Design of a New Single-Cell Flow Field Based on the Multi-Physical Coupling Simulation for PEMFC Durability

: The fuel cell with a ten-channel serpentine ﬂow ﬁeld has a low operating pressure drop, which is conducive to extended test operations and stable use. According to numerical results of the ten-channel serpentine ﬂow ﬁeld fuel cell, the multi-channel ﬂow ﬁeld usually has poor mass transmission under the ribs, and the lower pressure drop is not favorable for drainage from the outlet. In this paper, an optimized ﬂow ﬁeld is developed to address these two disadvantages of the ten-channel fuel cell. As per numerical simulation, the optimized ﬂow ﬁeld improves the gas distribution in the reaction area, increases the gas ﬂow between the adjacent ribs, improves the performance of PEMFC, and enhances the drainage effect. The optimized ﬂow ﬁeld can enhance water pipe performance, increase fuel cell durability, and decelerate aging rates. According to further experimental tests, the performance of the optimized ﬂow ﬁeld fuel cell was better than that of the ten-channel serpentine ﬂow ﬁeld at high current density, and the reﬂux design requires sufﬁcient gas ﬂow to ensure the full play of the superior performance.


Introduction
As a consequence of global warming and the structural changes in the world energy system over the years, hydrogen energy development and the implementation of technology represented by fuel cell technology are progressively emerging as hot spots in the development and research of new energy for attaining the long-term goal of carbon peak and carbon neutrality. Hydrogen energy includes the cleanliness of renewable energy and the sustainability of traditional energy. In the hydrogen power generation system, as long as there is enough hydrogen as a fuel supply, fuel cells can be continuous and provide clean power generation. Proton exchange membrane fuel cell (PEMFC) is the most extensively used and durable type of fuel cell due to its low operating temperature [1]. Since the water content inside the membrane has a significant impact on the efficiency of hydrogen ion transport in PEMFC, its working temperature is usually lower than the boiling point of liquid water. Currently, Nafion is the primary perfluorosulfonic acid membrane used, with sulfonic acid groups serving as proton-conducting agents that only dissociate protons in the presence of water. Insufficient water content leads to reduced proton dissociation and active sites for conduction, ultimately limiting current density and power density. However, model of PEMFC, which contains adjacent flow channels and rib channels. It was demonstrated that a flow field with the characteristics of an in-plate countercurrent increases the uniformity of current density and material distribution, and the offset effect enhances the transport of water across the ribs [12]. Through simulation and experimental verification, Wen et al. developed a small intersecting channel that performed better than the singlechannel serpentine flow field in the same reaction area [13]. Alizadeh et al. designed the flow fields of different flow channels that were merged step by step and determined the optimal flow channel merging layout scheme via simulation [14].
Based on the aforementioned research findings, it is evident that multi-physical field simulation is a crucial method for flow field optimization in PEMFC. Moreover, the optimization of the traditional serpentine flow field mainly increases the flow disturbance due to the complexity of the gas flow path in the increasing field. The specific design ideas are primarily focused on the mass transfer characteristics of the flow passage itself or the overall path layout of the flow passage. Thus, it is important to implement the design concepts of a multi-channel flow field to optimize the serpentine flow field.
The primary focus of this study is on further optimizing the design of the existing ten-channel serpentine flow field scheme and proposing a design scheme for grouping shunt confluence flow fields by changing the gas path design. Furthermore, the difference between the optimized flow field and the prototype flow field is compared via the simulation calculation of experimental verification parameters. Figure 1 presents the 3D model of the PEMFC for simulation, which includes the flow passage of the anode and cathode, the bipolar plate, the gas diffusion layer (GDL), the catalyst layer (CL), and the proton exchange membrane. Figure 2 displays the 10-channel serpentine flow channel and the flow field model after the optimized design.

