Performance improvement and numerical study on cathode channel for air-cooled open-cathode proton exchange membrane fuel cells

Abstract

Bipolar plates perform multiple functions for the proton exchange membrane fuel cell (PEMFC). This study focuses on optimizing cathode channels to leverage a local loss mechanism to enhance gas transfer and diffusion efficiency. Through the investigation of 3D simulations, this research delves into the effects of curvature of cathode channels on both reactant transfer and diffusion. The results illustrated that compared with straight channels, the cell performance improves as the bending angle ($\theta$) of 2.5° and 5° at different current densities. Specifically, at a bending angle of 5°, a 5.5% higher current density than the channel of 0° is obtained. This suggests that moderate curvature can effectively promote efficient mass transport and diffusion, ultimately contributing to enhanced cell performance. Furthermore, the analysis of local mass transfer and diffusion around the bends of channels underscores the importance of the balance between these factors. While bending angles within the range of 2.5° to 5° offer optimal performance gains, excessive curvature, such as a 10° angle, may lead to diminished cell performance. By identifying the optimal bending angle range and elucidating the underlying mechanisms driving performance improvements, this study provides insights into the design and optimization of cathode flow fields in AO-PEMFC.

KEYWORDS:

• Air-cooled open-cathode proton exchange membrane fuel cell
• diffusion
• bending angle
• local loss mechanism
• performance

1. Introduction

The progressive increase in greenhouse gases requires the utilization of clean energy sources. Hydrogen has emerged as a promising candidate for replacing fossil fuels due to its potential to address environmental concerns (Sharaf & Orhan, 2014). Proton Exchange Membrane Fuel Cells (PEMFCs), powered only by hydrogen and air/oxygen with near-zero emissions and high-energy efficiency, positioning them as the next-generation energy conversion technology (Luca et al., 2016; Zhang et al., 2023a). It has been applied to automotive systems, power generation, aerospace, and other fields (Yin et al., 2021). However, their widespread commercialization has been hindered by high costs and limited energy-conversion rates. To address these challenges, researchers have explored two main approaches. One approach involves developing new materials to replace expensive platinum catalysts (Tian et al., 2018). However, the development of new catalysts that are economical while maintaining Pt-like activity and stability is challenging and slow (Chung et al., 2017; Shen et al., 2018). Another more effective approach is to optimize the configuration of PEMFC components such as flow fields, operating parameters to increase system energy efficiency.

Among these factors, the design of the flow fields plays a crucial role in influencing cell performance by affecting reactant transfer and diffusion (Fan et al., 2022; Xing et al., 2021). Various flow field designs, including serpentine, straight-parallel, and interdigitated flow fields have shed light on the intricate relationship between flow channel design and cell performance (Ashrafi & Shams, 2017; Jiao et al., 2021; Nuttapol & Patcharawat, 2015; Vazifeshenas et al., 2015; Wang et al., 2007). Shimpalee et al. (Ashrafi & Shams, 2017) demonstrated that the variation of flow channel path length and cross-section dimension, including both the channel and rib, can significantly impact the uniformity of fuel cells. They underscore the importance of meticulously engineering flow channel geometries to ensure optimal reactant distribution and utilization within the cell. Jiao et al. (2021) made a noteworthy revelation regarding the flow field, highlighting their effectiveness in enhancing PEMFC performance. This insight underscores the multifaceted nature of flow dynamics within the cell and underscores the potential for leveraging convective phenomena to optimize cell operation. Nuttapol and Patcharawat (2015) delved into the realm of compound flow configurations, specifically exploring the parallel in series flow field. Their investigation unveiled the significant role played by flow channel interaction in improving reactant transport behaviours. By elucidating the synergistic effects of flow channel configurations, this study offers valuable insights into enhancing mass transfer within PEMFCs. These studies all highlight the pivotal role played by flow channel design in mass transport phenomena within PEMFC and emphasize the importance of optimizing flow channel configurations to maximize cell efficiency. Recently, novel configurations such as 3D flow fields, radial flow fields, bionics flow field and foam flow fields have been proposed to increase power density (Cho et al., 2019; Guo et al., 2014; Huo et al., 2021; Niu et al., 2018; Zhang et al., 2023b). Those improved designs of flow fields acquired better cell performance due to their increased capacity for mass transfer and water removal in plane. However, most of those designs present a significant deficiency in manufacturability.

Moreover, enhancing through-plane mass transfer is recognized as an effective strategy to reduce mass loss and improve the efficiency of PEMFC. Several studies have focused on leveraging the convection effect within flow fields to enhance the capacity of reactant transfer. These efforts encompass a range of innovative approaches, including the addition of various baffles, utilization of wave fields, and implementation of 3D inclined flow fields (Chen et al., 2021a; Chen et al., 2021b; Choi et al., 2022; Liao et al., 2021; Yan et al., 2019; Yin et al., 2018; Zhang et al., 2018). For instance, Chen et al. (2021a) and Yin et al. (2018) conducted research aimed at augmenting the convection effect in flow fields by incorporating baffles of varying configurations. Their studies demonstrated that strategically placed baffles can effectively enhance convective flow patterns, thereby promoting more efficient reactant transport within the cell. In a similar vein, Fontana et al. (Choi et al., 2022) investigated the impact of channel inclination angle on cathode oxygen concentration and cell performance. They observed that channels with inclined angles can significantly increase cathode oxygen concentration. Specifically, when the channel inclination angle was set at 0.75° and 0.5°, the maximum current density of the cell exhibited remarkable enhancements of 9.5% and 5.65%, respectively. These findings highlight the potential of inclined flow fields to enhance mass transfer and improve overall PEMFC performance. Overall, these studies underscore the importance of leveraging convective effects within flow fields to enhance mass transfer and optimize PEMFC performance.

