INTRODUCTION
The development of alternative energy sources became crucial due to energy shortage and environmental challenge posed by fossil fuels. Recently, PEMFC have garnered interest due to its high-power density and minimal emission [1]. Compared to conventional heat engine power generation, PEMFC converted fuel chemical energy into electricity, resulting in power generation efficiency up to 40%–60%. Additionally, the reaction products were water and heat, which were not harmful to the environment. Due to these advantages, PEMFC became the preferred choice for transportation, portable power sources, and distributed generation [2–5]. Accurate modeling was necessary to assess the overall performance of PEMFC and make targeted improvement to enhance their commercial viability [6–8].
The alteration of the channel structure directly influenced the output performance of PEMFC, with an outstanding channel structure capable of significantly boosting the efficiency of PEMFC [9]. Efficient transportation of reactant gas across the electrode surface was crucial for proper cell function. Uniform distribution of reactant enhanced electrochemical reaction, water management, current density, and temperature regulation. Effective removal of liquid water was essential to prevent clogging and leakage issue. Uneven temperature distribution could increase membrane resistance, reducing conductivity and lifespan. Hence, optimizing flow field structure was vital to address these concerns [10–13]. Improved flow channel design enhanced heat dissipation and liquid water removal efficiency, reducing accumulation and ensuring uniform gas distribution. This approach minimized pressure drop, maximizing gas delivery for complete reaction and reduced mass transfer loss [14,15]. Recent research focused on optimizing conventional flow channel exploring parameter like rib-width ratio [16], channel shape [17], and adding obstacle to achieve homogeneous fluid distribution under low-pressure condition [18–20].
Intensive study of bionic led to the discovery of many biological structures that were efficient and complied with the law of thermodynamic and hydrodynamic. For instance, plant had leaf vein structure with numerous fine channel that efficiently transported nutrient to various part, while animal had lung with major bronchial tube that branched into interconnected fine bronchial tube with low pressure and suitable fluid velocity [21,22]. Drawing inspiration form bionic. Kang [23] and fellow researchers endeavored to replicate the flow pattern found in leaf vein. They conducted comparative analysis between the ginkgo-inspired flow channel and two conventional designs, namely, serpentine and parallel flow channel. Results indicated that the maximum power density achieved by the ginkgo channel was 7% lower than that of the serpentine configuration, but 40% higher than that of the parallel channel. Moreover, the ginkgo-inspired flow field exhibited the highest available power density among all configuration tested. Guo and colleagues [24] investigated the dispersion of reactant and pressure drop within channel and GDL, inspired by the intricate structure of leaf veins. Their finding revealed that the application of biomimetic crossover design led to notable enhancement in fuel cell performance, with the improvement of 20%–25% compared to conventional design. Li et al. [25] devised novel bionic flow channel, drawing inspiration from the intricate internal framework of the nautilus. This innovative channel configuration resulted in substantial enhancement, with notable 46.7% surge in peak current density and 21.53% rise in peak power density. Furthermore, it exhibited superior uniformity in dispersing reactant and effectively managing water removal in contrast to the conventional serpentine flow channel. Xia et al. [26] introduced enhanced leaf-vein bionic flow channel, inspired by the distinctive feature of the leafvein lattice structure. Through their investigation, they determined that optimal power output was achieved when incorporating 10 branch channels on one side of the main channel, resulting in 5.8% improvement in output performance compared to the conventional serpentine flow channel. Cho et al. [27] used neutron radiography to assess the formation and movement of liquid water in lung-suction and serpentine flow configurations. Their finding revealed that higher airflow velocity and elevated channel pressure drop led to more rapid elimination of liquid water. Zhang et al. [28] proposed and investigated honeycomb flow channel that demonstrated current densities 14% and 10.4% higher than those of parallel and serpentine flow channels, respectively. Damian-Ascencio et al. [29] introduced novel tree flow channel design determined by vein bifurcation count and their angle of inclination. The results indicated that the application of tree flow channel featuring two bifurcation levels at 37o inclination effectively enhanced water removal, consequently boosting current density. Xuan et al. [30] introduced 3D bionic flow channel inspired by the villi found in the small intestine. Simulation outcome demonstrated that this novel flow channel design enhanced the contact area between the GDL and the flow channel, thereby improving gas mass transfer and expediting the removal of liquid water. Dong et al.[31] introduced pioneering flow channel inspired by biosuction and Murray’s Law. The results illustrated that this innovative flow channel not only improved the uniformity of gas distribution during reaction and minimized pressure drop. However, it also boosted maximum output power by 114% compared to parallel flow channel of equivalent dimension. Huang et al. [32] devised innovative bionic flow channel, comprising 10 refined channels, demonstrated reduced pressure drop, even distribution of reactant and increased output power. Notably, the peak power density of the novel flow channel surpassed that of the serpentine flow channel by 17.8%.
