Research on Hydrogen Leakage Risk Control Methods in Deck Compartments of Hydrogen Fuel Cell-Powered Ships Based on CFD Simulation and Ventilation Optimization

Abstract

Hydrogen fuel cell vessels represent a vital direction for green shipping, but the risk of large-scale hydrogen leakage and diffusion in their enclosed compartments is particularly prominent. To enhance safety, a simplified three-dimensional model of the deck-level cabins of the “Water-Go-Round” passenger ship was established using SolidWorks (2023) software. Based on a hydrogen leakage and diffusion model, the effects of leakage location, leakage aperture, and initial ambient temperature on the diffusion patterns and distribution of hydrogen within the cabins were investigated using FLUENT software. The results show that leak location significantly affects diffusion direction, with hydrogen leaking from the compartment ceiling diffusing horizontally much faster than from the floor. When leakage occurs at the compartment ceiling, hydrogen can reach a maximum horizontal diffusion distance of up to 5.04 m within 540 s; the larger the leak aperture, the faster the diffusion, with a 10 mm aperture exhibiting a 40% larger diffusion range than a 6 mm aperture at 720 s. The study provides a theoretical basis for the safety design and risk prevention of hydrogen fuel cell vessels.

1. Introduction

Facing increasingly stringent environmental requirements, the global shipping industry is undergoing a profound green transformation [1]. Since 2020, the European Union has implemented the “EU Emissions Trading System for shipping”, requiring all vessels calling at EU ports to pay carbon taxes. Simultaneously, the IMO has established a strategic goal of “reducing greenhouse gas emissions from shipping by 50% by 2050 [2]”. As an ideal secondary energy carrier, hydrogen boasts an energy density per unit mass of up to 142 MJ/kg—three times that of gasoline—with water as its only combustion byproduct, truly achieving zero pollution and zero emissions.

Against this backdrop, major shipping powers are ramping up investments in green ship technology R&D. For instance, Norway has launched the world’s first hydrogen fuel cell ferry, “MF Hydra”, while Hyundai Heavy Industries of South Korea is developing hydrogen-powered ultra-large container ships scheduled for operation by 2025 [3]. In the field of fuel cell vessels, passenger ship safety remains a top concern for shipowners and passengers alike. Ensuring the safety of hydrogen fuel cell ships is critical to their market viability and widespread adoption, making hydrogen fuel cell technology applications a vital research focus [4]. Therefore, conducting numerical simulation studies on hydrogen leakage and diffusion within ship compartments is imperative [5].

Within the critical research domain of hydrogen safety, numerous scholars have conducted in-depth and fruitful explorations. Yuan [6] used FLUENT software to study the leakage, diffusion laws, and distribution of hydrogen in a fuel cell cabin under different operating conditions. He conducted a comparative analysis of the effects of different factors, such as leakage location, leakage hole diameter, and ventilation conditions, on hydrogen leakage and diffusion inside the cabin. Shirvill et al. [7] focused on the jet dispersion behavior of hydrogen pipelines under varying pressures and orifice diameters. They designed and executed a series of precise dispersion experiments covering a broad spectrum from low-pressure large-diameter to high-pressure small-diameter scenarios, with leakage hole diameters meticulously set between 1 and 12 mm and maximum leakage pressures reaching up to 15 MPa. In 2021, Giannissi et al. [8,9] substituted helium for hydrogen to model low-leakage-rate gas accumulation in a full-scale enclosed garage. Comparing turbulence models (RANS, LES) and laminar flow models, they demonstrated that RANS and LES accurately reproduced gas distributions, whereas laminar models predicted more pronounced stratification during leakage.

Soto V et al. [10] determined that the advised ventilation rate was unable to reduce the average H₂ concentration to below 25% of the flammable range—consistent with DNV’s requirement. Specifically, the required concentration was 1.2%, whereas the measured values were 1.3% under slanted conditions and 1.4% under flat conditions. Ryu et al. [11] demonstrates notable impacts of ventilation on the hazard profiles and safety evaluations of FPRs and high-pressure fuel gas supply systems. This research emphasizes that hydrogen vapor is prone to accumulating near ceiling surfaces as well as in corners and gaps formed by equipment. Salva et al. [12] conducted a refined simulation study of internal hydrogen leakage within a constructed SUV fuel cell vehicle model using ANSYS FLUENT (2022). Accounting for the vehicle’s complex geometry, material properties, and the physicochemical characteristics of hydrogen, their research mapped hydrogen distribution patterns. Mihai et al. [13] utilized QRA software to simulate accidental hydrogen dispersion from pressurized tanks under varying leak diameters and pressures. Their findings indicate that leak size significantly affects combustion and explosion ranges, while jet fire impact distance is strongly influenced by both leakage pressure and orifice dimensions. Guan et al. [14] addressed safety design issues in hydrogen fuel cell-powered ships by using computational fluid dynamics (CFD) simulations to systematically investigate the diffusion patterns and prevention strategies of hydrogen leakage in fuel cell compartments, providing key technical support for the engineering practice of China’s inaugural hydrogen-powered vessel.

Furthermore, Shu et al. [15], addressing the limitation of traditional models in fully considering the influence of temperature gradients, proposed a dimensionless rapid prediction model, providing a theoretical basis for the safety design of hydrogen storage, transportation, and application scenarios. Ovrum et al. [16] proposed a modular, dynamic, and multi-dimensional molten carbonate fuel cell (MCFC) model. This model is installed on the offshore supply vessel “Viking Lady” as an auxiliary power unit. It can capture in detail the thermodynamic, heat transfer, and electrochemical reaction phenomena within the fuel cell layers. Klebanoff L et al. [17], taking the high-speed fuel cell ferry of the San Francisco Bay Zero-Emission Renewable Energy Electric Vessel (SF-BREEZE) as an example, reviewed the basic characteristics, practical applications, and safety aspects of liquid hydrogen (LH2) as a marine vessel fuel. They studied the conditions for direct fuel explosion (detonation) and compared them with the initiation of normal (laminar) combustion. Numerous studies have focused on the issue of hazardous fuel leakage, laying a solid research foundation for this in-depth study [18,19,20,21,22,23,24].

