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Performance enhancement in a proton exchange membrane fuel cell with a novel 3D flow field
Applied Thermal Engineering 164 (2020) 114464
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Performance enhancement in a proton exchange membrane fuel cell with a novel 3D flow field
T
⁎
Jun Shena,b, Zhengkai Tua,b, , Siew Hwa Chanb a b
School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China Energy Research Institute, Nanyang Technological University, 50 Nanyang Avenue, 637553 Singapore, Singapore
H I GH L IG H T S
water could be effectively separated from the gas flow using 3D flow field. • Liquid synergy angles is introduced to verify the superiority of 3D flow field. • Cathode • Effective mass transfer coefficient is proposed for the performance evaluation.
A R T I C LE I N FO
A B S T R A C T
Keywords: PEMFC 3D flow field Average synergy angle Effective mass transfer coefficient
Flow field plays a vital role in the design and application of a proton exchange membrane fuel cell (PEMFC). Combined with the enhancement of the abilities of mass transfer and water removal in the flow channel, a new optimized three-dimensional (3D) flow field is proposed to investigate the water transport and cell operating characteristics. The 3D flow field is composed of several straight flow units arranged in a staggered manner with an inclination at the end, and the transition areas and subchannels between the flow units are subjected to hydrophilic treatment. The result indicates that the new type of flow field can effectively separate liquid water from the reactant flow and water can be partially removed through the subchannel. Compared with the conventional flow field, the 3D flow field could enhance the mass transfer ability and improve the PEMFC performance, especially at high current densities. Based on the field synergy principle, we prove that the synergic degree between the velocity vector and concentration gradient agrees with the performance changes under the turbulence of the staggered flow units and the effective mass transfer coefficient (EMTC) in the direction of electrochemical reaction of the 3D flow field is also enhanced.
1. Introduction Proton exchange membrane fuel cell (PEMFC) has attracted increasing attention as a promising energy conversion device in the future [1–3]. With the advantages of light weight, high energy density, low noise, environment friendly, and low infrared radiation, PEMFC has been widely used in civilian and military fields [4–6]. During the operation process, water management seriously affects the performance and operating safety of PEMFCs. Once liquid water accumulates inside the PEMFC, flooding, which results in a decreased diffusion area, can lead to the decrease in the cell performance and even its lifetime. Flow field design influences not only the reactant distribution but also the water distribution, which is one of the key issues for the design of PEMFC. Many studies focused on the effect of flow field design on the fuel
⁎
cell performance [7–10]. Aiyejina and Sastry [11] performed research on performance improvement through flow field optimization and suggested that the cell performance could be improved by using small size channel and rib of a serpentine flow field at low operating voltages and by adding baffles. Manso et al. [12] reviewed the influence of geometric parameters of a flow field on the cell performance, including the flow field form, channel dimension, channel number, cross-sectional shape, and so on. In a specific study, Shimpalee et al. [13] reported the impact of gas path number and gas path dimensions on PEMFC performance. Cooper et al. [14] conducted experimental tests to determine the main reason for the performance enhancement in decreasing channel length to width ratio of interdigitated flow fields. Wang et al. [15] used a conventional cathode parallel flow field design with a subchannel to improve the uniformity of reactant distribution, the ability of water removal, and the cell performance. Seven flow fields
Corresponding author at: School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China. E-mail address: [email protected] (Z. Tu).
https://doi.org/10.1016/j.applthermaleng.2019.114464 Received 5 August 2019; Received in revised form 24 September 2019; Accepted 29 September 2019 Available online 30 September 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature cp ck cr D e F F k keff K Mi p pc pwv psat rw R Rref Ran Rcat s
S t T u v
specific heat capacity (J·kg−1·K−1) concentration of species i (mol·m−3) condensation constant (s−1) diffusion coefficient (m2·s−1) effective mass transfer coefficient body force (N) Faraday constant 9.6487 × 104 (C·mol−1) curvature radius (m) effective thermal conductivity (W·m−1·K−1) permeability (m2) molecular weight of species i (kg·kmol−1) pressure (Pa) capillary pressure (Pa) pressure of water vapor (Pa) pressure of saturated water (Pa) condensation rate (kg·m−3·s−1) gas constant 8.314 (J·mol−1·K−1) reference volumetric transfer current density (A·m−3) anode volumetric transfer current density (A·m−3) cathode volumetric transfer current density (A·m−3) liquid volume fraction
source term of governing equations time (s) temperature (K) velocity vector (m·s−1) velocity components in y directions (m·s−1)
Greek letter α αan αcat αi γ γan γcat ε η μ ρ σ σe σm φ
inclination angle (°) anode transfer coefficient cathode transfer coefficient volume fraction of species i synergy angle (°) anode concentration dependence cathode concentration dependence porosity overpotential (V) dynamic viscosity (N·s·m−2) density (kg·m−3) surface tension (N·m−1) electrical conductivity (S·m−1) electrical conductivity (S·m−1) electric potential (V)
the multi-pass serpentine flow field showed more evenly distribution of temperature than other designs under the same pressure drop level. Wave-like flow channels often appeared in the design and optimization of flow field [20–24]. Kuo et al. [20,21] evaluated the performance of PEMFCs with a wave-like flow channel using synergic degree between the velocity vector and temperature gradient. To reduce the concentration loss, Han et al. [22] suggested cathode channel design parameters with a wave shape, including the heights and distances of
were analyzed by Rahimi-Esbo et al. [16], and it was found that a twoto-one serpentine flow channel (two serpentine channels at the entrance converged to one at the exit) showed the best performance, especially at high current densities. Zeng and Liu et al. [17,18] established a 3D, non-isothermal model of PEMFCs and adopted a genetic algorithm to obtain an optimal channel design and operating conditions. Baek et al. [19] investigated the effect of coolant flow field design on cooling performance and temperature distribution, and the results revealed that
Fig. 1. The schematic of flow fields (a) Conventional parallel flow field (b) 3D flow field (c) 4 × 3 structure (d) Number of main channels and inclination angle. 2
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Table 1 Geometric parameters.