Although many researchers have conducted experimental and simulation studies on various design parameters of the cathode side channel, primarily focusing on factors such as channel depth and width in linear configurations, our team has also contributed to this research through comprehensive experimental studies (Xing et al., 2021; Zhao et al., 2020). However, there remains a scarcity of reported optimization designs aimed at further enhancing mass transfer and diffusion, particularly concerning the addition of vortices within the flow channel itself. As we know, the oxygen mass transfer can be enhanced through the introduction of vortices in the cathode side flow channel, with some studies proposing waved flow fields to capitalize on this principle (Chen et al., 2021a; Chen et al., 2021b; Liao et al., 2021; Yan et al., 2019). These studies have explored the utilization of wave fields within flow channels to enhance convective transport and promote more efficient reactant distribution. Nevertheless, most of these designs have centred on waves perpendicular to the Membrane Electrode Assembly (MEA), directing velocity components towards the reaction site as guided by the waved channel (Chen et al., 2021a; Yan et al., 2019). Few investigations have explored the effects of parallel wave flow fields on gas transportation. Yet, scant attention has been paid to the alteration of gas transport induced by velocity disparities between the two sides of the channel resulting from parallel bending structures.

In our preliminary work (Zhao et al., 2020), the cathode channel is optimized from a straight channel to a curve with a bending angle. Leveraging the in-plane local loss induced by the curved channels, momentum is transferred to promote through-plane oxygen diffusion. It is observed that a minor adjustment in the horizontal orientation of flow channels can significantly enhance the performance of PEMFC. This observation suggests that, without notably increasing manufacturing costs, improvements in cell performance can be achieved compared to more complex optimizations of flow field structures. However, determining the most advantageous bending configuration, which optimally enhances oxygen mass transfer, diffusion, and heat dissipation, remains a challenge yet to be resolved. Based on this, the research endeavours to introduce a novel flow fields for air-cooled open-cathode PEMFC (AO-PEMFC), which are more susceptible to concentration losses as they typically rely on passive air supplied by a fan that is not directly integrated with the flow channels, as opposed to directly connected with a pressurized air delivery system.

To address and elucidate the efficacy of this optimization design and its internal reaction mechanism, our study integrates previous experimental research results (Zhao et al., 2020) with advanced numerical modelling techniques. Specifically, 3D multi-channel simulations of AO-PEMFC are employed to delve deeper into the properties of reactant diffusion and transfer induced by bent flow channels. These properties, which are challenging to observe or measure directly through experimentation, are rigorously assessed through computational simulations. By systematically examining these parameters to identify the optimal range of bending angles that effectively utilize local loss to enhance PEMFC performance, results reveal that the efficiency of energy conversion can be improved by changing the cathode channel bending within a small range. It is significant for the development and design of cathode flow fields for AO-PEMFC.

2. Model development

2.1. Model geometry

A numerical analysis of 4 fuel cells with different bending angles of the cathode channels is employed. Figure 1 shows the configurations of the anode and cathode plate, which are consistent with our experiments (Zhao et al., 2020) for cathode channels of 0°, 5° and 10°. Besides, in order to clearly compare the flow fields in the experiment and simulation, a schematic diagram of the channels of 2.5° is placed on the right of Figure 1, which is not tested in the experiment (Zhao et al., 2020) but was added to the simulation to further detail the optimal range of the channel bending and its impact on mass transfer and diffusion.

Figure 1. (a) Anode plate design for experiment and simulation serpentine channel; (b) different configurations of experimental cathode plate design; (c) different configurations of simulated cathode plate design; (d) simulated configurations of AO-PEMFC for different cathode channel.

The computational three-dimensional model is built for each of the 4 geometries considered, which is similar to the dimensions used by the previous experimental investigation (Zhao et al., 2020). The corresponding geometric parameters are listed in Table 1. Figure 2 shows the model developed for the fuel cell with 0° cathode channel. Since the design of anode and cathode flow fields is periodic, a portion of the overall cell (6cm²) is analyzed to save time and computational resources. This simplification has been proved reasonable (Jiao et al., 2014; Rostami et al., 2016).

Figure 2. Computational domain and mesh for flow channel of 0°.

Table 1. Component parameters of the AO-PEMFC (Zhao et al., 2020).

Parameter	Value
Catalyst-coated membrane (CCM) thickness	30 µm
Membrane thickness	15 µm
Anode catalyst layer (CL) thickness	5 µm
Cathode CL thickness	10 µm
Gas diffusion layer (GDL) thickness	200 µm
GDL porosity	0.6
Anode bipolar thickness	1mm
Cathode bipolar thickness	2mm
Anode channel width/depth	0.45 mm/0.3 mm
Cathode channel width/depth	1.1 mm/1.3 mm

2.2. Governing equations

In this study, several essential assumptions are made for the CFD simulations as follows: laminar flow, steady state, non-isothermal, isotropic and homogeneous materials. Simulation parameters are shown in Table 2, which are consistent with our experiments (Zhao et al., 2020). The Eulerian-Eulerian model was used to solve the two sets of mass and momentum conservation equations for both gas and liquid phases as described below:

Table 2. Simulation parameters of the AO-PEMFC (Zhao et al., 2020).

Definition	Value
Cell Current Density	0–1.0 A/cm^2
Anode Inlet Temperature	30 °C
Anode Inlet Pressure	5 kPa
Relative Humidity of Anode Gas	0%
Cathode Inlet Temperature	25 °C
Cathode Inlet Pressure	1.5 kPa
Relative Humidity of Cathode Gas	35%
The Stoichiometric Ratio of Anode Gas	1.8
The Stoichiometric Ratio of Cathode Gas	2.0

Mass conservation equation (Li et al., 2017): (1) $\begin{array}{r}\frac{\mathrm{\partial }\left(ϵ{\text{s}}_{\text{l/g}}\rho \right)}{\mathrm{\partial }t}+\mathrm{\nabla }\cdot \left(ϵ{\text{s}}_{\text{l/g}}\rho \overrightarrow{\nu }\right)=S_m\end{array}$(1) Where $s_{\text{l/}g}$ is the phase volume fraction and $s_l+s_g=1$, S_m denotes the mass source term that corresponds to the production or consumption of reaction species. The source term is solved individually for each distinct region shown in Table 3.

