Numerical and experimental investigation of baffle plate arrangement on proton exchange membrane fuel cell performance

Journal of Power Sources 457 (2020) 228034

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Numerical and experimental investigation of baffle plate arrangement on proton exchange membrane fuel cell performance Xuefeng Wang , Yanzhou Qin *, Shiyu Wu , Xiang Shangguan , Junfeng Zhang , Yan Yin ** State Key Laboratory of Engines, Tianjin University, Tianjin, China

H I G H L I G H T S

� Staggered trapezoid baffle plate flow field is proposed to enhance fuel cell performance. � The flow field is investigated using a fuel cell model with Forchheimer’s inertial effect. � Superiority of the proposed flow field is validated numerically and experimentally. � Staggered trapezoid baffle plate flow field performs well at high humidity. A R T I C L E I N F O

A B S T R A C T

Keywords: Proton exchange membrane fuel cell Staggered trapezoid baffle plate Reactant uniformity Water management Pressure drop

Reactant distribution and water management are critically important to the performance of proton exchange membrane fuel cell (PEMFC). The application of baffle plate is an effective way to improve reactant transport and water removal in the porous electrode of PEMFC. In this study, a three-dimensional multiphase PEMFC model is developed with Forchheimer’s inertial effect in the porous electrode to better simulate the convective flow induced by the baffle plate, which is validated experimentally. Three kinds of flow field design including the conventional parallel flow field, parallel trapezoid baffle plate (PTBP) and staggered trapezoid baffle plate (STBP) flow fields are investigated both numerically and experimentally, on the PEMFC mass transport char­ acteristics and performance. It is found that both the PTBP and STBP flow fields form the over-block-convection around the baffle plate which is beneficial to mass transfer from channel to electrode. The STBP flow field further forms the over-rib-convection (or cross flow) induced by a stable pressure gradient between the adjacent flow channels. The cross flow stem from the STBP arrangement further improves the uniformity of reactant distri­ bution and removes the excess liquid water in the porous electrode, and hence enhances the PEMFC performance in a large range of operating conditions.

1. Introduction Proton exchange membrane fuel cell (PEMFC) is an electrochemical device which can directly convert the chemical energy of fuel and oxidant into electricity. High energy conversion efficiency, fast response and zero-emission of PEMFC have made it popular in the automobile application. However, there still remain many challenges to expand its application, including the cost, performance limitation and durability. Non-ideal flow field can result in non-uniform reactant distribution. The PEMFC working area distributed with more reactant has fast electro­ chemical reaction and produces a large amount of water which will easily accumulate in the porous electrode and block the reactant

transport passage, which in turn damages the reaction. On the other hand, the working area with less reactant suffers from fuel starvation, leading to poor fuel cell current density, catalyst sintering and mem­ brane degradation. Therefore, the design of flow field is crucial for the performance and durability of PEMFC [1,2]. There are mainly three types of PEMFC conventional flow fields, and each has its own characteristics. The parallel flow field produces a low pressure drop but easily suffers from water flooding, the serpentine flow field shows better performance in water removal but has higher pressure drop and the interdigitated flow field has the best water removal ability and fuel cell performance but the pressure drop is extremely large compared with the other two types of flow fields [3]. Due to its

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Y. Qin), [email protected] (Y. Yin). https://doi.org/10.1016/j.jpowsour.2020.228034 Received 30 September 2019; Received in revised form 7 March 2020; Accepted 12 March 2020 Available online 19 March 2020 0378-7753/© 2020 Elsevier B.V. All rights reserved.

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Fig. 1. Schematic of the baffle plate geometry (a), the PTBP and STBP flow fields (b) and the detailed cross-sectional views (c).

importance, a lot of work has been done on the development of PEMFC flow field [4]. Belcor et al. [5] combined the structure of parallel flow field with serpentine flow field and found the complex flow field could obtain more uniform reactant distribution. A novel design combining the parallel flow field with interdigitated flow field was also proposed, and its advantages on reactant distribution in the porous electrode and fuel cell performance were experimentally verified [6]. Some re­ searchers paid more attention on the detailed design parameters of the flow channel. For instant, the influence of the channel width [7,8], depth [8,9], length [8,10], number [11,12] and header width [10,13] on water and reactant distribution were investigated and optimized ac­ cording to the fuel cell performance and pressure drop. The tapered flow channel was also proposed to improve the water management, and its angle was shown to have crucial influence on liquid water removal [14, 15]. Song et al. [16] compared water removal with various flow field designs and emphasized its importance on the durability of fuel cell. In addition, some research works were focused on the bionic channel de­ signs which were inspired from the biological systems like the structure of plant body [17], blood circulation system [18–20] and leaf venation [21–23], considering their superiority in mass transport. Iranzo et al. [24] reviewed the development of biomimetic designs of bipolar plate for PEMFC and spotted that the biomimetic designs had not yet achieved their full potential. Nevertheless, the bionic structures are more difficult to fabricate and the gas supply system also needs further improvement to be consistent with the bionic flow field. Moreover, the topology optimization method was proposed by Secanell et al. [25] to improve the flow field design in fuel cell. Kim and Sun [26] applied the topology