3D Multi-Physics Model Development
number of shunts on the flow path through step-by-step merging rather than pursuing a more dense and subdivided flow channel design.
Recent years have witnessed an increase in the flow field optimization of proton exchange membrane fuel cells using multi-physical field coupling simulation. Using computer-aided engineering (CAE), Zhang et al. developed a single-layer isothermal 3D model of PEMFC, which contains adjacent flow channels and rib channels. It was demonstrated that a flow field with the characteristics of an in-plate countercurrent increases the uniformity of current density and material distribution, and the offset effect enhances the transport of water across the ribs [12]. Through simulation and experimental verification, Wen et al. developed a small intersecting channel that performed be er than the singlechannel serpentine flow field in the same reaction area [13]. Alizadeh et al. designed the flow fields of different flow channels that were merged step by step and determined the optimal flow channel merging layout scheme via simulation [14].
Based on the aforementioned research findings, it is evident that multi-physical field simulation is a crucial method for flow field optimization in PEMFC. Moreover, the optimization of the traditional serpentine flow field mainly increases the flow disturbance due to the complexity of the gas flow path in the increasing field. The specific design ideas are primarily focused on the mass transfer characteristics of the flow passage itself or the overall path layout of the flow passage. Thus, it is important to implement the design concepts of a multi-channel flow field to optimize the serpentine flow field.
The primary focus of this study is on further optimizing the design of the existing ten-channel serpentine flow field scheme and proposing a design scheme for grouping shunt confluence flow fields by changing the gas path design. Furthermore, the difference between the optimized flow field and the prototype flow field is compared via the simulation calculation of experimental verification parameters. Figure 1 presents the 3D model of the PEMFC for simulation, which includes the flow passage of the anode and cathode, the bipolar plate, the gas diffusion layer (GDL), the catalyst layer (CL), and the proton exchange membrane. Figure 2 displays the 10-channel serpentine flow channel and the flow field model after the optimized design.   In terms of both performance and pressure drop, the ten-channel serpentine flow field has a lower pressure drop than the single-snake flow field and retains the zigzag characteristics of the serpentine flow field. Shimpalee S. et al. found that the multi-channel serpentine flow channel is generally a parallel flow design, and the gases in different flow channels have similar flow processes at the same flow time. Therefore, the pressure difference between adjacent flow channels is small, which results in a large difference in the concentration of mass transfer of gas under the flow channel and the rib, thereby underutilizing the reaction area [15]. The pressure drop generated on the flow path when gas flows in the flow passage can be employed to enhance the mass transfer of sub-costal gas. The middle and low-pressure sections of a channel are placed adjacent to the high-pressure sections using manifold design to produce more pressure differences on either side of the rib, promote sub-costal convection, and boost performance.

