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Yan, Lu, Yao, Pei, and Fan: Research and Optimization of Four Serpentine-Wave Flow Fields in PEMFC


The layout of the cathode flow field largely determines the net output power of the proton exchange membrane fuel cell (PEMFC). To make the normal mass transfer effect best, the longitudinal channel was waved based on four serpentine flow channels, and the effects of sag depth and longitudinal channel width on the output efficiency of the cell were explored. The results show that the wave channel design systematically enhances the forced convection between adjacent channels, which can prevent a large zone of oxygen starvation zone at the outlet of the channel. The increase of the normal velocity in the gas transmission process will inevitably induce a significant enhancement of the mass transfer effect and obtain a higher current density in the reaction zone. For the longitudinal channel width, it is found that increasing its size in the effective range can greatly reduce the channel pressure drop without reducing the output power, thereby improving the overall efficiency. When the sag depth and longitudinal channel width gradient are 0.6 mm and 0.2 mm respectively, PEMFC can obtain the best comprehensive performance.

1. Introduction

Due to the characteristics of traditional fuels such as non-renewable and environmentally destructive combustion products, energy conversion and replacement has become an inevitable choice for sustainable social development [13]. PEMFC is an electrical energy conversion device using clean gases (hydrogen and oxygen) as raw materials, and to a certain extent can achieve the ideal target of zero pollution because liquid water is its single product [46]. Despite the significant advantages, the amount of electricity produced by a single PEMFC chemical reaction is not enough to meet the needs of commercial applications such as vehicles, and this disadvantage can be well eliminated by stacking them alternately and combining them in series to form a stack structure. The role of bipolar plates (BPP) in the stack structure is significant, and the flow field structure present inside them can induce the diffusion pattern of reactants in the channel of the stack gas [79]. Numerous studies in the literature have shown that hydrothermal management is a decisive factor for cell efficiency [1013]. As the initial location for the presence of reactants and the only channel for the discharge of liquid water, the design and development of flow fields are increasingly favored by scholars from various countries.
Optimizing the shape and size of the existing flow field structure that has been applied on a large scale can effectively save costs while increasing the output power. Korkischko et al. [14] parameterized the conventional rectangular cross-section DC and found that although the inverted trapezoidal channel structure reduced its contact area with the GDL, the existence of the tilt angle correspondingly increased the normal permeability of the reaction gas, in which the substance arriving at the reaction site is more adequate. Santamaria et al. [15] have optimized the channel length as an effective means to improve the PEMFC with interdigitated flow field. The experiment selected a 5 mm channel as the best solution, which can prevent water from plugging into the diffusion layer hole while taking into account the output stability of current and power density. Relatively speaking, Cooper et al. have obtained through many experiments that the contribution of stoichiometric ratio on cell power generation efficiency is higher than that of channel size [16]. In addition, adding blockages to the channel has now become a common means of changing its cross-sectional area. Chen et al. [17] set up an incremental step-like obstruction along the channel. The performance show that this operation can effectively enhance the low reaction efficiency caused by insufficient oxygen supply in the second half of the flow field. In addition, opening grooves of different shapes at a specific spacing will also have an important bearing on oxygen transport properties [18,19]. Cai et al. [20] analyzed and compared nine different blocking shapes for the cathode flow channel and finally concluded that the inverted trapezoidal blocking structure had a better comprehensive effect than the parallel flow channel, and the power density increased by 16%.
With the classical flow field continuing to be optimized, many studies are also committed to the exploitation of new styles of flow field structure [2125]. The bionic flow field has the advantages of combining biotechnology with practice and has broad development prospects [2628]. Dang et al. [29] focused on the location and state of water, and used the principle of visualization to observe the water distribution of the lobe-like bionic flow field at distinct times. They have discovered that the water is uniformly dispersed inside the bionic flow field, and the sub-branch gas flow rate decay state was not obvious. The serpentine channel has a special bionic structure, the earliest start, and is very skilled. The research report of Zhang et al. proposed that the multi-serpentine flow field has superior properties over the single-serpentine flow field [30].
As a special form of blocking flow field, a wavy flow field is considered to be effective in enhancing mass transfer and maintaining the internal water and heat balance of the entire cell system [31]. This study employs a sinusoidal waveform as the wave pattern, with the aim of reducing fluid resistance in the flow channel. The objective is to create a more favorable fluid dynamic environment. Additionally, the choice of this shape aligns with mathematical principles, facilitating improved processing in manufacturing. Research indicates that a wavy flow field is more effective in achieving uniform gas distribution and enhancing mass transfer. Under certain conditions, the wavy flow field may induce lift effects, contributing to intensified mass transfer, uniform reactant distribution, and enhanced electrochemical reactions. Moreover, it facilitates efficient water removal, leading to a significant improvement in the power and efficiency of PEMFC [46,48]. After searching the literature, we found that the current research on wavy channels still stays based on a single serpentine flow field. To observe the forced convection between adjacent channels more obviously, a four serpentine-wave flow field (FSWFF) is introduced in this paper. The introduction of the serpentine flow field is motivated by its distinct advantages compared to the latest 3D channels. Firstly, the serpentine flow field possesses a relatively simple geometric structure, facilitating more convenient manufacturing. Secondly, the serpentine flow field demonstrates superior mass transfer and water removal capabilities compared to parallel flow fields [47]. Lastly, while emerging 3D channel structures offer additional benefits in terms of heat and mass transfer in certain aspects, the simplicity and economic viability of the serpentine channel continue to render it a valuable subject of study under specific conditions. Among them, the wavy channel exists in the main channel part of the whole flow field. The sag depth and channel width are identified as the main research objects, and multiple sets of single variable models are selected respectively. Through the comparison and analysis of the simulation software COMSOL Multiphysics, the design scheme with the best actual effect can be obtained.