optimization method to find the optimum flow channel route. Reza et al. [27] improved the bionics flow field using the topology optimization method, and better reactant distribution and cell performance were achieved with this method. Recently, adding baffle plates in the flow field has been proved to be an effective strategy to enhance the fuel cell performance which is inspired from the design of the interdigitated flow field [28,29]. Re­ searchers have creatively applied partially blocked baffle plates to obstruct the reactant transport in various positions of channel rather than only the end of channel like the interdigitated flow field. The convective flow induced by the partially blocked baffle plate not only removes excessive liquid water but also forces reactant to enter the porous electrode [30]; and the issue of high pressure drop is also miti­ gated compared with fully blocked channel [31]. Based on the design of partially blocked baffle plate, the detailed parameters of baffle plate such as the height [32,33], width [34,35] and number [36,37] were investigated, especially focusing on the influence on the reactant dis­ tribution and water removal. The baffle plate shape design is also crucial. Perng et al. [38] developed a trapezoid baffle plate with the sloped angle of 60� and found the PEMFC produced higher net power and lower pressure drop than the rectangular baffle plate. The baffle plates were also applied in the tapered flow channel to further enhance the water removal ability [39,40]. Fairshaped structure has also been applied in the baffle plate design. The wavy cathode surface was designed out to optimize the pressure drop and PEMFC performance [41, 42]. A gradient-depth wavy cathode flow field is further proposed to improve the mass transport efficiency in both the in-plane and 2

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as the repetitive unit in the computation. The computational domain consists of the bipolar plate, flow channel, gas diffusion layer (GDL), catalyst layer (CL) and membrane. Four trapezoid baffle plates distribute evenly along the X direction in each channel for the PTBP flow field, and the baffle plates are staggered in the adjacent channels for the STBP flow field.

Table 1 PEMFC design and operating parameters. Parameters

Values

Units

Thickness of membrane Thickness of CL Thickness of GDL Thickness of bipolar plate Active area Anode inlet temperature Cathode inlet temperature Anode inlet relative humidity Cathode inlet relative humidity Anode stoichiometric ratio Cathode stoichiometric ratio Porosity of GDL Porosity of CL Effective hydraulic diameter (dp) of GDL Effective hydraulic diameter (dp) of CL

0.0508 0.01 0.2 1.5 26.95 348.15 348.15 40%, 60%, 80%, 100% 40%, 60%, 80%, 100% 1.5 1.5, 2.0, 3.0 0.7 0.3 1.55 � 10 5 1.55 � 10 5

mm mm mm mm cm2 K K – – – – – m m

2.2. Assumptions and governing equations The PEMFC model is established based on the following assumptions: 1. The fuel cell is assumed to operate under steady-state condition. 2. The ideal gas law is used to calculate the gas mixture property. 3. The GDLs and CLs are assumed to be homogeneous and isotropic, and the membrane is impermeable to gas species. 4. The Butler-Volmer equation is employed to solve the electrochemical reactions in the CLs. 5. Constant temperature boundary conditions are applied in the PEMFC outer surfaces. 6. The thermal and electrical contact resistances are neglected.

through-plane directions, which could overcome the severe water flooding and oxygen starvation in the channel downstream region [43]. However, most studies of the baffle plate design are on the basis of the single flow channel, with few concerning the arrangement of baffle plate in the whole flow field. The baffle plate arrangement between the adjacent flow channels or in the whole flow field is also a crucial factor on the performance and durability of PEMFC. In addition, the hydraulic pressure loss in the porous electrode calculated by the Darcy’s law is no longer suited for the mass transport process in such a complex flow field where the convective transport mechanism is induced by the installation of baffle plate in the channel [44,45]. In such a situation, the For­ chheimer’s inertial effect is more practical than the Darcy’s law to depict the mass transport in the complicated flow field [45,46], especially under high current density conditions, but it has been ignored in most previous simulations of baffle plate effect in PEMFC. In the present study, a three-dimensional multiphase PEMFC model is developed with the Forchheimer’s inertial effect in the porous elec­ trode. Two sets of baffle plate arrangements in the flow field, the stag­ gered trapezoid baffle plates (STBP) and parallel trapezoid baffle plates (PTBP) shown in Fig. 1, are designed and investigated both numerically and experimentally. It is demonstrated that the STBP flow field can achieve high mass transport efficiency and PEMFC performance, since besides the over-block-convection effect induced by the installation of baffle plates, additional over-rib-convection (or cross flow) is formed between the adjacent channels and improves the reactant uniformity in the rib region.

Then, the conservation equations governing the mass, momentum, Table 2 Physical properties and input parameters.

