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Effects of operating parameters on transport phenomena and cell performance of PEM fuel cells with conventional and contracted flow field designs
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Effects of operating parameters on transport phenomena and cell performance of PEM fuel cells with conventional and contracted flow field designs Xiao-Dong Wang a,b,*, Wei-Mon Yan c,**, Wen-Chung Won c, Duu-Jong Lee d a
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China b Beijing Key Laboratory of Multiphase Flow and Heat Transfer for Low Grade Energy, North China Electric Power University, Beijing 102206, China c Department of Greenergy Engineering, National University of Tainan, Tainan 700, Taiwan d Department of Chemical Engineering, College of Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan
article info
abstract
Article history:
A contracted parallel flow field design was developed to improve fuel cell performance
Received 5 December 2011
compared with the conventional parallel flow field design. A three-dimensional model was
Received in revised form
used to compare the cell performance for both designs. The effects of the cathode reactant
20 February 2012
inlet velocity and cathode reactant inlet relative humidity on the cell performance for both
Accepted 24 February 2012
designs were also investigated. For operating voltages greater than 0.7 V because the
Available online 20 March 2012
electrochemical reaction rates are lower with less oxygen consumption and less liquid water production, the cell performance is independent of the flow field designs and
Keywords:
operating parameters. However, for lower operating voltages where the electrochemical
PEMFC
reaction rates gradually increase, the oxygen transport and the liquid water removal effi-
Parallel flow field design
ciency differ for the various flow field designs and operating parameters; therefore, the cell
Contracted flow field design
performance is strongly dependent on both the design and operating parameters. For lower
Cell performance
operating voltages, the cell performance for the contracted design is better than for the conventional design because the reactant flow velocities in the contracted region significantly increase, which enhances liquid water removal and reduces the oxygen transport resistance. For lower operating voltages, as the cathode reactant inlet velocity increases and the cathode reactant inlet relative humidity decreases, the cell performance for both designs improves. Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
The proton exchange membrane fuel cell (PEMFC) is a promising alternative energy source because of the simplicity of its
design and operation. Some attractive characteristics of a PEMFC system include lightweight, high energy density, no or low pollutant emission and low operating temperature. Cell performance of PEMFCs strongly depends on the operating
* Corresponding author. State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China. Tel./fax: þ86 10 62321277. ** Corresponding author. Tel.: þ886 6 2602251; fax: þ886 6 2602205. E-mail addresses: [email protected] (X.-D. Wang), [email protected] (W.-M. Yan). 0360-3199/$ e see front matter Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2012.02.145
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conditions, transport phenomena in the cells, electrochemical reaction kinetics, mechanical design, and manufacturing process. To reduce research costs and shorten the design cycle, modeling and simulations are being used extensively in research institutions and in industry around the world to gain a better understanding of the fundamental processes in these fuel cells. In recent years, many analyses, models and numerical simulations have been developed [1e18] to study various transport phenomena and the electrochemical kinetics to gain a better understanding and to develop strategies for optimal design and operating scenarios. Springer et al. [1] presented a one-dimensional steadystate model for a PEMFC based on experimentally determined transport parameters. Bernardi and Verbrugge [2,3] developed a full cell model to investigate the water transport mechanisms. Fuller et al. [4] and Nguyen et al. [5] proposed twodimensional transport models to examine the water management problems in a PEMFC. Ge and Yi [6] developed a two-dimensional model to investigate the effects of operating conditions and membrane thicknesses on the water transport. Okada et al. [7] studied the water transport at the anode side and gave a linear transport equation based on the water diffusion and electro-osmotic water drag to analyze the water concentration profiles. Gurau et al. [8] considered the variations of the concentrations and the partial pressures in the gas channels and developed a two-dimensional model for the entire sandwich of a PEMFC. They further derived a halfcell model for the cathode side and obtained rigorous analytical solutions which account for the liquid water content in the gas diffusion layer [9]. Um et al. [10] developed a multi-dimensional model to study the electrochemical kinetics, current distributions, fuel and oxidant flows, and multi-component transport in a PEMFC with an interdigitated flow field. Djilali and Lu [11] focused on the modeling of nonisothermal and non-isobaric effects to analyze the cell performance and water transport over a range of operating current densities. A quasi-three-dimensional model of water transport in PEMFCs was proposed by Kulikovsky [12] to analyze the non-linear diffusion of liquid water in the membrane. Mazumder and Cole [13,14] developed a threedimensional model to investigate the cell performance of PEMFCs with consideration of the liquid water effects. Wang and co-workers [15e17] developed two-dimensional and three-dimensional models for the reactants and water transport and the cell performance in PEMFCs. The effects of liquid water formation on the reactant transport were taken into account in the modeling and examined in the analysis. Recently, Wang [18] reviewed the fundamental PEMFC models. The flow field design in the bipolar plates is one of the most important issues in a PEMFC. An appropriate flow field design in the bipolar plates can improve the reactant transport, the thermal efficiency and the water management. To this end, different flow field configurations, including parallel, serpentine, interdigitated, and many other combined versions, have been developed. Many efforts have been devoted to optimize the flow field design to improve cell performance [15e44]. Recently, Soong et al. [41] proposed a relatively novel configuration with partially blocked reactant channels. They focused on the blockage effects of various gap ratios and
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number of baffles on the reactant transport and the pressure losses. They found that reducing the gap size and/or increasing the number of baffles enhanced the reactant transport. Liu et al. [42] developed a two-dimensional model to examine the reactant transport and the cell performance of a PEMFC with a tapered parallel flow channel. Numerical predictions showed that the cell performance was enhanced by the tapered reactant channel, with the enhancement is more evident at lower voltages. Later, Yan et al. [43] developed a three-dimensional model to investigate a parallel flow channel design with tapered heights or widths for improving the reactant utilization efficiency in PEMFCs. Their results showed that with the tapered channel designs, the flow area contraction along the flow channel led to increased reactant velocities; thus, enhancing the reactant transport through the porous layers, reactant utilization, and liquid water removal. The results also showed that the cell performance could be improved by either decreasing the height taper ratio or increasing the width taper ratio. Recently, Yan et al. [44] proposed a novel serpentine flow field with outlet channels having modified heights or lengths to improve reactant utilization and liquid water removal in PEMFCs. Their predictions showed that reductions of the outlet channel flow areas increased the reactant velocities in these regions, which enhanced reactant transport, reactant utilization, and liquid water removal; therefore, the cell performance was improved compared with the conventional serpentine flow field. It is well known that for parallel flow fields, a large amount of liquid water accumulates in the gas diffusion layer (GDL) and the catalyst layer (CL) near the outlet region of the flow channels, which significantly reduces the reactant transport rates in the porous layers compared with that near the flow channels inlets. As an extension of previous studies [42e44], this paper describes a novel parallel flow field design with reduced cress-sectional areas for the last part of the flow channel. This design is expected to increase the reactant flow velocity in the outlet region, which will enhance liquid water removal and reactant utilization. A three-dimensional numerical model was used to examine the effect of the contracted channel design on the cell performance. The local transport characteristics in the cell were analyzed to give reasons for the improved cell performance for the contracted channel design. The pressure drops in the contracted channel design were also evaluated as a reference for practical PEMFC designs. This paper also discussed the effect of the cathode reactant inlet velocity and cathode reactant inlet relative humidity on the cell performance for the conventional and contracted designs.
2.
Numerical model
A three-dimensional full-cell model was used to analyze the electrochemical reactions and the transport phenomena of the reactants and the products in the cell using the finite volume method. The cell was divided into the anode flow channels, membrane electrode assembly (MEA, including the anode GDL, anode CL, proton exchange membrane (PEM), cathode CL, and cathode GDL), and the cathode flow channels. The governing equations include the mass, momentum,
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species and electrical potential conservation equations. The model assumes that the system is three-dimensional and steady; the inlet reactants are ideal gases; the system is isothermal; the flow is laminar; the fluid is incompressible; the thermo-physical properties of the reactants and products are constant; and the porous layers such as the GDL, the CL the and the PEM are isotropic. This model includes continuity, momentum and species equations for gaseous species, water transport equations for channels, gas diffusion layers, and catalyst layers, a water transport equation for the membrane, and electron and proton transport equations. The ButlereVolmer equation was employed to describe the electrochemical reactions in catalyst layers. The primary governing equations are as follows. Continuity equation for gaseous species: u g ¼ SL V$ 3 rg !