Table 3. The source terms used in these equations

Source terms	Expressions	Areas
(1)	$\begin{array}{l}{S}_m=S_{H_2}+S_{H_2{O}_{\text{a}}}\\ S_m=S_{O_2}+S_{H_{2}O\text{c}}\\ S_m=0\end{array}$	anode CL cathode CL otherwise
(2)	$\begin{array}{l}{S}_{\text{mom}}=-{ϵ}^2{s}_{\text{l/g}}^2{\displaystyle \frac{\mathrm{\mu v}}{K{K}_r}}+ϵs_{\text{l/g}}{\displaystyle \frac{C_D\mathrm{Re}}{24}}\\ S_{\text{mom}}={\displaystyle \frac{C_D\mathrm{Re}}{24}}\end{array}$	porous region channel
(4)	$\begin{array}{l}{S}_E=S_{E,\text{ion}}\\ S_E=S_{E,\text{ele}}+S_{E,\text{ion}}+S_{E,\text{g - l}}+S_{E,\text{d - l}}+S_{E,\text{irv,ad}}\\ S_E=S_{E,\text{ele}}+S_{E,\text{ion}}+S_{E,\text{g - l}}+S_{E,\text{d - l}}+S_{E,\text{irv,cd}}\\ S_E=S_{E,\text{ele}}+S_{E,\text{g - l}}\\ S_E=S_{E,\text{ele}}\end{array}$	PEM Anode CL Cathode CL MPL, GDL Anode BP
(5)	$\begin{array}{l}{S}_{H_2}=-{\displaystyle \frac{M_{H_2}}{2F}}{j}_{\mathrm{an}}\\ S_{O_2}=-{\displaystyle \frac{M_{O_2}}{4F}}{j}_{\mathrm{cat}}\\ S_{H_{2}O}=-{\displaystyle \frac{M_{H_{2}O}}{2F}}{j}_{\mathrm{cat}}\\ S_i=0\end{array}$	anode CL Cathode CL anode/cathode CL otherwise
(10) (11)	$\begin{array}{l}{S}_{\text{ele}}=\{{}_{j_{\mathrm{cat}}}^{-j_{\mathrm{an}}}\\ \\ S_{\text{ion}}=\{{}_{-j_{\mathrm{cat}}}^{j_{\mathrm{an}}}\end{array}$	anode/cathode CL

Momentum conservation equation: (2) $\begin{array}{rl}& \frac{\mathrm{\partial }\left(ϵs_{\text{l/g}}\rho \overrightarrow{\nu }\right)}{\mathrm{\partial }t}+\mathrm{\nabla }\cdot \left(ϵs_{\text{l/g}}\rho \overrightarrow{\nu }\overrightarrow{\nu }\right)\\ & =-ϵs_{\text{l/g}}\mathrm{\nabla P}+\mathrm{\nabla }\cdot \tau +S_{m\text{o}m}\end{array}$(2) (3) $\begin{array}{rl}& \tau =s_{\text{l/g}}\mu \left(\mathrm{\nabla v}+\mathrm{\nabla }{v}^T\right)-\frac{2}{3}{s}_{\text{l/g}}\mu \mathrm{\nabla }\cdot \mathrm{vI}\end{array}$(3) Where $\tau$ is the stress–strain tensor, I is the unit matrix, S_mom represents the momentum source term, which is given by Darcy’s law in Table 3.

Energy conversation equation: (4) $\begin{array}{r}\frac{\mathrm{\partial }\left(\mathrm{ϵ\rho }{c}_{p}T\right)}{\mathrm{\partial }t}+\mathrm{\nabla }\cdot \left(\mathrm{ϵ\rho c}\overrightarrow{\nu }T\right)=\mathrm{\nabla }\cdot \left(k_{}^{\text{eff}}\mathrm{\nabla T}\right)+S_E\end{array}$(4) Where S_E is the energy source term, which is determined by the ohmic heat term from electron and ion conduction, the electric term induced by irreversible loss, and the heat of phase change. In the distinct region, the S_E is calculated with different source terms described in Table 3.