2. Numerical simulation 2.1. Computational domain The computational domains of the PTBP and STBP flow fields are shown in Fig. 1. Due to the symmetric property along Z direction, two half adjacent channels together with the rib region in between are taken

Parameters

Values

Units

Faraday’s constant Liquid water density Universal gas constant

96487 1000 8.314

Ionomer volume fraction Equivalent weight of ionomer Membrane density Anode/cathode transfer coefficient GDL/CL contact angle Liquid water surface tension [50] Intrinsic permeability of GDL [50] Intrinsic permeability of CL [50] Bulk diffusivity of hydrogen

0.21 1.1

C mol 1 kg m 3 J mol 1 K 1 kg m 3 kg mol 1

1:055 � 10 4 ðT=333:15Þ1:5 � ð101325 =PÞ

m2 s

Bulk diffusivity of oxygen

2:265 � 10 4 ðT=333:15Þ1:5 � ð101325 =PÞ

m2 ​ s

Bulk diffusivity of water vapor Anode reference concentration of hydrogen [52,53] Cathode reference concentration of oxygen [52,53]

Same with H 2 ðanodeÞ or O 2 ðcathodeÞ

m2 s

56.4

mol m

3

3.39

mol m

3

1980 0.5/0.5 120/120 6.25 � 10

kg m

� 2

Nm

1.0 � 10

12

m2

1.0 � 10

13

m2

Fig. 2. Schematic of the bipolar plates carved with the conventional parallel flow field, PTBP and STBP flow fields. 3

3

1

1

1

1

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energy, species, liquid water, dissolved water, electron and ion transport are obtained and listed as follows. Gas mixture mass conservation: � r ⋅ ρg ! u g ¼ Sm (1) Gas mixture momentum conservation: � r⋅

ε

�

ρg ! u g! ug 2 ð1

¼

2

ϕl Þ

� � rPg þ μg r ⋅ r

� � !T �� ! ug ug þr εð1 ϕl Þ εð1 ϕl Þ � � ! �� 2 ug μg r r ⋅ þ Su 3 εð1 ϕl Þ

(2)

Energy conservation: h i � � �eff eff r ⋅ ρCp fl ! u T ¼ r ⋅ kfl;sl rT þ ST

(3)

Gas species: � � r ⋅ ρg ! u g Yi ¼ r ⋅ ρg Deff i rYi þ Si

(4)

Liquid water [47–49]: � r ⋅ f ρg ! u g ¼ r ⋅ ðρl Dl rϕl Þ þ Sl

(5)

where fis the interfacial drag coefficient which can be defined as: f¼

Kl μg Kg μl

(6)

where μg and μl are the dynamic viscosities of gas phase and liquid phase, respectively. Kl and Kg are the permeabilities of liquid phase and gas phase, respectively. Both of the permeabilities are associated with the liquid water volume fraction which can be depicted as: Kg ¼ K0 ð1

(7)

ϕl Þ4:0

(8)

Kl ¼ K0 ϕ4:0 l

where K0 is the intrinsic permeability of the porous electrode and ϕl is the liquid water volume fraction. Dissolved water: 0¼

ρmem EW

� r ⋅ Deff d rλd þ Sd

(9)

where ρmem ​ is the density of the membrane in dry condition, EW is the eff

equivalent weight of the membrane, Dd is the effective diffusivity of the dissolved water and λd is the membrane water content which can be defined as: λd ¼

EW

ρmem

(10)

Cd

where Cd is the dissolved water concentration. Charge conservation equation (Electrons): � 0 ¼ r ⋅ κeff e rϕe þ Se

(11)

Charge conservation equation (Ions): � 0 ¼ r ⋅ κeff ion rϕion þ Sion

(12)

eff

eff

where κe and κion are the effective conductivities of electrons and ions, respectively, which can be calculated by the Bruggeman correction [50, 51]. The source terms in Eqs. (11) and (12) are the electrical current densities generated in the CLs, which can be calculated by the ButlerVolmer equation [50–53]:

Fig. 3. Comparison of the PEMFC polarization curves between the numerical and experimental results with different anode/cathode stoichiometric ratios: (a) Conventional parallel flow field; (b) PTBP flow field; (c) STBP flow field.

4

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Fig. 4. Velocity distributions in the GDL (Y ¼ 1.55 mm) at the cell voltage of 0.6 V: (a) Conventional parallel flow field; (b) PTBP flow field; (c) STBP flow field. The stoichiometric ratio is 1.5/3.0 (anode/cathode) and the relative humidity is 100%/100% (anode/cathode).

