Self-Driven Cycle and Thermal Characteristics of Seawater Battery System with a Preheater

Abstract

As a novel energy storage technology, seawater batteries exhibit significant application potential across various domains, including marine exploration, underwater communication, and island power supply. However, the deep-sea low-temperature environment adversely affects the performance of seawater battery systems. This paper proposes a seawater metal–air battery system equipped with a preheater (SMAB-P). This innovative system establishes stable natural circulation and utilizes the high-temperature seawater within the system to preheat the incoming low-temperature seawater, thereby effectively enhancing battery performance. It was found that, compared with the SMAB system without a preheater, when achieving a heat recovery rate of 100% the average temperature of seawater in the electrode plate area of the SMAB-P system can be increased by 54%. Consequently, the electrical conductivity of seawater within the system can be increased by approximately 20%, leading to a significant reduction in ohmic losses and an enhancement in the load voltage of the battery. Furthermore, increasing either the height or width of the electrode plate can enhance self-driven force and circulation flow rate, as well as both average and maximum temperatures of seawater in the electrode plate area to some extent. Reducing the annular space of the preheater can significantly increase the seawater temperature within the system, but excessive reduction may hinder the effective replacement of fresh seawater in the system. It is also noted that seawater velocity in the electrode plate channels remains relatively low and evenly distributed while exhibiting very small temperature variation.

1. Introduction

Marine development and exploration are crucial methods for humanity to understand and utilize marine resources, relying on advanced underwater instruments capable of stable long-term operation in marine environments, along with a reliable power supply system [1,2]. In complex marine environment, conventional electrical energy technologies face challenges such as short service life, maintenance difficulties, and inadequate safety and reliability, necessitating their placement within specific sealed and pressure-resistant containers during use. To address these issues, seawater metal–air batteries (SMABs) offer an effective solution. By utilizing seawater as the electrolyte, SMABs significantly reduce battery production costs. This technology has high safety and sustainability advantages and is considered a highly promising power source for marine operational equipment [3]. The functioning of SMABs relies on the corrosion and dissolution of the negative electrode metal material in seawater to generate the anode discharge current; concurrently, the positive electrode primarily depends on the reduction reaction of dissolved oxygen in seawater to produce the cathodic current [4]. Natural seawater is used as the electrolyte to ensure the directional movement of ions in electrode reactions and to form a continuous and stable current [5]. The working process of a SMAB can be summarized as follows:

$$Cathode:O_2+2H_{2}O+4_e^{-}\to 4O{H}^{-}$$

(1)

$$Anode:M\to M^{n+}+n{e}^{-}$$

(2)

After the dissolved oxygen in seawater is collected, it undergoes reduction through the oxygen reduction reaction. Concurrently, the negative electrode metal is oxidized, resulting in the formation of metallic hydroxides [6].

Currently, research on the performance optimization of SMABs primarily concentrates on enhancing cathode materials, anode materials, and related components.

Magnesium and aluminum exhibit excellent electrochemical activity and high energy density, making them usually utilized as anode materials in seawater batteries, which provide a long-term energy supply [7]. To mitigate the self-corrosion of magnesium or aluminum anodes and prevent electrode passivation resulting from prolonged exposure to seawater during discharge, strategies such as alloying can be employed to enhance both the corrosion resistance and discharge performance of these electrodes [8,9]. Li et al. [10] developed a series of Mg-Al-Zn alloys and studied the effect of indium (In) on its electrochemical performance as anodes. The addition of In significantly improved the electrochemical activity of AZ63 alloy, and the optimal amount of In added is 1.0%, considering both the corrosion resistance and electrochemical activity of the anode. Shi et al. [11] found that the addition of La significantly improved the corrosion resistance and discharge activity of Mg-Al-Pb-La alloy. For aluminum-based anodes, adding low-melting-point alloying elements such as Ga, In, Zn, and Sn is an effective method to remove the Al₂O₃ passivation film on the electrode surface [12,13]. Nestoridi et al. [14] found that the addition of Sn and Ga improved the corrosion resistance and current efficiency of Al alloys, due to the solid solubility of Sn in Al alloys and the accumulation of Ga at Al-Sn grain boundaries. Adding Zn to the Al-In alloy can reduce anodic polarization and the accumulation of Zn(OH)₂ on the electrode surface, thereby inhibiting the hydrogen evolution reaction and improving the anode utilization rate.

