INTERNATIONAL JOURNAL OF ENERGY RESEARCH Int. J. Energy Res. 2011; 35:2–14 Published online 16 June 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.1730
Numerical studies of cold-start phenomena in PEM fuel cells: A review Hua Meng,y,z and Bo Ruan School of Aeronautics and Astronautics, Zhejiang University, Hangzhou, Zhejiang 310027, People’s Republic of China
SUMMARY Successful startup from subfreezing temperatures is a prerequisite for PEM fuel cell commercialization. In this paper, a comprehensive review of recent research progress on PEM fuel cell cold-start phenomena has been presented. Experimental studies are first briefly summarized. A transient multiphase multi-dimensional PEM fuel cell model, accommodating ice formation and temperature variation, is introduced. Numerical results from both isothermal operations and non-isothermal self-starts at subfreezing startup temperatures have been analyzed. The effects of many key parameters, including the water vapor concentration in the cathode gas channel, the initial membrane water content, the operating current density, and the startup cell temperature, on PEM fuel cell coldstart behaviors have been carefully examined to elucidate the fundamental physics of PEM fuel cell cold starts. Copyright r 2010 John Wiley & Sons, Ltd. KEY WORDS PEM fuel cell; cold start; ice formation; subfreezing temperature; numerical modeling Correspondence *Hua Meng, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou, Zhejiang 310027, People’s Republic of China. y E-mail:
[email protected] z Proffessor. Contract/grant sponsor: National Natural Science Foundation of China; contract/grant number: 10972197. Received 4 June 2009; Accepted 14 January 2010 This article was published online on 16 June 2010. Received and accepted dates have been corrected. This notice is included in the online and print versions to indicate that both have been corrected [23 December 2010].
1. INTRODUCTION Numerical modeling and simulation is a complementary and indispensable tool for PEM fuel cell research and development. Many PEM fuel cell models have been developed [1–40] in the past ten years. These numerical models focus on elucidating the electrochemical and transport phenomena inside the PEM fuel cells, particularly the two-phase transport and liquid water distributions observed in the experimental studies [41–51]. Good progress has been achieved in this area. Prior to the commercialization of the PEM fuel cells, however, successful development of a rapid and reliable cold-start capability from the subfreezing environment temperature becomes a prerequisite. Given its paramount impact, much research has been expended in this area in recent years, including both extensive experimental and comprehensive numerical studies [52–79]. 2
In this paper, a comprehensive review of the experimental and numerical research on PEM fuel cell coldstart phenomena is provided. As a specific example, a transient multiphase multi-dimensional PEM fuel cell model with the accommodation of the ice formation and temperature variation is briefly described. Numerical results are carefully analyzed for elucidating both isothermal operation and non-isothermal self-start behaviors of PEM fuel cells, focusing on the effects of many key parameters, including the water vapor concentration in the cathode gas channel, the initial water content inside the membrane, and the operating current density.
2. PEM FUEL CELL COLD-START PHENOMENA 2.1. Experimental studies The early experimental work concerning PEM fuel cell cold starts focused on the effects of the repetitive Copyright r 2010 John Wiley & Sons, Ltd.