Fig. 5. O2 concentration in the GDL/CL interface at the cell voltage of 0.6 V for different flow fields: (a) Schematic of the O2 concentration sampling line; (b) the O2 concentration for the channel region; (c) the O2 concentration for the rib region. The stoichiometric ratio is 1.5/3.0 (anode/cathode) and the relative humidity is 100%/100% (anode/cathode).

ja ¼ ð1

ϕl Þjref 0;a

C H2 CHref2

jc ¼ ð1

ϕl Þjref 0;c

C O2 COref2

ref

!0:5 � exp !�

� � 2F αa ηact RT

� � 4Fαa exp ηact RT

� exp � exp

2F αc η RT act

hydrogen (oxygen), αa (αc ) is the anode (cathode) transfer coefficient

��

4F αc η RT act

(13)

ref

ref

and j0;a (j0;c ) is the anode (cathode) reference current density [52,53]. Other parameter definitions and correlations involved in the PEMFC modeling, as well as the source terms of the conservation equations can be found in the previous study [50,51].

�� (14)

ref

where CH2 (CO2 ) is the anode (cathode) reference concentration of 5

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Journal of Power Sources 457 (2020) 228034

and the anode and cathode inlet mass flow rates are defined as: m_ a ¼

ρag ξa Iref A 2FCH2

; m_ c ¼

ρcg ξc Iref A 4FCO2

(19)

where ξ is the stoichiometry ratio, Iref is the reference current density, A is the active area of fuel cell and F is the Faraday’s constant. The molar concentrations of H2 and O2 are determined as: � � � � Pag RHa Psat Pcg RHc Psat C H2 ¼ ; CO2 ¼ ​ (20) RT0 RT0 where RH is the inlet relative humidity. The pressure outlet boundary condition is applied at the channel outlet. The temperatures of the inlet gas and surrounding walls are set the same with the PEMFC operating temperature. The electric potentials at the anode and cathode bipolar plate surfaces are defined as: ( ϕa;end ¼ Vrev Vcell ¼ ηtotal e (21) ϕc;end ¼0 e Fig. 6. Liquid water volume fraction along Z ¼ 1 mm line in the GDL/CL interface at the cell voltage of 0.6 V for different flow fields. The stoichiometric ratio is 1.5/3.0 (anode/cathode), and the relative humidity is 100%/100% (anode/cathode).

where Vrev , Vcell and ηtotal are the fuel cell reversible voltage, output voltage and voltage loss, respectively. The reversible cell voltage Vrev can be calculated as: � � RT0 1 in Vrev ¼ 1:229 0:9 � 10 3 ðT0 298:15Þ þ (22) lnPin H2 þ lnPO2 2 2F

2.3. Forchheimer’s inertial effect In the modeling of PEMFC with the conventional parallel flow field, the Reynolds number is small in the porous electrode, and the Darcy’s law accounted for the viscous effect is commonly deployed by researches to depict the hydraulic head loss [43–45,54], which is implemented in the momentum conservation equation (Eq. (2)) through a source term: Su ¼ rPviscidity ¼

μ! K

3 X

u ¼

Dij μuj

2.5. Numerical procedures and model validation method The three-dimensional multiphase model developed in the present study is implemented in a commercially used CFD software, ANSYS FLUENT 14.0. The user-defined functions (UDFs) are used to solve the updated equations and physical parameters. The SIMPLE algorithm is applied for the pressure-velocity coupling and the algebraic multigrid (AMG) method is used to accelerate the process of calculation. The second-order upwind difference scheme is used to discretize the equa­ tions in the model. Strict convergence criterion with the residual of 10 8 is applied for each variable. Additional monitors such as the liquid water volume fraction are also examined to ensure the convergence of computation. The grid density selected is typical in PEMFC simulation using similar models [50–53]. There are totally 99,180 grid cells used to discretize the computational domain with the STBP flow field including a majority of structural grids and a small part of unstructured grids around the trapezoid baffle plate. The grid independence has also been tested. The predicted current density and O2 concentration variations are less than 1% when doubling or halving the grid number. The experimental investigation is also carried out. The developed PEMFC model is validated by comparing the predicted and measured fuel cell polarization curves. All the PEMFC design and operating pa­ rameters are consistent with the experimental conditions for the purpose of model validation. The PEMFC design and operating parameters are listed in Table 1.

(15)

j¼1

where Dij is the Darcy’s coefficient. The Darcy’s law is limited to the transport process with small Reynolds number. However, the Reynolds number increases significantly due to the strong convective flow induced by the trapezoid baffle plate. In this way, the inertial effect can be considerable with the viscous effect in the permeation process. And the Forchheimer’s inertial effect is more practical and suitable in such a complex flow field. The Forchheimer’s inertial effect can be calculated as [45,46]: 3 X

Cij

rPinertia ¼ j¼1

� � 1 ρuj juj 2

(16)

where Cij is the Forchheimer’s coefficient. As a consequence, the source term can be updated by combining the Darcy’s viscous effect with the Forchheimer’s inertial effect [45,46]: ! 3 3 X X 1 Su ¼ rP ¼ rPviscidity þ rPinertia ¼ Dij μuj þ Cij ρuj juj (17) 2 j¼1 j¼1

