engine room or fuel cell room (FCR) [34][35][36].
Figure 1 presents the hydrogen leakage event tree in enclosed or confined spaces.Leakage, detection, ignition sources, and cloud formation are the initiating events in the development of hydrogen accidents.Therefore, investigating the evolution characteristics of these events is crucial for controlling hydrogen safety and is a key focus of research on hydrogen-powered ships [37].For example, L.E.Klebanoff et al. analysed the safety properties of liquid hydrogen using the "SF-BREEZE" high-speed FC ferry as a case study.They emphasised preventing hydrogen fuel leaks [38].Meanwhile, F. Li et al. conducted computational fluid dynamics (CFD) simulations on hydrogen leakage in cabins of the "SF-BREEZE", and the findings offered guidance for the general arrangement of FC ships [39].Similarly, Mao, X et al. predicted overpressure and high temperature after hydrogen explosions caused by FGC in different rooms of the "SF-BREEZE" ferry using ANSYS fluent software.They found that the hydrogen FCR was most affected [40].Park, S et al. compared the explosion overpressure caused by hydrogen and hydrocarbon-based gases in ship ventilation pipes.They found that hydrogen caused higher overpressure [41].Yuan, Y et al. investigated the effectiveness of a fine water mist in suppressing the temperature of hydrogen jet fires on FC ships using the CFD software FDS.They found that while the mist could reduce the fire field temperature, it did not extinguish the fires [42].The IMO issued the Interim Guidelines for the Safety of Ships Using Fuel Cell Power Installations in 2022 to meet the growing demand for FC ships [43].The guidelines provided safety design requirements for ships using FC installations but not for hydrogen storage and supply on ships.Chen, L. et al. calculated the minimum ventilation capacity for the hydrogen FCR on a ship under normal operating conditions based on IMO guidelines and IEC 60079-10-1:2020.Safe design measures were proposed to reduce the level of the hazardous area in the FCR [44].Feng, Y. et al. used the CFD software FLACS to predict the dispersion distance of hydrogen FGC in a bunkering station on a cargo ship.The safety recommendations for the hydrogen bunkering operation were proposed based on the prediction [45].
Overall, previous studies have yet to provide detailed information about hydrogen piping systems and equipment in the FCR on ships powered by large-capacity hydrogen PEMFCs.Current studies have not accounted for various leakage diameters and directions, leading to incomplete leakage scenarios.Additionally, the dispersion and concentration of hydrogen in the FCR require more detailed investigation, including the detection time of hydrogen detectors at different locations.To address these gaps, this study uses the CFD software FLACS to investigate hydrogen safety in the FCR of a 560 kW hydrogen-PEMFC-powered ship.The following aspects regarding hydrogen leakage in the FCR were investigated:

•
The effect of leakage diameter on hydrogen concentration.

•
The optimal location for hydrogen detectors.

•
Safety design recommendations for future engineering applications of hydrogenpowered ships.
In this paper, Section 2 outlines the methodology.Section 3 presents the mathematical model and its validation.Section 4 discusses the results.Finally, Section 5 presents the conclusions.Overall, previous studies have yet to provide detailed information about hydrogen piping systems and equipment in the FCR on ships powered by large-capacity hydrogen PEMFCs.Current studies have not accounted for various leakage diameters and directions, leading to incomplete leakage scenarios.Additionally, the dispersion and concentration of hydrogen in the FCR require more detailed investigation, including the detection time of hydrogen detectors at different locations.To address these gaps, this study uses the CFD software FLACS to investigate hydrogen safety in the FCR of a 560 kW hydrogen-PEMFC-powered ship.The following aspects regarding hydrogen leakage in the FCR were investigated:

•
The effect of leakage diameter on hydrogen concentration.

•
The optimal location for hydrogen detectors.

•
Safety design recommendations for future engineering applications of hydrogenpowered ships.
In this paper, Section 2 outlines the methodology.Section 3 presents the mathematical model and its validation.Section 4 discusses the results.Finally, Section 5 presents the conclusions.

Methodology
The study framework, presented in Figure 2, involves three stages.Firstly, the design philosophy of HGSS was analysed based on the function structure of the hydrogen fuel system and the safety requirements of IMO guidelines.This analysis helped to determine the hydrogen leakage scenarios and calculation parameters.Secondly, this study focused on the analysis of the theory of hydrogen leakage and dispersion, including the mathematical model of numerical calculation.The previous study results were used to validate the CFD simulation model, and the input parameters were established in the CFD model.Thirdly, the simulation results were used to analyse the impacts of various factors on hydrogen dispersion and concentration in the FCR.Based on the findings, safety design recommendations for the ships were proposed.

