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Transient mass transport and cell performance of a PEM fuel cell
International Journal of Heat and Mass Transfer 107 (2017) 646–656
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Transient mass transport and cell performance of a PEM fuel cell Wei-Mon Yan a,⇑, Hung-Yi Li b, Wen-Chung Weng b a b
Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei 10608, Taiwan Department of Mechatronic Engineering, Huafan University, Shihtin, New Taipei 22301, Taiwan
a r t i c l e
i n f o
Article history: Received 25 October 2016 Received in revised form 18 November 2016 Accepted 18 November 2016
Keywords: Transient mass transport Serpentine flow field design Transient response time Local current density distribution
a b s t r a c t This study aims to establish an unsteady, three-dimensional mathematical model of proton exchange membrane fuel cells (PEMFCs) with four serpentine flow field designs. The effects of the serpentine flow field designs on the transient characteristics of the PEMFCs are evaluated in terms of transient response of local current density and mass concentration under sudden change in loading. When the operating voltage is 0.7 V, the weak electrochemical reactions result in a local current density distribution that is only minimally affected by the serpentine flow field designs. However, when operating voltage instantaneously drops from 0.7 V to 0.5 V, electrochemical reactions increase. To ensure a sufficient fuel cell oxygen supply, the oxygen mass fractions are high and uniform in the cathode gas diffusion and cathode catalyst layers, which cause overshoot phenomena in the local current density distribution. Because the inlet fuel flow rate is identical in all PEMFCs, the inlet fuel flow velocity decreases as the cathode inlet number increases. When the operating voltage abruptly drops, the low inlet fuel velocity prevents the PEMFC from maintaining a steady state. Therefore, the transient response time needed to reach a steady state in the quadruple serpentine flow field design is longest when overshoot or undershoot phenomena occur. Additionally, cells with large inlet fuel flow rates perform best and reach a steady state condition fastest when cell voltage changes occur suddenly. Ó 2016 Published by Elsevier Ltd.
1. Introduction Proton exchange membrane fuel cells (PEMFCs) are considered promising alternatives for generating clean power for portable, mobile and stationary applications because of their low to zero emissions, low-temperature operation, high power density and fast start-up. Therefore, numerous experimental and numerical studies have been constructed to understand the physical phenomena and steady state or transient characteristics of PEMFCs. The advantages of mathematical simulations include the reduced time and cost of research and development, the easy comparison of experimental data, and the capability to calculate physical quantities that are difficult or impossible to measure. Most studies of experimental methods [1–6] and numerical simulations of fuel cells emphasize the steady state characteristics of the flow field design [7–13] and parameter design [14–18]. Most of the literatures on fuel cells describe numerical simulations of steady state characteristics. In contrast, despite the recognized importance of transient response time and transient characteristics of fuel cells, transient models and corresponding
⇑ Corresponding author. E-mail address: [email protected] (W.-M. Yan). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.11.075 0017-9310/Ó 2016 Published by Elsevier Ltd.
numerical simulations of fuel cells are rare [19–35]. In stationary or automotive applications of PEMFCs, transient load changes during operation are common. One example is a sudden load variation when device starts or when a vehicle is accelerated or decelerated. The current density overshoots its final steady state value when the operating voltage changes abruptly from high to low whereas the current density undershoots its final steady state value when the operating voltage changes abruptly from low to high. The transient response times needed for overshoot and undershoot phenomena to reach steady states are important for evaluating the dynamic performance of PEMFCs. Thus, numerical models of transient characteristics are needed to analyze PEMFCs under operating conditions that vary over time. A one-dimensional mathematical model developed by Friede et al. [19] to characterize the transient behavior of PEMFCs showed that membrane water transport has a major effect on fuel cell transients. Moreover, Hu and Fan [21] developed a transient three-dimensional non-isothermal PEMFC model of overshoot and undershoot phenomena in PEMFCs, which showed the very short transient response time of PEMFC, the effects of inlet fuel flow rates, the relative humidity of the fuel, and the voltage loading on transient characteristics. Wu et al. [23] developed a transient two-dimensional single-phase non-isothermal PEMFC model that included a heat transfer
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647
Nomenclature Ajref 0 C D F i I j kc ke kp M p nd R s Sc Sj SL S!u T t ! u Vcell x, y, z
reference exchange current density (Am3) mass fraction mass diffusivity (m2s1) Faraday constant (96,487 Cmol1) current density (Am2) average current density (Am2) transfer current density (Am3) coefficient of water vapor condensation rate (s1) coefficient of water vapor evaporation rate (atm1 s1) permeability (m2) molecular weight (kg mol1) pressure (atm) electro-osmotic drag coefficient universal gas constant (8.314 Jmol1 K1) saturation of liquid water source term in the species equation source term in the electric potential equation source term due to phase change of water source term in the momentum equation temperature (K) time (s) velocity (ms1) operating voltage (V) coordinates (m)
ac e q rm rs l s
Um Us
electrical transfer coefficient in backward reaction porosity density (kg m3) ionic conductivity (X-1 m1) electronic conductivity (X-1 m1) dynamic viscosity (Pas) tortuosity of the pores in the porous material electric potential of the ionic phase (V) electric potential of the electronic phase (V)
Subscripts and superscripts a anode c cathode ch channel CL catalyst layer eff effective value k kth species of the mixture GDL gas diffusion layer g gas H2 hydrogen H2O water l liquid m membrane O2 oxygen sat saturation
Greek symbols aa electrical transfer coefficient in forward reaction
equation. The transient processes considered in the model included electrochemical double-layer charging/discharging, species transport, membrane hydration/dehydration, and heat transport processes. Their numerical results confirmed that the heat transfer process significantly affects fuel cell dynamic responses. A time dependence of three-dimensional simulation including water phase change and heat transfer of a PEMFC model was investigated numerically by Shimpalee et al. [24]. The current distribution and temperature distribution as well as their dynamic changes in fuel cell stack were evaluated in situ by Yan et al. [25]. The experimental results show that the local current and temperature rise when load rapidly. The extent of temperature fluctuation during dynamic loading is significantly influenced by air stoichiometries, loading rates, and air relative humidities. The overshoot behavior has been observed during a change in the electrical load during operation with fixed flow rates of hydrogen and air. Siroma et al. [26] measured local phenomena in a PEMFC during a transitional state induced by changing of the feeding gas. The potential distribution in the electrolyte was observed using three quasireference electrodes located locally. Sophie et al. [27] examined a transient model predicting PEMFC voltage response to a step change in the cooling water temperature. They found that an undershoot voltage response is observed when the characteristic time for water transport is longer than the transient thermal regime. A 3D dynamic thermal model of a single fuel cell is presented by Adzakpa et al. [28] to study the temperature distribution in a fuel cell cooled from the bottom to the top with air. They indicated that the temperatures are higher at the top part of the cell than at the bottom part. Cho et al. [29] studied the transient response of proton-exchange membrane fuel cells. They found that the undershoot behavior consists of two stages with different time delays. An unsteady two phase nonisothermal model is used by Mishra and Wu [30] to study the
start-up characteristics of a PEM fuel cell. They disclosed that as the gas diffusion layer thickness was increased, the influence of liquid water was delayed. Haddad et al. [31] numerically examined 1-D transient mass and charge transfer in a PEM fuel cell. The concentration profiles and concentration variations with time and membrane thickness were presented. A three-dimensional transient two-phase isothermal model was developed by KhajehHosseini-Dalasm et al. [32] for the cathode side of a proton exchange membrane fuel cell. Prediction results showed that it takes less time for a high average current density to attain the steady state condition which is due to the capillary pressure gradient inside the porous media. Hinaje et al. [33] proposed a dynamic model of PEM fuel cell using EIS method. They indicated that a defective cathodic GDL has more consequences on cell performance than if it occurs at anode side. Wang et al. [34] established a three-dimensional, two-phase transient model to analyze transient characteristics of PEMFCs with parallel and interdigitated flow field designs. The effects of various voltage loading changes, width ratios of the channel to the rib, and cathode inlet flow rates on the transient response were examined in both flow field designs. Li et al. [35] established a three-dimensional transient numerical PEMFC model with different cathode flow field designs to determine the effects of flow field designs and voltage loading on transient characteristics of PEMFCs. Comparisons of the effects of overshoot and undershoot phenomena in different cathode flow field designs showed that the transient response time needed to reach the steady state was longest in a parallel flow field with a baffled design. Recently, Kim et al. [36] investigated the effects of operating and controlling parameters on the transient response of a PEMFC for achieving more stable cell performance under load change conditions. The transient response of a PEMFC was measured and analyzed by varying air stoichiometry, air humidity, and air excess ratio (AER). The
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dynamic cell performance of a kW-grade proton exchange membrane fuel cell stack with anode dead-ended mode fuel supply was experimentally examined by Jang [37]. Experimental results indicated an optimal purge interval and duration for water management and cell performance of the fuel cell stack. Most of the proposed models of transient characteristics of fuel cells in the literatures have been one-dimensional or twodimensional models with parallel or serpentine flow field designs. Some recently developed three-dimensional models assume a single phase. Moreover, most studies have focused on step voltage changes rather than on the effects of flow field designs and parameters on transient response characteristics. Therefore, this study constructs three-dimensional computational models of PEMFCs with varying numbers of cathode inlets, i.e., a single serpentine flow field design, a double serpentine flow field design, a triple serpentine flow field design and a quadruple serpentine flow field design. The effects of the serpentine flow field designs and the inlet fuel flow rates on transient characteristics of PEMFCs were analyzed to elucidate overshoot and undershoot phenomena, transient response times, local current density distributions and oxygen mass fraction distributions. 2. Analysis The three-dimensional transient numerical models of PEMFCs with four serpentine flow field designs with varying numbers of
cathode inlets were constructed by finite volume method. Fig. 1 shows that the flow field designs in the PEMFCs included a single serpentine flow field design, a double serpentine flow field design, a triple serpentine flow field design, and a quadruple serpentine flow field design. The effects of the serpentine flow field designs and the different inlet fuel flow rates on the transient characteristics of the PEMFCs are examined by analyzing the electrochemical reactions and transport phenomena of various reactants and products in the PEMFCs. The major fuel cell components are the anode gas flow field, the anode gas diffusion layer, the anode catalyst layer, the proton exchange membrane, the cathode catalyst layer, the cathode gas diffusion layer, and the cathode gas flow field. Equations for mass, momentum, species and electric potential equations are used in the analysis. The simulations are based on the following assumptions: the cell system is isothermal; the reactants and products are ideal gases; the flow is laminar and incompressible; the electrochemical reactions only occur in the catalyst layer; the porous layers, such as the gas diffusion layer, the catalyst layer and the proton exchange membrane, are isotropic. The fuel cell dimensions are 23 mm 23 mm 2.645 mm and all flow field heights and widths are 1 mm. The thicknesses of the diffusion layer, the catalyst layer and the proton exchange membrane are set to 0.3 mm, 0.005 mm and 0.035 mm, respectively. Finally, the assumed operating conditions for the fuel cells were fuel cell temperature of 323 K, reactant gases on the anode side including hydrogen and
Fig. 1. Numerical models of PEMFCs with serpentine flow field designs with varying numbers of cathode inlets: (a) single serpentine flow field design, (b) double serpentine flow field design, (c) triple serpentine flow field design, and (d) quadruple serpentine flow field design.
