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A dot matrix and sloping baffle cathode flow field of proton exchange membrane fuel cell
Journal of Power Sources 434 (2019) 226741
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A dot matrix and sloping baffle cathode flow field of proton exchange membrane fuel cell Bowen Wang a, Wenmiao Chen b, Fengwen Pan b, Siyuan Wu c, Guobin Zhang a, Jae Wan Park c, Biao Xie a, Yan Yin a, Kui Jiao a, * a b c
State Key Laboratory of Engines, Tianjin University, 135 Yaguan Road, Tianjin, 300350, China Weichai Power Co. Ltd., 197A Fushou St. E., Weifang, 261016, China Department of Mechanical and Aerospace Engineering, University of California, Davis, One Shields Ave., Davis, CA, 95616, USA
H I G H L I G H T S
� A novel dot matrix and sloping baffle cathode flow field of PEMFC is designed. � The features of the plate include a large fluid domain and air guidance. � The matrix flow field is evaluated by full cell model and VOF model. � The matrix flow field fits high current density demand of PEMFC well. � Adequate contact area between the plate and GDL for current conductor is critical. A R T I C L E I N F O
A B S T R A C T
Keywords: PEMFC Flow field design Dot matrix Sloping baffle Three-dimensional full cell model VOF model
A novel dot matrix and sloping baffle flow field plate for proton exchange membrane fuel cell (PEMFC) cathode is designed. The plate consists of dispersive and arrayed blocks with sloping angles as shoulders. Features of the plate include a large fluid domain, and air guidance in two directions is achieved by sloping sides of the block. The cell output performance, internal transport process and liquid water removal process of the PEMFC with the matrix flow field are numerically investigated by three-dimensional two-phase full cell model and volume of fluid (VOF) model. The simulation results show that compared with the parallel and serpentine flow field, the matrix flow field can achieve high cell output performance by both improving oxygen supply to gas diffusion layer (GDL) and uniform distribution. Comparing five matrix flow fields with different block sizes and numbers shows that adequate contact area between the plate and GDL for current conductor is critical. For liquid water removal process in the matrix flow field, liquid water is hardly blocked by arrayed blocks and can leave GDL quickly. In summary, the matrix flow field fits high current density demand of PEMFC well, and some new perspectives on flow field design are presented.
1. Introduction With increasing fossil energy shortage and stringent emission control regulations in many countries, development of renewable and ecofriendly energy conversion devices to replace internal combustion en gines in vehicles is extremely urgent for automobile enterprises [1,2]. In recent years, proton exchange membrane fuel cell (PEMFC) for vehicles is widely recognized as a sustainable technology by many automobile enterprises because it is suitable for long range driving compared with electric batteries. Insufficient lifetime and high cost are the two major
drawbacks which limit wide commercialization of PEMFC for vehicles [2,3]. Increasing output power density of a single cell without extra cost is one effective method to solve these problems, and indeed, the oper ating current density increases continuously in recent years. As far as the authors’ knowledge, the operating current density of 0.65 V output voltage can reach 1.6 A cm 2 for a commercial PEMFC now. As the target of the US Department of Energy (DOE) before 2020, the operating current density of 0.8 V output voltage should reach 3.0 A cm 2 [4]. It can be found that the technical gap is apparent and increasing operating current density is critical. Generally, increasing operating current den sity is limited by insufficient oxygen supply to the catalyst layer (CL) in
* Corresponding author. E-mail address: [email protected] (K. Jiao). https://doi.org/10.1016/j.jpowsour.2019.226741 Received 10 April 2019; Received in revised form 31 May 2019; Accepted 6 June 2019 Available online 11 June 2019 0378-7753/© 2019 Elsevier B.V. All rights reserved.
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the cathode, because reaction kinetics of the cathode is much lower than the anode and the generated liquid water in the cathode will block ox ygen transport. Besides sufficient oxygen supply to CL, oxygen distri bution also affects the local current density distribution and cell output performance. Flow field plate design and optimization is a critical job in the R&D of PEMFC, and a good flow field can facilitate oxygen supply to porous electrode, improve oxygen distribution and therefore increase current density [5,6]. The conventional designs include the parallel, serpentine and interdigitated flow field. For the parallel flow field, flow velocity in the flow field is mainly in in-plane direction and diffusion is the main mass transport to the gas diffusion layer (GDL). It may lead to insuffi cient gas supply and gas starvation with high current density operation. Some level of local forced convection exists in the serpentine flow field, and at the dead-end in the interdigitated flow field, but the pressure drop is really large which increases pumping loss and decreases energy efficiency. To improve gas supply to GDL, especially in the cathode, inspiring convection in through-plane direction is one popular method for the flow field design. Installing baffles in the channel was therefore reported [7–15]. Some baffle designs added the dead-end or incomplete block ages in channels which can be viewed as the optimized designs of the interdigitated flow field [7–10]. Effects of different baffle blockage rate, dimensions, numbers and positions in parallel and serpentine channels were investigated by both numerical and experimental methods in the previous literature [7–10]. Generally, there is a trade-off between output voltage and pressure drop. High mass transport rate and large output voltage can be achieved by increasing blockage level, such as increasing blockage rate or baffle numbers, but it causes high pressure drop and pumping loss as well. Therefore, counting net output power is necessary to evaluate a baffle flow field, and the optimized combination of these baffle parameters is selected in terms of maximum net output
power. In addition, the high pressure drop in the cathode causing damage to the membrane and over requirement of air compressor also need to be considered. Besides the dead-ended baffles, sloping plates in channels which can cause some level of convection to GDL was also reported in many studies [11–15]. Guo et al. [11] investigated the ef fects of some basic baffle shapes, including rectangular, trapezoidal, waved, semicircular and triangular in the straight channel on cell output performance and mass transport by conducting two-dimensional two- phase modeling. Then, the rectangular baffle design was optimized as the streamline windward side and sloped leeward side which could reduce flow resistance and increase net output power. Yin et al. [12] numerically investigated effects of sloping angle and baffle numbers in the straight channel of the cathode. In terms of the maximum of net output power, the optimized sloping angle and baffle number are 45� and six, respectively. Fan et al. [13] designed the novel multi-plates structure and integrated structure which can be easily inserted in channels of the cathode, and the two designs both consisted of sloping baffles. Besides full cell modeling on cell output performance, Niu et al. [14] simulated the liquid water removal process of the two sloping baffle structures by volume of fluid (VOF) method. The simulation results showed that liquid droplets would leave the surface of GDL and move along the upward sloping baffle to the top surface of the channel. Yan et al. [15] designed a serpentine flow field with waved top surface in the channel and the channel depth was gradient. Channels with waved top surface can be also viewed as one kind of baffle designs. In summary, although pressure drop and pumping loss are increasing, net output power is still increasing by using baffle structure. Baffle structure is therefore considered as an effective optimization of the flow field design. However, the optimized baffle designs in the above-mentioned studies were all based on linear channels, including the parallel or serpentine flow field. For numerical works, the computational domain was usually one channel, but not the whole flow field, so gas distribution
Nomenclature Aact Ain Ach-GDL Ash-GDL Cp,l Cp,g Deff i Deff mw Erev EW F I Jion K kl keff nd Pl Se Sion Sm Si Sl Smw ST s STc T
uc ug Vm Vout Yi
Activation area (m2) Inlet area (m2) Area of the interface between the fluid domain and GDL Area of the interface between blocks and GDL Specific heat capacity of liquid water (J mol 1 K 1) Reversible voltage (V) Equivalent weight of proton exchange membrane
Cathode inlet velocity (m s 1) Velocity of gas mixture (m s 1) Molar volume (m3 mol 1) Output voltage (V) Molar fraction of gas species i
Abbreviation ACL Anode catalyst layer AGDL Anode gas diffusion layer AMPL Anode micro-porous layer CCL Cathode catalyst layer CGDL Cathode gas diffusion layer CMPL Cathode micro-porous layer PEM Proton exchange membrane
Faraday constant (96485C mol 1) Reversible voltage (V) Equivalent weight of proton exchange membrane Faraday constant (96485C mol 1) Current density (A m 2) Ionic current density (A m 2) Intrinsic permeability (m2) Relative permeability of liquid phase Effective thermal conductivity (W m 1 K 1) Electro-osmotic drag coefficient Liquid pressure (Pa) Source term of electric potential (A m 3) Source term of ionic potential (A m 3) Source term of gas mixture (kg m 3 s 1) Source term of gas species i (kg m 3 s 1) Source term of liquid water (mol m 3 s 1) Source term of membrane water (mol m 3 s 1) Source term of energy (W m 3) Liquid saturation Cathode stoichiometry Temperature (K)
Greek letters Porosity Effective channel-shoulder ratio Electric conductivity (S m 1) Ionic conductivity (S m 1) Density of gas mixture(kg m 3) Density of liquid water (kg m 3) Density of liquid water (kg m 3) Dry density of membrane (kg m 3) λ Ionomer volume fraction κeff Water content e κeff Effective ionic conductivity (S m 1) ion ϕe Electric potential (V) ϕion Ionic potential (V) μl Dynamic viscosity of liquid water (kg m
ε εch-sh σs σm ρg ρl ρmem ω
2
1
s 1)
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Journal of Power Sources 434 (2019) 226741
Fig. 1. (a) Schematic of the designed matrix flow field plate (b) Three views of the single block (c) Computational domain of full cell model (d) Computational domain of VOF model.
