Zijun Li, Shubo Wang, Sai Yao, Xueke Wang, Weiwei Li, Tong Zhu,*, Xiaofeng Xie,*

1 School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China

2 Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China

3 Beijing Institute of Space Launch Technology, Beijing 100076, China

Keywords:Fuel cells Transport process Computational fluid dynamics Flow regimes Water management

ABSTRACT The performance and operation stability of proton exchange membrane fuel cells (PEMFCs) are closely related to the transportation of reactants and water management in the membrane electrode assembly(MEA) and flow field.In this paper, a new three-dimensional wave parallel flow field (WPFF) in cathode was designed and analyzed throughout simulation studies and an experimental method.The experimental results show that the performance of PEMFC with WPFF outperforms that of PEMFC with straight parallel flow field(SPFF).Specifically,the peak power density increased by 13.45%for the PEMFC with WPFF as opposed to PEMFC with SPFF.In addition, the flow field with area of 11.56 cm2 was formed by the assembly of transparent end plate used for cathode and the traditional graphite plate used for anode.To understand the mechanism of the novel flow field improving the performance of PEMFC, a model of PEMFC was proposed based on the geometry, operating conditions and MEA parameters.The thickness of gas diffusion layers (GDL), catalytic layers (CL) and proton exchange membrane were measured by scanning electron microscope.The simulation result shows that compared with SPFF, the WPFF based PEMFC promote the oxygen transfer from flow channel to the surface of CL through GDL,and it was beneficial to remove the liquid water in the flow channel and the MEA.

1.Introduction

Proton exchange membrane fuel cells(PEMFCs)have the advantages of high energy transformation rate and their ability of zero emission,which are considered as one of the most potential energy sources in the future [1,2].PEMFC is mainly composed of proton exchange membrane, catalyst layers (CL), gas diffusion layers(GDL)and bipolar plates.The bipolar plate plays an important role in the performance, because it acts as the reactions distributor which delivers the hydrogen and oxidant to the reaction electrode site.In addition, this component supplies the mechanical support for the PEMFC in stack.The optimal design of the flow field is significant to increase the effective utilization of fuels and the catalyst layers.

The transportation of reactants in the flow field to the catalyst layers has a critical effect on the PEMFC performance.Poor transportation results in lower concentration of reactants in the catalyst site, which leads to greater concentration polarization when the current density increases and a limitation of the maximum output power density.The design of flow field directly affects the distribution and transmission of reactive gases, water management, fuel utilization of the PEMFC and ultimately affects their output performance.It is one of the most important research points of PEMFC.

Various approaches have been developed to study the influence of flow field on PEMFC performance.Wanget al.[3]presented a three-dimension and two-phase model for serpentine flow fields to investigate the effect of channel size on the performance for PEMFC.The conclusion shows that smaller channel size enhanced the PEMFC performance.Bodduet al.[4]used a computational fluid dynamics modeling of a PEMFC with serpentine flow fields,they demonstrate the more number of parallel channels and smaller size could increase the contract surface area and decreased the pressure drop.Srinivasaet al.[5]designed bio-inspired flow field with lung and leaf shape.Compared with the triple serpentine flow field the leaf channel has the best performance.Hanet al.[6]proposed a novel channel with Concus-Finn condition.They used the visualization experiment and simulation to study the water removal behavior of the new channel shape.They found that this kind of channel could prevent the flooding phenomenon.The cross flow in PEMFC with parallel flow fields was studied by experiment and numerical simulation methods [7,8].They used back pressure devices in part of the flow channel to achieve the different pressure between adjacent channels and found the active back pressure had up to 24% enhancement in current density.The numerical results indicate the oxygen and liquid water has better distribution characteristic in cross flow effect.