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water vapor with relative humidity of 100%, reactant gases on the cathode side including oxygen, nitrogen, and water vapor with relative humidity of 100%, and the inlet pressure of 1 atm on both anode and cathode sides. Given the above assumptions, the governing equations are as follows. Continuity equation:
@ðeeff qg Þ ! þ r ðeeff qg u g Þ ¼ SL @t
ð1Þ
where eeff denotes the effective porosity of the porous material, qg ! ug
represents the density of the gaseous mixture, is the velocity of the gaseous mixture, and SL is the source term due to phase change of water. Momentum equation: !
@ðqg u g Þ ! ! e þ r ðqg u g u g Þ @t ð1 sÞ ð1 sÞ2
e
¼ erpg þ
e
ð1 sÞ
!
r ðlg r ug Þ þ S!
ð2Þ
u
where e denotes the porosity of the porous material, s represents the saturation of liquid water (defined as the ratio of liquid water volume to pore volume in the porous material), pg is the pressure of the gas mixture, and lg denotes the dynamic viscosity of the gas mixture. Finally, S!u represents the source term based on the Darcy drag force imposed by the pore wall on the fluid. Species equation:
@ðeeff qg C k Þ ! þ r ðeeff qg u g C k Þ ¼ r ðqg Dk;eff rC k Þ þ Sc SL @t
ð3Þ
where Ck represents the mass fraction of the kth species and Dk,eff is the effective mass diffusivity of the kth species. In the catalyst layer, the source term Sc in the species equation represents the source term produced by the electrochemical reactions and has different values for different reactants, i.e., ðja =2FÞM H2 for hydrogen, ðjc =4FÞM O2 for oxygen, and ðjc =2FÞM H2 O for water vapor. The potential equation is used to calculate the electric potential and the electric current produced by the electrochemical reactions.
where ql denotes the density of liquid water, ll represents the dynamic viscosity of liquid water, pc is the capillary pressure, MH2 O denotes the molecular weight of water, krl represents the relative permeability of liquid water, and nd is the electro-osmotic drag coefficient. When the partial pressure of the water vapor exceeds its saturation pressure, the water vapor assumedly condenses and reduces the porosity of the material. The source term, SL, is evaluated using [8]
( SL ¼
M H2 O kc
eð1sÞxH2 O RT
ðpH2 O psat Þ if
pH2 O > psat
if
pH2 O < psat
ke esq1 ðpH2 O psat Þ
where kc denotes the condensation rate constant of water, ke represents the evaporation rate constant of water, xH2 O is the mole fraction of water vapor, and psat denotes the saturation pressure of water vapor. The boundary conditions in the anode and cathode flow channels are as follows: the inlet fuel flow rates are 65 ccmin1 and 175 ccmin1 on the anode and cathode sides, respectively. Further, the flows are fully developed at the outlets of the anode and cathode flow channels. The solid walls are assumed to be no slip walls with zero fluxes. The analysis assumes equality of the velocities, mass fractions, momentum fluxes, and mass fluxes at interfaces between the gas channels, diffusion layers, catalyst layers, and PEM. Table 1 lists the model parameters. These parameters and a given operating voltage were used to obtain the steady state solution that was set as the initial condition in the simulation. The nonuniformly distributed elements in the x, y, and z directions are 93 93 47, and the time step is 0.002 s in this study. The independence of the grid points in space and in time was also examined in the separate numerical runs. The accuracy of the present transient model was demonstrated by Li et al. [35]. 3. Results and discussion This study establishes three-dimensional transient numerical models of PEMFCs with four serpentine flow field designs with varying numbers of cathode inlets, including the single serpentine
!
The current density includes the ionic current density, i m , and the !
electronic current density, i s . The equation for current conservation is as follows [7] !
!
r im þr is ¼ 0
ð4Þ
Based on the Ohm law, the following two equations are obtained:
r ðrm rUm Þ ¼ Sj
ð5Þ
r ðrs rUs Þ ¼ Sj
ð6Þ
where rm denotes the ionic conductivity, rs represents the electronic conductivity, Um is the electric potential of the ionic phase, Us denotes the electric potential of the electronic phase, and Sj is the source term, which is zero in the PEM without electrochemical reaction and ja or jc on the anode or cathode sides, respectively. In the flow fields, gas diffusion layers and catalyst layers, the equation governing liquid water transport and formation is expressed using the generalized Richards equation [38].
@ðeq1 sÞ ql kp kr1 @pc qkk þr rs r 1 p r1 rpg @t l1 @s l1 nd MH2 O ! þr i m ¼ SL F
ð7Þ
ð8Þ
Table 1 Fuel cell parameters (Gurau et al. [39], Mazumder and Cole [7,8]). Parameter
Quantity
ech eGDL eCL em
1 0.5 0.4 0.28 1 1.76 1010 m2 1.76 1011 m2 1.8 1018 m2 1 1.5 1.5 Dagan model 9.227 108 Am3
kp,ch kp,GDL kp,CL kp,m
sch sGDL sCL sm Ajref 0;a ref
Aj0;c
aa/ac (anode) aa/ac (cathode) kc ke
rs rm,CL ql qdry ll Mm
1.05 106 Am3 0.5/0.5 1.5/1.5 100 s1 100 atm1 s1 5000 X1 m1 4.2 X1 m1 1000 kg m3 1980 kg m3 3.65 104 Pas 1.1 kg mol1
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flow field design, the double serpentine flow field design, the triple serpentine flow field design, and the quadruple serpentine flow field design. The effects of the serpentine flow field designs and the inlet fuel flow rates on the transient response time, the local current density distribution, and the oxygen mass fraction distribution are observed when operating voltage is instantaneously decreased from 0.7 V to 0.5 V and instantaneously increased from 0.5 V to 0.7 V. Fig. 2 shows how dynamic voltage load affects performance in PEMFCs with the four serpentine flow field designs and varying numbers of cathode inlets. Fig. 2(a) shows the Vcell-t curve of the PEMFCs where Vcell = 0.7 V for t < 0 s, Vcell = 0.5 V for 0 s < t < 0.3 s, Vcell = 0.7 V for 0.3 s < t < 0.6 s, and Vcell = 0.5 V for 0.6 s < t. At t = 0 s, 0.3 s and 0.6 s, voltage load decreases from 0.7 V to 0.5 V, increases from 0.5 V to 0.7 V, and decreases from 0.7 V to 0.5 V, respectively. Fig. 2(b) shows the I-t curves of the PEMFCs. At t < 0 s, Vcell = 0.7 V, which produces a steady state condition in all fuel cells, and all four serpentine flow field designs exhibit similar cell performance due to the weak electrochemical reactions. In the study of dynamic loading of PEM fuel cell, the transient response time which indicates the time from start-up to steady state is important. At t = 0 s, the operating voltage decreases abruptly from 0.7 V to 0.5 V. Therefore, the current density increases instantaneously and causes an overshoot and then decreases before achieving a steady state condition. After an overshoot, the transient response time needed to return to steady state is 0.15 s for the single serpentine flow field design, 0.176 s for the double serpentine
0.75
(a)
Voltage Loading Effects : 0.7V-0.5V-0.7V-0.5V
0.7
0.6
V
cell
(V)
0.65
0.55
0.5
0.45 0
0.2
(b)
16000
0.4
t (s)
0.6
0.8
flow field design, 0.2 s for the triple serpentine flow field design, and 0.212 s for the quadruple serpentine flow field design. At t = 0.3 s, an undershoot phenomenon results from a sudden increase in operating voltage from 0.5 V to 0.7 V and a sudden decrease in current density. The current density then increases and stabilizes before achieving a steady state condition. The transient response time required to reach steady state after an undershoot is 0.182 s for the single serpentine flow field design, 0.182 s for the double serpentine flow field design, 0.192 s for the triple serpentine flow field design, and 0.194 s for the quadruple serpentine flow field design. Fig. 2(b) shows that, because the PEMFCs have identical inlet fuel flow rates, inlet fuel flow velocity is inversely related to cathode inlet number. When the operating voltage decreases or increases abruptly, the lower inlet fuel flow velocity is unfavorable for the PEMFC to reach the steady state. To summarize, when overshoot or undershoot occurs, the quadruple serpentine flow field design exhibits the smallest variation in current density and the longest transient response time. Fig. 3 shows the distributions of local current density over time in the middle of the PEMFCs in the AA0 direction as shown in Fig. 1 for the single and the quadruple serpentine flow field designs. At t < 0 s, the operating voltage is 0.7 V, and the electrochemical reactions are mild. Both flow field designs have uniform local current density distributions. At t = 0.004 s, however, a decreases in operating voltage to 0.5 V causes an increase in the strength of the electrochemical reactions. The local current density distribution also increases markedly. The local current densities under the channels and ribs are generally unchanged. The local current density distribution is larger than that corresponding to the steady state at an operating voltage of 0.5 V when an overshoot occurs. At t = 0.1 s, the local current density distribution is smaller than that at t = 0.004 s. Additionally, the decrease in local current densities under the ribs is larger, and the differences in the local current density distribution under the channels and ribs increase. Therefore, as the overshoot decays to the steady state condition, the current density decreases and becomes non-uniform. The local current density distributions do not substantially differ between t = 0.28 s and 0.1 s, which indicates that the steady state is reached. Fig. 4 shows the local current density distributions in cell membranes in the single and the quadruple serpentine flow field designs. Fig. 4(a) shows that, at t < 0 s, electrochemical reactions are weak. Therefore, the differences in the local current density distributions from the inlet to the outlet of the flow field are small in both flow field designs. Fig. 4(b) shows that, at t = 0.004 s, the 0.5 V operating voltage substantially increases the strength of the
Single Serpentine Flow Field Double Serpentine Flow Field Triple Serpentine Flow Field Quadruple Serpentine Flow Field
25000
20000
t = 0.004s
Quadruple Serpentine Flow Field
t = 0.1s
t < 0s
t = 0.28s
-2
I (Am )
-2
I (Am )
12000
Single Serpentine Flow Field
15000
x
8000
10000
4000
Along the AA' Direction
Voltage Loading Effects : 0.7V-0.5V-0.7V-0.5V 0
0.2
0.4
t (s)
0.6
5000
0.8
Fig. 2. Effects of dynamic voltage loading on the cell performance of PEMFCs with serpentine flow field designs and varying numbers of cathode inlets: (a) dynamic voltage loading and (b) dynamic response of cell performance.