3D Multi-Physics Model Development
According to Rahimi-Esbo et al. and Velisala et al., the progressive combination of multi-inlet air intake through the flow passage can disturb the gas and improve the flow velocity, mass transfer, and drainage capacity of the gas in the rear of the flow passage [8,16]. However, due to the step-by-step merging of multiple entrances, the area of the outlet is reduced. If all ten snake flow fields are set for step-by-step merging, the outlet area may be extremely small, making drainage difficult, or the single outlet passage may be excessively wide, hindering performance.
Zhang et al. developed a honeycomb flow field in which the flow is more disordered than the usual honeycomb flow field. This non-linear flow can amplify the disturbance in the flow field. However, it also suggests that the disturbance mode must be planned for optimization [8].
Therefore, in this paper (Figure 2b), the optimized flow field adopts the design of grouping and merging. Moreover, it uses eight inlet flow channels and divides them into four groups. Each group of two channels is combined into one channel at an export area. Once it reaches the export area, the combined flow changes direction and then proceeds through the path that is adjacent to the path of the incoming channel until it arrives at the entrance area. Finally, it changes the flow direction and proceeds through the path again to the exits.
Depending on the channel design, the following benefits can be obtained: In terms of both performance and pressure drop, the ten-channel serpentine flow field has a lower pressure drop than the single-snake flow field and retains the zigzag characteristics of the serpentine flow field. Shimpalee S. et al. found that the multi-channel serpentine flow channel is generally a parallel flow design, and the gases in different flow channels have similar flow processes at the same flow time. Therefore, the pressure difference between adjacent flow channels is small, which results in a large difference in the concentration of mass transfer of gas under the flow channel and the rib, thereby underutilizing the reaction area [15]. The pressure drop generated on the flow path when gas flows in the flow passage can be employed to enhance the mass transfer of sub-costal gas. The middle and low-pressure sections of a channel are placed adjacent to the highpressure sections using manifold design to produce more pressure differences on either side of the rib, promote sub-costal convection, and boost performance.
According to Rahimi-Esbo et al. and Velisala et al., the progressive combination of multi-inlet air intake through the flow passage can disturb the gas and improve the flow velocity, mass transfer, and drainage capacity of the gas in the rear of the flow passage [8,16]. However, due to the step-by-step merging of multiple entrances, the area of the outlet is reduced. If all ten snake flow fields are set for step-by-step merging, the outlet area may be extremely small, making drainage difficult, or the single outlet passage may be excessively wide, hindering performance.
Zhang et al. developed a honeycomb flow field in which the flow is more disordered than the usual honeycomb flow field. This non-linear flow can amplify the disturbance in the flow field. However, it also suggests that the disturbance mode must be planned for optimization [8].
Therefore, in this paper (Figure 2b), the optimized flow field adopts the design of grouping and merging. Moreover, it uses eight inlet flow channels and divides them into four groups. Each group of two channels is combined into one channel at an export area. Once it reaches the export area, the combined flow changes direction and then proceeds through the path that is adjacent to the path of the incoming channel until it arrives at the entrance area. Finally, it changes the flow direction and proceeds through the path again to the exits.
Depending on the channel design, the following benefits can be obtained: (i) In the flow field, the eight flow channels converge only once. In contrast to the design of continuous merging of the flow channels in the flow field, this not only maintains the effect of increasing the pressure in the single flow channel due to the flow channel confluence but also prevents the pressure drop in the entire flow field from rising excessively due to frequent merging. (ii) The combined flow channels change the direction of flow, directing the working medium gas to flow from the exit back to the entrance and then again to the exit. Such a flow path breaks the single flow pattern of the working medium from side to side in the traditional flow field. Hence, due to this linear trend, it improves the linear difference caused by gas consumption in the import and export areas of the flow field and balances the pressure distribution and the concentration distribution of substances in the import and export areas. (iii) Since the internal gas in the combined channels has been flowing for a long time, the internal pressure is smaller than that of the front flow channel of the flow field. Due to the pressure difference between the two kinds of channels, the subrib convection is strengthened, providing the gas more possibilities to participate in the reaction and improving the overall performance.
To validate the effectiveness of the flow field optimization design, commercial computational fluid dynamics (CFD) software, Ansys Fluent 2021R1, is utilized in this study to perform multi-physical field coupling simulation calculations. The simulation objects include a ten-channel serpentine single-layer fuel cell and an optimized flow field single fuel cell.

Model Assumptions
The numerical model is selected based on the following assumptions: The first four assumptions are extensively utilized in the CFD simulation of PEMFC, which is valid in scenarios of low flow rates and low temperatures [16,17]. The fifth assumption is a simplified hypothesis for the calculation of liquid water. It is primarily the water in the porous medium that unilaterally impacts the pressure drop in the flow passage when the liquid saturation model is utilized to modify the pressure in the flow passage. Thus, as verified by Alfredo Iranzo et al., the use of this model will not directly affect the electrochemical calculation results in the simulation [18].