The SMAB cathode functions as a gas electrode, necessitating the use of suitable materials such as graphite, copper, and stainless steel. Under conditions that ensure a sufficiently large surface area and a compact structure, both copper and stainless steel are considered ideal materials for cathodes. Notably, employing graphite as the cathode can yield a higher open circuit potential compared to copper and stainless steel. Currently, the cathode materials that have been practically implemented primarily consist of carbon-based substances, including carbon rods, carbon cloth, carbon felt, and carbon fibers [15]. As the depth of seawater increases, both the concentration and temperature of dissolved oxygen exhibit a gradual decline. Conventional carbon materials demonstrate limited cathodic activity, inadequate oxygen enrichment capacity, and low oxygen reduction efficiency in oxygen reduction reactions. Research indicates that oxidizing the surface of carbon fiber materials and incorporating active functional groups can significantly enhance their electrocatalytic performance for oxygen reduction processes [16,17]. The catalytic performance of the oxygen reduction reaction at the battery cathode can be enhanced by fabricating composite electrodes that incorporate various oxygen reduction catalysts through chemical methods [18,19].

In summary, research on SMABs has primarily concentrated on electrode materials and preparation processes. However, in practice, the open structure of SMABs relies heavily on the continuous supply of dissolved oxygen from seawater, which is predominantly facilitated by natural ocean currents. This dependence renders the performance of SMAB systems highly susceptible to variations in the marine environment. In fact, the marine environment itself is quite complex [20]. The temperature of seawater varies with ocean depth, with the deep sea (3000–4000 m) exhibiting a temperature range of 0–4 °C. Due to thermodynamic and kinetic factors, low-temperature deep-sea environment are unfavorable for the operation of seawater batteries [21]. Hasvold et al. [22] found that the decrease in seawater temperature can weaken the conductivity of seawater and increase the internal ohmic losses of seawater batteries, which is not beneficial for increasing the load voltage of the battery. Lu et al. [23] tested the electrochemical performance of a modified positive electrode carbon fiber brush (MPAN-CFB) at different temperatures and found that its reaction mechanism and controlled process were the same under simulated deep-sea low temperature (4 °C) and sea surface temperature (15 °C), but low temperature would lead to a decrease in mass transfer rate at the electrode interface and an increase in solution internal resistance, thereby affecting the positive electrode chemical reaction rate. Liu et al. [24] studied the performance of SMABs at temperatures of 25 °C, 15 °C, and −1 °C, and found that a decrease in seawater temperature would slow down electrode kinetics, increase the ohmic resistance of the electrolyte, and exacerbate polarization losses, resulting in a significant decrease in battery performance. At present, although some studies have reported the adverse effects of the low-temperature environment on SMAB systems, there remains a scarcity of research focused on corresponding improvement methods.

In this paper, a SMAB system with a preheater (SMAB-P) is proposed, which utilizes high-temperature seawater that has undergone oxygen reduction reactions within the system to preheat the low-temperature incoming seawater in the preheater. This process effectively raises the seawater temperature in the electrode plate area and significantly enhances the SMAB-P system performance in deep-sea environments. The primary components of the SWA-P system include its main body, preheater, and connecting tubes, as illustrated in Figure 1a. In the SMAB-P system, the self-driven circulation loop is established based on the special structural design. As an integral component of this system, the preheater is incorporated into its self-driven circulation loop, thereby eliminating any need for additional energy consumption. Both the tube-side channel and the shell-side channel inside the preheater are components of the system’s circulation loop. Furthermore, both the structure and dimensions of the preheater are critical factors influencing the performance of the SMAB-P system. The main body of the SMAB-P has a rectangular prism shape. A support column is positioned centrally within this main body. One end of all the electrode plates is mounted on the support column, while their other ends are secured to the outer shell of the main body. The anode plates and cathode plates are installed at intervals such that each anode plate has cathode plates flanking it, as shown in Figure 1b. All electrode plates are uniformly arranged throughout the space to form parallel channels, ensuring that seawater flow rates through each channel remain comparable. The internal center vertical channel at the center of the support column functions as a component of the inlet tube. The upper section of the SMAB-P system is fitted with the preheater, which utilizes a simple double-pipe configuration. Both the casing and support columns of the main body of the SMAB-P system are constructed from insulating materials. To minimize heat loss, an insulation layer envelops the entire outer surface of the SMAB-P system. Additionally, there is an insulation layer inside the tube wall of the support column to avoid heat exchange between the inlet seawater and the seawater in the electrode plate area.

