Simulation of Hydrogen Deflagration on Battery-Powered Ship

Abstract

Lead–acid batteries are widely used in modern battery-powered ships. During the charging process of lead–acid batteries, hydrogen gas is released, which poses a potential hazard to ship safety. To address this, this paper first establishes a turbulent flow model for hydrogen deflagration. Then, using FDS6.7.9 software, simulations of hydrogen deflagration are conducted, and a simulation model of the ship’s cabin is constructed. The changes in temperature and pressure during the hydrogen deflagration process in the ship’s cabin are analyzed, and the evolution process of hydrogen deflagration in the ship’s cabin is derived. Hydrogen deflagration poses a significant threat to the fire safety of battery-powered ships. Additionally, a comparative analysis of hydrogen deflagration under different hydrogen concentrations is performed. It is concluded that battery-powered ships using lead–acid batteries should pay attention to controlling the hydrogen concentration below 4%.

1. Introduction

Currently, battery-powered ships mainly use lithium batteries and lead–acid batteries as energy storage, but the thermal runaway problem of lithium batteries has been difficult to solve so far. Compared with lithium batteries, traditional lead–acid batteries are safer, but they are prone to producing hydrogen, which will explode when it meets open fire once the concentration reaches 4~74.2%, and there is a great safety hazard.

Relevant research has been carried out on the deflagration of hydrogen released from lead–acid batteries. Zhou Yuzhe [1] analyzed the causes of fires in lead–acid batteries and designed an intelligent fire prevention and control system to ensure the safety of electric bicycles, as well as personal and property safety. Zhang Weihua et al. [2] fundamentally analyzed the causes and mechanisms of lead–acid battery fires based on the working principle of lead–acid batteries and proposed methods for preventing lead–acid batteries from catching fire. Zong Xiyuan et al. [3] mainly studied the time required for the hydrogen released from valve-regulated lead–acid batteries to reach the explosive volume concentration in air and discussed explosion-proof measures that should be adopted in the explosive hazard area. Li Z et al. [4] focused on analyzing four failure modes of valve-regulated lead–acid batteries, namely “negative plate sulfation”, “positive plate corrosion”, “water loss”, and “acid leakage”. However, these studies did not take into account the deflagration of hydrogen under the conditions of battery-powered ships. The current research aims to provide guidance regarding hydrogen deflagration in battery-powered ships, but it is not fully consistent with the actual situation.

Keenan J J et al. [5] proposed a model of Rayleigh–Taylor instability during premixed combustion. Instability plays an important role throughout the coherent deflagration process, and the proposal of this model is of great significance for studying hydrogen deflagration phenomena. Makarov D et al. [6] introduced two original models, which serve as novel tools for designing hydrogen–air deflagration mitigation systems for equipment and enclosures. This research has guiding significance for studying hydrogen deflagration in cabin air. Makarov D et al. [7] presented models and simulation results for mitigating hydrogen–air deflagration through pipeline ventilation and further developed a Large Eddy Simulation (LES) model to simulate hydrogen–air explosions discharged through pipelines. Molkov V et al. [8] studied the relationship between the size of exhaust ports and hydrogen–air deflagration under the conditions of low-intensity equipment and buildings. Molkov V V et al. [9] further improved an exhaust explosion dynamic model in enclosures with inertial exhaust covers by selecting spring-loaded covers as exhaust devices. Molkov V V [10] conducted research on the nature of coherent deflagration phenomena in a ventilated enclosure–atmosphere system, discussed the mechanism of combustion intensification in the atmosphere, and provided quantitative estimates of the ad hoc parameters of the model. The contributions of these scholars to hydrogen deflagration research have important guiding significance for subsequent scholars’ studies on hydrogen deflagration and have laid a solid theoretical foundation for this paper’s research on hydrogen deflagration phenomena under the conditions of battery-powered ships.

In this paper, FDS software simulation is used to explore how marine lead–acid batteries act in the hydrogen combustion process and combustion with different hydrogen concentrations in order to prevent fires caused by marine lead–acid battery charging in advance.

2. Simulation Model of Hydrogen Deflagration in Ship Compartments

2.1. Numerical Modelling of Compartments

The simulation software platform used in this paper is selected as the fire simulation software program FDS [5] (Fire Dynamics Simulator, version 6.5) developed by the National Institute of Standards and Technology (NIST), whose numerical solution relies on the Navier–Stokes equations, which can be used to construct a hydrogen deflagration simulation model to investigate its deflagration process.