Species transport equation: (5) $\begin{array}{rl}\frac{\mathrm{\partial }\left(ϵs_{\text{l/g}}{c}_i\right)}{\mathrm{\partial }t}+\mathrm{\nabla }\cdot \left(ϵs_{\text{l/g}}v{c}_{\text{i}}\right)& =\mathrm{\nabla }\cdot \left(s_{\text{l/g}}\rho D_i^{\mathrm{eff}}\mathrm{\nabla }{c}_i\right)+S_i,i\\ & =H_2,O_2,H_{2}O\end{array}$(5) Where S_i is the species source term and detailed in Table 3, and $D_i^{\mathrm{eff}}$ is the effective diffusion coefficient for species i: (6) $\begin{array}{r}{D}_i^{\mathrm{eff}}={ϵ}^{1.5}(1-s{)}^{2.5}{D}_i^0\left(\frac{101325}{P}\right){\left(\frac{T}{300}\right)}^{1.5}\end{array}$(6) Butler–Volmer equation: (7) $\begin{array}{rl}{j}_{\mathrm{an}}^{B-V}& ={\xi }_{\mathrm{an}}{i}_{\mathrm{an}}^{\mathrm{ref}}{\left(\frac{c_{H_2}}{c_{H_2}^{\mathrm{ref}}}\right)}^{{\gamma }_{\mathrm{an}}}\left[e^{\frac{{\alpha }_{\mathrm{an}}F{\eta }_{\mathrm{an}}}{\mathrm{RT}}}-e^{\frac{{\alpha }_{\mathrm{cat}}F{\eta }_{\mathrm{an}}}{\mathrm{RT}}}\right]\end{array}$(7) (8) $\begin{array}{rl}{j}_{\mathrm{cat}}^{B-V}& ={\xi }_{\mathrm{cat}}{i}_{\mathrm{cat}}^{\mathrm{ref}}{\left(\frac{c_{O_2}}{c_{O_2}^{\mathrm{ref}}}\right)}^{{\gamma }_{\mathrm{cat}}}\left[-e^{\frac{{\alpha }_{\mathrm{an}}F{\eta }_{\mathrm{cat}}}{\mathrm{RT}}}+e^{\frac{-{\alpha }_{\mathrm{cat}}F{\eta }_{\mathrm{cat}}}{\mathrm{RT}}}\right]\end{array}$(8) Where the overpotential are solved as: (9) $\begin{array}{rl}{\eta }_{\mathrm{an}}& ={\phi }_{\mathrm{ele}}-{\phi }_{\mathrm{ion}}\end{array}$(9) (10) $\begin{array}{rl}{\eta }_{\mathrm{cat}}& ={\phi }_{\mathrm{ele}}-{\phi }_{\mathrm{ion}}-V_{\mathrm{OC}}\end{array}$(10) Current conservation equation: (11) $\begin{array}{r}\mathrm{\nabla }\cdot \left({\sigma }_{\mathrm{ele}}\mathrm{\nabla }{\phi }_{\mathrm{ele}}\right)+S_{\mathrm{ele}}=0\end{array}$(11) (12) $\begin{array}{r}\mathrm{\nabla }\cdot \left({\sigma }_{\mathrm{ion}}\mathrm{\nabla }{\phi }_{\mathrm{ion}}\right)+S_{\mathrm{ion}}=0\end{array}$(12) Where S_ele and S_ion are source terms of electronic and ionic in Table 3.

In the momentum source terms, the first term on the right represents the viscous resistance determined by Darcy's Law. K denotes the permeability, which is calculated by the Kozeny-Carman model. The second term represents the drag function calculated by Schiller-Naumann model, where Re represents the relative Reynolds number and C_D the drag coefficient: (13) $\begin{array}{rl}K& =\frac{{\text{d}}_{\text{p}}^{\text{2}}}{\text{180}}\frac{{ϵ}^3}{{\left(1-ϵ\right)}^2}\end{array}$(13) (14) $\begin{array}{rl}{C}_D& =\{\begin{array}{ll}24(1+0.15{\mathrm{Re}}^{0.687})/\mathrm{Re}& \text{ Re}\le \text{1000}\\ 0.44& \text{ Re}>\text{1000 }\end{array}\end{array}$(14) The energy source terms include the Joule heat, the heat phase transition and the energy source resulting from irreversible loss. (15) $\begin{array}{rl}& \{\begin{array}{l}S{}_{E,\text{ion}}={||\mathrm{\nabla }{\phi }_{\text{ion}}||}^2{k}_{\text{ion}}^{\text{eff}}\\ S{}_{E,\text{ele}}={||\mathrm{\nabla }{\phi }_{\text{ele}}||}^2{k}_{\text{ele}}^{\text{eff}}\end{array}\end{array}$(15) (16) $\begin{array}{rl}& \{\begin{array}{l}{S}_{E,\text{d}-\text{l}}=S_{\text{d - l}}{H}_{\mathrm{cnd}}\\ S_{E,g-\text{l}}=S_{\text{g - l}}{H}_{\mathrm{cnd}}\end{array}\end{array}$(16) (17) $\begin{array}{rl}& \{\begin{array}{l}{S}_{E,\mathrm{irv},\text{cat}}=j_{\mathrm{cat}}(|{\eta }_{\text{cat}}|-{\displaystyle \frac{T\mathrm{\nabla }{S}_{\text{cat}}}{4F}})\\ S_{E,\mathrm{irv},\text{an}}=j_{\mathrm{an}}(|{\eta }_{\text{an}}|-{\displaystyle \frac{T\mathrm{\nabla }{S}_{\text{an}}}{2F}})\end{array}\end{array}$(17)

Eqs. (1)–(17) form a set of governing equations in the PEMFC, and the electrochemical model parameters are presented in Table 4. According to these governing equations, the models computed the performance with various cathode flow fields of AO-PEMFC at temperature 25 °C and relative humidity 25%, completely same as the experiment conditions (Zhao et al., 2020), which is typically operating condition for AO-PEMFC (Zhang et al., 2020). Boundary conditions at the anode and cathode channels are constant pressure with a direction normal to the inlet boundary, the inlet reactant compositions are constant and are fully developed at the outlets of the channels. The main parameters are listed in Table 2. The external surfaces of the model are assumed as no slip walls. For the external surfaces of the cell, the electric flux at the anode side is I_sol= 0 and at the cathode side is I_sol= I_cell.

Table 4. Electrochemical model parameters.