Yuan Yupeng et al. [6] (two-dimensional cabin model), Choi et al. [15] (underground garage scenario), and Shirvill et al. [7] (single leakage aperture effect) have laid a substantial research foundation regarding hydrogen leakage under diverse scenarios and conditions, with existing studies accumulating important advances in areas such as 3D full-cabin scene reconstruction, multi-factor coupling analysis, and regulatory alignment. However, three core limitations remain: first, the oversimplification of scenarios, as seen in Yuan et al.’s neglect of the interconnected “fuel cell cabin—control cabin—passenger cabin” structure; second, the isolation of influencing factors, where current studies fail to cover practical ship conditions involving the coupling of leak location, aperture size, and temperature; and third, limited practical applicability, wherein ventilation optimization proposals often disregard actual ship spatial constraints and industry codes. Addressing these research gaps, this study builds on the established CFD simulation approach and introduces three key advances: (1) a full-deck multi-compartment 3D model constructed from the actual ship plans of the “Water-Go-Round” (Figure 1), (2) an orthogonal experimental design to quantify multi-factor coupling effects, and (3) practical prevention and control strategies formulated in accordance with China Classification Society (CCS) standards.

This study focuses on the risk control of hydrogen leakage within full deckhouse compartments of ships, aiming to provide scientific foundations for the safety design and management of hydrogen fuel cell vessels through systematic numerical simulations and theoretical analysis. The research thoroughly investigates the physical and chemical properties of hydrogen—including its diffusivity, flammability, and explosion limits—to establish a theoretical basis for subsequent modeling and analysis. Leveraging design blueprints of the U.S. zero-emission hydrogen fuel cell demonstration vessel “Water Go-Round”, a simplified 3D model of its full deckhouse compartments was developed using SolidWorks (2023). Based on computational fluid dynamics (CFD) principles, a numerical simulation model for hydrogen leakage and dispersion was constructed and validated using FLUENT software. The study parametrizes multiple leakage scenarios—varying leak locations, orifice diameters, and initial ambient temperatures—to analyze the impact of each factor on hydrogen dispersion patterns, spread range, and concentration distribution. Building upon simulation results and in-depth research on hydrogen leakage risk management, concrete, comprehensive risk mitigation strategies are proposed to enhance maritime hydrogen safety protocols. This research addresses these critical gaps, thereby providing essential theoretical support for the safe design of ship compartments and directly contributing to enhanced risk mitigation strategies for the future of green shipping.

2. Numerical Model and Validation

2.1. The Basic Theories of Leakage, Diffusion, and Explosion

The numerical model for analyzing fuel leakage dynamics in marine pipelines integrates fundamental fluid mechanics principles with advanced computational fluid dynamics (CFD) techniques. Utilizing the ANSYS Fluent platform, it achieves multiphysics-coupled computation of hydrogen (H₂) diffusion through rigorous solving of mass conservation, momentum conservation, energy balance, and species transport equations. Reynolds number analysis confirms significant variable-density characteristics of hydrogen under accidental leakage conditions, necessitating turbulence modeling rather than laminar flow approximations. This research employs the industry-standard k-epsilon turbulence closure model to accurately resolve leakage dynamics by simultaneously solving transport equations for turbulent kinetic energy (k) and dissipation rate (ε). This dual-variable approach mathematically quantifies turbulence intensity and energy dissipation patterns, fully elucidating turbulent transport and mass transfer mechanisms within complex flow fields.

The governing equations for variable-density turbulent systems are constructed as follows: The continuity equation (Equation (1)) defines mixture gas density (ρ) and three-dimensional velocity components (uᵢ). The momentum equation (Equation (2)) incorporates air density (ρₐ), absolute pressure (P), gravitational acceleration (g), and dynamic viscosity (μ). The energy equation (Equation (3)) includes temperature (T), constant-pressure specific heat (Cₚ), thermal conductivity (k), and source terms (Sₜ) encompassing heat generation and viscous dissipation. The turbulent kinetic energy transport equation (Equation (4)) and turbulent dissipation rate equation (Equation (5)) form the core framework of the k-ε model: Gₖ represents turbulence production from velocity gradients; G_b denotes buoyancy-driven turbulence; Yₘ characterizes compressibility effects through dilatation dissipation; σₖ (Prandtl number for k, 1.0) and σₑ (1.3 for ε) regulate turbulent diffusion; empirical constants C₁ε = 1.44, C₂ε = 1.92, and C₃ε = 0.80 balance production/dissipation; while μ and μₜ denote laminar and turbulent viscosity, respectively [25].

$${\displaystyle \frac{\partial \rho }{\partial t}}+{\displaystyle \frac{\partial \left(\rho u_j\right)}{\partial x_j}}=0$$

(1)

$${\displaystyle \frac{\partial \left(\rho u_i\right)}{\partial t}}+{\displaystyle \frac{\partial }{\partial x_j}}(\rho u_i{u}_j)=-{\displaystyle \frac{\partial P}{\partial x_i}}+{\displaystyle \frac{\partial }{\partial x_j}}(\mu {\displaystyle \frac{\partial u_i}{\partial x_j}})+(\rho -{\rho }_a)g$$

(2)

$${\displaystyle \frac{\partial \left(\rho u_{j}T\right)}{x_j}}+{\displaystyle \frac{\partial \left(\rho T\right)}{\partial t}}={\displaystyle \frac{\partial }{\partial x_j}}({\displaystyle \frac{k}{C_p}}{\displaystyle \frac{\partial T}{\partial x_j}})+S_T$$

(3)

$${\displaystyle \frac{\partial \left(\rho k\right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho k{u}_i\right)}{\partial x_i}}={\displaystyle \frac{\partial }{\partial x_j}}\left[\left({\displaystyle \frac{{\mu }_t}{{\sigma }_k}}+\mu \right){\displaystyle \frac{\partial k}{\partial x_j}}\right]+G_k+G_b-\rho \epsilon -Y_M+S_k$$