3. Experimental setup

Considering the property of the porous electrode, the Darcy’s coef­ ficient and Forchheimer’s coefficient can be written, respectively, as [44,45,55]: Dij ¼

dp2 ε3 3:5 ð1 εÞ ; ​ Cij ¼ dp 150 ð1 εÞ2 ε3

Three types of flow fields are designed by AutoCAD software and investigated. The STBP and PTBP flow fields together with the con­ ventional parallel flow field are designed and machined out on the flexible graphite plates, as shown in Fig. 2. The fuel cell has an active area of 26.95 cm2 (55 mm � 49 mm). Excluding the channel header width of 2.5 mm on both sides, the single channel length is 50 mm. The channel cross-sectional area is 1 mm � 1 mm. The thicknesses of the bipolar plate, GDL, CL and membrane are 0.5 mm, 0.2 mm, 0.01 mm and 0.0508 mm, respectively. The height of the trapezoid baffle plate is 0.8 mm which has been optimized in a previous study [50], and both the front and back sloping angles of the trapezoid baffle plate are 45�

(18)

where dp is the effective hydraulic diameter of the porous media. 2.4. Boundary conditions The mass flow inlet boundary is implemented for the channel inlet, 6

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Fig. 7. Comparison of the PEMFC performance with different flow fields: (a) polarization curve with the anode/cathode stoichiometric ratios of 1.5/1.5; (b) po­ larization curve with the anode/cathode stoichiometric ratios of 1.5/2.0; (c) polarization curve with the anode/cathode stoichiometric ratios of 1.5/3.0; (d) pressure drop and net power density with the anode/cathode stoichiometric ratios of 1.5/3.0.

considering the flow resistance and pressure distribution [51]. Four trapezoid baffle plates are distributed evenly in each channel for the PTBP flow field, and the baffle plates are staggered for a distance of 5 mm every other channel for the STBP flow field. Identical membrane-electrode assemblies (MEAs) are fabricated for all the flow fields by the Kunshan Sunlaite New Energy Technology Co. Ltd (China). The Nafion-212 membrane is selected as the PEM and the TGP-H-060 is chosen as the GDL which is attached with Pt/C catalyst (40%) of 0.24 mg cm 2 in the anode and Pt/C (40%) catalyst of 0.48 mg cm 2 in the cathode. After the PEMFC is assembled, the G60 fuel cell test system (Greenlight Innovation Company, Canada) is used to monitor and con­ trol the stoichiometric ratio, pressure, temperature, humidity and elec­ tric load of PEMFC, and to obtain the pressure drop across the channel and the fuel cell polarization curve. The humidities of anode and cath­ ode supply gases are set by controlling the dewpoint temperature in the respective humidifiers. The working temperatures of PEMFC for all the cases are set as 348.15 K. The anode stoichiometric ratio is fixed at 1.5, while the cathode stoichiometric ratio is varied from 1.5 to 3.0. The

measurements of the fuel cell polarization curve are started after all the working parameters maintain stable. The polarization curves are tested by current control with the current increment of 3 A per step (26 tested data points in total). And each data point is measured until it reaches stable for over 3 min. The channel inlet and outlet pressures at each test point are recorded to obtain the pressure drop. The test data are aver­ aged for three independent tests. The baffle plate flow fields commonly result in larger flow resistance and pressure drop compared with the conventional parallel flow field. It is more practical to investigate the PEMFC net power considering the pumping power for gas supply. The PEMFC net power equals the fuel cell output power subtracting the pumping power, which is calculated by the following equation: Wnet ¼ WFC

WP

(23)

where Wnet is the net power, WFC is the output power, WP is the pumping power. The pumping power will scale up with the current density for a fixed stoichiometric ratio. The pumping power can be defined as [42]:

7

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2 �γ 1 � m_ c CP T 6 Pin γ WP ¼ 4 η Patm

3 7 15

(24)