Forced convection has superior mass transfer advantages,which could promote the transportation of reactants.Compared with conventional flow field, Yanet al.[9]developed the interdigital gas distribution by cutting off the connection between the inlet and outlet flow channels, the result implies that the PEMFC with interdigital channel can offer a better performance at high oxygen utilization.The interdigital flow fields delay the occurrence of voltage drop or mass transfer loss at higher current density because higher reactants in the channel can be forced into the surface of catalyst to enhance the reaction rate.Liuet al.[10]developed a model to investigate the application of baffle-block in channel for oxygen transport and performance of PEMFC.The baffles were arranged in the form of arrays.Their study shows that the performance of PEMFC could be improved by the arrangement of the baffles enhancing the local current density.Suet al.[11]designed a stepped flow channel applied to parallel flow field and serpentine flow field respectively.The results show that it has an obvious effect on parallel flow field,but has little effect on the performance of serpentine flow field and mass transfer in diffusion layer.Pernget al.[12]established a three-dimensional (3D) numerical simulation to study the influence of trapezoidal baffles on the PEMFC net power.The geometric parameters of trapezoidal baffles were used in the channel include the angle and height.The results show that the trapezoid block with an angle of 60°and a height of 1.125 mm achieve the maximum enhancement of PEMFC.

Many people have designed 3D flow filed to promote PEMFC performance through forced convection.However, rectangular or trapezoid are used to form the 3D shapes channel mostly and the design of this kind of sharp turn may increase the internal pressure drop of the channel.Moreover, fewer experimental studies of obstacle channel have been reported.In this regard, a novel type of parallel flow field with the smooth obstacle channel was designed in this study.This study combines the experimental method and simulating method in the same active area of 11.56 cm2.The transparent PEMFC with straight parallel flow field(SPFF) and wave parallel flow field (WPFF) were designed for performance comparison and analysis, and the liquid water distribution in the flow field was observed.In order to deeply understand the mechanism of PEMFC with WPFF, the simulation results were verified by the polarization curves obtained from experiments, and then the oxygen concentration, liquid water,velocity and current density distribution were analyzed in this study.

2.Experimental

2.1.Transparent PEMFCs

A transparent PEMFC on one side was designed to study the performance of different flow field, as schematically shown in Fig.1.The transparent PEMFC consists of cathode transparent endplate, cathode collector, gaskets, membrane electrode assembly(MEA), anode graphite bipolar plate, anode collector and anode end-plate.Both of the collector of anode and cathode were red copper and the thickness was 1 mm with the gold plating.As the current collector in cathode, it had 13 through slots, 30 mm long,0.8 mm wide and the distance between each slot was 1.6 mm (as shown in Fig.1(a)).The transparent end-plate was made of acrylic plate,which was processed into two structures,one was rectangular convex structure(as shown in Fig.1(b)),the other was periodic 3D wave convex structure (as shown in Fig.1(c)).When it was matched with the cathode collector, two kinds of flow channels were formed [6].The assembled PEMFC was as shown in Fig.2.The flow channel shape can refer to the schematic diagram of simulation structure (as shown in Fig.3).In order to install heating device on the anode side adopts graphite flow channel.The anode flow field plate was made of graphite,the shape of anode flow field was serpentine flow channel and the width, depth and rid of flow channel were 1 mm.The silica gel plate acted as a sealing gasket,which was assembled between the anode graphite bipolar plate and the cathode collector.

Fig.1. Scheme of transparent PEMFC and transparent end-plate:(a)construction of single cell in the experiment, (b) SPFF transparent end-plate, and (c) WPFF transparent end-plate.

Fig.2. Photo of the transparent PEMFC.

2.2.MEA and test condition

The MEA in this study has an active area of 3.4 cm × 3.4 cm(11.56 cm2) and the proton exchange membrane (PEM) is Gore M820.15 (Gore Inc, USA), the thickness of the membrane is 15 μm.The platinum loading is 0.4 mg·cm-2Pt on cathode side and 0.1 mg·cm-2Pt on anode side.The gas diffusion layer is SGL 29BC.The test was performed with anode H2and cathode O2.The stoichiometric ratio of hydrogen and oxygen were fixed with 2 and 2.The PEMFC temperature is 65 °C and the gas is 100%humidified without back pressure.

2.3.SEM test

Using a scanning electron microscope (GeminiSEM 500, Zeiss,Germany) under the electron acceleration voltage of 0.02-30 kV to study the thickness of the catalyst layers and the hot-pressing GDL,which was used in the simulation for each components thickness of MEA (as shown in Fig.4(c)).The cross section of MEA was prepared by fracturing liquid nitrogen.