The self-driven force of the SMAB-P system primarily comes from the density difference of the seawater in the upward flow tubes and that in the downward flow tubes within the system, which is evidently reflected as the temperature difference between these tubes. When the self-driven force of the system equilibrates with the system flow resistance, a stable state is achieved. Furthermore, the SMAB-P system can adjust adaptively to changing working conditions, thereby reaching a new stable operating state. A key distinction of the SMAB-P system compared with conventional systems lies in its preheater component. This preheater utilizes the high-temperature seawater within the system to preheat the incoming low-temperature seawater, effectively reusing the heat generated by the electrode plates and elevating the working temperature in the electrode plate area. In fact, various factors, such as heat transfer structure, thermal load, and thermophysical properties of the working fluid, can influence the operational performance of the SMAB-P system. By optimizing the SMAB-P system’s structural design, it becomes possible to effectively maintain working temperatures in electrode plate areas within desired ranges. An increase in these temperatures can enhance the performance of SMAB-P systems in deep-sea environments. Considering that water is susceptible to scaling at excessively high temperatures, the optimization seawater temperature objective of the SMAB-P system is usually to increase the seawater temperature as much as possible within the range below 40 °C. The operation process of the SMAB-P system involves natural circulation flow and heat exchange. As a reliable energy conversion and transfer system, natural circulation has been extensively studied [25,26,27,28] and is widely applied across various engineering fields [29], including nuclear energy [30,31,32], construction [33,34], refrigeration [35], motors [36], etc.

As shown in Figure 1c, the internal seawater flow process of the SMAB-P system is described as follows: the low-temperature seawater from the external environment flows into the tube side of the preheater and exchanges heat with the high-temperature seawater in the shell side, which flows from the electrode plate area. After absorbing heat, the low-temperature seawater rises in temperature and becomes medium-temperature seawater. Subsequently, the medium-temperature seawater continues to flow downward along the inlet tube and enters the system’s main body. Under the action of the self-driven force, the seawater flows upward in the channels between the electrode plates. As the seawater flows through the electrode plate area, it absorbs the heat emitted by the electrode plates to become high-temperature seawater. The high-temperature seawater gathers at the top of the system’s main body, and after flowing into the riser it enters the shell side of the preheater. In the preheater, the high-temperature seawater transfers heat to the low-temperature seawater from the external environment, and then it is discharged into the external environment through the outlet. In Figure 1c, the arrows represent the direction of seawater flow.

In this work, the operation performance of the SMAB-P system in deep-sea environments was deeply studied through simulation of the system loop model. Zinc plate and copper plate are used as anode and cathode materials of the SMAB-P system in this paper, with seawater as the electrolyte. The influences of parameters such as the system structure size and heat recovery rate on the system operation performance and the seawater temperature in the electrode plate area were discussed in detail. Then, based on the recommended main parameters of the SMAB-P system, the seawater temperature distribution and velocity distribution in the electrode plate area were deeply studied through the physical field simulation.

2. Operating Characteristics of SMAB-P System

2.1. The Loop Model of SMAB-P System

Since the cycle of the SMAB-P system is self-established, a key feature of the system loop model is the equilibrium between the self-driven force and the total flow resistance. Under specific operating conditions, when the self-driven force equals the system flow resistance, it achieves a stable operational state. In the simulation of the SMAB-P system loop model, single-phase flow resistance and single-phase heat transfer are involved.

The single-phase frictional flow resistance in a circular tube is given by

$$∆P={\displaystyle \raisebox{1ex}{$2f{G}^{2}L$}\!\left/ \!\raisebox{-1ex}{$\rho d$}\right.}$$

(3)

where $∆P$ is frictional flow resistance, $f$ is the friction factor, $G$ is the mass flow rate of the work fluid, $L$ is the length of the tube, and $d$ is the diameter of the circular tube. In the flow resistance calculation of the annular channel within the double-pipe preheater, the equivalent diameter is used. The calculation of the frictional factor adopts the following formula,

$$f={\displaystyle \raisebox{1ex}{$16$}\!\left/ \!\raisebox{-1ex}{$Re$}\right.}Re<2000$$

(4)

$$f=0.079{Re}^{-0.25}Re\ge 2000$$

(5)

where $Re$ is the Reynolds number.