Governing Equations
In this paper, the simulation is supported by the PEMFC module in ANSYS FLUENT. The following mathematical models are coupled internally.
Conductivity equation: The conduction equation is used to describe the generation and transmission of the current in fuel cells. According to the reaction mechanism of fuel cells, the metal conduction process and the ion conduction process are, respectively, defined by two sets of conduction equations: The forms of the source term (R) in the cathode catalyst layer and the anode catalyst layer are provided in Equations (3) and (4). The classical Butler-Volmer (BV) equation describes the relationship between the material and current in a fuel cell: where i re f 0 represents the reference exchange current density (A m −3 ), and ξ represents the specific active surface area (m −1 ). Equations (3) and (4) include the overpotential (η), which is the difference between the solid phase potential and the membrane phase potential. γ represents the concentration dependence, and α denotes the electrode transfer coefficient.  The equation for liquid water transport in porous media, Equation (5), describes the transformation and transport of liquid water in porous media (GDL, MPL, and CL).
where (ρ l ) denotes the liquid water density, µ l denotes the liquid dynamic viscosity, (K) represents the absolute permeability, and (K r ) represents the relative permeability. (s) denotes the saturation of liquid water in a porous medium, which is defined as the percentage of the volume of liquid water in the mass transfer channel volume in the porous medium. Therefore, (s) can be utilized to rectify the actual flux or source term in other equations involving mass transfer. Membrane water transport equation: The equation governing the transport of water in the dissolved phase can be defined as: where (λ) denotes the water content, which is the main parameter reflecting the local dissolved phase water. The distribution of dissolved water in the catalyst layer and proton Energies 2023, 16, 5932 7 of 17 exchange membrane is obtained by solving the transport equation of water in the dissolved phase. According to Equation (6), the factors affecting (λ) include the porosity of porous media (ε i ), ionic current density ( → i m ), the resistance permeability coefficient of water in the film (n d ), the source term provided by water generated by electrochemical reaction (S λ ), the source term exchanged with gaseous water (S gd ), and the source term exchanged with liquid water (S ld ).
Here, the diffusion coefficient of water (D i w ) is calculated using Equation (7), and f is calculated using Equation (8). Table 1 lists the main boundary conditions used in the simulation. Table 2 lists the simulation operation parameters and physical parameters of each part. The parameters in Table 1 are derived from the parameter settings used in testing the ten-channel serpentine flow field. Some of the parameters in Table 2 refer to the PEMFC simulation parameter settings of related papers. These basic parameters were used to adjust the multi-physical field coupling model used in the paper, and the electrochemical parameters were adjusted to fit the experimental data curve. In the experiment, the electric cell flow field was enclosed in a larger clamping configuration, equipped with a heating device, and the heating temperature was set to 80 • C. Consequently, the surrounding wall in the simulation model is set to the constant temperature boundary condition, and the temperature value is set to 353.15 K.

Numerical Procedures
The model was built using SCDM. HyperMesh was used to discretize the model using a hexahedral mesh. The solution method is SIMPLE, which utilizes the second-order upwind scheme forward discrete. The under-relaxation factor is calculated by gradually increasing the capillary pressure, and the water content model is combined to maintain a stable calculation. The final results are calculated according to the following criteria to determine calculation convergence: (1) The residual values of the equations of all models are less than 1 × 10 −6 [21].
(2) Water content, current density, and the proportion of material mass fraction all presented nearly stable variation trends in the CL layer [22]. (3) The reported value and the generated current calculated by the conservation of matter differ by less than 1% [23].

Numerical Procedures
The model was built using SCDM. HyperMesh was used to discretize the model using a hexahedral mesh. The solution method is SIMPLE, which utilizes the second-order upwind scheme forward discrete. The under-relaxation factor is calculated by gradually increasing the capillary pressure, and the water content model is combined to maintain a stable calculation. The final results are calculated according to the following criteria to determine calculation convergence: (1) The residual values of the equations of all models are less than 1 × 10 −6 [21].
(2) Water content, current density, and the proportion of material mass fraction all presented nearly stable variation trends in the CL layer [22]. (3) The reported value and the generated current calculated by the conservation of matter differ by less than 1% [23].   Figure 4 displays the comparison between experimental data and simulation data of a 10-channel serpentine single cell. It is observed that the experimental and simulation parameters fit well when the voltage is higher than 0.7 V. Moreover, the gap between experimental and simulation data increases gradually as the current density increases. However, the prediction model for liquid water in the flow channel in the PEMFC module is relatively rough, and the liquid water saturation equation in the flow channel is insufficient to accurately describe the interaction between liquid water in the flow channel and mass transfer. Consequently, the simulation results do not include the influence of mass  Figure 4 displays the comparison between experimental data and simulation data of a 10-channel serpentine single cell. It is observed that the experimental and simulation parameters fit well when the voltage is higher than 0.7 V. Moreover, the gap between experimental and simulation data increases gradually as the current density increases. However, the prediction model for liquid water in the flow channel in the PEMFC module is relatively rough, and the liquid water saturation equation in the flow channel is insufficient to accurately describe the interaction between liquid water in the flow channel and mass transfer. Consequently, the simulation results do not include the influence of mass transfer deterioration in the channels, and the final simulation parameter results are gradually larger than the experimental data. It is important to note that the maximum difference between simulation and experiment is within 15%, and the overall trend is consistent. According to related studies, the simulation model has a certain effect of reflecting the actual experiment in the range of discussed working conditions, which can be used for optimization discussions.