Current collector Main channel Sub-channel Gas diffusion layer Catalyst layer Membrane
Table 2 Boundary conditions of water transport. Height/mm
Width/mm
Length/mm
Parameter
Value
4 2.5 2.5 0.25 0.012 0.012
24.5 2 1.5 24.5 24.5 24.5
19 19 19 19 19 19
Operating pressure (Pa) Back pressure (Pa) Gas inlet velocity (m·s−1) Static contact angle of main channel (°) Static contact angle of sub-channel (°) Coefficient of gas-liquid surface tension (N·m−1)
101,325 0 2 135 45 0.072
the waveform. Yi et al. [23] adopted stamped perforated bipolar plates with an open rate of 28.26% to increase the volumetric power density and specific power of the novel structured stack. Pourrahmani et al. [24] utilized wave-like porous rib in the flow channel to improve the cell performance, and artificial neural network (ANN) was used for sensitivity analysis and optimization. In addition to conventional flow field, 3D flow field has attracted more and more attention. Yoshida and Kojima [25] introduced MIRAI with 3D flow field, high efficiency catalyst, and thin membrane, performing a 2.4 times larger current density than that with the 2008 model. Waved serpentine flow fields with a bend radius of 0.5 mm and different slope angles were investigated in a 50 cm2 PEMFC [26]. The thus-assembled fuel cell with the waved structure design exhibited better performance and much higher oxygen mass fraction than that with conventional design. Cai et al. [27] presented a 3D cathode flow field and proposed a performance evaluation criterion (PEC) to estimate the performance of PEMFCs. It was found that the PEC value was positively correlated with the cell performance. Zhang et al. [28] built a multi-phase numerical model of a PEMFC to investigate the water distribution in a 3D flow field, suggesting that the 3D flow field could improve the supply of reactant and facilitate water removal. Yan et al. [29] proposed two types of 3D flow fields, own waved channels and gradient waved channels. Both experimental and numerical results showed the advantages of 3D design in the improvements of cell performance and oxygen convection. Although novel flow field designs for PEMFCs had been studied in many literatures, few publications mentioned the mechanism of performance improvement and criterion for optimizing the structure design. Combined with the enhancement of mass transfer and optimization of water transport characteristic in the flow channel, a new optimized 3D flow field was proposed and the according operation characteristics were evaluated. The structure of each unit was a straight flow channel with an inclination at the end, which offered a regular and easy process compared with the channel unit of MIRAI and other waved channels. The inclination was beneficial for reducing the concentration overpotential due to the reactant consumption. Cathode average synergy angle and effective mass transfer coefficient (EMTC) were also proposed to determine the mass transfer ability of the PEMFC [30].
Table 3 Operating conditions of PEMFC. Parameter
Value
Operating pressure (Pa) Back pressure (Pa) Operating temperature (K) Air inlet temperature (K) H2 inlet temperature (K) Air stoichiometry H2 stoichiometry Air relative humidity H2 relative humidity Open circuit voltage (V)
101,325 0 338 338 338 2 1.5 100% 100% 1.066
Table 4 Main physical property parameter of PEMFC. Parameter
Value
Current collector effective conductivity (S/m) Current collector thermal conductivity [W/(m·K)] Gas diffusion layer porosity Gas diffusion layer viscous resistance (1/m2) Gas diffusion layer effective conductivity (S/m) Gas diffusion layer thermal conductivity [W/(m·K)] Catalyst layer porosity Catalyst layer surface-volume ratio (1/m) Catalyst layer effective conductivity (S/m) Catalyst layer thermal conductivity [W/(m·K)] Electrolyte equivalent weight (kg/kmol) Contact resistance [(1/S)·m2]
83,000 85.5 0.5 1 × 1012 5000 1.7 0.5 2 × 105 1000 8 1100 2 × 10-6
Fig. 2. Mass transfer in the PEMFC.
2. Design of a 3D flow field The schematics of the conventional parallel and 3D flow fields are shown in Fig. 1(a) and Fig. 1(b). The design process of the 3D flow field was that a conventional parallel flow channel was cut off at a certain length, which formed a transition area for gas mixture and redistribution. Then, an offset between adjacent channels along the gas flow direction was set to enhance the disturbance and convective mass transfer of the reactants. Inclinations were provided at the end of each flow unit to increase the velocity of the reactants. The structure of the 3D flow field was defined as a 4 × 3 structure, as shown in Fig. 1(c), which included four main channels and each channel was divided into three parts. The location of each main channel is numbered in Fig. 1(d), with inclination angle α at the end of each part. In the main channel, the gas in the channel participated in the electrochemical reaction, whereas the gas in the subchannel was mainly
expected to be used for water drainage. In addition, the transition area and subchannel according to the rib area of the parallel flow field were treated with hydrophilic coating to accelerate the liquid water drainage.
3. Modeling and methodology 3.1. Water transport model The volume of fluid (VOF) model in FLUENT using advanced Lagrangian interface-tracking scheme is adopted to investigate the water transport characteristics in a 3D flow channel. The government equations are shown below [31]. 3
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Fig. 3. Water distribution in 3D flow channel with time evolution. (a) 1 ms (b) 2 ms (c) 4 ms (d) 10 ms.
study of fuel cell operation. The governing equations are given as follow.
3.1.1. Mass conservation equation
∂ρ u) = 0 + ∇ (ρ ·→ ∂t
(1)
3.2.1. Mass conservation equation
where ρ is the volume average density.
∂ (ερ) u ) = Sm + ∇ (ερ→ ∂t
3.1.2. Volume conservation equation
∂αi +→ u · ∇α i = 0 ∂t
where ε is the porosity and Sm is the source term of mass. Sm is individually solved for each distinct region [32].
(2)
where α i is the volume fraction of species i, α1 represents the gas phase, and α2 represents the liquid phase.
3.2.2. Momentum conservation equation
u) ∂ (ερ→ u u ) = −ε∇p + ∇ (εμ∇→ u ) + Su + ∇ (ερ→→ ∂t
3.1.3. Momentum conservation equation
∂ (ρ→ u) T →+→ + ∇ ·(ρ→→ u u ) = −∇p + ∇ ·[μ (∇→ u + ∇→ u )] + ρg F ∂t
(6)
where p is the pressure, μ is the dynamic viscosity, and Su is the source term of the momentum. (3) 3.2.3. Energy conservation equation
where: Phase volume: α1 + α2 = 1 Volume average density: ρ = α2 ρ2 + (1 − α2) ρ1 Volume average dynamic viscosity: μ = α2 μ 2 + (1 − α2) μ1 The source term of the momentum conservation equation due to the surface tension and wall adhesion is expressed as
→ F = 2σij ρki ∇αi/(ρi + ρj )
(5)
∂ (ερcp T ) ∂t
u T ) = ∇ ·(k eff ∇T ) + SQ + ∇ (ερcp →
(7)
k eff
is the effective here, cp is the specific heat at constant pressure, thermal conductivity, T is the temperature, and SQ is the energy source term.
(4) 3.2.4. Species conservation equation
where σij is the surface tension and k is the radius of curvature.
∂ (εck ) + ∇ (ε→ u ck ) = ∇ ·(Dkeff ∇ck ) + Sk ∂t
3.2. Mathematical model of PEMFC
Dkeff ,
(8)
Here, ck , and Sk are the species concentration, species effective diffusion coefficient, and species source term, respectively.