Methodology
The study framework, presented in Figure 2, involves three stages.Firstly, the design philosophy of HGSS was analysed based on the function structure of the hydrogen fuel system and the safety requirements of IMO guidelines.This analysis helped to determine the hydrogen leakage scenarios and calculation parameters.Secondly, this study focused on the analysis of the theory of hydrogen leakage and dispersion, including the mathematical model of numerical calculation.The previous study results were used to validate the CFD simulation model, and the input parameters were established in the CFD model.Thirdly, the simulation results were used to analyse the impacts of various factors on hydrogen dispersion and concentration in the FCR.Based on the findings, safety design recommendations for the ships were proposed.

Research Object
The "San Xia Qing Zhou 1 (Three Gorges Hydrogen Boat 1)" is a catamaran passenger ship that is currently being constructed [14].The ship uses hydrogen FCs as its primary power source and lithium batteries for energy storage.This study focuses on the

Research Object
The "San Xia Qing Zhou 1 (Three Gorges Hydrogen Boat 1)" is a catamaran passenger ship that is currently being constructed [14].The ship uses hydrogen FCs as its primary power source and lithium batteries for energy storage.This study focuses on the safety analysis of FCR and HGSS, as their design directly impacts the safety of ships.Table 1 displays the main parameters of the ship.Figure 3 shows the general arrangement of the vessel, and Figure 4 illustrates the arrangement of the FCR.

Research Object
The "San Xia Qing Zhou 1 (Three Gorges Hydrogen Boat 1)" is a catamaran passenger ship that is currently being constructed [14].The ship uses hydrogen FCs as its primary power source and lithium batteries for energy storage.This study focuses on the safety analysis of FCR and HGSS, as their design directly impacts the safety of ships.Table 1 displays the main parameters of the ship.Figure 3 shows the general arrangement of the vessel, and Figure 4 illustrates the arrangement of the FCR.

Hydrogen Fuel System and Leakage Risk
The ship's HGSS consists of four functional modules, namely hydrogen bunkering, storage, fuel supply, and hydrogen FCs, as depicted in Figure 5.During bunkering, compressed hydrogen gas is injected into cylinders with a pressure of 35 MPa.Control valves are installed on the pipelines to prevent hydrogen from entering the cylinders in case of an emergency.The storage system consists of 32 hydrogen cylinders with a pressure of 35 MPa, fixed with a metal frame and with a capacity of 240 kg.Before entering the PEMFCs, the hydrogen gas is reduced to 0.8 MPa from 35 MPa to meet the demand of the FCs [46].The FCR contains eight FC modules of 70 kW each, enclosed in a box with an independent

Hydrogen Fuel System and Leakage Risk
The ship's HGSS consists of four functional modules, namely hydrogen bunkering, storage, fuel supply, and hydrogen FCs, as depicted in Figure 5.During bunkering, compressed hydrogen gas is injected into cylinders with a pressure of 35 MPa.Control valves are installed on the pipelines to prevent hydrogen from entering the cylinders in case of an emergency.The storage system consists of 32 hydrogen cylinders with a pressure of 35 MPa, fixed with a metal frame and with a capacity of 240 kg.Before entering the PEMFCs, the hydrogen gas is reduced to 0.8 MPa from 35 MPa to meet the demand of the FCs [46].The FCR contains eight FC modules of 70 kW each, enclosed in a box with an independent ventilation system.The ship's HGSS consists of four functional modules, namely hydrogen bunkering, storage, fuel supply, and hydrogen FCs, as depicted in Figure 5.During bunkering, compressed hydrogen gas is injected into cylinders with a pressure of 35 MPa.Control valves are installed on the pipelines to prevent hydrogen from entering the cylinders in case of an emergency.The storage system consists of 32 hydrogen cylinders with a pressure of 35 MPa, fixed with a metal frame and with a capacity of 240 kg.Before entering the PEMFCs, the hydrogen gas is reduced to 0.8 MPa from 35 MPa to meet the demand of the FCs [46].The FCR contains eight FC modules of 70 kW each, enclosed in a box with an independent ventilation system.Hydrogen leakage in the FCR may occur from the FC modules, valves, and pipe joints such as threaded or jacketed joints.Table 2 lists various reasons for the possible leakage of valve fittings and pipe components in the hydrogen piping systems [47].The pre-tightening force on the sleeve or thread is too small Hydrogen leakage in the FCR may occur from the FC modules, valves, and pipe joints such as threaded or jacketed joints.Table 2 lists various reasons for the possible leakage of valve fittings and pipe components in the hydrogen piping systems [47].

•
The pre-tightening force on the sleeve or thread is too small Under normal operations, valves and pipe joints do not release hydrogen but may leak hydrogen gas during accidents, as indicated in Table 2. Compared to other alternative fuel supply systems, the HGSS has a higher probability of leakage due to high permeability, hydrogen embrittlement effects, and high pressure [48].Furthermore, using more valves in the hydrogen supply system increases the likelihood of hydrogen leakage.