where ηis the pump efficiency, Pin is the measured inlet pressure, Patm is the atmospheric pressure and γis the specific heat ratio. 4. Results and discussion The numerical and experimental results are compared first to vali­ date the developed PEMFC model. Then, the PEMFC transport charac­ teristics with the PTBP and STBP flow fields are investigated numerically using the PEMFC model. Consistent with the experimental parameters, the PEMFC dimensions along X, Y and Z directions are 50.0 mm � 3.4708 mm � 2.0 mm, respectively, and the thicknesses of the bipolar plate, GDL, CL and membrane are 1.5 mm, 0.2 mm, 0.01 mm and 0.0508 mm, respectively. The baffle plate dimensions are also the same with the experiments. Finally, the PEMFC performance is experimen­ tally investigated and analyzed, under various stoichiometric ratios and relative humidities. 4.1. Comparisons between numerical and experimental results Comparisons between the numerical and experimental results are made for the purpose of model validation. All the geometric and oper­ ating parameters used in the numerical simulation are selected the same with the experimental test, as shown in Table 1. The key physical properties and input parameters for the PEMFC model are given in Table 2. Other parameters associated with the ion, electron, energy and liquid water transport are the same with those in Ref. [50]. Two sets of the anode/cathode stoichiometric ratios of 1.5/1.5 and 1.5/3.0 are used in the comparisons to obtain more convincing validation. The polari­ zation curves predicted by the numerical simulation agree well the experimental results for the conventional parallel flow field without baffle plate, the PTBP flow field and the STBP flow field, as shown in Fig. 3. Some discrepancy is noticed at low current density that the simulated cell voltage is higher than the experimental results. There are some potential reasons: PEMFC needs to be activated first, some liquid water may exist in PEMFC before the test, and the liquid water is diffi­ cult to be removed due to small mass flow rate at low current density, leading to the electrode blockage and lower cell voltage; In addition, the reactant permeation through the membrane reduces the fuel cell per­ formance, and this effect is more evident at low current density since voltage losses due to other effects are relatively small. These factors are not considered in the numerical work, causing the discrepancy between numerical and experimental results at low current density. In addition, besides the polarization curve, the operando localized electrochemical and transport characterization detections, despite not included in the present study, can also be employed for better model validation [56]. Liquid water distribution in operating PEMFC can be detected with X-ray computed tomography (X-CT) [57], soft X-ray [58], X-ray radiography [59] and neutron radiography [60]. Current and voltage distributions are measurable through printed circuit board (PCB), segmented current collector plates, Hall effect sensors, magnetic-flux detection, etc. [61]. Temperature distribution can be detected by intrusive method such as thermocouples [62] and nonin­ trusive infra-red (IR) thermal imaging [63]. Even simultaneous water, current and heat maps over the same area of operating PEMFC are measurable combining several detection techniques [64]. With the operando characterization of water, current and temperature distribu­ tions, transport process and electrochemical performance of PEMFC can be better explained which is also helpful to understand the degradation process of PEMFC [56], and reasonable inputs for the boundary condi­ tion and validation for PEMFC modeling are available.

Fig. 8. Effect of the relative humidity on the polarization curve of PEMFC with different flow fields: (a) the conventional parallel flow field; (b) the PTBP flow field; and (c) the STBP flow field.

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4.2. PEMFC transport characteristics

PEMFC performance is directly connected with the transport charac­ teristics, which will be tested and verified experimentally.

The transport characteristics of PEMFC with different baffle plate arrangements in the flow field are investigated numerically. Fig. 4 de­ picts the velocity distributions in the porous electrode of PEMFC with the conventional parallel, PTBP and STBP flow fields. It is found that the gas velocity is small and distributed uniformly for the conventional parallel flow field, as shown in Fig. 4(a). Due to the installation of baffle plate in the flow field, the local gas velocity is accelerated around the baffle plate, forming the so-called over-block-convection, as clearly shown in Fig. 4(b) and the previous studies [50] for the PTBP flow field. However, the over-block-convection only takes effect locally around the baffle plate, and the gas velocity is small in other places in the PTBP flow field. Enhancing the convective mass transport by increasing the baffle plate number is a possible solution, but it is only effective in a certain extent. The flow resistance becomes too high and the reactant transport is blocked severely, resulting in large pumping power and reactant starvation in the downstream of the flow field [50]. Staggering the baffle plates in the adjacent flow channels is another possible solution. As the baffle plates are staggered in the STBP flow field, the pressure distri­ bution is no longer the same and pressure difference is formed in the adjacent channels. Due to the existence of the pressure gradient in the adjacent channels, besides the over-block-convection, the reactant gas is also transported transversely in the STBP flow field shown in Fig. 4(c). This kind of transport feature is named cross flow or over-rib-convection. The cross flow helps remove liquid water and deliver reactant gas in porous electrode along the rib region, and its effect is globally in the whole flow field. The reactant distributions along the intersecting lines between the interface of GDL/CL and X–Y plane with different Z dimensions in the PTBP and STBP flow fields are presented in Fig. 5, with Z equal to 0 and 2 mm representing the channel region and Z equal to 1 mm representing the rib region, as shown in Fig. 5(a). Fig. 5(b) depicts the O2 concen­ tration along the X direction in the channel region. The O2 concentration enhancement can be observed obviously in the locations around the trapezoid baffle plates in both the flow fields. The two curves are overlapped due to the symmetric property in the PTBP flow field. The overall O2 concentration for the channel region, which is calculated by integrating the area beneath the curves, is a little higher in the STBP flow field than the PTBP flow field. As for the O2 concentration in the rib region shown in Fig. 5(c), it is much higher and distributed more uni­ formly with negligibly visible spikes in the STBP flow field. This can be well explained by the pressure and velocity distribution discussed earlier. In the PTBP flow field, the effect of over-block-convections are overlapped since the baffle plates are in the same position of the adja­ cent channels, and significant O2 concentration spikes appear in the curve; whereas the over-block-convections are staggered and the overrib-convections are formed in STBP flow field, making the O2 distrib­ uted more uniformly in the whole flow field. The significance of For­ chheimer’s inertial effect is also noticed in the modeling of O2 concentration distribution. The average O2 concentration in the channel region of PTBP flow field is found to be 3.6 mol m 3, while the value is 3.35 mol m 3 if only considering Darcy’s viscous effect. The present model considering Forchheimer’s inertial effect achieves 7.5% higher oxygen concentration, indicating its significant influence on the trans­ port characteristics. The produced liquid water tends to accumulate in the porous elec­ trode with non-uniform reactant distribution which can block the reactant transport in turn. Fig. 6 shows the liquid water distribution in the rib region of PTBP and STBP flow fields. Although the PTBP flow field shows more intensive liquid water reduction where the trapezoid baffle plates lie in due to the overlapped over-block-convection, the liquid water volume fraction is distributed more uniformly and lower in the STBP flow field due to the over-rib-convection effect. That verifies the good liquid water removal ability of the staggered baffle plate arrangement compared with the parallel baffle plate arrangement. The