Numerical studies of cold-start phenomena
thermal cycling, i.e. from 40 to 801C, on fuel cell performance degradation, material, and component integrity [52–55]. McDonald et al. [52] examined the physical and chemical property changes in the membrane and the membrane-electrode assembly (MEA) after repetitive freeze/thaw thermal cycling between 80 and 401C, and they observed no catastrophic failures in the membranes and MEA, which were assembled in the fuel cell stack under ambient humidity conditions. Cho et al. [53] studied the PEM fuel cell characteristics after repetitive freeze/thaw thermal cycling between 80 and 101C. It was found that the cell performance degraded with the increased polarization resistance and ohmic losses after a number of thermal cycles. They concluded that the increase in the polarization resistance could be attributed to the deformation of the electrode structure, while the increase in the ohmic resistance was due mainly to the increase of the contact resistance between the membrane and the electrode. Both phenomena were caused by the volume dilatation during the freezing process. To maintain cell performance after repetitive cold-start processes, Cho et al. [54] proposed the gas-purging method, removing water inside the fuel cell through feeding dry gases into the cell after each cell operation. Hou et al. [55] further demonstrated that with appropriate gas purging, no performance degradation and MEA delamination in a PEM fuel cell would occur after 20 freeze/thaw cycles from 20 to 601C. Instead of focusing on the thermal cycling effects, Kagami et al. [56] directly studied PEM fuel cell coldstart processes from subfreezing temperatures under constant current densities. They found that a successful self-start without external heating could only be achieved with the start-up temperature above 51C. This conclusion is consistent with that of Yan et al. [57], who investigated cold-start processes using a PEM fuel cell with a 25 cm2 active area. To further understand the fundamental cold-start mechanisms of PEM fuel cells, Oszcipok et al. [58] conducted isothermal potentiostatic cold-start measurements of a single cell. It was shown that the product water initially increased the membrane humidity at subfreezing temperatures, and after the membrane humidity reached its maximum, the product water would flood the catalyst layer and the gas diffusion layer (GDL) and became frozen. Ice formation would subsequently lead to strong current density decay and cell degradation. They also carried out a mathematic curve fitting and statistic regression analyses, and showed that dryer membrane and high gas flow rates would benefit the PEM fuel cell cold-start operations. Oszcipok et al. [59] further developed a physical PEM fuel cell model to describe the transient behaviors of a PEM fuel cell under isothermal subfreezing operations. The model was able to account for the effects of the reduction of the active catalyst surface and the increase of the contact resistance on the cell performance. Int. J. Energy Res. 2011; 35:2–14 r 2010 John Wiley & Sons, Ltd. DOI: 10.1002/er
H . Meng and B. Ruan
Tajiri et al. [60] further advanced the experimental procedures for isothermal cold-start studies by introducing an equilibrium gas-purging method, which could maintain a well-controlled initial water distribution inside a PEM fuel cell before its cold-start operations. Tajiri et al. [61] also experimentally investigated the parametric effects on PEM fuel cell cold start, including the purging methods, startup temperatures, current densities, and membrane thicknesses. Thompson et al. [62] developed an experimental procedure to examine the oxygen reduction reaction (ORR) kinetics during cold-start processes and found no fundamental change in the ORR reaction mechanism under subfreezing temperatures. They also measured low-temperature proton conductivity inside the Nafion membrane and revealed the effect of water freezing/melting on this parameter [63]. Thompson et al. [64] recently further quantified water accumulation inside the membrane and cathode electrode of a PEM fuel cell at subfreezing operation conditions. To obtain direct pictures of ice formation in a PEM fuel cell during cold starts from subfreezing temperatures, Ge and Wang [65] developed a transparent cell with a silver mesh used as the cathode GDL and conducted visualization experiments on liquid water transport and ice formation using this cell. It was concluded that the freezing-point depression of water in the cathode catalyst layer should be less than 21C and its role in cold-start practice should thus be negligible. They later further narrowed down the value range to 1.070.51C [66]. Ishikawa et al. [67] also investigated water generation and ice formation in a PEM fuel cell using both visible and infrared images, but they observed supercooled liquid water at a subfreezing temperature of 101C. They recently clarified, however, that the super-cooled liquid water could only appear after a thorough purging of the fuel cell using non-humidified gases before its cold start, thus removing all the remaining water that could freeze and serve as the seed ice during the startup processes [68].