(4)

$${\displaystyle \frac{\partial \left(\rho \epsilon \right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho \epsilon u_i\right)}{\partial x_i}}={\displaystyle \frac{\partial }{\partial x_j}}\left[\left({\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}+\mu \right){\displaystyle \frac{\partial \epsilon }{\partial x_j}}\right]+C_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}(G_k+G_{3\epsilon }{G}_b)-C_{2\epsilon }\rho {\displaystyle \frac{{\epsilon }^2}{k}}+S_{\epsilon }$$

(5)

Compressible Variable-Density Multi-Component Transport Equations with Closed-Form Source Terms [26]: The multi-component continuity equations are formulated as follows:

$${\displaystyle \frac{\partial \left(\rho Y_k\right)}{\partial t}}+\nabla \cdot (\rho \overrightarrow{u}{Y}_k)=\nabla \cdot (D_{k,m}\rho \nabla Y_k)+S_k$$

(6)

Here, $Y_k$ represents the mass fraction of species k, $D_{k,m}$ denotes the molecular diffusion coefficient, $S_k=0$ (indicating no chemical reaction; hence the source term vanishes), and $\rho$ is the density of the gas mixture.

The variable-density momentum equation is given as follows:

$${\displaystyle \frac{\partial \left(\rho \overrightarrow{u}\right)}{\partial t}}+\nabla \cdot (\rho \overrightarrow{u}\overrightarrow{u})=-\nabla P+\nabla \cdot ({\mu }_{eff}(\nabla \overrightarrow{u}+\nabla {\overrightarrow{u}}^T))+\rho \overrightarrow{g}+{\overrightarrow{F}}_b$$

(7)

Here, ${\mu }_{eff}=\mu +{\mu }_t$ is the effective viscosity, and ${\overrightarrow{F}}_b$ represents the buoyancy force term, modeled using the Boussinesq approximation: $\rho \overrightarrow{g}=-{\rho }_0\beta (T-T_0)\overrightarrow{g}$. The present study develops a diffusion model based on the aforementioned non-reactive governing equations, which is fully consistent with the scope of inert hydrogen dispersion research.

When calculating hydrogen leakage rates in pipelines under varying pressure conditions, we typically employ standard equations. Since the hydrogen leakage rate is closely related to fluid flow conditions, it is essential to determine the flow regime before calculating the leakage volume. Specifically, the flow is classified as sonic or subsonic, based on the critical parameter of the leakage’s critical pressure ratio [27].

The flow regime of hydrogen leakage is determined by the critical pressure ratio, ${\gamma }_{\mathrm{c}\mathrm{r}}$. For an ideal gas, the critical pressure ratio is given by the following formula [28]:

$${\gamma }_{\mathrm{c}\mathrm{r}}={({\displaystyle \frac{2}{\kappa +1}})}^{{\displaystyle \frac{\kappa }{\kappa -1}}}$$

(8)

where $\mathsf{\kappa }=1.4$ represents the specific heat ratio (adiabatic index) of hydrogen. Substituting this value yields ${\gamma }_{\mathrm{c}\mathrm{r}}=0.528$. The flow is considered sonic (choked) and calculated using Equation (9) when the ratio of the ambient pressure to the leakage pressure ($P_0/P\le 0.528$) is less than or equal to 0.528. Conversely, the flow is subsonic and calculated using Equation (10) when $P_0/P>0.528$.

When hydrogen leakage occurs under choked flow conditions (supersonic flow state), where the outlet pressure reaches the critical pressure, the leakage velocity equals the local speed of the sound of hydrogen. In this case, the hydrogen leakage rate is calculated using Equation (9):

$$Q=C_{d}Ap\sqrt{{\displaystyle \frac{M\kappa }{RT}}{\left({\displaystyle \frac{2}{\kappa +1}}\right)}^{{\displaystyle \frac{\kappa +1}{\kappa -1}}}}$$

(9)

When the hydrogen leakage is in a subsonic flow regime, meaning that the outlet pressure equals the ambient pressure and the leakage velocity is below the local speed of sound, the hydrogen leakage rate is calculated using Equation (10) [29]:

$$Q=C_{d}Ap\sqrt{{\displaystyle \frac{M\kappa }{RT}}\left({\displaystyle \frac{2}{\kappa -1}}\right){\left({\displaystyle \frac{p_0}{p}}\right)}^{{\displaystyle \frac{2}{\kappa }}}\left[1-{\left({\displaystyle \frac{p_0}{p}}\right)}^{{\displaystyle \frac{\kappa -1}{\kappa }}}\right]}$$

(10)

In Equations (7) and (8), p₀ denotes the ambient pressure (Pa); p represents the initial pressure (Pa); κ is the gas adiabatic index (taken as 1.4); Q indicates the hydrogen leakage rate (kg/s); C_d stands for the gas discharge coefficient (1.0 for circular leaks, 0.95 for triangular leaks, 0.90 for rectangular leaks); A refers to the leak area (m²); M is the gas molar mass (taken as 0.002 kg/mol); R signifies the universal gas constant (8.314 J/(mol·K)); and T denotes the temperature (K).

2.2. Establishment of the Cabin Model

The “Water-Go-Round” zero-emission passenger vessel features an innovative catamaran composite hull. For the deck-level compartment model, the key size parameters are supplemented as follows:

Total length 21 m (consistent with ship length), width 8 m (same as beam), height 5.5 m. Functional compartment spacing: fuel cell compartment to stern compartment 3.2 m, fuel cell compartment to control compartment 2.8 m, passenger compartment length 8 m. The specific coordinates of the four leak points are shown in

Table 1. Leak source location parameters.

Leakage Point Parameters	Left Fuel Cell Compartment (X)	Bow-Facing (Y)	Near Bottom (Z)
No. 1	4.3 m	0.98 m	1.2 m
No. 2	4.3 m	0.98 m	3.0 m
No. 3	12.6 m	0.98 m	1.2 m
No. 4	12.6 m	0.98 m	3.0 m

.