(1)
Momentum equation for gaseous species: 3 2
ð1 sÞ
V$ rg ! u g! u g ¼ 3 Vpg þ
V$ mg V! u g þ S! u ð1 sÞ 3
(2)
Species equation for gaseous species: V$ 3 rg ! u g Ck ¼ V$ rg Dk;eff VCk þ Sc SL
(3)
Water transport equation for flow channels, gas diffusion layers and catalyst layers: r kp krl vpc r kp krl nd MH2 O ! Vs V$ l i m ¼ SL Vpg þ V$ V$ l ml vs ml F
Table 1 e Parametric values used in the models. Parameter Flow channel length Flow channel height Flow channel width Rib length Rib height Rib width Gas diffusion layer thickness Catalyst layer thickness PEM thickness Gas diffusion layer porosity Catalyst layer porosity PEM porosity Gas diffusion layer permeability Catalyst layer permeability PEM permeability Gas diffusion layer conductivity Catalyst layer conductivity Reference current density at the anode Reference current density at the cathode
Value
Unit
100 1 1 100 1 1 0.3 0.01 0.035 0.4 0.4 0.28 1.76 1011 1.76 1011 1.8 1018 53 53 9.23 108 1.05 106
mm mm mm mm mm mm mm mm mm e e e m2 m2 m2 V1 m1 V1 m1 A m3 A m3
height contraction ratio, dx, and the length contraction ratio, dy, are defined as dx ¼ H1/H0 and dy ¼ L1/L0 where H0 is the inlet channel height, H1 is the outlet channel height, L0 is the total channel length, and L1 is the un-contracted channel length. However, in the conventional parallel flow field design, the channel height is constant along whole channel.
(4)
Water transport equation for the membrane: MH2 O rdry ad MH2 O ! i m l Dl Vl ¼ 0 V$ F Mm
(5)
Proton and electron transport equations: V$ðsm VFm Þ ¼ Sj
(6)
V$ðss VFs Þ ¼ Sj
(7)
Energy equation for the PEMFC: i2 V$ 3 ð1sÞrg ! u g Cp;g T þV$ 3 srl ! u l Cp;l T ¼V$ leff VT þjhþ þhfg SL s (8) More details on the numerical model and solution procedure were given elsewhere [15e17]. Most previous studies have used small fuel cell models to reduce the computational costs of the three-dimensional simulations. However, the results for short flow channels do not agree well with the general performance of large cells. The present work aims to analyze a relatively large fuel cell with an active area of 10 10 cm2. The cell dimensions and main parameters used in this simulation are listed in Table 1. Considering the symmetry of the fuel cell configuration, only an essential part of the fuel cell model (shown in Fig. 1) is used as the computational domain to reduce the computational time. Fig. 2 shows a schematic of the three-dimensional contracted channel design, where the channel height changes suddenly from H0 to H1 at a specific location. The
Fig. 1 e Schematics of the numerical PEMFC models. (a) conventional parallel flow field design; (b) contracted flow field design.
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Fig. 2 e Three-dimensional views of the contracted flow field design.
This paper compares the cell performance for the conventional and contracted parallel flow field designs and investigates the effects of the cathode reactant inlet velocity and the cathode reactant inlet relative humidity on the cell performance and local transport phenomena for both flow field designs. For the comparison of the cell performance for both designs, dx and dy were chosen to be 0.6 and 0.7 for the contracted design. In addition, the base operating conditions for the fuel cell were assumed to be a fuel cell temperature of 323 K, the reactant gases on the anode side include hydrogen and water vapor with a relative humidity of 100%, the reactant gases on the cathode side contain oxygen, nitrogen, and water vapor with a relative humidity of 100%, the inlet flow velocity on the anode side is 2.0 m/s, the inlet flow velocity on the cathode side is 0.5 m/s, and the inlet pressures on the anode and cathode sides are both 1 atm. The effect of the cathode reactant inlet velocity on the cell performance for both designs was investigated using cathode reactant inlet
velocities of 1.0 m/s, 2.0 m/s, and 3.0 m/s with the other conditions the same as the base case operating conditions. The effect of the cathode reactant inlet relative humidity on the cell performance for both designs was investigated using cathode reactant inlet relative humidities of 25%, 50%, 75%, and 100% with the other conditions the same as the base case operating conditions. The grid independence was examined in preliminary test runs. Three non-uniformly distributed grid configurations were evaluated for the PEMFC with the parallel flow field at an operating voltage of 0.3 V. The numbers of elements in the x, y and z directions were: (I) 30 80 69, (II) 41 100 87, and (III) 52 120 105. The influence of the number of elements on the local current density is shown in Fig. 3. The difference between the local current densities was 0.62% for girds (I) and (III) and 0.17% for grids (II) and (III). Thus grid (II) was chosen for the simulations as a tradeoff between accuracy and execution time.
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10000
Gridlines x x y x z = 30 x 80 x 69 Gridlines x x y x z = 41 x 100 x 87 Gridlines x x y x z = 52 x 120 x 105
2
I (A/m )
9500
Anode Fuel = H
y
9000
2
Cathode Fuel = O
2
Anode Fuel RH = 100% Cathode Fuel RH = 100% Anode Flow Velocity = 0.5m/s Cathode Flow Velocity = 2m/s
8500
8000
0
0.02
0.04
0.06
0.08
0.1
y (m) Fig. 3 e Effect of the element number on the local current densities at an operating voltage of 0.3 V.
3.
Results and discussion
3.1. Comparison of cell performance for conventional and contracted flow field designs Fig. 4(a) shows the IeVcell polarization curves for the conventional and contracted designs. Fig. 4(a) shows that for 1
(a) x
0.9
(V)
0.6
y
= 0.7
cell
V
0.8 0.7
= 0.6_
Without Contraction With Liquid Water Effect Without Liquid Water Effect
0.5 0.4 0.3
0
5000
10000
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20000
25000
30000
2
I(A/m ) 400
(b) x
350 300 2
(N/m )
= 0.6_
y
= 0.7
Without Contraction With Liquid Water Effect Without Liquid Water Effect
250 200 150 100 50
0
5000
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2 I(A/m )
Fig. 4 e Cell performance for the conventional and contracted designs. (a) polarization curves; (b) pressure drops.
operating voltages higher than 0.7 V, both designs have almost the same performance since the electrochemical reaction rates are low with a small amount of oxygen consumption and liquid water production. However, for operating voltages lower than 0.7 V, the contracted design has better performance than the conventional design. As the operating voltage decreases, the electrochemical reaction rates gradually increase. Since the two designs have different liquid water removal rates and oxygen transport rates to the cathode CL, their cell performances differ. The contracted design increases the reactant velocity in the contracted flow channel region which improves the liquid water removal, which then results in the improved cell performance. The cell performance without the liquid water effect (single-phase model) was also simulated. At high operating voltages, the differences between the cell performances with and without liquid water effects were negligible. Thus, the reactant transport in the PEM fuel cell can be safely modeled as single-phase flow at high voltages. However, at low voltages, liquid water has a significant effect on the cell performance, so the liquid water can not be neglected in the model. This confirms the observation that the mass transport at lower voltages is more significant with more water generated in the catalyst layer on the cathode side, so the two-phase flow effects should be considered at low voltages. Fig. 4(b) shows the pressure drops for both designs for various current densities. The pressure drop slightly increases with increasing current density because more liquid water is produced at higher current densities, which increases the flow resistance of the reactants in the channels. Fig. 4(b) shows that although the contracted design enhances liquid water removal and oxygen transport, it also increases the pressure drops, thus, the pressure drop for the contracted design is about twice that of the conventional design. Fig. 5(a) and (b) shows the local current densities on the middle cross-section in the PEM at an operating voltage of 0.4 V for the conventional and contracted designs. For both designs, the maximum local current densities occur at the channel inlet and then gradually decrease along the flow direction as the oxygen is gradually consumed by the electrochemical reaction. For the conventional design, the minimum local current densities occur at the channel outlet, while for the contracted design, the current densities in the contracted region of the flow channel are far higher than for the conventional design, indicating that the oxygen mass flow rates to the cathode GDL in the contracted region are increased by the flow channel contractions. Fig. 5 also shows that for both designs, the local current densities under the flow channel are larger than under the rib since the diffusion path for oxygen arriving in the catalyst layer under the ribs is longer than that under the flow channels and the stronger shear stresses under the flow channels enhance the liquid water removal. Fig. 6(a) and (b) shows the liquid water concentrations along the cathode GDL-CL interface at the operating voltage of 0.4 V for both designs. Comparison of Figs. 5and 6 shows that the liquid water distributions are opposite to the local current density distributions. This occurs because the liquid water accumulation in the pores in the porous layers increases the oxygen transport resistance, so the oxygen mass flow rates to
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Fig. 5 e Local current density distributions on the middle cross-section in the PEM at an operating voltage of 0.4 V for the conventional and contracted designs. (a) contracted channel design with dx [ 0.6, dy [ 0.7; (b) conventional design.
the cathode CL and the local current densities decrease. Fig. 6(a) shows that with the contracted design, the liquid water concentration is significantly reduced in the contracted region of the flow channel because the flow channel contractions increase the reactant velocity and enhance liquid water removal. Fig. 7 shows the variation of the reactant velocities in the cathode channel along the flow direction from the inlet to the outlet at 0.4 V for both designs. The velocity slowly increases from the inlet to the outlet in the conventional design. In the contracted design, the velocity abruptly increases at y ¼ 0.07 m (the beginning of the contracted region) due to the reduced cross-sectional area of the flow channel. In addition, the velocity without consideration of the liquid water effect is higher than with the liquid water effect because the liquid water formation increases the flow resistance.