2.2. Numerical modeling and simulations The results and observations from the experiments have laid a solid foundation for simplified analytical analyses and detailed numerical studies of the coldstart mechanisms of PEM fuel cells. The analytical models in the open literature focused on fundamental understanding of the cold-start processes of PEM fuel cells. Mao and Wang [69] and Wang [70] both developed analytical models and conducted parametric studies of the cold-start processes of PEM fuel cells. To gain deeper insight of the intricate phenomena, a series of numerical models were further developed, including the one-dimensional thermal models for stack studies [71,72] and the multi-dimensional multiphase CFD models for detailed cold-start simulations 3
H . Meng and B. Ruan
[73–79]. Sundaresan and Moore [71] developed a stack thermal model to study PEM fuel cell cold start. They focused on a layered model, which separated the stack into different layers, to determine the temperature distribution within the stack. The model could reveal the effects of the endplate thermal mass and the internal heating method on the stack cold-start operations. Khandelwal et al. [72] developed a onedimensional thermal model for a PEM fuel cell stack to investigate the cell cold-start capability and the corresponding energy requirement at various operating and ambient conditions. They observed that an optimum range of operating current density existed for a given stack design for rapid cold startup and recommended thermal isolation of the stack at the endplates to reduce the startup time. It was also found that flow of heated coolant above 01C was an effective way to achieve rapid stack cold start. Ahluwalia and Wang [73] developed a simple twodimensional model of a single cell for simulating PEM fuel cell cold start. It was shown that for rapid and robust cell self-start, operation of the fuel cell near the short-circuit condition was desirable because of its maximum hydrogen utilization and favorable waste heat production. They concluded that preheating the feed gases, electrically heating the cell stack, and the cell operating pressure produced only small effects on the ability of the cell self-start and startup time. Mao and Wang [74] presented a three-dimensional PEM fuel cell model, considering ice formation in the cathode electrode. The numerical model was used for studying cell performance and revealing detailed distributions of current density and ice fraction in a PEM fuel cell undergoing isothermal cold-start processes. The model has later been used to examine the close interactions between ice formation and heat generation during the non-isothermal cold start of a PEM fuel cell [75]. The effect of rising cell temperature on PEM fuel cell cold start was explored by comparing the results from non-isothermal cold-start processes with those from isothermal cold starts. Meng [76] developed a multi-dimensional PEM fuel cell model with accommodation of ice formation in the cathode catalyst layer based on a previously established mixed-domain approach [14,15,33,34]. The numerical model has been applied for elucidating fuel cell isothermal cold-start processes at a subfreezing temperature of 201C under both constant current and constant cell voltage conditions. The effects of many key parameters on fuel cell isothermal cold-start behaviors were examined in detail [77]. The numerical model has further been developed to consider the temperature effect [78]. The resulting non-isothermal multi-dimensional model was employed in a twodimensional cross section of a PEM fuel cell to elucidate the non-isothermal self-start behaviors of the fuel cell from subfreezing startup temperatures, focusing on the coupled phenomena between ice formation and cell 4