2. Model setting

2.1 Geometric model construction

The forced convection effect of the serpentine structure is more prominent in many flow field structures, which is mainly reflected in the longitudinal channel and between adjacent channels. For normal mass transfer, a wavy flow field is a better choice. Therefore, a joint study of the two is considered very necessary, the new FSWFF can maximize the advantages of both. As depicted in Fig. 1(a), the single-cell model consists of FSWFF, gas diffusion layer (GDL), catalyst layer (CL), and proton exchange membrane [32]. The specific geometric dimensions of the model contained in the calculation domain are depicted in Table 1. The selection of a proton exchange membrane is not a matter of thicker or thinner being better. If the membrane is too thin, prolonged usage may lead to mechanical damage-induced decay and membrane degradation caused by electrochemical processes. During operation, the membrane undergoes repeated cycles of expansion and contraction, creating stress cycles that could ultimately result in crack formation. These cracks may promote leakage of reaction gases and cross-permeation, exacerbating electrochemical degradation. Additionally, defects arising from electrochemical degradation can become areas of stress concentration, further accelerating mechanical damage [41,42]. On the other hand, if the proton exchange membrane is too thick, it can lead to the issue of reverse diffusion of water, making it difficult for water to pass through the membrane. Therefore, this study has opted for the Nafion 117 membrane with a thickness of 0.183 millimeters. This membrane is currently commercialized and widely employed at a large scale [40]. For FSWFF, as evident by Fig. 1(b) that the wavy channels are arranged longitudinally and the adjacent channels are parallel to each other. The total wavelength and single wavelength are fixed to 22 mm and 2 mm. To make the contrast effect more obvious, the flow field is divided into four parts with the same area including Part 1–4. Under the premise that the total activation area is 32 mm × 32 mm, the effects of sag depth (H) and channel width (CW) on the total cell performance as well as pressure drop are investigated.