In this research, an innovative flow channel design inspired by the dual structure of Ginkgo biloba leaf vein was introduced, as showed in Fig. 1. The effect of number and arrangement of refinement flow channel on PEMFC performance was compared and determined the optimal structure. Six sets of refined bionic flow fields were examined for runners (BIFCs), contrasting them with both conventional parallel flow channel (CPFC) and conventional serpentine flow channel (CSFC). The optimized flow paths were compared for output characteristics and internal mass transfer. Subsequent studies were conducted for the width of the refined flow channel, and the change in the output performance of the fuel cell was observed by increasing the width of the refined flow channel. Previous research revealed that while the performance of enhanced bionic flow channel surpassed CPFC, it marginally trailed CSFC. Therefore, forthcoming research endeavored prioritized further refinement of the flow channel structure.
MODEL BUILDING
Geometric parameter
Fig. 2 illustrated the six sets of bionic flow channels developed in this study, drawing inspiration from the leaf vein architecture of Ginkgo biloba. The results of BI-0 showed that there was under-reaction in certain regions of the flow field, which directly affected the reaction efficiency in these areas and led to decreasing in overall output power. In order to solve this issue, leaf vein structure was borrowed in this study. The structure of leaf veins efficiently distributed water and nutrients to each leaf cell, and this uniform distribution was key factor to solving the problem. However, the distribution of leaf veins was intricate, and how to allocate the refined channels became the focus of this study. The authors designed nine arrangements based on variations in key structural parameters to ensure that the reactants could sufficiently reach the catalytic layer, thus enhancing the efficiency of chemical reactions within the fuel cell. These channels were categorized into BI-0 to BI-6, with BI-0 representing the original design, BI-1 to BI-3 incorporating aligned refinement channels, and BI-4 to BI-6 utilizing staggered refinement channels. Fig. 3 illustrated the schematic representation of the bionic flow channel structure. The PEMFC model comprised anode and cathode bipolar plate, gas channel, GDL, CL, and PEM. The BIFC comprised main flow channel, several branch flow channel and refined flow channel. The entire flow channel was symmetrically divided into two parts by main flow channel, and two symmetrical parts were distributed with the same number of branch flow channel. Different number and arrangement of refinement runner were integrated between the branch runner throughout the flow channel. Each of the six BIFCs featured effective reaction area of 35 mm × 33mm, with channel width and depth set at 1 mm. Table 1 summarized the model’s fundamental parameter.
Mathematical modeling
In order to fully simulate the complex dynamic of fluid flow, mass transfer, and electrochemical reaction in PEMFC, advanced three-dimensional two-phase mathematical model were devised. This model was meticulously crafted to encompass a range of crucial equation governing various physical phenomena within the cell. It incorporated equation for continuity, which ensured mass conservation, momentum conservation to accurately capture fluid flow behavior, energy conservation to track heat transfer mechanism, matter conservation to monitor species transport, current conservation to model electron flow, liquid water formation and transport equation to account for water management within the cell.
Model assumption
Several simplifying assumptions were considered for modeling the PEMFC:
(1) Steady-state operation was assumed.
(2) Flow was assumed to be laminar and incompressible.
(3) Consider the reaction and the resulting gas as ideal gas.
(4) The GDL, CL, and membrane were treated as homogeneous and isotropic porous media.
(5) Negligible effect of gravity was considered.