Numerical studies of cold-start phenomena
temperature increase, and on the effects of a number of key parameters, including the water vapor concentration in the cathode gas channel, the initial water content inside the membrane, the operating current density, and the initial cell temperature, on the startup processes and the related self-start mechanisms [78]. Jiao and Li [79] recently presented a multi-phase three-dimensional mathematical model to study the cold-start processes in PEM fuel cells. A unique feature in this model lied in its consideration of the water freezing phenomenon in the membrane electrolyte. Numerical results indicated that increasing the ionomer fraction in the cathode catalyst layer could produce more significant effects on ice reduction than increasing the membrane thickness. Ice-melting processes above the freezing temperature were also investigated in this paper. Results showed that ice melted first in the catalyst layer under the gas channel. 2.2.1. Mathematical model description. A transient multi-phase multi-dimensional PEM fuel cell model with accommodation of the ice formation [76–79] will be briefly described in this section, as a specific example. It includes the following transient conservation equations: Mass conservation: @½eð1 sice Þr 1H ðr~ uÞ ¼ Sm @t
ð1Þ
Momentum conservation: 1 @ðr~ uÞ 1 1 H ðr~ u~ uÞ eð1 sice Þ @t e2 ð1 sice Þ2 ¼ Hp1H t1Su
ð2Þ
Species conservation (including hydrogen, oxygen, and water vapor): @½eeff ð1 sice Þci 1H ð~ uci Þ ¼ H ðDeff i Hci Þ1Si @t
ð3Þ
Ice conservation: @ðerice sice Þ ¼ Svi Ww @t
ð4Þ
Water content conservation inside the membrane: @ rm lnf ¼ H ðDl Hlnf Þ1Slnf 1Snf ð5Þ @t EW Energy conservation: @ uTÞ ¼ H ðkeff HTÞ1ST ½ðrCp Þeff T1H ðrCp ~ @t
ð6Þ
Proton transport: H ðkeff Hfe Þ1Se ¼ 0
ð7Þ
Electron transport: H ðseff Hfs Þ1Ss ¼ 0
ð8Þ
The conservation equations for proton and electron transport, Equations (7) and (8), remain in steady-state Int. J. Energy Res. 2011; 35:2–14 r 2010 John Wiley & Sons, Ltd. DOI: 10.1002/er
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H . Meng and B. Ruan
form because the electrochemical charging/discharging processes in the double layers are very fast. In this model, ice precipitation is through direct water vapor desublimation, based on the experimental observations of Ge and Wang [65,66]. The volumetric desublimation rate is expressed in the following form [76–78]: Svi ¼ hpc ðpv psat Þ
ð9Þ
where the desublimation parameter is defined as v p psat kc eð1 sice Þxv 11 v ð10Þ hpc ¼ p psat 2Ru T This formulation indicates that water vapor would start to freeze after it reaches its saturation value. During the cold-start process, a fraction of the membrane water content could become frozen [63]. The water freezing/melting phenomenon inside the membrane electrolyte can be considered as [79], 8 r < znf m ðlnf lsat Þ lnf Xlsat EW ð11Þ Snf ¼ : znf rm lf lnf olsat EW where the parameter, zn–f, is the water transfer rate. This equation indicates that the freezing or melting of the membrane water content depends on the maximum allowable non-frozen water content at a subzero temperature, lsat. More details concerning this modeling feature can be found in [79]. The model-related electrochemical and physical relationships are listed in Tables I and II. More details
