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Enhancement of mass transfer in a proton exchange membrane fuel cell with blockage in the flow channel
Accepted Manuscript Enhancement of mass transfer in a proton exchange membrane fuel cell with blockage in the flow channel Jun Shen, Zhengkai Tu, Siew Hwa Chan PII: DOI: Reference:
S1359-4311(18)36529-3 https://doi.org/10.1016/j.applthermaleng.2018.12.138 ATE 13145
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
25 October 2018 13 December 2018 25 December 2018
Please cite this article as: J. Shen, Z. Tu, S. Hwa Chan, Enhancement of mass transfer in a proton exchange membrane fuel cell with blockage in the flow channel, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/ j.applthermaleng.2018.12.138
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Enhancement of mass transfer in a proton exchange membrane fuel cell with blockage in the flow channel Jun Shen1, Zhengkai Tu1, 2*, Siew Hwa Chan2 1
School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China
2
Energy Research Institute, Nanyang Technological University, 50 Nanyang Avenue, 637553, Singapore
*
Corresponding author: e-mail: [email protected]
Tel.: +86 (0) 15102756731; Fax: +86 27 87540724
Abstract: Flow field design is very important for performance enhancement of a proton exchange membrane fuel cell (PEMFC). The most common method for the evaluation of the improved performance of a particular PEMFC design is the polarization curve. The principle of field synergy based on enhanced mass transfer theory is introduced and applied to flow channel design in this study. A single PEMFC with different flow patterns was used to validate the theory both numerically and experimentally. Compared with a PEMFC having a conventional single serpentine flow field, the performance of a PEMFC with four different blockages in the flow channel was investigated in detail. Based on the field synergy principle, the synergy angle and effective mass transfer coefficient were defined to verify the results. With the addition of blockages, the average synergy angle between the gas velocity and the concentration gradient at the cathode decreased, while the effective mass transfer coefficient improved, thus enhancing the performance of the PEMFC. This novel use of the principle of field synergy offers a new dimension for optimizing the flow field design for PEMFCs. Keywords: PEMFC; Flow field; Blockage; Field synergy; Mass transfer coefficient; Synergy angle
1 Introduction Proton exchange membrane fuel cells (PEMFCs) have attracted considerable interest for both mobile and stationary applications owing to their high efficiency, low or zero-emissions, and low noise [1-4]. During the operation of a PEMFC, however, losses due to phenomena such as activation overpotential, ohmic overpotential, and concentration overpotential are inevitable. Minimizing these irreversible losses and maintaining efficient operation are key issues in fuel cell development. Optimizing the structural design, using novel materials, and adopting new technologies are effective ways to achieve high efficiency and steady operation of a PEMFC [5-10]. Gamburzev et al. [11] used pore-forming additives, new types of proton exchange membranes, and the higher activity of carbon-supported platinum as an electrocatalyst to improve the performance of a PEMFC for the same platinum loading. Gerteisen et al. [12] proposed a new customized gas diffusion layer (GDL) design modified by laser perforation to enhance liquid water transport from the electrode to the gas channel. They found that the dynamic and overall performance of a PEMFC with the perforated GDL was improved compared to that without a modified GDL. Zhou et al. [13] developed a numerical method to study the effects of compression deformation of the gas diffusion layer on the performance of a PEMFC. The combined effects of the compression ratio, interfacial contact resistivity, catalyst layer (CL) thickness, GDL wettability, and relative humidity of the air were investigated. Yang et al. [14] considered three land ratios of channel and rib with a serpentine-type channel in a PEMFC by using the commercial software COMSOL.
The result showed that narrower rib generated higher species concentration distribution in both the anode and the cathode, which resulted in higher fuel cell performance. And Rahimi-Esbo et al. [15] analyzed seven flow fields and investigated their performance at the optimum channel to rib ratio. Liu et al. [16] developed a 2D steady model to investigate the flow and mass transfer characteristics of a PEMFC. The results showed that increasing the hydrogen inlet velocity and inlet mass fraction, while reducing the thickness of the catalyst layer, could facilitate the mass transfer of reactants. Chun et al. [17] investigated the influence of GDL properties on the performance of a PEMFC using a one-dimensional phase mixture model. They found that a GDL with a high contact angle, high gas permeability, and low thickness had improved performance, particularly for high current density conditions. In addition to the optimizations mentioned above, introducing obstacles inside the flow channel [18-22] is also a common and effective method to achieve performance improvement in PEMFCs. Ghanbarian et al. [23] numerically investigated the enhancement of PEM fuel cell performance due to a partial blockage for three flow channel profile shapes in a parallel flow field. It was observed that a trapezoid blockage provided the best results in terms of improved net power density. Perng et al. [24] numerically examined the use of trapezoid baffles in the flow channel, and determined that maximum enhancement of the cell’s net power was 90% and was achieved with baffles of 60 and 1.125 mm in height. Tiss et al. [25] developed a two-dimensional CFD model for a PEMFC and used it to investigate mass transport in a PEMFC with partial blockages inserted in the gas channel. The simulation results
revealed that the tilted angle of the partial blocks was critical to PEMFC performance, particularly for the minimization of concentration overpotential. Kuo et al. [26-28] used a three-dimensional model to investigate the performance characteristics of a PEMFC with straight and wave-like gas flow field channels. The results indicated that a wave-like channel could enhance transport of the reaction gases through the porous layer, increase the uniformity of temperature distribution, and improve the cell voltage. Heidary et al. [29] experimentally investigated the effects of in-line and staggered blockage configurations in a parallel flow field and compared them with a baseline parallel flow field without any blockages. The results indicated that performance was more stable with a staggered configuration than with the others. Adding blockages can provide some improvement in the performance of a PEMFC, but the underlying physical mechanism is not completely understood. In addition, no parameter has yet been defined to guide the design of a PEMFC. In this paper, the field synergy concept is introduced and the utility of this method for the design of flow channels in a PEMFC is demonstrated. 2 Methodology As previously described, mass transfer is very important for a PEMFC [30-32]. The performance of a PEMFC is closely related to operating parameters such as the mass flow rate and concentration [33-36]. However, no single methodology is presently available to evaluate the superiority of flow channel designs in a PEMFC. The ultimate performance improvement is often verified with polarization curves. However, this is not robust for the design of a full-scale PEMFC, particularly in the
pre-design stage involving complicated flow channels [37]. Mass transfer enhancement could be used as a guide for the optimization of PEMFC design, and it could be developed as an analogue of the theory of heat transfer enhancement [38, 39]. The field synergy principle was proposed by Guo [38] in 1998, showed that increasing the included angle between the dimensionless velocity and temperature gradient vectors could enhance the heat transfer. Liu et al. [39, 40] proposed the concept of physical quantity synergy in a laminar flow field, and revealed the synergy regulation among physical quantities as well as the relationship between synergy angles and heat transfer enhancement. Chen et al. [41] extended the principle of field synergy to the process of convective mass transfer, and believed that the synergy between the velocity vector and the concentration gradient could enhance the convective mass transfer. The field synergy principle applied to convection mass transfer in PEMFC, reactants diffusing from the gas channel to the gas diffusion layers and the catalyst layer, could provide effective prediction for structure optimization. Synergy regulation between synergy angles and mass transfer enhancement can be verified by simulation results, and an effective mass transfer coefficient is proposed to offer a new mechanism for the optimal design of a PEMFC. 2.1 Synergy angle The equation for a two-dimensional, steady, constant property mass transfer by diffusion can be written as follows:
D(
2c 2c ) n 0 x 2 y 2
(1)
Where, D , c and n are the diffusion coefficient, concentration, and internal mass generation rate, respectively. Similarly, the equation for a two-dimensional, steady, constant property mass transfer by convection with no internal generation can be written as
u
c c 2c 2c v D( 2 2 ) x y x y
(2)