3.Model Description

3.1.The design of flow field

Two types of flow field model were designed and studied in the area of 11.56 cm2for PEMFC,which were consistent with the MEA active area in the experiment.The flow channel is parallel field,including the straight parallel flow field(SPFF)and the wave parallel flow field(WPFF)in the cathode.As shown in Fig.3,the depth in the SPFF is a constant valueHfor 1 mm.In the WPFF, the maximum and minimum depth of flow channel isHandhfor 0.4 mm, respectively.The equation of the curve streamline can be explained as the cosine curve equation:

The rid width is 1.6 mm and the flow field of anode was designed in serpentine channels, which is completely consistent with the experimental flow field shape.In the experiment, the thickness of MEA after hot pressing is 0.36 mm and the proton exchange membrane with catalyst layers was scanned by SEM.As shown in Fig.4(c), the thicknesses of anode and cathode catalytic layers were 4 and 11 μm, respectively.The thickness of membrane was 15 μm and the thickness of GDL was 0.165 μm.The thickness of MEA structures in the model was designed by the data obtained in the experiment.

As shown in the Fig.3,lines of AA1 and BB1 were established in the center of the most middle channel (the 7th channel from the left)to study the oxygen,water and velocity distribution at different positions and different interfaces in PEMFC.

Fig.3. Schematic diagram of cathode flow channel: (a) WPFF (maximum channel depth H is 1 mm, minimum channel depth h is 0.4 mm.The channel curve is y = 0.3cos(2x)) and (b) SPFF (the channel depth is constant value of 1 mm).

3.2.Governing equations

Assumption [13,14]:

(1) Operation is assumed to be steady-state conditions.

(2) All gases are considered as ideal gas.

(3) The flow is incompressible and laminar flow.

(4) GDL, CL and proton exchange membrane are treated as isotropic porous media

(5) The PEMFC temperature is constant value.

3.2.1.Conservation equation

Mass continuity equation [15]:

whereSmis the mass source term and for all the zones is zero.

Momentum continuity equation [16]:The terms on the left side of the equation are unsteady term and convective term, respectively.The first and second terms on the right are diffusion terms and the third term is momentum source term.In the region of gas diffusion layer, Eq.(3) can be reduced to Darcy’s law [17]:

Energy conservation equation [18]:

The right side of Eq.(6)in proper order are ohmic heating,heat of formation of water, electric work and latent heat of water.

Species conservation equation [18]:

whereSiis the species source term.

For the consumption of reactants which are on the surface of catalyst layer, in the region of channel, gas diffusion layers and membrane:

For catalyst layers:

is the mass diffusivity of speciesiat corresponding saturation, pressure and temperature.

Current conservation equation [19-22]:

The electrochemical reaction center is used to calculate the rate of hydrogen oxidation and oxygen reduction.These electrochemical reactions take place at the interface between the catalytic layer and the proton exchange membrane.The driving force of the electrochemical reaction is the surface overpotential, which is the difference between the phase potential of solid and the phase potential of membrane.The solid phase contains collector,gas diffusion layers and catalyst layers in Eq.(13) account the electrons and the membrane phase contain proton exchange membrane and catalyst layers in Eq.(14) account the protons.

The source terms of current conservation equation is called exchange current density,which is calculated by Eqs.(19)and(20)

The activation loss η is the driving force to the reaction.

where theVocis the open circuit voltage, which is calculated from Nernst equation:

3.2.2.Liquid water formation

The water vapor will liquefy into liquid water at low operate temperature(＜100°C),especially at high current density.The generated liquid water will keep the proton exchange membrane hydrated and too much liquid water will block the gas diffusion layers, which reduce the diffusion rate and the effective reaction area of the catalytic layers.In order to know more about the liquid water effects of fuel cells, saturation model is used to model the formation and transport of liquid water.The conservation is as follows [23]:

The source termrwis the condensation rate which is modeled as:

For highly-resistant porous zones, the convective term in Eq.(24) can be replaced by capillary diffusion term.

wherepcis the capillary pressure,which is computed as a function of liquid saturation.

where μlis the viscosity of liquid.As for two-phase mixture of gas and liquid:

where the parameter g represents the gas,slis the water saturation,which defined as the ratio of the volume of liquid water to the pore volume in the porous materials.

