Numerical Analysis of the Effects of Ship Motion on Hydrogen Release and Dispersion in an Enclosed Area

Abstract

Hydrogen is an alternative to conventional heavy marine fuel oil following the initial strategy of the International Maritime Organization (IMO) for reducing greenhouse gas emissions. Although hydrogen energy has many advantages (zero-emission, high efficiency, and low noise), it has considerable fire and explosion risks due to its thermal and chemical characteristics (wide flammable concentration range and low ignition energy). Thus, safety is a key concern related to the use of hydrogen. Whereas most previous studies focused on the terrestrial environment, we aim to analyze the effects of the ship’s motion on hydrogen dispersion (using commercial FLUENT code) in an enclosed area. When compared to the steady state, our results revealed that hydrogen reached specific sensors in 63% and 52% less time depending on vessel motion type and direction. Since ships carry and use a large amount of hydrogen as a power source, the risk of hydrogen leakage from collision or damage necessitates studying the correspondence between leakage, diffusion, and motion characteristics of the ship to position the sensor correctly.

1. Introduction

Increasing concerns regarding climate change attributed to air pollution have led to the establishment of stringent regulations for reducing greenhouse gas (GHG) emissions and air pollutants, which are one of the main causes of air pollution [1]. The shipping industry transports about 90% of world trade. The GHGs and pollutants comprising CO₂, CH₄, SO_x, and NO_x are generated by the process of fuel consumption in ships [2,3,4]. Based on a IMO GHG study, marine shipping emitted 1056 million tons of CO₂ in 2018, representing 2.89% of the world’s total emission. These emissions are predicted to increase by about 90–130% from the 2008 emissions (921 million tons) by 2050 if no action is initiated [5]. Furthermore, at the 72nd Meeting (2018) of the Marine Environment Protection Committee (MEPC), the International Maritime Organization (IMO) adopted the Initial Strategy for IMO GHG Reduction. In accordance with this strategy, the volume of the total annual GHG emissions from international shipping must reduce by at least 50% by 2050, compared with 2008 [6,7]. Based on these strategies, Det Norske Veritas (DNV) announced that the most innovative approach for reducing carbon dioxide emissions is to change marine fuels to eco-friendly fuels [8]. In Lloyd’s Register, hydrogen, biofuel, ammonia, methanol, and electricity are selected as fuel alternatives to reduce CO₂; the advantages and disadvantages of each fuel are compared, and the price change is predicted by year. Thus, hydrogen energy was evaluated to be superior in cost and reduced air pollutants, fine dust, and greenhouse gases [9]. Although hydrogen energy is one of the most promising alternative fuels for ships in the future, it has a low ignition energy (0.02 mJ) and a wide combustibility range (4–75%); therefore, there is a high possibility of fire or explosion accidents in the case of a hydrogen leak [10]. Therefore, leakage management, detection, and ventilation systems are important for increasing safety during fires and explosions while using hydrogen energy. In this regard, the IMO adopted resolution MSC.391(95), the International Code of Safety for Ships using Gases or Low-flashpoint Fuels (IGF Code) such as hydrogen [11]. In accordance with this resolution, the IMO recommends using gas dispersal analysis or a physical smoke test for leak detection equipment best arrangement. Therefore, for hydrogen leakage detection, it is necessary to quantitatively analyze hydrogen dispersion characteristics under various parameter conditions (release pressure, velocity, diameter, etc.) for installing a detector based on these characteristics.

Table 1. Recent studies related to hydrogen release and diffusion.