Because concentration varies to a lesser extent in the flow direction than that in the
2c 2c , the equation can be simplified to x 2 y 2
vertical direction, i.e.,
u
c c 2c v D 2 . x y y
(3)
According to the boundary layer theory, the mass transfer by convection in the concentration boundary layer is equal to the mass transfer by diffusion in the adjacent layer, and can be expressed as c 0 [V c]dy cos 0 [ V c ]dy D y . 0
(4)
Where is the thickness of the boundary layer. From Eq. (4), it can be seen that mass transfer by convection is dependent on the flow velocity, concentration gradient, and the included angle of the two vectors. The synergy angle , between the velocity
V and concentration gradient c is defined as V c . cos V c
(5)
Although this theory is deduced in two dimensions, it can also be applied in three-dimensional conditions [42]. 2.2 Effective mass transfer coefficient
The effective mass transfer coefficient (EMTC) is proposed in this study and is defined as the product of the velocity and the concentration gradient in the normal direction of the proton exchange membrane. The EMTC indicates the mass transfer of reactants involved in the electrochemical reaction in a PEMFC, and can also provide an explanation for performance improvement. The EMTC using e , is defined as follows
e v
c y
(6)
3 Simulation and Experiments 3.1 Experimental setup In this study, PEMFCs with different flow field designs based on a single serpentine flow field were assembled and tested, including conventional single serpentine flow field, addition of in-line blockages with interval of 5 mm, and in-line blockages with interval of 10 mm, shown in Fig. 1. And the physical dimensions of the test fuel cell were listed in Table 1. The membrane electrode assemblies (MEAs) with polymer electrolyte membranes were loaded with 0.4 mg·cm-2 platinum on carbon supports. Performance evaluation of the fuel cells was carried out on a FCATS G50 (Greenlight Innovation Company, Canada) [43].There were five configurations of the three types of flow field plates, as summarized in Table 2. 3.2 Numerical model A 3D model is developed to investigate the effects of blockages in the flow channels. The physical dimensions of the model are 52 mm (length) × 52 mm (width) × 4.536
mm (height) with 1mm ridge all sides to ensure the same design of flow field with experimental fuel cell, using hexahedral mesh grids and a total grid quantity of 3,515,200. The schematic of conventional single serpentine flow channel adding blockages is shown in Fig. 2, while details of the mesh generation are summarized in Table 3. 3.3 Grid independent test Due to the regular structure, the model could be meshed by structured hexahedral grids. The simulations were conducted by three different grid sizes. The mesh count of Mesh 1, Mesh 2 and Mesh 3 were 2812160, 3515200 and 4867200, respectively. Based on Mesh 1, Mesh 2 and Mesh 3 refined the meshes of gas diffusion layers, catalyst layers and membrane. Grid independent test was conducted at output voltage of 0.55V, and the influence of the grid numbers on the computed results was shown in Table 4. At output voltage of 0.55V, Mesh 1 and Mesh 3 yielded deviations of approximately 6.59% and 2.98% for the current density compared to Mesh 2. This indicated that the calculation result was independent of the number of grids, while the number was greater than 3515200 [44]. The majority of the species transport was along the height direction, high mesh density in height was necessary. Due to the large scale of fuel cell width, 1mm of channel width was resolved with 4 elements while 1mm of channel height was resolved with 10 elements. Considering the calculation time and calculation accuracy, we chose Mesh 2 as the calculation model, and the mesh information was shown in Table 3. 3.4 Governing equations
The numerical simulation is performed using the commercially available CFD solver FLUENT based on the finite volume method, and was conducted on computer servers with 20 dual-core CPUs and 240 GB RAM. The operational conditions are summarized in Table 5, and the governing equations are described below [45]. Mass conservation equation
( ) ( u ) S m t
(7)
Where, is the porosity, is the density, S m is the source term of mass conservation and is solved individually for each distinct region. For gas channels and GDLs,
Sm 0
(8)
For the anode catalyst,
Sm
M H2 2F
Ran
(9)
For the cathode catalyst,
Sm
M H 2O 2F
Rcat
M O2 4F
Rcat
(10)
Here, F is Faraday's number, M i is the molecular weight of species i, Ran and
Rcat are the anode volumetric transfer current and cathode volumetric transfer current. Momentum conservation equation ( u ) ( uu ) p ( u ) S u t
(11)
Where p is the pressure, is the dynamic viscosity, and S u is the source term of momentum conservation. According to Darcy’s law, the momentum conservation
equation for porous media can be written as follows, where K is the permeability.
Su
K
u
(12)
Energy conservation equation
( c pT ) t
( c p uT ) (k eff T ) SQ
(13)
Here, c p is the specific heat at constant pressure, k eff is the effective thermal conductivity, T is the temperature and S Q is the energy source term. The energy source term includes the heat released by the electrochemical reaction, heat due to the phase change, ohm heat, and heat transfer from the energy to maintain the electrode reaction rate, and can be expressed as follows SQ hreact Ran,catan,cat I 2 Rohm hL rw
(14)
Where hreact is the net enthalpy change due to the electrochemical reactions,
Ran,cat an,cat is the product of the transfer current and the overpotential in the anode or the cathode, Rohm is the ohmic resistivity of the conducting media, hL is the enthalpy change due to condensation/vaporization of water, and rw is the condensation rate. Species conservation equation
(ck ) (uck ) ( Dkeff ck ) S k t Here, c k , Dkeff and S k
(15)
are species concentration, species effective diffusion
coefficient and species source term, respectively. For hydrogen and oxygen, the species source terms are the mass of the reactant. The species source term for the liquid water includes the mass from water generation, water transport due to electro-osmotic drag, and water condensation due to phase changes. For gas channels and GDLs,
Sk 0
(16)
For the catalyst layer,
1 Ran 2F 1 SO2 Rcat 4F 1 S H 2O Rcat 2F SH2
(17) (18) (19)
Volume fraction conservation In gas channels
( l s) ( sl ul ) rw t p psat rw cr max[(1 s) wv M H 2O , s1 ] RT
(20) (21)
Here, 1 , c r is the condensation constant hardwired to 100 s-1, and rw is determined by the pressure difference between the water vapor and the saturated vapor pressure, and the volume fraction of liquid water s . In this case, rw is the vaporization rate that is added to the species conservation equation as the mass source of water vapor. In GDLs and CLs
( l s) Ks 3 dpc [l s] rw t l ds
pc
(22)
cos c 1.417(1 s) 2.12(1 s) 2 1.263(1 s) 3 c 90 0.5 (K / )
(23)
cos c 1.417s 2.12s 2 1.263s 3 0.5 (K / )
(24)
pc
c 90
Where p c is the capillary pressure, is the surface tension, and c is the contact angle. With liquid water handled in the porous zones, water saturation would affect the water transport in the fuel cell by changing the value of capillary
pressure without considering the influence of permeability K and porosity ε. Conservation of charge
( ee ) Se 0
(25)
( mm ) S m 0
(26)
Here, e and m are electrical conductivity, e and m are the solid phase potential and the membrane phase potential, S e and S m are the electron flow source term and the proton flow source term. The source terms representing the transfer current can be calculated with the Butler–Volmer equation. In the anode,
S m Ran and Se Ran , while in the cathode, S m Rcat and Se Rcat . ref Ran Ran (
CH 2 C H2
ref Rcat Rcat (
ref ref Where Ran and Rcat
ref
CO2 C Oref2
) an [exp(
an,an F an
) cat [exp(
RT
) exp(
cat,cat Fcat RT
cat,an F cat
) exp(
RT
)]
an,cat Fcat RT
(27)
)]
(28)
are the reference current densities, an and cat are
concentration dependence, is the transfer coefficient, and is the local surface overpotential. 4 Results and discussion 4.1 Polarization curves Fig. 3(a) and Fig. 3(b) show the experimental and numerical polarization curves for fuel cells with five different flow field configurations. In general, the simulation results were in good agreement with the experimental data. By adding blockages in the anode and/or the cathode gas channels, the performance was improved, particularly at high current densities. While at low current densities, the decrease of
voltage was mainly due to the activation overpotential, less affected by the structure of gas channels. In the experimental results, the difference between the maximum and minimum values at the same current density was as high as 0.16 V, which was considerable for practical applications. Compared with Case 1, Case 2 with blockage addition in the flow channel at the cathode was more effective than that at the anode. The reason for this was that pure hydrogen was used in the anode, whereas oxygen comprised only 21% by volume of the cathodic flow. As a result, the optimal design of flow channels in the cathode was proven to be more significant [46]. Moreover, the flow resistance of hydrogen was lower than that of oxygen in the same flow channel owing to the higher diffusion coefficient of hydrogen with small stoichiometry at the anode. In addition, a closer arrangement of blockages in the cathode was more effective than in the anode. The larger the number of blockages added, the better the performance was. Cases 3 and 4 exhibited more significant performance enhancement than the other three cases. As seen in Fig. 3(a), the highest power output appeared at a current density of 1.3 A·cm-2 in the conventional serpentine flow field. In the other blockage cases, the corresponding current density increased gradually confirming the benefit of adding blockages in the flow channels. It was also found that the corresponding current density for the highest output power of Case 4 increased to greater than 1.6 A·cm-2. This suggested that adding blockages in the gas channel not only increased the output power, but also broadened the range of operating current density. The simulation results for the polarization curves are shown in Fig. 3(b). The