Model Validation
Energies 2023, 16, x FOR PEER REVIEW 9 of 18 transfer deterioration in the channels, and the final simulation parameter results are gradually larger than the experimental data. It is important to note that the maximum difference between simulation and experiment is within 15%, and the overall trend is consistent. According to related studies, the simulation model has a certain effect of reflecting the actual experiment in the range of discussed working conditions, which can be used for optimization discussions.  Figure 5 illustrates the oxygen concentration distribution diagram. As shown in the figure, the oxygen distribution of the ten-channel serpentine flow field gradually decreased from the inlet area to the outlet area, mainly because the overall flow trend of the air side of the working medium decreased linearly from left to right. The linear decrease in the concentration of the working medium from the entrance to the exit results in a significant difference in reaction conditions between the entrance and exit zones. In the inlet area, there is a high concentration of the working medium, a significantly higher airway pressure, and relatively more ideal we ing conditions. Due to the relatively low flow and reaction, low concentration of reactants, and excessive accumulation of liquid water, the pressure has an impact on mass transfer in the outlet area.

Results and Discussion
In the new type of flow field, the working medium is directed from the exit to the entry point and then back to the exit, a design that breaks the traditional flow path of the serpentine flow field. The linear gradient of concentration varies from the entrance area to the exit area, increasing the complexity of flow in the reaction zone. The gas flow in the internal channels is more likely to enter the porous medium for cross-rib flow under the action of the pressure gradient between the internal channels so as to enhance mass transfer and improve the reaction performance.  Figure 5 illustrates the oxygen concentration distribution diagram. As shown in the figure, the oxygen distribution of the ten-channel serpentine flow field gradually decreased from the inlet area to the outlet area, mainly because the overall flow trend of the air side of the working medium decreased linearly from left to right. The linear decrease in the concentration of the working medium from the entrance to the exit results in a significant difference in reaction conditions between the entrance and exit zones. In the inlet area, there is a high concentration of the working medium, a significantly higher airway pressure, and relatively more ideal wetting conditions. Due to the relatively low flow and reaction, low concentration of reactants, and excessive accumulation of liquid water, the pressure has an impact on mass transfer in the outlet area.