2.2 Calculation formula

In the calculation domain of PEMFC, there are many physical changes such as velocity, pressure, and composition. This shows that in addition to the dominant electrochemical equation in the calculation process, there are also a series of other control equations to ensure the balance of multi-physical fields. The specific performance is as follows [33,34]:

(1) Mass conservation equation

It can ensure the balance of reaction gas flow in and out per unit of time without any additional loss.
In the formula, ɛ, ρ, and u represent the porosity of porous media, fluid density, and velocity vector respectively. It is worth noting that ɛu represents the volume flow per unit area during the normal infiltration process, and ɛ has different values in different domains. In the flow field, ɛ = 1, while in other porous media, ɛ < 1. In addition, Sm to the right of the equation represents the quality source term.

(2) Momentum conservation equation

In formula (2), μ and P are fluid dynamic viscosity as well as pressure, the left side of the equation represents the unsteady and convective terms respectively, the right side Su is the momentum source term and the remaining is the steady state term.

(3) Energy conservation equation

Energy only has different forms of mutual transformation, and will not disappear. Similarly, the energy generated by the electrochemical reaction exists in various forms including heat energy, electric energy, and loss, and the total amount is equal. The specific performance is:
In the formula, CP, T and keff represent the steady pressure specific heat, temperature, and efficient thermal conductivity, respectively. The right side SQ is the energy source term including reaction heat, ohmic heat, and overpotential heat.

(4) Component conservation equation

Compared with the mass conservation equation, the component conservation equation can better describe the state of a material change in each region.
The first and second terms of the equation are the equation is the unsteady and convective terms, and the right side is the diffusion and source terms. where i is the component code, Ci and are the component concentration and effective diffusion coefficient, and Si represents the component source term. In formulas 1 – 4, the specific composition of each source term is shown in Table 2.

(5) Electrochemical equation

In terms of current conservation, there are:
Among them, sol and mem represent the solid phase and membrane phase respectively. σ, Ø and R represent the conductivity, potential, and current source terms. The anode side and cathode side are Rmem =Rsol.
As the calculation equation of the polarization curve, the Butler-Volmer equation describes the most basic dynamic relationship. In the calculation of the model, the mass flow, temperature, and pressure as the initial boundary conditions, and the specific physical parameters are shown in Table 3 [35].
Among them, ξ and j represent the active specific surface area and swap current density, respectively. α is the dimensionless charge transmission coefficient, η is the activation over-potential, and C represents the specific concentration. It is worth noting that in the actual working state, the polarization phenomenon will lead to the original equilibrium state being broken, and the actual output voltage is slightly lower.
Activation polarization:
Vact=-ξa+ξbT+ξcTln(CO2)+ξdTln I
Ohmic polarization:
Concentration polarization:
In formula 9–11, I and R are current and resistance respectively, and c is an empirical coefficient.

3. Model assumptions

  • (1) Due to the low Reynolds number, the flow state of a fuel cell is laminar flow and the flow process is stable [36].

  • (2) In the effective area of GDL, CL, and membrane, the porosity is uniform.

  • (3) The reaction gas is fully wetted before entering and the flow process is not easy to compress.

  • (4) Cell temperature is constant.

  • (5) Ignore the gas exchange phenomenon in the membrane.

4. Model and Grid validation

To guarantee the correctness of the conclusion data, the rationality of the model needs to be verified before the actual simulation process. This study validates the effectiveness of the model using experimental results from a flow field with a similar structure proposed by Chowdhury et al. [37] and Freire et al. [49]. On the premise of ensuring that the conditions including size and operating parameters are completely consistent, the target flow field is simulated and analyzed and the corresponding polarization curve is obtained. The outcome is depicted in Fig. 2. The Fig. 2 illustrates that, while there are some differences between experimental and simulation results, the overall fitting is high, with an error below 5%. Therefore, the simulation results can be considered valid.
Special consideration is given to the fact that the number of grids and the division method can affect the final results of the simulation to a certain extent. Therefore, the process of verifying grid independence is necessary. In the process of upgrading the grid amount of the model indicated in Fig. 3 from 363923 to 1621399, the limiting current density of the cell also increases. The results are shown in Table 4. We know that when the grid quantity is higher than 1240836, the current density values converge almost completely. Therefore, to guarantee the correctness of the calculation results, the grid construction method of #4 is selected for the simulation calculation of all models.