Design of Fuel Cell Room
The IMO guidelines proposed design concepts for FCR and piping arrangement for FC power systems.However, these concepts are based on the amount of fuel leakage under normal operating conditions and do not consider accidental hydrogen leakage, as shown in Table 2.
According to the IMO guidelines, the design scheme of the hydrogen-fuelled ship should assess the degree of hazardous areas in the FCR following IEC 60079-10-1:2020.The FC modules should be designed to be airtight, and the mechanical exhaust vents of the cabinets should be arranged in safe areas [44].The FCRs in "San Xia Qing Zhou 1" were designed to be non-hazardous areas based on the IMO guidelines and the IEC standard.For this purpose, a minimum ventilation rate of 90 air changes per h is required [44].Increasing the ventilation rate further, in relation to the potential release rates, can lower the probability of an explosive gas atmosphere.However, this comes at the cost of increased electricity consumption and noise levels.Ventilation systems of natural intake and mechanical extraction (5000 m 3 /h) were used in each FCR.The working pressure of the hydrogen system was described in Section 2.1.1,and the pipeline diameter is 10 mm.
Considering the high risk of hydrogen leakage [47], the double-wall piping type was used to reduce the probability of hydrogen leakage in the FCR.The probability of hydrogen leakage was not studied because this work focuses on the consequences of hydrogen leakage.

Parameters and Leakage Scenarios 2.2.1. Parameters of Hydrogen Fuel Cell Room
The simulation object selected for this study was one of the FCRs on the port side.The boundary conditions for hydrogen leakage scenarios in the FCR are presented in Table 3.The dimensions of the selected FCR are 6500 mm in length, 3200 mm in width, and 2000 mm in height.The equipment size parameters provided by the shipyard were used for the simulation.The equipment, which had a roughly cuboid shape, was modelled as a cuboid in the simulation.The dimensions and positions of the equipment in the FCR are displayed in Table 4. Note: the lower left corner of the fuel cell room is the origin of coordinates (0, 0, 0), and the space position (X, Y, Z) is the vertex of the equipment near the origin of coordinates.

Hydrogen Leakage Scenarios
Various factors impact the hydrogen dispersion behaviour in an enclosed space, such as release pressure, leakage flow rate [49], leakage diameter [50], ventilation conditions, direction of leakage, and obstacles in the space [51,52].To achieve the research objective, different leakage diameters and directions were included in the scenarios.The following hypotheses were established for this study: (1) the leaked hydrogen was not ignited, (2) the hydrogen was released with a constant pressure of 0.8MPa for 100 s, which was longer than the time required for the concentration to exceed 1.6%, (3) circular leakage holes with diameters of 10%, 30%, 50%, and 100% of the hydrogen pipeline diameter (10 mm) were considered, (4) the scenario of vertical downward leakage was excluded due to the presence of a valves module with a fixed base plank at the bottom of the FCR, and (5) five directions of leakage were considered, resulting in twenty-four hydrogen leakage scenarios, as presented in Table 5.

Mathematical Model and Model Validation
FLACS-Hydrogen (v10.6), a specialised computational fluid dynamics (CFD) tool for hydrogen safety engineering, was used for numerical simulations.It can be used for simulating hydrogen dispersion and assessing the potential FGC risk in various leakage scenarios.FLACS utilises the porosity distributed resistance theory to model complex geometrical features, such as porosities for a control volume on relatively coarse meshes, which is a unique feature distinguishing it from other CFD software.The compressible Navier-Stokes equations are solved on a three-dimensional grid using a finite volume method in FLACS.The standard k-ε model for turbulence is utilised with some modifications, which are turbulence generation behind sub-grid objects and turbulent wall functions [53].The steps performed during the modelling phase are summarised as follows: • A computational geometry model was built using the equipment dimensions and locations in the FCR.

•
Grid sizes of the FCR were selected for computational geometry model.

•
The simulation was performed using scenarios that involved a combination of leakage parameters and computational geometry models.