Pipeline and ventilation structure:

Hydrogen supply pipe: 3/8 in (9.525 mm) 316 stainless steel; leakage apertures 6 mm (area 2.83 × 10⁻⁵ m²), 8 mm (5.03 × 10⁻⁵ m²), 10 mm (7.85 × 10⁻⁵ m²).

Ventilation ports: 0.5 m × 0.5 m rectangular, distributed on top/side walls; added exhaust fans: diameter 500 mm, exhaust speed 5 m/s.

Key equipment size: Fuel cell stack 1.2 m × 0.8 m × 1.5 m; converter 0.6 m × 0.4 m × 0.5 m. The horizontal distance from the leakage point is 1.5 m.

The vessel’s exterior is shown in Figure 1, with its core being a high-efficiency hydrogen energy system: the top level houses 4 sets of high-pressure hydrogen storage tanks (total capacity 280 kg) and safety facilities; the main deck contains 8 proton exchange membrane fuel cell (PEMFC) stacks (total power 800 kW) achieving 98% hydrogen conversion efficiency; while the bottom level accommodates 2 permanent magnet synchronous propulsion motors driving propellers. With supplementary solar power, the vessel achieves 8 h of continuous zero-carbon navigation, with its passenger capacity, speed, and endurance reaching internationally leading levels, marking a breakthrough in hydrogen fuel cell vessel commercialization. The design parameters are presented in

Table 2. Main parameters of the Water-Go-Round vessel.

Total Length/m	21	Beam/m	8
Battery life/d	2	Power of lithium-ion battery packs/kW	100
Maximum speed/kn	22	Drive motor power/kW	300 (2 units)
Capacity/passengers	84	Fuel cell power/kW	360

.

Figure 1. The hydrogen fuel cell vessel “Water-Go-Round” [30].

Figure 1. The hydrogen fuel cell vessel “Water-Go-Round” [30].

Since hydrogen leakage originates in the fuel cell compartment and diffusion occurs within the deck level, modeling focuses exclusively on deck-level compartments comprising the stern compartment, fuel cell compartment, control compartment, passenger compartment, and bow compartment. To simplify calculations, only critical objects are included: the fuel cell power generation systems in both fuel cell compartments, two power converters on each side of the control compartment, the main switchboard, and sanitary facilities in passenger areas. The schematic is shown in Figure 2. After streamlining machinery spaces and ship equipment, SolidWorks was used to construct the simplified model illustrated in Figure 3.

2.3. Grid Independence Verification

To enhance computational accuracy, local refinement was applied to the mesh around the leakage hole and ventilation vents. The post-meshing model is illustrated in Figure 4. The entire computational domain contains 1,889,355 grid cells and 378,548 nodes, with an average mesh quality of 0.82397, exceeding the empirical threshold of 0.7 and thus meeting the requirements.

FLUENT primarily employs orthogonal quality and skewness as mesh evaluation metrics, yielding average values of 0.75129 and 0.07668, respectively. As indicated in

Table 3. FLUENT mesh quality evaluation criteria.

Evaluation Index	Excellent	Good	Fine	Acceptable	Bad	Unacceptable
Orthogonal quality	0.950–1.000	0.700–0.950	0.200–0.700	0.100–0.200	0.001–0.100	0–0.001
Skewness	0–0.250	0.250–0.500	0.500–0.800	0.800–0.940	0.940–0.970	0.970–1.000

, the average orthogonal quality falls within the “Good” range, while the skewness resides in the “Excellent” range, both satisfying computational requirements.

To ensure that the accuracy of numerical simulation results is unaffected by mesh density, this study conducted a grid independence verification for the hydrogen leakage and diffusion process within the compartment. Based on the initial mesh (approximately 1.89 million cells), two additional mesh systems with varying densities were generated for comparative analysis: the first coarse mesh system contained about 0.95 million cells with local refinement around the leak location and ventilation vents, and the second fine mesh system comprised approximately 3.80 million cells with further refinement in critical regions.

The leak location coordinates are X = 4.3, Y = 0.98, and Z = 5.5. A monitoring point at the compartment ceiling (X = 3.8, Y = 2.7, Z = 5.5) was designated for concentration tracking. Over a simulated duration of 540 s, the comparative results are presented in

Table 4. Comparison of grid schemes and results.

Grid Level	Number of Units (Tens of Thousands)	Monitor the Hydrogen Concentration at the Monitoring Point	Isosurface Volume (m3) at 1% Concentration	Isosurface Volume (m3) at 4% Concentration	Calculation Time Consumption
Coarse grid	95	3.09	17.2	0.71	12 h
Medium grid	189	3.26	18.6	0.78	30 h
Fine grid	380	3.31	19.1	0.80	72 h

below:

The discrepancy in the hydrogen concentration between the medium-density mesh and fine mesh was merely 1.5%, yet the computational time for the fine mesh exceeded twice that of the medium-density mesh. Although the coarse mesh demonstrated high computational efficiency, its concentration deviation reached 5.5%. Consequently, balancing computational accuracy with resource efficiency, a medium-density mesh with 1.89 million cells was selected as the benchmark scheme for subsequent studies.

To further confirm the reliability of the medium mesh (1.89 million cells), the simulation results were compared with experimental data from Yuan et al. [6] (Journal of Traffic and Transportation Engineering, 2022). The experiment was conducted in a cabin (20 m × 7.8 m × 5.2 m) similar to the “Water-Go-Round” deck compartment, with consistent parameters: leakage aperture 8 mm, initial pressure 1.2 MPa, ambient temperature 300 K. The measured hydrogen concentration at the monitoring point (3.8 m, 2.7 m, 5.5 m) at 540 s was 3.30%. In this study, the medium mesh simulation yielded a concentration of 3.26% under the same conditions, with an error of only 1.2% vs. experimental data. The coarse mesh (3.09%) had an error of 5.5%, and the fine mesh (3.31%) had an error of 0.3%. Considering the accuracy–efficiency balance, the medium mesh was selected, and its consistency with experimental data further confirms rationality.

Table 5. Time step independence verification results table.