concerning cold-start modeling can also be found in the references [33,34,76–79]. It should be noted that for the multi-dimensional simulation of PEM fuel cell cold starts, Mao and Wang [74] have also developed a multiphase model with consideration of the ice formation in the cathode electrode. Based on the large-source technique of Voller [80], the ice formation rate in their model was determined in the water species conservation equation by fixing the local water vapor concentration at its saturation value. More details regarding this model can be found in the open literature [74,75]. 2.2.2. Numerical result analyses. Multi-phase multidimensional numerical studies have been conducted in the open literature to gain deep understanding of the fundamental physics of PEM fuel cell cold-start processes [74–79]. Numerical results from these calculations showed consistent trend with the experimental data [58–61], i.e. the two-stage evolution of the cell performance under both constant current and constant cell voltage conditions. In the following sections, the effects of many key parameters, including the water vapor concentration in the cathode gas channel, the initial water content inside the membrane, the operating current density/cell voltage, and the startup cell temperature, on PEM fuel cell isothermal and non-isothermal cold-start behaviors will be analyzed. For the convenience of parametric studies and discussions, the numerical results are
Table I. Electrochemical and physical relationships. Description Transfer current density [2]
Over potential [2,8] Open-circuit potential [8,12] Electro-osmotic drag coefficient [8] Water activity Water saturation pressure [2] Partial pressure of water vapor Membrane water diffusivity [8] Water content diffusivity Proton conductivity [2,8] Ice fraction [74,76] Effective catalytic area [74,76] Effective diffusivity [74,76]
Expression
Unit
cH2 1=2 aa 1ac ref j ¼ aeff j0;a F Z in anode cH2;ref RT cO2 ac eff ref F Z in cathode j ¼ a j0;c exp cO2;ref RT Z ¼ fs fe in anode side Z ¼ fs fe U0 in cathode side U0 ¼ 1:23 0:9 103 ðT 298Þ 1:0 for lnf p14 nd ¼ 1:5=8ðlnf 14Þ11:0 otherwise Cw Ru T a¼ psat log10 psat ¼ 2:179410:02953ðT 273:15Þ 9:1837 105 ðT 273:15Þ2
11:4454 107 ðT 273:15Þ3 pv ¼ C w R u T 3:1 107 lnf ðe0:28lnf 1Þ e½2346=T ¼ Dm w 4:17 108 lnf ð11161elnf Þ e½2346=T r Dlnf ¼ m Dm EW w 1 1 k ¼ ð0:5139lnf 0:326Þexp 1268 303 T Vice sice ¼ Vp aeff ¼ ð1 sice Þa 1:5 1:5 Deff i ¼ Di e ð1 sice Þ
Int. J. Energy Res. 2011; 35:2–14 r 2010 John Wiley & Sons, Ltd. DOI: 10.1002/er
0olnf p3 otherwise
3
Am
V V
atm Pa m2 s1 mol m1 s1 S m1
m2 m2 s1
5
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Table II. Physicochemical parameters. Anode volumetric exchange current density, aj0 (A m3) [8] Cathode volumetric exchange current density, aj0 (A m3) [8] Reference hydrogen concentration, CH2 (mol m3) [8] Reference oxygen concentration, CO2 (mol m3) [8] Anode transfer coefficients [8] Cathode transfer coefficient [8] Faraday constant, F (C mol1) GDL porosity [2,8] Porosity of catalyst layer [2,8] Volume fraction of ionomer in catalyst layer [2,8] GDL permeability (m2) [2,8] Catalyst layer permeability (m2) [2,8] Equivalent weight of ionomer (kg mol1) [2,8] Dry membrane density (kg m3) [2,8] Effective electronic conductivity in CL/GDL (S m1) [8] Electronic conductivity of current collector (S m1) [8] Operation pressure (atm) Desublimation rate coefficient (s1) [76] Water transfer rate (s1) [79] Thermal conductivity of GDL (W m1 K1) [12,34] Thermal conductivity of CL (W m1 K1) [12,34] Thermal conductivity of the membrane (W m1 K1) [12,34] Thermal conductivity of current collector (W m1 K1) [12] Enthalpy of desublimation (J kg1) [76] Density of carbon material (kg m3) [34,76] Density of ice (kg m3) [76] Density of current collector (kg m3) [78] Heat capacity of carbon material (J kg1 K1) [34,76] Heat capacity of membrane material (J kg1 K1) [34,76] Heat capacity of ice (J kg1 K1) [76] Heat capacity of current collector (J kg1 K1) [78]
1.0 109 1.0 104 40 40 aa 5 ac 5 1 ac 5 1 96 487 0.6 0.2 0.4 1.0 1012 1.0 1013 1.1 1980 5000 20 000 2 3.0 107 1.0 1.5 1.5 0.5 20 2.64 106 2200 900 1900 1050 1050 2100 710
Table III. Geometric parameters.
Figure 1. A two-dimensional PEM fuel cell cross section.