A built-in Fuel Cell and Electrolysis Module in Fluent is used for the 4
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Fig. 4. Water distribution with the effects of inlet velocity and contact angle (a) 2 ms (Velocity of 3 m·s−1) (b) 10 ms (Velocity of 3 m·s−1) (c) 2 ms (With modified surfaces) (d) 10 ms (With modified surfaces).
here, ε = 1, cr is the condensation constant hardwired to 100 s−1, and rw is determined by the pressure difference between the water vapor and saturated vapor pressure. The volume fraction of the liquid water is s . In the gas diffusion and catalyst layers
∂ (ερl s ) Ks 3 dpc ⎤ ∇s = rw + ∇ ·⎡ρl ⎥ ⎢ ∂t ⎣ μl ds ⎦
(11)
where pc is the capillary pressure and K is the permeability. 3.2.6. Conservation of charge
pwv − psat RT
(13)
γan
ref ⎛ CO2 ⎞ R cat = Rcat ⎜ C ref ⎟ ⎝ O2 ⎠
(9)
MH2 O , −sρ1]
∇ (σm ∇φm) + Sm = 0
ref ⎛ CH2 ⎞ Ran = Ran ⎜ C ref ⎟ ⎝ H2 ⎠
3.2.5. Volume fraction conservation In the gas channels:
rw = crmax [(1 − s )
(12)
Here, σe and σm are the electrical conductivity, φe and φm are the solid phase and membrane phase potentials, respectively, Se and Sm are the electron flow and proton flow source terms, respectively. The source terms were calculated by the Butler–Volmer equation. In the anode, Sm = Ran and Se = −Ran , while in the cathode, Sm = −R cat and Se = R cat .
Fig. 5. Performance comparison between conventional parallel flow channel and 3D cathode flow channel.
∂ (ερl s ) ul ) = rw + ∇ (sρl → ∂t
∇ (σe ∇φe ) + Se = 0
[exp (
α cat Fηan αan Fηan ) − exp (− )] RT RT
γcat
[exp (−
αan Fηcat α cat Fηcat ) − exp ( )] RT RT
(14)
(15)
where Ran and R cat are anode and cathode volumetric transfer current density, Rref is reference value, C and C ref are the species concentration and reference value, γan and γcat are anode and cathode concentration
(10) 5
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Fig. 6. Velocity distribution contour of 3D cathode flow channel. (a) Main channel (b) Subchannel.
Fig. 7. Mole concentration of oxygen at the interface between gas diffusion layer and catalyst layer of conventional and 3D cathode flow channels (1.0 A·cm−2). (a) Conventional cathode flow channel (b) 3D cathode flow channel.
3.4. Field synergy methodology
dependence, αan and α cat are the transfer coefficient of anode and cathode, F is the Faraday constant, R is the gas constant and η is the activation loss.
In PEMFC, the gas flow is in the horizontal direction, whereas the electrochemical reaction is in the vertical direction, shown in Fig. 2. According to the field synergy principle [33–36], enhanced mass transfer in PEMFC requires the well synergy between the flow velocity and concentration gradient. The synergy angle γ is defined as
3.3. Geometry model According to the local simplified model of a 3D flow field, the current collectors, gas diffusion layers, catalyst layers, and membrane were added to investigate the operating characteristic of the fuel cell. The geometric parameters of the fuel cell are listed in Table 1. The whole domain was spatially discretized with an unstructured tetrahedral mesh and the mesh counts at inclination angles of 30°, 45°, and 60° were 1,081,772, 1,149,178, and 1,087,639, respectively, considering both the accuracy of the grid and computing resource. The boundary condition of the water transport and operating conditions of a PEMFC are listed in Tables 2 and 3, respectively. In addition, Table 4 gives the main physical property parameters of PEMFC, including the porosity, conductivity and so on.
→ u · ∇c cosγ = → | u |·|∇c|
(16)
where → u is the velocity and∇c is the concentration gradient. EMTC is also proposed to measure the mass transfer capability of the fuel cell, and the expression is presented as
e= v
∂c ∂y
here v is the component of the velocity in the y direction. 6
(17)
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flow channel increased and existed in small parts, although most water existed in the second part. To accelerate the removal of liquid water in the flow channel, the increase in the inlet reactant velocity and modification of surface wettability were considered. 4.1.1. Effect of inlet velocity With the increase of the inlet reactant velocity from 2 to 3 m·s−1, the movement time of the liquid water in the flow channel decreased. Fig. 4(a) shows the water distribution at 2 ms. The water droplet flowed through the first part of the channel, spread, and attached to the transition area in the second part of the channel. The motion of liquid water was significantly faster compared with that shown in Fig. 3(b). Moreover, Fig. 4(b) depicted that the water distribution in the flow channel at 10 ms was more even than that at 2 m·s−1. Meanwhile, the amount of liquid water in the outlet section increased comparing with the velocity of 2 m·s−1, indicating better water removal ability due to the increase of the inlet reactant velocity. Fig. 8. Pressure drop.
4.1.2. Effect of contact angle The water distribution at 2 ms is shown in Fig. 4(c) with the surfaces modified. The surface contact angle of the main channel increased from 135° to 155°, whereas the subchannel angle decreased from 45° to 25°. Slight changes in the shape of the water droplet could be observed, and the motion characteristics were almost the same as those in the basic case. Moreover, the liquid water distribution shown in Fig. 4(d) exhibited the same distribution tendency as that shown in Fig. 3(d), where the concentrated distribution of liquid water was in the second part of the flow channel. The third part contained a little amount of liquid water. Because of the decrease in the contact angle of the subchannel, the amount of liquid water in the subchannel increased with the increased hydrophilicity of subchannels.
