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Numerical studies of cold-start phenomenon in PEM fuel cells
Electrochimica Acta 53 (2008) 6521–6529
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Numerical studies of cold-start phenomenon in PEM fuel cells Hua Meng ∗ Center for Engineering and Scientific Computation, School of Aeronautics and Astronautics, P.O. Box 1455, Zhejiang University, Hangzhou, Zhejiang 310027, PR China
a r t i c l e
i n f o
Article history: Received 18 February 2008 Received in revised form 2 April 2008 Accepted 15 April 2008 Available online 22 April 2008 Keywords: Cold start Subfreezing temperature Ice formation Mixed-domain model Constant current density Constant cell voltage
a b s t r a c t In this paper, a PEM fuel cell model for cold-start simulations has been employed for numerical investigations of the cell startup characteristics from subfreezing temperatures. The effects of many key parameters on fuel cell isothermal cold-start behaviors have been carefully examined. Numerical results indicate that a high gas flow rate in the cathode gas channel, a low initial membrane water content, a low current density under the constant current condition, and a high cell voltage under the constant cell voltage operation are beneficial for the PEM fuel cell isothermal cold-start processes. Increasing the startup cell temperature would significantly delay ice formation and consequently lead to longer cold-start time. Therefore, incorporating internal and external heating sources in the cell design scheme is very important for achieving fast and successful cold start of a PEM fuel cell from subfreezing temperatures. © 2008 Elsevier Ltd. All rights reserved.
1. Introduction Successful startup of a PEM fuel cell from subfreezing temperatures is a crucial research issue for automotive applications. During the cold-start process, water inside the fuel cell, both retained after the previous cell operation and produced during the present operation, would freeze under a subzero temperature. The ice could subsequently melt if the cell temperature would rise above 0 ◦ C. This freeze/thaw cycle could compromise the fuel cell performance, material and component integrity. In order to fully understand this important phenomenon, much research effort has recently been expended in this area. The existing experimental researches on the PEM fuel cell cold-start phenomenon have been conducted from different perspectives. McDonald et al. [1] focused on the physical and chemical changes in the membrane and the membrane-electrode assembly (MEA) after repetitive freeze/thaw thermal cycling between 80 and −40 ◦ C, and no catastrophic failures were observed in the membranes and MEA, which were assembled in the fuel cell stack under ambient humidity conditions. Cho et al. [2] studied the cell performance degradation after repetitive thermal cycling from 80 to −10 ◦ C, and found that the cell performance could decrease at a rate of 2.3% due to water freezing and melting. To prevent cell performance loss, they [3] proposed the gas-purging and solutionpurging methods, which effectively eliminated cell performance
∗ Tel.: +86 571 87952990; fax: +86 571 87953167. E-mail address: [email protected]. 0013-4686/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2008.04.044
degradation. The research work of Hou et al. [4] investigated the effectiveness of the purging method with low-humidity gases fed into a PEM fuel cell. Instead of focusing on the thermal cycling effects, Kagami et al. [5] directly studied PEM fuel cell cold-start processes from subfreezing temperatures under constant current densities. They found that a successful self-starting without external heating could only be achieved with the startup temperature above −5 ◦ C. This conclusion is consistent with that of Yan et al. [6], who investigated cold-start processes using a PEM fuel cell with a 25 cm2 active area. In order to elucidate the fundamental cold-start characteristics, Oszcipok et al. [7] conducted isothermal potentiostatic single-cell experiments, during which the fuel cell was purged using dry gases and placed inside a constant-temperature environment at −10 ◦ C. They performed statistic analysis of the experimental results and showed that