5. Results and Discussion

5.1 Sag depth

The introduction of wavy channels in the serpentine principal flow field will simultaneously change the diffusion properties of the reaction gas in the X, Y, and Z axis. In this section, a total of five sets of FSWFF with different sag depths (H) were set by controlling a single variable in steps of 0.2 mm, and the exact categorization is shown in Table 5.

5.1.1 FSWFF fuel cell performance under different H

Fig. 4 demonstrates the PEMFC polarization versus power density curves (U–I versus P–I curves) for five different H. It can be seen that all curves maintain the same overall trend, which demonstrates that the chemical reaction mechanism does not change with the change of size parameters. However, in the ohmic and concentration polarization processes, especially when the current density is above 0.5 A/ cm2, the output capability of each scheme shows some differences. Compared with Plan 1 (H = 0 mm), the wavy channel has certain advantages in boosting the output power. From the curves and histograms, it is discovered that the maximum cell power density has convex with the increase of H, peaking at Plan 4 (H = 0.6 mm) and then decreasing sharply. This means that after reaching the critical point, continuing to increase the depth of the sag will adversely affect the cell performance. The reason may be that due to the continuous consumption in the early stage, the concentration of the reaction gas is insufficient in the intermediate and rear sections of the flow field (Part 3 and 4). At this time, the normal mass transfer enhancement effect caused by FSWFF and the forced convection under the ribs bring higher current density. However, excessive H will lead to strong resistance when the reaction gas diffuses through the channel direction, which is more detrimental to its homogeneous distribution throughout the flow field. When compared to Plan 4, the maximum power density of Plan 5 is reduced by 5%.

5.1.2 Oxygen velocity and distribution

Fig. 5 exhibits the gas velocity analysis along the Z-axis direction at X = 1 mm (the outermost channel) of five different FSWFFs under 0.5 V operating voltage. It can be seen that when H = 0 mm, the reaction gas has almost no normal velocity in the channel, and its diffusion to CL is free penetration. By comparing Plan 2–5, it can be found that as H increases, the velocity component of the reaction gas along the Z-axis direction increases monotonically. In the Plan 2 channel, the gas normal velocity is only 0.27 m/s, while Plan 5 reaches 1.86 m/s. This shows that the periodic structure of the wavy channel will change the internal mass transfer mode of the flow field. Since the content of reactants in the catalytic layer is a decisive index affecting the chemical reaction rate, Plan 5 has the highest oxygen concentration and reaction intensity in Part 1 compared with Plan 1–4. The allocation of oxygen positions at the GDL–CL interface of five distinct PEMFC cathodes at 0.5 V operating voltage shown in Fig. 6 confirms this view.
From this Fig. 6, the oxygen molar concentration gradually drops from Part 1 to Part 4 due to the channel length and pressure gradient. It is worth noting that the wavy channel has a sufficient oxygen content in the back of the flow field, especially in the GDL–CL interface corresponding to Part 4, than the conventional channel. This is because passing through a GDL with a certain thickness needs to overcome certain resistance. At this time, the FSWFF advantage with the Z-axis velocity component in the oxygen-starved region is obvious. Fig. 7 shows the oxygen concentration difference of five PEMFCs on the CL surface at 0.5 V operating voltage. May see from the selected parts of the boxes in Fig. 6 and Fig. 7 that compared with other schemes, Plan 4 (H = 0.6 mm) has the most uniform oxygen concentration distribution and the highest total oxygen content. Although Plan 5 has a higher oxygen content in Part 1 than Plan 4, the opposite is true in Parts 2–4. The reason is that the presence of a wavy channel will have a “disturbance” effect on the oxygen flow, when H is larger, may see from the larger part of Fig. 6 that the oxygen distribution has a clear sense of hierarchy. However, the excessive longitudinal “disturbance” will hinder the convective mass transfer along the channel direction, which greatly reduces the oxygen concentration at the end of the flow field while increasing the channel pressure.