conventional serpentine flow field had the lowest performance, while Case 4 provided the highest value. Compared with Fig. 3(a), simulation results were higher than the experimental results at high current densities. This was due to the model used in the simulation, which couldn’t track the gas-liquid interface as VOF methodology [47, 48], and water saturation and water content were used to describe the liquid water description in the fuel cell. Thus water accumulation at high current densities couldn’t be accurately reflected by the model, but it had a great impact on the experimental results. Based on the present results, we could also infer that with the increase of current density, the output voltage would rapidly drop to 0 V, which was consistent with literature [49]. Fig. 3(c) and Fig. 3(d) show the performance differences between the experimental and numerical results for current densities of 0.6 and 1.5 A·cm-2, respectively. From the conventional flow field to Case 4, the performance of the PEMFC increased both experimentally and numerically, and the performance improvement was most significant at a high current density of 1.5 A·cm-2 in the experimental results. 4.2 Velocity and mole concentration distribution The experimental and numerical results indicate that adding blockages in the flow channel can improve the performance of a PEMFC. To confirm the mass transfer enhancement that results from the addition of blockages, the velocity contour and mole concentration contours of O2 for the five different cases are shown in Fig. 4 and Fig. 5, respectively. Contours of hydrogen velocity at the center channel cross-section of conventional case, Case 1 and Case 3 were compared in Fig. 4 (a). Meanwhile,
conventional case, Case 2 and Case 4 were chose to analyze the velocity distribution of oxygen in Fig. 4(b). A significant improvement of velocity occurred when blockages were added in the flow channel, particularly in the region near the GDL surface, which would be beneficial for the mass transfer of the reactants. In addition, the velocity magnitude of oxygen was larger than that of hydrogen due to larger stoichiometry of air in the cathode. The molar concentration contours of O2 on the center cross section of the flow channels for all cases are shown in Fig. 5. It gradually decreased from the inlet to the outlet as the reactions progressed. These results showed that Case 4 had the highest average molar concentration of O2, followed by Case 3 and Case 2, all of which were clearly enhanced by the addition of blockages in the cathode. Meanwhile, the lowest concentrations were observed in the conventional flow field and in Case 1 without the addition of blockages in the cathode. Therefore, increasing reactant concentration in the flow channel could facilitate the diffusion of reactants and be beneficial for the electrochemical reactions in the catalyst layer, and would improve the performance of a PEMFC. The distributions of the reactant molar concentrations were also consistent with the velocity distributions, revealing the mechanism of the performance improvement that occurred with the addition of blockages in the flow channels. Fig. 6(a) and Fig. 6(b) show quantitative mole concentration of H2 and O2 on the surface between the gas diffusion layer and the flow channel for five different cases, respectively. In general, the mole concentrations of reactants for cases with blockages were higher than that for conventional case, and the amplitude of enhancements were
greater than 5%. For cathode, the mole concentration of O2 increased in fluctuation while flowing through the blockages, and conventional flow field and Case 1 kept linear change without blockages. In addition, Case 4 with the highest density of blockages in the cathode had the highest mole concentration. For anode, the mole concentration of H2 increased with the blockage addition, even if the blockages were only added in the cathode. And the four optimization cases showed almost the same level of mole concentration of H2. This indicated that optimization of the cathodic flow field had greater influence and was more independent. The reason would be that pure H2 was used in the anode while O2 was 21% in the cathode reactant. Moreover, the amount of O2 consumed in the electrochemical reaction was half of H2, leading less partial pressure of O2. According to Nernst equation, partial pressure of O 2 became the main factor limiting the performance of PEMFCs. Velocity streamline distributions in the cathode for conventional case, Case 2 and Case 4 are shown in Fig. 7. In conventional flow channel, the fluid velocity was almost along the horizontal direction, leading to tiny velocity to the direction of the electrochemical reaction (Y-axis). Obviously, the direction of the velocity changed in Case 2 and Case 4 with the addition of blockages. Vortex were formed behind the blockages after the reactant flowed through, which would be beneficial for long staying of reactants in the flow channel and improvement of performance. 4.3 Pressure drop Pressure is another important parameter for performance improvement in a PEMFC [50]. Compared to the cathode, the pressure drop in the anode is usually neglected as
it is much less significant. As shown in Fig. 8, the conventional flow field had a minimal pressure drop in both the experimental and simulation results. Moreover, the pressure drop was very similar for the same flow field structure. For the cathode, the conventional flow field and Case 1 with no blockages, as well as Case 2 and Case 3 with placement of blockages at 10 mm intervals, the pressure drops were nearly coincident. For Case 4, which had a denser placement of blockages, had maximum pressure drops of 45 kPa and 38 kPa in the experiment and simulation, respectively. The reason for the larger pressure drop in the experimental results was the significant pressure loss at the inlet manifold [51]. Due to the difficult measurement in the experiment, the pressure loss at the inlet and outlet manifold could be obtained by theoretical analysis with reference to fluid mechanics. In addition, the cathode pressure drop increased with increasing current density, as more reactants were supplied to the PEMFC and a larger flow resistance was generated at higher current densities. With the addition of blockages, the performance of fuel cells was improved with the increased pressure drop, indicating that the pay-to-benefit ratio should be considered during the structure optimization. The pay-to-benefit ratio was expressed by J, that was, the ratio of the cathode power consumption to the output power was as follows. J
puAch VI
(29)
Where p is the cathode pressure drop, u is the cathode inlet velocity, and Ach is the cross-sectional area of the gas channel. Fig. 9 shows the pay-to-benefit ratio of different cases during the experiment. Seen
from the figure, at current densities of 0.2 ~ 0.4 A·cm-2, the J of optimized structures were smaller than the conventional flow field. Due to the low efficiency at low current density, the output efficiency of the fuel cell was improved by arranging the blockages in the flow channel and the value of J was decreased. With the increasing of current density, the pressure drop due to the gas consumption of optimized structures increased, leading to the increase of J. However, the pressure drop of conventional flow field was gentle, and the performance improvement by increasing the current density was more significant, resulting in the decrease of J. Because of the large pressure drop of single serpentine flow field, the pressure drop was the main factor infusing the comprehensive performance of PEMFC. The pay-to-benefit ratio of PEMFC was related to the performance and pressure drop, which needed to be analyzed according to the specific structure. 4.4 Field synergy evaluation 4.4.1 Cathode average synergy angle Fig. 10 shows the cathode average included angle between the gas velocity and the concentration gradient for the five different cases. The average angle exhibited the same characteristics with the same cathode structure. The angle of Case 4 with the highest density of blockages in the cathode was the smallest of the five cases, followed by Case 2 and Case 3 with blockages in the cathode, and finally Case 1 and the conventional flow field without any blockages were the largest. This showed that the addition of blockages in the flow channel could effectively reduce the angle between the velocity field and the concentration gradient. Combined with field