(i)

Navier–Stokes equations

The system of N-S equations [6] describes the properties of fluid motion at any instant of time, so it is applicable to both laminar and turbulent motion. The generalized N-S equations include the continuity and energy equations, i.e., the set of control differential equations describing the fluid motion [7]. The equations of motion in the general form are as follows:

$${\displaystyle \frac{D{u}_i}{Dt}}={\displaystyle \frac{\partial u_i}{\partial t}}+u_j{\displaystyle \frac{\partial u_i}{\partial x_j}}=f_i+{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial T_{ji}}{\mathit{\partial }{x}_j}}$$

(1)

For a Newtonian fluid, by generalizing Newton’s law and adopting Stokes’ second assumption µ′ = 0, the stress tensor is

$$T_{ji}=-p{\delta }_{ji}+{\tau }_{ji}=-p{\delta }_{ji}+{2\mu S}_{ji}-{\displaystyle \frac{2}{3}}{\mu S}_{ji}{\delta }_{ji}$$

(2)

Then the combined surface forces $\partial T_{ji}/\partial x_j$ per unit volume of fluid in the equation of motion are obtainable:

$${\displaystyle \frac{\partial T_{ji}}{\partial x_j}}=-{\displaystyle \frac{\partial p}{\partial x_i}}-{\displaystyle \frac{\partial }{\partial x_i}}\left({\displaystyle \frac{2}{3}}{\mu S}_{kk}\right)+{\displaystyle \frac{\partial }{\partial x_j}}\left(2{\mu S}_{ji}\right)$$

(3)

$${\displaystyle \frac{d{u}_i}{dt}}=f_i-{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial p}{\partial x_i}}-{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial }{\partial x_i}}\left({\displaystyle \frac{2}{3}}{\mu S}_{kk}\right)+{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial }{\partial x_j}}\left(2{\mu S}_{ji}\right)$$

(4)

where ${\displaystyle \frac{d{u}_i}{dt}}$ is the acceleration of the fluid and represents the inertial force per unit mass of the fluid; $f_i$ is the mass force per unit mass of the fluid.

(ii)

Rate of heat release from hydrogen deflagration

The main factors affecting hydrogen deflagration are the area of the room, the ventilation factor of the room, etc. The critical heat release rate for deflagration [8] can be calculated by the following formula:

$$\dot{Q_{cr}}=7.8A_t+378A_W{H}_W^{1/2}$$

(5)

where $\dot{Q_{cr}}$ is the critical fire power required for the room to reach blast ignition (kW); $A_t$ is the total surface area of the room (m²); $A_W$ is the area of the opening (m²); and H_W is the height of the opening (m).

2.2. Cabin Physical Modelling

The numerical results obtained for a specific ship geometry will be valuable. With reference to the structural arrangement of the ship’s compartment, the simulation model’s appearance of the interior setup basically presents a symmetrical distribution. The overall setup is 12 m × 8 m × 7.5 m, with reference to the diameter of the fire source, and the individual grid size used is 0.25 m × 0.25 m × 0.25 m, with a total of 46,080 grid cells, as shown in Figure 1. The interior is divided into three floors: navigation and communication modules are set up on the upper floor; the middle floor is divided into two parts, with a console and other equipment as well as staircases, entrances, and exits in the front part, and the rear part is the living area, with two living compartments, toilets, and staircases and entrances to access the upper floors; and the lower floor is the battery compartment.

In order to make the simulation data more comprehensive, a total of 21 measurement points are considered, distributed in all parts of the chamber, mainly to monitor the hydrogen deflagration process in the chamber as temperature and pressure change over time. The middle and lower partitions are taken as the horizontal plane, the ship’s width as the x-axis, the direction of the ship’s length as the y-axis, and the vertical direction as the z-axis. The location of each monitoring point’s coordinates is shown in

Table 1. The arrangement of the location of each temperature and pressure monitoring point.