4. Results and discussions 4.1. Water distribution To investigate the water transport characteristics of a 3D flow field, a water droplet with a radius of 0.5 mm was initialized at 2 mm away from the inlet of each main channel. The transient time step size was 5 × 10−6 s, and the number of time steps was set to 2000 during the simulation. With an inclination angle of 45°, inlet velocity of 2 m·s−1, main channel with surface static contact angle of 135°, and subchannel with an angle of 45°, the water distributions in the 3D flow channel are shown in Fig. 3. Because of the hydrophobic surface of the main channel, the water droplet maintained its shape of a sphere rolling at the center of the flow channel under the air shear force at 1 ms, as shown in Fig. 3(a). At 2 ms, as shown in Fig. 3(b), the water droplet moved to the end of the first part of the channel, being about to enter the transition area and to be redistributed with the reactants. Fig. 3(c) showed that liquid water partly existed in the second part of the main channel attached to the bottom and side walls and partly flowed through the transition area. Because the subchannel was above the main channel and the height difference between them indicated the channel thickness, most liquid water moved through the second part of the main channel, whereas a little liquid water flowed through the subchannel. Fig. 3(d) showed that the liquid water reached the outlet at 10 ms. With the time evolution, the liquid water in the third part of the
4.2. PEMFC operating characteristic 4.2.1. Performance comparison Compared with the conventional parallel flow field, the performance of the PEMFC with novel 3D cathode flow fields were improved, as illustrated in Fig. 5. Because of the low gas consumption at low current densities, the advantage of the modified structure in terms of the mass transfer was not obvious; thus, the performance barely improved at a current density below 0.2 A·cm−2. The output voltage of the 3D cathode flow channel was 0.852 V at 0.2 A·cm−2, whereas it was 0.841 V for the conventional parallel flow channel. However, the output voltage of the 3D cathode flow channel reached up to 0.690 V with an inclination angle of 45° at 1.2 A·cm−2, and it was only 0.551 V for the conventional parallel flow field under the same operation
Fig. 9. Field synergy (a) Cathode average synergy angle (b) Cathode effective mass transfer coefficient. 7
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cathode flow channels with different inclination angles are shown in Fig. 9(a) at current density of 0.2 and 1.6 A·cm −2. During the operation process, the mainstream direction of the gas flow was almost vertical to the concentration gradient. It was the key issue to improve the synergetic degree between the velocity and concentration gradient, which in turn improves the PEMFC performance. We found that the synergy angle of the conventional parallel flow channel was approximately 80° at 0.2 A·cm −2, whereas that of the 3D cathode flow channel was about 65°. The inclination angle of the 3D flow channel had little influence on the synergy angle, which was also consistent with the performance result. At 1.6 A·cm−2, the synergy angle of the conventional flow channel was reduced because the consumption of the reactants increased to maintain the electrochemical reaction at a high current density. However, the synergy angles of the 3D flow channels were still approximately 65°, which indicated that the 3D structure could enhance the mass transfer inside the PEMFC to satisfy the gas consumptions during the reaction at different current densities. Moreover, the structure of the flow channel with an inclination of 30° was the preferred section owing to the low flow resistance during the reaction. EMTC, which is a product of the normal velocity component of the PEMFC with the concentration gradient in the reaction direction, is shown in Fig. 9(b). The EMTC of the 3D cathode flow field was observed to be greater than that of the conventional flow field, which was consistent with the performance variations. The EMTC slightly decreased with the increase of current density as could be understood that large amount of reactants diffused into the catalyst layer to participate in the electrochemical reaction at high current density. Accordingly, the reactants left in the flow channel were less than those at low current density.
conditions. The performance improvement was approximately 25%, which confirmed that the 3D cathode flow field could effectively enhance the ability of mass transfer and reduce the concentration overpotential at high current density. As the current density continued to increase, the cell performance with the conventional flow field sharply dropped. Nevertheless, the performance with the 3D cathode flow channel maintained above 0.6 V at 1.6 A·cm−2. In addition, the inclination structure served as an additional blockage in the flow channel [10], which could also enhance the mass transfer inside the PEMFC. However, the angles of inclination exerted little influence on the cell performance, indicating that the effect of the staggered flow unit was much more serious than that of the inclination angle. 4.2.2. Velocity distribution Fig. 6(a) shows the velocity distribution contour at the center cross section of the main channel with an inclination angle of 45° at 1.0 A·cm−2. With the decrease in the channel height at the inclination, the flow velocity exhibited a significant increase, and the largest velocities were found at the end of each flow unit. Because of the staggered arrangement of the flow units, the velocity distribution in the flow channel to both sides greatly varied, whereas the changes in middle channel (Nos. 2 and 3) were small. From the inlet to the outlet, the flow velocity in main channel Nos. 1 and 2 displayed a trend of gradual increase, indicating severer electrochemical reaction in the inlet section and excess supply of reactants, which in turn resulted in more reactants being left in the outlet section. Fig. 6(b) is the velocity distribution contour at the center cross section of the subchannel. Because of the cross section close to the top wall of the main channel, the overall velocity in the main channel was lower than that in the subchannel. The considerable velocity in the subchannel also proved the advantages of the 3D flow field for water removal.
5. Conclusions A novel 3D flow field in a PEMFC was proposed in this paper to investigate the water transport and performance characteristics using numerical simulation. Combined with the field synergy principle, the conclusions are listed below.
4.2.3. Interface reactant concentration Fig. 7(a) shows that the mole concentration of oxygen in the cathode interface between the gas diffusion layer and catalyst layer of the conventional flow channel decreased gradually from the inlet to the outlet. By comparing the contours of the mole concentration of the conventional and 3D flow channels, the 3D flow channel was found to not only significantly enlarge the high concentration area but also effectively reduce the area where the concentration was almost zero, as shown in Fig. 7(b). In the conventional flow field, almost no reactant was found in the area under the interval between the gas channels, which wasted large activation area and caused uneven distribution of the current density because of the uneven reactant distribution. In contrast, the transition area could provide a possibility for the reactant to diffuse to the area under the subchannel in the 3D flow field. The increase in the reaction area and mole concentration of the reactant could be the very important factors for the performance improvement in the 3D cathode flow field.
(1) Liquid water could be effectively removed through the subchannel of the 3D flow field and the increase in the reactant inlet velocity could be beneficial for water removal. (2) The 3D flow field could enhance the mass transfer ability and improve the performance of PEMFC, especially at high current density. (3) The inclination angle of the channel had little influence on the performance, whereas a larger inclination would lead to a larger pressure drop. (4) The synergy angle between the velocity vector and concentration gradient agreed with the performance, and EMTC could be used to estimate the superiority of the 3D flow channel design for mass transfer enhancement in PEMFC.
4.2.4. Pressure drop The pressure drops of the conventional and 3D cathode flow channel was depicted in Fig. 8. Because of the reduced height at the end of flow unit and the remixing and redistribution of the reactants, the local pressure loss of the 3D flow field was larger than that of the conventional flow field. The bigger the angle of inclination was, the larger was the local pressure loss. Thus, the 3D cathode flow channel with an inclination angle of 60° exhibited the largest pressure drop, followed by the inclination angles of 45° and 30°. Since the pressure drop increase ratio of 3D flow field was less than the performance improvement ratio, the net output power of 3D flow field was still higher than that of the conventional flow field, particularly at high current density.
Declaration of Competing Interest The authors declared that they have no conflicts of interest to this work. Acknowledgement This work was supported by the National Key R&D Program of China (No. 2018YFC0810001) and the Natural Science Foundation of China (No. 51776144). Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.114464.