And satisfy the following equation:

The equation of water flux in membrane is as follow [24]:

λ is the water content

whereais the water activity that is defined as:

3.3.Computational domain and procedure

The PEMFC model was established by the software SOLIDWORKS and the grid was divided by ANSYS mesh, as shown in Fig.4(a) (The collectors are omitted in Fig.4).Due to the regular structure of PEMFC, the whole model adopted hexahedral structured grid.The whole computational domain contains 1,372,880 grids for WPFF.The grid independence was tested by reducing and increasing the grid elements by 30%and 40%.The results show that the average oxygen mass fraction difference on each interface was less than 1%,as shown in Table 1.The difference caused by the grid itself can be ignored.

The calculation model was based on the electronic system module for model 3 in Fluent.The calculation area includes nine parts including anode and cathode collectors, flow fields, GDLs, CLs and proton exchange membrane.The geometry dimension is 34 mm × 34 mm × 4.36 mm forX,Y,Zdirection.Fig.4(b) shows the grid division of the cross section.The five parts of GDLs, CLs and membrane as a one part to divide mesh and the interface between them are interiors.The flow fields and collectors were independent parts for grid division.The surface between the channels and GDLs are interface,the surface between the collectors and channel areas same.The boundary of the entrance of the anode and cathode are mass-flow inlet and the outlets are pressure-out.The solver adopts a pressure-based and simple separation algorithm.The gradient calculation is Green-Gauss cell based.For pressure interpolation, the standard is selected.The first order upward is selected for density, momentum, H2, O2, energy, electric potential,proton potential, water saturation, and water saturation.The calculation conditions are consistent with the experiment for stoichiometric ratio of H2/O2which is 2/2, the PEMFC temperature is 65 °C, the humidity 100% and the outlet pressure is atmospheric pressure.The properties and parameters are list in Table 2.

Table 1The influence of the number of grids on the simulation results for WPFF

Table 2Properties and parameters

Fig.4. Meshing of the computational domain:(a)enlarged view of PEMFC model,(b)meshing of cross view,and(c)partial enlarged view of coated-membrane with the SEM diagram compared with calculated size.

4.Results and Discussion

4.1.Polarization and power density curves

Experiment and simulation of polarization curve and power density data for the SPFF and WPFF based PEMFC are shown in Fig.5.It can be seen from the experiment that at the same current density of 4.9 A·cm-2at 0.5 V was obtained for the WPFF, which was higher than the SPFF (4.46 A·cm-2@ 0.5 V).The SPFF based PEMFC shows a peak power density of 2.23 and 2.53 W·cm-2for WPFF,which was 13.45%than that of SPFF.Moreover,in this study,the mathematical model results were used to validate the experiment data for SPFF and WPFF based PEMFC.It can be found that the simulation results of polarization curve and power density curve matched well with the general model of proton exchange membrane fuel cell results in Fig.5.

Fig.5. Comparison of experimental data and simulation data at 65 °C for SPFF and WPFF: (a) polarization curve and (b) power density curve.

4.2.Oxygen concentration distribution

Fig.6 shows the distribution of mass fraction of O2in PEMFC at 0.5 V, in which we can know more about the reactant transporta-tion in PEMFC.Fig.6(a) and (b) show the distribution of oxygen concentration on the upper wall of the flow fields for SPFF and WPFF.The two types of flow fields show the same distribution law which is similar to the results of previous studies [26,27].The concentration of oxygen in the parallel flow channel nearing the inlet and the outlet of the flow field is higher than that in the middle of flow channel.The reason is that the gas preferentially passes through the beginning and end flow channel in the parallel flow field.In the middle region of the flow fields the oxygen concentration decrease along the direction from the inlet to the outlet.The concentration of oxygen in the middle and lower part of the flow field is the lowest, which is attributed to the consumption of oxygen in the oxygen reduction reaction.The mass transfer in the PEMFC largely depends on the spontaneous mass transfer from the high concentration region to the low concentration region due to the concentration gradient.The distribution of oxygen concentration in the WPFF is higher than SPFF.The average oxygen distribution in the SPFF and WPFF are 0.587 and 0.603,respectively.The WPFF can generate a higher concentration gradient and enhance the transportation of reactants.