synergy principle, the better the synergy regulation between the velocity field and the concentration gradient, the higher the efficiency would be. Case 4 had the smallest average synergy angle and showed the best performance. These results could then be confirmed by the cathode effective mass transfer coefficient. 4.4.2 Effective mass transfer coefficient The cathode effective mass transfer coefficient is shown in Fig. 11 and exhibited the same behavior with a cathodic pressure drop. Structural improvement could result in changes in the pressure drop and mass transfer characteristics. Case 4 with the highest density of blockages in the cathode had the highest effective mass transfer coefficient, which coincided well with its performance. Case 2 and Case 3 with the same structure in the cathode, regardless of blockages in the anode, had effective mass transfer coefficients that coincided with each other, but were less than that for Case 4 at the same current density. The cathode effective mass transfer coefficients for the conventional flow field and Case 1 were close to 0, indicating that the y-velocity was very small. Adding blockages in the flow channel could promote an effective mass transfer coefficient, which is also an effective way to enhance the performance. 5 Conclusions In this paper, five PEM fuel cell configurations were built and investigated using numerical simulations and experimental studies. Based on the field synergy principle, the following conclusions can be drawn. (1) Adding blockages in the flow channel was an effective method to enhance the mass transfer and performance of the PEMFC, and the higher the current density was,
the more significant the performance improvement would be. In addition, adding blockages could broaden the range of operating current density. (2) Optimization of the cathodic flow channels was more effective than optimization of the anode. Because the diffusion coefficient of hydrogen was higher than that for oxygen, and practical operations had a dead-end anode design, there was a resulting forced mass transfer of hydrogen from the flow channels to the gas diffusion layer. Moreover, denser intervals of blockages in the flow field could achieve better performance. (3) With the addition of blockages, the performance of fuel cells was improved with the increased pressure drop, indicating that the pay-to-benefit ratio should be considered during the structure optimization. (4) The synergy angle between the cathodic reactant velocity and the concentration gradient, and the effective mass transfer coefficient have been proven to be useful parameters, which can precisely reflect the effectiveness of mass transfer in the PEM fuel cells, and are in good agreement with the performance of PEMFCs. Acknowledgement The current work is supported by the Natural Science Foundation of China (No. 51776144) and Natural Science Foundation of Hubei Province (No. 2016CFA041).
Nomenclature J·kg -1·k-1
cp
Specific heat capacity
ck
Concentration of species i
cr
Condensation constant
D
Diffusion coefficient
e
Effective mass transfer coefficient
F
Faraday constant
hreact
Net enthalpy change due to the electrochemical reactions
kmol·m-3
m2·s-1
9.6487×104 C·mol-1
W·m-2·k-1 hL
Enthalpy change due to condensation/vaporization of water W·m-2·k-1 A·cm-2
I
Current density
K
Permeability
Mi
Molecular weight of species i
p
Pressure
pc
Capillary pressure
pwv
Pressure of water vapor
psat
Pressure of saturated water
rw
condensation rate
s-1
R
Gas constant 8.314
J·mol-1·k-1
Rohm
Ohmic resistivity of media
Rref
Reference volumetric transfer current density
Ran
Anode volumetric transfer current density
Rcat
Cathode volumetric transfer current density
s
Liquid volume fraction
kg·kmol-1
N·m-2 N·m-2 N·m-2 N·m-2
Ω·m A·m-3 A·m-3 A·m-3
S
Source term of governing equations
t
Time
T
Temperature
u,v
Velocity components in x,y directions
s K
Greek letter α
Transfer coefficient
γ
Synergy angle
γan
Anode concentration dependence
γcat
Cathode concentration dependence
δ
Boundary layer thickness
ε
Porosity
η
Overpotential
V
θ
Contact angle
°
μ
Dynamic viscosity
ρ
Density
σ
Surface tension
σe
Electrical conductivity
S·m-1
σm
Electrical conductivity
S·m-1
φ
Electric potential
°
kg·m-1·s-1
kg·m-3 N·m-2
V
m·s-1
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Table captions Table 1 Dimensions of a single PEMFC Table 2 Configurations of the fuel cells Table 3 Model dimension and mesh generation Table 4 Influence of the grid numbers on the computed results Table 5 Operating conditions of PEMFC
Figure captions Fig. 1 Flow field plates used in the experiments: (a) conventional single-serpentine flow field plate; (b) in-line blockages (interval=10 mm); (c) in-line blockages (interval =5 mm) Fig. 2 Schematic of a single-serpentine PEM fuel cell used in the simulation Fig. 3 Performance of the five different configurations: (a) Experimental results; (b) Simulation results; (c) Results at a current density of 0.6 A·cm-2; (d) Results at a current density of 1.5 A·cm-2 Fig. 4 Contours of reactants velocity at the center channel cross-section: (a) Contours of hydrogen velocity; (b) Contours of oxygen velocity Fig. 5 Mole concentration of O2 for five configurations: (a) Conventional flow field; (b) Case 1; (c) Case 2; (d) Case 3; (e) Case 4 Fig. 6 Quantitative mole concentration of H2 and O2; (a) H2; (b) O2 Fig. 7 Velocity streamline distributions in the cathode for conventional case, Case 2 and Case 4 Fig. 8 Pressure drops for the different configurations: (a) Experimental results; (b) Simulation results Fig. 9 Pay-to-benefit ratio of different cases Fig. 10 Field synergy angles for the different cases Fig. 11 Effective mass transfer coefficients of the different cases
Fig.1
(a)
(b)
(c)
Fig.2
Fig.3
(a)
(b)
(c)
(d)
Fig.4
(a)
(b)
Fig.5
(a)
(b)
(c)
(d)
(e)
Fig.6
(a)
(b)
Fig.7
Fig.8
(a)
(b)
Fig.9
Fig. 10
Fig.11
Table 1 Dimension of a single PEMFC Parameter
Value
Activation area (m2)
25×10-4
Flow field depth (m)
1.0×10-3
Flow field width (m)
1.0×10-3
Flow field ridge width (m)
0.75×10-3
Gas diffusion layer thickness (m)
2.5×10-4
PEM thickness (m)
1.2×10-5
Catalyst layer thickness (m)
1.2×10-5
Table 2 Different configurations of fuel cell Anode
Interval
Cathode
Interval
Blockage
(mm)
Blockage
(mm)
/
/
/
/
Case 1
Yes
10
/
/
Case 2
/
/
Yes
10
Case 3
Yes
5
Yes
10
Case 4
Yes
10
Yes
5
Conventional
Table 3 Model dimension and mesh generation Length (mm) / mesh
Width (mm) / mesh Height (mm) / mesh
Current collector
52/260
52/208
2/20
Flow channel
50/250
1/4
1/10
Gas diffusion layer
52/260
52/208
0.25/5
Catalyst layer
52/260
52/208
0.012/5
Membrane
52/260
52/208
0.012/5
Table 4 Influence of the grid numbers on the computed results Current density
Relative Deviation
A·cm-2
%
Grid number
Mesh 1
2812160
0.9715
6.59
Mesh 2
3515200
1.04
-
Mesh 3
4867200
1.009
2.98
Table 5 Operating conditions of PEMFC Parameter Cell temperature (K) Operating pressure （Pa）
Value 338 101325
Air inlet temperature (K)
338
H2 inlet temperature (K)
338
Air stoichiometry
2.5
H2 stoichiometry
1.5
Air relative humidity
100%
H2 relative humidity
100%
Open circuit voltage (V)
0.95
Enhancement of mass transfer in a proton exchange membrane fuel cell with blockage in the flow channel
(1)A single fuel cell instead of a flow channel is considered for performance evaluation (2)Field synergy concept is introduced to verify the superiority of PEMFC (3)Cathode synergy angles are all consistent with performance variation (4)Effective mass transfer coefficient is proposed to evaluate mass transfer capability
S1359-4311(18)36529-3 https://doi.org/10.1016/j.applthermaleng.2018.12.138 ATE 13145
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
25 October 2018 13 December 2018 25 December 2018
Please cite this article as: J. Shen, Z. Tu, S. Hwa Chan, Enhancement of mass transfer in a proton exchange membrane fuel cell with blockage in the flow channel, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/ j.applthermaleng.2018.12.138
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Enhancement of mass transfer in a proton exchange membrane fuel cell with blockage in the flow channel Jun Shen1, Zhengkai Tu1, 2*, Siew Hwa Chan2 1
School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China
2
Energy Research Institute, Nanyang Technological University, 50 Nanyang Avenue, 637553, Singapore
*
Corresponding author: e-mail: [email protected]
Tel.: +86 (0) 15102756731; Fax: +86 27 87540724
Abstract: Flow field design is very important for performance enhancement of a proton exchange membrane fuel cell (PEMFC). The most common method for the evaluation of the improved performance of a particular PEMFC design is the polarization curve. The principle of field synergy based on enhanced mass transfer theory is introduced and applied to flow channel design in this study. A single PEMFC with different flow patterns was used to validate the theory both numerically and experimentally. Compared with a PEMFC having a conventional single serpentine flow field, the performance of a PEMFC with four different blockages in the flow channel was investigated in detail. Based on the field synergy principle, the synergy angle and effective mass transfer coefficient were defined to verify the results. With the addition of blockages, the average synergy angle between the gas velocity and the concentration gradient at the cathode decreased, while the effective mass transfer coefficient improved, thus enhancing the performance of the PEMFC. This novel use of the principle of field synergy offers a new dimension for optimizing the flow field design for PEMFCs. Keywords: PEMFC; Flow field; Blockage; Field synergy; Mass transfer coefficient; Synergy angle