Governing equation
The continuity equation was expressed as:
Where, Sm represented the mass source term, measured in kg/(m3·s), denoting material produced per second per cubic meter of space, commonly used in mass transfer processes. ∇ denoted the Hamiltonian operator, introducing vector differential operator. ε signified porosity, indicating the proportion of pores within the material to the total volume of the bulk material. ρ represented fluid density, measured in m/v, indicating the mass per unit volume of a fluid. u ¯
Where, F denoted the Faraday constant, measured in C/mol, serving as a fundamental constant representing the charge carried per mole of electron. MH2, MH2O, MO2 represented the molar mass of hydrogen, water vapor, and oxygen, respectively, measured in kg/mol. These values were crucial for understanding the composition and property of the gas involved in the electrochemical reaction. Ran and Rca signified the volume transfer current density. measured in A/m3. These parameters quantified the rate of mass transfer occurring at each electrode interface, influencing the overall performance of the PEMFC.
Momentum conservation equation
The expression of the momentum conservation equation was:
The equation was broken down into various terms: the first term on the left side represented instability, while the second term depicted convection. On the right side, the first two terms indicated diffusion. p denoted pressure, measured in kg/cm2, representing the force acting perpendicular to an object's surface. The dynamic viscosity of the liquid-gas mixture, denoted as η, quantified the ratio of stress to strain rate, with the unit of N·s/m2. SM represented the momentum source term, measuring the change in momentum per second per cubic meter of space, with the unit of N/m3. In the flow channel, SM was set to 0. For fluid flow in porous media, it could be expressed as:
Where, Kp denoted permeability in a porous medium, the unit was m2.
Equation for conservation of energy
The expression for the energy conservation equation was:
Where, cp represented the specific heat capacity at constant pressure, indicating the heat absorbed or released per unit mass of an object as it changed per unit temperature, with the unit of J/(kg·°C). k in keff was the thermal conductivity, the subscript eff indicated the effectiveness of the porous medium, with the unit of W/(m·K). T represented temperature, measured in K, and SQ was the energy source term, measured in W/m3. The energy source item SQ contained various heat sources generated during battery operation, such as electrochemical reaction heat (Srea), ohmic heat (Sohm), evaporation/condensation heat (Sl), and overpotential heat (Sη). SQ could be expressed as:
Where, I represented the surface current density, measured in A/m2. Rohm denoted the ohmic resistivity, with the unit of Ω·m. SH2O indicated the rate of production of water vapor. The enthalpy changes of chemical reaction, known as enthalpy of reaction (hreact), was expressed in kJ/mol when the temperature of the product and the reactant were the same, and only volumetric work was performed during the reaction under condition of constant pressure or constant temperature. rw represented the rate of phase change of water. hlg denoted the enthalpy of phase change of water, measured in J/kg. And η represented the overpotential, which signified the potential difference between the electrode, measured in V.
Component conservation equation
Where, ck represented the concentration of substance k, measured in mol/m3. D k e f f
Where, jan and jca were representative of the exchange current density, measured in A/m2.
Charge conservation equation
Where, s and m represented the solid and membrane phase, respectively. σ stood for conductivity, measured in S/m. While φ denoted potential, with the unit of V. R indicated the volumetric transfer current, calculated through the Butler–Volmer equation. Ran and Rca could be determined by.
Where, jref was the reference exchange current density per effective surface area, the unit was A/m2. ζ was specific active surface area, the unit was m2/g. γ was concentration dependence. And α was dimensionless charge transfer coefficient.
Where, Voc was the open circuit voltage on the cathode side, the unit was V.
Equation for the formation and transport of liquid water
Where, s represented the liquid water volume fraction, indicating the proportion of liquid water present in the porous medium. cr denoted the condensation rate constant, specifying the rate at which water vapor condenses into liquid water within the medium, measured in g/(m³·s). pwv indicated the pressure of water vapor, representing the partial pressure exerted by water vapor in the surrounding environment, measured in Pa. psat stood for the saturation vapor pressure of water, delineating the maximum pressure at which water vapor can exist in equilibrium with its liquid phase at a given temperature, measured in Pa.