Definition	Value
Electronic conductivity of Flow Field Plates, ${\sigma }_{\text{ele}}$	8.3e4 (1/($\mathrm{\Omega }\cdot \text{m}$))
Electronic conductivity of GDL, ${\sigma }_{\text{ele}}$	1e3 (1/($\mathrm{\Omega }\cdot \text{m}$))
Electronic conductivity of CL, ${\sigma }_{\text{ele}}$	1e3 (1/($\mathrm{\Omega }\cdot \text{m}$))
Anode exchange current density, $j_{\mathrm{an}}^{\mathrm{ref}}$	2e9 (A/m^3)
Cathode exchange current density, $j_{\mathrm{cat}}^{\mathrm{ref}}$	1e5 (A/m^3)
Anode transfer coefficient,${\alpha }_{\text{an}}$	0.5
Cathode transfer coefficient, ${\alpha }_{\text{cat}}$	0.5
Anode specific surface area, ${\xi }_{\text{an}}$	2e5 (1/m)
Cathode specific surface area, ${\xi }_{\text{cat}}$	2e5 (1/m)

2.3. Model verification

SIMPLE is a widely used numerical algorithm in Computational Fluid Dynamics (CFD) for solving the Navier-Stokes equations governing fluid flow problems. It is known for its stability and efficiency, making it a popular choice for simulating fluid dynamics in various engineering applications. Therefore, the CFD software FLUENT based on SIMPLE algorithm was used to conduct calculations (16-i7-9700 CPU @ 3.00 GHz). Mesh independence was tested by decreasing the numbers of mesh by 30% and increasing by 15% for the 0° model at the current density of 0.6 A/cm², and the results are shown in Table 5. The cell potential difference between case 1 and case 2 is 1.6‰, and only 0.36‰ between case 2 and 3. These almost identical values indicate that the difference caused by the mesh itself can be negligible. Therefore, the calculated model in this paper adopts case 2 with a grid number of 1037400.

Table 5. The verification of Grid Independence (Current Density = 0.6 A/cm²)

case	Grid numbers	Voltage (V)	error (with case2)
1	746928	0.5586	1.6‰
2	1037400	0.5577	–
3	1175720	0.5579	0.36‰

2.4. Model validation

The simulated polarization curve was compared with the data obtained by experiments to verify the accuracy of the model (Zhao et al., 2020). The same geometry of flow channels (the width and depth of the channels and ribs shown as Figure 1), as well as the thicknesses and porosity of the CCM and GDL as detailed in Table 1, were employed. Additionally, identical inlet temperatures, humidity, and stoichiometric ratios of gases, as listed in Table 2, were used to calculate the cell performance under different flow configurations. Figure 3 compares the polarization and power curves between the present numerical predictions and the experimental data. It can be seen that under high-voltage, the computed current density matches well with experimental results, whereas under low-voltage, there is a slight deviation between the simulated and the experimental data. This discrepancy mainly arises from the facts that at high current densities, the electrochemical reaction become intensify, which amplifies both the supply of reactants and the removal of products. The inherent simplifications in the model to a certain degree restrict the associated concentration losses, hence leading to deviations in the predictions at low voltage levels.

Figure 3. Comparisons of experimental and simulated Polarization and power curves.

Besides, the temperature of the outlet surface of the experiment and simulation is also compared, which is 313.95 K measured in the experiment and 317.5 K obtained in the simulation. This difference is because the temperature of the simulation is measured at the surface of 5 mm away from the outlet due to the constant temperature set on the outlet boundary, but the temperature on the outlet surface is measured in the experiment. Overall, this model can provide a commendably accurate computation of the cell performance and its internal temperature distribution. So, the accuracy of the model is demonstrated.

3. Results and discussion

3.1. Effect of different bending on the cell performance

The cell performance with different cathode flow fields was calculated by changing bending angles of 0°, 2.5°, 5°, and 10°. The cathode plate includes 9 flow channels, in which the width ratio of channel/rib was 1:0.7. Figure 4 illustrates the polarization curves of the cells with different bending angles. It could be seen clearly that within the range consistent with our experimental study (Zhao et al., 2020), the performance with the bending of 5° was better than that of others, it has approximately 5.5% performance improvement. While the bending of 10° corresponds to the worst performance, which is consistent with the previous experimental results.

Figure 4. The Polarization and power curves for different cathode bending flow fields.

During the simulation, a channel with the bending of 2.5° was also introduced and calculated to detail the optimal range of the bending angles for the AO-PEMFC. It can be seen from Figure 4 that the cell performance of the channel of 5° is slightly higher than that of the 2.5° when the current density is less than 0.8 A/cm². When the current density is less than 0.5 A/cm², the superiority is more obvious with the increase of the current density. However, as the current density continues to increase, the superiority of the channel of 5° compared to the channel of 2.5° gradually decreases. This trend suggests that the channel design with an angle of 5° is more suitable for operating conditions where the current density is relatively low, particularly below 0.5 A/cm². At this point, it achieves its peak advantage with a 1.5% improvement in performance over the 2.5° channel. However, beyond this threshold, especially when the current density reaches or exceeds 0.8 A/cm², the performance of the 5° channel starts to decline and becomes inferior to the 2.5° channel. Therefore, the optimal channel angle choice may depend on the specific operational requirements and expected current densities in the application.

From the results listed above, it can be summarized that a small increase in flow channel bending induces the improvement of the overall cell performance, but the improvement diminishes as the angle increases more. In order to determine the optimal range of bending angle, the cell potential with different cathode bending in various current densities is presented in Figure 5. It can be seen that the channel of 5° exhibits the best performance at the current density of 0.5 A/cm², 0.6 A/cm²,and 0.7 A/cm². But, the channel of 2.5° presents a higher performance than the channel of 5° at 0.8 A/cm². It indicates that there is an optimal bending angle range around 2.5° to 5°, which results in the best cell performance.

Figure 5. The cell potential for different cathode bending in various current density.

This study also compared the distribution of reactant concentrations, current density, pressure and velocity of gases with different cathode channel bending angles to further clarify the reactant transport mechanism and the local flow loss mechanism of fuel cells.