4.3. PEMFC performance The experimental results of the polarization curve and pressure drop are the crucial parameters to assess the PEMFC performance with various flow fields. Fig. 7(a)-(c) show the PEMFC polarization and power density curves for the conventional parallel, PTBP and STBP flow fields with the anode/cathode stoichiometric ratios of 1.5/1.5, 1.5/2.0 and 1.5/3.0, respectively. It shows that the flow fields with baffle plates obviously improves the PEMFC performance at high current densities for all the three sets of stoichiometric ratios, due to the enhancement of reactant delivery and liquid water removal discussed earlier. The STBP flow field shows even better PEMFC performance than the PTBP flow field, due to the additional over-rib-convection which leads to more uniform reactant distribution. Greater cathode stoichiometric ratio im­ proves the transport characteristics, and hence enhancing the PEMFC performance for all the three flow fields. However, the performance difference among the three flow fields becomes smaller, as the cathode stoichiometric ratio increases. This is straightforward since adding baffle plates mainly takes effect in tough PEMFC working conditions like water flooding and reactant starvation, and greater cathode stoichio­ metric ratio helps to promote water removal, improve PEMFC working conditions and hence reduces the cell performance difference among the three flow fields investigated. Fig. 7 (d) compares the tested pressure drop and net power density with various flow fields for the largest cathode stoichiometric ratio of 3.0. The conventional parallel flow field has a lowest pressure drop, but also a lowest net power due to the inefficiency of mass transport. The STBP flow field has a lower pressure drop compared with the PTBP flow field, as the staggered baffle plate decreases the flow resistance by the over-rib-convection effect, and it has the greatest net power density And the maximum increments of the power density and net power density of the STBP flow field can reach 8.97% and 6.39%, respectively, compared with those for the conventional parallel flow field. And the enhancement can still reach 3.39% and 2.54%, respectively, compared with those for the PTBP flow field. This verifies the superiority of STBP flow field because of lower pressure drop and better reactant transport, compared with the PTBP flow field. The relative humidity is also a crucial parameter in the operation of PEMFC. Fig. 8 depicts the effect of relative humidity on the PEMFC performance for the three different flow fields. The PEMFC voltage and power density generally increase with the relative humidity in the pre­ sent study, because higher relative humidity can maintain a high level of proton conductivity which can enhance the fuel cell performance with lower ohmic loss. It is pointed out that higher relative humidity might lead to water flooding in the porous electrode. Actually, there is a tradeoff between proton conductivity in membrane and water flooding in the PEMFC water management. The effect of the relative humidity on PEMFC performance greatly depends on the PEMFC material type, design and operating conditions. For the conditions investigated, the STBP flow field generally performs better than the PTBP flow field, and they both perform better than the conventional parallel flow field. The maximum power density of the conventional parallel flow field, the PTBP flow field and the STBP flow field are 1.118, 1.172 and 1.193 W cm 2, respectively, with the relative humidity of 100%. However, there is an exception for the STBP flow field with the relative humidity of 40%, as shown in Fig. 8(c), for which the fuel cell performance decreases dramatically, lower than the performance of the other two flow fields. This phenomenon may be resulted from the dehydration of membrane, as the strong convection in STBP flow field takes away too much water in porous electrode.