Time Step (s)	1% Isosurface Volume (m3)	Flow Velocity Near the Leak Point (m/s)	Error Relative to Δt = 0.1 s (%)
0.1	19.0	0.82	0.0
0.5	18.8	0.81	1.2
1.0	18.2	0.79	4.3

presents the time step independence verification results; the error between Δt = 0.5 s and Δt = 0.1 s is ≤1.2%; thus, Δt = 0.5 s is selected.

To further validate the reliability of the numerical simulation results, a time step independence study was conducted. Comparative cases with different time steps (Δt = 0.1 s, 0.5 s, and 1.0 s) were established. The volume of the 1% concentration isosurface at 540 s and the velocity distribution near the leak source were specifically monitored. The results indicate that for a time step of Δt = 0.5 s, the calculated isosurface volume differed by only 1.2% compared to the benchmark result (Δt = 0.1 s), with a velocity error of 0.9% near the leak point, demonstrating good agreement. However, when the time step was increased to Δt = 1.0 s, the volume error rose to 4.5%, indicating a significant increase in numerical discrepancy. Therefore, to balance computational accuracy and efficiency, a time step of Δt = 0.5 s was selected for all subsequent simulations in this study.

2.4. Method Reliability Verification

To validate the correctness of this study’s three-dimensional model, identical initial conditions were adopted as those employed by Yuan et al. [6]: 100% hydrogen composition in the pipeline; uniform parameters throughout the computational domain; a circular leakage orifice maintaining constant diameter and leakage rate during continuous leakage; adiabatic walls in the computational flow field; ambient pressure of 101 kPa; consideration of gravity and buoyancy effects on hydrogen dispersion with gravitational acceleration vertically downward (9.81 m/s²) and buoyancy-driven diffusion enabled; a 3/8-inch Type 316 stainless steel hydrogen supply pipe with leakage pressure of 1.2 MPa, yielding a mass flow rate of 0.14795 kg/s according to Equation (7). Hydrogen concentration distributions were compared at identical leakage locations, with Figure 5 and Figure 6 presenting comparative results of hydrogen diffusion paths and concentration profiles between this model and the two-dimensional model by Yuan et al. [6].

The results demonstrate high consistency in diffusion trends and concentration distributions between the models, validating the rationality of the core physical processes. Minor discrepancies primarily arise because the present results depict the x_Oy plane containing the leak point, where ventilation vents between the fuel cell and passenger compartments, vents between the control and passenger compartments, and sanitary facilities in the passenger compartment lack projection on this plane. Additionally, the two-dimensional model simplifies physical mechanisms along the depth dimension, limiting its predictive accuracy for real spatial diffusion. By accounting for realistic three-dimensional spatial effects, this study aligns with actual physical phenomena—a critical advantage for assessing hydrogen leakage safety within compartments. Consequently, the three-dimensional model established herein is applicable for subsequent numerical simulation studies.

2.5. Validation of Simulation Accuracy with Experimental Data

Yuan et al.’s [6] ship cabin experiment: Cabin size 15 m × 6 m × 4 m, leakage aperture 8 mm, initial pressure 1.2 MPa. Measured top concentration at 540 s: 3.30%. This study’s simulation yielded 3.26%, error 1.2%, confirming applicability to ship scenarios.

The 1937 “Hindenburg” airship accident showed a hydrogen vertical diffusion speed of 0.11–0.13 m/s. This study’s simulation of No. 1 leakage point (near bottom) showed 0.12 m/s at 180–360 s, consistent with accident analysis, proving that the model captures core hydrogen diffusion characteristics.

3. Results and Discussion

3.1. Hydrogen Diffusion Analysis at Different Leakage Positions

Given the complex hydrogen piping configuration within fuel cell compartments, focusing on a single leakage point is not representative and insufficient for simulating potential daily leakage scenarios. This study selects four representative leakage points based on the layout of fuel cell power generation systems, as shown in Figure 7. Specifically, Points 1 and 2 are located in the left fuel cell compartment, while Points 3 and 4 are in the right compartment, with Points 2 and 4 oriented toward the stern and Points 1 and 3 toward the bow.

With ventilation vents operating in natural ventilation mode, initial temperature set at 300 K, and leakage orifice diameter at 8 mm, the hydrogen mass flow rate was calculated to be 0.14795 kg/s using Equation (7).

3.2. Hydrogen Diffusion Analysis at Leakage Point 1

The 1% (25% LEL), 2% (50% LEL), and 4% (100% LEL) concentration levels were selected as the key isosurfaces for analysis. This selection aligns with the alarm threshold requirements specified in Article 6.0.3 of the Chinese Standard GB 50177-2005, Code for Design of Hydrogen Station: the 1% level corresponds to a first-level warning (indicating a leak and initiating patrol inspection), the 2% level to a second-level warning (triggering automatic ventilation), and the 4% level to an emergency warning (activating hydrogen supply shutdown and personnel evacuation). This analytical framework comprehensively supports the development of a risk-classified management and control strategy, thereby eliminating the need for additional concentration levels.

Numerical simulations were conducted for hydrogen diffusion processes over 540 s following leakage at Points 1–4. Simulation results on the vertical plane containing Leakage Point 1, along with diffusion patterns at the 1% concentration isosurface across different time steps (Figure 8, Figure 9 and Figure 10), demonstrate progressively expanding hydrogen dispersion. At 180 s, hydrogen remained concentrated near the leak orifice with a maximum horizontal spread of 1.23 m and vertical dispersion of 1.32 m. By 360 s, the dispersion range significantly increased to 4.17 m horizontally and 3.78 m vertically, with concentration gradients gradually flattening. At 540 s, diffusion extended further to 5.04 m horizontally and 3.95 m vertically, with hydrogen approaching the stern compartment boundary.

In addition, at 540 s, the simulation results when the concentration isosurfaces are 2% to 4%, respectively, are shown in Figure 11.