4.2.5. Field synergy The cathode average synergy angles of the conventional and 3D 8
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9
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Performance enhancement in a proton exchange membrane fuel cell with a novel 3D flow field
T
⁎
Jun Shena,b, Zhengkai Tua,b, , Siew Hwa Chanb a b
School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China Energy Research Institute, Nanyang Technological University, 50 Nanyang Avenue, 637553 Singapore, Singapore
H I GH L IG H T S
water could be effectively separated from the gas flow using 3D flow field. • Liquid synergy angles is introduced to verify the superiority of 3D flow field. • Cathode • Effective mass transfer coefficient is proposed for the performance evaluation.
A R T I C LE I N FO
A B S T R A C T
Keywords: PEMFC 3D flow field Average synergy angle Effective mass transfer coefficient
Flow field plays a vital role in the design and application of a proton exchange membrane fuel cell (PEMFC). Combined with the enhancement of the abilities of mass transfer and water removal in the flow channel, a new optimized three-dimensional (3D) flow field is proposed to investigate the water transport and cell operating characteristics. The 3D flow field is composed of several straight flow units arranged in a staggered manner with an inclination at the end, and the transition areas and subchannels between the flow units are subjected to hydrophilic treatment. The result indicates that the new type of flow field can effectively separate liquid water from the reactant flow and water can be partially removed through the subchannel. Compared with the conventional flow field, the 3D flow field could enhance the mass transfer ability and improve the PEMFC performance, especially at high current densities. Based on the field synergy principle, we prove that the synergic degree between the velocity vector and concentration gradient agrees with the performance changes under the turbulence of the staggered flow units and the effective mass transfer coefficient (EMTC) in the direction of electrochemical reaction of the 3D flow field is also enhanced.
1. Introduction Proton exchange membrane fuel cell (PEMFC) has attracted increasing attention as a promising energy conversion device in the future [1–3]. With the advantages of light weight, high energy density, low noise, environment friendly, and low infrared radiation, PEMFC has been widely used in civilian and military fields [4–6]. During the operation process, water management seriously affects the performance and operating safety of PEMFCs. Once liquid water accumulates inside the PEMFC, flooding, which results in a decreased diffusion area, can lead to the decrease in the cell performance and even its lifetime. Flow field design influences not only the reactant distribution but also the water distribution, which is one of the key issues for the design of PEMFC. Many studies focused on the effect of flow field design on the fuel
⁎
cell performance [7–10]. Aiyejina and Sastry [11] performed research on performance improvement through flow field optimization and suggested that the cell performance could be improved by using small size channel and rib of a serpentine flow field at low operating voltages and by adding baffles. Manso et al. [12] reviewed the influence of geometric parameters of a flow field on the cell performance, including the flow field form, channel dimension, channel number, cross-sectional shape, and so on. In a specific study, Shimpalee et al. [13] reported the impact of gas path number and gas path dimensions on PEMFC performance. Cooper et al. [14] conducted experimental tests to determine the main reason for the performance enhancement in decreasing channel length to width ratio of interdigitated flow fields. Wang et al. [15] used a conventional cathode parallel flow field design with a subchannel to improve the uniformity of reactant distribution, the ability of water removal, and the cell performance. Seven flow fields
Corresponding author at: School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China. E-mail address: [email protected] (Z. Tu).
https://doi.org/10.1016/j.applthermaleng.2019.114464 Received 5 August 2019; Received in revised form 24 September 2019; Accepted 29 September 2019 Available online 30 September 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature cp ck cr D e F F k keff K Mi p pc pwv psat rw R Rref Ran Rcat s
S t T u v
specific heat capacity (J·kg−1·K−1) concentration of species i (mol·m−3) condensation constant (s−1) diffusion coefficient (m2·s−1) effective mass transfer coefficient body force (N) Faraday constant 9.6487 × 104 (C·mol−1) curvature radius (m) effective thermal conductivity (W·m−1·K−1) permeability (m2) molecular weight of species i (kg·kmol−1) pressure (Pa) capillary pressure (Pa) pressure of water vapor (Pa) pressure of saturated water (Pa) condensation rate (kg·m−3·s−1) gas constant 8.314 (J·mol−1·K−1) reference volumetric transfer current density (A·m−3) anode volumetric transfer current density (A·m−3) cathode volumetric transfer current density (A·m−3) liquid volume fraction
source term of governing equations time (s) temperature (K) velocity vector (m·s−1) velocity components in y directions (m·s−1)
Greek letter α αan αcat αi γ γan γcat ε η μ ρ σ σe σm φ
inclination angle (°) anode transfer coefficient cathode transfer coefficient volume fraction of species i synergy angle (°) anode concentration dependence cathode concentration dependence porosity overpotential (V) dynamic viscosity (N·s·m−2) density (kg·m−3) surface tension (N·m−1) electrical conductivity (S·m−1) electrical conductivity (S·m−1) electric potential (V)
the multi-pass serpentine flow field showed more evenly distribution of temperature than other designs under the same pressure drop level. Wave-like flow channels often appeared in the design and optimization of flow field [20–24]. Kuo et al. [20,21] evaluated the performance of PEMFCs with a wave-like flow channel using synergic degree between the velocity vector and temperature gradient. To reduce the concentration loss, Han et al. [22] suggested cathode channel design parameters with a wave shape, including the heights and distances of
were analyzed by Rahimi-Esbo et al. [16], and it was found that a twoto-one serpentine flow channel (two serpentine channels at the entrance converged to one at the exit) showed the best performance, especially at high current densities. Zeng and Liu et al. [17,18] established a 3D, non-isothermal model of PEMFCs and adopted a genetic algorithm to obtain an optimal channel design and operating conditions. Baek et al. [19] investigated the effect of coolant flow field design on cooling performance and temperature distribution, and the results revealed that
Fig. 1. The schematic of flow fields (a) Conventional parallel flow field (b) 3D flow field (c) 4 × 3 structure (d) Number of main channels and inclination angle. 2
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Table 1 Geometric parameters.