dry membrane and high air flow rates were beneficial for PEM fuel cell cold start. They also concluded that during the cell operation, the product water first increased the membrane humidity; after the membrane was fully hydrated, the product water started to freeze. They [8] further established a simple physical model to aid better understanding of the cold-start processes and the related fundamental mechanisms. Tajiri et al. [9] introduced an experimental procedure of equilibrium purging using partially humidified gases with well-controlled relative humidity to effectively dictate the initial water distribution inside a PEM fuel cell. Based on this method, they studied isothermal cold-start processes under a constant current density from a subzero temperature of −30 ◦ C. They concluded that the membrane played a key role in enhancing the intrinsic capability of PEM fuel
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cell cold start. Tajiri et al. [10] also experimentally investigated the parametric effects on PEM fuel cell cold start, including the purging methods, startup temperatures, current densities, and membrane thicknesses. Aiming to visualize the ice formation mechanisms in a PEM fuel cell during startup from subfreezing temperatures, Ge and Wang [11] developed a transparent cell with a silver mesh used as the cathode gas diffusion layer (GDL) for direct observation of ice formation on the catalyst layer surface. They found that with a startup temperature at −5 ◦ C, water existed in the cathode catalyst layer in gaseous and solid phases, and concluded that the freezing-point depression of water is no larger than 2 ◦ C and thus played a negligible role in cell cold-start applications. Ge and Wang [12] further studied the fundamental characteristics during PEM fuel cell coldstart processes. In addition to narrow down the freezing-point depression of water in the cathode catalyst layer to 1.0 ± 0.5 ◦ C, they suggested that the gas-purging time should be between 90 and 120 s. Ishikawa et al. [13] also observed water generation and freezing phenomena with both visible and infrared images during PEM fuel cell cold start at −10 ◦ C. In contrast to Ge and Wang [11,12], they reported that water generated below the freezing point was in a super-cooled state. Ishikawa et al. [14] made further studies in this area and recently found that the super-cooled liquid water would not exist if the fuel cell was not thoroughly purged, leaving a small amount of liquid water inside the cell before cold start. The remaining liquid water would freeze and serve as seed ice to initiate the ice formation process of the product water during the cell cold start. Therefore, the super-cooled liquid water could only exist with thorough purging of the cell before its cold-start, removing all the liquid water and consequently the potential seed ice. Even with the existence of the super-cooled liquid water, the cell performance degradation was still dictated by the ice formation at the GDL/MEA interface during the cell cold start. More research work is still needed in this area to further clarify this issue. Thompson et al. [15] investigated low-temperature proton transport inside the Nafion membrane. They observed a crossover in the activation energy for proton transport with temperature coinciding with water phase transition, and concluded that water phase transition inside the membrane would affect proton transport mechanisms. Their results contradicted those of Tajiri et al. [9], who concluded that no water phase transition occurred inside the membrane. Therefore, more research work is apparently required in this area, as well. Thompson et al. [16] also developed an experimental procedure to study the electrochemical kinetics of the oxygen reduction reaction (ORR) in a PEM fuel cell operating at subfreezing temperatures, and they found no fundamental change in reaction mechanism. In parallel to experimental studies, numerical modeling and simulation of the PEM fuel cell cold-start phenomenon has also been conducted. Mao and Wang [17] and Wang [18] both developed analytic models to gain fundamental understandings of the coldstart behaviors of PEM fuel cells, and they investigated the effects of a number of key parameters, including the