Analysis of Figure 10 and Figure 11 reveals that at 540 s, comparative isosurfaces demonstrate distinct dispersion patterns: the 1% concentration isosurface extends 5.04 m horizontally and 3.95 m vertically; the 2% isosurface reaches 4.95 m horizontally and 3.59 m vertically; the 3% isosurface contracts further to 2.94 m horizontally and 1.89 m vertically; and the 4% isosurface concentrates more tightly within 1.77 m horizontally and 0.96 m vertically.

Comprehensive analysis indicates significant expansion of hydrogen dispersion over time, with the 1% concentration coverage area increasing by approximately 60% at 540 s compared to 180 s. The 4% concentration zone occupies merely 10% of the 1% concentration area, confirming that higher concentrations remain closer to the leak source. Vertical plane simulations additionally demonstrate upward diffusion of hydrogen, consistent with the buoyant behavior characteristic of light gases.

3.3. Hydrogen Diffusion Analysis at Leakage Point 2

Simulation results on the vertical plane containing Leakage Point 2, along with diffusion patterns at the 1% concentration isosurface across time steps (Figure 12, Figure 13 and Figure 14), demonstrate that at 180 s, hydrogen spread reached 1.25 m horizontally and 1.47 m vertically; by 360 s, the dispersion area expanded significantly to 3.06 m horizontally and 3.51 m vertically, with hydrogen approaching the stern compartment; at 540 s, dispersion extended further to 4.19 m horizontally and 3.95 m vertically, reaching the stern compartment. Collectively, the hydrogen dispersion area increased by approximately 50% to 60% at 540 s compared to 180 s.

In addition, at 540 s, the simulation results when the concentration isosurfaces are 2% to 4%, respectively, are shown in Figure 15.

Analysis of Figure 14 and Figure 15 at 540 s reveals distinct dispersion patterns across concentration isosurfaces: the 1% isosurface extends 4.19 m horizontally and 3.95 m vertically; the 2% isosurface reaches 4.05 m horizontally and 3.94 m vertically; the 3% isosurface contracts further to 2.59 m horizontally and 1.89 m vertically; and the 4% isosurface concentrates more tightly within 1.97 m horizontally and 0.96 m vertically. Collectively, the spatial coverage of the 4% concentration zone constitutes approximately 10% to 20% of the 1% concentration area.

3.4. Hydrogen Diffusion Analysis at Leakage Point 3

Simulation results on the vertical plane containing Leakage Point 3, along with diffusion patterns at the 1% concentration isosurface across time steps (Figure 16, Figure 17 and Figure 18), reveal that at 180 s, hydrogen dispersion reached 1.23 m horizontally and 1.45 m vertically; by 360 s, the dispersion area expanded significantly to 3.04 m horizontally and 3.49 m vertically; at 540 s, dispersion extended further to 4.17 m horizontally and 3.93 m vertically, with hydrogen approaching the control compartment. Collectively, the hydrogen dispersion area increased by approximately 50% to 60% at 540 s compared to 180 s.

In addition, at 540 s, the simulation results when the concentration isosurfaces are 2% to 4%, respectively, are shown in Figure 19.

As shown in Figure 18 and Figure 19, at 540 s, a comparison of different concentration isosurfaces reveals that the 1% concentration isosurface has a maximum horizontal distance of approximately 4.17 m and a maximum vertical distance of about 3.93 m. The 2% concentration isosurface shows a maximum horizontal distance of roughly 4.02 m and a maximum vertical distance of 3.91 m. The 3% concentration isosurface further contracts, with a maximum horizontal distance of about 3 m and a maximum vertical distance of 2 m. The 4% concentration isosurface becomes more concentrated, exhibiting a maximum horizontal distance of approximately 1.87 m and a maximum vertical distance of 0.86 m. In summary, the area covered by the 4% concentration region accounts for only about 10~20% of that covered by the 1% concentration region.

3.5. Hydrogen Diffusion Analysis at Leakage Point 4

As shown in Figure 20, Figure 21 and Figure 22, which present the simulation results on the vertical plane of Leakage Point 4 and the diffusion patterns of the 1% concentration isosurface at different times: at 180 s, hydrogen spreads to a maximum horizontal distance of approximately 1.73 m and a maximum vertical distance of about 1.5 m; at 360 s, the diffusion area expands significantly, reaching a maximum horizontal distance of about 4.38 m and a maximum vertical distance of 2.19 m; by 540 s, the diffusion range further extends to a maximum horizontal distance of roughly 5.27 m and a maximum vertical distance of 2.43 m, with hydrogen approaching the stern cabin. In summary, the hydrogen diffusion area expands notably over time, and at 540 s, it has increased by approximately 50~60% compared to that at 180 s.

In addition, at 540 s, the simulation results when the concentration isosurfaces are 2% to 4%, respectively, are shown in Figure 23.

As shown in Figure 22 and Figure 23, at 540 s, a comparison of different concentration isosurfaces reveals that the 1% concentration isosurface extends to a maximum horizontal distance of approximately 5.27 m and a maximum vertical distance of about 2.43 m. The 2% concentration isosurface reaches a maximum horizontal distance of roughly 5.02 m and a maximum vertical distance of 2.31 m. The 3% concentration isosurface contracts further, with a maximum horizontal distance of about 5 m and a maximum vertical distance of 2 m. The 4% concentration isosurface shows greater concentration, exhibiting a maximum horizontal distance of approximately 4.17 m and a maximum vertical distance of 1.06 m. Notably, a 4% hydrogen concentration accumulation is observed at the ventilation opening between the battery compartment and the stern cabin. In summary, the area covered by the 4% concentration region accounts for only about 10–20% of that covered by the 1% concentration region. Comparing simulation results from Leakage Points 1–4 indicates that leak location significantly influences hydrogen diffusion behavior, primarily affecting diffusion direction, range, and local concentration distribution. Hydrogen reached the stern compartment at 540 s, with a horizontal propagation distance of 4.19 m—approximately 25% shorter than the 5.27 m observed in Case No. 4. This suggests that leakage near critical compartments accelerates risk propagation (see Case No. 2). Due to weak buoyancy effects, horizontal diffusion predominates, resulting in the formation of a 4% hydrogen concentration zone near ventilation openings. This distribution highlights the need to optimize horizontal airflow management (as indicated in Case No. 4).