The total flow resistance of the SMAB-P system includes all the frictional resistances and the local flow resistances and can be given by

$$∆P_{total}=∆P_{0-1}+∆P_{1-2}+∆P_{2-3}+∆P_{3-4}+∆P_{4-5}+∆P_{5-6}+∆P_{local}$$

(6)

where $∆P_{total}$ is the system total flow resistance and $∆P_{local}$ is all the local flow resistances, and the subscript codes represent the corresponding tube sections in Figure 1c.

The self-driven force of the SMAB-P system can be expressed and calculated by the gravity pressure drop, which is given by

$$F={\rho }_{a}g{H}_{6-5}+{\rho }_{1-2}g{H}_{1-2}-\overline{{\rho }_{2-3}}g{H}_{2-3}-{\rho }_{3-4}g{H}_{3-4}-{\rho }_{5-6}g{H}_{5-6}$$

(7)

where $F$ is the system’s self-driven force, $\rho$ is the density of seawater, $H$ is the vertical height of the pipe section, the subscript code ‘a’ represents the ambient seawater outside the system. Although the SMAB-P system appears to be a non-closed loop, in reality, an invisible flow path is formed in the local seawater area between the system outlet and the inlet. Therefore, in the calculating process of the system’s self-driven force, the gravitational pressure drop in this invisible flow path should also be taken into account, as shown in Equation (7). In pipe section 2–3 (as shown in Figure 1c), as the seawater absorbs the heat dissipated by the electrode plates and its temperature rises, the density of the seawater changes along the height direction of the electrode plates. Therefore, in Equation (7), the seawater density value in pipe section 2–3 is expressed as the average density.

Under steady-state conditions, due to the self-driven force of the system being equal to the total flow resistance, the value of the mass flow rate can be obtained by solving Equations (6) and (7) simultaneously. Figure 2 shows the flow chart of the simulation of the SMAB-P system loop model.

Due to the temperature variation range of the SMAB-P system in this paper being very small, the system’s self-driven force and mass flow rate are also very small, and the flow state of the seawater medium in all the tubes is laminar. In the heat transfer calculation of the double-pipe preheater, the heat transfer of laminar flow in the annular channel is involved, and the calculation method used is shown in

Table 1. Fully developed convective heat transfer Nu number in annular channel.

$\mathbf{Ratio}\mathbf{of}\mathbf{Inner}\mathbf{and}\mathbf{Outer}\mathbf{Diameters}{\mathit{d}}_{\mathit{i}}/{\mathit{d}}_{\mathit{o}}$	$\mathbf{Inner}\mathbf{Wall}{\mathit{N}\mathit{u}}_{\mathit{i}}$	$\mathbf{Outer}\mathbf{Wall}{\mathit{N}\mathit{u}}_{\mathit{o}}$
0	/	3.66
0.05	17.46	4.06
0.10	11.56	4.11
0.25	7.37	4.23
0.5	5.74	4.43
1.00	4.86	4.86

, where $d_i$ and $d_o$ represent the inner diameter and the outer diameter of the annular channel, respectively.

In the loop model of the SMAB-P system, the inner diameter and height of the system’s main body are 0.27 m and 0.34 m. The width and height of each electrode plate are 0.07 m and 0.27 m. The diameter of the inlet tube is 0.03 m.

In the simulation, the external environment of the SMAB-P system is assumed to be deep sea, and the ambient seawater temperature is set to 4 °C. The heat flux density generated on the surfaces of the electrode plates is assumed to be 10.2 W/m². In fact, the chemical heat generated by the electrode plates varies with the temperature of the seawater medium, but in order to better analyze the thermal and hydraulic performance of the SMAB-P system the heat flux density generated by the electrode plates is assumed to be a constant value.

Based on the simulation results of the SMAB-P system loop model, the influence of factors such as system structure and heat recovery rate on the operating characteristics of the system were analyzed in depth.