5.1.3 The water distribution

Because of the low transport efficiency of oxygen in liquid water, excellent drainage performance is the key to flow field design. Fig. 8 shows the water molar concentration of five PEMFCs on the CL surface at 0.5 V voltage. For Plan 1–5, the overall characteristic is that the molar concentration of water increases continuously along the horizontal diffusion direction of the gas, and the water accumulation is more severe in the area under the ribs compared to the channel location. Compared with Plan 1, the water removal performance of Plan 2–4 was effectively improved. This is because the product water needs a certain shear force to reflow into the cathode channel. This Fig. 5 that the wavy channel can greatly improve the normal permeability of oxygen by forced convection.
Fig. 9 shows the water concentration difference of five PEMFCs on the CL surface at 0.5 V voltage. It can be observed that the water concentration difference of Plan 1–5 is concave. In Plan 4 (H = 0.6 mm), the non-uniformity is the smallest (6.52 mol/m3). This is attributed to the fact that Plan 4 has a more intense impact force than Plan 1–3 when oxygen is transmitted in the Z-axis direction, which reduces the possibility of a large accumulation of water vapor to a certain extent. However, continuing to increase H, the water removal capacity of the flow field is severely reduced, and the water concentration distribution in the whole CL domain is extremely uneven, especially in Part 4 where the water accumulation is serious. When water flooding occurs, water vapor reaches the saturation vapor pressure, condensing into a substantial amount of liquid water, causing stagnation or inappropriate movement of water within the flow field. Additionally, liquid water accumulates in the gaps of the diffusion layer and catalytic layer, hindering the transfer of hydrogen and oxygen. This obstruction results in a reduction in the rate of electrochemical reactions, leading to a decline in the performance of PEMFC. As depicted in Fig. 6, the latter part of the Plan 5 flow field exhibits lower oxygen concentrations, causing the product water to nearly completely reside on the surface of the Catalytic Layer.

5.2 Channel width (CW)

According to the analysis results in Section 5.1, Plan 4 (H = 0.6 mm, CW = 1 mm) has the best performance among the five comparison models. According to Chowdhury, changes in channel width in a serpentine flow field affect the output properties of the cell by affecting sub-rib gas convection. Based on this situation, we introduce a channel width gradient change flow field structure. It is notable that to ensure the uniqueness of the variable, the size change only exists in the Y-axis direction containing the wave channel. The model is shown in Fig. 10.
Specifically, Parts 1–4 have specific channel widths and uniform numerical changes. To make the comparison results more obvious, 0.1 mm step length is omitted and 0.2 mm and 0.3 mm are used directly, which correspond to four types of flow fields, #a, #b, #d, and #e respectively. There is no change in the channel width of the #b and #f type flow fields. Generally speaking, the flow field types include gradient decreasing flow field (GDFF), gradient increasing flow field (GIFF), and constant width flow field (CWFF). The size distribution is shown in Table 6.

5.2.1 Fuel cell property with different CW flow fields

After ensuring that CW is the only variable, the U–I and P–I curves corresponding to each scheme under 0.5 V voltage conditions in Fig. 11 can effectively reflect the actual property of the cell. As compared to Fig. 4, the difference between each curve in Fig. 11 is more obvious. It can be found that GIFF is better than GDFF and CWFF in improving the limiting current density, but when GIFF is the same, the output current is not sensitive to the change of CW (less than 0.01%), and the two curves of #d and #e in Fig. 11 are almost completely coincident. This conclusion can be more conveniently drawn from the maximum current and power density of #a–#f displayed in Fig. 12.
Notably, #c has the highest output power, but this phenomenon only exists in the current density below 0.72 A/cm2 stage. The reason may be that in the second half of the flow field (Part 3, Part 4 area), #c appeared a certain degree of oxygen supply shortage and was accompanied by water accumulation in the flow channel and membrane. In addition, from this Fig. 11 and Fig. 12 that the output effect of #a and #b is poor, especially #a. Compared with #c, the maximum power density is reduced by 13.8%.