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5. Conclusions

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In this study, staggered trapezoid baffle plate (STBP) flow field is proposed and the baffle plate arrangement is investigated on the transport characteristics and performance of the proton exchange membrane fuel cell (PEMFC). A three-dimensional multiphase PEMFC model is develop incorporating the Forchheimer’s inertial effect to better simulate the convective flow in the porous electrode induced by the baffle plate. The simulation results predict that the STBP flow field can form stable pressure drops between the adjacent channels which can drive the reactant to transport through the rib region (over-rib-con­ vection or cross flow). In this way, the O2 concentration in rib region is higher and more uniform compared with the parallel trapezoid baffle plate (PTBP) flow field. Meanwhile, the enhanced cross flow induced by the STBP flow field can also improve the liquid water removal in the electrode. The experimental results verify the superiority of STBP flow field due to the lower pressure drop and higher power density compared with the PTBP flow field. The maximum net power enhancement of STBP flow field can reach 6.39% and 2.54%, compared with the con­ ventional parallel flow field and STBP flow field, respectively. The PEMFC performance increases with the relative humidity (RH) for the three types of flow fields. The STBP flow field performs best for the RH of 60%, 80% and 100% investigated, while it performs worst for the RH of 40%, possible due to the membrane dehydration induced by strongest convection of the STBP flow field. 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. CRediT authorship contribution statement Xuefeng Wang: Software, Methodology, Investigation, Data cura­ tion, Writing - original draft. Yanzhou Qin: Conceptualization, Meth­ odology, Formal analysis, Writing - review & editing, Supervision. Shiyu Wu: Software, Investigation. Xiang Shangguan: Investigation, Visualization. Junfeng Zhang: Investigation, Formal analysis. Yan Yin: Resources, Formal analysis, Supervision. Acknowledgement This work is supported by the National Natural Science Foundation of China (Grant No. 51706153) and the Natural Science Foundation of Tianjin, China (Grant No. 17JCZDJC31000). References [1] X. Li, I. Sabir, Review of bipolar plates in PEM fuel cells: flow-field designs, Int. J. Hydrogen Energy 30 (2005) 359–371. [2] K. Huseyin, M.F. Orhan, Flow field bipolar plates in a proton exchange membrane fuel cell: analysis & modeling, Energy Convers. Manag. 133 (2017) 363–384. [3] A. Aiyejina, M.K.S. Sastry, PEMFC flow channel geometry optimization: a review, J. Fuel Cell Sci. Technol. 9 (2012), 011011-1. [4] P.J. Hamilton, B.G. Pollet, Polymer electrolyte membrane fuel cell (PEMFC) flow field plate: design, materials and characterisation, Fuel Cell. 10 (2010) 489–509. [5] P.M. Belchor, M.M.C. Forte, Parallel serpentine-baffle flow field design for water management in a proton exchange membrane fuel cell, Int. J. Hydrogen Energy 37 (2012) 11904–11911. [6] N.J. Cooper, T. Smith, A.D. Santamaria, J.W. Park, Experimental optimization of parallel and interdigitated PEMFC flow-field channel geometry, Int. J. Hydrogen Energy 41 (2016) 1213–1223. [7] B.H. Lim, E.H. Majlan, W.R.W. Daud, M.I. Rosli, T. Husaini, Numerical analysis of modified parallel flow field designs for fuel cells, Int. J. Hydrogen Energy 42 (2017) 9210–9218. [8] A.P. Manso, F.F. Marzo, J. Barranco, X. Garikano, M.G. Mujika, Influence of geometric parameters of the flow fields on the performance of a PEM fuel cell. A review, Int. J. Hydrogen Energy 37 (2012) 15256–15287.

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Nomenclature

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A: active area of fuel cell (m2) C: molar concentration (mol m 3) or Forchheimer’s coefficient (m 1) Cp: specific heat (J kg 1 K 1) dp: effective hydraulic diameter of porous media (m) D: mass diffusivity (m2 s 1) or Darcy’s coefficient (m 2) EW: equivalent weight of membrane (g mol 1) f: interfacial drag coefficient F: Faraday’s constant (C mol 1) h: baffle plate height (m) I: current density (A cm 2) jo: volumetric exchange current density (A m 3) k: thermal conductivity (W m 1 K 1) K: permeability (m2) K0: intrinsic permeability (m2) L: baffle plate length (m) _ mass flow rate (kg s 1) m: P: pressure (Pa) R: universal gas constant (J mol 1 K 1) RH: relative humidity (%) S: source term T: temperature (K) T0: volume averaged cell temperature (K) u, ! u : velocity (m s 1) V: electrical potential (V) W: power (W) Y: mass fractionGreek Letters α: transfer coefficient or baffle plate left angle (º) β: baffle plate right angle (º) γ: specific heat ratio ε: porosity η: over potential (V) or pump efficiency κ: electrical conductivity (S m 1) λ: water content in ionomer μ: dynamic viscosity (kg m 1 s 1) ξ: stoichiometry ratio ρ: density (kg m 3) ϕ: electrical potential (V) or liquid water volume fractionSubscripts a: anode act: activation atm: atmospheric c: cathode cell: fuel cell d: dissolved water eff: effective e: electronic end: bipolar plate end surface FC: fuel cell fl: fluid phase g: gas phase H2: hydrogen i, j: the i th and j th components in: inlet inertia: inertia ion: ionic l: liquid water m: mass (for source term) mem: membrane net: net O2: oxygen P: pumping ref: reference state rev: reversible sat: saturation sl: solid phase T: energy (for source term) total: total u: momentum (for source term) viscidity: viscidity

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