Where, μl was the dynamic viscosity of liquid water, measured in Pa·s. pc was the capillary pressure, and was calculated as:
(21)
The formula for calculating the water content in PEM is as follows:
Where, a was the water activity, which could be calculated by the following equation:
Boundary condition
Injection of reaction gas into the inlet and outlet, respectively, with the inlet temperature maintained at 353.15 K. The anode and cathode runner inlet reactive gas flow rate were related to the stoichiometric ratio, reference current density, membrane geometric area, runner cross-sectional area, and cell operating temperature and pressure, and could be calculated by the following equation:
Where, iref was the maximum average current density, measured in A/m2. was the stoichiometric number. Am was the cell activation area, measured in m2. Ach was the cross-sectional area of the runner inlet, measured in m2.
Grid independence check
In order to analyze the effect of mesh density on numerical result, meshing feature in COMSOL Multiphysics was used to generate meshes for all models. The original bionic flow field (BI-0) was regarded as the benchmark for evaluating mesh independence. Table 3 provided summarized the test results for various scenarios, including grid independence analysis of BI-0 using four different mesh densities. With the operational voltage of 0.5 V, the discrepancy between simulation using mesh densities of 2489658 and 3589344 was only 0.187%. Considering computational expense and accuracy, this research selected scheme 3 with the mesh density of 2489658 for subsequent simulation.
Experimental validation
This research compared the simulation of the polarization curve under single serpentine flow channel with experimental results from Miansari et al. to confirm the proposed PEMFC mathematical model in this study [33]. With the current density below 0.8 A/cm², the result obtained closely corresponded with the referenced experimental data. However, when current density exceeded 0.8 A/cm², the results slightly surpassed the experimental data, indicating a minor discrepancy. With high current densities, water generated by the electrochemical reaction accumulated in the catalyst layer or in the gas diffusion layer, leading to water blockage. The water blockage not only hindered the transport of reactant gases (e.g., oxygen or hydrogen), but also affected the efficiency of overall reaction process. Simulations failed to fully capture these complex water management issues, especially in the dynamic processes of water generation and discharge. These processes were not only related to the reaction rate, but also influenced by various factors, such as the hydrophilicity of the material, pore structure, and gas-liquid two-phase flow. Especially with high current densities, this led to deviation of the simulation results from the actual situation. Consequently, the model in this study was deemed reliable, offering a practical framework for application in other flow channel models.
RESULTS AND DISCUSSION
In order to investigate the gain effect of the refinement channels on the output performance of PEMFC, a series of refinement channels were added to the conventional flow field in this paper. The number (primary, secondary, and tertiary) and arrangement (aligned distribution, staggered distribution) of the refinement channels were discussed with respect to the output characteristics of the fuel cell and the material transfer at the GDL-CL intersection on the cathode side.
PEMFC output performance analysis
This part focused on assessing PEMFC performance through key metrics like the power density and polarization curve. The effect of refinement channel number and arrangement on the performance PEMFC was examined by comparing BIFCs, CPFC, and CSFC. The results were shown in Fig. 6, where the polarization curves rose rapidly and then fell slowly in the low-current-density region, and the differences between the groups were not obvious. This was due to the fact that the fuel cell consumed the same amount of oxygen for the electrochemical reaction in the activation polarization region, and therefore the activation energy consumed by H+ in the transfer process was almost the same. However, the polarization curves gradually and slowly decreased with the increase of current density, and the gap between the polarization curves of each shape became gradually obvious with the increase of the number of refinement channels. The greater the number of refinement channels, the greater the diffusion resistance generated during the reaction gas transfer. The diffusion resistance prevented the reactants from reaching the cathode and anode in time, leading to the continuous accumulation of reactants and products, which causing the reactants concentration changed. Notably, BI-6 exhibited current density closest to CSFC, suggesting that increasing refinement channels reasonably enhanced mass transfer capability and PEMFC performance. In the traditional flow channel, the ability of reactant gas to be transmitted through the reaction itself, like GDL and CL, was limited, and part of the reactant gas entered into the flow channel and flowed out without reaction, making the reaction ineffective. While the refinement of the flow channel in the overall flow channel structure mainly played role in the inflow, prompting more reactant gas through the GDL into the CL. The more reactant gas entered the CL, the higher the local current density, greatly improving the utilization efficiency of reactant gas. In BIFC, the peak power density increased with the increasing of refinement channels number, and regardless of the arrangement of the refinement channels, the fuel cell output characteristics were significantly improved with the increasing of refinement channels number. The power density of the staggered channels was always higher than that of the aligned channels, and BI-6 had the highest power density. Specifically, BI-6 achieved 38.8% increasing in peak power density compared with CPFC and 9.4% compared with BI-0, reaching 0.58 W/cm².