initial membrane water content and the startup temperature, on the cell cold-start processes. Ahluwalia and Wang [19] developed a two-dimensional model, considering the through-membrane and along-channel directions, to determine the electric field, current distribution, species concentration, and ice formation and melting in a PEM fuel cell starting up from subfreezing temperatures. They made parametric studies to determine optimized conditions for achieving rapid self-start. Mao and Wang [20] developed a three-dimensional PEM fuel cell model based on a single-domain framework, considering ice formation in the cathode catalyst layer and GDL. They applied the numerical model for predicting cell performance and revealing
three-dimensional distributions of current density, temperature, membrane water content, and ice fraction in a PEM fuel cell undergoing isothermal cold start. Meng [21] recently 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 [22–25], which has been used for solving two-phase transient phenomena. The numerical model has been applied for elucidating fuel cell isothermal cold-start processes at a subfreezing temperature of −20 ◦ C under both constant current and constant cell voltage conditions. Numerical results indicated that the cold-start process of a PEM fuel cell with an initial low water content inside the membrane would experience a two-stage evolution, including an initial cell performance increase attributable to membrane hydration by the product water and an subsequent performance drop due to ice formation in the cathode catalyst layer, which would block oxygen transport and cover up the active catalyst surface. The trend is consistent with the experimental results of Oszcipok et al. [7,8] and Tajiri et al. [9,10]. In this paper, the PEM fuel cell model for cold-start simulations developed by Meng [21] are applied in a two-dimensional cross section for parametric studies of the isothermal cold-start phenomenon, focusing on the effects of many key parameters, including the initial membrane water content, the air flow rate in the cathode gas channel, the startup temperature, the current density, and the cell voltage, on the startup processes and the related intrinsic mechanisms. 2. Theoretical formulation The transient multi-phase multi-dimensional PEM fuel cell model for cold-start simulations have been presented in an earlier publication [21], and thus are only briefly described in this paper. The transient conservation equations in the gaseous phase are Mass conservation: ∂[ε(1 − sice )] ) = Sm + ∇ · (u ∂t
(1)
Momentum conservation: ) ∂(u 1 1 + ∇ (u u ) = −∇p + ∇ · + Su ε(1 − sice ) ∂t ε2 (1 − sice )2
(2)
Species conservation: ∂[εeff (1 − sice )ci ] ci ) = ∇ · (Dieff ∇ci ) + Si + ∇ · (u ∂t
(3)
In Eq. (1), the source term, Sm , arises from the coupling of the flow-field and the species transport processes, including the phase-change effect, and the details have been discussed in a previous publication [23]. It should be noted that in the present two-dimensional calculations, since the convective effect can be neglected, this mass source term would not exert any influence on the numerical results. The above equations are established in a mixed-domain framework [22–25]. The effect of ice formation on the effective gaseous species diffusion is considered by the following expression: Dieff = Di ε1.5 (1 − sice )1.5
(4)
In addition, ice coverage of the active catalyst surface is modeled as aeff = (1 − sice )a
(5)
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Table 1 Electrochemical and physical relationships Description
Expression
1/2
˛a + ˛c ·F · RT ˛c ref j = aeff j0,c ·F · exp − RT cO2 ,ref in anode side = s − e = s − e − U0 in cathode side 1.23 − 0.9 × 10−3 (T − 298) U0 = 1.0 for ≤ 14 nd = 1.5/8( − 14) + 1.0 otherwise ref j = aeff j0,a
Transfer current density [29] (A/m3 )
Over potential (V) [29,30] Open-circuit potential (V) [26,30] Electro-osmotic drag coefficient [30]
cH2
cHc2 ,ref O2
in anode side in cathode side
C w Ru T psat
Water activity
a=
Water saturation pressure (atm) [29] Partial pressure of water vapor (Pa)
log10 psat = −2.1794 + 0.02953(T − 273.15) − 9.1837 × 10−5 (T − 273.15)2 + 1.4454 × 10−7 (T − 273.15)3 pv = C w Ru T 3.1 × 10−7 (e0.28 − 1) · e[−2346/T ] 0<≤3 m = Dw 4.17 × 10−8 (1 + 161e− ) · e[−2346/T ] otherwise m m D = EW Dw