Mathematical Model
The mathematical model utilised in this study includes the continuity, motion, energy, concentration transfer, and ideal gas state equations.These equations have been discussed in detail in previous studies [54,55].The main governing equations are briefly outlined.
The mass conservation equation: where β v is the volume porosity; β j is the area porosities; ρ is the gas density; and x j and u j denote the spatial coordinate variable and velocity component in j-th direction, respectively.
The transportation equations for the momentum, enthalpy, and mass fraction of the fuel and mixture fraction are described as follows: where β v is the volume porosity, ρ is the gas density, p is the pressure, h is the enthalpy, .
Q is the heat flow rate, V is the volume, x j is the j-coordinate spatial variable, β j is the area porosity, and u i and u j are the velocity components in the i and j directions, respectively.σ ij is the stress tensor, σ fuel and σ h are the Prandtl-Schmidt numbers of fuel and enthalpy, respectively, both at 0.7, µ eff is the effective viscosity of fuel, F o,i is the flow resistance due to sub-grid obstructions, F w,i is the flow resistance produced by friction of the wall, Y fuel is the fuel mass fraction, and R fuel is the fuel reaction rate.
The gas turbulence in FLACS-Hydrogen was modelled according to the standard k-ε model to obtain the turbulent kinetic energy and its dissipation.The Reynolds stress tensor was modelled using the eddy viscosity based on the eddy viscosity assumption.
Classical k-ε model is used to deal with turbulence, which involves two transport equations: one for turbulent kinetic energy and one for dissipation of turbulent kinetic energy: where k is the turbulent kinetic energy, ε is the dissipation of turbulent kinetic energy, P k is the overpressure, G s is the flow shear stress, G w is the wall shear stress, G b is the buoyancy, G o represent the sub grid objects, σ h and σ ε are the Prandtl numbers of turbulence for k and ε, given as 1.0 and 1.3, respectively, C 1ε , C 2ε , and C 3ε are constants, taken as 1.44, 1.92, and 0.8, respectively, R f is the model for the buoyancy term, u i u j is the mean velocity in the i and j directions, and δ ij is the Kronecker delta function (δ ij = 1 if i = j, otherwise δ ij = 0).

Model Validation
The accuracy and validity of hydrogen dispersion prediction by the CFD tool FLACS-Hydrogen were demonstrated through various validation techniques, including comparisons between experimental and numerically simulated concentrations.Additionally, some of the simulations were performed as blind predictions.The validation tests include experiments involving free jets of hydrogen [56], gas leak dispersion and subsequent explosions [53], and hydrogen gas leakage in confined spaces [37].These simulations showed good agreement with experimental results for various scenarios of hydrogen release and dispersion.Sandia National Laboratories performed experiments to validate FLACS simu-lations of hydrogen release at a scaled warehouse facility, and good agreement was found between the simulation and experimental results [57,58].Moen et al. summarised that the Standard k-ε turbulence model performed best in validating gas dispersion after accidental releases, particularly for hydrogen jet dispersion scenarios [59].An analytical model was also established to predict gas flow behaviours in different hydrogen leakage scenarios, providing high accuracy compared to numerical simulations [60,61].
This study used the experimental work by Ji, H.W et al. to verify the accuracy of the hydrogen leakage simulation model.In their study, a volume of 11.484 m 3 of enclosed spaces was built to test hydrogen leakage in the FC rooms [62].Simulation of case 27 showed similar results to the experiment (Figure 6), with hydrogen concentration peaks of 10% and 3% in agreement.However, there were some differences in the time to reach the concentration, likely due to lag time of the hydrogen detectors.Overall, the agreement between predictions and experiments was considered sufficient to verify the model's accuracy.
The accuracy and validity of hydrogen dispersion prediction by the CFD tool FLACS-Hydrogen were demonstrated through various validation techniques, including comparisons between experimental and numerically simulated concentrations.Additionally, some of the simulations were performed as blind predictions.The validation tests include experiments involving free jets of hydrogen [56], gas leak dispersion and subsequent explosions [53], and hydrogen gas leakage in confined spaces [37].These simulations showed good agreement with experimental results for various scenarios of hydrogen release and dispersion.Sandia National Laboratories performed experiments to validate FLACS simulations of hydrogen release at a scaled warehouse facility, and good agreement was found between the simulation and experimental results [57,58].Moen et al. summarised that the Standard k-ε turbulence model performed best in validating gas dispersion after accidental releases, particularly for hydrogen jet dispersion scenarios [59].An analytical model was also established to predict gas flow behaviours in different hydrogen leakage scenarios, providing high accuracy compared to numerical simulations [60,61].
This study used the experimental work by Ji, H.W et al. to verify the accuracy of the hydrogen leakage simulation model.In their study, a volume of 11.484 m 3 of enclosed spaces was built to test hydrogen leakage in the FC rooms [62].Simulation of case 27 showed similar results to the experiment (Figure 6), with hydrogen concentration peaks of 10% and 3% in agreement.However, there were some differences in the time to reach the concentration, likely due to lag time of the hydrogen detectors.Overall, the agreement between predictions and experiments was considered sufficient to verify the model's accuracy.