mesh flow field by Toyota Mirai [24–26], were presented in recent years. These highly refined flow fields could achieve uniform and suf ficient oxygen supply and good liquid water removal, but they also face the problems of poor durability and high cost [27]. An easy-to-manufacture flow field with these advantages is needed. In this study, a novel cathode flow field plate with dot matrix and sloping baffle is designed. It synthesizes characteristics and advantages of dot matrix design and sloping baffle design which can be expected to both achieve high oxygen supply to GDL and uniform oxygen distribution among the flow field. To evaluate the matrix flow field, the cell output perfor mance, internal transport process and liquid water removal process are numerically investigated by conducting three-dimensional two-phase full cell and VOF simulations. Moreover, the effects of different sizes and numbers of dot blocks in the flow field are investigated to guide the design optimization.
effect was not fully considered. There exist clear borders between channels and shoulders for the conventional flow fields, and the presence of shoulders is of no benefit to mass transport, resulting in relatively low gas reactantconcentration in the area of GDL under shoulders and non-uniform gas distribution among the activation surface. Liquid water accumulation in the area of GDL under shoulders is more serious than the area under channels because GDL under shoulders is thinner [16]. Therefore, we can guess reducing volume ratio of shoulders in the flow field or reducing the land area in a proper level can improve mass transport and gas distribution. Yoon et al. [17] experimentally investigated cell output performance with different channel and shoulder widths of flow field plates. The channel width was fixed as 1 mm and the shoulder width was varied from 0.5 to 3 mm. The experimental results showed that cell output performance became better with the narrower rib width in the investi gated range. This result confirmed our guess and reducing volume ratio of shoulders in the flow field might be a good idea for the flow field design. The dot matrix flow field which its shoulders are dispersive blocks, but not continuous and linear, was presented in some studies [18–20]. Zhang et al. [18] designed the inlet and outlet distribution zone of the cathode flow field as the dot matrix which could improve gas distribution. Wen et al. [19] designed a intersectant flow field and the dot block is diamond shape. The sloping edge of diamond can guide air flow and improve gas distribution in the flow field. In this design, channels were still broken lines and dot blocks still occupied a consid erable proportion of the flow field. Atyabi and Afshari [20] designed a honeycomb flow field of the cathode with regular hexagon dot blocks. The flow field was a zone, but not linear channels anymore. Oxygen distribution was therefore improved, but gas concentration in the area of GDL under dot blocks was still quite low. Besides the conventional flow field, some novel flow fields with new materials and structures, such as porous flow field [21–23], 3D fine
2. Flow field design The schematic of the designed flow field plate with dot matrix and sloping baffle is shown in Fig. 1(a). The designed flow field is called as the matrix flow field in the following. The plate consists of dispersive and arrayed blocks with sloping angles as the shoulder. The top surface of each block is diamond shape which its two internal acute angles are pointed to the inlet and outlet, respectively. It can guide air flow along the short-edge of the plate and improve air distribution in the flow filed. Each block slopes from the inlet to the outlet in through-plane direction which can be viewed as a sloping baffle to block air flow and guide air transport from the flow field to GDL. The features of the designed plate are described as above. For nu merical investigation, the matrix flow filed plates with specific di mensions are presented. The plate area is 53 mm*12 mm. The thickness of side walls is 0.5 mm. In order to make the simulation approach to the 3
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Journal of Power Sources 434 (2019) 226741
Table 1 Five designs of the matrix flow field. Side length of blocks Rows along the short-edge Interval of blocks along the short -edge Rows along the long-edge Interval of blocks along the long-edge Total number of blocks Effective channel-shoulder ratio
Mat1.0_3 � 12
Mat1.0_3 � 16
Mat1.0_3 � 20 (baseline)
Mat0.9_3 � 12
Mat0.9_4 � 12
1 mm 3 3 mm 12 4 mm 36 5.90
1 mm 3 3 mm 16 3 mm 48 5.20
1 mm 3 3 mm 20 2.4 mm 60 4.63
0.9 mm 3 3 mm 12 4 mm 36 6.37
0.9 mm 4 2 mm 12 4 mm 48 5.72
3. Full cell model
Table 2 Cell properties and operating conditions. Parameter
Value
Temperature Output voltage Back pressure Inlet relative humidity Stoichiometry Thickness of GDL,MPL, PEM Porosity of GDL, MPL Contact angle of GDL, MPL, CL Intrinsic permeability of GDL, MPL, CL, PEM EW of PEM Thickness of CL Pt loading in CL Pt-carbon rate in CL Ionomer-carbon rate in CL Carbon particle radius in CL Ionomer coverage in CL Density of Pt, carbon Electrical conductivity of BP, GDL, MPL, CL
80 � C 0.9 V to 0.3 V Anode: 1.5atm Cathode:1.5atm Anode: 1.0 Cathode: 1.0 Anode: 1.5 Cathode: 2.0 200 mm, 20 mm, 25.4 mm 0.6, 0.5 120� , 120� , 95� 2.0e 12, 1.0e 12, 1.0e 13, 2.0e
Thermal conductivity of BP, MPL, CL,PEM Thermal conductivity of GDL Transfer coefficient Reference gas reactant concentration Reference exchange current density Phase change rate between liquid water and water vapor Transfer rate between membrane water and water vapor or liquid water
20
1.1 kg mol 1 Anode: 6 mm Cathode: 10 mm Anode: 0.1 Cathode: 0.3 Anode: 0.2 Cathode: 0.4 Anode: 0.7 Cathode: 0.9 2.5e-8 0.9 21450 kg m 3, 2000 kg m 3 20000 S m 1, 8000 S m 1, 5000 S m 1, 5000 S m 1 20 W m 1 K 1, 1 W m 1 K 1, 1 W m K 1, 0.95 W m 1 K 1 In-plane: 21 W m 1 K 1 Throughplane: 1.7 W m 1 K 1 0.5 Anode: 56.4 mol m 3 Cathode: 3.39 mol m 3 Anode: 3.0 A m 2 Cathode: 3.0e 4A m 2 100s 1 1.3s
To investigate cell output performance and internal transport process of the PEMFC with the designed cathode flow field, a previously developed three-dimensional two-phase steady-state full cell model is utilized in the study [25]. The computational domain is shown in Fig. 1 (c). The anode plate is parallel flow field with six straight channels. The cross section area of straight channels is 1 mm � 1 mm and the shoulder width is 1 mm. Five designs listed in Table 1 are all employed as the cathode flow field. As shown in Fig. 1(c), inlets and outlets of the anode and cathode both extend 10 mm to avoid reverse flow at the outlets during the iteration process and improve numerical stability. The extended sections have not much influence on the flow field when calculation is convergent [18]. Nafion 211 membrane and counter-flow configuration are employed for the simulated fuel cell. The cell prop erties and operating conditions are listed in Table 2. In our previous study, two-phase flow in flow fields was simulated by Eulerian – Eulerian model. Simulation results showed that the value of liquid saturation in flow fields was usually lower than 1.0 3 and the state of liquid water was considered as mist [18]. For model simplification, single-phase flow in flow fields is considered in this study by assuming that liquid water in flow fields can be blown away quickly by air flow and liquid saturation in flow fields is zero. To realize the water removal capacity of the matrix flow field, a two-phase flow analysis by VOF method will be conducted in the next section. Other modeling assump tions are the same as that in Ref. [25]. The involved conservation equations are briefly represented as following. Electronic potential conservation: � 0 ¼ r⋅ κeff (2) e rϕe þ Se
1
1
Ionic potential conservation: � 0 ¼ r⋅ κeff ion rϕion þ Sion
real-scale automobile PEMFC [18], the inlet and outlet are located diagonally on the short-edge of the plate, and widths of the inlet and outlet are both 3 mm. The total height of the plate is 2 mm and the depth of the fluid domain is 1 mm. For the single block, the internal acute angle of diamond shape is 60∘, and the sloping angle in through-plane direc tion is 30∘. The height of blocks is equal to the depth of the fluid domain, 1 mm. Three views of the single block is shown in Fig. 1(b). Five matrix flow fields with different block sizes and numbers are presented in Table 1, which are called Mat1.0_3 � 12, Mat1.0_3 � 16, Mat1.0_3 � 20, Mat0.9_3 � 12, Mat1.0_4 � 12, respectively. Effective channel-shoulder ratio is defined as:
εch
sh
¼
Ach Ash
GDL GDL
(3)
Gas mixture mass conservation:
∂ εð1 ∂t
� � sÞρg þ r⋅ ρg ug ¼ Sm
Gas mixture momentum conservation: ! � � � � ρg ug ρg ug ug ug ∂ ¼ rPg þ μg r⋅ r þ r⋅ 2 ∂t εð1 sÞ εð1 sÞ ε2 ð1 sÞ � �� T ug þr εð1 sÞ � � �� 2 ug ug r r⋅ þ Su 3 εð1 sÞ
(4)
�
(1)
(5)
Gas species conservation (i: hydrogen, oxygen and water vapor):
where εch-sh is effective channel-shoulder ratio, Ach-GDL is the area of the interface between the fluid domain and GDL, and Ash-GDL is the area of the interface between blocks and GDL. Effective channel-shoulder ratios of the five matrix flow field design are therefore calculated and listed in Table 1.