5.2.2 Distribution of oxygen and water in the various CW flow fields

To more distinctly show the impact of CW changes on the reaction rate at the GDL/CL position of the cell, Fig. 13 and 14 give the oxygen distribution and water distribution of three type flow fields on the CL surface under 0.5 V conditions. It can be noticed from Fig. 13 that the oxygen distribution uniformity of GDFF is poor, and the reaction stagnation is almost completely caused in Part 3–4 region. In addition, a raise in channel width seems to raise the overall oxygen amount of the CL surface. From this the back-end position of the flow field shown by the dotted box that the oxygen content and distribution uniformity in the #d longitudinal channel are in the best state in #c–#e. This is because there is no diversion phenomenon of oxygen in the process of serpentine flow field transmission. At the moment, the rib width of the flow field decreasing sequentially will enhance the convection effect between adjacent channels. Comparing #c – #f shows that this effect increases with increasing CW when the intake flow rate is certain.
Resemble the results presented in Fig. 13, #f in Fig. 14 has the best water removal effect in six different CW flow fields, and there is no obvious water molecule in Part 1–2. At the same time, #f has the lowest water concentration difference (6.12 mol/m3). Although #d (6.13 mol/m3) is also in the ideal range, its maximum water mole fraction is 1.2% higher than #f. Therefore, it can be considered that GIFF is superior to GDFF in water and oxygen removal, and the larger the CW value, the better the effect.
However, the output property of the cell is not directly related to the oxygen concentration. The reality is that the output performance of #f is significantly weaker than GIFF. As can be seen from the variation of values shown in Fig. 12, the maximum power density of #f is reduced by about 4.8% over #d and #e. The most direct reason is that most of the electrons will avoid the gas flow area and move to both sides during the transfer process. As a good conductor, the structural size of the rib has a great influence on the total current output. The narrow rib width in #f seriously reduces the electron transmission capacity. Fig. 13 shows the electrolyte current density of #e and #f in the circular box. Can be seen the current density distribution of #f is extremely uneven. Furthermore, it is evident from Fig. 14 that compared with #d and #e, the #f has lower water content, which limits the proton conduction rate and results in lower oxygen utilization. Therefore, when Parts 1–4 are all large-size channels, the performance is weaker than GIFF.

5.2.3 Pressure drop comparison

As an important reference index for the comprehensive performance of the battery, the voltage drop needs to be considered. Fig. 15 exhibits the pressure drop of six different CW flow fields. It is observed that the pressure drop of GDFF is much higher than GIFF and CWFF. This is due to the small size of the GDFF back-end channel, which increases fluid flow resistance. In #c–#f, #d is similar to #e. Compared with #f, #e pressure drops increased by 95.39%. However, considering that the limiting current density of #f is only 0.229 A/cm2, the low-pressure drop is the main reason for its poor output effect. Therefore, the #e with both low-pressure drop and high output power has the best comprehensive effect.

5.3. Validation of the Optimal Channel

Due to variations in proton membrane thickness, it not only impacts the issue of water back diffusion but also complicates the prediction of water management problems. Therefore, it is necessary to investigate whether the four-serpentine wave channel continues to exhibit the previously mentioned effects under different membrane thicknesses. In this section, while maintaining the original foundational conditions, the proton exchange membrane thickness is adjusted to 0.0254 mm [51] to validate the performance of the channel under these altered conditions.