Current collector Main channel Sub-channel Gas diffusion layer Catalyst layer Membrane
Table 2 Boundary conditions of water transport. Height/mm
Width/mm
Length/mm
Parameter
Value
4 2.5 2.5 0.25 0.012 0.012
24.5 2 1.5 24.5 24.5 24.5
19 19 19 19 19 19
Operating pressure (Pa) Back pressure (Pa) Gas inlet velocity (m·s−1) Static contact angle of main channel (°) Static contact angle of sub-channel (°) Coefficient of gas-liquid surface tension (N·m−1)
101,325 0 2 135 45 0.072
the waveform. Yi et al. [23] adopted stamped perforated bipolar plates with an open rate of 28.26% to increase the volumetric power density and specific power of the novel structured stack. Pourrahmani et al. [24] utilized wave-like porous rib in the flow channel to improve the cell performance, and artificial neural network (ANN) was used for sensitivity analysis and optimization. In addition to conventional flow field, 3D flow field has attracted more and more attention. Yoshida and Kojima [25] introduced MIRAI with 3D flow field, high efficiency catalyst, and thin membrane, performing a 2.4 times larger current density than that with the 2008 model. Waved serpentine flow fields with a bend radius of 0.5 mm and different slope angles were investigated in a 50 cm2 PEMFC [26]. The thus-assembled fuel cell with the waved structure design exhibited better performance and much higher oxygen mass fraction than that with conventional design. Cai et al. [27] presented a 3D cathode flow field and proposed a performance evaluation criterion (PEC) to estimate the performance of PEMFCs. It was found that the PEC value was positively correlated with the cell performance. Zhang et al. [28] built a multi-phase numerical model of a PEMFC to investigate the water distribution in a 3D flow field, suggesting that the 3D flow field could improve the supply of reactant and facilitate water removal. Yan et al. [29] proposed two types of 3D flow fields, own waved channels and gradient waved channels. Both experimental and numerical results showed the advantages of 3D design in the improvements of cell performance and oxygen convection. Although novel flow field designs for PEMFCs had been studied in many literatures, few publications mentioned the mechanism of performance improvement and criterion for optimizing the structure design. Combined with the enhancement of mass transfer and optimization of water transport characteristic in the flow channel, a new optimized 3D flow field was proposed and the according operation characteristics were evaluated. The structure of each unit was a straight flow channel with an inclination at the end, which offered a regular and easy process compared with the channel unit of MIRAI and other waved channels. The inclination was beneficial for reducing the concentration overpotential due to the reactant consumption. Cathode average synergy angle and effective mass transfer coefficient (EMTC) were also proposed to determine the mass transfer ability of the PEMFC [30].
Table 3 Operating conditions of PEMFC. Parameter
Value
Operating pressure (Pa) Back pressure (Pa) Operating temperature (K) Air inlet temperature (K) H2 inlet temperature (K) Air stoichiometry H2 stoichiometry Air relative humidity H2 relative humidity Open circuit voltage (V)
101,325 0 338 338 338 2 1.5 100% 100% 1.066
Table 4 Main physical property parameter of PEMFC. Parameter
Value
Current collector effective conductivity (S/m) Current collector thermal conductivity [W/(m·K)] Gas diffusion layer porosity Gas diffusion layer viscous resistance (1/m2) Gas diffusion layer effective conductivity (S/m) Gas diffusion layer thermal conductivity [W/(m·K)] Catalyst layer porosity Catalyst layer surface-volume ratio (1/m) Catalyst layer effective conductivity (S/m) Catalyst layer thermal conductivity [W/(m·K)] Electrolyte equivalent weight (kg/kmol) Contact resistance [(1/S)·m2]
83,000 85.5 0.5 1 × 1012 5000 1.7 0.5 2 × 105 1000 8 1100 2 × 10-6
Fig. 2. Mass transfer in the PEMFC.
2. Design of a 3D flow field The schematics of the conventional parallel and 3D flow fields are shown in Fig. 1(a) and Fig. 1(b). The design process of the 3D flow field was that a conventional parallel flow channel was cut off at a certain length, which formed a transition area for gas mixture and redistribution. Then, an offset between adjacent channels along the gas flow direction was set to enhance the disturbance and convective mass transfer of the reactants. Inclinations were provided at the end of each flow unit to increase the velocity of the reactants. The structure of the 3D flow field was defined as a 4 × 3 structure, as shown in Fig. 1(c), which included four main channels and each channel was divided into three parts. The location of each main channel is numbered in Fig. 1(d), with inclination angle α at the end of each part. In the main channel, the gas in the channel participated in the electrochemical reaction, whereas the gas in the subchannel was mainly
expected to be used for water drainage. In addition, the transition area and subchannel according to the rib area of the parallel flow field were treated with hydrophilic coating to accelerate the liquid water drainage.
3. Modeling and methodology 3.1. Water transport model The volume of fluid (VOF) model in FLUENT using advanced Lagrangian interface-tracking scheme is adopted to investigate the water transport characteristics in a 3D flow channel. The government equations are shown below [31]. 3
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Fig. 3. Water distribution in 3D flow channel with time evolution. (a) 1 ms (b) 2 ms (c) 4 ms (d) 10 ms.
study of fuel cell operation. The governing equations are given as follow.
3.1.1. Mass conservation equation
∂ρ u) = 0 + ∇ (ρ ·→ ∂t
(1)
3.2.1. Mass conservation equation
where ρ is the volume average density.
∂ (ερ) u ) = Sm + ∇ (ερ→ ∂t
3.1.2. Volume conservation equation
∂αi +→ u · ∇α i = 0 ∂t
where ε is the porosity and Sm is the source term of mass. Sm is individually solved for each distinct region [32].
(2)
where α i is the volume fraction of species i, α1 represents the gas phase, and α2 represents the liquid phase.
3.2.2. Momentum conservation equation
u) ∂ (ερ→ u u ) = −ε∇p + ∇ (εμ∇→ u ) + Su + ∇ (ερ→→ ∂t
3.1.3. Momentum conservation equation
∂ (ρ→ u) T →+→ + ∇ ·(ρ→→ u u ) = −∇p + ∇ ·[μ (∇→ u + ∇→ u )] + ρg F ∂t
(6)
where p is the pressure, μ is the dynamic viscosity, and Su is the source term of the momentum. (3) 3.2.3. Energy conservation equation
where: Phase volume: α1 + α2 = 1 Volume average density: ρ = α2 ρ2 + (1 − α2) ρ1 Volume average dynamic viscosity: μ = α2 μ 2 + (1 − α2) μ1 The source term of the momentum conservation equation due to the surface tension and wall adhesion is expressed as
→ F = 2σij ρki ∇αi/(ρi + ρj )
(5)
∂ (ερcp T ) ∂t
u T ) = ∇ ·(k eff ∇T ) + SQ + ∇ (ερcp →
(7)
k eff
is the effective here, cp is the specific heat at constant pressure, thermal conductivity, T is the temperature, and SQ is the energy source term.
(4) 3.2.4. Species conservation equation
where σij is the surface tension and k is the radius of curvature.
∂ (εck ) + ∇ (ε→ u ck ) = ∇ ·(Dkeff ∇ck ) + Sk ∂t
3.2. Mathematical model of PEMFC
Dkeff ,
(8)
Here, ck , and Sk are the species concentration, species effective diffusion coefficient, and species source term, respectively.