Membrane water diffusivity (m2 /s) [30] Water content diffusivity (mol m−1 s−1 )
= (0.5139 − 0.326) exp 1268
Proton conductivity (S/m) [29,30]
where the effective surface area, aeff , is related to the electrochemical kinetics. A transient conservation equation of the ice phase, which is formed by direct water vapor desublimation, is derived as ∂(εice sice ) = Svi Ww ∂t
(6)
where the parameter, sice , is the ice fraction, defined as the ratio of the volume of ice to the pore volume in the porous materials sice =
Vice Vp
(7)
The volumetric desublimation rate in Eq. (6), Svi , is expressed in the following form: Svi = hpc (pv − psat )
(8)
where the desublimation parameter is defined as hpc
kc ε(1 − sice )xv = 2Ru T
|pv − psat | 1+ v p − psat
(9)
More details concerning these expressions can be found in reference [21]. A transient water content conservation equation is solved inside the membrane ∂ ∂t
m EW
= ∇ · (D ∇) + S
(10)
A transient conservation equation of energy is provided in the following form: ∂ T ) = ∇ · (keff ∇T ) + ST [(Cp )eff T ] + ∇ · (Cp u ∂t
(11)
where the source term considering the heat of desublimation can be derived as [21,26]
ST = j + T
dU0 dT
+
i2 + hvi Ww Svi cond
(12)
The conservation equations of proton and electron transport are solved in the following steady-state form because of rapid electric charging/discharging processes [27,28]: Proton transport:
∇ ( eff ∇e ) + Se = 0
(13)
Electron transport:
∇ ( eff ∇s ) + Ss = 0
(14)
1 303
−
1 T
The relevant expressions for the electrochemical and physical relationships are listed in Table 1. The source terms and definitions of boundary conditions can be found in the earlier publications [21,24]. The physicochemical parameters employed for the present numerical studies are provided in Table 2. The temperature effect on physicochemical and transport parameters has been considered in the present numerical model, but it is noteworthy that because of the lack of sufficient experimental data and also existing uncertainties in the experimental studies, some of the expressions could be further improved specifically for cold-start simulations. They are, however, sufficient for the present qualitative parametric studies. In the present numerical model, the influence of the possible super-cooled liquid water during the cold-start process is neglected but could be incorporated once the issue is finally clarified. This PEM fuel cell model for cold-start simulations has been applied in a two-dimensional cross section, as shown in Fig. 1, for parametric studies of the isothermal cold-start phenomenon under both constant current and constant cell voltage conditions, focusing on the effects of many key parameters on the startup processes and the related intrinsic mechanisms. Table 2 Physicochemical parameters Anode volumetric exchange current density, aj0 (A/m3 ) [30] Cathode volumetric exchange current density, aj0 (A/m3 ) [30] Reference hydrogen concentration, CH2 (mol/m3 ) [30] Reference oxygen concentration, CO2 (mol/m3 ) [30] Anode transfer coefficients [30] Cathode transfer coefficient [30] Faraday constant, F (C/mol) GDL porosity Porosity of catalyst layer Volume fraction of ionomer in catalyst layer GDL permeability (m2 ) Catalyst layer permeability (m2 ) Equivalent weight of ionomer (kg/mol) [30] Dry membrane density (kg/m3 ) [30] Effective electronic conductivity in CL/GDL (S/m) [30] Operation pressure (atm) Desublimation rate coefficient (s−1 ) Thermal conductivity of GDL (W m−1 K−1 ) [26] Thermal conductivity of CL (W m−1 K−1 ) [26] Thermal conductivity of the membrane (W m−1 K−1 ) [26] Enthalpy of desublimation (J/kg) [21] Density of carbon material (kg m−3 ) [28] Density of ice (kg m−3 ) [21] Heat capacity of carbon material (J kg−1 K−1 ) [28] Heat capacity of membrane material (J kg−1 K−1 ) [28] Heat capacity of ice (J kg−1 K−1 ) [21]
1.0E+9 1.0E+4 40 40 ˛a = ˛c = 1 ˛c = 1 96,487 0.6 0.2 0.4 1.0E−12 1.0E−13 1.1 1980 5000 2 3.0E+7 1.5 1.5 0.5 2.64E+6 2200 900 1050 1050 2100
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Fig. 1. A two-dimensional cross section of a PEM fuel cell.
Fig. 2. Time evolution of cell voltage with different water vapor concentrations defined at boundary 2.