0
0.005
0.01
x (m)
0.015
0.02
Fig. 3. Local current density distributions over time in the middle of PEMFCs for the single and the quadruple serpentine flow field designs.
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(a) t < 0s
(b) t = 0.004s
(c) t = 0.1s
(d) t = 0.28s
Fig. 4. Local current density distributions in cell membranes of PEMFCs with the single and the quadruple serpentine flow field designs: (a) t < 0 s, (b) t = 0.004 s, (c) t = 0.1 s, and (d) t = 0.28 s.
0.3
0.25
O2
0.2
C
electrochemical reactions, which then increases the local current density distributions. Since the local current density distributions at t = 0.004 s exceed the steady state values at 0.5 V, overshoot phenomena occur. At t = 0.1 s, the current density distributions for both flow field designs decrease as overshoot phenomena decay toward the steady state conditions. In Fig. 4(c), the local current density distributions are smaller than those at t = 0.004 s, and the differences are more obvious from the inlet to the outlet of the flow field for both flow field designs. In Fig. 4(d), the local current density distributions at t = 0.28 s are similar to those at t = 0.1 s for both flow field designs, which suggests that the local current density distributions at t = 0.28 s represent the steady state conditions. The current density distributions therefore decrease slightly when operating time increases from t = 0.1 s to t = 0.28 s. Fig. 5 shows the oxygen mass fraction distributions at different times at the middle of the interface of the cathode gas diffusion and catalyst layers of PEMFCs along the AA0 direction as shown in Fig. 1 for the single and the quadruple serpentine flow field designs. At t < 0 s, the cell operating voltage remains at 0.7 V, and the electrochemical reactions are mild. Therefore, oxygen consumption is low, and oxygen mass fraction distributions remain high and uniform under the channels and ribs in both flow field designs. At t = 0.004 s, a decrease in operating voltage to 0.5 V increases the strength of electrochemical reactions. At this time, the oxygen mass fraction distributions are high, and the local current density distributions substantially increase and exceed the steady state values at 0.5 V in both flow field designs, which causes overshoot phenomena. The high and uniform oxygen mass fraction distributions under the channels and ribs also increase the uniformity of the local current density distributions. Therefore, overshoot phenomena result from the high and uniform oxygen mass fraction distributions when the operating voltage suddenly decreases from high to low. At t = 0.1 s, oxygen consumed by the strong electrochemical reactions results in oxygen mass fraction distributions that are lower and less uniform compared to those at t = 0.004 s. The variation under the channels and ribs is also higher in both flow field designs, which results in lower and less uniform local
Single Serpentine Flow Field
t = 0.004s
Quadruple Serpentine Flow Field
t = 0.1s
t < 0s
t = 0.28s
0.15
0.1
0.05
Along the AA' Direction 0 0
0.005
0.01
x (m)
0.015
0.02
Fig. 5. Oxygen mass fraction distributions at different times at the middle of the interface of the cathode gas diffusion and catalyst layers of PEMFCs with the single and the quadruple serpentine flow field designs.
current density distributions. At t = 0.28 s, the oxygen mass fraction distributions almost overlap with those at t = 0.1 s in both flow field designs, which implies that the fuel cells are in steady state conditions. Generally, the oxygen mass fraction distribution critically influences the overshoot phenomenon and the local current density distribution of PEMFCs with both the single and the quadruple serpentine flow field designs. Fig. 6 shows the oxygen mass fraction distributions at the interface between the cathode gas diffusion and catalyst layers of PEMFCs with the single and the quadruple serpentine flow field designs. In Fig. 6(a), when t < 0 s, the 0.7 V operating voltage causes only mild electrochemical reactions resulting in small variations in the oxygen mass fraction distributions from the inlet to the outlet of the flow field in both flow field designs. Fig. 6(b) shows that, at t = 0.004 s, the drop in operating voltage to 0.5 V causes violent electrochemical reactions resulting in decreased oxygen mass
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(a) t < 0s
(b) t = 0.004s
(c) t = 0.1s
(d) t = 0.28s
Fig. 6. Oxygen mass fraction distributions at the interface between the cathode gas diffusion and catalyst layers of PEMFCs with the single and the quadruple serpentine flow field designs: (a) t < 0 s, (b) t = 0.004 s, (c) t = 0.1 s, and (d) t = 0.28 s.
0.75
(a)
Voltage Loading Effects : 0.7V-0.5V-0.7V-0.5V
0.7
0.6
V
cell
(V)
0.65
0.55
0.5
0.45 0
24000
0.2
(b)
0.4
-1
Q = 85 ccmin , Q = 215 ccmin
0.8
-1
C
-1
Q = 65 ccmin , Q = 175 ccmin A
-1
C
-1
Q = 45 ccmin , Q = 135 ccmin A
16000
0.6
t (s)
A
-1
C
Single Serpentine Flow Field Quadruple Serpentine Flow Field
-2
I (Am )
fraction distributions from the inlet to the outlet of the flow field in both flow field designs. At t = 0.1 s and t = 0.28 s (Fig. 6(c) and (d), respectively), the oxygen mass fraction distributions are smaller than those at t = 0.004 s, and the differences in oxygen mass fraction distributions between the inlet to outlet of the flow field are larger because of the increased oxygen consumed along the flow field. Apparently, the cells reach the steady state conditions because of the very similar oxygen mass fraction distributions at t = 0.1 s and t = 0.28 s. Fig. 7 illustrates the effects of dynamic voltage loading on PEMFC performance with three different inlet fuel flow rates on the anode and cathode sides. Fig. 7(a) shows the Vcell-t curve of the PEMFCs, where Vcell = 0.7 V for t < 0 s, Vcell = 0.5 V for 0 s < t < 0.3 s, Vcell = 0.7 V for 0.3 s < t < 0.6 s, and Vcell = 0.5 V for 0.6 s < t. Fig. 7(b) shows the I-t curves of the PEMFCs. At t < 0 s, the operating voltage is Vcell = 0.7 V. The inlet fuel flow rate has a negligible effect on cell performance in the single and the quadruple serpentine flow field designs when the electrochemical reactions are weak. At t = 0 s, an overshoot phenomenon results from an abrupt increase in current density caused by a sudden drop in operating voltage from 0.7 V to 0.5 V. The current density then decreases gradually before achieving a steady state condition. In the single serpentine flow field design, the transient response times needed to return to the steady state after an overshoot are 0.128 s, 0.15 s, and 0.182 s when the inlet flow rates on the anode and cathode sides are 85 ccmin1 and 215 ccmin1, 65 ccmin1 and 175 ccmin1 and 45 ccmin1 and 135 ccmin1, respectively. In the quadruple serpentine flow field design, the transient response times needed to return to the steady state after an overshoot are 0.14 s, 0.212 s, and 0.218 s when the inlet flow rates on the anode and cathode sides are 85 ccmin1 and 215 ccmin1, 65 ccmin1 and 175 ccmin1, and 45 ccmin1 and 135 ccmin1, respectively. The higher the inlet fuel flow rate, the better the performance, and the faster the cell can reach a steady state after a sudden change in operating voltage. At t = 0.3 s, a sudden increase in operating voltage from 0.5 V to 0.7 V and a decrease in current density cause an undershoot phenomenon. The current density
8000
Voltage Loading Effects : 0.7V-0.5V-0.7V-0.5V 0
0.2
0.4
t (s)
0.6
0.8
Fig. 7. Effects of dynamic voltage loading on the cell performance of the PEMFC with three different inlet fuel flow rates: (a) dynamic voltage loading and (b) dynamic response of cell performance.