3.2.
Effect of cathode inlet velocity
The anode reactants entering the fuel cell are assumed to be humidified hydrogen, while the cathode reactant gas assumed to be humidified air; thus, the most economic means for improving cell performance is to change the cathode air flow rates. Fig. 8(a) presents the effect of the cathode reactant inlet velocity on the IeVcell polarization curves for the conventional and contracted designs. For operating voltages higher than
0.7 V, the average current densities for the various cathode inlet velocities in the two flow field designs are almost the same, indicating that the flow field design and inlet velocities do not affect the cell performance. This is because the electrochemical reaction rate is low and only a limited amount of oxygen is consumed with only a small amount of liquid water produced for the higher operating voltages. Therefore, the oxygen transport rates for both flow field designs and all cathode inlet velocities are sufficient to maintain the electrochemical reaction rates. However, for operating voltages lower than 0.7 V, the flow field designs and cathode inlet velocities significantly impact the cell performance. As the cathode inlet velocities increase, the average current densities increase and the cell performance improves, but the rate of increase gradually weakens. As the operating voltage is gradually reduced, the electrochemical reaction rates increase and the oxygen consumption increases. Then, since increasing cathode inlet velocities increase the oxygen inlet velocities, more oxygen is provided to the catalyst layer for the electrochemical reaction and the higher oxygen velocities also help remove the liquid water. At the low reactant inlet velocity of 1.0 m/s, the oxygen supply is not sufficient for the electrochemical reaction at high current densities. In addition, the liquid water produced by the electrochemical reaction is not easily removed from the rear part of the flow channel due to the slow flow velocity. The liquid water then blocks the pores
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Fig. 6 e Liquid water distributions along the cathode GDL-CL interface at an operating voltage of 0.4 V for the conventional and contracted designs. (a) contracted channel design with dx [ 0.6, dy [ 0.7; (b) conventional design.
in the GDL and CL. Consequently, the cell performance is the worst for the lowest reactant inlet velocity. Fig. 8(a) also shows that the cell performance at various cathode inlet velocities for the contracted flow field design is superior to that for conventional flow field design as described in section 3.1. Fig. 8(b) shows the effect of the cathode reactant inlet velocity
9
V 8
= 0.4V_ Cathode x
7
vch(m/s)
cell
= 0.6_
y
= 0.7
Without Contraction With Liquid Water Effect Without Liquid Water Effect
6 5 4 3 2
0
0.02
0.04
0.06
0.08
y (m) Fig. 7 e Reactant velocity distributions along the flow direction in the cathode flow channel at an operating voltage of 0.4 V for the conventional and contracted designs.
0.1
on the pressure drop between the inlet and the outlet of the cathode flow channel for various current densities. The increase in the cathode inlet velocity increase the pressure drops. In addition, the pressure drops for the contracted design are higher than that for the conventional design. Fig. 9 shows the effect of the cathode reactant inlet velocity on the local current density distributions on the middle crosssection in the PEM at an operating voltage of 0.4 V. For both flow field designs, at vc ¼ 3.0 m/s, the oxygen supply is sufficient and the liquid water removal is better than for vc ¼ 2.0 m/ s or vc ¼ 1.0 m/s, so the cell performance with vc ¼ 3.0 m/s is better than with vc ¼ 1.0 m/s and vc ¼ 2.0 m/s. For the contracted design, the contraction effect increases the reactant velocity in the contracted region of the flow channel and more oxygen flows into the cathode GDL and CL to participate in the electrochemical reactions, so the local current densities near the flow channel outlet significantly increase compared with the conventional design. Fig. 10 shows the effect of the cathode reactant inlet velocity on the liquid water concentrations along the cathode GDL-CL interface at an operating voltage of 0.4 V for both designs. For both designs, as the cathode reactant inlet velocity increases, the liquid water removal capability increases and the liquid water concentrations decrease. For example, the liquid water concentrations under the flow channel and the rib for vc ¼ 3.0 m/s are significantly less than for vc ¼ 1.0 m/s and vc ¼ 2.0 m/s. Because the contracted design removes more
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 5 8 0 8 e1 5 8 1 9
a
1
v = 1m/s c
0.9
v = 2m/s v = 3m/s
(V)
0.7
Without Contraction
V
c
0.8
0.6
_
y = 0.7
Cell
x = 0.6
0.5 0.4 0.3
0
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3.3.
I(A/m )
300
v = 1m/s c
v = 2m/s c
x
= 0.6_
y
= 0.7
Without Contraction
v = 3m/s c
2
P(N/m )
250
200
150
100
50
0
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10000
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liquid water produced by electrochemical reactions, the liquid water concentrations near the flow channel outlet are less than in the conventional design. Fig. 11 shows the reactant velocity distributions along the flow direction in the cathode flow channel at an operating voltage of 0.4 V for various cathode reactant inlet velocities for both designs. As the cathode reactant inlet velocity increases, the reactant velocity in the flow channel also increases. For the contracted design, the reactant velocity sharply increases at y ¼ 0.07 mm (the beginning of the contracted region) due to the reduced cross-sectional area of the flow channel, so the liquid water removal capability is improved.
30000
2
b 350
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I(A/m )
Fig. 8 e Effect of cathode reactant inlet velocity on the performance for the conventional and contracted designs. (a) polarization curves; (b) pressure drops.
Effect of cathode inlet relative humidity
The PEMFC performance is strongly dependent on the water management in the cell which includes two aspects. First, the membrane hydration must be maintained for proton transport. Secondly, when the water generation rate on the cathode side caused by electro-osmotic drag and the oxygen reduction reaction exceeds the water removal rate from the cathode to the anode by back-diffusion, evaporation, and capillary transport of liquid water through the cathode GDL and CL, the cathode becomes flooded. Excessive accumulated liquid water blocks the gas pores in the GDL and CL, which forms a barrier over the catalyst active surface in the catalyst layer, worsening the performance. In general, humidification of the reactants can ensure membrane hydration, but may induce cathode flooding. This section analyzes the effect of the cathode reactant inlet relative humidity on the cell performance for the conventional and contracted designs. Fig. 12(a) shows the effect of the cathode reactant inlet relative humidity, RHc, on the IeVcell polarization curves for both designs. For operating voltages greater than 0.7 V, the
Fig. 9 e Effect of cathode reactant inlet velocity on the local current density distributions on the middle cross-section in the PEM at an operating voltage of 0.4 V for the conventional and contracted designs. dx [ 0.6, dy [ 0.7: (a) vc [ 1.0 m/s; (b) vc [ 2.0 m/s; (c) vc [ 3.0 m/s; conventional design: (d) vc [ 1.0 m/s; (e) vc [ 2.0 m/s; (f) vc [ 3.0 m/s.
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Fig. 10 e Effect of cathode reactant inlet velocity on the liquid water distributions along the cathode GDL-CL interface at an operating voltage of 0.4 V for the conventional and contracted designs. dx [ 0.6, dy [ 0.7: (a) vc [ 1.0 m/s; (b) vc [ 2.0 m/s; (c) vc [ 3.0 m/s; conventional design: (d) vc [ 1.0 m/s; (e) vc [ 2.0 m/s; (f) vc [ 3.0 m/s.
a
1
RH = 100% c
0.9
RH = 75% c
RH = 50%
0.8
c c
0.7 x
Cell
(V)
RH = 25%
V
polarization curves for the various RHc for both designs almost coincide, indicating that the cell performance is not dependent on the flow field design and RHc. However, for operating voltages lower than 0.7 V, the cell performance curves for the various RHc start to differ. At low operating voltages for both flow field designs, the cell performance decreases as RHc increases. The cell performance is best for RHc ¼ 25% and worst for RHc ¼ 100% because at low operating voltages, the electrochemical reactions are stronger with more liquid water produced on the cathode side, so the backdiffusion of water and the high anode relative humidity, RHa ¼ 100%, provide sufficient water for the membrane. Thus, the cell performance is mainly dependent on the cathode
= 0.6_
y
= 0.7
Without Contraction
0.6 0.5 0.4 0.3
0
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b
12
V
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10
= 0.4V_ Cathode
v = 1m/s c
v = 2m/s c
y
250
= 0.7
Without Contraction 200
v = 3m/s c
RH = 100%
2
P(N/m )
6
ch
v (m/s)
8
x = 0.6_
I(A/m )
4
c
RH = 75% c
x
RH = 50% c
150
= 0.6_
y
= 0.7
Without Contraction
RH = 25% c
2
0
0
0.02
0.04
0.06
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0.1
y(m) Fig. 11 e Reactant velocity distributions along the flow direction in the cathode flow channel at an operating voltage of 0.4 V for various cathode reactant inlet velocities for the conventional and contracted designs.