3. Result and discussion The cell geometry and the geometric parameters for the present numerical studies are provided in Fig. 1 and Table 3, respectively. Unless otherwise stated, the PEM fuel cell is operated at 2 atm on both the anode and cathode sides; the cell stoichiometry number is two on both sides with a reference current density at 50 mA/cm2 . Present studies simulate isothermal cold-start phenomena by fixing the cell boundary temperature. The initial water content in the membrane is controlled by equilibrium gas-purging and is assumed to be uniformly distributed. The initial ice fraction inside the cell is neglected in the present numerical studies. Dry hydrogen and dry air are fed into the anode and cathode side, respectively. The numerical model applied in the present numerical studies has been previously developed for elucidating the isothermal cold-start mechanisms of a PEM fuel cell at a constant boundary temperature of −20 ◦ C [21]. Numerical results from the previous calculations showed consistent trend with the experimental data, i.e. the two-stage evolution of the cell performance under both constant current and constant cell voltage conditions. Detailed discussions could be found in reference [21]. The numerical model has been employed in this paper for extensive parametric studies to gain fundamental understandings of the roles played by many key parameters on fuel cell cold-start characteristics. These important parameters include the water vapor concentration in the cathode gas channel, which is closely related to the air flow rate, the initial membrane water content, the startup temperature or boundary temperature, the current density under a constant current condition, and the cell voltage under a constant cell voltage condition.
3.1. Effect of water vapor concentration in the cathode gas channel In the present numerical model, based on the experimental observations of Ge et al. [11,12], ice is assumed to form by desublimation directly from water vapor in the cathode catalyst layer. Since the water vapor concentration at boundary 2, an interface between the GDL and gas channel on the cathode side, influences the water vapor distribution inside the catalyst layer, it would affect ice precipitation and growth inside the fuel cell. The effect of the water vapor concentration in the cathode gas channel on ice formation and cell performance is investigated by specifying different water vapor concentrations at boundary 2, which could represent different downstream locations along the flow direction as the water vapor concentration increases in this direction or different air flow rates in the gas channel as high gas flow in the channel reduces the overall water vapor concentration, especially in the section close to the cathode inlet. Under a constant current density at 50 mA/cm2 and a constant cell boundary temperature of −20 ◦ C, numerical calculations are conducted with two different water vapor concentrations of
Table 3 Cell geometric parameters Fuel cell geometry (mm) Layer thickness Diffusion Catalyst Membrane Land width Channel width Computational cell numbers
0.3 0.01 0.025 0.5 1.0 ∼1600
Fig. 3. Time evolution of cell voltage under different relative humidity of the purging gas.
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Fig. 4. Time evolution of ice fraction in the cathode catalyst layer: (a) with the purging gas relative humidity at 0.5, and (b) with the purging gas relative humidity at 0.75.
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0.074 and 0.033 mol/m3 at boundary 2, representing 100% relative humidity and 45% relative humidity in the cathode gas channel, respectively. The fuel cell is purged to an equilibrium condition using a dry gas with 25% relative humidity on both the anode and cathode sides prior to its cold start. Transient variations of the cell voltage are shown in Fig. 2. Both curves in Fig. 2 clearly show two-stage evolutions, namely an initial voltage recovery period owing to the membrane hydration by the product water, and an voltage drop-down period caused by ice formation and its subsequent blockage of oxygen transport and coverage of the active catalyst surface. This trend is consistent with the experimental observation of Tajiri et al. [9,10]. With a higher water vapor concentration, i.e. 0.074 mol/m3 , specified at boundary 2, the fuel cell cold-start operation shuts down sooner at around 200 s, since in this case the water vapor concentration inside the cathode catalyst layer and GDL reaches its saturation value and start to freeze earlier. This result clearly indicates that high gas flow rates on the cathode side could increase the fuel cell operation time and benefit the cold-start process, a conclusion consistent with the experimental result of Oszcipok et al. [7]. More detailed discussion concerning this issue could be found in an earlier publication [21].
Fig. 5. Transient variation of water content in the middle of the membrane: (a) with the purging gas relative humidity at 0.5, and (b) with the purging gas relative humidity at 0.75.