chosen from two-dimensional calculations, focusing on a cross section as shown in Figure 1. The corresponding cell geometric parameters are listed in Table III. For a two-dimensional numerical calculation, the following boundary conditions should be implemented [78]. Boundary 1 is at the edge of the bipolar plate on the anode side; the boundary conditions are defined as
6
Layer thickness (mm) Diffusion Catalyst Membrane Land width (mm) Channel width (mm) Land depth (mm) Channel depth (mm) Computational cell numbers
(
T ¼ T0
0.3 0.01 0.025 0.5 1.0 2.0 1.0 3200
Hfe ¼ 0
ð12cÞ
fs ¼ 0
ð12dÞ
isothermal ð12eÞ
HT ¼ 0 non isothermal
Hci ¼ 0
ð12aÞ
Boundary 2 is on the cathode side with the same boundary conditions as boundary 1, except that a constant current density is defined,
Hsice ¼ 0
ð12bÞ
~ seff bpp Hfs ¼ i0
ð13Þ
Int. J. Energy Res. 2011; 35:2–14 r 2010 John Wiley & Sons, Ltd. DOI: 10.1002/er
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H . Meng and B. Ruan
Boundary 3 is at the interface between the GDL and the gas channel on the anode side with the following boundary conditions: ci ¼ ci;0
ð14aÞ
Hsice ¼ 0
ð14bÞ
Hfe ¼ Hfs ¼ 0
ð14cÞ
HT ¼ 0
ð14dÞ
Boundary 4 is at the GDL and gas channel interface on the cathode side, the same type of boundary conditions as those in Equation (14) are defined. All the other boundaries are grouped into boundary 5, and no-flux boundary conditions are defined for all the variables. The initial water content in the membrane can be controlled by an equilibrium gas purging and is assumed to be uniformly distributed. The initial ice fraction inside the cell is zero in the numerical calculations. Dry hydrogen and dry air are fed into the anode and cathode sides, and the inlet values are defined initially as uniform values on the anode and cathode sides, respectively. Temperature is defined initially as a uniform value in the entire cell. A total of 3200 computational cells are found sufficient for obtaining grid-independent solutions in the numerical simulations. A non-uniform grid system is employed in the through-membrane direction, with 10 computational cells in the membrane, 10 in each of the GDLs, and 5 in each of the catalyst layers. Variable time step is employed with an initial minimum time step at 0.25 s, while it increases gradually to 1 s as the calculation progresses. 2.2.2.1. Isothermal cold start. Numerical studies of the cold-start processes of a PEM fuel cell under the isothermal condition by defining a constant temperature at the outside boundaries 1 and 2 are first discussed. The isothermal condition is designed to reveal the fundamental mechanisms of the cold-start processes of a PEM fuel cell since the intricate interactions of ice formation and temperature rise would be decoupled and the cold-start phenomena would consequently be simplified. Unless otherwise stated, numerical results examined in this section are obtained under a constant operating current density of 50 mA cm2 and a boundary temperature at 201C. Figure 2 shows the effect of the water vapor concentration inside the cathode gas channel on the isothermal cold-start processes of a PEM fuel cell. Since the water vapor concentration inside the cathode gas channel would influence the water vapor distribution inside the cathode catalysts layer, it could significantly affect ice precipitation and thus the cold-start process. As shown in Figure 2, decreasing the water vapor concentration would drastically increase the cold-start time. In a true three-dimensional case, the water vapor concentration in the cathode gas channel would vary Int. J. Energy Res. 2011; 35:2–14 r 2010 John Wiley & Sons, Ltd. DOI: 10.1002/er
Figure 2. Effect of gas channel water vapor concentration on isothermal cold start.
Figure 3. Effect of initial membrane water content on isothermal cold start.
with the downstream location, as the water vapor concentration increases along the flow direction, and with the inlet gas velocity, as a high inlet velocity would decrease the water vapor concentration, especially near the inlet section. Therefore, ice formation and distribution inside a PEM fuel cell during isothermal cold starts would vary significantly with inlet velocity and along the flow direction. The effect of the initial membrane water content on the isothermal cold-start behaviors of a PEM fuel cell is illustrated in Figure 3. The initial membrane water content is dictated by the relative humidity of the purging gas using the equilibrium purging method [60]. Decreasing the relative humidity of the purging gas would decrease the initial water content inside the membrane and thus increase its water absorption capability, resulting in delayed ice precipitation and longer cold-start time for a PEM fuel cell. 7
H . Meng and B. Ruan
Figure 4. Effect of cell temperature on isothermal cold start.
Figure 5. Effect of operating current density on isothermal cold start.