2.2. The Influence of Heat Recovery Rate on SMAB-P System Performance

The heat recovery rate of the SMAB-P system is defined as the ratio of the heat used in the preheater for preheating the inlet seawater to the heat generated during the power generation process of the SMAB-P system. This heat recovery rate directly determines the capacity of the preheater and significantly influences the temperature levels within the electrode plate area. As shown in Figure 3, with the increase of heat recovery rate the average temperature in the electrode plate area gradually rises, while the maximum temperature shows a trend of first decreasing and then increasing. This is because, on the one hand, as the heat recovery rate increases, the density difference of seawater between the upward flow tubes and the downward flow tubes in the system increases, resulting in the increase of system flow rate, which can cause the seawater temperature in the electrode plate area to decrease. On the other hand, the increase in the heat recovery rate will raise the temperature of seawater entering the electrode plate area, which is conducive to increasing the maximum seawater temperature of the system. Under the combined effect of those two factors, the maximum temperature in the electrode plate area shows a non-monotonic changing trend with the increase of heat recovery rate. Compared with the system without a preheater, the implementation of the SMAB-P system results in an increase of 54% in the average temperature and 15% in the maximum temperature of seawater within the electrode plate area.

Based on the above temperature results, the electrical conductivity of seawater within the system was analyzed by referring to the calculation correlation of seawater conductivity in the literature [37] (as shown in Equation (8)) and the calculation correlation of seawater salinity in the literature [38] (as shown in Equation (9)),

$$\log L=0.57627+0.892\log \left(Cl\mathrm{‰}\right)-{10}^{-4}T\left[88.3+55T+0.0107T^2-Cl\mathrm{‰}(0.145-0.002T+0.002T^2)\right]$$

(8)

$$S\mathrm{‰}=1.80655Cl\mathrm{‰}$$

(9)

where $L$ is the electrical conductivity of seawater, $\mathrm{m}\mathsf{\Omega }/\mathrm{c}\mathrm{m}$; $Cl\mathrm{‰}$ is the chlorine content of seawater; $S\mathrm{‰}$ is the seawater salinity; and $T=25-t$, where $t$ is the seawater temperature, ℃. In the calculation process, the salinity of seawater is set at 35‰.

It was found that within the parameter range of this paper, the electrical conductivity of seawater in the SMAB-P system could be increased by approximately 20%. This increase can significantly reduce the internal ohmic loss of the battery, thereby effectively enhancing the load voltage of the battery and fully demonstrating the technical advantage of improving system performance.

2.3. The Influence of Electrode Plate Height on SMAB-P System Performance

In natural circulation systems, the primary factors influencing operational states typically include system structure and operating conditions. Consequently, a detailed analysis of system performance under varying electrode plate sizes is conducted.

In natural circulation systems, the primary factor influencing operational states typically include system structure and operating conditions. Consequently, a detailed analysis of system performance under varying electrode plate sizes is conducted. Figure 4 shows the effect of electrode plate height on the system’s self-driven force and total flow resistance of the SMAB-P system. It can be seen that the self-driven pressure head curve and circulating flow resistance curve of the system show opposite trends with the changes in system flow rate. The intersection of the two curves is the operation point of the system. Actually, the height of the electrode plates greatly affects the gravitational head in the system. It can be found that when the flow rate is constant, an increase in the height of the electrode plates can significantly enhance the self-driven force of the system. On the other hand, the increase in the height of the electrode plates slightly reduces the circulating flow resistance of the system. This is because the increase in the height of the electrode plates leads to an increase in the heat dissipation of the system, thereby raising the overall seawater temperature within the system, reducing the density and viscosity of the seawater and ultimately resulting in a lower circulating flow resistance. Affected by the above factors, the flow rate of the system shows a gradually increasing trend with the increase of the height of the electrode plates.

Figure 5 shows the average and maximum temperatures in the electrode plate area at different plate heights. It can be observed that as the height of the electrode plates increases, both the average temperature and the maximum temperature increase, but the magnitude of the increase is relatively small, not exceeding 3.1%. It is evident that increasing the height of the electrode plates has a relatively modest impact on enhancing the overall temperature within the area of the electrode plates.