3.2. Effect of initial membrane water content The initial water content inside the membrane could be wellcontrolled by the relative humidity of the purging gas prior to the cell startup using an equilibrium purging method discussed by Tajiri et al. [9]. The initial membrane water content or the relative humidity of the purging gas significantly affects the cold-start characteristics of a PEM fuel cell, as clearly illustrated in Fig. 3, in which the relative humidity of the purging gas at 0.25, 0.5, and 0.75 corresponds to the initial membrane water content at 2.57, 3.49, and 6.17, respectively. Numerical calculations are performed under a subfreezing boundary temperature of −20 ◦ C and a constant operating current density at 50 mA/cm2 . For all the three cases, the water vapor concentration inside the cathode gas channel and defined at the boundary 2 are at a fully humidified value at −20 ◦ C, i.e. 0.074 mol/m3 . Results in Fig. 3 indicate that with a higher initial membrane water content, the cell shows a better performance once started, as expected, but the cell operation also shuts down sooner. The two curves corresponding to the relative humidity of the purging gas at 0.25 and 0.5 clearly show two-stage evolutions, a phenomenon discussed in detail in the preceding section. The third curve corresponding to a relative humidity of the purging gas at 0.75 also shows a two-stage evolution, but the first stage of performance increase becomes very short, around 25 s, and the cell performance only increases slightly. After an initial short period, the third curve starts to move slowly downslope due to ice precipitation, as illustrated in Fig. 4b. As explained in the earlier publications [7,20,21], the membrane plays a crucial role for a PEM fuel cell cold-start process. A drier membrane would initially absorb more water produced during the cell operation, thus delaying the ice precipitation in the cathode catalyst layer. The time evolutions of the ice formation in the cathode catalyst layer are illustrated in Fig. 4 for the two cases corresponding to the relative humidity of the purging gas at 0.5 and 0.75. The pictures corresponding to the third case, with a lower initial membrane water content or relative humidity of the purging gas, was provided in an earlier publication [21]. These figures clearly indicate that with a higher initial membrane water content, ice precipitation inside the cell starts sooner. In addition, ice grows faster under the current-collecting land and at the interface between the catalyst layer and GDL.
Fig. 6. Time evolution of cell voltage under different cell boundary temperatures.
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Fig. 7. Time evolution of ice fraction in the cathode catalyst layer under a cell boundary temperature of −10 ◦ C.
Transient variations of the water content in the middle of the membrane for the two cases corresponding to the relative humidity of the purging gas at 0.5 and 0.75 are shown in Fig. 5. Again, the figure for the third case was provided earlier [21]. The water content inside the membrane initially distributes uniformly in the lateral direction, and it increases continuously during the entire cold-start process. However, the increasing rate becomes slower as time elapses, indicating that less water is absorbed in the membrane and more water becomes frozen. The water content inside the membrane shows higher value directly under the currentcollecting land since the water vapor concentration is higher in this region. 3.3. Effect of startup cell temperature The effect of the startup cell temperature on PEM fuel cell cold start is numerically investigated by defining different boundary temperatures at the boundaries 3 and 4. Again, numerical calculations are performed under a constant operating current density at 50 mA/cm2 . It is noteworthy that for the present calculations, the water vapor inside the cathode gas channel is defined to be fully humidified, with different concentrations corresponding to different startup cell temperatures. In fact, unless otherwise stated, the numerical studies performed in the following sections in this paper are all under the fully humidified water vapor condition at boundary 2. As discussed in an earlier publication [21], the temperature inside the fuel cell increases only slightly from the boundary temperature, i.e. less than 0.2 ◦ C, and therefore the boundary temperature could be considered as the startup cell temperature, leading to essentially an isothermal cold-start process. As shown in Fig. 6, with a higher startup cell temperature, the cell performs much better, since the electrochemical kinetics and ionic