3.2. Effect of different bending on the distribution of oxygen

The distribution of oxygen and water can reflect the performance of AO-PEMFC with various cathode channel-bending angles. Figure 6 illustrates the distribution of oxygen at the interface of cathode GDL and CL (GDL-CL). The oxygen is gradually consumed from the inlet to the outlet along every single channel. It should be noted that the reactant transfer interferes with each other’s between channels only at the entrance region. In the middle and downstream region, the oxygen transmission between adjacent channels does not interfere with each other for the channel of 0°. By contrast, in the channels with bending, the distribution of oxygen shifts and the interference between channels can be obviously observed around the bend of the channels. The interaction between channels increases the uniformity of oxygen distribution, which would be beneficial for the electrochemical reaction rate.

Figure 6. The distribution of oxygen at the cathode GDL-CL interface for (a) 0°(b) 2.5°. (c) 5°(d) 10°flow fields at current density of 0.6 A/cm².

In order to analyze the influence of the cathode channel-bending angle on gas diffusion to catalyst sites along through plane and quantitative analysis of reactant transfer along the in-plane direction, Figure 7 quantifies the volume-average molar concentration of oxygen in the GDL, CL, and cathode channel of AO-PEMFC with various bending angles channels. The oxygen content of the diffusion layer and catalyst layer increased with an increase in bending for the channel of 2.5° and 5°, but in the cathode channel, the oxygen concentration is almost equal for the bending angles of 0°, 2.5° and 5°. This implies that more reactants diffused along through plane to the catalyst sites to react, which is consistent with Figure 5. For the bending angle of 10°, the oxygen content is lower than the channel of 0° in all regions. Since the total amount of oxygen supplied to various flow fields is constant, the lower oxygen in all regions indicates that more oxygen escapes along the channel.

Figure 7. The volume-average molar concentration of O₂ on the diffusion layer, catalyst layer and cathode channel of AO-PEMFC with various bending channel.

This phenomenon above reveals that an optimal range of cathode channel bending angles is beneficial for improving the oxygen content and distribution uniformity within the reaction layer, but a larger curvature of the channel leads to the escape of the reactant. This is caused by the velocity and pressure differences resulting from channel bending, which will be discussed in detail in the following chapters.

3.3. Effect of different bending on the distribution of water

The water inside the fuel cell is mainly produced by the electrochemical reaction and the humidification of the reactant, the distribution of water can reflect both the reaction rate and water removal of the cell. Figure 8 depicts the water distribution at the cathode GDL-CL interface for different cathode channel bending angles. Similar to the distribution of oxygen, the water distribution in each flow channel is basically independent without interference between channels for channel of 0°, and the distribution of water is more uniform for curved channels. Higher water content has also been discovered in all flow fields, as shown in Figure 8a. In particular, in the upstream of the channel of 0°, even if the water content under channel area in the upstream is low, it is high under rib area. Water is generated in the reaction layer and diffused into the flow channel through the diffusion layer, and then discharged from the channel. This indicates that it is difficult to diffuse water from the GDL to the flow channel for the straight flow fields due to the lack of convection in the through-plane direction. However, for the curved channel, water in the upstream of the cell is effectively removed downstream and drained.

Figure 8. The distribution of water at the cathode GDL-CL interface for (a) 0°(b) 2.5°. (c) 5°(d) 10°flow fields at current density of 0.6 A/cm²

As seen in Figure 9, the increase of water content in the reaction layer and channel is almost consistent for channels of 0°, 2.5° and 5°, so the capacity of water production and removal are balanced. Furthermore, the 48.1% and 54.5% higher water content in the reaction layer in channels of 2.5° and 5° than the channel of 0° indicates a higher reaction rate. While the water content of GDL and CL for the channel of 10° is also higher than the channel of 0°, the water content in the cathode channel is decreased. These phenomena can be attributed to the water in the reaction layer not being discharged from the channel, resulting in more water accumulating in the reaction layer rather than being produced by the increased reaction rate.

Figure 9. The volume-average molar concentration of H₂O on the diffusion layer, catalyst layer and cathode channel of AO-PEMFC with various bending channel.

3.4. Effect of different bending on the distribution of current density

The current density can intuitively reflect the internal chemical reaction and the utilization rate of the active area of AO-PEMFC, an optimal flow field configuration produces a uniform distribution of current density across the entire active surface area. Figure 10 shows the current density distribution on the interface of the cathode GDL-CL with different flow fields at a current density of 0.6 A/cm². As Figure 10 illustrates, the current density beneath the rib regions is consistently higher for all flow fields compared to the areas directly underneath the channels. This phenomenon can be attributed to the compression exerted by the ribs onto the GDL, which reduces the contact resistance between the GDL and the CCM. Consequently, in these rib-under areas, reactants effectively interact with electrons, leading to a higher current density.

Figure 10. The current density distribution on GDL-CL layer for (a)0°(b)2.5°(c)5°(d)10°flow fields at current density of 0.6 A/cm².

It can also be seen from Figure 10a that the current density distribution around the centre area for channel of 0° is lower, since the accumulation of the water under the rib, ad seen in Fig.8a. It is noted in Figure 10b and Figure 10c, the distribution of current density is more uniform for channels of 2.5° and 5°, especially in the middle area of the cathode GDL-CL Besides, it is also observed in Figure 10b and Figure 10c that the higher current density concentrated in the middle area of the overall GDL-CL surfaces, especially in the regions where the channels bend. This implies that more sufficient electrochemical reactions occur in those regions, attributed to more reactant supply, as evidenced by the velocity distributions presented later in the text. And due to the more sufficient reaction in a larger area, the better overall cell performance can be obtained on channels of 2.5° and 5°. However, in contrast to channels of 2.5° and 5°, the higher current density of channel of 10° is mainly distributed in the regions around the upstream and downstream regions of the flow channel as shown in Figure 10d. It indicates that the electrochemical reaction mainly occurs in the region with a smaller area, resulting in the active area not be fully utilized and the overall performance becomes worse.