100
0
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Fig. 12 e Effect of cathode reactant inlet relative humidity on the cell performance for the conventional and contracted designs. (a) polarization curves; (b) pressure drops.
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Fig. 13 e Effect of cathode reactant inlet relative humidity on the local current density distributions on the middle crosssection in the PEM at an operating voltage of 0.4 V for the conventional and contracted designs. dx [ 0.6, dy [ 0.7: (a) RHc [ 100%; (b) RHc [ 75%; (c) RHc [ 50%; (d) RHc [ 25%; conventional design: (e) RHc [ 100%; (f) RHc [ 75%; (g) RHc [ 50%; (h) RHc [ 25%.
mass transport limitations due to the liquid water blockage effect. When RHc is lower, the oxygen concentration in the reactants is higher and the water vapor concentration on the cathode side is lower, which reduces the cathode flooding, so the cell performance improves. For the contracted design, the contraction effect increases the reactant velocity in the contracted region of the flow channel which improves the liquid water removal and causes more oxygen to flow into the
porous layers, which then results in improved cell performance. Fig. 12(b) shows the effect of RHc on the pressure drops between the inlet and the outlet of the cathode flow channel for various current densities for both designs. RHc has less effect on the pressure drops, with the main influence coming from the contracted flow field design. Fig. 13 shows the effect of RHc on the local current densities on the middle cross-section in the PEM at an operating voltage
Fig. 14 e Effect of cathode reactant inlet relative humidity on the liquid water distributions along the cathode GDL-CL interface at an operating voltage of 0.4 V for the conventional and contracted designs. dx [ 0.6, dy [ 0.7: (a) RHc [ 100%; (b) RHc [ 75%; (c) RHc [ 50%; (d) RHc [ 25%; conventional design: (e) RHc [ 100%; (f) RHc [ 75%; (g) RHc [ 50%; (h) RHc [ 25%.
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of 0.4 V for both designs. For both designs, the local current densities near the flow channel outlet for RHc ¼ 25% are both higher than for the other three cathode relative humidities, so the cell performance is best for RHc ¼ 25%. For the contracted design, the local current densities significantly increase near the flow channel outlet due to the increased reactant velocities in the contracted region compared with the conventional design, which improves liquid water removal and reduces cathode flooding. Fig. 14 shows the effect of RHc on the liquid water concentrations along the cathode GDL-CL interface at an operating voltage of 0.4 V for both designs. For both designs, the liquid water concentrations at the low operating voltage of 0.4 V are higher, which supports the observation that the mass transport limitation due to cathode flooding is the main factor affecting the cell performance at lower operating voltages. Fig. 14 shows that at the lower operating voltage of 0.4 V, for both designs, the liquid water concentrations are largest for RHc ¼ 100% with the severest concentration polarization, so the cell performance is the worst. For the conventional design, the liquid water concentrations gradually increase from the inlet to the outlet along the flow direction. However, for the contracted design, the liquid water concentrations near the flow channel outlet are significantly lower than for the conventional design, which confirms that the contracted design has more efficient liquid water removal than the conventional design and significantly reduces cathode flooding. Therefore, as shown in Fig. 12(a), the concentration polarization in the polarization curves for the contracted design is not significant compared to that for the conventional design.
4.
Conclusions
A contracted parallel flow field design was developed to improve PEM fuel cell performance compared with the conventional parallel flow field design. A three-dimensional model was used to compare the cell performance and the local transport phenomena in both designs. In addition, the effect of the several operating parameters, including the cathode reactant inlet velocities and cathode reactant inlet relative humidities, on the cell performance for both designs was also investigated. The conclusions drawn from the analyses are: 1 For operating voltages greater than 0.7 V, the electrochemical reaction rates are lower with less oxygen consumption and less liquid water production, so the cell performance is not dependent on the flow field designs and the operating parameters. However, for lower operating voltages, the electrochemical reaction rates gradually increase as the operating voltage decreases. The oxygen transport capability and the liquid water removal efficiency then differ in the two flow field designs and for the various operating parameters; therefore, the cell performance is strongly dependent on the flow field designs and operating parameters. 2 For lower operating voltages, the cell performance for the contracted design is better than that for the conventional
design because the reactant flow velocities in the contracted region significantly increase, which enhances liquid water removal and reduces oxygen transport resistances. 3 For lower operating voltages, as the cathode reactant inlet velocity increases, the cell performance for both designs is improved because more oxygen is provided to the cathode GDL and CL to participate in the electrochemical reactions and the high reactant velocities help remove the liquid water trapped in the pores of the cathode GDL and CL, which reduces cathode flooding. 4 For lower operating voltages, as the cathode reactant relative humidity decreases, the cell performance for both designs is enhanced because the cell performance is mainly dependent on the cathode mass transport limitations due to the liquid water blockage effect. As RHc decreases, the oxygen concentration in the reactants increases and the water vapor concentration on the cathode side decreases, which reduces cathode flooding and improves the cell performance.
Acknowledgments This study was supported by the National Natural Science Foundation of China (No. 51076009), by National Basic Research Program of China (973 program, No. 2009CB219803), by Program for New Century Excellent Talents in University, and by the Fundamental Research Funds for the Central Universities (No. 11ZG01).
references
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[11] Djilali N, Lu D. Influence of heat transfer on gas and water transport. Int J Therm Sci 2002;41:29e40. [12] Kulikovsky AA. Quasi-3d modeling of water transport in polymer electrolyte fuel cells. J Electrochem Soc 2003;150: A1432e9. [13] Mazumder S, Cole JV. Rigorous 3-d mathematical modeling of PEM fuel cells I. Model predictions without liquid water transfer. J Electrochem Soc 2003;150:A1503e9. [14] Mazumder S, Cole JV. Rigorous 3-d mathematical modeling of PEM fuel cells II. Model predictions with liquid water transfer. J Electrochem Soc 2003;150:A1510e7. [15] Wang XD, Xu JL, Yan WM, Lee DJ, Su A. Transient response of PEM fuel cells with parallel and interdigitated flow field designs. Int J Heat Mass Trans 2011;54:2375e86. [16] Wang XD, Zhang XX, Yan WM, Lee DJ, Su A. Non-isothermal effects of single or double serpentine proton exchange membrane fuel cells. Electrochim Acta 2010;55:4926e34. [17] Wang XD, Huang YX, Cheng CH, Jang JY, Lee DJ, Yan WM, et al. An inverse geometry design problem for optimization of single serpentine flow field of PEM fuel cell. Int J Hydrogen Energy 2010;35:4247e57. [18] Wang CY. Fundamental models for fuel cell engineering. Chem Rev 2004;104:4727e66. [19] Nguyen TV. A gas distributor design for proton exchange membrane fuel cells. J Electrochem Soc 1996;143:L103e5. [20] Cha SW, O’Hayre R, Saito Y, Prinz FB. The scaling behavior of flow patterns: a model investigation. J Power Sources 2004; 134:57e71. [21] Cha SW, Lee SJ, O’Hayre R, Saito Y, Prinz FB. Geometric scale effect of flow channels on performance of fuel cells. J Electrochem Soc 2004;151:A1856e64. [22] Williams MV, Kunz HR, Fenton JM. Influence of convection through gas-diffusion layers on limiting current in PEMFCs using a serpentine flow field. J Electrochem Soc 2004;151: A1617e27. [23] Weng FB, Su A, Jung GB, Chiu YC, Chan SH. Numerical prediction of concentration and current distributions in PEMFC. J Power Sources 2005;145:546e54. [24] Jang JH, Yan WM, Li HY, Chou YC. Humidity of reactant fuel on the cell performance of PEM fuel cell with baffle-blocked flow field designs. J Power Sources 2006;159:468e77. [25] Wang XD, Duan YY, Yan WM. Numerical study of cell performance and local transport phenomena in PEM fuel cells with various flow channel area ratios. J Power Sources 2007;172:265e77. [26] Scholta J, Haussler F, Zhang W, Kuppers L, Jorissen L, Lehnert W. Development of a stack having an optimized flow field structure with low cross transport effects. J Power Sources 2006;155:60e5. [27] Wang Y, Wang CY. Ultra large-scale simulation of polymer electrolyte fuel cells. J Power Sources 2006;153:130e5. [28] Sun L, Oosthuizen PH, McAuley KB. A numerical study of channel-to-channel flow cross-over through gas diffusion layer in a PEM fuel cell flow system using a serpentine channel with a trapezoidal cross-sectional shape. Int J Therm Sci 2006;45:1021e6.