2.4. The Influence of Electrode Plate Width on SMAB-P System Performance

Figure 6 shows the influence of the electrode plate width on the operation state of the SMAB-P system. It can be observed that with the electrode plate width increasing, both the system flow rate and total pressure head under the operation point condition show an upward trend. In fact, when the flow rate is constant, an increase in the width of the electrode plates will increase the overall heat dissipation of the electrode plates, thereby increasing the system’s self-driven force. Meanwhile, increasing the width of the electrode plates can enhance the flow area within each channel between the plates, thereby effectively reducing the flow resistance of the system. Consequently, an increase in the electrode plate width is advantageous for promoting a higher system flow rate.

As shown in Figure 7, an increase in the width of the electrode plate will cause the average and maximum temperatures of the seawater in the electrode plate area to gradually rise, but at the same time the extent of the increase in seawater temperature gradually decreases. Therefore, it can be seen that increasing the width of the electrode plates can only raise the system seawater temperature to a certain extent. The excessive increase in electrode plate width may not achieve the desired effect on raising seawater temperature.

2.5. The Influence of Annular Gap of the Double-Pipe Preheater on SMAB-P System Performance

The structure design of the preheater is extremely important for its heat exchange performance and directly affects the overall temperature distribution of the SMAB-P system. The preheater adopts the double-pipe structure, and the flow resistance in the shell side is much greater than that in the tube side. Therefore, the shell-side structure will have a more significant impact on the operation performance of the system. Figure 8 shows the influence of the annular spatial spacing in the shell side of the preheater on the system flow rate and temperatures in the electrode plate area. It can be seen that as the annular spatial spacing decreases, the average and maximum temperatures in the electrode plate area gradually increase, and the magnitude of the temperature changes shows a gradually increasing trend. When the annular spatial spacing is less than 0.004 m, the change rate of the temperature curve is relatively faster, indicating that the effect of raising the system seawater temperature is more significant, which is conducive to improving the power generation efficiency of the system. However, it is worth noting that the reduction of the annular space will lead to an increase in the system flow resistance and a decrease in the system flow rate, which will have an adverse effect on the replacement of seawater in the electrode plate area. In fact, the power generation process of the electrode plates needs to react with a certain amount of continuously replenished fresh seawater. Therefore, it is necessary to comprehensively consider both the seawater flow demand for the power generation of the SMAB-P system and the optimization objective temperature range of the system. This approach will facilitate the selection of an appropriate annular spatial spacing optimization value.

3. Distribution Characteristics of Physical Field in SMAB-P System

Based on the simulation results of the system loop model, the main optimization parameters of the SMAB-P system are recommended as the height and width of the electrode plate being 0.27 m and 0.73 m, respectively, the annular spatial spacing within the preheater being 0.003 m, and the heat recovery rate of the system being 100%.

3.1. The Simulation Model of Physical Field

The established three-dimensional model of the SMAB-P system, as shown in Figure 9a, consists of three computational domains, namely, the system seawater domain (fluid domain), the preheater domain (solid domain), and the ambient seawater domain (fluid domain). In order to avoid the mutual thermal interference of the ambient seawater in the local area near the inlet and outlet, the tube section at the inlet was extended to a certain extent along the vertical downward direction, as shown in Figure 9b. In practical applications, the SMAB-P system is enveloped by the ambient seawater on all sides. However, it is important to note that the heat and mass transfer processes of seawater in the vicinity of the system’s inlet and outlet are significantly more pronounced than those occurring at greater distances from the SMAB-P system. Additionally, an excessively large setting for the ambient seawater domain can result in decreased simulation calculation efficiency. Therefore, the ambient seawater domain has been reduced and set as a cuboid with external dimensions of 0.7 m × 0.22 m × 0.22 m. Within the cuboid, a hollow cuboidal space of 0.7 m × 0.22 m × 0.22 m has been created. The bottom surface of this cuboidal space is adjacent to the inlet of the system seawater domain, and the top surface is adjacent to the outlet of the system seawater domain. The initial temperatures of both the ambient seawater domain and the system seawater domain are set at 4 °C. The set value of the heat density of the electrode plates is consistent with the simulation of the system loop model. Figure 10 shows the mesh partitioning diagram of the three-dimensional model of the SMAB-P system.