3.5. Effect of different bending on the distribution of temperature

The local temperature profiles of the middle and two side surfaces, 5 mm away from the inlet and outlet for various bending angles of the cathode channel at 0.6 A/cm² are compared to reveal the influence of the curvature on the region where the reaction takes place, results are shown in Figure 11. A similar temperature distribution on three surfaces is generated by the channel of 0°, but the different temperature profiles on the middle surface and side surface are produced due to the curvature of the channel. In other words, in the channel of 0°, the electrochemical reaction occurs in the entire reaction layer of the fuel cell evenly, but the bending of the channel causes reactants to be distributed in different areas of the cell. Similar to the distribution of current density, the reactions of the channel of 2.5° and 5° mainly take place in the centre region of the cell, while it occurred in the sides area of the cell for channel of 10°. Additionally, it can be seen that the high temperature of the channel of 0° is distributed on both sides around a single channel evenly, while the high temperature region is concentrated on one side around a single channel for the channels of 2.5°, 5°, and 10°. Due to the local loss during the gas transfer process caused by the channel bending, more gases diffuse to the reaction layer through one side of the channels.

Figure 11. The temperature distribution of PEMFC for (a) 0°(b) 2.5°(c) 5°(d) 10°flow fields at current density of 0.6 A/cm².

3.6. Effect of different bending on the distribution of pressure

The pressure distribution in the flow field determines the transfer and diffusion of gas, which directly influences the reactant distribution in the flow channel and the diffusion layer. The pressure distribution in the centre of the cathode channel is presented in Figure 12. It is found that the pressure gradually decreases along the gas flow from the inlet to the outlet, with a minimum value observed at the outlet.

Figure 12. The pressure distribution on the centre section of the cathode flow channel of PEMFC for (a) 0° (b) 2.5°(c) 5° (d) 10° flow fields at current density of 0.6 A/cm².

In order to illustrate the pressure drop of various channel bending, the total pressure drop from the inlet to the outlet of channels with different bending angles is compared. The pressure drop between the inlet and outlet of the cathode channel is defined as $\mathrm{\Delta P}=P_{\mathrm{inlet}}-P_{\mathrm{outlet}}$. As shown in Figure 13, as the channel bending angle increases, the total pressure drop also increases. Compared with the channel of 0°, the pressure drops of the channels of 2.5° and 5° is increased by 1.3% and 9.7%, respectively. However, since oxygen is supplied by the atmosphere at the cathode for AO-PEMFC, no additional gas supply equipment is required, so there is no additional efficiency loss due to the small increase in pressure drop. Besides, the pressure loss is mainly caused by the linear loss related to the length of the channel and the local loss from the bending of the channels. Owing to the longest length and the largest bending angle, the maximum pressure drop of 831 Pa corresponds to the channel of 10°, which is 36.7% higher than that of the channel of 0°.

Figure 13. The pressure drop with different flow fields at current density of 0.6 A/cm².

Furthermore, it can also be observed from Figure 12 that there are pressure differences between the two sides of the channels. In order to observe the pressure differences between two sides of the channels caused by the bending clearly, the pressure on the insides of every single channel (marked with red circles in Figure 12d) and the outside of channels (black circle in Fig.12d) is shown as Figure 14. Since there are 9 cathode channels for every calculated model, 18 points are selected. Each points in Figure 14 represent the pressure on the inside or outside of a channel respectively, and the first point corresponds to the pressure inside of the first flow channel (marked with red circles in Figure 12d). As shown in Figure 14, the pressure on two sides of the flow channel of 0° is basically the same, but this is differs for curved channels. It can be ascribed to the pressure on the outsides of the channel increases and decreases on the insides due to centrifugal inertia force when gas flows through the bending channel. The pressure difference around the channel bending improves through-plane convection in the channel to diffuse more gases to the reaction layer as Figure 7 described. However, as the pressure difference increased due to the bending angle increased, the reactant escaped from one side of the channel and fewer gases diffuse to the reaction layer as analysis in Figure 7.

Figure 14. The differential pressure between two sides of channel at the central section of cathode channel with different flow fields (A-A in Figure 12d) at current density of 0.6 A/cm².

Furthermore, as presented in Figure 14, it is clear that the pressure difference between the inside and outside of the single channel grows with the increasing bending angle. The channel of 10° exhibits the largest differences, up to 24 Pa between the two sides of the channel. Therefore, the gas escape from the outside of the channel for channel of 10°intensively since the differential pressure results in fewer gases diffuse to the MEA from inside of the channel depicted as Figure 15b. However, as shown in Figure 15a, convection of the under-rib occurs on both sides for the channel of 0° uniformly owing to the consistent pressure gradient.

Figure 15. The reactant velocity vector under the cathode side rid for (a) channel of 0° and (b) channel of 10°.

For channels with angles of 2.5° and 5°, the differential pressure on two sides of channel is 6 and 10 Pa, respectively, which are so small that the gases cannot be concentrated on one side to transport to the outlet. On the contrary, the gases accumulate in the central area due to the bending of the channel. Benefiting from the higher convection caused by the pressure changes on the sides of the channel, the gas is facilitated to diffuse to the MEA along through-plane. It indicated that the local loss in the in plane due to channel bending can be utilized to improve the cell performance by an optimal curvature of the channel.