∂ εð1 ∂t
� � � sÞρg Yi þ r⋅ ρg ug Yi ¼ r⋅ ρg Deff i rYi þ Si
Liquid pressure conservation in porous electrode: � � ∂ Kkl ðεsρl Þ ¼ r⋅ ρl rPl þ Sl ∂t μl
4
(6)
(7)
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∂ εsρl Cp;l T þ εð1 ∂t
� sÞρg Cp;g T þ r⋅ εsρl Cp;l ul T þ εð1
� ¼ r⋅ keff rT þ ST
sÞρg Cp;g ug T
� (9)
In order to reflect the effect of oxygen transport on cell output per formance precisely, especially under high current density operation, the agglomerate model of CL is employed in this model. Details about the agglomerate model, transport parameters and source terms in the con servation equations can be found in Ref. [25]. Mass flow rates at the anode and cathode inlet are defined by real output current density and stoichiometry. The outlets of flow fields are defined as the pressure-outlet and pressure drops of flow fields are also counted to correct inlet pressure during the calculation procedure. Constant temperature thermal boundary conditions are defined on outside surfaces of the cell. The potentiostatic mode is carried out for all simulated cases by defining electronic potentials at the anode and cathode BP end surface as 0 V and Erev-Vout, respectively [28]. Numerical procedures are implemented by a commercial CFD soft ware, Fluent, coupling with self-written codes of user defined function (UDF). Structured grid cells are employed in the whole computational domain with 265 � 79 � 60 grid cells in X � Y � Z directions, respec tively. For the grid-independence test, the simulation results show no much difference on output current density, local current density and gas distribution by further increasing grid cells to 318 � 110 � 72. The simulation results including polarization curves and ohmic loss were compared with experiments and a good agreement was achieved which can be found in Ref. [25]. 4. Two-phase model by VOF Two-phase flow modeling by VOF method is utilized to simulate the liquid water removal process in the matrix flow field. As shown in Fig. 1 (d), the computational domain is the fluid domain of Mat1.0_3 � 20, the inlet and outlet are extended for 10 mm. The bottom wall represents the interface between the flow field and GDL, and other walls represent internal surfaces of the plate. The basic assumptions include unsteady, isothermal and laminar flow conditions. VOF method is employed to track the two-phase interface between liquid water and air. The conservation equations include continuity equation, momentum equation and volume fraction of liquid water and air by VOF method. Numerical procedures are implemented by the software, Fluent, and the involved equations are build-in. More details can be found in Ref. [29]. The inlet and outlet are set as velocity-inlet and pressure-outlet, respectively. Absolute pressure of the outlet is 1.5atm. The inlet veloc ity is estimated as: uc ¼
(10)
where uc (m s 1) is cathode inlet velocity, I(A m 2) is current density, Vm(m3 mol 1) is molar volume of air, Aact (m2) is the activation area, STc is cathode stoichiometry, 0.21 represents the oxygen volume fraction of air, F is the Faraday constant, Ain(m2) is the inlet area. The molar volume Vm can be calculated by the ideal gas law when P ¼ 1.5atm and T ¼ 353.15 K. Current density is assumed as 2.0 A cm 2, and inlet gas is assumed as dry air. Other parameters, such as Aact,Ain and STc, are the same with full cell model in Table 2. The estimated inlet velocity is therefore calculated as 2.1 m s 1. Contact angles of the bottom, top and side wall are set as 150∘, 30∘, 90∘, respectively. Nine liquid water droplets with radius of 0.2 mm are initialized at different positions of the up stream, middle and downstream of the flow field, respectively. Maximum element size is set as 0.1 mm and the time step is set as 1.0 6s. The grid-independence test is carried out by increasing the total grid number by 40%, and difference of simulation results including pressure drop and liquid water removal can be ignored.
Fig. 2. (a) Polarization curves (b) Net output power (c) Pressure drop of PEMFC with the five matrix, parallel and serpentine flow fields.
Membrane water conservation: � � � ρmem ∂ Jion ρ ðωλÞ þ r⋅ nd ¼ mem r⋅ Deff mw rλ þ Smw EW ∂t F EW
IVm Aact STc 0:21 � 4FAin
(8)
Energy conservation: 5
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Fig. 3. Contour of -Y velocity at the middle plane of the five matrix flow fields.
5. Results and discussion
drop difference among the five is very a little. Decreasing block interval and increasing block number of the matrix flow field in the investigated range will increase only a little pressure drop, but improve cell output performance greatly. We can also find that cell output performance generally increases with increasing contact area between the flow field plate and GDL in the investigated range. Although contact area of Mat1.0_3 � 16 is larger than that of Mat0.9_4 � 12, cell output perfor mance of these are similar. As we know, the flow field with fine structure (small scale) would have a good performance. Detailed reasons will be discussed in the following sections.
The cell output performance, internal multi-physical quantities dis tribution and liquid water removal process of PEMFC with the matrix flow fields are predicted by conducting full cell model and VOF model. The five matrix, parallel and serpentine flow fields are simulated and discussed to explain the characteristic of the designed matrix flow field. 5.1. Output performance Fig. 2 shows polarization curves, net output power and pressure drop of PEMFC with the five matrix, parallel and serpentine cathode flow fields. Although output performance of the cells with matrix flow fields are similar or even a little worse than that with parallel and serpentine flow fields in the low current density region (<2.0 A cm 2), the ad vantages of matrix flow fields become very significant with further increasing current density. Moreover, pressure drop of matrix flow fields is far lower than the serpentine, and even lower than the parallel which is due to the decreasing shoulder volume and increasing fluid domain of matrix flow fields. It can be summarized that the matrix flow field can improve cell output performance without increasing pressure drop, especially in the high current density region. Therefore, the matrix flow field fits the increasing current density demand of PEMFC well. Comparing cell output performance of the five matrix flow fields, Mat1.0_3 � 20 > Mat0.9_4 � 12 � Mat1.0_3 � 16 > Mat1.0_3 � 12 > Mat0.9_3 � 12. Pressure drop is the same order, although pressure
5.2. Air guidance in the matrix flow field In order to both achieve high energy efficiency and output power density, output voltage of PEMFC is usually between 0.6 V and 0.8 V. As shown in Fig. 2(a), output voltage corresponding to the maximum output power of PEMFC with the five matrix, parallel and serpentine flow fields are all around 0.6 V. Therefore, all the results shown in this and following sections are based on Vout ¼ 0.6 V. In this section, air guidance effects of sloping blocks are investigated and discussed. Fig. 3 shows -Y velocity at the middle plane of the cathode flow field among the five matrix flow fields. Since the direction of air supply to GDL is the negative direction of Y, the positive velocity value in Fig. 3 represents flow velocity to GDL. It can be found that there exists obvious flow convection to GDL caused by the slope of blocks which are mainly located in the interval region between blocks along the 6
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Journal of Power Sources 434 (2019) 226741
Fig. 4. Streamline of velocity in X-Z plane and contour of Z velocity at the middle plane of the five matrix flow fields.
long-edge of the plate. The matrix flow field has a large fluid domain for air transport, but the area of GDL under blocks still faces insufficient air supply. Flow convection around blocks can improve air supply to the area of GDL under blocks. There also exists flow velocity away from GDL in the interval region between blocks along the short-edge of the plate, which is especially obvious in Mat1.0_3 � 20 and Mat0.9_4 � 12. In this region, air flow can make liquid water move upwards and depart from the surface of GDL. This effect will be further discussed in Section 5.5. Fig. 4 shows the streamline of velocity in X-Z plane and the contour of Z velocity at the middle plane of the five matrix flow fields. The vector length is set as uniform and the streamline only represents the flow di rection. Air flow is guided by the slope edge of diamond blocks in Z direction which can improve air distribution along the short-edge of the plate. The importance of air distribution along the short-edge of the plate will become more obvious with increasing the scale and width of the plate. Comparing the five matrix flow fields in Figs. 3 and 4, Mat0.9_3 � 12 has the larger area of air guidance to GDL (-Y direction), but Mat1.0_3 � 20 has the larger area of air guidance along the shortedge (Z direction), and the two effects both benefit to air transport and cell output performance. We can summarize that there is a trade-off between air guidance to GDL and air guidance along the short-edge for different block sizes and numbers.
5.3. Oxygen concentration and liquid saturation In this section, distribution of oxygen concentration and liquid saturation are presented to explain the advantages of the designed ma trix flow field. Fig. 5(a) and (b) show oxygen concentration and liquid saturation at the interface between cathode CL and MPL among the five matrix, parallel and serpentine flow fields, respectively. The distribution characteristic of the matrix flow field can be described as relatively low oxygen concentration and high liquid saturation under blocks. Compared with the parallel and serpentine flow field, we can easily found that the average value of oxygen concentration is larger and that of liquid saturation is smaller for the matrix flow field, and distribution of oxygen and liquid are more uniform. Oxygen starvation in down stream and oxygen distribution along the short-edge of the matrix flow field are obviously improved. And the matrix flow field could also decrease liquid saturation under shoulders due to the large fluid domain. Furthermore, comparing the five matrix flow fields in Fig. 5(a) and (b), we can feel that Mat0.9_3 � 12 has the maximum average value of ox ygen concentration and Mat1.0_3 � 20 has the minimum, and Mat0.9_3 � 12 has the minimum average value of liquid saturation and Mat1.0_3 � 20 has the maximum. It can be also found that distribution along the long-edge of the plate is more uniform for Mat0.9_3 � 12 and distribution along the short-edge of the plate is more uniform for Mat1.0_3 � 20 and Mat0.9_4 � 12. For quantitative comparison, Fig. 6(a) and (b) show the average 7
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Fig. 5. Contour of (a) oxygen concentration (b) liquid saturation at the interface between cathode CL and MPL among the five matrix, parallel and serpentine flow fields.