A built-in Fuel Cell and Electrolysis Module in Fluent is used for the 4
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Fig. 4. Water distribution with the effects of inlet velocity and contact angle (a) 2 ms (Velocity of 3 m·s−1) (b) 10 ms (Velocity of 3 m·s−1) (c) 2 ms (With modified surfaces) (d) 10 ms (With modified surfaces).
here, ε = 1, cr is the condensation constant hardwired to 100 s−1, and rw is determined by the pressure difference between the water vapor and saturated vapor pressure. The volume fraction of the liquid water is s . In the gas diffusion and catalyst layers
∂ (ερl s ) Ks 3 dpc ⎤ ∇s = rw + ∇ ·⎡ρl ⎥ ⎢ ∂t ⎣ μl ds ⎦
(11)
where pc is the capillary pressure and K is the permeability. 3.2.6. Conservation of charge
pwv − psat RT
(13)
γan
ref ⎛ CO2 ⎞ R cat = Rcat ⎜ C ref ⎟ ⎝ O2 ⎠
(9)
MH2 O , −sρ1]
∇ (σm ∇φm) + Sm = 0
ref ⎛ CH2 ⎞ Ran = Ran ⎜ C ref ⎟ ⎝ H2 ⎠
3.2.5. Volume fraction conservation In the gas channels:
rw = crmax [(1 − s )
(12)
Here, σe and σm are the electrical conductivity, φe and φm are the solid phase and membrane phase potentials, respectively, Se and Sm are the electron flow and proton flow source terms, respectively. The source terms were calculated by the Butler–Volmer equation. In the anode, Sm = Ran and Se = −Ran , while in the cathode, Sm = −R cat and Se = R cat .
Fig. 5. Performance comparison between conventional parallel flow channel and 3D cathode flow channel.
∂ (ερl s ) ul ) = rw + ∇ (sρl → ∂t
∇ (σe ∇φe ) + Se = 0
[exp (
α cat Fηan αan Fηan ) − exp (− )] RT RT
γcat
[exp (−
αan Fηcat α cat Fηcat ) − exp ( )] RT RT
(14)
(15)
where Ran and R cat are anode and cathode volumetric transfer current density, Rref is reference value, C and C ref are the species concentration and reference value, γan and γcat are anode and cathode concentration
(10) 5
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Fig. 6. Velocity distribution contour of 3D cathode flow channel. (a) Main channel (b) Subchannel.
Fig. 7. Mole concentration of oxygen at the interface between gas diffusion layer and catalyst layer of conventional and 3D cathode flow channels (1.0 A·cm−2). (a) Conventional cathode flow channel (b) 3D cathode flow channel.
3.4. Field synergy methodology
dependence, αan and α cat are the transfer coefficient of anode and cathode, F is the Faraday constant, R is the gas constant and η is the activation loss.
In PEMFC, the gas flow is in the horizontal direction, whereas the electrochemical reaction is in the vertical direction, shown in Fig. 2. According to the field synergy principle [33–36], enhanced mass transfer in PEMFC requires the well synergy between the flow velocity and concentration gradient. The synergy angle γ is defined as
3.3. Geometry model According to the local simplified model of a 3D flow field, the current collectors, gas diffusion layers, catalyst layers, and membrane were added to investigate the operating characteristic of the fuel cell. The geometric parameters of the fuel cell are listed in Table 1. The whole domain was spatially discretized with an unstructured tetrahedral mesh and the mesh counts at inclination angles of 30°, 45°, and 60° were 1,081,772, 1,149,178, and 1,087,639, respectively, considering both the accuracy of the grid and computing resource. The boundary condition of the water transport and operating conditions of a PEMFC are listed in Tables 2 and 3, respectively. In addition, Table 4 gives the main physical property parameters of PEMFC, including the porosity, conductivity and so on.
→ u · ∇c cosγ = → | u |·|∇c|
(16)
where → u is the velocity and∇c is the concentration gradient. EMTC is also proposed to measure the mass transfer capability of the fuel cell, and the expression is presented as
e= v
∂c ∂y
here v is the component of the velocity in the y direction. 6
(17)
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flow channel increased and existed in small parts, although most water existed in the second part. To accelerate the removal of liquid water in the flow channel, the increase in the inlet reactant velocity and modification of surface wettability were considered. 4.1.1. Effect of inlet velocity With the increase of the inlet reactant velocity from 2 to 3 m·s−1, the movement time of the liquid water in the flow channel decreased. Fig. 4(a) shows the water distribution at 2 ms. The water droplet flowed through the first part of the channel, spread, and attached to the transition area in the second part of the channel. The motion of liquid water was significantly faster compared with that shown in Fig. 3(b). Moreover, Fig. 4(b) depicted that the water distribution in the flow channel at 10 ms was more even than that at 2 m·s−1. Meanwhile, the amount of liquid water in the outlet section increased comparing with the velocity of 2 m·s−1, indicating better water removal ability due to the increase of the inlet reactant velocity. Fig. 8. Pressure drop.
4.1.2. Effect of contact angle The water distribution at 2 ms is shown in Fig. 4(c) with the surfaces modified. The surface contact angle of the main channel increased from 135° to 155°, whereas the subchannel angle decreased from 45° to 25°. Slight changes in the shape of the water droplet could be observed, and the motion characteristics were almost the same as those in the basic case. Moreover, the liquid water distribution shown in Fig. 4(d) exhibited the same distribution tendency as that shown in Fig. 3(d), where the concentrated distribution of liquid water was in the second part of the flow channel. The third part contained a little amount of liquid water. Because of the decrease in the contact angle of the subchannel, the amount of liquid water in the subchannel increased with the increased hydrophilicity of subchannels.