Monitoring Point Number	Position Coordinate (x,y,z)/m	Monitoring Point Number	Position Coordinate (x,y,z)/m
1	(0,1,2)	12	(−3,1,1)
2	(0,10,2)	13	(0,4,1)
3	(2,11,0)	14	(3,4,1)
4	(−2,11,0)	15	(−3,4,1)
5	(0,1,3)	16	(0,10,1)
6	(0,3,3)	17	(3,6,1)
7	(0,5,3)	18	(−3,6,1)
8	(0,7,3)	19	(0,6,1)
9	(0,10,3)	20	(6,3,−1.5)
10	(0,1,1)	21	(6,−3,−1.5)
11	(3,1,1)

. Monitoring points 1–4 are located in the upper, middle, and lower three layers of the chamber and the opening of the staircase; monitoring points 5–9 are located in the middle symmetrical surface of the upper cabin; monitoring points 10–15 are located in the rear part of the living area of the middle cabin; monitoring points 16–19 are located in the front part of the middle cabin; monitoring points 20 and 21 are located in the lower cabin.

Considering the FDS software simulation and the fire characteristics of the ship’s compartment [9], the hydrogen combustion simulation experiments mainly use the following conditions:

(1) Initial temperature: 20 °C.

(2) Initial pressure: standard atmospheric pressure.

(3) The radiation and thermal conductivity of heat loss are not taken into account; the compartment walls are adiabatic.

(4) The ignition position is located in the middle compartment and the rear of the living area in the middle of the living compartment, while the position of the monitoring point is near that of 10.

(5) Simulation calculation conditions: hydrogen concentration in the space was set to 4.0%, 8%, and 10%.

First, 10% hydrogen concentration was used in the compartment as an example of the hydrogen deflagration process and then reduced to 8% to explore the changes in the deflagration process after the reduction in hydrogen concentration. Finally, it was reduced to 4% hydrogen concentration to observe what occurs at the lower hydrogen deflagration limit.

3. Analysis of Hydrogen Deflagration Simulation Results in Ship Compartments

3.1. Chamber Deflagration Process

Taking the hydrogen diffusion concentration of 10% in the chamber as an example, a numerical simulation of the deflagration phenomenon in the chamber was carried out to investigate the hydrogen deflagration process in the chamber. The gas temperature and pressure of the axial longitudinal cross-section of the chamber with respect to the time of change are shown in cloud diagrams in Figure 2 and Figure 3.

In the deflagration process, the location of the temperature change gradient is also the location of the flame surface, so Figure 2 can be seen as displaying the deflagration flame propagation process in the deflagration process. The simulation model is divided into four spaces by the wall and the deck, and each space is connected by four staircase openings. When observing the temperature change process of the chamber from the temperature cloud, the ignition point is located near the position of monitoring point 10. Regarding hydrogen ignition, the first ignition position was near the high-temperature zone, and with respect to the deflagration process, the flame was shown to first appear in the high-temperature zone, followed by the flame surface, before spreading to the entire chamber. Although the location of the ignition is located in the middle chamber of the rear living area, it can be seen that in the chambers of the four main spaces, the flame surface first reaches the upper chamber, but it then fills the area in front of the middle chamber, followed by the upper chamber, and then the rear of the middle chamber area; finally, the flame fills the area of the lower chamber. We then analyze the reasons for this phenomenon. In the hydrogen deflagration process, with the propagation of the flame, the gas pressure within the chambers of the various spaces changes. Due to the existence of pressure differences between the spaces, the gas moves in the various spaces through the connection of the openings for flow, resulting in a change in the speed of gas. When the direction of the gas flow and the direction of the propagation of the flame are consistent with the direction of the flame, this causes the flame propagation of the flame surface to accelerate, while when the gas flow direction is opposite to the flame propagation direction, the flame surface propagation speed decreases at the same time.

As shown in Figure 3, in the process of hydrogen deflagration, the gas pressure in each space is approximately equal, and there is a more obvious pressure difference between the various spaces, which can be seen in the smaller staircase opening area, wherein the propagation of gas pressure has an obstructive effect. In the initial moment of deflagration, the deflagration flame is located in the middle chamber rear space, and the gas pressure in this space is the first to rise. The openings are connected to the upper chamber to form upward air velocity, so the flame is the first to spread to the upper space. Afterwards, the airflow flows through the opening towards the space in front of the middle compartment, causing the flame to propagate to the space in front of the middle compartment as well. In this space, the disturbance of the airflow is larger, causing the flame to propagate faster, and the airflow resistance is larger due to the smaller openings at the connection of the lower space. As a result, the gas pressure in the space in front of the central chamber rises rapidly and exceeds the gas pressure in the upper space within a short time, causing a reverse gas flow. The reverse gas flow causes the original flame surface propagation speed of the upper compartment to decrease, and a flame surface propagating from the space in front of the middle compartment to the upper compartment appears while the flame begins to spread to the lower compartment. As the hydrogen in the space in front of the middle compartment is consumed, its space pressure reaches its maximum and then gradually decreases, and the pressure difference with the rest of the space begins to decrease. Due to the late start of the hydrogen combustion process in the lower compartment, at the later stage of deflagration, when the hydrogen combustion in the rest of the space is finished, the hydrogen in the lower compartment is still burning, causing the pressure in its space to start to be higher than that of the rest of the compartment and to form a reverse upward airflow in the opening connecting it to the middle compartment, as shown in Figure 3d. As the burning of hydrogen in the lower compartment ended, the gas pressure gradually homogenized between the compartments.