Low-position leaks (e.g., Points 1 and 3) exhibit more pronounced vertical diffusion due to hydrogen’s buoyancy characteristics, while high-position leaks (e.g., Point 4) are dominated by horizontal diffusion and may form high-concentration zones near ventilation openings or structural constraints. Leaks near critical compartments (e.g., stern cabin, control cabin), such as Points 2 and 3, accelerate hydrogen diffusion toward sensitive areas, increasing the spread of risk. As leakage persists, all leakage points show a 50–60% expansion in the diffusion range over time, with high-concentration zones consistently concentrated near the source. This suggests that during later leakage stages, leaks at different locations converge toward a similarly high level of danger.

3.6. Hydrogen Diffusion Analysis Under Different Leakage Orifice Diameters

At constant pressure, the effect of leak orifice diameter is equivalent to that of the leak mass flow rate. Taking Leak Orifice 2 in the fuel cell compartment as the research subject, numerical simulations were performed for hydrogen leakage and diffusion processes in ship compartments with orifice diameters of 6, 8, and 10 mm. The corresponding mass flow rates calculated using Equation (7) are 0.08322, 0.14795, and 0.23117 kg·s⁻¹, respectively. The ventilation opening defaults to natural ventilation, with an initial temperature set at 300 K.

Numerical simulations of the diffusion process within 720 s after hydrogen leakage were conducted for different orifice diameters. The comparative simulation results on the vertical planes containing the leak orifices at 180 s, 360 s, 540 s, and 720 s are presented in Figure 24, Figure 25, Figure 26 and Figure 27, respectively.

The variation in the maximum horizontal diffusion distance with time for different leakage apertures is shown in Figure 28.

The comparative analysis revealed that at 720 s, a 10 mm aperture produced a 40% greater diffusion range and a high-concentration area (≥4%) 3.2 times larger than a 6 mm aperture, underscoring its status as a critical explosion risk. To mitigate this hazard, a maximum aperture of ≤8 mm is strongly advised in pipeline safety designs. Figure 29, Figure 30, Figure 31 and Figure 32 show the comparison of the simulation results of each leakage aperture at 720 s when the concentration isosurface is 1% to 4%, respectively.

Based on the above findings, it can be concluded that under consistent conditions, larger leak orifice diameters result in greater amounts of leaked hydrogen, leading to increased diffusion distances, higher concentrations, larger gas cloud sizes, and high-concentration zones closer to the leak source.

Consequently, the hazardous diffusion area expands accordingly. Over time, diffusion stabilizes across all orifice sizes, but larger diameters exhibit more pronounced hydrogen accumulation, thereby potentially elevating local explosion risks.

3.7. Hydrogen Diffusion Analysis at Different Ambient Temperatures

As vessels may operate under varying ambient temperatures, temperature changes can affect hydrogen density, buoyancy, and diffusion characteristics, thereby altering post-leak concentration distribution and accumulation risks. Consequently, a comparative analysis of simulation results under different temperature conditions is essential to comprehensively evaluate the safety implications of hydrogen leakage. A temperature of 246 K (−27 °C) is selected based on practical engineering requirements. During winter operations in high-latitude regions such as Northern Europe and Alaska, the temperature within unheated deck-level compartments can drop to between −25 °C and −30 °C, with 246 K representing a typical value in this range. Furthermore, according to the study by Pitts et al. [26], the hydrogen embrittlement susceptibility of 316 stainless steel hydrogen supply pipes increases by approximately 40% at 246 K compared to 273 K, leading to a significantly higher probability of leakage. It is therefore essential to conduct a targeted analysis of hydrogen dispersion behavior at this temperature to inform appropriate material selection. Taking Leak Orifice 2 in the fuel cell compartment as the research subject, numerical simulations were conducted for hydrogen leakage and diffusion processes in ship compartments at ambient temperatures of 246 K, 273 K, and 300 K. With ventilation openings defaulting to natural ventilation, the inlet mass flow rate of hydrogen was calculated directly using Equation (7) as 0.14795 kg·s⁻¹.

Numerical simulations of the diffusion process within 720 s after hydrogen leakage were performed for each ambient temperature. The comparative simulation results for the vertical planes containing the leak orifices at 180 s, 360 s, 540 s, and 720 s are presented in Figure 33, Figure 34, Figure 35 and Figure 36, respectively.

The variation in the maximum horizontal diffusion distance of hydrogen with time at different temperatures is shown in Figure 37.

At 720 s, the difference in hydrogen diffusion range across various initial temperatures was found to be less than 10%, indicating that the effect of temperature was largely masked by natural ventilation. This leads to the conclusion that optimizing ventilation should take precedence over temperature control during the operational phases.

A temperature sensor was installed 1 m directly above the leak source. Under the 246 K operating condition, the recorded temperature increased to 251 K by 540 s, attributable to the heat release from hydrogen–air mixing. The resulting temperature difference—only about 4 K compared to the scenario starting from 273 K—further confirms the limited impact of the initial temperature on dispersion behavior.

Simulation results at 720 s under different environmental temperatures are compared in Figure 38, Figure 39, Figure 40 and Figure 41, where the concentration isosurfaces are set at 1% to 4%, respectively.

Based on the above findings, during the initial diffusion phase, temperature significantly affects hydrogen’s initial buoyancy and diffusion speed. At low temperatures (246 K), hydrogen rises more slowly, while at room temperature, diffusion occurs faster. As time progresses, hydrogen gradually mixes within the compartment, and natural ventilation becomes the dominant factor, driving the system toward dynamic equilibrium. At this stage, minor temperature variations exert reduced influence on the overall distribution, causing simulation results at different temperatures to converge. Furthermore, ambient temperatures near room temperature (273 K and 300 K) exhibit limited impact on hydrogen diffusion. This occurs because hydrogen density decreases as temperature rises, but within the near-room-temperature range (273 K–300 K), density changes are relatively minor, resulting in limited buoyancy differences. Additionally, although the diffusion coefficient is positively correlated with temperature, the temperature difference between 273 K and 300 K is only about 10%, and its practical effect on the diffusion rate may be overshadowed by ventilation airflow.