From BI-0 to BI-6, the polarization curves showed significant changing at 0.5 V operating voltage, which because the increasing of refinement channels effectively reduced the polarization loss, resulting in significant increasing of maximum power density. However, as the voltage was further reduced, the power density decreased, reflecting the more significant effect of mass transfer resistance at low voltage. By optimizing the design of the refinement channels, these resistances could be overcome to certain extent, thus improving the overall performance of the fuel cell.
Overpotential, or voltage loss, measured how much the output voltage differs from equilibrium potential while maintaining the same net current. Lower overpotential indicated reduced polarization and improved performance. At equilibrium potential, positive and negative reaction rate balanced, resulting in no net current output. Pumping power could be determined from pressure drop and inlet flow rate using the following formula:
In this equation, wp represented pumping work, measured in W. P stood for pressure drop, measured in Pa. Qin denoted the inlet flow rate, signified the pumping efficiency, which was set at 0.8 [34].
Fig. 7 illustrated the relationship between pressure drops and net power density for each model. Increasing the number of refinement channels enhanced mass transfer effectiveness, yet also led to larger pressure drops, particularly at channel corner. This was because the gas flow paths become more complex, increasing the hydrodynamic resistance. Consequently, the increasing of refinement channels number resulted in relatively higher pressure drops. However, examining the magnitude of net power density revealed that more refinement channel correlated with higher net power density. Notably, staggered distribution of refinement channels yielded greater net power density compared to aligned distribution. This was due to the fact that the staggered distribution design could better promote the uniform distribution and transport of the gas, reduce the local concentration differences, and thus reduce the concentration overpotential loss. In addition, the staggered distribution of the refined channels could also increase the degree of mixing of the gas in the flow channel and improve the contact opportunities between the reactants and the CL, thus further enhancing the overall performance of the fuel cell.
Oxygen molar concentration distribution
The distribution of oxygen concentration at the GDL-CL interface at the cathode side could further affect the stability and output performance of the fuel cell. Increasing the oxygen mass fraction was advantageous for boosting the oxygen flow towards the reaction interface. As depicted in Fig. 8, with the increasing of refinement channels number, the oxygen distribution at the GDL-CL interface on the cathode side was gradually improved. However, the oxygen distribution improvement varied with different arrangements of the refinement channels. This was attributed to the fact that when the reactant gas flowed through the refinement channels, certain diffusion resistance was generated because the widths of the refinement channels were smaller than those of the branch channels. This resulted in significant enhancement of the effect of the under-rib convection of the reactant gas and forced the reactant gas to flow toward the GDL and the CL. The oxygen mass fraction distribution within the cathode at the GDL/CL interface decreased gradually from inlet to outlet due to substantial oxygen consumption during the redox reaction. In the BIFCs, oxygen concentration was higher in the main flow channel and lower in the branched flow channel. However, as the number of refinement runners increased, the oxygen distribution near these runners gradually rose, shrinking and eventually eliminating oxygen-deficient zone. This suggested that enhanced oxygen towards the reaction interface, thereby advancing the process and improving fuel cell output power.
Water molar concentration distribution
The primary factor that affected oxygen diffusion in porous material was the presence of liquid water. Therefore, the distribution of liquid water played vital role in determining both the rate of oxygen transmission and the performance of PEMFC. Fig. 9 showed the cloud diagram demonstrating the distribution of liquid water at the interface between the cathode GDL and the CL. In the BI-0 region, significant accumulation of liquid water in the rear portion obstructed oxygen passage, leading to sizable oxygen-deficient zone and diminished performance. Conversely, in CSFC liquid water predominantly gathered in the sub-ribbed area near the outlet, resulting in minimal accumulation, which leading to superior performance. Enhanced flow rate of reactive gas from the channel to the CL and accelerated water removal through the addition of refined flow path, thereby boosting reaction rate and overall system performance. The water removal effect of the flow channel structure with staggered distribution of refined flow channel was significantly higher than that of the flow channel structure with parallel distribution of refined flow channel, and the improvement effect was gradually amplified with the increasing of refined flow channel number. BI-6 and CSFC exhibited the least liquid water accumulation.