Increasing the startup cell temperature would increase the saturation water vapor concentration. Since ice precipitation starts only after the water vapor becomes saturated, as shown in Equations (9) and (10) in the earlier section, increasing the cell temperature would consequently lead to delayed ice formation and, therefore, prolonged cold-start process, as clearly indicated in Figure 4. The effect of the operating current density on the isothermal cold-start processes of a PEM fuel cell is presented in Figure 5. Since more water would be produced under a higher operating current density, which would then lead to faster ice precipitation during the startup process, the cold-start time would be significantly reduced under a higher operating current density, i.e. 75 mA cm2. 2.2.2.2. Non-isothermal self start. Numerical results of the non-isothermal self-start of a PEM fuel cell from subfreezing startup temperatures are reviewed and 8
Numerical studies of cold-start phenomena
Figure 6. Effect of gas channel water vapor concentration on non-isothermal self start.
discussed in this section. In these numerical calculations, the boundary conditions at boundaries 1 and 2, as shown in Figure 1, are both defined as isolated, meaning that the PEM fuel cell starts up from subzero temperatures relying on its own heat release without any external heating source. The present numerical results are intended for further understanding of the coupled phenomena between the ice formation and cell temperature rise. Unless otherwise stated, the numerical results in this section are obtained under a constant operating current density of 100 mA cm2 and an initial cell temperature at 201C. The effect of the water vapor concentration inside the cathode gas channel on the non-isothermal coldstart processes is clearly illustrated in Figure 6. As already discussed in the preceding section, in the present two-dimensional calculations, different water vapor concentrations in the cathode gas channel indicate different downstream locations along the flow direction and/or different inlet velocities, especially near the inlet section. As shown in Figure 6, decreasing the channel water vapor concentration from 0.15 to 0.074 mol m3 would lead to a successful self-start of the PEM fuel cell, because a lower water vapor concentration results in slower ice formation and would thus earn sufficient time for the cell temperature rising to above 01C. The transient distributions of the cell temperature during the self-start process with a gas channel water vapor concentration at 0.074 mol m3 are presented in Figure 7. At each operation time, the cell obtains a maximum temperature directly under the gas channel in the cathode catalyst layer because the sluggish ORR produces more waste heat in this location. The temperature distribution profile remains similar at each operating instant, although the overall cell temperature is increasing as the operation time progresses. These results indicate that a similarity solution for the temperature distribution could be assumed during the transient fuel cell startup process. Int. J. Energy Res. 2011; 35:2–14 r 2010 John Wiley & Sons, Ltd. DOI: 10.1002/er
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H . Meng and B. Ruan
Figure 7. Transient distributions of cell temperature during a successful self start.
Figure 8. Time evolution of ice fraction distribution in the cathode catalyst layer.
The time evolution of the ice fraction distribution in the cathode catalyst layer with an interfacial water vapor concentration at 0.15 mol m3 is illustrated in Figure 8. Since the water vapor concentration in the cathode gas channel is initially set at a high value, ice precipitates faster directly under the middle of the gas channel inside the catalyst layer, from start up to 30 s of the cell operation time. As the cell operation time increases, more water vapor becomes easily accumulated under the two current-collecting lands in the cathode catalyst layers, resulting in faster ice precipitation and higher ice fraction in these two regions. In addition, numerical results indicate that ice also accumulates more at the interface between the catalyst layer and GDL, because the electrochemical reaction (ORR) and consequently the water production mainly Int. J. Energy Res. 2011; 35:2–14 r 2010 John Wiley & Sons, Ltd. DOI: 10.1002/er
occur near this location at low current density operations. Figure 9 displays the effect of the initial water content inside the membrane on the non-isothermal selfstart processes of a PEM fuel cell. Decreasing the initial membrane water content from 6.17 to 2.57 would dramatically increase the water absorption capability of the membrane, leading to a successful self-start of the PEM fuel cell. In these two-dimensional studies, the water vapor concentration inside the cathode gas channel is set at a low value of 0.074 mol m3. It should be emphasized that in the real-world operations, the water vapor concentration would increase along the flow direction on the cathode side, leading to faster ice precipitation and possibly cell operation shut-down. Therefore, these two-dimensional results are only 9
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Figure 9. Effect of initial membrane water content on nonisothermal self start.
Numerical studies of cold-start phenomena
Figure 11. Effect of startup temperature on non-isothermal self start.