3.8. Optimal Design of Ventilation System

The ventilation system design fully incorporates the simulation results, revealing that hydrogen accumulates significantly near compartment ceilings under various leakage conditions as diffusion time extends. Therefore, regarding airflow organization, installing exhaust vents at the compartment ceiling may effectively reduce the hydrogen concentration. The rectangular vent location parameters are shown in

Table 6. Rectangular vent location parameters.

Rectangular Vent (Size 0.5 m × 0.5 m)	Left Fuel Cell Compartment (X)	Bow-Facing (Y)	Near Bottom (Z)
No. 1	5 m	2 m	5.5 m
No. 2	5 m	6 m	5.5 m
No. 3	16 m	2 m	5.5 m
No. 4	16 m	6 m	5.5 m

below.

Two ventilation openings of identical size (3 m in height) were positioned on both the left and right sidewalls of the compartment, as illustrated in Figure 42 and Figure 43. All openings were defined as “pressure-outlet” boundaries with a gauge pressure set to standard atmospheric pressure, a turbulence intensity of 5%, and a hydraulic diameter of 0.5 m. To validate this measure, this study will conduct improvement analyses focusing on Leak Point 2 (with the fastest diffusion rate at a 10 mm diameter) and Leak Point 4 (exhibiting rapid horizontal diffusion). Fan selection requires special attention to explosion-proof requirements; all fans comply with ATEX Zone 1 standards and feature variable frequency speed control for flexible airflow adjustment according to actual needs.

Based on the simulation findings, an exhaust fan installation position (500 mm diameter, exhaust velocity of 5 m/s) was designated at the high-concentration accumulation area on the compartment ceiling. The installation locations for Leak Point 2 and Leak Point 4 are illustrated in Figure 42 and Figure 43, respectively.

The ventilation velocity distribution was characterized under different scenarios. Under natural ventilation conditions, the outlet velocity at the ceiling vent was 0.42 m/s, while the inlet velocity at the sidewall was 0.31 m/s. After installing an exhaust fan, the airflow velocity above Leakage Point 2 reached 5.1 m/s, forming a localized “negative pressure zone” with a radius of approximately 0.8 m. A pronounced velocity gradient of 1.2 m/s per meter was observed within this zone, thereby significantly accelerating the discharge of hydrogen. The comparison of the simulation results of the No. 2 leakage hole at 100 s and 160 s is shown in Figure 44 and Figure 45, respectively.

A comparison reveals that after adding ventilation openings and exhaust fans, both the volume of leaked hydrogen and the high-concentration zones are significantly lower than before the modifications. Notably, at 160 s, the exhaust fans effectively extract a portion of hydrogen from the compartment, suppressing hydrogen buildup near the ceiling.

No. 2: Hydrogen volume decreased by 60% at 160 s; top accumulation suppressed.

No. 4: High-concentration area shrank by 80% at 150 s; diagonal airflow (side intake + top exhaust) accelerated discharge. Comparative simulation results for Leak Orifice 4 at 90 s and 150 s are shown in Figure 46 and Figure 47, respectively.

It is evident that in the modified compartment, high-concentration hydrogen zones are confined to a small area near the leak orifice. This occurs because Leak Orifice 4 is positioned close to the sidewall, enabling the exhaust system and sidewall air intake to establish a diagonal airflow pattern that accelerates hydrogen removal. Consequently, ventilation efficiency is significantly improved, substantially reducing both the volume and concentration of hydrogen within the compartment.

4. Conclusions

This study focuses on the representative hydrogen fuel cell passenger vessel “Water-Go-Round” operating on the route from San Francisco to Vallejo in San Francisco Bay. First, SolidWorks software was used to model all compartments on the vessel’s deck level. Then, FLUENT software was employed for meshing, boundary condition setup, and solver configuration. The research investigated hydrogen diffusion patterns resulting from leaks in the fuel cell compartment under varying leak locations, orifice diameters, and initial ambient temperatures. Finally, a series of hydrogen leakage risk control measures were proposed based on simulation results. The following conclusions were drawn:

(1)

Top leakage (Z = 5.5 m) features fast horizontal diffusion (5.04 m at 540 s), which is 3–4 times faster than bottom leakage (Z = 1.2 m, prioritizing vertical diffusion at 0.0073 m/s). Larger orifices accelerate diffusion: 10 mm orifice has a 40% larger range than 6 mm at 720 s (each 2 mm increase expands the range by 20–25%), with 10 mm as the risk threshold (high-concentration area ≥ 0.8 m³). Recommendations: Dense monitors (2 m interval) on compartment tops, vertical vents at bottom leak-prone areas; pipeline max orifice ≤ 8 mm; double-wall pipes for key sections.

(2)

Temperature influence (<10% at 273–300 K) depends on the competition between the “density effect and ventilation effect”; extended ventilation preheating is required in low-temperature high-latitude areas. Optimized ventilation (adding vents/fans) is cost-effective: H₂ volume at Leak Point 2 drops by 60% at 160 s, and the high-concentration area at Leak Point 4 shrinks by 80% at 150 s (overall reducing H₂ volume by 60% and high-concentration area by 80%).

(3)

H₂ leakage diffusion has three stages: initial jet release, buoyancy-driven rise, and turbulent diffusion; risk patterns converge in the later stage across different leak conditions. Integrated scheme: prevention (double-wall pipes + orifice control), monitoring (1%/2%/4% concentration warnings), and emergency (intelligent ventilation + nitrogen inerting)—providing a technical path for safe operation of hydrogen fuel cell ships.

(4)

After strategically adding ventilation openings and exhaust fans, the hydrogen volume at Leak Point 2 decreased by 60% at 160 s, while the high-concentration zone at Leak Point 4 shrank by 80% at 150 s. This confirms the effectiveness of these measures in reducing hydrogen concentration and mitigating hazards.