3.2. Distribution Characteristics of Temperature Field

As shown in Figure 11a, in the stable state, the highest seawater temperature in the electrode plate area occurs in the top area inside the main body of the SMAB-P system. The distribution of the seawater temperature gradient along the height direction of the electrode plate is relatively uniform, and this distribution trend is consistent with the simulation results of the system loop model. The temperature distribution inside the preheater can be clearly observed from this figure. The seawater temperature in the tube side of the preheater shows an increasing trend along the flow direction, while the seawater temperature in the shell side shows a decreasing trend along the flow direction. Due to the substantial heat capacity of seawater, the high-temperature seawater flowing out of the SMAB-P system has a relatively minor influence on the surrounding seawater in the vicinity.

The temperature distribution within the cross-section of the electrode plate area is shown in Figure 11b. In the radial direction, the temperature field shows a non-uniform distribution, with the higher seawater temperature in the area near the included angle between two adjacent electrode plates and lower seawater temperature in the area near the outer edge boundary. This is mainly because, influenced by the shape characteristics of the fan-shaped cross section, the unit flow of seawater absorbs slightly more heat near the included angle area. However, the temperature difference across the flow cross-section is only 0.1 °C, so this difference can be ignored. Therefore, the relatively uniform distribution of seawater temperature on the cross-section of the electrode plate area does not result in a significant temperature difference between the electrode plates.

The simulation results of physical field show that, in the steady state, the flow rate of the SMAB-P system is 1.7 L/h and the maximum temperature in the electrode plate area is 28.49 °C. Both of these values are slightly higher than the simulation results of the system loop model. The comparative analysis results show that the relative error of the maximum temperature obtained by the two simulation methods is less than 5%, and the relative error of the system flow rate is less than 12%. This indicates that the results of the two simulation methods are basically consistent.

3.3. Distribution Characteristics of Velocity Field

The distribution of seawater velocity within the longitudinal section of the electrode plate area is shown in Figure 12a. It can be seen that the seawater velocity in the electrode plate channels is relatively low and evenly distributed, which allows seawater to more fully contact the electrode plates, facilitating the corrosion dissolution of the negative electrode plates and the reduction reaction of dissolved oxygen on the positive electrode plates. The seawater velocities in the top collection area and the bottom separation area within the system main body are slightly higher, and there are some local eddies, but they do not have adverse effects on the heat transfer in the electrode plate area.

As shown in Figure 12b, the velocity distributions in each channel between the electrode plates are almost the same. It can be observed that the velocity distribution within each channel cross-section is uneven, with the maximum velocity occurring in the local area near the included angle of the fan-shaped cross-section. This is because the local flow resistance is greater in the included angle area. However, the slight difference in velocity generated will not have an adverse effect on the thermal performance of the system.

4. Conclusions

In this work, the self-driven cycle characteristics and thermal performance of the proposed SMAB-P system were comprehensively investigated through the simulations of a system loop model and three-dimensional physics fields. The main conclusions are as follows:

(1)

With the increase of the system’s heat recovery rate, the average temperature in the electrode plate area gradually increases, and the maximum temperature shows a non-monotonic changing trend. By implementing the proposed SMAB-P system, the average and maximum temperatures of seawater in the electrode plate area can be enhanced by 54% and 15%, respectively. Consequently, the electrical conductivity of seawater within the system can be increased by approximately 20%, leading to a significant reduction in ohmic losses and an enhancement in the load voltage of the battery.

(2)

Increasing the height or width of the electrode plates can enhance the system’s self-driven force, the circulation flow rate, and the average and maximum temperatures in the electrode plate area. However, excessive increase in the height and width of the electrode plates has a relatively limited effect on raising the seawater temperature in the electrode plate area.

(3)

The reduction of the annular space in the double-pipe preheater can enhance the seawater temperature in the electrode plate area, particularly when the annular spatial spacing is less than 0.004 m, where the impact is more pronounced. However, excessively reducing the annular space may lead to an increase in system flow resistance and a decrease in flow rate, which could adversely affect the seawater replacement within the electrode plate area.

(4)

In the electrode plate area, the distribution of seawater temperature gradient along the height direction of the electrode plates is relatively uniform. The temperature difference on the flow cross-section is very small and can be ignored. The seawater velocities in the electrode plate channels are relatively low and evenly distributed, and the velocity distribution in each channel is similar.

(5)

Comparing the results of the two simulation methods, the relative error of the maximum temperature is less than 5%, and the relative error of the system flow rate is less than 12%, indicating that the results of the two simulation calculation methods are basically consistent.