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[29] Hsieh SS, Yang SH, Feng CL. Characterization of the operational parameters of a H2/air micro PEMFC with different flow fields by impedance spectroscopy. J Power Sources 2006;162:262e70. [30] Yan WM, Li HY, Tsai WC. Three-dimensional analysis of PEM fuel cells with different flow channel designs. J Electrochem Soc 2006;153:A1984e91. [31] Feser JP, Prasad AK, Advani SG. On the relative influence of convection in serpentine flow fields of PEM fuel cells. J Power Sources 2006;161:404e12. [32] Shimpalee S, Greenway S, Van Zee JW. The impact of channel path length on PEMFC flow-field design. J Power Source 2006;160:398e406. [33] Xu C, He YL, Zhao TS, Chen R, Ye Q. Analysis of mass transport of methanol at the anode of a direct methanol fuel cell. J Electrochem Soc 2006;153:A1358e64. [34] Wang XD, Yan WM, Duan YY, Weng FB, Jung GB, Lee CY. Numerical study on channel size effect for proton exchange membrane fuel cell with serpentine flow field. Energy Convers Manage 2010;51:959e68. [35] Ahmed DH, Sung HJ. Effects of channel geometrical configuration and shoulder width on PEMFC performance at high current density. J Power Sources 2006;162: 327e39. [36] Xu C, Zhao TS. A new flow field design for polymer electrolyte-based fuel cells. Electrochem Commun 2007;9: 497e503. [37] Shimpalee S, Van Zee JW. Numerical studies on rib & channel dimension of flow-field on PEMFC performance. Int J Hydrogen Energy 2007;32:842e56. [38] Wang XD, Duan YY, Yan WM. Novel serpentine-baffle flow field design for proton exchange membrane fuel cells. J Power Sources 2007;173:210e21. [39] Wang XD, Duan YY, Yan WM, Peng XF. Local transport phenomena and cell performance of PEM fuel cells with various serpentine flow field designs. J Power Sources 2008; 175:397e407. [40] Wang XD, Duan YY, Yan WM, Weng FB. Effect of humidity of reactants on the cell performance of PEM fuel cells with parallel and interdigitated flow field designs. J Power Sources 2008;176:247e58. [41] Soong CY, Yan WM, Tseng CY, Liu HC, Chen FL, Chu HS. Analysis of reactant gas transport in a PEM fuel cell with partially blocked fuel flow channels. J Power Sources 2005; 143:36e47. [42] Liu HC, Yan WM, Soong CY, Chen FL, Chu HS. Reactant gas transport and cell performance of proton exchange membrane fuel cells with tapered flow field design. J Power Sources 2006;158:78e87. [43] Yan WM, Liu HC, Soong CY, Chen FL, Cheng CH. Numerical study on cell performance and local transport phenomena of PEM fuel cells with novel flow field designs. J Power Sources 2006;161:907e19. [44] Yan WM, Li HY, Chiu PC, Wang XD. Effects of serpentine flow field with outlet channel contraction on cell performance of PEM fuel cells. J Power Sources 2008;178:174e80.
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Effects of operating parameters on transport phenomena and cell performance of PEM fuel cells with conventional and contracted flow field designs Xiao-Dong Wang a,b,*, Wei-Mon Yan c,**, Wen-Chung Won c, Duu-Jong Lee d a
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China b Beijing Key Laboratory of Multiphase Flow and Heat Transfer for Low Grade Energy, North China Electric Power University, Beijing 102206, China c Department of Greenergy Engineering, National University of Tainan, Tainan 700, Taiwan d Department of Chemical Engineering, College of Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan
article info
abstract
Article history:
A contracted parallel flow field design was developed to improve fuel cell performance
Received 5 December 2011
compared with the conventional parallel flow field design. A three-dimensional model was
Received in revised form
used to compare the cell performance for both designs. The effects of the cathode reactant
20 February 2012
inlet velocity and cathode reactant inlet relative humidity on the cell performance for both
Accepted 24 February 2012
designs were also investigated. For operating voltages greater than 0.7 V because the
Available online 20 March 2012
electrochemical reaction rates are lower with less oxygen consumption and less liquid water production, the cell performance is independent of the flow field designs and
Keywords:
operating parameters. However, for lower operating voltages where the electrochemical
PEMFC
reaction rates gradually increase, the oxygen transport and the liquid water removal effi-
Parallel flow field design
ciency differ for the various flow field designs and operating parameters; therefore, the cell
Contracted flow field design
performance is strongly dependent on both the design and operating parameters. For lower
Cell performance
operating voltages, the cell performance for the contracted design is better than for the conventional design because the reactant flow velocities in the contracted region significantly increase, which enhances liquid water removal and reduces the oxygen transport resistance. For lower operating voltages, as the cathode reactant inlet velocity increases and the cathode reactant inlet relative humidity decreases, the cell performance for both designs improves. Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
The proton exchange membrane fuel cell (PEMFC) is a promising alternative energy source because of the simplicity of its
design and operation. Some attractive characteristics of a PEMFC system include lightweight, high energy density, no or low pollutant emission and low operating temperature. Cell performance of PEMFCs strongly depends on the operating
* Corresponding author. State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China. Tel./fax: þ86 10 62321277. ** Corresponding author. Tel.: þ886 6 2602251; fax: þ886 6 2602205. E-mail addresses: [email protected] (X.-D. Wang), [email protected] (W.-M. Yan). 0360-3199/$ e see front matter Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2012.02.145
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conditions, transport phenomena in the cells, electrochemical reaction kinetics, mechanical design, and manufacturing process. To reduce research costs and shorten the design cycle, modeling and simulations are being used extensively in research institutions and in industry around the world to gain a better understanding of the fundamental processes in these fuel cells. In recent years, many analyses, models and numerical simulations have been developed [1e18] to study various transport phenomena and the electrochemical kinetics to gain a better understanding and to develop strategies for optimal design and operating scenarios. Springer et al. [1] presented a one-dimensional steadystate model for a PEMFC based on experimentally determined transport parameters. Bernardi and Verbrugge [2,3] developed a full cell model to investigate the water transport mechanisms. Fuller et al. [4] and Nguyen et al. [5] proposed twodimensional transport models to examine the water management problems in a PEMFC. Ge and Yi [6] developed a two-dimensional model to investigate the effects of operating conditions and membrane thicknesses on the water transport. Okada et al. [7] studied the water transport at the anode side and gave a linear transport equation based on the water diffusion and electro-osmotic water drag to analyze the water concentration profiles. Gurau et al. [8] considered the variations of the concentrations and the partial pressures in the gas channels and developed a two-dimensional model for the entire sandwich of a PEMFC. They further derived a halfcell model for the cathode side and obtained rigorous analytical solutions which account for the liquid water content in the gas diffusion layer [9]. Um et al. [10] developed a multi-dimensional model to study the electrochemical kinetics, current distributions, fuel and oxidant flows, and multi-component transport in a PEMFC with an interdigitated flow field. Djilali and Lu [11] focused on the modeling of nonisothermal and non-isobaric effects to analyze the cell performance and water transport over a range of operating current densities. A quasi-three-dimensional model of water transport in PEMFCs was proposed by Kulikovsky [12] to analyze the non-linear diffusion of liquid water in the membrane. Mazumder and Cole [13,14] developed a threedimensional model to investigate the cell performance of PEMFCs with consideration of the liquid water effects. Wang and co-workers [15e17] developed two-dimensional and three-dimensional models for the reactants and water transport and the cell performance in PEMFCs. The effects of liquid water formation on the reactant transport were taken into account in the modeling and examined in the analysis. Recently, Wang [18] reviewed the fundamental PEMFC models. The flow field design in the bipolar plates is one of the most important issues in a PEMFC. An appropriate flow field design in the bipolar plates can improve the reactant transport, the thermal efficiency and the water management. To this end, different flow field configurations, including parallel, serpentine, interdigitated, and many other combined versions, have been developed. Many efforts have been devoted to optimize the flow field design to improve cell performance [15e44]. Recently, Soong et al. [41] proposed a relatively novel configuration with partially blocked reactant channels. They focused on the blockage effects of various gap ratios and
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number of baffles on the reactant transport and the pressure losses. They found that reducing the gap size and/or increasing the number of baffles enhanced the reactant transport. Liu et al. [42] developed a two-dimensional model to examine the reactant transport and the cell performance of a PEMFC with a tapered parallel flow channel. Numerical predictions showed that the cell performance was enhanced by the tapered reactant channel, with the enhancement is more evident at lower voltages. Later, Yan et al. [43] developed a three-dimensional model to investigate a parallel flow channel design with tapered heights or widths for improving the reactant utilization efficiency in PEMFCs. Their results showed that with the tapered channel designs, the flow area contraction along the flow channel led to increased reactant velocities; thus, enhancing the reactant transport through the porous layers, reactant utilization, and liquid water removal. The results also showed that the cell performance could be improved by either decreasing the height taper ratio or increasing the width taper ratio. Recently, Yan et al. [44] proposed a novel serpentine flow field with outlet channels having modified heights or lengths to improve reactant utilization and liquid water removal in PEMFCs. Their predictions showed that reductions of the outlet channel flow areas increased the reactant velocities in these regions, which enhanced reactant transport, reactant utilization, and liquid water removal; therefore, the cell performance was improved compared with the conventional serpentine flow field. It is well known that for parallel flow fields, a large amount of liquid water accumulates in the gas diffusion layer (GDL) and the catalyst layer (CL) near the outlet region of the flow channels, which significantly reduces the reactant transport rates in the porous layers compared with that near the flow channels inlets. As an extension of previous studies [42e44], this paper describes a novel parallel flow field design with reduced cress-sectional areas for the last part of the flow channel. This design is expected to increase the reactant flow velocity in the outlet region, which will enhance liquid water removal and reactant utilization. A three-dimensional numerical model was used to examine the effect of the contracted channel design on the cell performance. The local transport characteristics in the cell were analyzed to give reasons for the improved cell performance for the contracted channel design. The pressure drops in the contracted channel design were also evaluated as a reference for practical PEMFC designs. This paper also discussed the effect of the cathode reactant inlet velocity and cathode reactant inlet relative humidity on the cell performance for the conventional and contracted designs.