value and standard deviation of oxygen concentration and liquid satu ration at the interface between cathode CL and MPL among the five matrix flow fields. Although decreasing block interval and increasing block number decreases the average value of oxygen concentration and increases the average value of liquid saturation, distribution of the two parameters becomes uniform overall. For different single block sizes, decreasing block size and without decreasing contact area between the flow field plate and GDL (by increasing block number) are helpful for increasing oxygen concentration, decreasing liquid saturation and uni form distribution. This result also fits and further explains the trade-off effect of block size and number we presented in the last section. Increasing block number means increasing flow resistance and pressure drop, but also benefits oxygen uniform distribution. Small scale of single block is positive but providing sufficient contact area is more important for the matrix flow filed plate.
low liquid saturation. On the contrary, regions of high reaction rate for the parallel and serpentine flow field are mainly the area under channels due to sufficient shoulders for current conductor, and oxygen concen tration and liquid saturation take an important role on reaction rate distribution. Now we can explain why current densities of the parallel and serpentine flow field when Vout ¼ 0.6 V are similar or even a little higher than the matrix flow field, even then the average values of oxygen concentration and liquid saturation are worse and these distributions are more non-uniform (Fig. 5(a) and (b)). We can conclude that the matrix flow field increases fluid domain but also decreases the area for current conductor which may be against cell output performance. For the matrix flow field, the other trade-off effect of contact area is presented. A large fluid domain is helpful for air transport, but adequate contact area be tween the flow field plate and GDL for current conductor is also demanded for the matrix flow field. As cell output performance pre sented in Fig. 2(a), Mat1.0_3 � 20 is the best in the investigated range.
5.4. Reaction rate
5.5. Water removal process
Discussion of the last two sections is about mass transport effects of the matrix flow field, but one of the most basic feature of the dot matrix, current conductor, is not involved. In this section, the characteristic of the matrix flow field on cell output performance is discussed overall. Fig. 7 shows reaction rate at the middle plane of cathode CL among the five matrix, parallel and serpentine flow fields. For the five matrix flow fields, regions of high reaction rate are mainly the surrounding area of blocks but not necessarily regions of high oxygen concentration and
The liquid water removal process in the Mat1.0_3 � 20 flow field is shown in Fig. 8. The initialized droplets can be divided into three series which are located at the upstream, middle and downstream of the flow field, respectively. For the droplets initialized at the downstream, one drop leaves the flow field quickly, and the other two droplets adhere to the top surface after hitting the front wall. For the droplets initialized at the upstream and middle, only very small fraction of liquid water 8
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Fig. 6. The average value and standard deviation of (a) oxygen concentration (b) liquid saturation at the interface between cathode CL and MPL among the five matrix flow fields.
removal is blocked by the matrix blocks, and most of liquid water moves ahead quickly. Besides moving ahead, liquid water also moves along X direction caused by the air flow guidance along the short-edge of the plate. As the discussion in Section 5.2, flow velocity is away from GDL to the top surface of the flow field (Y direction) in the interval region be tween blocks along the short-edge of the plate. This effect makes liquid water move upwards and depart from the surface of GDL. After 15 ms, almost all liquid water has left the surface of GDL. This phenomenon can avoid the porous blockage by liquid water and benefits oxygen transport.
with the designed matrix flow field. Furthermore, five matrix flow fields with different sizes and numbers of blocks are compared. The simulation results show that the matrix flow field can effectively improve cell output performance, especially in high current density region. Based on the analysis of internal transport process, the advantages of the matrix flow field include two points. Firstly, a large fluid domain increases the area of air supply from the flow field to GDL and water removal from GDL to the flow field, and oxygen distribution is also improved. Sec ondly, the two air guidance of sloping blocks are effective, including air guidance along the short-edge of the plate caused by the sloping edge of diamond shape, and air guidance to GDL in through-plane direction caused by the sloping block. In summary, the matrix flow field can enhance oxygen supply to GDL and improve oxygen uniform distribu tion compared with the parallel and serpentine flow fields. By comparing the five matrix flow fields with different block sizes and numbers, we also find that adequate contact area between the flow field plate and GDL for current conductor is also demanded. There is a trade-off between increasing the fluid domain for air transport and providing adequate contact area for current conductor. Increasing block number in a proper level also benefits oxygen uniform distribution. Small scale of single block is also positive but providing sufficient
6. Conclusion A novel dot matrix and sloping baffle flow field plate of the cathode is designed in this study. The plate consists of dispersive and arrayed blocks with sloping angles as shoulders. The top surface of each block is diamond shape which its two internal acute angles are pointed to the inlet and outlet, respectively. Each block slopes from the inlet to the outlet in through-plane direction. Three-dimensional two-phase full cell model and VOF model are conducted to predict cell output performance, internal transport process and liquid water removal process of PEMFC 9
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Fig. 7. Contour of reaction rate at the middle plane of cathode CL among the five matrix, parallel and serpentine cathode flow fields.
contact area is more important. But we should also note that decreasing the size of single block will certainly increase the difficulty of manu facture. In the investigated range, Mat1.0_3 � 20 which has the most block number has the best cell output performance. The simulation of liquid water removal in the matrix flow field by VOF model shows that liquid water removal is hardly blocked by the arrayed blocks in the matrix flow field. Furthermore, liquid water will move upwards and depart from GDL quickly. Because some region exists the obvious flow velocity away from GDL. This effect can avoid the porous blockage by liquid water and benefit oxygen transport. To sum up the analysis of cell output performance, internal multiphysical quantities distribution and liquid water removal process, we
can conclude that the designed matrix flow field fits the increasing current density demand of PEMFC well. And these advantages could be achieved in the case that the scale of the single block, which is 1 mm and 0.9 mm, does not have to be too small. This study not only presents a detailed flow field design, but more importantly provides some new perspectives on how to enhance oxygen transport and improve oxygen distribution for flow field design. Manufacture of the matrix flow field plate, assembly of the fuel cell and test would be our next step work, and providing sufficient clamping force by the matrix flow field plate should also be considered.
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Fig. 8. (a) Top view (b) Front view of liquid water droplets removal process in the Mat1.0_3 � 20 flow field.
Acknowledgements
[6] S. Tong, J. Bachman, A. Santamaria, et al., Experimental investigation on a polymer electrolyte membrane fuel cell (PEMFC) parallel flow field design with external two-valve regulation on cathode channels, J. Power Sources 242 (2013) 195–201. [7] P.M. Belchor, M.M.C. Forte, D.E.O.S. Carpenter, Parallel serpentine-baffle flow field design for water management in a proton exchange membrane fuel cell, Int. J. Hydrogen Energy 37 (2012) 11904–11911. [8] Y. Yin, X. Wang, X. Shangguan, et al., Numerical investigation on the characteristics of mass transport and performance of PEMFC with baffle plates installed in the flow channel, Int. J. Hydrogen Energy 43 (2018) 8048–8062. [9] J. Shen, Z. Tu, S.H. Chan, Enhancement of mass transfer in a proton exchange membrane fuel cell with blockage in the flow channel, Appl. Therm. Eng. 149 (2019) 1408–1418. [10] J.-H. Jang, W.-M. Yan, H.-Y. Li, et al., Humidity of reactant fuel on the cell performance of PEM fuel cell with baffle-blocked flow field designs, J. Power Sources 159 (2006) 468–477. [11] H. Guo, H. Chen, F. Ye, et al., Baffle shape effects on mass transfer and power loss of proton exchange membrane fuel cells with different baffled flow channels, Int. J. Energy Res. 43 (7) (2019) 2737–2755. [12] Y. Yin, J.X. WangZhang, et al., Influence of sloping baffle plates on the mass transport and performance of PEMFC, Int. J. Energy Res. 43 (7) (2019) 2643–2655. [13] L. Fan, Z. Niu, G. Zhang, et al., Optimization design of the cathode flow channel for proton exchange membrane fuel cells, Energy Convers. Manag. 171 (2018) 1813–1821. [14] Z. Niu, L. Fan, Z. Bao, et al., Numerical investigation of innovative 3D cathode flow channel in proton exchange membrane fuel cell, Int. J. Energy Res. 42 (2018) 3328–3338. [15] X. Yan, C. Guan, Y. Zhang, et al., Flow field design with 3D geometry for proton exchange membrane fuel cells, Appl. Therm. Eng. 147 (2019) 1107–1114.
This research is supported by the National Key Research and Development Program of China (Grant No. 2018YFB0105601), and the China-UK International Cooperation and Exchange Project (Newton Advanced Fellowship) jointly supported by the National Natural Science Foundation of China (Grant No. 51861130359) and the UK Royal So ciety (Grant No. NAF\R1\180146), and the National Natural Science Foundation of Tianjin (China) for Distinguished Young Scholars (Grant No. 18JCJQJC46700). References [1] K. Song, F. Li, X. Hu, et al., Multi-mode energy management strategy for fuel cell electric vehicles based on driving pattern identification using learning vector quantization neural network algorithm, J. Power Sources 389 (2018) 230–239. [2] H. Li, A. Ravey, A. N’Diaye, et al., A novel equivalent consumption minimization strategy for hybrid electric vehicle powered by fuel cell, battery and supercapacitor, J. Power Sources 395 (2018) 262–270. [3] A. Talke, U. Misz, G. Konrad, et al., Influence of urban air on proton exchange membrane fuel cell vehicles - long term effects of air contaminants in an authentic driving cycle, J. Power Sources 400 (2018) 556–565. [4] https://www.hydrogen.energy.gov/annual_progress17.html.2019.3.14. [5] Y. Wang, L. Yue, S. Wang, New design of a cathode flow-field with a sub-channel to improve the polymer electrolyte membrane fuel cell performance, J. Power Sources 344 (2017) 32–38.