Object	Method	Parameters			Ref
		Initial Pressure	Release Flow Rate	Diameter [mm]
Hydrogen fuel cell ship	Simulation/FLUENT	10 MPa	0.467	10	[12]
Hydrogen storage tank	Simulation/FLUENT	42 MPa	-	0.5, 1, 2, 5	[13]
Hydrogen fuel cell vehicle	Simulation/FDS	-	6.7 × 10−4 kg/s	-	[14]
Semi-closed space	Simulation/STAR-CCM+	2, 5, 20 bar	-	0.4572, 0.8	[15]
Simple geometric spaces	Experiment	-	0.2, 1 kg/s	5, 10, 20	[16]

summarizes various types of hydrogen release scenarios considered in the experimental or numerical methods, including gaseous releases, fuel cell ships, vehicles, semi-closed, and confined environments. Li et al. [12] numerically studied the release of hydrogen in a hydrogen fuel cell ship and analyzed the effects of different ventilation conditions on hydrogen dispersion behavior. Their results indicated the optimal positions for hydrogen sensors and ventilation. Liu et al. [13] conducted a CFD simulation on high-pressure hydrogen released from storage tanks; furthermore, factors such as wind speed, ambient temperature, leak location, leak hole diameter, and obstructions on hydrogen diffusion were evaluated. Dadashzadeh et al. [14] summarized their results on the dispersion behavior of hydrogen gas from a hydrogen fuel cell car in an enclosed area and provided safety measures for using hydrogen in ventilation conditions. Malakhov et al. [15] compared experimental data with CFD computed results for a hydrogen release in a semi-closed ventilation facility and assessed the efficiency of forced ventilation. A simulation was performed using STAR-CCM+. Lacome et al. [16] performed large-scale hydrogen release experiments to analyze the formation of flammable clouds inside a confined area with an internal volume of 80 m³. Earlier studies related to hydrogen leakage and diffusion focused on terrestrial environments.

However, the safety risks and accident levels are considerably higher than those of hydrogen vehicles on land because many electrical facilities can act as ignition sources for hydrogen leaks in hydrogen ships, and the hydrogen storage tank’s capacity is large. The ship has an airtight structure; therefore, hydrogen cannot be easily discharged outside. The risk is considerably greater at a hydrogen refueling station when an accident such as an explosion occurs [12,17]. Despite these risks, few studies have focused on hydrogen diffusion behavior for hydrogen ships. Previous studies only considered the structural conditions of the ship, whereas environmental factors, such as the motion conditions of the ship, have not been published. We analyzed the effects of the ship’s kinetic characteristics on the hydrogen diffusion behavior and conducted safety analysis using simulations attributed to environmental factors of the ship. We detected the time required by hydrogen to reach each sensor due to the ship’s motion conditions. Furthermore, we indicated the need for selecting an appropriate location for installing a detector by considering kinetic characteristics such as motion types, directions, and periods.

The rest of this manuscript is organized as follows: Section 2 presents the methodology for analyzing hydrogen diffusion behavior while considering the ship’s motion. Section 3 provides definitions of the ship’s motion caused by hydrogen diffusion based on the ship motion and hydrogen diffusion characteristics for scenarios including ship motion type, period, and direction. Finally, Section 4 summarizes the main results of our study and reviews its limitations.

2. Methodology

We conducted our study based on the following procedure to analyze the effect of ship motion on hydrogen dispersion behavior:

(1)

A hydrogen leak test was performed in a steady state, and the effectiveness of the numerical analysis tool was verified by comparing the experimental and numerical analyses results;

(2)

The effect of ship motion on hydrogen diffusion was analyzed by applying the ship motion scenario to the CFD simulation.

The overall methodology of the current study, including the verification of the numerical analysis tool and analysis of hydrogen dispersion behavior applied to ship motion, are shown in Figure 1.

2.1. CFD Modeling

The CFD code FLUENT19.2 was used as a numerical tool to evaluate the effects of the ship’s motion on diffusion in the event of a hydrogen leak. The governing equations employed to numerically simulate the hydrogen release and dispersion include the continuity, momentum, energy, species transport, turbulent kinetic energy, and dissipation rate equations of turbulent kinetic energy [18].

The conservation of mass is provided by:

$$\frac{\partial \rho }{\partial t}+\nabla ·\left(\overrightarrow{\rho v}\right)=0,$$

(1)

where $\rho$, $t$, and $\overrightarrow{v}$ represent the density, time, and overall velocity vector, respectively.