2.
Numerical model
A three-dimensional full-cell model was used to analyze the electrochemical reactions and the transport phenomena of the reactants and the products in the cell using the finite volume method. The cell was divided into the anode flow channels, membrane electrode assembly (MEA, including the anode GDL, anode CL, proton exchange membrane (PEM), cathode CL, and cathode GDL), and the cathode flow channels. The governing equations include the mass, momentum,
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species and electrical potential conservation equations. The model assumes that the system is three-dimensional and steady; the inlet reactants are ideal gases; the system is isothermal; the flow is laminar; the fluid is incompressible; the thermo-physical properties of the reactants and products are constant; and the porous layers such as the GDL, the CL the and the PEM are isotropic. This model includes continuity, momentum and species equations for gaseous species, water transport equations for channels, gas diffusion layers, and catalyst layers, a water transport equation for the membrane, and electron and proton transport equations. The ButlereVolmer equation was employed to describe the electrochemical reactions in catalyst layers. The primary governing equations are as follows. Continuity equation for gaseous species: u g ¼ SL V$ 3 rg !
(1)
Momentum equation for gaseous species: 3 2
ð1 sÞ
V$ rg ! u g! u g ¼ 3 Vpg þ
V$ mg V! u g þ S! u ð1 sÞ 3
(2)
Species equation for gaseous species: V$ 3 rg ! u g Ck ¼ V$ rg Dk;eff VCk þ Sc SL
(3)
Water transport equation for flow channels, gas diffusion layers and catalyst layers: r kp krl vpc r kp krl nd MH2 O ! Vs V$ l i m ¼ SL Vpg þ V$ V$ l ml vs ml F
Table 1 e Parametric values used in the models. Parameter Flow channel length Flow channel height Flow channel width Rib length Rib height Rib width Gas diffusion layer thickness Catalyst layer thickness PEM thickness Gas diffusion layer porosity Catalyst layer porosity PEM porosity Gas diffusion layer permeability Catalyst layer permeability PEM permeability Gas diffusion layer conductivity Catalyst layer conductivity Reference current density at the anode Reference current density at the cathode
Value
Unit
100 1 1 100 1 1 0.3 0.01 0.035 0.4 0.4 0.28 1.76 1011 1.76 1011 1.8 1018 53 53 9.23 108 1.05 106
mm mm mm mm mm mm mm mm mm e e e m2 m2 m2 V1 m1 V1 m1 A m3 A m3
height contraction ratio, dx, and the length contraction ratio, dy, are defined as dx ¼ H1/H0 and dy ¼ L1/L0 where H0 is the inlet channel height, H1 is the outlet channel height, L0 is the total channel length, and L1 is the un-contracted channel length. However, in the conventional parallel flow field design, the channel height is constant along whole channel.
(4)
Water transport equation for the membrane: MH2 O rdry ad MH2 O ! i m l Dl Vl ¼ 0 V$ F Mm
(5)
Proton and electron transport equations: V$ðsm VFm Þ ¼ Sj
(6)
V$ðss VFs Þ ¼ Sj
(7)
Energy equation for the PEMFC: i2 V$ 3 ð1sÞrg ! u g Cp;g T þV$ 3 srl ! u l Cp;l T ¼V$ leff VT þjhþ þhfg SL s (8) More details on the numerical model and solution procedure were given elsewhere [15e17]. Most previous studies have used small fuel cell models to reduce the computational costs of the three-dimensional simulations. However, the results for short flow channels do not agree well with the general performance of large cells. The present work aims to analyze a relatively large fuel cell with an active area of 10 10 cm2. The cell dimensions and main parameters used in this simulation are listed in Table 1. Considering the symmetry of the fuel cell configuration, only an essential part of the fuel cell model (shown in Fig. 1) is used as the computational domain to reduce the computational time. Fig. 2 shows a schematic of the three-dimensional contracted channel design, where the channel height changes suddenly from H0 to H1 at a specific location. The
Fig. 1 e Schematics of the numerical PEMFC models. (a) conventional parallel flow field design; (b) contracted flow field design.
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Fig. 2 e Three-dimensional views of the contracted flow field design.
This paper compares the cell performance for the conventional and contracted parallel flow field designs and investigates the effects of the cathode reactant inlet velocity and the cathode reactant inlet relative humidity on the cell performance and local transport phenomena for both flow field designs. For the comparison of the cell performance for both designs, dx and dy were chosen to be 0.6 and 0.7 for the contracted design. In addition, the base operating conditions for the fuel cell were assumed to be a fuel cell temperature of 323 K, the reactant gases on the anode side include hydrogen and water vapor with a relative humidity of 100%, the reactant gases on the cathode side contain oxygen, nitrogen, and water vapor with a relative humidity of 100%, the inlet flow velocity on the anode side is 2.0 m/s, the inlet flow velocity on the cathode side is 0.5 m/s, and the inlet pressures on the anode and cathode sides are both 1 atm. The effect of the cathode reactant inlet velocity on the cell performance for both designs was investigated using cathode reactant inlet
velocities of 1.0 m/s, 2.0 m/s, and 3.0 m/s with the other conditions the same as the base case operating conditions. The effect of the cathode reactant inlet relative humidity on the cell performance for both designs was investigated using cathode reactant inlet relative humidities of 25%, 50%, 75%, and 100% with the other conditions the same as the base case operating conditions. The grid independence was examined in preliminary test runs. Three non-uniformly distributed grid configurations were evaluated for the PEMFC with the parallel flow field at an operating voltage of 0.3 V. The numbers of elements in the x, y and z directions were: (I) 30 80 69, (II) 41 100 87, and (III) 52 120 105. The influence of the number of elements on the local current density is shown in Fig. 3. The difference between the local current densities was 0.62% for girds (I) and (III) and 0.17% for grids (II) and (III). Thus grid (II) was chosen for the simulations as a tradeoff between accuracy and execution time.
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10000
Gridlines x x y x z = 30 x 80 x 69 Gridlines x x y x z = 41 x 100 x 87 Gridlines x x y x z = 52 x 120 x 105
2
I (A/m )
9500
Anode Fuel = H
y
9000
2
Cathode Fuel = O
2
Anode Fuel RH = 100% Cathode Fuel RH = 100% Anode Flow Velocity = 0.5m/s Cathode Flow Velocity = 2m/s
8500
8000
0
0.02
0.04
0.06
0.08
0.1
y (m) Fig. 3 e Effect of the element number on the local current densities at an operating voltage of 0.3 V.
3.