W.-M. Yan et al. / International Journal of Heat and Mass Transfer 107 (2017) 646–656
653
(a) t < 0s
(b) t = 0.004s
QA = 85 ccmin-1, QC = 215 ccmin-1
QA = 65 ccmin-1, QC = 175 ccmin-1
QA = 45 ccmin-1, QC = 135 ccmin-1
QA = 65 ccmin-1, QC = 175 ccmin-1
QA = 45 ccmin-1, QC = 135 ccmin-1
(c) t = 0.1s
(d) t = 0.28s
QA = 85 ccmin-1, QC = 215 ccmin-1
Fig. 8. Local current density distributions in the membrane of the PEMFC with the single serpentine flow field design at three different inlet fuel flow rates: (a) t < 0 s, (b) t = 0.004 s, (c) t = 0.1 s, and (d) t = 0.28 s.
increases and stabilizes before achieving a steady state condition. In the single serpentine flow field design, the transient response times needed for the undershoot phenomenon to reach a steady state are 0.136 s, 0.182 s, and 0.21 s when the inlet flow rates on the anode and cathode sides are 85 ccmin1 and 215 ccmin1,
65 ccmin1 and 175 ccmin1, and 45 ccmin1 and 135 ccmin1, respectively. In the quadruple serpentine flow field design, the transient response times needed for the undershoot phenomenon to reach a steady state are 0.164 s, 0.194 s, and 0.238 s when the inlet flow rates on the anode and cathode sides are 85 ccmin1
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(a) t < 0s
(b) t = 0.004s
QA = 85 ccmin-1, QC = 215 ccmin-1
QA = 65 ccmin-1, QC = 175 ccmin-1
QA = 45 ccmin-1, QC = 135 ccmin-1
QA = 65 ccmin-1, QC = 175 ccmin-1
QA = 45 ccmin-1, QC = 135 ccmin-1
(c) t = 0.1s
(d) t = 0.28s
QA = 85 ccmin-1, QC = 215 ccmin-1
Fig. 9. Oxygen mass fraction distributions at the interface between the cathode gas diffusion and catalyst layers of the PEMFC with the single serpentine flow field design at three different inlet fuel flow rates: (a) t < 0 s, (b) t = 0.004 s, (c) t = 0.1 s, and (d) t = 0.28 s.
and 215 ccmin1, 65 ccmin1 and 175 ccmin1, and 45 ccmin1 and 135 ccmin1, respectively. As the inlet fuel flow rate increases, the cell performance improves because the return to the steady state condition is faster after a sudden increase in operating
voltage. To summarize, because the cathode inlet number in the single serpentine flow field design is less than the quadruple flow field design, it has a faster inlet fuel flow velocity. Therefore, overshoot and undershoot phenomena are more severe in the single
W.-M. Yan et al. / International Journal of Heat and Mass Transfer 107 (2017) 646–656
serpentine flow field design than in the quadruple serpentine flow field design. Moreover, transient response time is shorter in the PEMFC with the single serpentine flow field design than with the quadruple serpentine flow field design. Fig. 8 shows the local current density distributions in the membrane of the PEMFC with the single serpentine flow field design at three different inlet fuel flow rates. Fig. 8(a) shows that the 0.7 V operating voltage at t < 0 s produces weak electrochemical reactions. Regardless of the inlet fuel flow rates applied, the differences in the local current density distributions are negligible. Moreover, the local current density distributions decrease from the inlet to the outlet of the flow field. Fig. 8(b) shows that, at t = 0.004 s, the drop in operating voltage to 0.5 V causes strong electrochemical reactions, which then cause rapid increases in the local current density distributions. Fig. 8(c), at t = 0.1 s shows that, when the inlet fuel flow rate is low (QA = 45 ccmin1, QC = 135 ccmin1), the decrease in the local current density distribution from the inlet to the outlet of the flow field increases as the amount of oxygen consumed downstream becomes insufficient. The values of the local current density distributions at t = 0.1 s are smaller than those at t = 0.004 s. In Fig. 8(d), the local current density distribution at t = 0.28 s is similar to that at t = 0.1 s for each inlet fuel flow rate, which indicates that the local current density distributions should reach a steady state condition. Fig. 9 shows the oxygen mass fraction distributions at the interface between the cathode gas diffusion and catalyst layers of the PEMFC with the single serpentine flow field design at three different inlet fuel flow rates. Fig. 9(a) shows that, when the operating voltage is 0.7 V at t < 0 s, the electrochemical reactions are mild, and oxygen mass fraction distributions from the inlet to the outlet of the flow field show only minimal variation for all three inlet fuel flow rates. However, as the inlet fuel flow rate increases, the oxygen mass fraction increases in the downstream flow field. In Fig. 9 (b), at t = 0.004 s, the operating voltage decreases to 0.5 V, violent electrochemical reactions decreases the oxygen mass fraction distributions from the inlet to the outlet of the flow field. Figs. 9 (c) and (d) show that, at t = 0.1 s and t = 0.28 s, respectively, the oxygen mass fraction distributions are smaller than those at t = 0.004 s. The decreases of the oxygen mass fraction distributions from the inlet to the outlet of the flow field are also apparent, especially when inlet fuel flow rate is low. 4. Conclusions This study constructed three-dimensional transient numerical models of PEMFCs with serpentine flow field designs and varying numbers of cathode inlets. The PEMFC designs included single, double, triple, and quadruple serpentine flow field designs. To determine the effects of serpentine flow field designs and inlet fuel flow rates on the transient characteristics of the PEMFCs, electrochemical reactions and transport phenomena of the various reactants and products in the PEMFCs were analyzed in terms of transient response time and overshoot and undershoot phenomena. The conclusions in this study are summarized as follows: 1. At a cell operating voltage of 0.7 V, weak electrochemical reactions result in a uniformly low local current density in all four serpentine flow field designs. 2. When operating voltage is suddenly reduced from 0.7 V to 0.5 V, the overshoot phenomenon in the current density distribution results from the higher and more uniform oxygen mass fraction distribution in the cathode gas diffusion and catalyst layers, which provide sufficient oxygen for strong electrochemical reactions. The quadruple serpentine flow field design has the lowest oxygen mass fraction distribution among the four serpentine flow field designs. Thus, the quadruple serpentine
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flow field design has the smallest variation in the current density distribution and the longest transient response time when overshoot or undershoot phenomena occur. 3. After overshoot or undershoot phenomena occur, the time required for the local current density distributions in the PEMFCs to reach the steady state conditions in the four serpentine flow field designs increases, in order from fastest to slowest, as follows: the single serpentine flow field design, the double serpentine flow field design, the triple serpentine flow field design, and the quadruple serpentine flow field design. 4. When the cell voltage changes suddenly, the time needed for the cell to reach the steady state condition correlates positively with the inlet fuel flow rates.
Acknowledgement The financial support of this study by the Ministry of Science and Technology of Taiwan, through the grant number: MOST 103-2221-E-027-107-MY2, is appreciated. References [1] H. Yang, T.S. Zhao, Q. Ye, In situ visualization study of CO2 gas bubble behavior in DMFC anode flow fields, J. Power Sources 139 (2005) 79–90. [2] J. Scholta, F. Haussler, W. Zhang, L. Kuppers, L. Jorissen, W. Lehnert, Development of a stack having an optimized flow field structure with low cross transport effects, J. Power Sources 155 (2006) 60–65. [3] S.S. Hsieh, S.H. Yang, C.L. Feng, Characterization of the operational parameters of a H2/air micro PEMFC with different flow fields by impedance spectroscopy, J. Power Sources 162 (2006) 262–270. [4] C. Xu, T.S. Zhao, A new flow field design for polymer electrolyte-based fuel cells, Electrochem. Commun. 9 (2007) 497–503. [5] Q. Shen, M. Hou, X. Yan, D. Liang, Z. Zang, L. Hao, Z. Shao, Z. Hou, P. Ming, B. Yi, The voltage characteristics of proton exchange membrane fuel cell (PEMFC) under steady and transient states, J. Power Sources 179 (2008) 292–296. [6] S. Shimpalee, M. Ohashi, J.W. Van Zee, C. Ziegler, C. Stoeckmann, C. Sadeler, C. Hebling, Experimental and numerical studies of portable PEMFC stack, Electrochim. Acta 54 (2009) 2899–2911. [7] S. Mazumder, J.V. Cole, Rigorous 3-D mathematical modeling of PEM fuel cells I. Model predictions without liquid water transport, J. Electrochem. Soc. 150 (2003) A1503–A1509. [8] S. Mazumder, J.V. Cole, Rigorous 3-D mathematical modeling of PEM fuel cells II. Model predictions with liquid water transport, J. Electrochem. Soc. 150 (2003) A1510–A1517. [9] L. Sun, P.H. Oosthuizen, K.B. McAuley, A numerical study of channel-to-channel flow cross-over through the gas diffusion layer in a PEM-fuel-cell flow system using a serpentine channel with a trapezoidal cross-sectional shape, Int. J. Therm. Sci. 45 (2006) 1021–1026. [10] T. Kanezaki, X. Li, J.J. Baschuk, Cross-leakage flow between adjacent flow channels in PEM fuel cells, J. Power Sources 162 (2006) 415–425. [11] X.D. Wang, Y.Y. Duan, W.M. Yan, Numerical study of cell performance and local transport phenomena in PEM fuel cells with various flow channel area ratios, J. Power Sources 172 (2007) 265–277. [12] Z. Liu, H. Zhang, C. Wang, Z. Mao, Numerical simulation for rib and channel position effect on PEMFC performances, Int. J. Hydrogen Energy 35 (2010) 2802–2806. [13] K.S. Choi, H.M. Kim, S.M. Moon, Numerical studies on the geometrical characterization of serpentine flow-field for efficient PEMFC, Int. J. Hydrogen Energy 36 (2011) 1613–1627. [14] P. Berg, K. Promislow, J.S. Pierre, J. Stumper, B. Wetton, Water management in PEM fuel cells, J. Electrochem. Soc. 151 (2004) A341–A353. [15] M. Najjari, F. Khemili, S.B. Nasrallah, The effects of the cathode flooding on the transient responses of a PEM fuel cell, Renewable Energy 33 (2008) 1824–1831. [16] A. Su, Y.M. Ferng, F.C. Shih, CFD investigating the effects of different operating conditions on the performance and the characteristics of a high-temperature PEMFC, Energy 35 (2010) 16–27. [17] H.W. Wu, H.W. Ku, The optimal parameters estimation for rectangular cylinders installed transversely in the flow channel of PEMFC from a threedimensional PEMFC model and the Taguchi method, Appl. Energy 88 (2011) 4879–4890. [18] S.J. Cheng, J.M. Miao, S.J. Wu, Investigating the effects of operational factors on PEMFC performance based on CFD simulations using a three-level full-factorial design, Renewable Energy 39 (2012) 250–260. [19] W. Friede, S. Rael, B. Davat, Mathematical model and characterization of the transient behavior of a PEM fuel cell, IEEE Trans. Power Electronics 19 (2004) 1234–1241. [20] D. Song, Q. Wang, Z.S. Liu, C. Huang, Transient analysis for the cathode gas diffusion layer of PEM fuel cells, J. Power Sources 159 (2006) 928–942.