The conservation of momentum is expressed as:

$$\frac{\partial }{\partial \mathrm{t}}\left(\mathsf{\rho }\overrightarrow{v}\right)+\nabla ·\left(\mathsf{\rho }\overrightarrow{vv}\right)=-\nabla p+\nabla ·\stackrel{=}{\tau }+\mathsf{\rho }\overrightarrow{g}+\overrightarrow{F},$$

(2)

where $p$, $\stackrel{=}{\tau }$, $\overrightarrow{g}$, and $\overrightarrow{F}$ represent the pressure, stress tensor, gravitational acceleration, and force vector, respectively.

The conservation of energy is provided by:

$$\frac{\partial }{\partial \mathrm{t}}\left(\rho E\right)+\nabla ·\left(\overrightarrow{v}\left(\rho E+p\right)\right)=\nabla ·k_{eff}\nabla T-{{\displaystyle \sum }}_j{h}_j\overrightarrow{J_j}+\left(\stackrel{=}{{\tau }_{eff}}·\overrightarrow{v}\right)),$$

(3)

where $E$, $k_{eff}$, $T$, $h_j$, and $\overrightarrow{J_j}$ represent the total energy, effective conductivity, temperature, sensible enthalpy of species j, and diffusion flux of species j, respectively.

The species transport equation is:

$$\frac{\partial }{\partial \mathrm{t}}\left(\rho Y_i\right)+\nabla ·\left(\rho \overrightarrow{v}{Y}_i\right)=-\nabla ·\overrightarrow{J_i}+R_i+S_i,$$

(4)

where $Y_i$, $R_i$, and $S_i$ denote the mass fraction of each species, net rate of the product of species i by chemical reaction, and the rate of creation by additions from the dispersed phase plus any user-defined sources, respectively.

2.2. Model Validation

2.2.1. Experimental Description

The experimental space was a rectangular box (1.0 m long × 0.5 m wide × 0.75 m high). A vent (diameter = 0.02 m) was located toward the left side of the ceiling to ensure constant pressure conditions. The internal pressure of the hydrogen gas was 120 × 10⁵ Pa, whereas the pressure value after the regulator leaked to 14 × 10⁵ Pa. Hydrogen was released at a mass flow rate of 0.965 × 10⁻⁵ kg/s through a 1/16-inch (0.001587 m) diameter tube from the right side of the enclosure and directed horizontally. The experiment was conducted for 240 s to reach a steady-state hydrogen distribution inside the enclosure. A detailed description of the experiment is shown in Figure 2 and

Table 2. Experiment conditions.

Experimental facility	W × L × H (m)	0.5 × 1.0 × 0.75
	Volume (m3)	0.1596
Hydrogen leak	Diameter (m)	0.001587 (1/16 inch)
	Inlet (kg/s)	0.965 × 10−5
	Pressure (Pa)	1,400,000
Natural ventilation opening	Diameter (m)	0.01

. Seven hydrogen sensors were employed to measure the hydrogen concentration, as shown in Figure 3.

2.2.2. Grid Independence Test

A tetrahedral grid was generated for a shape on the same scale using ANSYS Meshing for the verification experiment. The grid near the hydrogen leakage area and the natural ventilation opening were locally dense to balance the accuracy of the numerical analysis and computing time efficiency. A grid independence test was performed according to the number of grids to determine the numerical validity of the generated grid. Under the aforementioned conditions, an unsteady analysis was performed on six grids from approximately 370,000 to 920,000 grids based on the number of grids. The hydrogen concentration of the ceiling height at a total calculation time of 60 s was compared to examine the effect of the number of grids. The hydrogen gas concentration at the ceiling height from this comparison was used to predict the main flow and development of the concentration field based on the analysis of 492,406 grids or more. According to our results, a grid independence test was conducted for 492,406 grids, as shown in Figure 4.

2.2.3. Numerical Details

The computational domain has the same size as the actual experiment facility (1.0 m long × 0.5 m wide × 0.75 m high) and includes the hydrogen sensor. Boundary conditions such as the leakage flow rate and pressure conditions were applied in the same manner as the experimental conditions. After the geometric model was established, a tetrahedral mesh was generated with a total of 492,406 elements. For the hydrogen leakage and diffusion analysis, the internal flow was assumed to be a three-dimensional, unsteady, incompressible, and turbulent flow. Furthermore, the SIMPLEC algorithm was employed for calculating the pressure and velocity [19,20]. The overall simulation time was 240 s.