4. Results and discussions 4.1. Water distribution To investigate the water transport characteristics of a 3D flow field, a water droplet with a radius of 0.5 mm was initialized at 2 mm away from the inlet of each main channel. The transient time step size was 5 × 10−6 s, and the number of time steps was set to 2000 during the simulation. With an inclination angle of 45°, inlet velocity of 2 m·s−1, main channel with surface static contact angle of 135°, and subchannel with an angle of 45°, the water distributions in the 3D flow channel are shown in Fig. 3. Because of the hydrophobic surface of the main channel, the water droplet maintained its shape of a sphere rolling at the center of the flow channel under the air shear force at 1 ms, as shown in Fig. 3(a). At 2 ms, as shown in Fig. 3(b), the water droplet moved to the end of the first part of the channel, being about to enter the transition area and to be redistributed with the reactants. Fig. 3(c) showed that liquid water partly existed in the second part of the main channel attached to the bottom and side walls and partly flowed through the transition area. Because the subchannel was above the main channel and the height difference between them indicated the channel thickness, most liquid water moved through the second part of the main channel, whereas a little liquid water flowed through the subchannel. Fig. 3(d) showed that the liquid water reached the outlet at 10 ms. With the time evolution, the liquid water in the third part of the
4.2. PEMFC operating characteristic 4.2.1. Performance comparison Compared with the conventional parallel flow field, the performance of the PEMFC with novel 3D cathode flow fields were improved, as illustrated in Fig. 5. Because of the low gas consumption at low current densities, the advantage of the modified structure in terms of the mass transfer was not obvious; thus, the performance barely improved at a current density below 0.2 A·cm−2. The output voltage of the 3D cathode flow channel was 0.852 V at 0.2 A·cm−2, whereas it was 0.841 V for the conventional parallel flow channel. However, the output voltage of the 3D cathode flow channel reached up to 0.690 V with an inclination angle of 45° at 1.2 A·cm−2, and it was only 0.551 V for the conventional parallel flow field under the same operation
Fig. 9. Field synergy (a) Cathode average synergy angle (b) Cathode effective mass transfer coefficient. 7
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cathode flow channels with different inclination angles are shown in Fig. 9(a) at current density of 0.2 and 1.6 A·cm −2. During the operation process, the mainstream direction of the gas flow was almost vertical to the concentration gradient. It was the key issue to improve the synergetic degree between the velocity and concentration gradient, which in turn improves the PEMFC performance. We found that the synergy angle of the conventional parallel flow channel was approximately 80° at 0.2 A·cm −2, whereas that of the 3D cathode flow channel was about 65°. The inclination angle of the 3D flow channel had little influence on the synergy angle, which was also consistent with the performance result. At 1.6 A·cm−2, the synergy angle of the conventional flow channel was reduced because the consumption of the reactants increased to maintain the electrochemical reaction at a high current density. However, the synergy angles of the 3D flow channels were still approximately 65°, which indicated that the 3D structure could enhance the mass transfer inside the PEMFC to satisfy the gas consumptions during the reaction at different current densities. Moreover, the structure of the flow channel with an inclination of 30° was the preferred section owing to the low flow resistance during the reaction. EMTC, which is a product of the normal velocity component of the PEMFC with the concentration gradient in the reaction direction, is shown in Fig. 9(b). The EMTC of the 3D cathode flow field was observed to be greater than that of the conventional flow field, which was consistent with the performance variations. The EMTC slightly decreased with the increase of current density as could be understood that large amount of reactants diffused into the catalyst layer to participate in the electrochemical reaction at high current density. Accordingly, the reactants left in the flow channel were less than those at low current density.
conditions. The performance improvement was approximately 25%, which confirmed that the 3D cathode flow field could effectively enhance the ability of mass transfer and reduce the concentration overpotential at high current density. As the current density continued to increase, the cell performance with the conventional flow field sharply dropped. Nevertheless, the performance with the 3D cathode flow channel maintained above 0.6 V at 1.6 A·cm−2. In addition, the inclination structure served as an additional blockage in the flow channel [10], which could also enhance the mass transfer inside the PEMFC. However, the angles of inclination exerted little influence on the cell performance, indicating that the effect of the staggered flow unit was much more serious than that of the inclination angle. 4.2.2. Velocity distribution Fig. 6(a) shows the velocity distribution contour at the center cross section of the main channel with an inclination angle of 45° at 1.0 A·cm−2. With the decrease in the channel height at the inclination, the flow velocity exhibited a significant increase, and the largest velocities were found at the end of each flow unit. Because of the staggered arrangement of the flow units, the velocity distribution in the flow channel to both sides greatly varied, whereas the changes in middle channel (Nos. 2 and 3) were small. From the inlet to the outlet, the flow velocity in main channel Nos. 1 and 2 displayed a trend of gradual increase, indicating severer electrochemical reaction in the inlet section and excess supply of reactants, which in turn resulted in more reactants being left in the outlet section. Fig. 6(b) is the velocity distribution contour at the center cross section of the subchannel. Because of the cross section close to the top wall of the main channel, the overall velocity in the main channel was lower than that in the subchannel. The considerable velocity in the subchannel also proved the advantages of the 3D flow field for water removal.
5. Conclusions A novel 3D flow field in a PEMFC was proposed in this paper to investigate the water transport and performance characteristics using numerical simulation. Combined with the field synergy principle, the conclusions are listed below.
4.2.3. Interface reactant concentration Fig. 7(a) shows that the mole concentration of oxygen in the cathode interface between the gas diffusion layer and catalyst layer of the conventional flow channel decreased gradually from the inlet to the outlet. By comparing the contours of the mole concentration of the conventional and 3D flow channels, the 3D flow channel was found to not only significantly enlarge the high concentration area but also effectively reduce the area where the concentration was almost zero, as shown in Fig. 7(b). In the conventional flow field, almost no reactant was found in the area under the interval between the gas channels, which wasted large activation area and caused uneven distribution of the current density because of the uneven reactant distribution. In contrast, the transition area could provide a possibility for the reactant to diffuse to the area under the subchannel in the 3D flow field. The increase in the reaction area and mole concentration of the reactant could be the very important factors for the performance improvement in the 3D cathode flow field.
(1) Liquid water could be effectively removed through the subchannel of the 3D flow field and the increase in the reactant inlet velocity could be beneficial for water removal. (2) The 3D flow field could enhance the mass transfer ability and improve the performance of PEMFC, especially at high current density. (3) The inclination angle of the channel had little influence on the performance, whereas a larger inclination would lead to a larger pressure drop. (4) The synergy angle between the velocity vector and concentration gradient agreed with the performance, and EMTC could be used to estimate the superiority of the 3D flow channel design for mass transfer enhancement in PEMFC.
4.2.4. Pressure drop The pressure drops of the conventional and 3D cathode flow channel was depicted in Fig. 8. Because of the reduced height at the end of flow unit and the remixing and redistribution of the reactants, the local pressure loss of the 3D flow field was larger than that of the conventional flow field. The bigger the angle of inclination was, the larger was the local pressure loss. Thus, the 3D cathode flow channel with an inclination angle of 60° exhibited the largest pressure drop, followed by the inclination angles of 45° and 30°. Since the pressure drop increase ratio of 3D flow field was less than the performance improvement ratio, the net output power of 3D flow field was still higher than that of the conventional flow field, particularly at high current density.
Declaration of Competing Interest The authors declared that they have no conflicts of interest to this work. Acknowledgement This work was supported by the National Key R&D Program of China (No. 2018YFC0810001) and the Natural Science Foundation of China (No. 51776144). Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.114464.
4.2.5. Field synergy The cathode average synergy angles of the conventional and 3D 8
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