Current density distribution
Fig. 10 displayed the current density distribution at the GDL and CL interface. Elevated current density was noted at the entry point of both the primary channel and its branches, attributed to heightened flow resistance. This condition facilitated advantageous diffusion of reactive gas throughout the cell. With the increasing of refined channel number, the convection effect beneath the rib strength, resulting in higher concentration and more uniform current density distribution. This was due to the enhanced gas flow velocity at the junction of the main and branch channel, more reactive gas entered into the CL for reaction, and the current density distribution on the surface of the CL was gradually homogenized, which promoted the thorough reaction. Notably, BI-6 exhibited the most uniform current distribution. At 0.6 V, BI-6 recorded current density of 0.83 A/cm², 29.7% higher than that of CPFC (0.64 A/cm²) and decreased 4.8% compared with CSFC (0.87 A/cm²).
Hence, through the comprehensive analysis of the data from the six models, it became evident that enhancing the electrochemical performance of PEMFC was achievable by augmenting the number of refinement channel. Notably, the performance of fuel cell featuring staggered distribution of refinement flow channel surpasses that of those with aligned distribution. This underscored the significance of optimizing channel arrangement for maximizing cell efficiency. Additionally, the findings underscore the potential of refinement channel to mitigate issues such as uneven current distribution and excessive liquid water accumulation, thereby fostering more uniform reaction across the cell. Such insight was pivotal for advancing PEMFC technology towards enhanced reliability and efficiency, crucial for widespread adoption in various application including automotive, portable electronic, and stationary power generation.
EFFECT OF WIDTH OF REFINEMENT CHANNEL ON PEMFC OUTPUT PERFORMANCE
According to Chapter 3, it was concluded that the introduction of refinement channels in the flow field of double Ginkgo biloba leaf veins significantly improved the output performance of the PEMFC, with the effect of staggered distribution of refinement channels being more pronounced. This was attributed to the fact that the refinement channels increased the surface area of the gas in contact with the CL, thereby enhancing the reactant transport efficiency. In this chapter, the output performance of PEMFC was further investigated with respect to the width of the refinement channels.
Models
The flow of gas through the channel followed the basic principles of fluid mechanics, including the continuity equation and the momentum equation. The width of the channel directly affected the fluid flow rate and velocity. In fuel cells, when the concentration of reactants decreased, it led to concentration polarization and negatively impacted cell performance. By optimizing the channel width and increasing the gas flow rate, the concentration polarization phenomenon was effectively reduced, and the performance of the fuel cell was improved. Therefore, the authors gradually adjusted the channel width to create ideal flow path, ensuring that the gas maintained appropriate flow rate when passing through different regions. In this chapter, the width of the refinement channel was set to 0.2 mm, 0.4 mm, 0.6 mm, 0.8 mm, 1 mm and 1.2 mm, while the rest of the geometric features were kept consistent. The model diagrams of the refinement channels with different width were shown in Fig. 11.
Effect of refined channel width on fuel cell output characteristics
Fig. 12 showed the polarization curves and power density of the PEMFC with different width refinement channels. As showed in Fig. 12, in the low voltage region, the size and change trend of each scheme were the same, and all of them were characterized by rapid increasing first and then slow increasing. This indicated that in the initial stage, the transfer efficiency of electrons and ions was high and the performance of the battery was rapidly improved. However, with the further increasing of voltage, the speed of improvement gradually slowed down. In the high voltage region, the values of each scheme then differed significantly. This was because when the width of the refinement channel was smaller than the tributary channel, the reactant gas passing through the refinement channel generated resistance. When the width of the refinement channel was larger than that of the tributary channel, this diffusion resistance decreased. The diffusion resistance prevented the reactants reaching the cathode and anode in time, leading to the continuous accumulation of reactants and products, which causing concentration of reactants gas changed. As the width of the refinement channel increased, the peak power density of each scheme increased. However, when the width of the refinement channel exceeded the width of the tributary channel (1 mm), the peak power density decreased. Among them, type-5 had the highest peak power density and showed the optimal performance, reached 0.612 W/cm2, improved 15.5% compared with the ordinary double ginkgo biloba leaf vein flow channel. This meant that by adjusting the width of the channel, the power output of the cell could be significantly affected, and the optimized design could improve the overall efficiency and performance of the fuel cell.