Results and Discussion
In the new type of flow field, the working medium is directed from the exit to the entry point and then back to the exit, a design that breaks the traditional flow path of the serpentine flow field. The linear gradient of concentration varies from the entrance area to the exit area, increasing the complexity of flow in the reaction zone. The gas flow in the internal channels is more likely to enter the porous medium for cross-rib flow under the action of the pressure gradient between the internal channels so as to enhance mass transfer and improve the reaction performance.
Furthermore, the vector diagram in GDL ( Figure 6) indicates that since the merged channel has low channel pressure due to the pressure loss caused by the flow, it can strengthen the subcostal convection and further enhance the subcostal mass transfer and subcostal water scavenging when adjacent to the flow channel before merging, thereby improving the performance. Energies 2023, 16, x FOR PEER REVIEW 10 of 18 Furthermore, the vector diagram in GDL ( Figure 6) indicates that since the merged channel has low channel pressure due to the pressure loss caused by the flow, it can strengthen the subcostal convection and further enhance the subcostal mass transfer and subcostal water scavenging when adjacent to the flow channel before merging, thereby improving the performance. The performance curve validation in Figure 7 shows that the optimized flow field performs be er than the ten-channel serpentine flow field, and the performance improvement increases when the current density exceeds 1.25 A/cm 2 .  Furthermore, the vector diagram in GDL ( Figure 6) indicates that since the merged channel has low channel pressure due to the pressure loss caused by the flow, it can strengthen the subcostal convection and further enhance the subcostal mass transfer and subcostal water scavenging when adjacent to the flow channel before merging, thereby improving the performance. The performance curve validation in Figure 7 shows that the optimized flow field performs be er than the ten-channel serpentine flow field, and the performance improvement increases when the current density exceeds 1.25 A/cm 2 . The performance curve validation in Figure 7 shows that the optimized flow field performs better than the ten-channel serpentine flow field, and the performance improvement increases when the current density exceeds 1.25 A/cm 2 .  Figure 8 depicts the distribution of current density. The current density distribution of the new flow field has no obvious linear regional shift as compared to the ten-channel serpentine flow field. The high current density area and low current density area are staggered in the left and right halves of the flow channel because of the confluence and circumfluence se ings of the flow channel. This helps in improving the overall uniformity of the reaction region and the reaction conditions in the import and export regions caused by the regional distribution of linear flow.  Figure 8 depicts the distribution of current density. The current density distribution of the new flow field has no obvious linear regional shift as compared to the ten-channel serpentine flow field. The high current density area and low current density area are staggered in the left and right halves of the flow channel because of the confluence and circumfluence settings of the flow channel. This helps in improving the overall uniformity of the reaction region and the reaction conditions in the import and export regions caused by the regional distribution of linear flow.  Figure 8 depicts the distribution of current density. The current density distribution of the new flow field has no obvious linear regional shift as compared to the ten-channel serpentine flow field. The high current density area and low current density area are staggered in the left and right halves of the flow channel because of the confluence and circumfluence se ings of the flow channel. This helps in improving the overall uniformity of the reaction region and the reaction conditions in the import and export regions caused by the regional distribution of linear flow.   [24], the decline in fuel cell performance after long-term use is primarily a ributed to proton exchange membrane degradation and catalyst dissolution and aggregation. Insufficient gas supply in localized flow fields can lead to low or even reversed potential, which damages the catalyst and reduces fuel cell durability. Therefore, optimizing the flow field improves  Figure 9 depicts the distribution of liquid water in the porous medium at the cathode of the catalyst layer. Combining the current density and oxygen concentration distribution, the oxygen concentration under the fin increases as compared to the parallel snake-like flow field due to the new design of the flow field that places the high-pressure flow channel and the low-pressure flow channel close to each other. Furthermore, the distribution of high liquid water saturation under the fin shifts to the side of the flow channel, which aids in increasing the mass transfer under the fin and increases the utilization rate of the reaction area. According to Lin et al.'s research on the durability of PEMFC [24], the decline in fuel cell performance after long-term use is primarily attributed to proton exchange membrane degradation and catalyst dissolution and aggregation. Insufficient gas supply in localized flow fields can lead to low or even reversed potential, which damages the catalyst and reduces fuel cell durability. Therefore, optimizing the flow field improves water purging under the ribs, enhances gas supply patency in the membrane electrode, increases the durability, and slows down aging rate. water purging under the ribs, enhances gas supply patency in the membrane electrode, increases the durability, and slows down aging rate. According to the liquid water model in the PEMFC module, the liquid water in the channel is assumed to be fog droplets. Moreover, the movement speed of the droplets is determined by the local gas velocity ratio, which is usually set to 1 (fog droplets and the gas flow are at the same speed). However, the simulation model can only roughly determine the distribution and situation of the liquid water in the channel. Therefore, a separate two-phase flow simulation is required to determine the distribution and situation of liquid water in the flow field. This paper presents a two-phase flow simulation (air phase and liquid water phase). Figure 10 depicts the simulation model and boundary se ings. According to the liquid water model in the PEMFC module, the liquid water in the channel is assumed to be fog droplets. Moreover, the movement speed of the droplets is determined by the local gas velocity ratio, which is usually set to 1 (fog droplets and the gas flow are at the same speed). However, the simulation model can only roughly determine the distribution and situation of the liquid water in the channel. Therefore, a separate two-phase flow simulation is required to determine the distribution and situation of liquid water in the flow field. This paper presents a two-phase flow simulation (air phase and liquid water phase). Figure 10 depicts the simulation model and boundary settings. This paper presents a two-phase flow simulation (air phase and liquid water phase). Figure 10 depicts the simulation model and boundary se ings. The fluid domain part of the porous medium and the flow channel: the porosity and the thickness of the porous medium area were set to 0.78 and 0.2 mm, respectively, and this thickness is consistent with the GDL layer thickness of the previous simulation model. The bo om surface of the porous medium was set to the uniform seepage surface (liquid water inlet boundary condition), and the simplified amount of liquid water entry was set to the mass of all water produced under the operating condition of 2 A/cm 2 . The inlet and outlet of the flow channel served as the mass flow boundary conditions of the gas; the intake type was air, and the dry air quality coefficient was 4 under an operating condition of 2 A/cm 2 .