3.2. Gas Pressure Changes During Deflagration

The hydrogen deflagration process in the chamber of the main space within the measurement point pressure change process is shown in Figure 4. It can be seen that in the simulation of the chamber in the main space, the gas pressure change at each monitoring point is basically the same. Meanwhile, the pressure change curves of different chamber spaces have different shapes. This indicates that the main obstacle to the propagation of gas pressure between the main spaces of the chamber is the size of the four openings connecting each space. Observing Figure 4c, in the space in front of the middle chamber, in the late deflagration stage, gas pressure reaches the maximum value near the gas pressure vibration; presumably this phenomenon is caused by the front of the middle chamber in the space of the electrical cabinet and other irregularly shaped equipment being influenced by turbulence and pulsation in the deflagration flame propagation process, resulting in pressure fluctuations.

Typical monitoring points in the four main spaces of the compartment were selected, and the changes in gas pressure at these points during the hydrogen deflagration process were compared, as shown in Figure 5. The pressure change trends in the four main spaces of the compartment are significantly different, and the patterns they show are consistent with the analyzed deflagration process. During the deflagration process, the peak pressures in the rear space of the middle deck compartment and the upper deck compartment both appear after the completion of deflagration when the compartment pressure becomes uniform, at approximately 2.44 s, reaching 0.339 MPa (gauge pressure). The front space of the middle deck compartment has two pressure peaks during the deflagration process: the first peak appears at around 1.22 s, when the pressure reaches 0.347 MPa as the hydrogen in this space is about to be consumed; the second peak occurs at the moment when the compartment pressure becomes uniform at the end of deflagration. The pressure peak in the lower deck compartment appears at around 1.74 s, reaching 0.36 MPa.

3.3. Gas Temperature Changes During the Deflagration Process

The temperature variation curves of each measuring point in different spaces of the compartment during the hydrogen deflagration process are shown in Figure 6. The temperature change at the measuring points is mainly related to the passage of the flame front. When the flame front sweeps over the measuring point, the temperature at the point rises from normal temperature to the flame temperature in an extremely short time. The temperatures at each monitoring point in the rear space of the middle deck compartment and the upper deck compartment show two stepwise rising processes during the ascending phase; in contrast, the temperature changes at the monitoring points in the front space of the middle deck compartment and the lower deck compartment present a downward trend similar to the pressure change. It is found that the first rising process in the temperature changes shown in Figure 6a,b is caused by the sweeping of the flame front, while the second rising process starts at around 1.15 s. Combined with the pressure change mentioned earlier, this is exactly the initial stage of the rapid pressure rise in the compartment, and this temperature rise is caused by the significant increase in the compartment pressure. Moreover, the temperature changes shown in Figure 6c,d are also related to the pressure changes in the corresponding spaces.

During the hydrogen deflagration process in the compartment, the maximum temperature monitored in the upper deck compartment is 1505 K; the maximum temperature monitored in the rear space of the middle deck compartment is 1479 K; the maximum temperature monitored in the front space of the middle deck compartment is 1378 K; and the maximum temperature monitored in the lower deck compartment is 1353 K. Since heat dissipation is not considered, the temperature at each monitoring point is relatively high during the deflagration process, but all measuring points can reach above 1000 K, indicating that the danger caused by hydrogen deflagration is extremely high, posing a great challenge to ship safety.

4. Comparative Analysis of Deflagration Results Under Different Hydrogen Concentrations

4.1. Compartment Concentration: 8%

When only the hydrogen concentration changes, during the hydrogen deflagration process in the compartment, the flame propagation law and the variation laws of various gas parameters in the space remain basically unchanged. What mainly change are the values of various gas parameters and the timing of their occurrence. Therefore, to reduce the amount of calculation, the lower compartment space was closed in the simulation process of this section, and the connecting opening between the lower compartment and the front space of the middle compartment was blocked. On this basis, the deflagration process when the hydrogen concentration diffused in the compartment was 8% was simulated, and the changes in various parameters were observed.