3.7. Effect of different bending on the distribution of gas velocity

The velocity profile in the flow channel can evidently reflect the mass flow rate of the reactant, hence the distribution of velocity is plotted to analyze the effect of channel bending on the velocity. A curved channel produces a higher velocity deviated from the centre of channel as shown in Figure 16 since the induced-flow area around the bend of the channel. The air velocity increment accelerates the in-plane mass transfer and water removal, as well as the through-plane reactant diffusion, simultaneously. Observing the velocity profile where the velocity varied greatly (as circled in Figure 16), and the detailed velocity distribution shown in the lower right corner of Figure 16. It can be found that the velocity distribution in the 0° channel presents a parabolic distribution of symmetrical centre with a maximum of 2.38 m/s located in the middle of the channel. As the bending angle increases, the maximum velocity of gases gradually increases and deviates away from the middle of the channel. The maximum velocities for the channels of 2.5° and 5° are 2.54 and 2.9 m/s, and deviate away from the middle of 5% and 10%, respectively. These larger velocities with small offsets lead to more significant convection, offering the reaction layer more reactant. Furthermore, a larger velocity can improve the capacity of water removal for promoting cell performance.

Figure 16. The distribution of velocity on GDL-CL for (a) 0° (b) 2.5°(c) 5° (d) 10° flow fields at current density of 0.6 A/cm².

However, the maximum velocity of the 10° channel is 8.64 m/s, which is 263% greater than that of 0° channel, and it deviates away from the middle of the channel by about 30%. The high-velocity in the in-plane direction concentrates the reactant on one side due to pressure differences and escapes from the channel, but prevents the gases permeating to the MEA along the through-plane direction. Less oxygen is supplied to the reaction layer for electrochemical reaction in the region, corresponding to poor cell performance. The same distribution of the velocity is observed in each channel of the cells with various cathode channel curvature as depicted in Figure 17.

Figure 17. The differential velocity between two sides of channel at the central section of cathode channel with different flow fields (A-A in Figure 12) at current density of 0.6 A/cm².

Lastly, the various performance parameters of AO-PEMFCs under different angle flow channel bending compared and listed in Table 6. An effective enhancement is discovered in both the cell performance and thermal management at flow channel angles is 2.5° and 5°, despite a minimal increase in pressure drop losses. Notably, since the gas supply in AO-PEMFCs relies on a fan, the increase in pressure drop does not lead to additional parasitic losses. However, when the flow channel angle increased to 10°, a noticeable decline in cell performance is observed. n summary, a reasonable optimization design for flow fields of AO-PEMFC, which can effectively utilize the local loss of the gas transportation in the cathode channels, improves the reaction rate while ensuring the balance between reactant transmission and diffusion.

Table 6. The cell performance of different angle flow channel bending at 0.6 A/cm²

Angle of channel bending	Cell potential (V)	Temperature at outlet (K)	Pressure drop (Pa)
0°	0.5577	317.5	608
2.5°	0.5714	316.7	616
5°	0.5804	315.8	667
10°	0.5382	317	831

4. Conclusions

In this work, four bending angle channels geometry are modelled to improve fuel cell performance and explore the optimal bending angle for the cathode channel. The model was validated in polarization curves and temperature by experiment. The effects of various cathode channel bending angles (0°, 2.5°, 5° and 10°) on the distribution of internal current density, pressure, velocity and reactant concentration were synthetically analyzed to clarify the design and optimization strategies of cathode channel bending angles in order to achieve the high-performance AO-PEMFC. The conclusions are summarized as follows:

• It is insufficient to improve the capacity of water removal and heat dissipation, as well as reaction intensity by only optimizing the air velocity in the in-plane or through-plane direction. To this end, the mechanism of the local loss caused by the bending of the cathode channels is exploited to increase and balance mass transfer and water removal, and further improve the energy conversion rate and cell performance.

• When the air flows through the channel bending angles of 2.5° to 5°, the small velocity difference between two sides of the channel can create increasing flow velocity at both the in-plane and through-plane direction. The increment of velocity for the through-plane induced more oxygen to reaction sites, and its in through-plane accelerated the discharge of water but not too intense to cause the gas to escape from the channels. Overcoming oxygen starvation and water flooding in the downstream area, and resulting in high cell performance.

• For the channel of 10°, the increase of velocity in the in-plane direction is greater than that of the through-plane directional element. Although the oxygen diffused to the reaction site on two sides of the flow field increases, more oxygen escapes along the flow channel, resulting in poorer current density uniformity and overall performance.

• While improving the mass transfer in PEMFC, it is also sensitive to ensure the mass transport in the in-plane direction and the reactant diffusion in through-plane, which should be comprehensively considered when optimizing flow field of PEMFC.

Nomenclature

cp	=	specific heat (J kg−1 K−1)
c	=	species concentration (-)
D	=	diffusivity coefficient (m2 s−1)
F	=	Faraday constant (96487 C mol−1)
ir	=	reference current density (A cm−2)
j	=	volumetric transfer current (A cm−3)
k	=	permeability (m2)
kef	=	effective thermal conductivity (W m−1 K−1
M	=	molar mass (-)
P	=	Pressure (Pa)
R	=	universal gas constant (J kg−1 mol−1)
S	=	source term (-)
s	=	water saturation (-)
T	=	temperature (K)
$\overrightarrow{\nu }$	=	velocity (m s−1)

Subscripts and superscripts

an	=	anode
cat	=	cathode
cell	=	cell
E	=	energy (for source term)
eff	=	effective
ele	=	electronic
g	=	gas phase
i	=	species i
l	=	fluid phase
m	=	mass (for source term)
mom	=	momentum (for source term)
ref	=	reference
sol	=	solid phase
ion	=	ionic

Greek letters

ϵ	=	porosity (-)
ρ	=	density (kg m−3)
µ	=	dynamic viscosity (kg m−1 s−1)
$\alpha$	=	transfer coefficient
$\eta$	=	overpotential (V)
$\phi$	=	phase potential V

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was financially supported by Research Projects of Department of Education of Guangdong Province (2023ZDZX3078), Natural Science Foundation of Guangdong Province, General project (Atomic level characterization and multi-physics coupling optimization mechanism of the freezing phenomenon in air-cooled open-cathode PEMFCs at low temperature).