3. CONCLUDING REMARKS
Figure 10. Effect of operating current density on non-isothermal self start.
intended for elucidating fundamental cold-start behaviors of a PEM fuel cell. Figure 10 shows the effect of the operating current density on the self-start processes of a PEM fuel cell. In the two-dimensional calculations, decreasing the operating current density from 100 to 50 mA cm2 would lead to a successful self-start process, since a lower operating current density results in slower water production and subsequently slower ice formation inside the cathode catalyst layer. On the other hand, a low operating current density at 50 mA cm2 would certainly produce less waste heat for the fuel cell selfheating. In this case, it is the water production rate that dictates the cold-start process. The effect of the startup cell temperature on the selfstart processes of a PEM fuel cell is illustrated in Figure 11. Increasing the startup cell temperature would make the cell temperature rise to above 01C much quicker, rendering a successful self start of the PEM fuel cell. 10
In this paper, a comprehensive review of recent research progress on PEM fuel cell cold-start phenomena has been presented, including both experimental and numerical studies. A transient multiphase multidimensional PEM fuel cell model with the accommodation of ice formation and temperature variation has been briefly described. Both isothermal cold-start operations and non-isothermal self starts of a PEM fuel cell from subfreezing startup temperatures have been carefully examined. Numerical results show that the water vapor concentration inside the cathode gas channel affects ice formation in the cathode catalyst layer and thus the cold-start process of the fuel cell. The effects of many other key parameters on PEM fuel cell cold-start behaviors have also been discussed. It is concluded that decreasing the initial water content inside the membrane and the operating current density, and increasing the startup cell temperature are beneficial for PEM fuel cell cold starts. These results elucidate the underlying physics of PEM fuel cell coldstart processes and thus could serve as guidelines for the future cold-start technology development.
NOMENCLATURE a c Cp D Dl EW F
5 water activity or surface area 5 molar concentration (mol m3) 5 constant-pressure heat capacity (J kg1 K1) 5 mass diffusivity (m2 s1) 5 water content diffusivity (mol m1 s1) 5 equivalent weight of the membrane (kg mol1) 5 Faraday constant, 96487 (C mol1)
Int. J. Energy Res. 2011; 35:2–14 r 2010 John Wiley & Sons, Ltd. DOI: 10.1002/er
Numerical studies of cold-start phenomena
i j k kc K nd p Ru sice S t T u Uo V W
5 current density (A m2) 5 transfer current density (A m3) 5 thermal conductivity (W m1 K1) 5 desublimation rate coefficient (s1) 5 permeability (m2) 5 electro-osmotic drag coefficient 5 gas-phase pressure (Pa) 5 universal gas constant (J mol1 K1) 5 ice fraction 5 source term 5 time (s) 5 temperature (K) 5 gas-phase velocity (m s1) 5 open-circuit potential (V) 5 volume (m3) 5 molecular weight (kg mol1)
Greek w e F Z k l r s t
5 mole fraction 5 porosity 5 phase potential (V) 5 over-potential (V) 5 proton conductivity (S m1) 5 water content 5 gaseous density (kg m3) 5 electronic conductivity (S m1) 5 viscous stress tensor
Superscripts eff m ref sat v
5 effective value 5 membrane 5 reference value 5 saturation value 5 vapor phase
Subscripts 0 bpp e i n–f nf m s sat vi w lnf
5 boundary value 5 bipolar plate 5 electrolyte or energy 5 species 5 non-frozen membrane water content to frozen water content 5 non-frozen membrane water content 5 membrane 5 electron or solid phase 5 maximum allowable non-frozen membrane water content 5 water vapor to ice phase 5 water 5 non-frozen membrane water content
ACKNOWLEDGEMENTS This research work was financially supported by the National Natural Science Foundation of China (No. 10972197). Int. J. Energy Res. 2011; 35:2–14 r 2010 John Wiley & Sons, Ltd. DOI: 10.1002/er
H . Meng and B. Ruan
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