5.3.1 Validate the optimal sag depth

Initially, under the conditions maintained in Section 5.1, the thickness of the proton membrane is changed to 0.0254 mm to validate the optimal sag depth. As shown in Fig. 16(a), the U–I and P–I curves for Plan 1–5 are presented. It is evident that, except for Plan5, the other Plans almost converge. This is attributed to the relatively thin proton membrane, where different sag depths do not significantly affect the U–I and P–I curves. Therefore, U–I and P–I curves alone cannot distinctly determine the superiority of a particular Plan. To further explore their advantages and disadvantages, Fig. 16(b) displays the statistical chart of the average molar concentrations of water and oxygen at the interface between the cathode region GDL and CL for different Plans, with the proton membrane thickness set at 0.0254 mm. It is apparent that Plan4 exhibits the highest average oxygen concentration and the lowest average water molar concentration. Additionally, Fig. 16(c,d) illustrate the distribution of water and oxygen molar concentrations at the interface between the cathode region GDL and CL. From these figures, it is evident that Plan4 has a more uniform distribution of oxygen and water concentrations, marked at the respective positions. This indicates that Plan4 performs better at H = 0.6 (Plan 4).

5.3.2 The validation of channel width

After confirming that H = 0.6 mm (Plan 4) is the optimal sag depth under different sag depths, the settings from Section 5.2 are kept unchanged, and the proton membrane thickness is modified to 0.0254 mm for the validation of channel width. As shown in Fig. 17(a), the U–I and P–I curves for #d and #e are significantly superior to other schemes, and the two almost overlap. To further investigate the differences between channel widths, Fig. 17(b) presents the line chart of the peak current and maximum power density for #a–#f. It is evident from the chart that #c has higher output power, while #e has a higher peak current. Fig. 17(c) illustrates the cathode pressure drop distribution from #a to #f, showing a gradual decrease in cathode pressure drop for #a-#f, with a small gap between #d and #e at 300.27 Pa and 300.5 Pa, respectively. Fig. 17(d) displays the distribution of oxygen molar concentrations from #a to #f, where #d and #e have a small difference, and compared to other schemes, they exhibit a more uniform distribution of oxygen molar concentrations. In Fig. 17(e), the water molar concentration is shown from #a to #f, with #f demonstrating better drainage performance, followed by #d and #e, which have a small difference between them. The rest of the water molar concentration distributions are less favorable. In summary, compared to other schemes, #d and #e exhibit outstanding performance with clear advantages. However, in terms of maximum power, #e demonstrates better output performance.
In summary, the utilization of both the 0.0254 mm thin membrane thickness and the previously employed 0.183 mm membrane thickness demonstrated favorable channel effects for the bending depth H = 0.6 mm (Plan 4) and #e (GIFF, step size = 0.2 mm). Thus, it verifies the presence of the channel effects mentioned under thin membrane conditions, further substantiating the rationale behind this channel design.

6. Conclusions

In this paper, the sag depth (H) and channel width (CW) are set as the research focus, and the performance of the four-serpentine wavy flow field (FSWFF) is investigated by the CFD simulation method. The conclusions are as follows:
  • (a) For sag depth. The concave and convex changes in the wavy channel can enhance the normal permeability of the gas, which facilitates the discharge of excess water at the reaction position and obtain a more homogeneous oxygen allocation on the CL surface.

  • (b) For sag depth. When H = 0.6 mm (Plan 4), the resulting cell output is optimal. Compared with the conventional channel flow field, its power density is elevated by 5.72%.

  • (c) For channel width. Gradient decreasing flow field and CW = 1.9 mm constant width flow field, the output effect is not ideal. This indicates that the cell property does not alter monotonously with the change of CW. It can be found that the improved gradient increasing flow field has the maximum power density value, and the flow field configuration with the channel width of Part 1–4 increasing in a constant step is more conducive to generating and transmitting current.

  • (d) For channel width. When both are gradient-increasing flow fields, #d and #e have their advantages. After fully considering the current and power density and the inlet and outlet pressure drop, it can be considered that #e (GIFF, Step length = 0.2 mm) has the best-integrated effect.


The authors thank the Shandong Province Major Science and Technology Innovation Project (2018CXGC0803) for funding!



All authors state no conflicts in this article!