According to the simulation findings, the saturation of liquid water in the two flow areas tended to stabilize in approximately 3 s at the beginning of water seepage and air intake. Figure 11 illustrates changes in the distribution of liquid water over time. In the ten-channel serpentine flow field, the liquid water first penetrates the flow field from the The fluid domain part of the porous medium and the flow channel: the porosity and the thickness of the porous medium area were set to 0.78 and 0.2 mm, respectively, and this thickness is consistent with the GDL layer thickness of the previous simulation model. The bottom surface of the porous medium was set to the uniform seepage surface (liquid water inlet boundary condition), and the simplified amount of liquid water entry was set to the mass of all water produced under the operating condition of 2 A/cm 2 . The inlet and outlet of the flow channel served as the mass flow boundary conditions of the gas; the intake type was air, and the dry air quality coefficient was 4 under an operating condition of 2 A/cm 2 .
According to the simulation findings, the saturation of liquid water in the two flow areas tended to stabilize in approximately 3 s at the beginning of water seepage and air intake. Figure 11 illustrates changes in the distribution of liquid water over time. In the ten-channel serpentine flow field, the liquid water first penetrates the flow field from the fourth corner at the end of the flow field and then begins to converge at the exit of the flow field. Finally, the liquid water mostly accumulates in the corner area in the middle and back half of the flow field. In the optimized flow field, liquid water was initially produced in the central and exit areas of the flow field. Then, the fluid accumulates in the second corner area and the outer part of the upper part of the flow field. Finally, the liquid water is mainly accumulated in the second corner area and the exit area.
After the distribution had stabilized, the average volume of liquid water saturation in the ten-channel serpentine flow field was 1.903479 × 10 −6 . Meanwhile, the average volume of the liquid water saturation in the optimized flow field was 1.7181223 × 10 −6 , which is smaller than that in the serpentine flow field. Thus, the optimized flow field improves the drainage effect of liquid water in the flow channel.
However, the results of the two-phase flow simulation reveal a noteworthy fact. Although the simulation results imply a lower water content than the ten-channel snake flow field, liquid water is dispersed in all channels, including multiple sets of channels flowing to the inlet area after the outlet confluence. In practical battery applications, the accumulated or produced liquid water in the exit area due to the impact of gravity will not return through the flow channel to the inlet. Instead, it sinks in the low flow field area and enters the nearest exit field via the GDL layer, similar to the cross-toe flow field. This results in poor performance at low gas flow rates since liquid water is not effectively discharged. To verify this conjecture, a pair of 5 cm × 5 cm (active area) graphite bipolar plates were produced (Figure 12) based on the optimized model Then, experimental tests were conducted with the same membrane electrode as before, using experimental parameters that completely referenced the simulation conditions. The test bench used YK-A10 of Yuke Company, the proton exchange membrane used was the 12-micron membrane from Gore Company, the GDL material was carbon paper, the catalyst used platinum carbon catalyst, the load was 0.35 ca/0.05 an (mg/cm 2 ). The test temperature was 80 • C, the humidity was 0.8, the outlet pressure was set to 150 kPa, the anode stoichiometric ratio was 1.5, and the cathode stoichiometric ratio was 3.0-5.0. During testing, the battery was positioned vertically according to experimental requirements. the nearest exit field via the GDL layer, similar to the cross-toe flow field. This results in poor performance at low gas flow rates since liquid water is not effectively discharged.
To verify this conjecture, a pair of 5 cm × 5 cm (active area) graphite bipolar plates were produced (Figure 12) based on the optimized model Then, experimental tests were conducted with the same membrane electrode as before, using experimental parameters that completely referenced the simulation conditions. The test bench used YK-A10 of Yuke Company, the proton exchange membrane used was the 12-micron membrane from Gore Company, the GDL material was carbon paper, the catalyst used platinum carbon catalyst, the load was 0.35 ca/0.05 an (mg/cm 2 ). The test temperature was 80 °C, the humidity was 0.8, the outlet pressure was set to 150kPa, the anode stoichiometric ratio was 1.5, and the cathode stoichiometric ratio was 3.0-5.0. During testing, the ba ery was positioned vertically according to experimental requirements.  Figure 13 presents the performance comparison curves. Figure 13a shows that although the simulation and test curves are partially similar in the overall trend, the deviation gradually increases after 0.7 V voltage. The main reason is that the simulation did not take into account the influence of liquid water, and it is difficult for the actual fuel cell to backflow according to the design if the water-clogged gas is generated at the end of the fuel cell. Hence, the difference between the mass transfer polarization zone in the IV curve and the simulation result gradually increases. Figure 13b shows that  Figure 13 presents the performance comparison curves. Figure 13a shows that although the simulation and test curves are partially similar in the overall trend, the deviation gradually increases after 0.7 V voltage. The main reason is that the simulation did not take into account the influence of liquid water, and it is difficult for the actual fuel cell to backflow according to the design if the water-clogged gas is generated at the end of the fuel cell. Hence, the difference between the mass transfer polarization zone in the IV curve and the simulation result gradually increases. Figure 13b shows that the optimized flow field exhibits poor performance at low current densities. However, the performance improves as the current density increases to 1.4 A/cm 2 and eventually exceeds that of the ten-channel snake flow field at 1.8 A/cm 2 . The performance of the fuel cell considerably declined after reducing the air stoichiometry to 3.0, particularly in the mass transfer polarization region at the end of the IV curve. The fuel cell performance slightly improved after the stoichiometric ratio was adjusted to 5.0, and the terminal performance exceeded the 10-channel snake flow field at 1.64 A/cm 2 . Due to the constant excess ratio measurement used in the test, the air intake will increase with the increase of the current density. When the current density increases to a certain value, the water sinking at the bottom will be more effectively blown by the increase of air volume, thus improving the overall air distribution and improving performance. Hence, according to experimental results, the optimized flow field operates effectively in practical applications under high current densities, although its significant advantages are evident only during sufficient gas purging.