Results and discussion
3.1. Comparison of cell performance for conventional and contracted flow field designs Fig. 4(a) shows the IeVcell polarization curves for the conventional and contracted designs. Fig. 4(a) shows that for 1
(a) x
0.9
(V)
0.6
y
= 0.7
cell
V
0.8 0.7
= 0.6_
Without Contraction With Liquid Water Effect Without Liquid Water Effect
0.5 0.4 0.3
0
5000
10000
15000
20000
25000
30000
2
I(A/m ) 400
(b) x
350 300 2
(N/m )
= 0.6_
y
= 0.7
Without Contraction With Liquid Water Effect Without Liquid Water Effect
250 200 150 100 50
0
5000
10000
15000
20000
25000
30000
2 I(A/m )
Fig. 4 e Cell performance for the conventional and contracted designs. (a) polarization curves; (b) pressure drops.
operating voltages higher than 0.7 V, both designs have almost the same performance since the electrochemical reaction rates are low with a small amount of oxygen consumption and liquid water production. However, for operating voltages lower than 0.7 V, the contracted design has better performance than the conventional design. As the operating voltage decreases, the electrochemical reaction rates gradually increase. Since the two designs have different liquid water removal rates and oxygen transport rates to the cathode CL, their cell performances differ. The contracted design increases the reactant velocity in the contracted flow channel region which improves the liquid water removal, which then results in the improved cell performance. The cell performance without the liquid water effect (single-phase model) was also simulated. At high operating voltages, the differences between the cell performances with and without liquid water effects were negligible. Thus, the reactant transport in the PEM fuel cell can be safely modeled as single-phase flow at high voltages. However, at low voltages, liquid water has a significant effect on the cell performance, so the liquid water can not be neglected in the model. This confirms the observation that the mass transport at lower voltages is more significant with more water generated in the catalyst layer on the cathode side, so the two-phase flow effects should be considered at low voltages. Fig. 4(b) shows the pressure drops for both designs for various current densities. The pressure drop slightly increases with increasing current density because more liquid water is produced at higher current densities, which increases the flow resistance of the reactants in the channels. Fig. 4(b) shows that although the contracted design enhances liquid water removal and oxygen transport, it also increases the pressure drops, thus, the pressure drop for the contracted design is about twice that of the conventional design. Fig. 5(a) and (b) shows the local current densities on the middle cross-section in the PEM at an operating voltage of 0.4 V for the conventional and contracted designs. For both designs, the maximum local current densities occur at the channel inlet and then gradually decrease along the flow direction as the oxygen is gradually consumed by the electrochemical reaction. For the conventional design, the minimum local current densities occur at the channel outlet, while for the contracted design, the current densities in the contracted region of the flow channel are far higher than for the conventional design, indicating that the oxygen mass flow rates to the cathode GDL in the contracted region are increased by the flow channel contractions. Fig. 5 also shows that for both designs, the local current densities under the flow channel are larger than under the rib since the diffusion path for oxygen arriving in the catalyst layer under the ribs is longer than that under the flow channels and the stronger shear stresses under the flow channels enhance the liquid water removal. Fig. 6(a) and (b) shows the liquid water concentrations along the cathode GDL-CL interface at the operating voltage of 0.4 V for both designs. Comparison of Figs. 5and 6 shows that the liquid water distributions are opposite to the local current density distributions. This occurs because the liquid water accumulation in the pores in the porous layers increases the oxygen transport resistance, so the oxygen mass flow rates to
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Fig. 5 e Local current density distributions on the middle cross-section in the PEM at an operating voltage of 0.4 V for the conventional and contracted designs. (a) contracted channel design with dx [ 0.6, dy [ 0.7; (b) conventional design.
the cathode CL and the local current densities decrease. Fig. 6(a) shows that with the contracted design, the liquid water concentration is significantly reduced in the contracted region of the flow channel because the flow channel contractions increase the reactant velocity and enhance liquid water removal. Fig. 7 shows the variation of the reactant velocities in the cathode channel along the flow direction from the inlet to the outlet at 0.4 V for both designs. The velocity slowly increases from the inlet to the outlet in the conventional design. In the contracted design, the velocity abruptly increases at y ¼ 0.07 m (the beginning of the contracted region) due to the reduced cross-sectional area of the flow channel. In addition, the velocity without consideration of the liquid water effect is higher than with the liquid water effect because the liquid water formation increases the flow resistance.
3.2.
Effect of cathode inlet velocity
The anode reactants entering the fuel cell are assumed to be humidified hydrogen, while the cathode reactant gas assumed to be humidified air; thus, the most economic means for improving cell performance is to change the cathode air flow rates. Fig. 8(a) presents the effect of the cathode reactant inlet velocity on the IeVcell polarization curves for the conventional and contracted designs. For operating voltages higher than
0.7 V, the average current densities for the various cathode inlet velocities in the two flow field designs are almost the same, indicating that the flow field design and inlet velocities do not affect the cell performance. This is because the electrochemical reaction rate is low and only a limited amount of oxygen is consumed with only a small amount of liquid water produced for the higher operating voltages. Therefore, the oxygen transport rates for both flow field designs and all cathode inlet velocities are sufficient to maintain the electrochemical reaction rates. However, for operating voltages lower than 0.7 V, the flow field designs and cathode inlet velocities significantly impact the cell performance. As the cathode inlet velocities increase, the average current densities increase and the cell performance improves, but the rate of increase gradually weakens. As the operating voltage is gradually reduced, the electrochemical reaction rates increase and the oxygen consumption increases. Then, since increasing cathode inlet velocities increase the oxygen inlet velocities, more oxygen is provided to the catalyst layer for the electrochemical reaction and the higher oxygen velocities also help remove the liquid water. At the low reactant inlet velocity of 1.0 m/s, the oxygen supply is not sufficient for the electrochemical reaction at high current densities. In addition, the liquid water produced by the electrochemical reaction is not easily removed from the rear part of the flow channel due to the slow flow velocity. The liquid water then blocks the pores
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Fig. 6 e Liquid water distributions along the cathode GDL-CL interface at an operating voltage of 0.4 V for the conventional and contracted designs. (a) contracted channel design with dx [ 0.6, dy [ 0.7; (b) conventional design.
in the GDL and CL. Consequently, the cell performance is the worst for the lowest reactant inlet velocity. Fig. 8(a) also shows that the cell performance at various cathode inlet velocities for the contracted flow field design is superior to that for conventional flow field design as described in section 3.1. Fig. 8(b) shows the effect of the cathode reactant inlet velocity
9
V 8
= 0.4V_ Cathode x
7
vch(m/s)
cell
= 0.6_
y
= 0.7
Without Contraction With Liquid Water Effect Without Liquid Water Effect
6 5 4 3 2
0
0.02
0.04
0.06
0.08
y (m) Fig. 7 e Reactant velocity distributions along the flow direction in the cathode flow channel at an operating voltage of 0.4 V for the conventional and contracted designs.
0.1
on the pressure drop between the inlet and the outlet of the cathode flow channel for various current densities. The increase in the cathode inlet velocity increase the pressure drops. In addition, the pressure drops for the contracted design are higher than that for the conventional design. Fig. 9 shows the effect of the cathode reactant inlet velocity on the local current density distributions on the middle crosssection in the PEM at an operating voltage of 0.4 V. For both flow field designs, at vc ¼ 3.0 m/s, the oxygen supply is sufficient and the liquid water removal is better than for vc ¼ 2.0 m/ s or vc ¼ 1.0 m/s, so the cell performance with vc ¼ 3.0 m/s is better than with vc ¼ 1.0 m/s and vc ¼ 2.0 m/s. For the contracted design, the contraction effect increases the reactant velocity in the contracted region of the flow channel and more oxygen flows into the cathode GDL and CL to participate in the electrochemical reactions, so the local current densities near the flow channel outlet significantly increase compared with the conventional design. Fig. 10 shows the effect of the cathode reactant inlet velocity on the liquid water concentrations along the cathode GDL-CL interface at an operating voltage of 0.4 V for both designs. For both designs, as the cathode reactant inlet velocity increases, the liquid water removal capability increases and the liquid water concentrations decrease. For example, the liquid water concentrations under the flow channel and the rib for vc ¼ 3.0 m/s are significantly less than for vc ¼ 1.0 m/s and vc ¼ 2.0 m/s. Because the contracted design removes more
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 5 8 0 8 e1 5 8 1 9
a
1
v = 1m/s c
0.9
v = 2m/s v = 3m/s
(V)
0.7
Without Contraction
V
c
0.8
0.6
_
y = 0.7
Cell
x = 0.6
0.5 0.4 0.3
0
5000
10000
15000
20000
25000
3.3.
I(A/m )
300
v = 1m/s c
v = 2m/s c
x
= 0.6_
y
= 0.7
Without Contraction
v = 3m/s c
2
P(N/m )
250
200
150
100
50
0
5000
10000
15000
liquid water produced by electrochemical reactions, the liquid water concentrations near the flow channel outlet are less than in the conventional design. Fig. 11 shows the reactant velocity distributions along the flow direction in the cathode flow channel at an operating voltage of 0.4 V for various cathode reactant inlet velocities for both designs. As the cathode reactant inlet velocity increases, the reactant velocity in the flow channel also increases. For the contracted design, the reactant velocity sharply increases at y ¼ 0.07 mm (the beginning of the contracted region) due to the reduced cross-sectional area of the flow channel, so the liquid water removal capability is improved.
30000
2
b 350
20000
25000
15815
30000
2
I(A/m )
Fig. 8 e Effect of cathode reactant inlet velocity on the performance for the conventional and contracted designs. (a) polarization curves; (b) pressure drops.