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Journal of Power Sources 434 (2019) 226741 [23] J. Kim, N. Cunningham, Development of porous carbon foam polymer electrolyte membrane fuel cell, J. Power Sources 195 (2010) 2291–2300. [24] T. Yoshida, K. Kojima, Toyota MIRAI fuel cell vehicle and progress toward a future hydrogen society, Electrochem. Soc. Interface 24 (2015) 45–49. [25] G. Zhang, B. Xie, Z. Bao, et al., Multi-phase simulation of proton exchange membrane fuel cell with 3D fine mesh flow field, Int. J. Energy Res. 42 (2018) 4697–4709. [26] J. Kim, G. Luo, C.-Y. Wang, Modeling two-phase flow in three-dimensional complex flow-fields of proton exchange membrane fuel cells, J. Power Sources 365 (2017) 419–429. [27] G. Zhang, K. Jiao, Multi-phase models for water and thermal management of proton exchange membrane fuel cell: a review, J. Power Sources 391 (2018) 120–133. [28] K. Jiao, X. Li, Water transport in polymer electrolyte membrane fuel cells, Prog. Energy Combust. Sci. 37 (2011) 221–291. [29] Y. Hou, G. Zhang, Y. Qin, et al., Numerical simulation of gas liquid two-phase flow in anode channel of low-temperature fuel cells, Int. J. Hydrogen Energy 42 (2017) 3250–3258.
[16] A.D. Santamaria, P.K. Das, J.C. Macdonald, et al., Liquid-water interactions with gas-diffusion-layer surfaces, J. Electrochem. Soc. 161 (2014) F1184–F1193. [17] Y. Yoon, W. Lee, G. Park, et al., Effects of channel and rib widths of flow field plates on the performance of a PEMFC, Int. J. Hydrogen Energy 30 (2005) 1363–1366. [18] G. Zhang, X. Xie, B. Biao, et al., Large-scale multi-phase simulation of proton exchange membrane fuel cell, Int. J. Heat Mass Transf. 130 (2019) 555–563. [19] D. Wen, L. Yin, Z. Piao, et al., Performance investigation of proton exchange membrane fuel cell with intersectant flow field, Int. J. Heat Mass Transf. 121 (2018) 775–787. [20] S.A. Atyabi, E. Afshari, Three-dimensional multiphase model of proton exchange membrane fuel cell with honeycomb flow field at the cathode side, J. Clean. Prod. 214 (2019) 738–748. [21] A. Fly, D. Butcher, Q. Meyer, et al., Characterisation of the diffusion properties of metal foam hybrid flow-fields for fuel cells using optical flow visualisation and Xray computed tomography, J. Power Sources 395 (2018) 171–178. [22] S. Litster, J. Santiaog, Dry gas operation of proton exchange membrane fuel cells with parallel channels: non-porous versus porous plates, J. Power Sources 188 (2009) 82–88.
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Contents lists available at ScienceDirect
Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour
A dot matrix and sloping baffle cathode flow field of proton exchange membrane fuel cell Bowen Wang a, Wenmiao Chen b, Fengwen Pan b, Siyuan Wu c, Guobin Zhang a, Jae Wan Park c, Biao Xie a, Yan Yin a, Kui Jiao a, * a b c
State Key Laboratory of Engines, Tianjin University, 135 Yaguan Road, Tianjin, 300350, China Weichai Power Co. Ltd., 197A Fushou St. E., Weifang, 261016, China Department of Mechanical and Aerospace Engineering, University of California, Davis, One Shields Ave., Davis, CA, 95616, USA
H I G H L I G H T S
� A novel dot matrix and sloping baffle cathode flow field of PEMFC is designed. � The features of the plate include a large fluid domain and air guidance. � The matrix flow field is evaluated by full cell model and VOF model. � The matrix flow field fits high current density demand of PEMFC well. � Adequate contact area between the plate and GDL for current conductor is critical. A R T I C L E I N F O
A B S T R A C T
Keywords: PEMFC Flow field design Dot matrix Sloping baffle Three-dimensional full cell model VOF model
A novel dot matrix and sloping baffle flow field plate for proton exchange membrane fuel cell (PEMFC) cathode is designed. The plate consists of dispersive and arrayed blocks with sloping angles as shoulders. Features of the plate include a large fluid domain, and air guidance in two directions is achieved by sloping sides of the block. The cell output performance, internal transport process and liquid water removal process of the PEMFC with the matrix flow field are numerically investigated by three-dimensional two-phase full cell model and volume of fluid (VOF) model. The simulation results show that compared with the parallel and serpentine flow field, the matrix flow field can achieve high cell output performance by both improving oxygen supply to gas diffusion layer (GDL) and uniform distribution. Comparing five matrix flow fields with different block sizes and numbers shows that adequate contact area between the plate and GDL for current conductor is critical. For liquid water removal process in the matrix flow field, liquid water is hardly blocked by arrayed blocks and can leave GDL quickly. In summary, the matrix flow field fits high current density demand of PEMFC well, and some new perspectives on flow field design are presented.
1. Introduction With increasing fossil energy shortage and stringent emission control regulations in many countries, development of renewable and ecofriendly energy conversion devices to replace internal combustion en gines in vehicles is extremely urgent for automobile enterprises [1,2]. In recent years, proton exchange membrane fuel cell (PEMFC) for vehicles is widely recognized as a sustainable technology by many automobile enterprises because it is suitable for long range driving compared with electric batteries. Insufficient lifetime and high cost are the two major
drawbacks which limit wide commercialization of PEMFC for vehicles [2,3]. Increasing output power density of a single cell without extra cost is one effective method to solve these problems, and indeed, the oper ating current density increases continuously in recent years. As far as the authors’ knowledge, the operating current density of 0.65 V output voltage can reach 1.6 A cm 2 for a commercial PEMFC now. As the target of the US Department of Energy (DOE) before 2020, the operating current density of 0.8 V output voltage should reach 3.0 A cm 2 [4]. It can be found that the technical gap is apparent and increasing operating current density is critical. Generally, increasing operating current den sity is limited by insufficient oxygen supply to the catalyst layer (CL) in
* Corresponding author. E-mail address: [email protected] (K. Jiao). https://doi.org/10.1016/j.jpowsour.2019.226741 Received 10 April 2019; Received in revised form 31 May 2019; Accepted 6 June 2019 Available online 11 June 2019 0378-7753/© 2019 Elsevier B.V. All rights reserved.