conductivity inside the membrane increase with an increasing cell temperature. Furthermore, with a higher startup cell temperature, the cold-start time could be significantly prolonged, because the saturation water vapor concentration increases with an increasing cell temperature and ice precipitation only starts after the water vapor becomes saturated. Under a startup temperature of −5 ◦ C, the cold-start operation could last more than 500 s, still showing no noticeable performance deterioration. In fact, in this case, cell performance decreases at around 400 s, but the decreasing pace is very slow and thus negligible within 500 s. The ice distribution and evolution with a startup cell temperature of −10 ◦ C are displayed in Fig. 7. Comparing with the results at a startup cell temperature of −20 ◦ C presented earlier [21], it is clear that with a higher startup cell temperature, ice precipitation is significantly delayed. For example, ice starts to appear at around 50 s at a startup cell temperature of −20 ◦ C [21] while it only does so at around 150 s at −10 ◦ C. In addition, higher startup cell temperature influences the ice formation and distribution directly under the gas channel, resulting in very low and quite uniform ice fraction in this region before 250 s, as illustrated in Fig. 7. 3.4. Effect of current density Increasing the operating current would produce more water and drastically reduce the isothermal cold-start time of a PEM fuel cell, as indicated in Fig. 8. This figure shows that increasing the operating current density from 50 to 75 mA/cm2 decreases the cell voltage, as expected. In addition, under a relatively higher current density of 75 mA/cm2 , the initial rate of cell performance increase becomes much faster, and the transition stage between cell voltage increase and decrease disappears, resulting in a cold-start time just slightly longer than 100 s.
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Fig. 8. Time evolution of cell voltage under different operating current densities at a subfreezing boundary temperature of −20 ◦ C.
Fig. 10. Time evolution of current density under different operation cell voltages at a subfreezing boundary temperature of −20 ◦ C.
The time evolution of the water content distribution in the middle of the membrane under a constant current density of 75 mA/cm2 and a startup cell temperature at −20 ◦ C is presented in Fig. 9. As discussed in an earlier section, the water content inside the membrane increases continuously during the startup process owing to product water absorption, but the increasing rate slows down as time elapses. Under a relatively higher current density of 75 mA/cm2 , the membrane does not become as well hydrated as in the case under a lower current density of 50 mA/cm2 . At the end of the cold-start process, the highest water content in the middle of the membrane in Fig. 9 reaches less than 8 while it is close to 9.5 in the earlier case under a lower current density of 50 mA/cm2 [21]. 3.5. Effect of cell voltage Under a constant cell voltage conditions, decreasing the operating cell voltage of a PEM fuel cell would increase the output current density, as shown in Fig. 10. The result in this figure indicates that at a relatively low cell voltage of 0.5 V, the initial increase of the Fig. 11. Transient variation of water content in the middle of the membrane under a constant cell voltage of 0.5 V.
cell performance, or current density, becomes very rapid, i.e. the current density rising from around 75 to 130 mA/cm2 in 30 s. Since a higher current leads to more product water, ice starts to form in the cathode catalyst layer sooner and grows faster, causing a very sharp decrease of the cell performance in the second stage of the two-stage evolution of the cell performance. The PEM fuel cell shuts down its operation at around 60 s in this case. The time evolution and distribution of the water content in the middle of the membrane under a constant cell voltage of 0.5 V are presented in Fig. 11. Since the fuel cell shuts down its operation very quickly, there is no sufficient time for the membrane to become well hydrated, leaving the highest water content in the middle of the membrane at around 6 at the end of the cold-start process. 4. Conclusions
Fig. 9. Transient variation of water content in the middle of the membrane under a constant current density of 75 mA/cm2 .