Effect of cathode inlet relative humidity
The PEMFC performance is strongly dependent on the water management in the cell which includes two aspects. First, the membrane hydration must be maintained for proton transport. Secondly, when the water generation rate on the cathode side caused by electro-osmotic drag and the oxygen reduction reaction exceeds the water removal rate from the cathode to the anode by back-diffusion, evaporation, and capillary transport of liquid water through the cathode GDL and CL, the cathode becomes flooded. Excessive accumulated liquid water blocks the gas pores in the GDL and CL, which forms a barrier over the catalyst active surface in the catalyst layer, worsening the performance. In general, humidification of the reactants can ensure membrane hydration, but may induce cathode flooding. This section analyzes the effect of the cathode reactant inlet relative humidity on the cell performance for the conventional and contracted designs. Fig. 12(a) shows the effect of the cathode reactant inlet relative humidity, RHc, on the IeVcell polarization curves for both designs. For operating voltages greater than 0.7 V, the
Fig. 9 e Effect of cathode reactant inlet velocity on the local current density distributions on the middle cross-section in the PEM at an operating voltage of 0.4 V for the conventional and contracted designs. dx [ 0.6, dy [ 0.7: (a) vc [ 1.0 m/s; (b) vc [ 2.0 m/s; (c) vc [ 3.0 m/s; conventional design: (d) vc [ 1.0 m/s; (e) vc [ 2.0 m/s; (f) vc [ 3.0 m/s.
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Fig. 10 e Effect of cathode reactant inlet velocity on the liquid water distributions along the cathode GDL-CL interface at an operating voltage of 0.4 V for the conventional and contracted designs. dx [ 0.6, dy [ 0.7: (a) vc [ 1.0 m/s; (b) vc [ 2.0 m/s; (c) vc [ 3.0 m/s; conventional design: (d) vc [ 1.0 m/s; (e) vc [ 2.0 m/s; (f) vc [ 3.0 m/s.
a
1
RH = 100% c
0.9
RH = 75% c
RH = 50%
0.8
c c
0.7 x
Cell
(V)
RH = 25%
V
polarization curves for the various RHc for both designs almost coincide, indicating that the cell performance is not dependent on the flow field design and RHc. However, for operating voltages lower than 0.7 V, the cell performance curves for the various RHc start to differ. At low operating voltages for both flow field designs, the cell performance decreases as RHc increases. The cell performance is best for RHc ¼ 25% and worst for RHc ¼ 100% because at low operating voltages, the electrochemical reactions are stronger with more liquid water produced on the cathode side, so the backdiffusion of water and the high anode relative humidity, RHa ¼ 100%, provide sufficient water for the membrane. Thus, the cell performance is mainly dependent on the cathode
= 0.6_
y
= 0.7
Without Contraction
0.6 0.5 0.4 0.3
0
5000
10000
15000
20000
25000
30000
2
b
12
V
Cell
10
= 0.4V_ Cathode
v = 1m/s c
v = 2m/s c
y
250
= 0.7
Without Contraction 200
v = 3m/s c
RH = 100%
2
P(N/m )
6
ch
v (m/s)
8
x = 0.6_
I(A/m )
4
c
RH = 75% c
x
RH = 50% c
150
= 0.6_
y
= 0.7
Without Contraction
RH = 25% c
2
0
0
0.02
0.04
0.06
0.08
0.1
y(m) Fig. 11 e Reactant velocity distributions along the flow direction in the cathode flow channel at an operating voltage of 0.4 V for various cathode reactant inlet velocities for the conventional and contracted designs.
100
0
5000
10000
15000
20000
25000
30000
2
I(A/m )
Fig. 12 e Effect of cathode reactant inlet relative humidity on the cell performance for the conventional and contracted designs. (a) polarization curves; (b) pressure drops.
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Fig. 13 e Effect of cathode reactant inlet relative humidity on the local current density distributions on the middle crosssection in the PEM at an operating voltage of 0.4 V for the conventional and contracted designs. dx [ 0.6, dy [ 0.7: (a) RHc [ 100%; (b) RHc [ 75%; (c) RHc [ 50%; (d) RHc [ 25%; conventional design: (e) RHc [ 100%; (f) RHc [ 75%; (g) RHc [ 50%; (h) RHc [ 25%.
mass transport limitations due to the liquid water blockage effect. When RHc is lower, the oxygen concentration in the reactants is higher and the water vapor concentration on the cathode side is lower, which reduces the cathode flooding, so the cell performance improves. For the contracted design, the contraction effect increases the reactant velocity in the contracted region of the flow channel which improves the liquid water removal and causes more oxygen to flow into the
porous layers, which then results in improved cell performance. Fig. 12(b) shows the effect of RHc on the pressure drops between the inlet and the outlet of the cathode flow channel for various current densities for both designs. RHc has less effect on the pressure drops, with the main influence coming from the contracted flow field design. Fig. 13 shows the effect of RHc on the local current densities on the middle cross-section in the PEM at an operating voltage
Fig. 14 e Effect of cathode reactant inlet relative humidity on the liquid water distributions along the cathode GDL-CL interface at an operating voltage of 0.4 V for the conventional and contracted designs. dx [ 0.6, dy [ 0.7: (a) RHc [ 100%; (b) RHc [ 75%; (c) RHc [ 50%; (d) RHc [ 25%; conventional design: (e) RHc [ 100%; (f) RHc [ 75%; (g) RHc [ 50%; (h) RHc [ 25%.
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of 0.4 V for both designs. For both designs, the local current densities near the flow channel outlet for RHc ¼ 25% are both higher than for the other three cathode relative humidities, so the cell performance is best for RHc ¼ 25%. For the contracted design, the local current densities significantly increase near the flow channel outlet due to the increased reactant velocities in the contracted region compared with the conventional design, which improves liquid water removal and reduces cathode flooding. Fig. 14 shows the effect of RHc on the liquid water concentrations along the cathode GDL-CL interface at an operating voltage of 0.4 V for both designs. For both designs, the liquid water concentrations at the low operating voltage of 0.4 V are higher, which supports the observation that the mass transport limitation due to cathode flooding is the main factor affecting the cell performance at lower operating voltages. Fig. 14 shows that at the lower operating voltage of 0.4 V, for both designs, the liquid water concentrations are largest for RHc ¼ 100% with the severest concentration polarization, so the cell performance is the worst. For the conventional design, the liquid water concentrations gradually increase from the inlet to the outlet along the flow direction. However, for the contracted design, the liquid water concentrations near the flow channel outlet are significantly lower than for the conventional design, which confirms that the contracted design has more efficient liquid water removal than the conventional design and significantly reduces cathode flooding. Therefore, as shown in Fig. 12(a), the concentration polarization in the polarization curves for the contracted design is not significant compared to that for the conventional design.
4.
Conclusions
A contracted parallel flow field design was developed to improve PEM fuel cell performance compared with the conventional parallel flow field design. A three-dimensional model was used to compare the cell performance and the local transport phenomena in both designs. In addition, the effect of the several operating parameters, including the cathode reactant inlet velocities and cathode reactant inlet relative humidities, on the cell performance for both designs was also investigated. The conclusions drawn from the analyses are: 1 For operating voltages greater than 0.7 V, the electrochemical reaction rates are lower with less oxygen consumption and less liquid water production, so the cell performance is not dependent on the flow field designs and the operating parameters. However, for lower operating voltages, the electrochemical reaction rates gradually increase as the operating voltage decreases. The oxygen transport capability and the liquid water removal efficiency then differ in the two flow field designs and for the various operating parameters; therefore, the cell performance is strongly dependent on the flow field designs and operating parameters. 2 For lower operating voltages, the cell performance for the contracted design is better than that for the conventional
design because the reactant flow velocities in the contracted region significantly increase, which enhances liquid water removal and reduces oxygen transport resistances. 3 For lower operating voltages, as the cathode reactant inlet velocity increases, the cell performance for both designs is improved because more oxygen is provided to the cathode GDL and CL to participate in the electrochemical reactions and the high reactant velocities help remove the liquid water trapped in the pores of the cathode GDL and CL, which reduces cathode flooding. 4 For lower operating voltages, as the cathode reactant relative humidity decreases, the cell performance for both designs is enhanced because the cell performance is mainly dependent on the cathode mass transport limitations due to the liquid water blockage effect. As RHc decreases, the oxygen concentration in the reactants increases and the water vapor concentration on the cathode side decreases, which reduces cathode flooding and improves the cell performance.
Acknowledgments This study was supported by the National Natural Science Foundation of China (No. 51076009), by National Basic Research Program of China (973 program, No. 2009CB219803), by Program for New Century Excellent Talents in University, and by the Fundamental Research Funds for the Central Universities (No. 11ZG01).
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