Grid Size
A numerical study of hydrogen leakage and dispersion demonstrated grid independence verification for core domain grid sizes of 0.1 m, 0.2 m, and 0.4 m for a 5 mm diameter release [63].The study found that grid sizes of 0.1 m and 0.2 m were appropriate for the

Grid Size
A numerical study of hydrogen leakage and dispersion demonstrated grid independence verification for core domain grid sizes of 0.1 m, 0.2 m, and 0.4 m for a 5 mm diameter release [63].The study found that grid sizes of 0.1 m and 0.2 m were appropriate for the simulation, and in this study, a grid size of 0.1 m was chosen for achieving higher accuracy.The pseudo-source model (also known as notional nozzle) is used for simulating hydrogen releases from small orifices, to bypass the compute-intensive Mach disk zone next to the nozzle exit.The concept of the notional nozzle and sub-grid models in FLACS was validated by the experimental campaign for the second blind prediction study in the HySEA, supported by the European Union's Horizon 2020 research and innovation programme [64].The 3D model, grid sizes of the FCR, and the internal equipment are shown in Figure 7.
simulation, and in this study, a grid size of 0.1 m was chosen for achieving higher accuracy.The pseudo-source model (also known as notional nozzle) is used for simulating hydrogen releases from small orifices, to bypass the compute-intensive Mach disk zone next to the nozzle exit.The concept of the notional nozzle and sub-grid models in FLACS was validated by the experimental campaign for the second blind prediction study in the HySEA, supported by the European Union's Horizon 2020 research and innovation programme [64].The 3D model, grid sizes of the FCR, and the internal equipment are shown in Figure 7.

Results and Discussion
This section discusses the dispersion behaviour of hydrogen gas in scenarios 1 to 4, as presented in Table 5. Section 4.1 analyses the phenomenon of hydrogen gas dispersion within the FCR.Section 4.2 examines the impact of different leakage hole sizes on hydrogen gas concentration within the FCR.Section 4.3 analyses the arrangement of hydrogen detectors in scenarios 5 to 24, as presented in Table 5.

• 100% LFL (volume concentration: 4.0%).
There are 32 gas monitoring points in the CFD model.These monitoring points are located at the ventilation inlet and outlet, equipment vertices, endpoints, and midpoints of each side of the room, and the centre positions of the wall surfaces except the bottom surface.Table 6 shows the coordinates of these monitoring points.

Results and Discussion
This section discusses the dispersion behaviour of hydrogen gas in scenarios 1 to 4, as presented in Table 5. Section 4.1 analyses the phenomenon of hydrogen gas dispersion within the FCR.Section 4.2 examines the impact of different leakage hole sizes on hydrogen gas concentration within the FCR.Section 4.3 analyses the arrangement of hydrogen detectors in scenarios 5 to 24, as presented in Table 5.
According to the IMO guidelines, this section considers the distribution of flammable hydrogen gas at the following three volume concentration values [43]: 20% lower flammable limit (LFL) (volume concentration: 0.8%).
There are 32 gas monitoring points in the CFD model.These monitoring points are located at the ventilation inlet and outlet, equipment vertices, endpoints, and midpoints of each side of the room, and the centre positions of the wall surfaces except the bottom surface.Table 6 shows the coordinates of these monitoring points.

Hydrogen Gas Dispersion within the Fuel Cell Room
This section analyses the impact of different leakage hole sizes on hydrogen gas concentration within the FCR, focusing on scenarios 1 to 4 (with specific parameters outlined in Section 2.2.2).Taking scenario 4 as an example, Figure 8 shows a 3D view of hydrogen gas dispersion, while Figure 9 presents 2D slice views of the XZ and XY planes.In the calculations, hydrogen gas leakage begins from the 20th second to ensure sufficient time to establish a stable negative pressure airflow within the FCR.

Hydrogen Gas Dispersion within the Fuel Cell Room
This section analyses the impact of different leakage hole sizes on hydrogen gas concentration within the FCR, focusing on scenarios 1 to 4 (with specific parameters outlined in Section 2.2.2).Taking scenario 4 as an example, Figure 8 shows a 3D view of hydrogen gas dispersion, while Figure 9 presents 2D slice views of the XZ and XY planes.In the calculations, hydrogen gas leakage begins from the 20th second to ensure sufficient time to establish a stable negative pressure airflow within the FCR.From the above figures, it can be seen that when hydrogen leaks upward, a large amount of flammable hydrogen cloud accumulates in the space below the roof of the FCR in a very short time.In less than 1 s, the hydrogen reaches the roof, and then it spreads and flows along the roof.At around the third second, the hydrogen starts to disperse on the rear bulkhead (XZ section), and at this time the hydrogen cloud still has considerable momentum.A clear eddy is formed (XZ section at third second) when the cloud encounters the corner of the bottom of the room.This is consistent with the finding of [65].According to the XY slice views in Figure 9, after 3 s, the thickness of the hydrogen cloud on the top of the room rapidly increases.At the fifth second, the flammable gas cloud is about to fill the area near the top of the FCR.After 6 s, the concentration of the gas cloud tends to be stable.At this time, except for the ventilation inlet and outlet, the hydrogen concentration in almost all positions in the room reaches 4.0% (LFL).At this time, lighting bulbs and water and thermal management equipment inside the room are within the FGC and may become potential ignition sources.Therefore, it is recommended to avoid arranging the equipment, including non-explosion-proof equipment, equipment that is prone to high temperature, and equipment that is prone to generating sparks, which might be ignition sources inside the FCR, as much as possible.
In the time interval between the second and sixth second, the concentration of hydrogen in the area between the room roof ventilation inlet and outlet is consistently higher than that in other locations.This phenomenon is due to the formation of an air trap between the downward extension of the ventilation inlet duct (approximately 400 mm in height, as shown in Figure 7) and the outlet, which impedes hydrogen discharge from the FCR.This phenomenon should be taken into consideration in the design of ventilation systems.