Fig.6(c)and(d)are the distribution of oxygen concentration at the interface between the channel and the GDL.The distribution of oxygen concentration in the flow channel led to the same distribution law at this position.In the flow fields,there is a peak of oxygen concentration at the corner of each bend.This is because the air flow is prone to turbulence at the corner of the bend, resulting in high pressure drop, forced convection and high oxygen content.At the inlet, the difference of oxygen concentration distribution between the two type channels is not obvious.However, for the outlet section,the oxygen concentration in the SPFF is significantly lower than that in the WPFF,which would lead to uneven distribution of the concentration on the surface of the catalytic layer.The average value of oxygen concentration on the surface between channel and GDL for SPFF and the WPFF are 0.171 and 0.209,respectively.The oxygen concentration distribution changed abruptly in the narrow area.In contrast, the fuel distribution in the SPFF is relatively uniform.All these further prove improved oxygen transport into the porous GDL with WPFF.

Fig.6(e)and(f)shows the oxygen concentration distribution on the surface of GDL-CL with an average oxygen concentration distribution of 0.120 and 0.162 for SPFF and WPFF, respectively.Fig.7 shows the oxygen concentration curve of AA1 and BB1 on the channel-GDL and GDL-CL interface(see Fig.3 for the specific position).The results indicate that due to the influence of electrochemical reaction,the oxygen distribution at the entrance of the channel is higher than that near the outlet.At the channel-GDL interface,the oxygen concentration of WPFF flow field is higher than that of SPFF flow field at all positions.At the GDL-CL interface,the oxygen concentration of WPFF flow field presents an obvious mutation trend.This is because the forced convection effect of the WPFF transfer higher fuel to the surface of the catalytic layer, which enhance the mass transfer efficiency and increase the reaction rate of the catalytic layer.

4.3.Velocity distribution

Fig.8 shows the surface velocity distribution of flow channel and gas diffusion layer.The area with higher velocity is concentrated in the first channel connected with the inlet and outlet of flow field.The principle of priority leads the gas preferentially passing through the flow channel with smaller resistance due to the larger resistance at the corner of parallel flow channel.The velocity distribution laws in SPFF and WPFF are similar, while the uniformity of velocity distribution in the whole narrow region of the WPFF is higher than that in the SPFF,which would make the fuels distribution more uniform.In addition, the gas flow rate for WPFF in the same position is higher than that in the SPFF due to the narrow region of the wave channel, especially in the middle region of the channel.Fig.8(c) shows the velocity curves of AA1 and BB1 on the channel-GDL interface.The concave convex structure of WPFF channel led to wavy gas velocity distribution, which is larger than that of SPFF.

Fig.9 shows the velocity distribution of interface AA1 and BB1 perpendicular to gas diffusion layer in the interface of channel and GDL.The PEMFC with WPFF causes fuel exist vertical to gas diffusion layer in narrow area, and the velocity in gas diffusion layer vertical to catalyst layer is larger than that in SPFF.The result shows that the novel structure in WPFF can introduce forced convection in the plane direction,which greatly promotes the oxygen transportation and water removal.

4.4.Water removal effect

The proton exchange membrane must be appropriately hydrated in operating process.The low water content of polymer electrolyte may cause excessively low conductivity.A large amount of liquid water forms on the surface of the cathode catalytic layer and then flows into the channel through the gas diffusion layer.PEMFC produce more water at higher current density,which may cause the water flooding[28].The diffusion coefficient of oxygen in air is four orders of magnitude larger than that in liquid water, so the behavior of liquid water is another key point to determine the oxygen transfer rate.The phenomenon of flooding will decrease the performance of fuel cells, so the water removal rate of flow field and the components of MEA are very important.

Fig.10(a)and(b)shows the distribution of water mole fraction in the flow field.The water distribution in flow channel closed to the inlet and outlet is less and in the middle of the flow fields is the most, which shows that the water decreased alone the middle to right and left two sides in turn.This is due to the speed distribution which is analyzed in the part of the velocity distribution and the water removal rate in the fast velocity area is higher.Compared with the two type channels, the water removal rate of WPFF is higher than that of SPFF especially for the part with the lowest velocity.

Fig.6. Distributions of mass fraction of O2 in PEMFCs at 0.5 V: (a and b) in SPFF and WPFF, respectively; (c and d) at the channel-GDL interface for SPFF and WPFF,respectively; (e and f) at the GDL-CL interface for SPFF and WPFF, respectively.