1 Introduction Proton exchange membrane fuel cells (PEMFCs) have attracted considerable interest for both mobile and stationary applications owing to their high efficiency, low or zero-emissions, and low noise [1-4]. During the operation of a PEMFC, however, losses due to phenomena such as activation overpotential, ohmic overpotential, and concentration overpotential are inevitable. Minimizing these irreversible losses and maintaining efficient operation are key issues in fuel cell development. Optimizing the structural design, using novel materials, and adopting new technologies are effective ways to achieve high efficiency and steady operation of a PEMFC [5-10]. Gamburzev et al. [11] used pore-forming additives, new types of proton exchange membranes, and the higher activity of carbon-supported platinum as an electrocatalyst to improve the performance of a PEMFC for the same platinum loading. Gerteisen et al. [12] proposed a new customized gas diffusion layer (GDL) design modified by laser perforation to enhance liquid water transport from the electrode to the gas channel. They found that the dynamic and overall performance of a PEMFC with the perforated GDL was improved compared to that without a modified GDL. Zhou et al. [13] developed a numerical method to study the effects of compression deformation of the gas diffusion layer on the performance of a PEMFC. The combined effects of the compression ratio, interfacial contact resistivity, catalyst layer (CL) thickness, GDL wettability, and relative humidity of the air were investigated. Yang et al. [14] considered three land ratios of channel and rib with a serpentine-type channel in a PEMFC by using the commercial software COMSOL.
The result showed that narrower rib generated higher species concentration distribution in both the anode and the cathode, which resulted in higher fuel cell performance. And Rahimi-Esbo et al. [15] analyzed seven flow fields and investigated their performance at the optimum channel to rib ratio. Liu et al. [16] developed a 2D steady model to investigate the flow and mass transfer characteristics of a PEMFC. The results showed that increasing the hydrogen inlet velocity and inlet mass fraction, while reducing the thickness of the catalyst layer, could facilitate the mass transfer of reactants. Chun et al. [17] investigated the influence of GDL properties on the performance of a PEMFC using a one-dimensional phase mixture model. They found that a GDL with a high contact angle, high gas permeability, and low thickness had improved performance, particularly for high current density conditions. In addition to the optimizations mentioned above, introducing obstacles inside the flow channel [18-22] is also a common and effective method to achieve performance improvement in PEMFCs. Ghanbarian et al. [23] numerically investigated the enhancement of PEM fuel cell performance due to a partial blockage for three flow channel profile shapes in a parallel flow field. It was observed that a trapezoid blockage provided the best results in terms of improved net power density. Perng et al. [24] numerically examined the use of trapezoid baffles in the flow channel, and determined that maximum enhancement of the cell’s net power was 90% and was achieved with baffles of 60 and 1.125 mm in height. Tiss et al. [25] developed a two-dimensional CFD model for a PEMFC and used it to investigate mass transport in a PEMFC with partial blockages inserted in the gas channel. The simulation results
revealed that the tilted angle of the partial blocks was critical to PEMFC performance, particularly for the minimization of concentration overpotential. Kuo et al. [26-28] used a three-dimensional model to investigate the performance characteristics of a PEMFC with straight and wave-like gas flow field channels. The results indicated that a wave-like channel could enhance transport of the reaction gases through the porous layer, increase the uniformity of temperature distribution, and improve the cell voltage. Heidary et al. [29] experimentally investigated the effects of in-line and staggered blockage configurations in a parallel flow field and compared them with a baseline parallel flow field without any blockages. The results indicated that performance was more stable with a staggered configuration than with the others. Adding blockages can provide some improvement in the performance of a PEMFC, but the underlying physical mechanism is not completely understood. In addition, no parameter has yet been defined to guide the design of a PEMFC. In this paper, the field synergy concept is introduced and the utility of this method for the design of flow channels in a PEMFC is demonstrated. 2 Methodology As previously described, mass transfer is very important for a PEMFC [30-32]. The performance of a PEMFC is closely related to operating parameters such as the mass flow rate and concentration [33-36]. However, no single methodology is presently available to evaluate the superiority of flow channel designs in a PEMFC. The ultimate performance improvement is often verified with polarization curves. However, this is not robust for the design of a full-scale PEMFC, particularly in the
pre-design stage involving complicated flow channels [37]. Mass transfer enhancement could be used as a guide for the optimization of PEMFC design, and it could be developed as an analogue of the theory of heat transfer enhancement [38, 39]. The field synergy principle was proposed by Guo [38] in 1998, showed that increasing the included angle between the dimensionless velocity and temperature gradient vectors could enhance the heat transfer. Liu et al. [39, 40] proposed the concept of physical quantity synergy in a laminar flow field, and revealed the synergy regulation among physical quantities as well as the relationship between synergy angles and heat transfer enhancement. Chen et al. [41] extended the principle of field synergy to the process of convective mass transfer, and believed that the synergy between the velocity vector and the concentration gradient could enhance the convective mass transfer. The field synergy principle applied to convection mass transfer in PEMFC, reactants diffusing from the gas channel to the gas diffusion layers and the catalyst layer, could provide effective prediction for structure optimization. Synergy regulation between synergy angles and mass transfer enhancement can be verified by simulation results, and an effective mass transfer coefficient is proposed to offer a new mechanism for the optimal design of a PEMFC. 2.1 Synergy angle The equation for a two-dimensional, steady, constant property mass transfer by diffusion can be written as follows:
D(
2c 2c ) n 0 x 2 y 2
(1)
Where, D , c and n are the diffusion coefficient, concentration, and internal mass generation rate, respectively. Similarly, the equation for a two-dimensional, steady, constant property mass transfer by convection with no internal generation can be written as
u
c c 2c 2c v D( 2 2 ) x y x y
(2)
Because concentration varies to a lesser extent in the flow direction than that in the
2c 2c , the equation can be simplified to x 2 y 2
vertical direction, i.e.,
u
c c 2c v D 2 . x y y
(3)
According to the boundary layer theory, the mass transfer by convection in the concentration boundary layer is equal to the mass transfer by diffusion in the adjacent layer, and can be expressed as c 0 [V c]dy cos 0 [ V c ]dy D y . 0
(4)
Where is the thickness of the boundary layer. From Eq. (4), it can be seen that mass transfer by convection is dependent on the flow velocity, concentration gradient, and the included angle of the two vectors. The synergy angle , between the velocity
V and concentration gradient c is defined as V c . cos V c
(5)
Although this theory is deduced in two dimensions, it can also be applied in three-dimensional conditions [42]. 2.2 Effective mass transfer coefficient
The effective mass transfer coefficient (EMTC) is proposed in this study and is defined as the product of the velocity and the concentration gradient in the normal direction of the proton exchange membrane. The EMTC indicates the mass transfer of reactants involved in the electrochemical reaction in a PEMFC, and can also provide an explanation for performance improvement. The EMTC using e , is defined as follows
e v
c y
(6)
3 Simulation and Experiments 3.1 Experimental setup In this study, PEMFCs with different flow field designs based on a single serpentine flow field were assembled and tested, including conventional single serpentine flow field, addition of in-line blockages with interval of 5 mm, and in-line blockages with interval of 10 mm, shown in Fig. 1. And the physical dimensions of the test fuel cell were listed in Table 1. The membrane electrode assemblies (MEAs) with polymer electrolyte membranes were loaded with 0.4 mg·cm-2 platinum on carbon supports. Performance evaluation of the fuel cells was carried out on a FCATS G50 (Greenlight Innovation Company, Canada) [43].There were five configurations of the three types of flow field plates, as summarized in Table 2. 3.2 Numerical model A 3D model is developed to investigate the effects of blockages in the flow channels. The physical dimensions of the model are 52 mm (length) × 52 mm (width) × 4.536