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[21] G. Hu, J. Fan, Transient computation fluid dynamics modeling of a single proton exchange membrane fuel cell with serpentine channel, J. Power Sources 165 (2007) 171–184. [22] H. Weydahl, M.H. Steffen, G. Hagen, B. Borresen, Transient response of a proton exchange membrane fuel cell, J. Power Sources 171 (2007) 321–330. [23] H. Wu, P. Berg, X. Li, Non-isothermal transient modeling of water transport in PEM fuel cells, J. Power Sources 165 (2007) 232–243. [24] S. Shimpalee, D. Spuckler, J.W. Van Zee, Prediction of transient response for a 25-cm2 PEM fuel cell, J. Power Sources 167 (2007) 130–138. [25] X. Yan, M. Hou, L. Sun, H. Cheng, Y. Hong, D. Liang, Q. Shen, P. Ming, B. Yi, The study on transient characteristic of proton exchange membrane fuel cell stack during dynamic loading, J. Power Sources 163 (2007) 966–970. [26] Z. Siroma, N. Fujiwara, T. Ioroi, S.I. Yamazaki, H. Senoh, K. Yasuda, K. Tanimoto, Transient phenomena in a PEMFC during the start-up of gas feeding observed with a 97-fold segmented cell, J. Power Sources 172 (2007) 155–162. [27] D. Sophie, L. Olivier, M. Gael, G. Thierry, PEM fuel cell voltage transient response to a thermal perturbation, Electrochim. Acta 53 (2008) 7313–7320. [28] K.P. Adzakpa, J. Ramousse, Y. Dube, H. Akremi, K. Agbossou, M. Dosite, A. Poulin, M. Fournier, Transient air cooling thermal modeling of a PEM fuel cell, J. Power Sources 179 (2008) 164–176. [29] J. Cho, H.S. Kim, K. Min, Transient response of a unit proton-exchange membrane fuel cell under various operating conditions, J. Power Sources 185 (2008) 118–128. [30] B. Mishra, J. Wu, Study of the effects of various parameters on the transient current density at polymer electrolyte membrane fuel cell start-up, Renewable Energy 34 (2009) 2296–2307.
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Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Transient mass transport and cell performance of a PEM fuel cell Wei-Mon Yan a,⇑, Hung-Yi Li b, Wen-Chung Weng b a b
Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei 10608, Taiwan Department of Mechatronic Engineering, Huafan University, Shihtin, New Taipei 22301, Taiwan
a r t i c l e
i n f o
Article history: Received 25 October 2016 Received in revised form 18 November 2016 Accepted 18 November 2016
Keywords: Transient mass transport Serpentine flow field design Transient response time Local current density distribution
a b s t r a c t This study aims to establish an unsteady, three-dimensional mathematical model of proton exchange membrane fuel cells (PEMFCs) with four serpentine flow field designs. The effects of the serpentine flow field designs on the transient characteristics of the PEMFCs are evaluated in terms of transient response of local current density and mass concentration under sudden change in loading. When the operating voltage is 0.7 V, the weak electrochemical reactions result in a local current density distribution that is only minimally affected by the serpentine flow field designs. However, when operating voltage instantaneously drops from 0.7 V to 0.5 V, electrochemical reactions increase. To ensure a sufficient fuel cell oxygen supply, the oxygen mass fractions are high and uniform in the cathode gas diffusion and cathode catalyst layers, which cause overshoot phenomena in the local current density distribution. Because the inlet fuel flow rate is identical in all PEMFCs, the inlet fuel flow velocity decreases as the cathode inlet number increases. When the operating voltage abruptly drops, the low inlet fuel velocity prevents the PEMFC from maintaining a steady state. Therefore, the transient response time needed to reach a steady state in the quadruple serpentine flow field design is longest when overshoot or undershoot phenomena occur. Additionally, cells with large inlet fuel flow rates perform best and reach a steady state condition fastest when cell voltage changes occur suddenly. Ó 2016 Published by Elsevier Ltd.
1. Introduction Proton exchange membrane fuel cells (PEMFCs) are considered promising alternatives for generating clean power for portable, mobile and stationary applications because of their low to zero emissions, low-temperature operation, high power density and fast start-up. Therefore, numerous experimental and numerical studies have been constructed to understand the physical phenomena and steady state or transient characteristics of PEMFCs. The advantages of mathematical simulations include the reduced time and cost of research and development, the easy comparison of experimental data, and the capability to calculate physical quantities that are difficult or impossible to measure. Most studies of experimental methods [1–6] and numerical simulations of fuel cells emphasize the steady state characteristics of the flow field design [7–13] and parameter design [14–18]. Most of the literatures on fuel cells describe numerical simulations of steady state characteristics. In contrast, despite the recognized importance of transient response time and transient characteristics of fuel cells, transient models and corresponding
⇑ Corresponding author. E-mail address: [email protected] (W.-M. Yan). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.11.075 0017-9310/Ó 2016 Published by Elsevier Ltd.
numerical simulations of fuel cells are rare [19–35]. In stationary or automotive applications of PEMFCs, transient load changes during operation are common. One example is a sudden load variation when device starts or when a vehicle is accelerated or decelerated. The current density overshoots its final steady state value when the operating voltage changes abruptly from high to low whereas the current density undershoots its final steady state value when the operating voltage changes abruptly from low to high. The transient response times needed for overshoot and undershoot phenomena to reach steady states are important for evaluating the dynamic performance of PEMFCs. Thus, numerical models of transient characteristics are needed to analyze PEMFCs under operating conditions that vary over time. A one-dimensional mathematical model developed by Friede et al. [19] to characterize the transient behavior of PEMFCs showed that membrane water transport has a major effect on fuel cell transients. Moreover, Hu and Fan [21] developed a transient three-dimensional non-isothermal PEMFC model of overshoot and undershoot phenomena in PEMFCs, which showed the very short transient response time of PEMFC, the effects of inlet fuel flow rates, the relative humidity of the fuel, and the voltage loading on transient characteristics. Wu et al. [23] developed a transient two-dimensional single-phase non-isothermal PEMFC model that included a heat transfer
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647
Nomenclature Ajref 0 C D F i I j kc ke kp M p nd R s Sc Sj SL S!u T t ! u Vcell x, y, z
reference exchange current density (Am3) mass fraction mass diffusivity (m2s1) Faraday constant (96,487 Cmol1) current density (Am2) average current density (Am2) transfer current density (Am3) coefficient of water vapor condensation rate (s1) coefficient of water vapor evaporation rate (atm1 s1) permeability (m2) molecular weight (kg mol1) pressure (atm) electro-osmotic drag coefficient universal gas constant (8.314 Jmol1 K1) saturation of liquid water source term in the species equation source term in the electric potential equation source term due to phase change of water source term in the momentum equation temperature (K) time (s) velocity (ms1) operating voltage (V) coordinates (m)
ac e q rm rs l s
Um Us
electrical transfer coefficient in backward reaction porosity density (kg m3) ionic conductivity (X-1 m1) electronic conductivity (X-1 m1) dynamic viscosity (Pas) tortuosity of the pores in the porous material electric potential of the ionic phase (V) electric potential of the electronic phase (V)
Subscripts and superscripts a anode c cathode ch channel CL catalyst layer eff effective value k kth species of the mixture GDL gas diffusion layer g gas H2 hydrogen H2O water l liquid m membrane O2 oxygen sat saturation
Greek symbols aa electrical transfer coefficient in forward reaction
equation. The transient processes considered in the model included electrochemical double-layer charging/discharging, species transport, membrane hydration/dehydration, and heat transport processes. Their numerical results confirmed that the heat transfer process significantly affects fuel cell dynamic responses. A time dependence of three-dimensional simulation including water phase change and heat transfer of a PEMFC model was investigated numerically by Shimpalee et al. [24]. The current distribution and temperature distribution as well as their dynamic changes in fuel cell stack were evaluated in situ by Yan et al. [25]. The experimental results show that the local current and temperature rise when load rapidly. The extent of temperature fluctuation during dynamic loading is significantly influenced by air stoichiometries, loading rates, and air relative humidities. The overshoot behavior has been observed during a change in the electrical load during operation with fixed flow rates of hydrogen and air. Siroma et al. [26] measured local phenomena in a PEMFC during a transitional state induced by changing of the feeding gas. The potential distribution in the electrolyte was observed using three quasireference electrodes located locally. Sophie et al. [27] examined a transient model predicting PEMFC voltage response to a step change in the cooling water temperature. They found that an undershoot voltage response is observed when the characteristic time for water transport is longer than the transient thermal regime. A 3D dynamic thermal model of a single fuel cell is presented by Adzakpa et al. [28] to study the temperature distribution in a fuel cell cooled from the bottom to the top with air. They indicated that the temperatures are higher at the top part of the cell than at the bottom part. Cho et al. [29] studied the transient response of proton-exchange membrane fuel cells. They found that the undershoot behavior consists of two stages with different time delays. An unsteady two phase nonisothermal model is used by Mishra and Wu [30] to study the