Fig.10(c)and(d)shows the water mass concentration distribution at the interface between the flow channel and the gas diffusion layer.The gas diffusion layer is an important part of the fuel that transfer the reactants to the surface of the catalytic layer.The increase of liquid water on the surface would lead to the poor transmission of the gas into the gas diffusion layer,resulting in the starvation of fuels and the performance of the PEMFC is reduced.The liquid water on the surface of the GDL in the WPFF is significantly lower than that in the SPFF,which is due to the larger velocity distribution.

Fig.7. Mass fractions of O2 at the section of A-A1 (WPFF) and B-B1 (SPFF) at the channel-GDL and GDL-CL interface related to 0.5 V.

Fig.10(e)and(f)shows the water concentration distribution at the interface between the gas diffusion layer and the catalytic layer.Too much liquid water on the surface of the catalytic layer will lead to flooding of the catalytic layer and affect the electrochemical reaction rate.The WPFF has a better removal effect on the liquid water on the surface of the catalytic layer.

Fig.11 shows the curve of the water concentration at AA1 and BB1 on the interface of channel-GDL and GDL-CL with the length of the channel.The result shows that the water concentration at the bottom of the channel is higher than that at the top because of the gravity of the water.The water concentration of WPFF at different positions on the two interfaces is lower than that of SPFF.

Fig.12 is a schematic diagram of saturation at 0.5 V.The gas diffusion layer and catalytic layer are porous structures and the accumulation of liquid water in the pores will also affect gas transmission.Therefore, it is important to study the saturation of liquid water in the two porous medium.Fig.12(a) and (b) shows the saturation of SPFF and WPFF at the interface of gas diffusion layer and flow channel.In the middle and lower areas of the GDL,the saturation of the GDL for SPFF is slightly higher than that of the WPFF but compared with the overall saturation, the saturation in the diffusion layer in the SPFF(0.299)was higher than that in the WPFF (0.262).When the pores of the catalytic layer were flooded by water, the catalytic area would be reduced.Fig.12(c)and (d) show the surface saturation of the catalytic layer and GDL.The average saturation values of the WPFF and SPFF for CL are 0.268 and 0.301, respectively.It can be seen that the WPFF is conducive to the removal of water in the pores of the GDL and catalytic layer.

Fig.8. Local flow velocity in the cathode flow fields at 0.5 V for the Channel-GDL interface at: (a) SPFF, (b) WPFF, (c) the section of A-A1 (WPFF) and B-B1 (SPFF).

Fig.9. The velocity in the Y-axis direction on the cathode flow channel and GDL with WPFF and SPFF at 0.5 V.

Fig.10. Distribution of mass fraction of H2O in PEMFCs at 0.5 V:(a and b)are distribution of mass fraction of H2O in SPFF and WPFF,respectively;(c and d)are distribution of mass fraction of H2O at the channel-GDL interface for SPFF and WPFF, respectively; (e and f) are distribution of mass fraction of H2O at the GDL-CL interface for SPFF and WPFF, respectively.

Fig.11. Mass fraction of H2O at the section of A-A1 (WPFF) and B-B1 (SPFF) at the Channel-GDL and GDL-CL interface related to 0.5 V.

Fig.13 is the schematic diagram of water distribution in cathode channel of transparent PEMFC under the condition of stable voltage test, and the EIS under this condition is also tested.The results show that the voltage stability of PEMFC with WPFF is better, the voltage can be maintained stable at low stoichiometric ratio.It can be seen from the Fig.13(a)and(b)that the water injection of the WPFF is less, and it is less prone to flooding.The water column distribution in the channel shows a trend of high in the middle and low on both sides.This result is similar to Fig.10,which proves the accuracy of the simulation.Fig.13(e) shows the electrochemical impedance spectroscopy (EIS) after running at the same current density for the same time.It can be seen from the result that in the low frequency region, a second arc appears in the SPFF, which is the concentration polarization phenomenon caused by water flooding.