2.2.4. Results

Figure 5 shows a comparison between the simulation and experimental results. According to the obtained results, the S1 sensor closest to the hydrogen leak hole responds 6 s after the leak and maintains a concentration of 0.1% thereafter. The sensor responds sequentially as hydrogen leaked from the experimental facility sends discharge through the ventilation opening. In accordance with the sensor position, sensor S4 responded at 33 s after the leak, whereas S6 responded at 73 s after the leak. Therefore, the response time varies based on the sensor position.

In addition, we confirmed that hydrogen moves along S1 through S4 after the leakage because of the low density of hydrogen’s physical characteristics. By comparing the overall hydrogen concentration results, we confirmed that the experimental and numerical analysis results predicted similar concentrations with a difference of approximately 15%.

3. Effect of Ship Motion on Hydrogen Dispersion

3.1. Ship Motion Coordinate System

A ship in contact with the sea level and moving with six degrees of motion is shown in Figure 6. As indicated by

Table 3. Ship motion.

Translation or Rotation	Type of Ship Motion	Axis	Positive Sense
Translation	Surge	Along x	Forwards
	Sway	Along y	To starboard
	Heave	Along z	Upwards
Rotation	Roll	About x	Port up
	Pitch	About y	Bow up
	Yaw	About z	Starboard to bow

, the coordinate system applied to the calculation has a positive x-axis in the bow direction, a positive y-axis in the starboard direction, and a positive z-axis in the opposite direction of gravity. Here, dynamic motions with periodicity are the roll, pitch, and yaw.

3.2. Ship Motion Scenario

Scenarios were selected using the ship motion type, period, and motion direction as variables for analyzing the effects of ship motion on hydrogen dispersion behavior. Since the motion type of the ship was limited to roll and pitch motion, the motion direction was also divided into clockwise and counterclockwise by considering only the x and y axes. Furthermore, the hydrogen concentration for each sensor location was investigated.

Firstly, only the roll and pitch motions were considered for the ship. Secondly, the ship motion period was calculated for a 15,000 gross tonnage ship according to the following equation provided by IMO’s intact stability code. The rolling period was calculated as 15 s and defined as [21]:

$$T=\frac{2CB}{\sqrt{GM}}$$

(5)

where $T$, $L$, $B$, $d$, $C$, and $GM$ represent the rolling period, length of the ship at the waterline (m), molded breadth of the ship (m), mean molded draught of the ship (m), block coefficient (-), and metacentric height corrected for the free surface effect (m), respectively. Furthermore, $C=0.373+0.023\left(\frac{B}{d}\right)-0.043\left(\frac{L}{100}\right)$.

In addition, simulations were performed by applying 60-s and 120-s cycles to confirm the effects of ship motion periods on the hydrogen concentration value. For the roll and pitch motions, the roll and heel angles were set to move from a minimum of −10° to a maximum of 10° [22]. Finally, the scenario was constructed by classifying ship motions in clockwise and counterclockwise directions. When the motion of the vessel was positive, it was expressed as starboard down and pitching to bow up. When the motion of the vessel was negative, it was expressed as starboard up and pitching down. Figure 7 and Figure 8 show the plane view and corresponding motion period graph, respectively, when the ship motion direction is positive and negative.

3.3. Effect of Ship Motion Types

A numerical analysis was performed by applying roll and pitch motions to the enclosed area; our results revealed the effects of vessel motion type on hydrogen diffusion behavior.

Table 4. Time for hydrogen to reach each sensor according to the ship motion types.