start-up characteristics of a PEM fuel cell. They disclosed that as the gas diffusion layer thickness was increased, the influence of liquid water was delayed. Haddad et al. [31] numerically examined 1-D transient mass and charge transfer in a PEM fuel cell. The concentration profiles and concentration variations with time and membrane thickness were presented. A three-dimensional transient two-phase isothermal model was developed by KhajehHosseini-Dalasm et al. [32] for the cathode side of a proton exchange membrane fuel cell. Prediction results showed that it takes less time for a high average current density to attain the steady state condition which is due to the capillary pressure gradient inside the porous media. Hinaje et al. [33] proposed a dynamic model of PEM fuel cell using EIS method. They indicated that a defective cathodic GDL has more consequences on cell performance than if it occurs at anode side. Wang et al. [34] established a three-dimensional, two-phase transient model to analyze transient characteristics of PEMFCs with parallel and interdigitated flow field designs. The effects of various voltage loading changes, width ratios of the channel to the rib, and cathode inlet flow rates on the transient response were examined in both flow field designs. Li et al. [35] established a three-dimensional transient numerical PEMFC model with different cathode flow field designs to determine the effects of flow field designs and voltage loading on transient characteristics of PEMFCs. Comparisons of the effects of overshoot and undershoot phenomena in different cathode flow field designs showed that the transient response time needed to reach the steady state was longest in a parallel flow field with a baffled design. Recently, Kim et al. [36] investigated the effects of operating and controlling parameters on the transient response of a PEMFC for achieving more stable cell performance under load change conditions. The transient response of a PEMFC was measured and analyzed by varying air stoichiometry, air humidity, and air excess ratio (AER). The
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dynamic cell performance of a kW-grade proton exchange membrane fuel cell stack with anode dead-ended mode fuel supply was experimentally examined by Jang [37]. Experimental results indicated an optimal purge interval and duration for water management and cell performance of the fuel cell stack. Most of the proposed models of transient characteristics of fuel cells in the literatures have been one-dimensional or twodimensional models with parallel or serpentine flow field designs. Some recently developed three-dimensional models assume a single phase. Moreover, most studies have focused on step voltage changes rather than on the effects of flow field designs and parameters on transient response characteristics. Therefore, this study constructs three-dimensional computational models of PEMFCs with varying numbers of cathode inlets, i.e., a single serpentine flow field design, a double serpentine flow field design, a triple serpentine flow field design and a quadruple serpentine flow field design. The effects of the serpentine flow field designs and the inlet fuel flow rates on transient characteristics of PEMFCs were analyzed to elucidate overshoot and undershoot phenomena, transient response times, local current density distributions and oxygen mass fraction distributions. 2. Analysis The three-dimensional transient numerical models of PEMFCs with four serpentine flow field designs with varying numbers of
cathode inlets were constructed by finite volume method. Fig. 1 shows that the flow field designs in the PEMFCs included a single serpentine flow field design, a double serpentine flow field design, a triple serpentine flow field design, and a quadruple serpentine flow field design. The effects of the serpentine flow field designs and the different inlet fuel flow rates on the transient characteristics of the PEMFCs are examined by analyzing the electrochemical reactions and transport phenomena of various reactants and products in the PEMFCs. The major fuel cell components are the anode gas flow field, the anode gas diffusion layer, the anode catalyst layer, the proton exchange membrane, the cathode catalyst layer, the cathode gas diffusion layer, and the cathode gas flow field. Equations for mass, momentum, species and electric potential equations are used in the analysis. The simulations are based on the following assumptions: the cell system is isothermal; the reactants and products are ideal gases; the flow is laminar and incompressible; the electrochemical reactions only occur in the catalyst layer; the porous layers, such as the gas diffusion layer, the catalyst layer and the proton exchange membrane, are isotropic. The fuel cell dimensions are 23 mm 23 mm 2.645 mm and all flow field heights and widths are 1 mm. The thicknesses of the diffusion layer, the catalyst layer and the proton exchange membrane are set to 0.3 mm, 0.005 mm and 0.035 mm, respectively. Finally, the assumed operating conditions for the fuel cells were fuel cell temperature of 323 K, reactant gases on the anode side including hydrogen and
Fig. 1. Numerical models of PEMFCs with serpentine flow field designs with varying numbers of cathode inlets: (a) single serpentine flow field design, (b) double serpentine flow field design, (c) triple serpentine flow field design, and (d) quadruple serpentine flow field design.
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water vapor with relative humidity of 100%, reactant gases on the cathode side including oxygen, nitrogen, and water vapor with relative humidity of 100%, and the inlet pressure of 1 atm on both anode and cathode sides. Given the above assumptions, the governing equations are as follows. Continuity equation:
@ðeeff qg Þ ! þ r ðeeff qg u g Þ ¼ SL @t
ð1Þ
where eeff denotes the effective porosity of the porous material, qg ! ug
represents the density of the gaseous mixture, is the velocity of the gaseous mixture, and SL is the source term due to phase change of water. Momentum equation: !
@ðqg u g Þ ! ! e þ r ðqg u g u g Þ @t ð1 sÞ ð1 sÞ2
e
¼ erpg þ
e
ð1 sÞ
!
r ðlg r ug Þ þ S!
ð2Þ
u
where e denotes the porosity of the porous material, s represents the saturation of liquid water (defined as the ratio of liquid water volume to pore volume in the porous material), pg is the pressure of the gas mixture, and lg denotes the dynamic viscosity of the gas mixture. Finally, S!u represents the source term based on the Darcy drag force imposed by the pore wall on the fluid. Species equation:
@ðeeff qg C k Þ ! þ r ðeeff qg u g C k Þ ¼ r ðqg Dk;eff rC k Þ þ Sc SL @t
ð3Þ
where Ck represents the mass fraction of the kth species and Dk,eff is the effective mass diffusivity of the kth species. In the catalyst layer, the source term Sc in the species equation represents the source term produced by the electrochemical reactions and has different values for different reactants, i.e., ðja =2FÞM H2 for hydrogen, ðjc =4FÞM O2 for oxygen, and ðjc =2FÞM H2 O for water vapor. The potential equation is used to calculate the electric potential and the electric current produced by the electrochemical reactions.
where ql denotes the density of liquid water, ll represents the dynamic viscosity of liquid water, pc is the capillary pressure, MH2 O denotes the molecular weight of water, krl represents the relative permeability of liquid water, and nd is the electro-osmotic drag coefficient. When the partial pressure of the water vapor exceeds its saturation pressure, the water vapor assumedly condenses and reduces the porosity of the material. The source term, SL, is evaluated using [8]
( SL ¼
M H2 O kc
eð1sÞxH2 O RT
ðpH2 O psat Þ if
pH2 O > psat
if
pH2 O < psat
ke esq1 ðpH2 O psat Þ
where kc denotes the condensation rate constant of water, ke represents the evaporation rate constant of water, xH2 O is the mole fraction of water vapor, and psat denotes the saturation pressure of water vapor. The boundary conditions in the anode and cathode flow channels are as follows: the inlet fuel flow rates are 65 ccmin1 and 175 ccmin1 on the anode and cathode sides, respectively. Further, the flows are fully developed at the outlets of the anode and cathode flow channels. The solid walls are assumed to be no slip walls with zero fluxes. The analysis assumes equality of the velocities, mass fractions, momentum fluxes, and mass fluxes at interfaces between the gas channels, diffusion layers, catalyst layers, and PEM. Table 1 lists the model parameters. These parameters and a given operating voltage were used to obtain the steady state solution that was set as the initial condition in the simulation. The nonuniformly distributed elements in the x, y, and z directions are 93 93 47, and the time step is 0.002 s in this study. The independence of the grid points in space and in time was also examined in the separate numerical runs. The accuracy of the present transient model was demonstrated by Li et al. [35]. 3. Results and discussion This study establishes three-dimensional transient numerical models of PEMFCs with four serpentine flow field designs with varying numbers of cathode inlets, including the single serpentine
!
The current density includes the ionic current density, i m , and the !
electronic current density, i s . The equation for current conservation is as follows [7] !
!
r im þr is ¼ 0
ð4Þ
Based on the Ohm law, the following two equations are obtained:
r ðrm rUm Þ ¼ Sj
ð5Þ
r ðrs rUs Þ ¼ Sj
ð6Þ
where rm denotes the ionic conductivity, rs represents the electronic conductivity, Um is the electric potential of the ionic phase, Us denotes the electric potential of the electronic phase, and Sj is the source term, which is zero in the PEM without electrochemical reaction and ja or jc on the anode or cathode sides, respectively. In the flow fields, gas diffusion layers and catalyst layers, the equation governing liquid water transport and formation is expressed using the generalized Richards equation [38].