mm (height) with 1mm ridge all sides to ensure the same design of flow field with experimental fuel cell, using hexahedral mesh grids and a total grid quantity of 3,515,200. The schematic of conventional single serpentine flow channel adding blockages is shown in Fig. 2, while details of the mesh generation are summarized in Table 3. 3.3 Grid independent test Due to the regular structure, the model could be meshed by structured hexahedral grids. The simulations were conducted by three different grid sizes. The mesh count of Mesh 1, Mesh 2 and Mesh 3 were 2812160, 3515200 and 4867200, respectively. Based on Mesh 1, Mesh 2 and Mesh 3 refined the meshes of gas diffusion layers, catalyst layers and membrane. Grid independent test was conducted at output voltage of 0.55V, and the influence of the grid numbers on the computed results was shown in Table 4. At output voltage of 0.55V, Mesh 1 and Mesh 3 yielded deviations of approximately 6.59% and 2.98% for the current density compared to Mesh 2. This indicated that the calculation result was independent of the number of grids, while the number was greater than 3515200 [44]. The majority of the species transport was along the height direction, high mesh density in height was necessary. Due to the large scale of fuel cell width, 1mm of channel width was resolved with 4 elements while 1mm of channel height was resolved with 10 elements. Considering the calculation time and calculation accuracy, we chose Mesh 2 as the calculation model, and the mesh information was shown in Table 3. 3.4 Governing equations
The numerical simulation is performed using the commercially available CFD solver FLUENT based on the finite volume method, and was conducted on computer servers with 20 dual-core CPUs and 240 GB RAM. The operational conditions are summarized in Table 5, and the governing equations are described below [45]. Mass conservation equation
( ) ( u ) S m t
(7)
Where, is the porosity, is the density, S m is the source term of mass conservation and is solved individually for each distinct region. For gas channels and GDLs,
Sm 0
(8)
For the anode catalyst,
Sm
M H2 2F
Ran
(9)
For the cathode catalyst,
Sm
M H 2O 2F
Rcat
M O2 4F
Rcat
(10)
Here, F is Faraday's number, M i is the molecular weight of species i, Ran and
Rcat are the anode volumetric transfer current and cathode volumetric transfer current. Momentum conservation equation ( u ) ( uu ) p ( u ) S u t
(11)
Where p is the pressure, is the dynamic viscosity, and S u is the source term of momentum conservation. According to Darcy’s law, the momentum conservation
equation for porous media can be written as follows, where K is the permeability.
Su
K
u
(12)
Energy conservation equation
( c pT ) t
( c p uT ) (k eff T ) SQ
(13)
Here, c p is the specific heat at constant pressure, k eff is the effective thermal conductivity, T is the temperature and S Q is the energy source term. The energy source term includes the heat released by the electrochemical reaction, heat due to the phase change, ohm heat, and heat transfer from the energy to maintain the electrode reaction rate, and can be expressed as follows SQ hreact Ran,catan,cat I 2 Rohm hL rw
(14)
Where hreact is the net enthalpy change due to the electrochemical reactions,
Ran,cat an,cat is the product of the transfer current and the overpotential in the anode or the cathode, Rohm is the ohmic resistivity of the conducting media, hL is the enthalpy change due to condensation/vaporization of water, and rw is the condensation rate. Species conservation equation
(ck ) (uck ) ( Dkeff ck ) S k t Here, c k , Dkeff and S k
(15)
are species concentration, species effective diffusion
coefficient and species source term, respectively. For hydrogen and oxygen, the species source terms are the mass of the reactant. The species source term for the liquid water includes the mass from water generation, water transport due to electro-osmotic drag, and water condensation due to phase changes. For gas channels and GDLs,
Sk 0
(16)
For the catalyst layer,
1 Ran 2F 1 SO2 Rcat 4F 1 S H 2O Rcat 2F SH2
(17) (18) (19)
Volume fraction conservation In gas channels
( l s) ( sl ul ) rw t p psat rw cr max[(1 s) wv M H 2O , s1 ] RT
(20) (21)
Here, 1 , c r is the condensation constant hardwired to 100 s-1, and rw is determined by the pressure difference between the water vapor and the saturated vapor pressure, and the volume fraction of liquid water s . In this case, rw is the vaporization rate that is added to the species conservation equation as the mass source of water vapor. In GDLs and CLs
( l s) Ks 3 dpc [l s] rw t l ds
pc
(22)
cos c 1.417(1 s) 2.12(1 s) 2 1.263(1 s) 3 c 90 0.5 (K / )
(23)
cos c 1.417s 2.12s 2 1.263s 3 0.5 (K / )
(24)
pc
c 90
Where p c is the capillary pressure, is the surface tension, and c is the contact angle. With liquid water handled in the porous zones, water saturation would affect the water transport in the fuel cell by changing the value of capillary
pressure without considering the influence of permeability K and porosity ε. Conservation of charge
( ee ) Se 0
(25)
( mm ) S m 0
(26)
Here, e and m are electrical conductivity, e and m are the solid phase potential and the membrane phase potential, S e and S m are the electron flow source term and the proton flow source term. The source terms representing the transfer current can be calculated with the Butler–Volmer equation. In the anode,
S m Ran and Se Ran , while in the cathode, S m Rcat and Se Rcat . ref Ran Ran (
CH 2 C H2
ref Rcat Rcat (
ref ref Where Ran and Rcat
ref
CO2 C Oref2
) an [exp(
an,an F an
) cat [exp(
RT
) exp(
cat,cat Fcat RT
cat,an F cat
) exp(
RT
)]
an,cat Fcat RT
(27)
)]
(28)
are the reference current densities, an and cat are
concentration dependence, is the transfer coefficient, and is the local surface overpotential. 4 Results and discussion 4.1 Polarization curves Fig. 3(a) and Fig. 3(b) show the experimental and numerical polarization curves for fuel cells with five different flow field configurations. In general, the simulation results were in good agreement with the experimental data. By adding blockages in the anode and/or the cathode gas channels, the performance was improved, particularly at high current densities. While at low current densities, the decrease of
voltage was mainly due to the activation overpotential, less affected by the structure of gas channels. In the experimental results, the difference between the maximum and minimum values at the same current density was as high as 0.16 V, which was considerable for practical applications. Compared with Case 1, Case 2 with blockage addition in the flow channel at the cathode was more effective than that at the anode. The reason for this was that pure hydrogen was used in the anode, whereas oxygen comprised only 21% by volume of the cathodic flow. As a result, the optimal design of flow channels in the cathode was proven to be more significant [46]. Moreover, the flow resistance of hydrogen was lower than that of oxygen in the same flow channel owing to the higher diffusion coefficient of hydrogen with small stoichiometry at the anode. In addition, a closer arrangement of blockages in the cathode was more effective than in the anode. The larger the number of blockages added, the better the performance was. Cases 3 and 4 exhibited more significant performance enhancement than the other three cases. As seen in Fig. 3(a), the highest power output appeared at a current density of 1.3 A·cm-2 in the conventional serpentine flow field. In the other blockage cases, the corresponding current density increased gradually confirming the benefit of adding blockages in the flow channels. It was also found that the corresponding current density for the highest output power of Case 4 increased to greater than 1.6 A·cm-2. This suggested that adding blockages in the gas channel not only increased the output power, but also broadened the range of operating current density. The simulation results for the polarization curves are shown in Fig. 3(b). The
conventional serpentine flow field had the lowest performance, while Case 4 provided the highest value. Compared with Fig. 3(a), simulation results were higher than the experimental results at high current densities. This was due to the model used in the simulation, which couldn’t track the gas-liquid interface as VOF methodology [47, 48], and water saturation and water content were used to describe the liquid water description in the fuel cell. Thus water accumulation at high current densities couldn’t be accurately reflected by the model, but it had a great impact on the experimental results. Based on the present results, we could also infer that with the increase of current density, the output voltage would rapidly drop to 0 V, which was consistent with literature [49]. Fig. 3(c) and Fig. 3(d) show the performance differences between the experimental and numerical results for current densities of 0.6 and 1.5 A·cm-2, respectively. From the conventional flow field to Case 4, the performance of the PEMFC increased both experimentally and numerically, and the performance improvement was most significant at a high current density of 1.5 A·cm-2 in the experimental results. 4.2 Velocity and mole concentration distribution The experimental and numerical results indicate that adding blockages in the flow channel can improve the performance of a PEMFC. To confirm the mass transfer enhancement that results from the addition of blockages, the velocity contour and mole concentration contours of O2 for the five different cases are shown in Fig. 4 and Fig. 5, respectively. Contours of hydrogen velocity at the center channel cross-section of conventional case, Case 1 and Case 3 were compared in Fig. 4 (a). Meanwhile,