	S2	S3	S4	S5	S6
Steady state	60 s	53 s	40 s	53 s	124 s
60 s period Pitching to bow up	45 s (−23%)	30 s (−43%)	15 s (−63%)	30 s (−43%)	60 s (−52%)
60 s period Rolling to port up	30 s (−50%)	45 s (−15%)	30 s (−25%)	45 s (−15%)	90 s (−27%)

compares the effects of ship motion type on the hydrogen response time for each sensor S2–S6. The percentages, shown below the time, represent differences in the hydrogen sensor’s response time in the motion compared to the steady state. Compared to the steady state, hydrogen reaches the sensor faster to S4 by approximately 63% (25 s) in pitch motion and S2 by approximately 50% (30 s) in roll motion.

Figure 9 and Figure 10 illustrate the hydrogen concentration values of sensors S4 and S6 located at the center of the ceiling’s leak space for roll and pitch motions with a period of 60 s; they move clockwise on each positive axis. Compared to the roll and pitch motions of S4 and S6 in the steady state, hydrogen reaches the sensor faster by 10 s, 25 s, 34 s, and 64 s, respectively. These results indicate that ship motion type significantly affects hydrogen diffusion.

Compared to the roll motion in Figure 9, the hydrogen concentration increases according to the 60-s cycle after 255 s of hydrogen leakage in the pitch motion. This trend can be explained as follows: After leaking from the hydrogen leak hole at the center of the bow’s side, the hydrogen rises to the ceiling due to the buoyancy attributed to the density difference and forms a ceiling jet flow in the longitudinal direction of the leak space.

Furthermore, it moves between the bow and stern under the effects of pitch motion, which is a longitudinal motion centered on S4; the concentration repeatedly rises and falls according to the cycle. In the case of roll motion, moving between the starboard and port compared with pitch motion, the change in position based on S4 is half, and the concentration diffusion speed is fast; therefore, the effect on the concentration value compared with pitch motion is relatively minor. This phenomenon is confirmed in Figure 10, which shows the hydrogen concentration near sensor S6. For roll motion, the hydrogen concentration rises repeatedly and falls in two cycles (30 s) during one pitch motion cycle (60 s). The hydrogen concentration ranges from 0.0634% at 75 s to 0.0374% at 120 s to 41% after hydrogen leakage in the roll motion, and from 0.0664% at 90 s to 0.0318% at 135 s in the pitch motion with a drop rate of 52%. A downward trend was observed; this tendency is attributed to the rotational force generated in the opposite direction of the leakage before the leaked hydrogen diffuses to the ceiling and forms a concentration layer. The latter occurs because hydrogen moves in the port direction in the case of roll motion.

3.4. Effect of Ship Motion Directions

The numerical analysis was performed by applying roll and pitch motions, which move clockwise and counterclockwise on each axis, to the enclosed area for understanding the effect of the ship’s motion direction on hydrogen diffusion behavior. The hydrogen response time for each sensor, S2–S6, is listed in

Table 5. Time for hydrogen to reach each sensor according to the ship motion directions.

		S2	S3	S4	S5	S6
Steady state		60 s	53 s	40 s	53 s	124 s
Pitch motion 15 s period	Bow up	68 s (+13%)	49 s (−8%)	23 s (−43%)	49 s (−8%)	60 s (−52%)
	Bow down	53 s (−12%)	79 s (+49%)	60 s (+50%)	79 s (+49%)	101 s (−19%)
Roll motion 15 s period	Port up	45 s (−25%)	41 s (−23%)	65 s (+63%)	64 s (+21%)	87 s (−30%)
	Port down	45 s (−25%)	64 s (+21%)	65 s (+63%)	41 s (−23%)	87 s (−30%)

to compare the effects of motion direction. Compared to the steady state, hydrogen reaches the S6 sensor faster by approximately 52% (64 s) during pitch motion and 30% (37 s) during roll motion. Figure 11 shows the central longitudinal cross-section of hydrogen concentration distribution contour based on the time required to reach sensor S6. As shown in Figure 11 and Figure 12, the distribution of hydrogen differs according to the direction of roll and pitch motion.