Influence of Different Leakage Diameters on Hydrogen Concentration
Taking scenarios 1, 2, 3, and 4 as examples, the maximum hydrogen concentrations (Volume %, m 3 /m 3 ) achieved after continuous leakage are 0.3%, 2.8%, 7.5%, and 24.8%, respectively, with the earliest detection times at 83s, 83s, 88s, and 94s.MP4, MP11, and MP20 firstly detect hydrogen concentrations of 0.8%, 1.6%, and 4.0%.Figure 10 shows the hydrogen concentration for the four scenarios, with MP11 used to show concentration changes in Figure 11.The hydrogen concentration trend in the FCR is consistent regardless of the leakage diameter, as shown in Figure 10.The maximum hydrogen concentration in the FCR decreased with decreasing leakage diameter, as seen in Figure 11.MP4 and MP20 show fluctuating hydrogen concentrations due to their proximity to the air inlet, which is affected by wind speed (the speed of the air inlet on this vessel is about 6.9 m/s).
The maximum hydrogen concentration of scenarios 1 and 2 is below the hydrogen LFL (4.0%), indicating that FGC explosion accidents will not occur if leaking hydrogen is not immediately ignited.FGC explosion is impossible in the FCR when there is singlepoint leakage in the hydrogen pipeline with an inner diameter not exceeding 3 mm.Effective mechanical ventilation systems of the extraction type and choosing a small enough inner diameter of the hydrogen pipelines can prevent FGC explosion in the FCR, but they are limited by engineering practicality.The hydrogen concentration trend in the FCR is consistent regardless of the leakage diameter, as shown in Figure 10.The maximum hydrogen concentration in the FCR decreased with decreasing leakage diameter, as seen in Figure 11.MP4 and MP20 show fluctuating hydrogen concentrations due to their proximity to the air inlet, which is affected by wind speed (the speed of the air inlet on this vessel is about 6.9 m/s).
The maximum hydrogen concentration of scenarios 1 and 2 is below the hydrogen LFL (4.0%), indicating that FGC explosion accidents will not occur if leaking hydrogen is not immediately ignited.FGC explosion is impossible in the FCR when there is single-point leakage in the hydrogen pipeline with an inner diameter not exceeding 3 mm.Effective mechanical ventilation systems of the extraction type and choosing a small enough inner diameter of the hydrogen pipelines can prevent FGC explosion in the FCR, but they are limited by engineering practicality.
According to Figure 11, in scenarios 3 and 4, the maximum hydrogen concentration exceeds 4.0%, and FGC explosion is possible.The hydrogen concentration increases linearly during the initial leakage stage, indicating the significant impact of the leakage diameter on hydrogen concentration.For example, in scenario 4, reducing the leakage diameter delayed the alarm time (alarm signal at 0.8%), shutdown time (shutdown signal at 1.6%), and the formation of FGC.Reducing the diameter of the hydrogen pipeline can provide more time for emergency rescue during the leakage event.
Despite a high ventilation rate of 5000 m 3 /h (approximately 90 air changes per h) in the FCR, the hydrogen concentration in the enclosed space remained constant due to continuous hydrogen leakage.However, appropriate mechanical ventilation can effectively control the increase in hydrogen concentration.These findings align with previous research by Lee et al. [62,66].Apparently, a combination of mechanical ventilation and leak source closure is necessary to reduce hydrogen concentration in enclosed spaces.