conventional case, Case 2 and Case 4 were chose to analyze the velocity distribution of oxygen in Fig. 4(b). A significant improvement of velocity occurred when blockages were added in the flow channel, particularly in the region near the GDL surface, which would be beneficial for the mass transfer of the reactants. In addition, the velocity magnitude of oxygen was larger than that of hydrogen due to larger stoichiometry of air in the cathode. The molar concentration contours of O2 on the center cross section of the flow channels for all cases are shown in Fig. 5. It gradually decreased from the inlet to the outlet as the reactions progressed. These results showed that Case 4 had the highest average molar concentration of O2, followed by Case 3 and Case 2, all of which were clearly enhanced by the addition of blockages in the cathode. Meanwhile, the lowest concentrations were observed in the conventional flow field and in Case 1 without the addition of blockages in the cathode. Therefore, increasing reactant concentration in the flow channel could facilitate the diffusion of reactants and be beneficial for the electrochemical reactions in the catalyst layer, and would improve the performance of a PEMFC. The distributions of the reactant molar concentrations were also consistent with the velocity distributions, revealing the mechanism of the performance improvement that occurred with the addition of blockages in the flow channels. Fig. 6(a) and Fig. 6(b) show quantitative mole concentration of H2 and O2 on the surface between the gas diffusion layer and the flow channel for five different cases, respectively. In general, the mole concentrations of reactants for cases with blockages were higher than that for conventional case, and the amplitude of enhancements were
greater than 5%. For cathode, the mole concentration of O2 increased in fluctuation while flowing through the blockages, and conventional flow field and Case 1 kept linear change without blockages. In addition, Case 4 with the highest density of blockages in the cathode had the highest mole concentration. For anode, the mole concentration of H2 increased with the blockage addition, even if the blockages were only added in the cathode. And the four optimization cases showed almost the same level of mole concentration of H2. This indicated that optimization of the cathodic flow field had greater influence and was more independent. The reason would be that pure H2 was used in the anode while O2 was 21% in the cathode reactant. Moreover, the amount of O2 consumed in the electrochemical reaction was half of H2, leading less partial pressure of O2. According to Nernst equation, partial pressure of O 2 became the main factor limiting the performance of PEMFCs. Velocity streamline distributions in the cathode for conventional case, Case 2 and Case 4 are shown in Fig. 7. In conventional flow channel, the fluid velocity was almost along the horizontal direction, leading to tiny velocity to the direction of the electrochemical reaction (Y-axis). Obviously, the direction of the velocity changed in Case 2 and Case 4 with the addition of blockages. Vortex were formed behind the blockages after the reactant flowed through, which would be beneficial for long staying of reactants in the flow channel and improvement of performance. 4.3 Pressure drop Pressure is another important parameter for performance improvement in a PEMFC [50]. Compared to the cathode, the pressure drop in the anode is usually neglected as
it is much less significant. As shown in Fig. 8, the conventional flow field had a minimal pressure drop in both the experimental and simulation results. Moreover, the pressure drop was very similar for the same flow field structure. For the cathode, the conventional flow field and Case 1 with no blockages, as well as Case 2 and Case 3 with placement of blockages at 10 mm intervals, the pressure drops were nearly coincident. For Case 4, which had a denser placement of blockages, had maximum pressure drops of 45 kPa and 38 kPa in the experiment and simulation, respectively. The reason for the larger pressure drop in the experimental results was the significant pressure loss at the inlet manifold [51]. Due to the difficult measurement in the experiment, the pressure loss at the inlet and outlet manifold could be obtained by theoretical analysis with reference to fluid mechanics. In addition, the cathode pressure drop increased with increasing current density, as more reactants were supplied to the PEMFC and a larger flow resistance was generated at higher current densities. With the addition of blockages, the performance of fuel cells was improved with the increased pressure drop, indicating that the pay-to-benefit ratio should be considered during the structure optimization. The pay-to-benefit ratio was expressed by J, that was, the ratio of the cathode power consumption to the output power was as follows. J
puAch VI
(29)
Where p is the cathode pressure drop, u is the cathode inlet velocity, and Ach is the cross-sectional area of the gas channel. Fig. 9 shows the pay-to-benefit ratio of different cases during the experiment. Seen
from the figure, at current densities of 0.2 ~ 0.4 A·cm-2, the J of optimized structures were smaller than the conventional flow field. Due to the low efficiency at low current density, the output efficiency of the fuel cell was improved by arranging the blockages in the flow channel and the value of J was decreased. With the increasing of current density, the pressure drop due to the gas consumption of optimized structures increased, leading to the increase of J. However, the pressure drop of conventional flow field was gentle, and the performance improvement by increasing the current density was more significant, resulting in the decrease of J. Because of the large pressure drop of single serpentine flow field, the pressure drop was the main factor infusing the comprehensive performance of PEMFC. The pay-to-benefit ratio of PEMFC was related to the performance and pressure drop, which needed to be analyzed according to the specific structure. 4.4 Field synergy evaluation 4.4.1 Cathode average synergy angle Fig. 10 shows the cathode average included angle between the gas velocity and the concentration gradient for the five different cases. The average angle exhibited the same characteristics with the same cathode structure. The angle of Case 4 with the highest density of blockages in the cathode was the smallest of the five cases, followed by Case 2 and Case 3 with blockages in the cathode, and finally Case 1 and the conventional flow field without any blockages were the largest. This showed that the addition of blockages in the flow channel could effectively reduce the angle between the velocity field and the concentration gradient. Combined with field
synergy principle, the better the synergy regulation between the velocity field and the concentration gradient, the higher the efficiency would be. Case 4 had the smallest average synergy angle and showed the best performance. These results could then be confirmed by the cathode effective mass transfer coefficient. 4.4.2 Effective mass transfer coefficient The cathode effective mass transfer coefficient is shown in Fig. 11 and exhibited the same behavior with a cathodic pressure drop. Structural improvement could result in changes in the pressure drop and mass transfer characteristics. Case 4 with the highest density of blockages in the cathode had the highest effective mass transfer coefficient, which coincided well with its performance. Case 2 and Case 3 with the same structure in the cathode, regardless of blockages in the anode, had effective mass transfer coefficients that coincided with each other, but were less than that for Case 4 at the same current density. The cathode effective mass transfer coefficients for the conventional flow field and Case 1 were close to 0, indicating that the y-velocity was very small. Adding blockages in the flow channel could promote an effective mass transfer coefficient, which is also an effective way to enhance the performance. 5 Conclusions In this paper, five PEM fuel cell configurations were built and investigated using numerical simulations and experimental studies. Based on the field synergy principle, the following conclusions can be drawn. (1) Adding blockages in the flow channel was an effective method to enhance the mass transfer and performance of the PEMFC, and the higher the current density was,
the more significant the performance improvement would be. In addition, adding blockages could broaden the range of operating current density. (2) Optimization of the cathodic flow channels was more effective than optimization of the anode. Because the diffusion coefficient of hydrogen was higher than that for oxygen, and practical operations had a dead-end anode design, there was a resulting forced mass transfer of hydrogen from the flow channels to the gas diffusion layer. Moreover, denser intervals of blockages in the flow field could achieve better performance. (3) With the addition of blockages, the performance of fuel cells was improved with the increased pressure drop, indicating that the pay-to-benefit ratio should be considered during the structure optimization. (4) The synergy angle between the cathodic reactant velocity and the concentration gradient, and the effective mass transfer coefficient have been proven to be useful parameters, which can precisely reflect the effectiveness of mass transfer in the PEM fuel cells, and are in good agreement with the performance of PEMFCs. Acknowledgement The current work is supported by the Natural Science Foundation of China (No. 51776144) and Natural Science Foundation of Hubei Province (No. 2016CFA041).