Data availability statement

All data obtained for this study are available by contacting the corresponding author.

Fig. 1
PEMFC model: (a) single cell model and (b) cathode flow field.
Fig. 2
Simulation and experimental results. (a) Compare experimental data and model simulation data by Chowdhury et al. [37]. (b) Compare experimental data and model simulation data by Freire et al. [49].
Fig. 3
Model grid structure.
Fig. 4
U–I and P–I curves.
Fig. 5
Distribution of gas velocity.
Fig. 6
Oxygen concentration distribution.
Fig. 7
Difference of oxygen concentration on CL surface under five different H conditions.
Fig. 8
Molar concentration of CL surface water at different H.
Fig. 9
Difference of water concentration on CL surface under five different H conditions.
Fig. 10
Schematic diagram of variable width channel model.
Fig. 11
U–I and P–I curves of different CW fuel cells.
Fig. 12
#a–#f maximum current and power density values.
Fig. 13
Surface oxygen concentration distribution of CL under different CW.
Fig. 14
Water concentration distribution at CL interface under different CW.
Fig. 15
Pressure drop at inlet and outlet of different CW flow fields.
Fig. 16
Validation of the optimal sag depth at proton membrane thickness of 0.0254 mm.
Fig. 17
Validation of the optimal channel width at proton membrane thickness of 0.0254 mm.
Table 1
Geometric model size
Name Numerical Unit
Activation area 1024 mm2
Transverse flow field length 32 mm
Longitudinal flow field length 32
Total wave length 22
Single wave length 2
Outlet/inlet area 1 mm2
Channel height 1 mm
GDL/CL/Membrane thickness 0.19/0.015/0.183 mm
Table 2
Expression of each source term
Source term Expression
Sm (Cathode) MH2O2FRC-MO24FRC
Su -μeffKu
SQ hrea + Ra,cηa,c + I2Rohm + hL
Si -12FRa(H2)-14FRC(O2)-12FRC(H2O)
Table 3
Operation parameters of the model
Name Numerical Unit Refs
Binary diffusion coefficient (H2-H2O/N2-H2O/O2-H2O/O2-N2) 11.68×10−5/3.27×10−5/3.58×10−5/3.05×10−5 m2/s [39]
Reference concentration (O2/H2) 40.88 mol/m3 [40]
CL porosity 0.3 [39]
GDL porosity 0.4 [34]
Membrane porosity 0.28 [50]
CL permeability 2.36×10−12 m2 [18]
Dynamic viscosity (Anode) 1.19×10−5 Pa·s [34]
Dynamic viscosity (Cathodic) 2.46×10−5 Pa·s [34]
Reference pressure 1.01×105 Pa [34]
GDL conductivity 222 S/m [34]
Membrane conductivity 9 S/m [39]
Cell temperature 353.15 K [39]
Initial velocity (Anode, Cathodic) 1 m/s
Inlet quality fraction (H2/H2O/O2) 0.963/0.037/0.228
GDL permeability 1.18×10−11 m2 [18]
Table 4
Limit current density of five grid schemes
Name #1 #2 #3 #4 #5
Grid number 363923 603821 968662 1240836 1621399
Limiting current density (A/cm2) 0.33240 0.69237 0.85243 0.89375 0.90454
Table 5
Classification of sag depth
Code Plan 1 Plan 2 Plan 3 Plan 4 Plan 5
H (mm) 0 0.2 0.4 0.6 0.8
Channel width (mm) 1 1 1 1 1
Table 6
Specific dimensions of the flow field with different channel widths
Flow field code Part 1/Part 2/Part 3/Part 4 channel width (mm) Step length Flow field type
#a 1/0.7/0.4/0.1 0.3 GDFF
#b 1/0.8/0.6/0.4 0.2
#c 1/1/1/1 0 CWFF
#d 1/1.3/1.6/1.9 0.3 GIFF
#e 1/1.2/1.4/1.6 0.2
#f 1.9/1.9/1.9/1.9 0 CWFF


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