@ðeq1 sÞ ql kp kr1 @pc qkk þr rs r 1 p r1 rpg @t l1 @s l1 nd MH2 O ! þr i m ¼ SL F
ð7Þ
ð8Þ
Table 1 Fuel cell parameters (Gurau et al. [39], Mazumder and Cole [7,8]). Parameter
Quantity
ech eGDL eCL em
1 0.5 0.4 0.28 1 1.76 1010 m2 1.76 1011 m2 1.8 1018 m2 1 1.5 1.5 Dagan model 9.227 108 Am3
kp,ch kp,GDL kp,CL kp,m
sch sGDL sCL sm Ajref 0;a ref
Aj0;c
aa/ac (anode) aa/ac (cathode) kc ke
rs rm,CL ql qdry ll Mm
1.05 106 Am3 0.5/0.5 1.5/1.5 100 s1 100 atm1 s1 5000 X1 m1 4.2 X1 m1 1000 kg m3 1980 kg m3 3.65 104 Pas 1.1 kg mol1
650
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flow field design, the double serpentine flow field design, the triple serpentine flow field design, and the quadruple serpentine flow field design. The effects of the serpentine flow field designs and the inlet fuel flow rates on the transient response time, the local current density distribution, and the oxygen mass fraction distribution are observed when operating voltage is instantaneously decreased from 0.7 V to 0.5 V and instantaneously increased from 0.5 V to 0.7 V. Fig. 2 shows how dynamic voltage load affects performance in PEMFCs with the four serpentine flow field designs and varying numbers of cathode inlets. Fig. 2(a) shows the Vcell-t curve of the PEMFCs where Vcell = 0.7 V for t < 0 s, Vcell = 0.5 V for 0 s < t < 0.3 s, Vcell = 0.7 V for 0.3 s < t < 0.6 s, and Vcell = 0.5 V for 0.6 s < t. At t = 0 s, 0.3 s and 0.6 s, voltage load decreases from 0.7 V to 0.5 V, increases from 0.5 V to 0.7 V, and decreases from 0.7 V to 0.5 V, respectively. Fig. 2(b) shows the I-t curves of the PEMFCs. At t < 0 s, Vcell = 0.7 V, which produces a steady state condition in all fuel cells, and all four serpentine flow field designs exhibit similar cell performance due to the weak electrochemical reactions. In the study of dynamic loading of PEM fuel cell, the transient response time which indicates the time from start-up to steady state is important. At t = 0 s, the operating voltage decreases abruptly from 0.7 V to 0.5 V. Therefore, the current density increases instantaneously and causes an overshoot and then decreases before achieving a steady state condition. After an overshoot, the transient response time needed to return to steady state is 0.15 s for the single serpentine flow field design, 0.176 s for the double serpentine
0.75
(a)
Voltage Loading Effects : 0.7V-0.5V-0.7V-0.5V
0.7
0.6
V
cell
(V)
0.65
0.55
0.5
0.45 0
0.2
(b)
16000
0.4
t (s)
0.6
0.8
flow field design, 0.2 s for the triple serpentine flow field design, and 0.212 s for the quadruple serpentine flow field design. At t = 0.3 s, an undershoot phenomenon results from a sudden increase in operating voltage from 0.5 V to 0.7 V and a sudden decrease in current density. The current density then increases and stabilizes before achieving a steady state condition. The transient response time required to reach steady state after an undershoot is 0.182 s for the single serpentine flow field design, 0.182 s for the double serpentine flow field design, 0.192 s for the triple serpentine flow field design, and 0.194 s for the quadruple serpentine flow field design. Fig. 2(b) shows that, because the PEMFCs have identical inlet fuel flow rates, inlet fuel flow velocity is inversely related to cathode inlet number. When the operating voltage decreases or increases abruptly, the lower inlet fuel flow velocity is unfavorable for the PEMFC to reach the steady state. To summarize, when overshoot or undershoot occurs, the quadruple serpentine flow field design exhibits the smallest variation in current density and the longest transient response time. Fig. 3 shows the distributions of local current density over time in the middle of the PEMFCs in the AA0 direction as shown in Fig. 1 for the single and the quadruple serpentine flow field designs. At t < 0 s, the operating voltage is 0.7 V, and the electrochemical reactions are mild. Both flow field designs have uniform local current density distributions. At t = 0.004 s, however, a decreases in operating voltage to 0.5 V causes an increase in the strength of the electrochemical reactions. The local current density distribution also increases markedly. The local current densities under the channels and ribs are generally unchanged. The local current density distribution is larger than that corresponding to the steady state at an operating voltage of 0.5 V when an overshoot occurs. At t = 0.1 s, the local current density distribution is smaller than that at t = 0.004 s. Additionally, the decrease in local current densities under the ribs is larger, and the differences in the local current density distribution under the channels and ribs increase. Therefore, as the overshoot decays to the steady state condition, the current density decreases and becomes non-uniform. The local current density distributions do not substantially differ between t = 0.28 s and 0.1 s, which indicates that the steady state is reached. Fig. 4 shows the local current density distributions in cell membranes in the single and the quadruple serpentine flow field designs. Fig. 4(a) shows that, at t < 0 s, electrochemical reactions are weak. Therefore, the differences in the local current density distributions from the inlet to the outlet of the flow field are small in both flow field designs. Fig. 4(b) shows that, at t = 0.004 s, the 0.5 V operating voltage substantially increases the strength of the
Single Serpentine Flow Field Double Serpentine Flow Field Triple Serpentine Flow Field Quadruple Serpentine Flow Field
25000
20000
t = 0.004s
Quadruple Serpentine Flow Field
t = 0.1s
t < 0s
t = 0.28s
-2
I (Am )
-2
I (Am )
12000
Single Serpentine Flow Field
15000
x
8000
10000
4000
Along the AA' Direction
Voltage Loading Effects : 0.7V-0.5V-0.7V-0.5V 0
0.2
0.4
t (s)
0.6
5000
0.8
Fig. 2. Effects of dynamic voltage loading on the cell performance of PEMFCs with serpentine flow field designs and varying numbers of cathode inlets: (a) dynamic voltage loading and (b) dynamic response of cell performance.
0
0.005
0.01
x (m)
0.015
0.02
Fig. 3. Local current density distributions over time in the middle of PEMFCs for the single and the quadruple serpentine flow field designs.
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(a) t < 0s
(b) t = 0.004s
(c) t = 0.1s
(d) t = 0.28s
Fig. 4. Local current density distributions in cell membranes of PEMFCs with the single and the quadruple serpentine flow field designs: (a) t < 0 s, (b) t = 0.004 s, (c) t = 0.1 s, and (d) t = 0.28 s.
0.3
0.25
O2
0.2
C
electrochemical reactions, which then increases the local current density distributions. Since the local current density distributions at t = 0.004 s exceed the steady state values at 0.5 V, overshoot phenomena occur. At t = 0.1 s, the current density distributions for both flow field designs decrease as overshoot phenomena decay toward the steady state conditions. In Fig. 4(c), the local current density distributions are smaller than those at t = 0.004 s, and the differences are more obvious from the inlet to the outlet of the flow field for both flow field designs. In Fig. 4(d), the local current density distributions at t = 0.28 s are similar to those at t = 0.1 s for both flow field designs, which suggests that the local current density distributions at t = 0.28 s represent the steady state conditions. The current density distributions therefore decrease slightly when operating time increases from t = 0.1 s to t = 0.28 s. Fig. 5 shows the oxygen mass fraction distributions at different times at the middle of the interface of the cathode gas diffusion and catalyst layers of PEMFCs along the AA0 direction as shown in Fig. 1 for the single and the quadruple serpentine flow field designs. At t < 0 s, the cell operating voltage remains at 0.7 V, and the electrochemical reactions are mild. Therefore, oxygen consumption is low, and oxygen mass fraction distributions remain high and uniform under the channels and ribs in both flow field designs. At t = 0.004 s, a decrease in operating voltage to 0.5 V increases the strength of electrochemical reactions. At this time, the oxygen mass fraction distributions are high, and the local current density distributions substantially increase and exceed the steady state values at 0.5 V in both flow field designs, which causes overshoot phenomena. The high and uniform oxygen mass fraction distributions under the channels and ribs also increase the uniformity of the local current density distributions. Therefore, overshoot phenomena result from the high and uniform oxygen mass fraction distributions when the operating voltage suddenly decreases from high to low. At t = 0.1 s, oxygen consumed by the strong electrochemical reactions results in oxygen mass fraction distributions that are lower and less uniform compared to those at t = 0.004 s. The variation under the channels and ribs is also higher in both flow field designs, which results in lower and less uniform local
Single Serpentine Flow Field
t = 0.004s
Quadruple Serpentine Flow Field
t = 0.1s
t < 0s
t = 0.28s
0.15
0.1
0.05
Along the AA' Direction 0 0
0.005
0.01
x (m)
0.015
0.02
Fig. 5. Oxygen mass fraction distributions at different times at the middle of the interface of the cathode gas diffusion and catalyst layers of PEMFCs with the single and the quadruple serpentine flow field designs.
current density distributions. At t = 0.28 s, the oxygen mass fraction distributions almost overlap with those at t = 0.1 s in both flow field designs, which implies that the fuel cells are in steady state conditions. Generally, the oxygen mass fraction distribution critically influences the overshoot phenomenon and the local current density distribution of PEMFCs with both the single and the quadruple serpentine flow field designs. Fig. 6 shows the oxygen mass fraction distributions at the interface between the cathode gas diffusion and catalyst layers of PEMFCs with the single and the quadruple serpentine flow field designs. In Fig. 6(a), when t < 0 s, the 0.7 V operating voltage causes only mild electrochemical reactions resulting in small variations in the oxygen mass fraction distributions from the inlet to the outlet of the flow field in both flow field designs. Fig. 6(b) shows that, at t = 0.004 s, the drop in operating voltage to 0.5 V causes violent electrochemical reactions resulting in decreased oxygen mass
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(a) t < 0s
(b) t = 0.004s
(c) t = 0.1s
(d) t = 0.28s
Fig. 6. Oxygen mass fraction distributions at the interface between the cathode gas diffusion and catalyst layers of PEMFCs with the single and the quadruple serpentine flow field designs: (a) t < 0 s, (b) t = 0.004 s, (c) t = 0.1 s, and (d) t = 0.28 s.