Detection Time at Monitoring Points
To determine the locations of the hydrogen detectors inside the FCR, the time points and corresponding monitoring points when the hydrogen concentration first reached 0.8% and 1.6% were identified from 32 monitoring points in the 20 scenarios above (Table 7).When the diameter of the leakage hole is 1 mm, the maximum hydrogen concentration is 0.3%, which is lower than the LFL.Thus, the effect of this leakage situation on the arrangement of monitoring points is ignored.Figure 12 shows the monitoring points identified for different leakage directions.The monitoring points corresponding to scenarios 6-20 are located on the bottom (XY plane), while those corresponding to scenarios 22-24 are located on the portside wall (XZ plane).In scenarios 6-20, the same monitoring point was identified for the first time when the hydrogen concentration reached 0.8% and 1.6% for the same leakage direction, regardless of the diameters of leakage holes.The identified monitoring points were located near the leakage points' projection points on the plane facing the leakage direction.This finding provides a basis for the arrangement of hydrogen detectors.It should be noted that the monitoring points in scenarios 10, 11, and 12 were inconsistent with the above finding.The reason is that two air filters (Figure 7) were installed near the point MP21 closest to the leakage source, which hindered the free dispersion of the hydrogen cloud to monitoring point MP21.Therefore, devices that hinder gas dispersion should be avoided when designing the hydrogen detector positions in detailed ship design.In addition, the monitoring points obtained in scenarios 23 and 24 were slightly different from the overall finding mentioned above, but the time difference was less than 0.5 s.From an engineering design perspective, this does not violate the principle of the hydrogen detector arrangement obtained above.

Safety Design Recommendations
Based on the above analysis, the following design recommendations are proposed: Hydrogen fuel cell room

•
Potential ignition sources, including non-explosion-proof electrical equipment, equipment prone to generating high temperatures, and equipment that may produce sparks, should be avoided as much as possible inside the room.If unavoidable, it should be placed as far away as possible from the possible hydrogen leak sources.

•
The lowest position of the ventilation duct inside the room should be kept as close to the top plane as possible to avoid forming an air trap.

Hydrogen Gas Supply System
• The inner diameter of the hydrogen supply pipeline inside the fuel cell room should be reduced as much as possible without affecting the performance of the fuel cell to reduce the diameters of the potential leak holes.

•
The smaller inner diameter of the HGSS in the fuel cell room can significantly decrease the likelihood of FGC, enhancing the overall hydrogen safety of the FCR.Furthermore, if there is a single point of leakage in the hydrogen pipeline with an inner diameter of less than 3 mm, FGC cannot occur within the FCR.

Layout of Hydrogen Detectors
• Hydrogen detectors should be installed close to potential leak sources such as valves, pipeline joints, and seals.As an alternative, they could be located near the leakage points' projection points on the plane facing the leakage direction.

•
No obstructions should be present near the hydrogen detectors.In scenarios 6-20, the same monitoring point was identified for the first time when the hydrogen concentration reached 0.8% and 1.6% for the same leakage direction, regardless of the diameters of leakage holes.The identified monitoring points were located near the leakage points' projection points on the plane facing the leakage direction.This finding provides a basis for the arrangement of hydrogen detectors.It should be noted that the monitoring points in scenarios 10, 11, and 12 were inconsistent with the above finding.The reason is that two air filters (Figure 7) were installed near the point MP21 closest to the leakage source, which hindered the free dispersion of the hydrogen cloud to monitoring point MP21.Therefore, devices that hinder gas dispersion should be avoided when designing the hydrogen detector positions in detailed ship design.In addition, the monitoring points obtained in scenarios 23 and 24 were slightly different from the overall finding mentioned above, but the time difference was less than 0.5 s.From an engineering design perspective, this does not violate the principle of the hydrogen detector arrangement obtained above.

Safety Design Recommendations
Based on the above analysis, the following design recommendations are proposed: Hydrogen fuel cell room • Potential ignition sources, including non-explosion-proof electrical equipment, equipment prone to generating high temperatures, and equipment that may produce sparks, should be avoided as much as possible inside the room.If unavoidable, it should be placed as far away as possible from the possible hydrogen leak sources.

•
The lowest position of the ventilation duct inside the room should be kept as close to the top plane as possible to avoid forming an air trap.
Hydrogen Gas Supply System

•
The inner diameter of the hydrogen supply pipeline inside the fuel cell room should be reduced as much as possible without affecting the performance of the fuel cell to reduce the diameters of the potential leak holes.

•
The smaller inner diameter of the HGSS in the fuel cell room can significantly decrease the likelihood of FGC, enhancing the overall hydrogen safety of the FCR.Furthermore, if there is a single point of leakage in the hydrogen pipeline with an inner diameter of less than 3 mm, FGC cannot occur within the FCR.

Layout of Hydrogen Detectors
• Hydrogen detectors should be installed close to potential leak sources such as valves, pipeline joints, and seals.As an alternative, they could be located near the leakage points' projection points on the plane facing the leakage direction.

•
No obstructions should be present near the hydrogen detectors.