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the cathode, because reaction kinetics of the cathode is much lower than the anode and the generated liquid water in the cathode will block ox ygen transport. Besides sufficient oxygen supply to CL, oxygen distri bution also affects the local current density distribution and cell output performance. Flow field plate design and optimization is a critical job in the R&D of PEMFC, and a good flow field can facilitate oxygen supply to porous electrode, improve oxygen distribution and therefore increase current density [5,6]. The conventional designs include the parallel, serpentine and interdigitated flow field. For the parallel flow field, flow velocity in the flow field is mainly in in-plane direction and diffusion is the main mass transport to the gas diffusion layer (GDL). It may lead to insuffi cient gas supply and gas starvation with high current density operation. Some level of local forced convection exists in the serpentine flow field, and at the dead-end in the interdigitated flow field, but the pressure drop is really large which increases pumping loss and decreases energy efficiency. To improve gas supply to GDL, especially in the cathode, inspiring convection in through-plane direction is one popular method for the flow field design. Installing baffles in the channel was therefore reported [7–15]. Some baffle designs added the dead-end or incomplete block ages in channels which can be viewed as the optimized designs of the interdigitated flow field [7–10]. Effects of different baffle blockage rate, dimensions, numbers and positions in parallel and serpentine channels were investigated by both numerical and experimental methods in the previous literature [7–10]. Generally, there is a trade-off between output voltage and pressure drop. High mass transport rate and large output voltage can be achieved by increasing blockage level, such as increasing blockage rate or baffle numbers, but it causes high pressure drop and pumping loss as well. Therefore, counting net output power is necessary to evaluate a baffle flow field, and the optimized combination of these baffle parameters is selected in terms of maximum net output
power. In addition, the high pressure drop in the cathode causing damage to the membrane and over requirement of air compressor also need to be considered. Besides the dead-ended baffles, sloping plates in channels which can cause some level of convection to GDL was also reported in many studies [11–15]. Guo et al. [11] investigated the ef fects of some basic baffle shapes, including rectangular, trapezoidal, waved, semicircular and triangular in the straight channel on cell output performance and mass transport by conducting two-dimensional two- phase modeling. Then, the rectangular baffle design was optimized as the streamline windward side and sloped leeward side which could reduce flow resistance and increase net output power. Yin et al. [12] numerically investigated effects of sloping angle and baffle numbers in the straight channel of the cathode. In terms of the maximum of net output power, the optimized sloping angle and baffle number are 45� and six, respectively. Fan et al. [13] designed the novel multi-plates structure and integrated structure which can be easily inserted in channels of the cathode, and the two designs both consisted of sloping baffles. Besides full cell modeling on cell output performance, Niu et al. [14] simulated the liquid water removal process of the two sloping baffle structures by volume of fluid (VOF) method. The simulation results showed that liquid droplets would leave the surface of GDL and move along the upward sloping baffle to the top surface of the channel. Yan et al. [15] designed a serpentine flow field with waved top surface in the channel and the channel depth was gradient. Channels with waved top surface can be also viewed as one kind of baffle designs. In summary, although pressure drop and pumping loss are increasing, net output power is still increasing by using baffle structure. Baffle structure is therefore considered as an effective optimization of the flow field design. However, the optimized baffle designs in the above-mentioned studies were all based on linear channels, including the parallel or serpentine flow field. For numerical works, the computational domain was usually one channel, but not the whole flow field, so gas distribution
Nomenclature Aact Ain Ach-GDL Ash-GDL Cp,l Cp,g Deff i Deff mw Erev EW F I Jion K kl keff nd Pl Se Sion Sm Si Sl Smw ST s STc T
uc ug Vm Vout Yi
Activation area (m2) Inlet area (m2) Area of the interface between the fluid domain and GDL Area of the interface between blocks and GDL Specific heat capacity of liquid water (J mol 1 K 1) Reversible voltage (V) Equivalent weight of proton exchange membrane
Cathode inlet velocity (m s 1) Velocity of gas mixture (m s 1) Molar volume (m3 mol 1) Output voltage (V) Molar fraction of gas species i
Abbreviation ACL Anode catalyst layer AGDL Anode gas diffusion layer AMPL Anode micro-porous layer CCL Cathode catalyst layer CGDL Cathode gas diffusion layer CMPL Cathode micro-porous layer PEM Proton exchange membrane
Faraday constant (96485C mol 1) Reversible voltage (V) Equivalent weight of proton exchange membrane Faraday constant (96485C mol 1) Current density (A m 2) Ionic current density (A m 2) Intrinsic permeability (m2) Relative permeability of liquid phase Effective thermal conductivity (W m 1 K 1) Electro-osmotic drag coefficient Liquid pressure (Pa) Source term of electric potential (A m 3) Source term of ionic potential (A m 3) Source term of gas mixture (kg m 3 s 1) Source term of gas species i (kg m 3 s 1) Source term of liquid water (mol m 3 s 1) Source term of membrane water (mol m 3 s 1) Source term of energy (W m 3) Liquid saturation Cathode stoichiometry Temperature (K)
Greek letters Porosity Effective channel-shoulder ratio Electric conductivity (S m 1) Ionic conductivity (S m 1) Density of gas mixture(kg m 3) Density of liquid water (kg m 3) Density of liquid water (kg m 3) Dry density of membrane (kg m 3) λ Ionomer volume fraction κeff Water content e κeff Effective ionic conductivity (S m 1) ion ϕe Electric potential (V) ϕion Ionic potential (V) μl Dynamic viscosity of liquid water (kg m
ε εch-sh σs σm ρg ρl ρmem ω
2
1
s 1)
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Fig. 1. (a) Schematic of the designed matrix flow field plate (b) Three views of the single block (c) Computational domain of full cell model (d) Computational domain of VOF model.
mesh flow field by Toyota Mirai [24–26], were presented in recent years. These highly refined flow fields could achieve uniform and suf ficient oxygen supply and good liquid water removal, but they also face the problems of poor durability and high cost [27]. An easy-to-manufacture flow field with these advantages is needed. In this study, a novel cathode flow field plate with dot matrix and sloping baffle is designed. It synthesizes characteristics and advantages of dot matrix design and sloping baffle design which can be expected to both achieve high oxygen supply to GDL and uniform oxygen distribution among the flow field. To evaluate the matrix flow field, the cell output perfor mance, internal transport process and liquid water removal process are numerically investigated by conducting three-dimensional two-phase full cell and VOF simulations. Moreover, the effects of different sizes and numbers of dot blocks in the flow field are investigated to guide the design optimization.
effect was not fully considered. There exist clear borders between channels and shoulders for the conventional flow fields, and the presence of shoulders is of no benefit to mass transport, resulting in relatively low gas reactantconcentration in the area of GDL under shoulders and non-uniform gas distribution among the activation surface. Liquid water accumulation in the area of GDL under shoulders is more serious than the area under channels because GDL under shoulders is thinner [16]. Therefore, we can guess reducing volume ratio of shoulders in the flow field or reducing the land area in a proper level can improve mass transport and gas distribution. Yoon et al. [17] experimentally investigated cell output performance with different channel and shoulder widths of flow field plates. The channel width was fixed as 1 mm and the shoulder width was varied from 0.5 to 3 mm. The experimental results showed that cell output performance became better with the narrower rib width in the investi gated range. This result confirmed our guess and reducing volume ratio of shoulders in the flow field might be a good idea for the flow field design. The dot matrix flow field which its shoulders are dispersive blocks, but not continuous and linear, was presented in some studies [18–20]. Zhang et al. [18] designed the inlet and outlet distribution zone of the cathode flow field as the dot matrix which could improve gas distribution. Wen et al. [19] designed a intersectant flow field and the dot block is diamond shape. The sloping edge of diamond can guide air flow and improve gas distribution in the flow field. In this design, channels were still broken lines and dot blocks still occupied a consid erable proportion of the flow field. Atyabi and Afshari [20] designed a honeycomb flow field of the cathode with regular hexagon dot blocks. The flow field was a zone, but not linear channels anymore. Oxygen distribution was therefore improved, but gas concentration in the area of GDL under dot blocks was still quite low. Besides the conventional flow field, some novel flow fields with new materials and structures, such as porous flow field [21–23], 3D fine
2. Flow field design The schematic of the designed flow field plate with dot matrix and sloping baffle is shown in Fig. 1(a). The designed flow field is called as the matrix flow field in the following. The plate consists of dispersive and arrayed blocks with sloping angles as the shoulder. The top surface of each block is diamond shape which its two internal acute angles are pointed to the inlet and outlet, respectively. It can guide air flow along the short-edge of the plate and improve air distribution in the flow filed. Each block slopes from the inlet to the outlet in through-plane direction which can be viewed as a sloping baffle to block air flow and guide air transport from the flow field to GDL. The features of the designed plate are described as above. For nu merical investigation, the matrix flow filed plates with specific di mensions are presented. The plate area is 53 mm*12 mm. The thickness of side walls is 0.5 mm. In order to make the simulation approach to the 3
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Table 1 Five designs of the matrix flow field. Side length of blocks Rows along the short-edge Interval of blocks along the short -edge Rows along the long-edge Interval of blocks along the long-edge Total number of blocks Effective channel-shoulder ratio
Mat1.0_3 � 12
Mat1.0_3 � 16
Mat1.0_3 � 20 (baseline)
Mat0.9_3 � 12
Mat0.9_4 � 12
1 mm 3 3 mm 12 4 mm 36 5.90
1 mm 3 3 mm 16 3 mm 48 5.20
1 mm 3 3 mm 20 2.4 mm 60 4.63
0.9 mm 3 3 mm 12 4 mm 36 6.37
0.9 mm 4 2 mm 12 4 mm 48 5.72
3. Full cell model
Table 2 Cell properties and operating conditions. Parameter
Value
Temperature Output voltage Back pressure Inlet relative humidity Stoichiometry Thickness of GDL,MPL, PEM Porosity of GDL, MPL Contact angle of GDL, MPL, CL Intrinsic permeability of GDL, MPL, CL, PEM EW of PEM Thickness of CL Pt loading in CL Pt-carbon rate in CL Ionomer-carbon rate in CL Carbon particle radius in CL Ionomer coverage in CL Density of Pt, carbon Electrical conductivity of BP, GDL, MPL, CL