For pitch motion with a period of 15 s, simulations were performed by dividing motions into clockwise and counterclockwise directions. S2 was close to the leak hole, and sensor S6 was located near the ceiling opening of the enclosed area. Hydrogen concentration values are illustrated in Figure 13 and Figure 14. The leakage port in the center of the stern is located higher than the existing position when moving in the same direction as the hydrogen leakage direction (clockwise). The hydrogen leakage attributed to the updraft reaches the ceiling faster. When S6 was located near the opening, the sensor detected the hydrogen concentration at 75 s for pitching to bow; however, in the opposite case, it was detected at 120 s, and a verifiable difference of approximately 45 s occurred. For S2 located near the hydrogen leak hole, the hydrogen concentration was detected at 64 s when moving in the same direction (clockwise) as the hydrogen leak direction; however, in the opposite case, it was detected at 8 s. For the roll motion shown in Figure 13 and Figure 14, lateral motion is less affected by the hydrogen leak hole located in the longitudinal direction than pitch motion, and there is no difference in time to reach the sensor; however, the motion cycle remains affected. According to the 15-s cycle, the concentration repeatedly rises and falls, and the overall hydrogen concentration increases. These results suggest that the ship’s motion characteristics must be considered in selecting the sensor location because the detection time for each sensor location varies depending on the location of the hydrogen leakage and the direction of motion.

3.5. Effect of Ship Motion Periods

The numerical analysis was performed by applying pitch motion with periods of 15 s, 60 s, and 120 s to the enclosed area; the results confirmed our understanding of the effects of the vessel’s motion direction on hydrogen diffusion behavior.

Table 6. Time for hydrogen to reach each sensor according to ship motion periods.

	S2	S3	S4	S5	S6
Steady state	60 s	53 s	40 s	53 s	124 s
15 s period Pitching to bow up	68 s (+13%)	49 s (−8%)	23 s (−43%)	49 s (−8%)	60 s (−52%)
60 s period Pitching to bow up	45 s (−23%)	30 s (−43%)	15 s (−63%)	30 s (−43%)	60 s (−52%)
120 s period Pitching to bow up	60 s (0%)	60 s (+13%)	40 s (0%)	60 s (+13%)	60 s (−52%)

summarizes the time required by hydrogen to reach each sensor according to the ship motion periods compared to the steady state. As the exercise cycle extends, hydrogen diffuses in a manner similar to the normal state and the time difference to reach the sensors is minor, except at sensor S6. The reason for this difference in S6 is due to the start direction of the pitch motion. Figure 15 shows the hydrogen concentration of S4 for each of the ship motion periods. As shown in Figure 15, the hydrogen concentration increases with the motion periods.

4. Conclusions

Hydrogen leakage diffusion under various ship motion conditions was simulated numerically in our study using the CFD code FLUENT for the enclosed area. Furthermore, we analyzed the hydrogen concentration distribution within the enclosed area and drew the following conclusions:

(1)

When the hydrogen leakage is located in the lateral direction, it reaches the sensors approximately 63% (15 s) faster during pitch (lateral) motion than in the steady state. On the other hand, in the case of longitudinal motion, it reaches the sensor approximately 50% (30 s) faster. When the direction of rotation is the same based on the hydrogen leak’s location, the effect on the hydrogen concentration distribution and diffusion is significant;

(2)

We confirmed that the difference in time required by hydrogen to reach the sensor depends on the direction of motion and location of the hydrogen leak. When moving in the same direction as the hydrogen leakage, it reaches the sensor 52% (64 s) faster than in the steady state due to updraft formation; however, in the opposite case, the time required to reach the sensor compared to the steady state increases by 50% (20 s);

(3)

By comparing the results of hydrogen concentration, we confirmed that the difference in time elapsed to reach the sensor, dependent on the motion period of the vessel, is smaller compared to the steady-state; the longer the cycle, the weaker the effect of the cycle period on hydrogen diffusion.

In summary, motion conditions must be considered to understand the leakage and diffusion characteristics of the hydrogen vessel and install a hydrogen sensor because hydrogen’s diffusion behavior varies according to the vessel’s motion characteristics. However, it is also necessary to evaluate the effects of hydrogen concentration diffusion by applying scenarios that combine the roll and pitch motions of a ship and various periods and amplitudes. These considerations can help overcome limitations in the future, such as analysis targets, leakage, and ship motion conditions.