0.75
(a)
Voltage Loading Effects : 0.7V-0.5V-0.7V-0.5V
0.7
0.6
V
cell
(V)
0.65
0.55
0.5
0.45 0
24000
0.2
(b)
0.4
-1
Q = 85 ccmin , Q = 215 ccmin
0.8
-1
C
-1
Q = 65 ccmin , Q = 175 ccmin A
-1
C
-1
Q = 45 ccmin , Q = 135 ccmin A
16000
0.6
t (s)
A
-1
C
Single Serpentine Flow Field Quadruple Serpentine Flow Field
-2
I (Am )
fraction distributions from the inlet to the outlet of the flow field in both flow field designs. At t = 0.1 s and t = 0.28 s (Fig. 6(c) and (d), respectively), the oxygen mass fraction distributions are smaller than those at t = 0.004 s, and the differences in oxygen mass fraction distributions between the inlet to outlet of the flow field are larger because of the increased oxygen consumed along the flow field. Apparently, the cells reach the steady state conditions because of the very similar oxygen mass fraction distributions at t = 0.1 s and t = 0.28 s. Fig. 7 illustrates the effects of dynamic voltage loading on PEMFC performance with three different inlet fuel flow rates on the anode and cathode sides. Fig. 7(a) shows the Vcell-t curve of the PEMFCs, where Vcell = 0.7 V for t < 0 s, Vcell = 0.5 V for 0 s < t < 0.3 s, Vcell = 0.7 V for 0.3 s < t < 0.6 s, and Vcell = 0.5 V for 0.6 s < t. Fig. 7(b) shows the I-t curves of the PEMFCs. At t < 0 s, the operating voltage is Vcell = 0.7 V. The inlet fuel flow rate has a negligible effect on cell performance in the single and the quadruple serpentine flow field designs when the electrochemical reactions are weak. At t = 0 s, an overshoot phenomenon results from an abrupt increase in current density caused by a sudden drop in operating voltage from 0.7 V to 0.5 V. The current density then decreases gradually before achieving a steady state condition. In the single serpentine flow field design, the transient response times needed to return to the steady state after an overshoot are 0.128 s, 0.15 s, and 0.182 s when the inlet flow rates on the anode and cathode sides are 85 ccmin1 and 215 ccmin1, 65 ccmin1 and 175 ccmin1 and 45 ccmin1 and 135 ccmin1, respectively. In the quadruple serpentine flow field design, the transient response times needed to return to the steady state after an overshoot are 0.14 s, 0.212 s, and 0.218 s when the inlet flow rates on the anode and cathode sides are 85 ccmin1 and 215 ccmin1, 65 ccmin1 and 175 ccmin1, and 45 ccmin1 and 135 ccmin1, respectively. The higher the inlet fuel flow rate, the better the performance, and the faster the cell can reach a steady state after a sudden change in operating voltage. At t = 0.3 s, a sudden increase in operating voltage from 0.5 V to 0.7 V and a decrease in current density cause an undershoot phenomenon. The current density
8000
Voltage Loading Effects : 0.7V-0.5V-0.7V-0.5V 0
0.2
0.4
t (s)
0.6
0.8
Fig. 7. Effects of dynamic voltage loading on the cell performance of the PEMFC with three different inlet fuel flow rates: (a) dynamic voltage loading and (b) dynamic response of cell performance.
W.-M. Yan et al. / International Journal of Heat and Mass Transfer 107 (2017) 646–656
653
(a) t < 0s
(b) t = 0.004s
QA = 85 ccmin-1, QC = 215 ccmin-1
QA = 65 ccmin-1, QC = 175 ccmin-1
QA = 45 ccmin-1, QC = 135 ccmin-1
QA = 65 ccmin-1, QC = 175 ccmin-1
QA = 45 ccmin-1, QC = 135 ccmin-1
(c) t = 0.1s
(d) t = 0.28s
QA = 85 ccmin-1, QC = 215 ccmin-1
Fig. 8. Local current density distributions in the membrane of the PEMFC with the single serpentine flow field design at three different inlet fuel flow rates: (a) t < 0 s, (b) t = 0.004 s, (c) t = 0.1 s, and (d) t = 0.28 s.
increases and stabilizes before achieving a steady state condition. In the single serpentine flow field design, the transient response times needed for the undershoot phenomenon to reach a steady state are 0.136 s, 0.182 s, and 0.21 s when the inlet flow rates on the anode and cathode sides are 85 ccmin1 and 215 ccmin1,
65 ccmin1 and 175 ccmin1, and 45 ccmin1 and 135 ccmin1, respectively. In the quadruple serpentine flow field design, the transient response times needed for the undershoot phenomenon to reach a steady state are 0.164 s, 0.194 s, and 0.238 s when the inlet flow rates on the anode and cathode sides are 85 ccmin1
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(a) t < 0s
(b) t = 0.004s
QA = 85 ccmin-1, QC = 215 ccmin-1
QA = 65 ccmin-1, QC = 175 ccmin-1
QA = 45 ccmin-1, QC = 135 ccmin-1
QA = 65 ccmin-1, QC = 175 ccmin-1
QA = 45 ccmin-1, QC = 135 ccmin-1
(c) t = 0.1s
(d) t = 0.28s
QA = 85 ccmin-1, QC = 215 ccmin-1
Fig. 9. Oxygen mass fraction distributions at the interface between the cathode gas diffusion and catalyst layers of the PEMFC with the single serpentine flow field design at three different inlet fuel flow rates: (a) t < 0 s, (b) t = 0.004 s, (c) t = 0.1 s, and (d) t = 0.28 s.
and 215 ccmin1, 65 ccmin1 and 175 ccmin1, and 45 ccmin1 and 135 ccmin1, respectively. As the inlet fuel flow rate increases, the cell performance improves because the return to the steady state condition is faster after a sudden increase in operating
voltage. To summarize, because the cathode inlet number in the single serpentine flow field design is less than the quadruple flow field design, it has a faster inlet fuel flow velocity. Therefore, overshoot and undershoot phenomena are more severe in the single
W.-M. Yan et al. / International Journal of Heat and Mass Transfer 107 (2017) 646–656
serpentine flow field design than in the quadruple serpentine flow field design. Moreover, transient response time is shorter in the PEMFC with the single serpentine flow field design than with the quadruple serpentine flow field design. Fig. 8 shows the local current density distributions in the membrane of the PEMFC with the single serpentine flow field design at three different inlet fuel flow rates. Fig. 8(a) shows that the 0.7 V operating voltage at t < 0 s produces weak electrochemical reactions. Regardless of the inlet fuel flow rates applied, the differences in the local current density distributions are negligible. Moreover, the local current density distributions decrease from the inlet to the outlet of the flow field. Fig. 8(b) shows that, at t = 0.004 s, the drop in operating voltage to 0.5 V causes strong electrochemical reactions, which then cause rapid increases in the local current density distributions. Fig. 8(c), at t = 0.1 s shows that, when the inlet fuel flow rate is low (QA = 45 ccmin1, QC = 135 ccmin1), the decrease in the local current density distribution from the inlet to the outlet of the flow field increases as the amount of oxygen consumed downstream becomes insufficient. The values of the local current density distributions at t = 0.1 s are smaller than those at t = 0.004 s. In Fig. 8(d), the local current density distribution at t = 0.28 s is similar to that at t = 0.1 s for each inlet fuel flow rate, which indicates that the local current density distributions should reach a steady state condition. Fig. 9 shows the oxygen mass fraction distributions at the interface between the cathode gas diffusion and catalyst layers of the PEMFC with the single serpentine flow field design at three different inlet fuel flow rates. Fig. 9(a) shows that, when the operating voltage is 0.7 V at t < 0 s, the electrochemical reactions are mild, and oxygen mass fraction distributions from the inlet to the outlet of the flow field show only minimal variation for all three inlet fuel flow rates. However, as the inlet fuel flow rate increases, the oxygen mass fraction increases in the downstream flow field. In Fig. 9 (b), at t = 0.004 s, the operating voltage decreases to 0.5 V, violent electrochemical reactions decreases the oxygen mass fraction distributions from the inlet to the outlet of the flow field. Figs. 9 (c) and (d) show that, at t = 0.1 s and t = 0.28 s, respectively, the oxygen mass fraction distributions are smaller than those at t = 0.004 s. The decreases of the oxygen mass fraction distributions from the inlet to the outlet of the flow field are also apparent, especially when inlet fuel flow rate is low. 4. Conclusions This study constructed three-dimensional transient numerical models of PEMFCs with serpentine flow field designs and varying numbers of cathode inlets. The PEMFC designs included single, double, triple, and quadruple serpentine flow field designs. To determine the effects of serpentine flow field designs and inlet fuel flow rates on the transient characteristics of the PEMFCs, electrochemical reactions and transport phenomena of the various reactants and products in the PEMFCs were analyzed in terms of transient response time and overshoot and undershoot phenomena. The conclusions in this study are summarized as follows: 1. At a cell operating voltage of 0.7 V, weak electrochemical reactions result in a uniformly low local current density in all four serpentine flow field designs. 2. When operating voltage is suddenly reduced from 0.7 V to 0.5 V, the overshoot phenomenon in the current density distribution results from the higher and more uniform oxygen mass fraction distribution in the cathode gas diffusion and catalyst layers, which provide sufficient oxygen for strong electrochemical reactions. The quadruple serpentine flow field design has the lowest oxygen mass fraction distribution among the four serpentine flow field designs. Thus, the quadruple serpentine
655
flow field design has the smallest variation in the current density distribution and the longest transient response time when overshoot or undershoot phenomena occur. 3. After overshoot or undershoot phenomena occur, the time required for the local current density distributions in the PEMFCs to reach the steady state conditions in the four serpentine flow field designs increases, in order from fastest to slowest, as follows: the single serpentine flow field design, the double serpentine flow field design, the triple serpentine flow field design, and the quadruple serpentine flow field design. 4. When the cell voltage changes suddenly, the time needed for the cell to reach the steady state condition correlates positively with the inlet fuel flow rates.
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