80 � C 0.9 V to 0.3 V Anode: 1.5atm Cathode:1.5atm Anode: 1.0 Cathode: 1.0 Anode: 1.5 Cathode: 2.0 200 mm, 20 mm, 25.4 mm 0.6, 0.5 120� , 120� , 95� 2.0e 12, 1.0e 12, 1.0e 13, 2.0e
Thermal conductivity of BP, MPL, CL,PEM Thermal conductivity of GDL Transfer coefficient Reference gas reactant concentration Reference exchange current density Phase change rate between liquid water and water vapor Transfer rate between membrane water and water vapor or liquid water
20
1.1 kg mol 1 Anode: 6 mm Cathode: 10 mm Anode: 0.1 Cathode: 0.3 Anode: 0.2 Cathode: 0.4 Anode: 0.7 Cathode: 0.9 2.5e-8 0.9 21450 kg m 3, 2000 kg m 3 20000 S m 1, 8000 S m 1, 5000 S m 1, 5000 S m 1 20 W m 1 K 1, 1 W m 1 K 1, 1 W m K 1, 0.95 W m 1 K 1 In-plane: 21 W m 1 K 1 Throughplane: 1.7 W m 1 K 1 0.5 Anode: 56.4 mol m 3 Cathode: 3.39 mol m 3 Anode: 3.0 A m 2 Cathode: 3.0e 4A m 2 100s 1 1.3s
To investigate cell output performance and internal transport process of the PEMFC with the designed cathode flow field, a previously developed three-dimensional two-phase steady-state full cell model is utilized in the study [25]. The computational domain is shown in Fig. 1 (c). The anode plate is parallel flow field with six straight channels. The cross section area of straight channels is 1 mm � 1 mm and the shoulder width is 1 mm. Five designs listed in Table 1 are all employed as the cathode flow field. As shown in Fig. 1(c), inlets and outlets of the anode and cathode both extend 10 mm to avoid reverse flow at the outlets during the iteration process and improve numerical stability. The extended sections have not much influence on the flow field when calculation is convergent [18]. Nafion 211 membrane and counter-flow configuration are employed for the simulated fuel cell. The cell prop erties and operating conditions are listed in Table 2. In our previous study, two-phase flow in flow fields was simulated by Eulerian – Eulerian model. Simulation results showed that the value of liquid saturation in flow fields was usually lower than 1.0 3 and the state of liquid water was considered as mist [18]. For model simplification, single-phase flow in flow fields is considered in this study by assuming that liquid water in flow fields can be blown away quickly by air flow and liquid saturation in flow fields is zero. To realize the water removal capacity of the matrix flow field, a two-phase flow analysis by VOF method will be conducted in the next section. Other modeling assump tions are the same as that in Ref. [25]. The involved conservation equations are briefly represented as following. Electronic potential conservation: � 0 ¼ r⋅ κeff (2) e rϕe þ Se
1
1
Ionic potential conservation: � 0 ¼ r⋅ κeff ion rϕion þ Sion
real-scale automobile PEMFC [18], the inlet and outlet are located diagonally on the short-edge of the plate, and widths of the inlet and outlet are both 3 mm. The total height of the plate is 2 mm and the depth of the fluid domain is 1 mm. For the single block, the internal acute angle of diamond shape is 60∘, and the sloping angle in through-plane direc tion is 30∘. The height of blocks is equal to the depth of the fluid domain, 1 mm. Three views of the single block is shown in Fig. 1(b). Five matrix flow fields with different block sizes and numbers are presented in Table 1, which are called Mat1.0_3 � 12, Mat1.0_3 � 16, Mat1.0_3 � 20, Mat0.9_3 � 12, Mat1.0_4 � 12, respectively. Effective channel-shoulder ratio is defined as:
εch
sh
¼
Ach Ash
GDL GDL
(3)
Gas mixture mass conservation:
∂ εð1 ∂t
� � sÞρg þ r⋅ ρg ug ¼ Sm
Gas mixture momentum conservation: ! � � � � ρg ug ρg ug ug ug ∂ ¼ rPg þ μg r⋅ r þ r⋅ 2 ∂t εð1 sÞ εð1 sÞ ε2 ð1 sÞ � �� T ug þr εð1 sÞ � � �� 2 ug ug r r⋅ þ Su 3 εð1 sÞ
(4)
�
(1)
(5)
Gas species conservation (i: hydrogen, oxygen and water vapor):
where εch-sh is effective channel-shoulder ratio, Ach-GDL is the area of the interface between the fluid domain and GDL, and Ash-GDL is the area of the interface between blocks and GDL. Effective channel-shoulder ratios of the five matrix flow field design are therefore calculated and listed in Table 1.
∂ εð1 ∂t
� � � sÞρg Yi þ r⋅ ρg ug Yi ¼ r⋅ ρg Deff i rYi þ Si
Liquid pressure conservation in porous electrode: � � ∂ Kkl ðεsρl Þ ¼ r⋅ ρl rPl þ Sl ∂t μl
4
(6)
(7)
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Journal of Power Sources 434 (2019) 226741
∂ εsρl Cp;l T þ εð1 ∂t
� sÞρg Cp;g T þ r⋅ εsρl Cp;l ul T þ εð1
� ¼ r⋅ keff rT þ ST
sÞρg Cp;g ug T
� (9)
In order to reflect the effect of oxygen transport on cell output per formance precisely, especially under high current density operation, the agglomerate model of CL is employed in this model. Details about the agglomerate model, transport parameters and source terms in the con servation equations can be found in Ref. [25]. Mass flow rates at the anode and cathode inlet are defined by real output current density and stoichiometry. The outlets of flow fields are defined as the pressure-outlet and pressure drops of flow fields are also counted to correct inlet pressure during the calculation procedure. Constant temperature thermal boundary conditions are defined on outside surfaces of the cell. The potentiostatic mode is carried out for all simulated cases by defining electronic potentials at the anode and cathode BP end surface as 0 V and Erev-Vout, respectively [28]. Numerical procedures are implemented by a commercial CFD soft ware, Fluent, coupling with self-written codes of user defined function (UDF). Structured grid cells are employed in the whole computational domain with 265 � 79 � 60 grid cells in X � Y � Z directions, respec tively. For the grid-independence test, the simulation results show no much difference on output current density, local current density and gas distribution by further increasing grid cells to 318 � 110 � 72. The simulation results including polarization curves and ohmic loss were compared with experiments and a good agreement was achieved which can be found in Ref. [25]. 4. Two-phase model by VOF Two-phase flow modeling by VOF method is utilized to simulate the liquid water removal process in the matrix flow field. As shown in Fig. 1 (d), the computational domain is the fluid domain of Mat1.0_3 � 20, the inlet and outlet are extended for 10 mm. The bottom wall represents the interface between the flow field and GDL, and other walls represent internal surfaces of the plate. The basic assumptions include unsteady, isothermal and laminar flow conditions. VOF method is employed to track the two-phase interface between liquid water and air. The conservation equations include continuity equation, momentum equation and volume fraction of liquid water and air by VOF method. Numerical procedures are implemented by the software, Fluent, and the involved equations are build-in. More details can be found in Ref. [29]. The inlet and outlet are set as velocity-inlet and pressure-outlet, respectively. Absolute pressure of the outlet is 1.5atm. The inlet veloc ity is estimated as: uc ¼
(10)
where uc (m s 1) is cathode inlet velocity, I(A m 2) is current density, Vm(m3 mol 1) is molar volume of air, Aact (m2) is the activation area, STc is cathode stoichiometry, 0.21 represents the oxygen volume fraction of air, F is the Faraday constant, Ain(m2) is the inlet area. The molar volume Vm can be calculated by the ideal gas law when P ¼ 1.5atm and T ¼ 353.15 K. Current density is assumed as 2.0 A cm 2, and inlet gas is assumed as dry air. Other parameters, such as Aact,Ain and STc, are the same with full cell model in Table 2. The estimated inlet velocity is therefore calculated as 2.1 m s 1. Contact angles of the bottom, top and side wall are set as 150∘, 30∘, 90∘, respectively. Nine liquid water droplets with radius of 0.2 mm are initialized at different positions of the up stream, middle and downstream of the flow field, respectively. Maximum element size is set as 0.1 mm and the time step is set as 1.0 6s. The grid-independence test is carried out by increasing the total grid number by 40%, and difference of simulation results including pressure drop and liquid water removal can be ignored.
Fig. 2. (a) Polarization curves (b) Net output power (c) Pressure drop of PEMFC with the five matrix, parallel and serpentine flow fields.
Membrane water conservation: � � � ρmem ∂ Jion ρ ðωλÞ þ r⋅ nd ¼ mem r⋅ Deff mw rλ þ Smw EW ∂t F EW
IVm Aact STc 0:21 � 4FAin
(8)
Energy conservation: 5
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Journal of Power Sources 434 (2019) 226741
Fig. 3. Contour of -Y velocity at the middle plane of the five matrix flow fields.
5. Results and discussion
drop difference among the five is very a little. Decreasing block interval and increasing block number of the matrix flow field in the investigated range will increase only a little pressure drop, but improve cell output performance greatly. We can also find that cell output performance generally increases with increasing contact area between the flow field plate and GDL in the investigated range. Although contact area of Mat1.0_3 � 16 is larger than that of Mat0.9_4 � 12, cell output perfor mance of these are similar. As we know, the flow field with fine structure (small scale) would have a good performance. Detailed reasons will be discussed in the following sections.
The cell output performance, internal multi-physical quantities dis tribution and liquid water removal process of PEMFC with the matrix flow fields are predicted by conducting full cell model and VOF model. The five matrix, parallel and serpentine flow fields are simulated and discussed to explain the characteristic of the designed matrix flow field. 5.1. Output performance Fig. 2 shows polarization curves, net output power and pressure drop of PEMFC with the five matrix, parallel and serpentine cathode flow fields. Although output performance of the cells with matrix flow fields are similar or even a little worse than that with parallel and serpentine flow fields in the low current density region (<2.0 A cm 2), the ad vantages of matrix flow fields become very significant with further increasing current density. Moreover, pressure drop of matrix flow fields is far lower than the serpentine, and even lower than the parallel which is due to the decreasing shoulder volume and increasing fluid domain of matrix flow fields. It can be summarized that the matrix flow field can improve cell output performance without increasing pressure drop, especially in the high current density region. Therefore, the matrix flow field fits the increasing current density demand of PEMFC well. Comparing cell output performance of the five matrix flow fields, Mat1.0_3 � 20 > Mat0.9_4 � 12 � Mat1.0_3 � 16 > Mat1.0_3 � 12 > Mat0.9_3 � 12. Pressure drop is the same order, although pressure
5.2. Air guidance in the matrix flow field In order to both achieve high energy efficiency and output power density, output voltage of PEMFC is usually between 0.6 V and 0.8 V. As shown in Fig. 2(a), output voltage corresponding to the maximum output power of PEMFC with the five matrix, parallel and serpentine flow fields are all around 0.6 V. Therefore, all the results shown in this and following sections are based on Vout ¼ 0.6 V. In this section, air guidance effects of sloping blocks are investigated and discussed. Fig. 3 shows -Y velocity at the middle plane of the cathode flow field among the five matrix flow fields. Since the direction of air supply to GDL is the negative direction of Y, the positive velocity value in Fig. 3 represents flow velocity to GDL. It can be found that there exists obvious flow convection to GDL caused by the slope of blocks which are mainly located in the interval region between blocks along the 6
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Journal of Power Sources 434 (2019) 226741
Fig. 4. Streamline of velocity in X-Z plane and contour of Z velocity at the middle plane of the five matrix flow fields.