4.5.The mechanism of the WPFF based cells improving the performance of PEMFCs

The hydrogen loses electrons at the anode catalytic layer which passes through the proton exchange membrane to the surface of the cathode catalytic layer react with oxygen and electrons from the external circuit to generate water and current.Fig.14 shows the current density distribution on the surface of the cathode CL and GDL.The electrochemical reaction mainly occurs in the area where the fuel flows.There is almost no current in the catalytic layer area below the rids.This is because where has no fuel gas,but some of the gas will diffuse to the catalytic layer under the rids due to the concentration gradient,while the irregular channel size in the WPFF enhanced the forced convection effect and the transmission of fuel gas, which generated higher electrons under rids(as in the red wire frame) and transmits them to the cathode catalytic layer along the external circuit.After that reacts with oxygen generated higher current.In addition, the WPFF of PEMFC also enhanced the uniformity of current density distribution.

Fig.12. Saturation of porous medium in PEMFCs at 0.5 V:(a and b)are the saturation of GDL at the channel-GDL interface for WPFF and SPFF,respectively:(c and d)are the saturation of CL at the GDL-CL interface for WPFF and SPFF, respectively.

Fig.13. The experiment results of water distribution in channel for WPFF and SPFF:(a and b)are the voltage stability of SPFF and WPFF for different stoichiometric ratio in cathode at 4.5 A·cm-2;(c and d)are the visualization of liquid water in cathode flow channels for SPFF and WPFF at 4.5 A·cm-2 and λ=2,respectively; (e)is the EIS for the transparent PEM fuel cell under SPFF and WPFF.

The distribution of hydrogen, oxygen and liquid water in the internal components of the PEMFC is shown in Fig.15.Hydrogen and oxygen were distributed over the GDL through the gas channel and diffused to the surface of the Pt carbon catalyst through the pores, which react and generate liquid water and electrons.Electrons generate current through the external circuit.It can be seen from Fig.15 that the narrow area inside the wave channel enhanced the distribution of oxygen on the surface of the GDL and changed the direction of speed to the inside of the GDL.Such velocity change can better remove the liquid water in the pores of the gas diffusion layer and the surface of the catalytic layer, which reduce the impact of water flooding on the performance of the PEMFCs.

Fig.15. The mechanism chart of enhancing the PEMFC performance with the WPFF.

Fig.14. Distribution of current density at the GDL-CL interface in PEMFCs at 0.5 V: (a) is the SPFF and (b) is the WPFF.

5.Conclusions

In this study,a parallel wave flow field with the change of crosssectional area was designed to improve the performance of PEMFC.From these three aspects of oxygen transportation, liquid water removal rate and current density distribution to study the mechanism of WPFF enhancing the performance of fuel cell by combining experimental and simulation research methods.The experimental results show that the performance of WPFF based PEMFC in high current density region is better than that of SPFF.The mechanism of WPFF based PEMFC enhanced the performance of PEMFC was studied by building a three-dimensional, steady, multi-phase,isothermal, laminar model.The result reveals the reason is that the forced convection in the wave channel enhances the transformation of reactants, increased the removal efficiency of water in the cell and the uniformity of current density distribution studied by simulate method.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was supported financially by National Key Research and Development Program of China (2017YFB0103001).

Nomenclature

cimass fraction of speciesi

cpspecific heat capacity, J·kg-1·K-1

crcondensation rate constant, s-1

Etheoretical potential, V

FFaraday’s constant, C·mol-1

Icurrent density, A·m-2

Jvolumetric current density, A·m-3

Ktemperature, K

keffeffective thermal conductivity, W·m-1·K-1

kpGDL permeability, m2

Mmolar mass, kg·mol-1

Ppressure, Pa

pccapillary pressure, Pa

RUniversal gas constant, J·mol-1·K-1

RohmOhmic resistant,Ω

rsexponent of pore blockage

Ssource term

ssaturation

uvelocity, ms-1

Vivolume of speciesi, m3

xH2O mole fraction of H2O

[H2] H2concentration, kg·mol·m-3

[O2] O2concentration, kg·mol·m-3

α concentration exponent

γ exchange coefficient

γp,γtexponent factors

ε porosity

η overpotential, V

θ contract angle, (°)

μ dynamic viscosity, N·s·m-2

ρ density, kg·m-3

σ conductivity,Ω-1·m-1

? phase potential, V

Superscripts

an anode

cat cathode

g gas phase

lliquid phase

mem membrane phase

sol solid phase

WV water vapour