Conclusions
In this paper, a multi-physical coupling simulation was performed for the ten-channel serpentine flow field by combining experimental and simulation data. According to the simulation results, the oxygen supply to the porous media in the parallel serpentine flow field gradually decreases from the inlet to the outlet. Generally, this is characteristic of high material concentration and high current density in the inlet area and low current density in the outlet area. Due to these distribution characteristics, the polarization of the region increases, resulting in insufficient utilization of the reaction region. Furthermore, there is a significant difference between the oxygen under the rib and that under the flow

Conclusions
In this paper, a multi-physical coupling simulation was performed for the ten-channel serpentine flow field by combining experimental and simulation data. According to the simulation results, the oxygen supply to the porous media in the parallel serpentine flow field gradually decreases from the inlet to the outlet. Generally, this is characteristic of high material concentration and high current density in the inlet area and low current density in the outlet area. Due to these distribution characteristics, the polarization of the region increases, resulting in insufficient utilization of the reaction region. Furthermore, there is a significant difference between the oxygen under the rib and that under the flow channel due to the relatively consistent pressure distribution in the adjacent flow channel. Consequently, the reaction area under the rib is wasted to a certain extent.
The new flow field improves the regionalization difference caused by the linear flow in the traditional serpentine flow field utilizing shunt, confluence, and reverse flow. Meanwhile, the pressure difference between the two sides of the rib is enhanced, as is the mass transfer under the rib, eventually resulting in improved performance of the fuel.
According to the simulation of two-phase flow, liquid water tends to accumulate in the flow corner area and exit area of the flow field. The average content of liquid water in the optimized flow field is less than that in the ten-channel serpentine flow field. Therefore, the optimized flow field enhances the drainage effect.
The results reveal that the optimized flow field performs better than the ten-channel snake channel. However, the accumulation of liquid water and gravity effects are not considered in the multi-physical field coupling simulation. Hence, in practical applications, the optimized flow field must guarantee a larger coefficient at higher current densities.

Data Availability Statement:
The geometric parameters, electrochemical setting conditions and boundary conditions of the simulation model in this paper have been defined, and can be calculated using the same simulation software. The experimental bipolar plate flow field, membrane electrode parameters, test bench progress and test conditions can be obtained in Table 2 and the discussion and analysis section.

Conflicts of Interest:
The authors declare no conflict of interest.