long-edge of the plate. The matrix flow field has a large fluid domain for air transport, but the area of GDL under blocks still faces insufficient air supply. Flow convection around blocks can improve air supply to the area of GDL under blocks. There also exists flow velocity away from GDL in the interval region between blocks along the short-edge of the plate, which is especially obvious in Mat1.0_3 � 20 and Mat0.9_4 � 12. In this region, air flow can make liquid water move upwards and depart from the surface of GDL. This effect will be further discussed in Section 5.5. Fig. 4 shows the streamline of velocity in X-Z plane and the contour of Z velocity at the middle plane of the five matrix flow fields. The vector length is set as uniform and the streamline only represents the flow di rection. Air flow is guided by the slope edge of diamond blocks in Z direction which can improve air distribution along the short-edge of the plate. The importance of air distribution along the short-edge of the plate will become more obvious with increasing the scale and width of the plate. Comparing the five matrix flow fields in Figs. 3 and 4, Mat0.9_3 � 12 has the larger area of air guidance to GDL (-Y direction), but Mat1.0_3 � 20 has the larger area of air guidance along the shortedge (Z direction), and the two effects both benefit to air transport and cell output performance. We can summarize that there is a trade-off between air guidance to GDL and air guidance along the short-edge for different block sizes and numbers.
5.3. Oxygen concentration and liquid saturation In this section, distribution of oxygen concentration and liquid saturation are presented to explain the advantages of the designed ma trix flow field. Fig. 5(a) and (b) show oxygen concentration and liquid saturation at the interface between cathode CL and MPL among the five matrix, parallel and serpentine flow fields, respectively. The distribution characteristic of the matrix flow field can be described as relatively low oxygen concentration and high liquid saturation under blocks. Compared with the parallel and serpentine flow field, we can easily found that the average value of oxygen concentration is larger and that of liquid saturation is smaller for the matrix flow field, and distribution of oxygen and liquid are more uniform. Oxygen starvation in down stream and oxygen distribution along the short-edge of the matrix flow field are obviously improved. And the matrix flow field could also decrease liquid saturation under shoulders due to the large fluid domain. Furthermore, comparing the five matrix flow fields in Fig. 5(a) and (b), we can feel that Mat0.9_3 � 12 has the maximum average value of ox ygen concentration and Mat1.0_3 � 20 has the minimum, and Mat0.9_3 � 12 has the minimum average value of liquid saturation and Mat1.0_3 � 20 has the maximum. It can be also found that distribution along the long-edge of the plate is more uniform for Mat0.9_3 � 12 and distribution along the short-edge of the plate is more uniform for Mat1.0_3 � 20 and Mat0.9_4 � 12. For quantitative comparison, Fig. 6(a) and (b) show the average 7
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Fig. 5. Contour of (a) oxygen concentration (b) liquid saturation at the interface between cathode CL and MPL among the five matrix, parallel and serpentine flow fields.
value and standard deviation of oxygen concentration and liquid satu ration at the interface between cathode CL and MPL among the five matrix flow fields. Although decreasing block interval and increasing block number decreases the average value of oxygen concentration and increases the average value of liquid saturation, distribution of the two parameters becomes uniform overall. For different single block sizes, decreasing block size and without decreasing contact area between the flow field plate and GDL (by increasing block number) are helpful for increasing oxygen concentration, decreasing liquid saturation and uni form distribution. This result also fits and further explains the trade-off effect of block size and number we presented in the last section. Increasing block number means increasing flow resistance and pressure drop, but also benefits oxygen uniform distribution. Small scale of single block is positive but providing sufficient contact area is more important for the matrix flow filed plate.
low liquid saturation. On the contrary, regions of high reaction rate for the parallel and serpentine flow field are mainly the area under channels due to sufficient shoulders for current conductor, and oxygen concen tration and liquid saturation take an important role on reaction rate distribution. Now we can explain why current densities of the parallel and serpentine flow field when Vout ¼ 0.6 V are similar or even a little higher than the matrix flow field, even then the average values of oxygen concentration and liquid saturation are worse and these distributions are more non-uniform (Fig. 5(a) and (b)). We can conclude that the matrix flow field increases fluid domain but also decreases the area for current conductor which may be against cell output performance. For the matrix flow field, the other trade-off effect of contact area is presented. A large fluid domain is helpful for air transport, but adequate contact area be tween the flow field plate and GDL for current conductor is also demanded for the matrix flow field. As cell output performance pre sented in Fig. 2(a), Mat1.0_3 � 20 is the best in the investigated range.
5.4. Reaction rate
5.5. Water removal process
Discussion of the last two sections is about mass transport effects of the matrix flow field, but one of the most basic feature of the dot matrix, current conductor, is not involved. In this section, the characteristic of the matrix flow field on cell output performance is discussed overall. Fig. 7 shows reaction rate at the middle plane of cathode CL among the five matrix, parallel and serpentine flow fields. For the five matrix flow fields, regions of high reaction rate are mainly the surrounding area of blocks but not necessarily regions of high oxygen concentration and
The liquid water removal process in the Mat1.0_3 � 20 flow field is shown in Fig. 8. The initialized droplets can be divided into three series which are located at the upstream, middle and downstream of the flow field, respectively. For the droplets initialized at the downstream, one drop leaves the flow field quickly, and the other two droplets adhere to the top surface after hitting the front wall. For the droplets initialized at the upstream and middle, only very small fraction of liquid water 8
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Fig. 6. The average value and standard deviation of (a) oxygen concentration (b) liquid saturation at the interface between cathode CL and MPL among the five matrix flow fields.
removal is blocked by the matrix blocks, and most of liquid water moves ahead quickly. Besides moving ahead, liquid water also moves along X direction caused by the air flow guidance along the short-edge of the plate. As the discussion in Section 5.2, flow velocity is away from GDL to the top surface of the flow field (Y direction) in the interval region be tween blocks along the short-edge of the plate. This effect makes liquid water move upwards and depart from the surface of GDL. After 15 ms, almost all liquid water has left the surface of GDL. This phenomenon can avoid the porous blockage by liquid water and benefits oxygen transport.
with the designed matrix flow field. Furthermore, five matrix flow fields with different sizes and numbers of blocks are compared. The simulation results show that the matrix flow field can effectively improve cell output performance, especially in high current density region. Based on the analysis of internal transport process, the advantages of the matrix flow field include two points. Firstly, a large fluid domain increases the area of air supply from the flow field to GDL and water removal from GDL to the flow field, and oxygen distribution is also improved. Sec ondly, the two air guidance of sloping blocks are effective, including air guidance along the short-edge of the plate caused by the sloping edge of diamond shape, and air guidance to GDL in through-plane direction caused by the sloping block. In summary, the matrix flow field can enhance oxygen supply to GDL and improve oxygen uniform distribu tion compared with the parallel and serpentine flow fields. By comparing the five matrix flow fields with different block sizes and numbers, we also find that adequate contact area between the flow field plate and GDL for current conductor is also demanded. There is a trade-off between increasing the fluid domain for air transport and providing adequate contact area for current conductor. Increasing block number in a proper level also benefits oxygen uniform distribution. Small scale of single block is also positive but providing sufficient
6. Conclusion A novel dot matrix and sloping baffle flow field plate of the cathode is designed in this study. The plate consists of dispersive and arrayed blocks with sloping angles as shoulders. The top surface of each block is diamond shape which its two internal acute angles are pointed to the inlet and outlet, respectively. Each block slopes from the inlet to the outlet in through-plane direction. Three-dimensional two-phase full cell model and VOF model are conducted to predict cell output performance, internal transport process and liquid water removal process of PEMFC 9
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Fig. 7. Contour of reaction rate at the middle plane of cathode CL among the five matrix, parallel and serpentine cathode flow fields.
contact area is more important. But we should also note that decreasing the size of single block will certainly increase the difficulty of manu facture. In the investigated range, Mat1.0_3 � 20 which has the most block number has the best cell output performance. The simulation of liquid water removal in the matrix flow field by VOF model shows that liquid water removal is hardly blocked by the arrayed blocks in the matrix flow field. Furthermore, liquid water will move upwards and depart from GDL quickly. Because some region exists the obvious flow velocity away from GDL. This effect can avoid the porous blockage by liquid water and benefit oxygen transport. To sum up the analysis of cell output performance, internal multiphysical quantities distribution and liquid water removal process, we
can conclude that the designed matrix flow field fits the increasing current density demand of PEMFC well. And these advantages could be achieved in the case that the scale of the single block, which is 1 mm and 0.9 mm, does not have to be too small. This study not only presents a detailed flow field design, but more importantly provides some new perspectives on how to enhance oxygen transport and improve oxygen distribution for flow field design. Manufacture of the matrix flow field plate, assembly of the fuel cell and test would be our next step work, and providing sufficient clamping force by the matrix flow field plate should also be considered.
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Fig. 8. (a) Top view (b) Front view of liquid water droplets removal process in the Mat1.0_3 � 20 flow field.
Acknowledgements
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