Fig. 13 showed the pressure drops and net power density of the cathode side for each scheme. It was seen that the pressure drops gradually decreased with the width of the refined channel increased. When the refined channel width was 0.2 mm and 0.4 mm, the refined channels reduced the cross-sectional area for gas flow, increased the flow rate, and enhanced friction, which led to higher pressure drops. When the refined channel width was 0.6 mm and 0.8 mm, as the channel width increased, the fluid flow rate decreased, and the friction between the channel wall and the fluid reduced, causing the pressure drops gradually decrease. When the refined channel width was 1 mm and 1.2 mm, the wider channels further reduced the flow rate and significantly decreased friction with the channel wall, resulting in the lowest pressure drops. At this point, the rate of pressure drops reduction became relatively slow, indicating that when the channel width increased to a certain extent, the change in pressure drops was no longer as sensitive as with narrower channels. By observing the net power density curve, it was seen that the net power density first increased and then decreased with the width of the refined channel increased. it was unfavorable for the effective transport of reactant gases regardless of whether it was excessively narrow and overly wide refined channels. When the width reached 1 mm, more reactant gases could enter the GDL/CL to participate in the reaction, promoting better local current density, and resulting in the highest net power density and the highest fuel cell output power. Therefore, with excessively wide refined channels, the fuel cell output power did not achieve an ideal improvement. Considering the other effects caused by high pressure drops and the manufacturing process, refined channel width of 1 mm was considered the optimal choice.
Influence of refined channel width on mass transfer
Fig. 14 showed oxygen distribution at the GDL-CL interface on the cathode side of PEMFC with the operating voltage of 0.6 V. Low concentration areas appeared in the region directly below the inlet, mainly due to the fact that the flow channel inlet was lateral entry and the gas diffused downward in smaller amount, which did not allow for better material transfer. From Fig. 14, it could be seen that as the width of the refinement channel increased, the gas concentration transferred to the tail increased gradually and the distribution uniformity was better. The oxygen concentration distribution of Type-6 was less effective than that of Type-5, this mainly because the width of the refinement channel was larger than that of the tributary channel, which made the impediment effect of the refinement channel to the gas transfer process smaller and reduced the diffusion of the gas to the CL. Type-5 showed the best oxygen concentration distribution.
Fig. 15 showed the water concentration distribution at the GDL-CL interface on the cathode side for different schemes at 0.6 V operating voltage. The water distribution was closely related to the oxygen distribution, and as the electrode reaction continued, oxygen was gradually consumed and large amount of water was produced. In general, higher gas flow rate was suitable for removing water from the flow channel cathode GDL because the gas flow could exert force on the water droplets adsorbed in the GDL, thus carrying more water into the flow channel. As the width of the refinement channel increased, the pressure drops in the flow channel became gradually larger, which enhanced the gas flow rate in the subchannel and accelerated the transfer of water from the CL through the GDL to the channel. This phenomenon indicated that optimizing the design of the refinement channel could effectively improve water management and reduce water accumulation at the cathode side, which in turn improved the performance and stability of the fuel cell. As water accumulation reduced, the mass transfer resistance increased due to water clogging could be avoided, thus ensuring that the reactive gas could reach the catalytic layer more efficiently and improving the overall efficiency of the fuel cell.
Fig. 16 showed the current density distribution on the CL surface at 0.6 V for each scheme. It could be seen that the current density at the corners of the main flow channel and the refinement channel was higher than that in other regions. In addition, as the width of the refinement channel increased, the current density increased and was more uniformly distributed. This was due to the fact that the gas was hindered in passing through the refinement channel and became more involved in the reaction, which promoted the reaction to proceed completely. Further observation revealed that Type-5 had the most uniform current density distribution. This indicated that the reaction uniformity inside the fuel cell could be significantly improved by rationally designing the width of the refinement channel, thus enhancing the overall performance of the fuel cell. The uniform current density distribution meant that the reactions in each region were more synchronized, reducing local overreaction or underreaction, which improved the efficiency and stability of the cell.