Conclusions
This study utilised CFD software to analyse the dispersion behaviour of hydrogen gas after leakage in the FCR of a hydrogen-fuel-cell-powered ship.Based on the findings, safety design recommendations for the ship were proposed, emphasising the importance of paying extra attention to the safe design of the FCR and hydrogen supply system.The safety of the FCR was influenced by factors such as hydrogen pipeline diameter, ventilation, and the presence of hydrogen detectors.
This study found that a smaller leakage diameter can effectively prevent FGC explosions in the FCR.When a hydrogen leak with a diameter of 10 mm occurred, the flammable gas cloud rapidly filled the room, taking only 6 s in this study.It is worth noting that the location of the monitoring point that triggers the hydrogen leak alarm and emergency shutdown of the hydrogen supply is not impacted by the leakage diameter.However, the location is affected by the direction of the leak and the presence of obstructions near the hydrogen detectors.
This study provides quantitative data that can be used to optimise hydrogen safety in hydrogen-fuel-cell-powered ships.However, the investigation did not include the risk associated with high-pressure hydrogen systems with a pressure of 35 MPa; future work will focus on this aspect.Overall, this study provides a reference for the safety design of hydrogen-fuel-cell-powered ships, which is especially relevant given the current early stages of demonstrations for such ships.

Figure 1 .
Figure 1.Hydrogen leakage event tree in enclosed space or confined space.

Figure 1 .
Figure 1.Hydrogen leakage event tree in enclosed space or confined space.

Figure 2 .
Figure 2. Framework of this study.

Figure 2 .
Figure 2. Framework of this study.

Figure 4 .
Figure 4. Top view of arrangement in fuel cell room.

Figure 4 .
Figure 4. Top view of arrangement in fuel cell room.

Figure 4 .
Figure 4. Top view of arrangement in fuel cell room.2.1.1.Hydrogen Fuel System and Leakage Risk

Figure 6 .
Figure 6.Comparison of the simulation results and the experimental results.

Figure 6 .
Figure 6.Comparison of the simulation results and the experimental results.

Figure 7 .
Figure 7. Three-dimensional view of the grid sizes, gas monitoring points on the YZ plane (X = 0.1 m), and internal equipment in the fuel cell room.

Figure 7 .
Figure 7. Three-dimensional view of the grid sizes, gas monitoring points on the YZ plane (X = 0.1 m), and internal equipment in the fuel cell room.

Figure 8 .
Figure 8. Three-dimensional views of hydrogen gas dispersion in the fuel cell room at different times from 1 s to 6 s. (the times represent the seconds after the start of hydrogen leakage).

Figure 8 .
Figure 8. Three-dimensional views of hydrogen gas dispersion in the fuel cell room at different times from 1 s to 6 s. (the times represent the seconds after the start of hydrogen leakage).

Figure 11 .
Figure 11.Hydrogen concentration at MP11 for different leak diameters.

Figure 11 .
Figure 11.Hydrogen concentration at MP11 for different leak diameters.

Figure 12 .
Figure 12.Monitoring points identified for different leakage directions.

Figure 12 .
Figure 12.Monitoring points identified for different leakage directions.

Table 2 .
Reasons for hydrogen leakage in hydrogen gas supply system.
• Improper transportation and storage of valves • The machining accuracy of pipe joint is too low • Valve's uneven wear during use • The surface finish of pipe joint does not meet the requirements • Impurities cause scratches on the sealing surface • Poor expansion welding technology • The symmetry of flange is poor in installation • Workers did not follow the installation process • Loose fastening sleeve or thread • Accidental collision of pipeline • Failure of sleeve joints or threaded joints • Pipeline safety protection measures are not in place • Uneven pre-tightening force on the sleeve or thread • Weld cracking • Aging of valves filler •

Table 2 .
Reasons for hydrogen leakage in hydrogen gas supply system.
•Improper transportation and storage of valves•The machining accuracy of pipe joint is too low • Valve's uneven wear during use • The surface finish of pipe joint does not meet the requirements • Impurities cause scratches on the sealing surface • Poor expansion welding technology • The symmetry of flange is poor in installation • Workers did not follow the installation process • Loose fastening sleeve or thread • Accidental collision of pipeline • Failure of sleeve joints or threaded joints • Pipeline safety protection measures are not in place• Uneven pre-tightening force on the sleeve or thread • Weld cracking • Aging of valves filler

Table 3 .
Environmental parameters and ventilation parameters of fuel cell room.

Table 4 .
Dimensions and locations of the equipment in the fuel cell room.

Table 5 .
Leakage scenarios and parameters.

Table 6 .
Coordinates of the gas monitoring points.

Table 6 .
Coordinates of the gas monitoring points.

Table 7 .
Time points and corresponding monitoring points when the hydrogen concentration first reached 0.8% and 1.6% in scenarios 5-24.