The pressure changes at each monitoring point during the hydrogen deflagration process are shown in Figure 7. The pressure variation law at each monitoring point in the compartment is basically consistent with that mentioned earlier. The difference is that the pressure peaks all appear at the final pressure equalization moment, and the first pressure peak generated during the deflagration process in the front space of the middle deck compartment is also lower. This is because the deflagration flame propagation speed is slower under this working condition, allowing the gas flow more time to flow into the remaining compartment spaces, thereby reducing the pressure difference between the main spaces of the compartment. The peak pressures in all spaces appear after the completion of deflagration when the compartment pressure becomes uniform, at approximately 4.95 s, reaching 0.2763 MPa (gauge pressure); the front space of the middle deck compartment has a relatively low pressure peak during the deflagration process, with the pressure reaching 0.25 MPa at around 3.1 s. Compared with the deflagration at a hydrogen concentration of 10%, the deflagration at 8% hydrogen concentration takes a longer time to end, the pressure oscillation in the front part of the middle deck compartment during the deflagration process is smaller, and the pressure difference between the three main spaces of the compartment is also smaller.

The temperature variation curves of each measuring point in different spaces of the compartment during the hydrogen deflagration process are shown in Figure 8. The temperature variation law is consistent with that when the hydrogen concentration is 10%. As the diffused concentration of hydrogen in the compartment decreases from 10% to 8%, the flame propagation speed decreases, the deflagration duration is prolonged, the pressure oscillation in the front part of the middle deck compartment weakens, and both the pressure and temperature values generated by the deflagration are significantly reduced. During the hydrogen deflagration process in the compartment, the maximum temperature monitored in the upper deck compartment is 1231 K, the maximum temperature monitored in the rear space of the middle deck compartment is 1218 K, and the maximum temperature monitored in the front space of the middle deck compartment is 1153 K. The adiabatic deflagration temperature at a hydrogen concentration of 8% in the compartment is lower than that at a hydrogen concentration of 10% under the working condition.

4.2. Compartment Concentration: 4%

Since 4% is the lower flammability limit of hydrogen at room temperature, when simulating the deflagration phenomenon with a hydrogen concentration of 4%, the software used determines that the deflagration reaction cannot occur. The gas pressure changes monitored at the measuring points in the four main spaces of the compartment are shown in Figure 9. The gas pressure in each main space of the compartment remains 0 at all times; therefore, hydrogen deflagration cannot occur under this working condition.

When the diffused concentration of hydrogen drops to 4%, the flame cannot propagate effectively, and the deflagration phenomenon cannot occur. Therefore, a decrease in the hydrogen concentration in the compartment not only reduces the degree of harm caused by deflagration, but also, the longer duration of deflagration provides an increased response time for various fire-fighting measures.

5. Conclusions

Based on the structural characteristics of the cabin of battery-powered ships, this paper constructs the physical environment of a typical cabin, which is as close as possible to the actual situation, and simulates the deflagration of different hydrogen concentrations generated by ship lead–acid batteries [11]. It analyzes the simulation results of the hydrogen deflagration process in the cabin and the changes in temperature and pressure and obtains the deflagration characteristics of hydrogen in ship cabins affected by changes in temperature and pressure [12,13]. The deflagration pressure in the same cabin is basically at the same level, while the pressure in different cabins varies [14]. The significant pressure difference at the opening between two cabins greatly affects the flow of deflagration gas, which in turn affects the temperature change in the cabins [15]. This has important guiding significance for fire prevention and control of battery-powered ships. After deflagration, the pressure of hydrogen increases sharply, and the temperature can reach above 1000 K, which brings great potential safety hazards to ship safety [16,17].

When the hydrogen concentration decreases from 10% to 8%, the trends in temperature and pressure during deflagration do not change significantly, while the deflagration speed and temperature decrease slightly, the duration of deflagration is slightly prolonged, and the pressure oscillation weakens. However, when the hydrogen concentration drops to 4%, deflagration cannot occur. Therefore, the hydrogen concentration in ship compartments should be limited below 4% to prevent hydrogen deflagration.