Effect of GDL porosity on fuel cell performance
This section investigated the effects of GDLs with porosities of 0.4, 0.5, 0.6, and 0.7 on the performance of PEMFC with dual ginkgo leaf vein flow field. Fig. 17 showed the oxygen mole concentration distribution in GDLs with different porosities with 0.6 V. The results indicated that as the porosity increased from 0.4 to 0.7, the oxygen mole concentration in the GDL gradually increased, indicating that more oxygen diffused from the dual ginkgo leaf flow channels into the GDL. This was because the higher porosity of the GDL resulted in larger transport channel volumes and lower flow resistance, allowing more oxygen to easily diffuse from the flow channels into the GDL to participate in chemical reactions. Fig. 18 showed the power density distribution of GDLs with different porosities with the voltage of 0.6 V. It could be seen that when the porosity of the GDL was 0.7, the current density effect of the fuel cell was very different from the first three cases. Fig. 19 showed the polarization and power density curves for different GDL porosities ranging from 0.4 to 0.7. It was observed that as the porosity increased from 0.4 to 0.6, both the current density and power density relatively increased, but when the porosity reached 0.7, the fuel cell performance declined. This was because as the porosity increased to 0.7, more gas diffused from the flow channels into the GDL, and the amount of water produced from the reaction also increased. At this point, more space in the flow field was filled with either gas or liquid, leading to the decreasing in the overall conductivity of the GDL. Poor conductivity increased ohmic losses within the cell, reducing the cell's output performance. At voltages above 0.8 V, the current density values for all porosities were similar. At the operating voltage of 0.45 V, the performance of the proton exchange membrane fuel cell was optimal with the porosity of 0.6, where the power density was 0.628 W/cm², 2.2% higher than that of the corresponding value with porosity of 0.4.
Simulations showed that the electrochemical performance of the PEMFC could be significantly improved by designing the width of the refinement channel. Increasing the width of the refinement channel effectively improved the output performance of the fuel cell. This was because wider refinement channel improved the flow and distribution of the gas, enhancing the transport efficiency of the reactants and improving the uniformity of the electrode reaction. However, it was worth noting that the width of the refinement channel could not exceed the width of the tributary channel. When the refinement channel was too wide, it could instead affect the reaction efficiency and overall performance. Therefore, the width of the refinement channel and the tributary channel had to be balanced during the design process to achieve the best electrochemical performance. In conclusion, the design of refinement channel width was crucial to improving the overall performance of the PEMFC, and reasonable design strategy could lead to significant performance enhancement.
CONCLUSIONS
This research improved the biomimetic flow channel inspired by the structure of double ginkgo biloba leaf veins and developed 3D model of PEMFC. The effect of the number, arrangement and width of refinement channels on the performance of BIFC was investigated. The main conclusions were outlined as follows:
(1) BIFC demonstrated superior performance and mass transfer capability compared to CPFC. Performance of BIFC gradually improved with the increasing of refined flow channel, with staggered refinement channel outperforming aligned ones. BI-6 exhibited performance closest to CSFC, with its peak power density only 3.91% lower than CSFC, 38.8% higher than CPFC and 9.4% higher than the base flow field (BI-0).
(2) Increasing the width of the refinement channel further improved the output performance of the fuel cell, and the results showed that the fuel cell performance reached its best when the width of the refinement channel was 1 mm (Type-5). At that point, the peak power density reached 0.612 W/cm2, which was 15.5% higher than that of BI-0.
(3) Increasing the number of refined flow channel improved oxygen distribution within BIFC, leading to the increasing of current density and more uniform distribution within the porous layer. Conversely, the reducing of refined flow channel number of resulted in larger area of low oxygen concentration inside the fuel cell, adversely affecting PEMFC stability.
(4) Increased the width of the refinement channel could enhance the utilization efficiency of the reactants in the flow channel. However, when the width of the refinement channel exceeded that of the tributary channel, the optimization effect diminished. Therefore, the width of the refinement channel needed to be reasonably designed.
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