Nomenclature J·kg -1·k-1
cp
Specific heat capacity
ck
Concentration of species i
cr
Condensation constant
D
Diffusion coefficient
e
Effective mass transfer coefficient
F
Faraday constant
hreact
Net enthalpy change due to the electrochemical reactions
kmol·m-3
m2·s-1
9.6487×104 C·mol-1
W·m-2·k-1 hL
Enthalpy change due to condensation/vaporization of water W·m-2·k-1 A·cm-2
I
Current density
K
Permeability
Mi
Molecular weight of species i
p
Pressure
pc
Capillary pressure
pwv
Pressure of water vapor
psat
Pressure of saturated water
rw
condensation rate
s-1
R
Gas constant 8.314
J·mol-1·k-1
Rohm
Ohmic resistivity of media
Rref
Reference volumetric transfer current density
Ran
Anode volumetric transfer current density
Rcat
Cathode volumetric transfer current density
s
Liquid volume fraction
kg·kmol-1
N·m-2 N·m-2 N·m-2 N·m-2
Ω·m A·m-3 A·m-3 A·m-3
S
Source term of governing equations
t
Time
T
Temperature
u,v
Velocity components in x,y directions
s K
Greek letter α
Transfer coefficient
γ
Synergy angle
γan
Anode concentration dependence
γcat
Cathode concentration dependence
δ
Boundary layer thickness
ε
Porosity
η
Overpotential
V
θ
Contact angle
°
μ
Dynamic viscosity
ρ
Density
σ
Surface tension
σe
Electrical conductivity
S·m-1
σm
Electrical conductivity
S·m-1
φ
Electric potential
°
kg·m-1·s-1
kg·m-3 N·m-2
V
m·s-1
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Table captions Table 1 Dimensions of a single PEMFC Table 2 Configurations of the fuel cells Table 3 Model dimension and mesh generation Table 4 Influence of the grid numbers on the computed results Table 5 Operating conditions of PEMFC
Figure captions Fig. 1 Flow field plates used in the experiments: (a) conventional single-serpentine flow field plate; (b) in-line blockages (interval=10 mm); (c) in-line blockages (interval =5 mm) Fig. 2 Schematic of a single-serpentine PEM fuel cell used in the simulation Fig. 3 Performance of the five different configurations: (a) Experimental results; (b) Simulation results; (c) Results at a current density of 0.6 A·cm-2; (d) Results at a current density of 1.5 A·cm-2 Fig. 4 Contours of reactants velocity at the center channel cross-section: (a) Contours of hydrogen velocity; (b) Contours of oxygen velocity Fig. 5 Mole concentration of O2 for five configurations: (a) Conventional flow field; (b) Case 1; (c) Case 2; (d) Case 3; (e) Case 4 Fig. 6 Quantitative mole concentration of H2 and O2; (a) H2; (b) O2 Fig. 7 Velocity streamline distributions in the cathode for conventional case, Case 2 and Case 4 Fig. 8 Pressure drops for the different configurations: (a) Experimental results; (b) Simulation results Fig. 9 Pay-to-benefit ratio of different cases Fig. 10 Field synergy angles for the different cases Fig. 11 Effective mass transfer coefficients of the different cases
Fig.1
(a)
(b)
(c)
Fig.2
Fig.3
(a)
(b)
(c)
(d)
Fig.4
(a)
(b)
Fig.5
(a)
(b)
(c)
(d)
(e)
Fig.6
(a)
(b)
Fig.7
Fig.8
(a)
(b)
Fig.9
Fig. 10
Fig.11
Table 1 Dimension of a single PEMFC Parameter
Value
Activation area (m2)
25×10-4
Flow field depth (m)
1.0×10-3
Flow field width (m)
1.0×10-3
Flow field ridge width (m)
0.75×10-3
Gas diffusion layer thickness (m)
2.5×10-4
PEM thickness (m)
1.2×10-5
Catalyst layer thickness (m)
1.2×10-5
Table 2 Different configurations of fuel cell Anode
Interval
Cathode
Interval
Blockage
(mm)
Blockage
(mm)
/
/
/
/
Case 1
Yes
10
/
/
Case 2
/
/
Yes
10
Case 3
Yes
5
Yes
10
Case 4
Yes
10
Yes
5
Conventional
Table 3 Model dimension and mesh generation Length (mm) / mesh
Width (mm) / mesh Height (mm) / mesh
Current collector
52/260
52/208
2/20
Flow channel
50/250
1/4
1/10
Gas diffusion layer
52/260
52/208
0.25/5
Catalyst layer
52/260
52/208
0.012/5
Membrane
52/260
52/208
0.012/5
Table 4 Influence of the grid numbers on the computed results Current density
Relative Deviation
A·cm-2
%
Grid number
Mesh 1
2812160
0.9715
6.59
Mesh 2
3515200
1.04
-
Mesh 3
4867200
1.009
2.98
Table 5 Operating conditions of PEMFC Parameter Cell temperature (K) Operating pressure （Pa）
Value 338 101325
Air inlet temperature (K)
338
H2 inlet temperature (K)
338
Air stoichiometry
2.5
H2 stoichiometry
1.5
Air relative humidity
100%
H2 relative humidity
100%
Open circuit voltage (V)
0.95
Enhancement of mass transfer in a proton exchange membrane fuel cell with blockage in the flow channel
(1)A single fuel cell instead of a flow channel is considered for performance evaluation (2)Field synergy concept is introduced to verify the superiority of PEMFC (3)Cathode synergy angles are all consistent with performance variation (4)Effective mass transfer coefficient is proposed to evaluate mass transfer capability