In this paper, a previously established PEM fuel cell model for cold-start simulations has been employed for numerical investigations of the isothermal startup characteristics under subfreezing
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cell temperatures, focusing on the effects of many key parameters on cold-start mechanisms, including the water vapor concentration or the gas flow rate in the cathode gas channel, the initial membrane water content, the startup cell temperature, the current density under the constant current condition, and the cell voltage under the constant cell voltage condition. Based on the present parametric studies, the following conclusions can be summarized: - Increasing the gas flow rate in the cathode gas channel is beneficial for the cold-start process, since it would decrease the water vapor concentration inside the channel, which in turn influences water vapor distribution and thus ice precipitation and growth in the cathode catalyst layer. - An initial drier membrane would absorb more product water and therefore delay ice formation and consequently prolong the coldstart process. - Operating a PEM fuel cell under a lower current density or higher cell voltage would produce less water and consequently prolong the cold-start process. However, in practical applications, in order to achieve the fastest startup from a subfreezing temperature, the operation current or cell voltage should be optimized to generate the most amount of waste heat in a desired startup time. - Increasing the startup cell temperature would significantly delay ice formation, which would then lead to longer cold-start time. Therefore, various internal and external heating sources should be considered in the PEM fuel cell design scheme for successful cold-start processes.
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Greek letters ˚ phase potential (V) mole fraction ε porosity fraction of the membrane phase in the catalyst layer εm over-potential (V) proton conductivity (S/m) water content viscosity (kg m−1 s−1 ) gaseous density (kg/m3 )
electronic conductivity (S/m) viscous stress tensor Superscripts cl catalyst layer eff effective value sat saturation value v vapor phase Subscripts cl catalyst layer e electrolyte or energy i species m membrane s electron or solid phase sat saturation value vi water vapor to ice phase w water
Appendix A. Nomenclature
a c cond Cp D D EW F hvi i j k kc K nd p Ru sice S t T u U0 V Vcell W
water activity or surface area molar concentration (mol/m3 ) proton or electron conductivity (S/m) constant-pressure heat capacity (J kg−1 K−1 ) mass diffusivity (m2 /s) water content diffusivity (mol m−1 s−1 ) equivalent weight of the membrane (kg/mol) Faraday constant 96,487 C/mol enthalpy of desublimation (J/kg) current density (A/m2 ) transfer current density (A/m3 ) thermal conductivity (W m−1 K−1 ) desublimation rate coefficient (s−1 ) permeability (m2 ) electro-osmotic drag coefficient gas-phase pressure (Pa) universal gas constant (J mol−1 K−1 ) ice fraction source term time (s) temperature (K) gas-phase velocity (m/s) open-circuit potential (V) volume (m3 ) cell voltage (V) molecular weight (kg/mol)
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Electrochimica Acta journal homepage: www.elsevier.com/locate/electacta
Numerical studies of cold-start phenomenon in PEM fuel cells Hua Meng ∗ Center for Engineering and Scientific Computation, School of Aeronautics and Astronautics, P.O. Box 1455, Zhejiang University, Hangzhou, Zhejiang 310027, PR China
a r t i c l e
i n f o
Article history: Received 18 February 2008 Received in revised form 2 April 2008 Accepted 15 April 2008 Available online 22 April 2008 Keywords: Cold start Subfreezing temperature Ice formation Mixed-domain model Constant current density Constant cell voltage
a b s t r a c t In this paper, a PEM fuel cell model for cold-start simulations has been employed for numerical investigations of the cell startup characteristics from subfreezing temperatures. The effects of many key parameters on fuel cell isothermal cold-start behaviors have been carefully examined. Numerical results indicate that a high gas flow rate in the cathode gas channel, a low initial membrane water content, a low current density under the constant current condition, and a high cell voltage under the constant cell voltage operation are beneficial for the PEM fuel cell isothermal cold-start processes. Increasing the startup cell temperature would significantly delay ice formation and consequently lead to longer cold-start time. Therefore, incorporating internal and external heating sources in the cell design scheme is very important for achieving fast and successful cold start of a PEM fuel cell from subfreezing temperatures. © 2008 Elsevier Ltd. All rights reserved.
1. Introduction Successful startup of a PEM fuel cell from subfreezing temperatures is a crucial research issue for automotive applications. During the cold-start process, water inside the fuel cell, both retained after the previous cell operation and produced during the present operation, would freeze under a subzero temperature. The ice could subsequently melt if the cell temperature would rise above 0 ◦ C. This freeze/thaw cycle could compromise the fuel cell performance, material and component integrity. In order to fully understand this important phenomenon, much research effort has recently been expended in this area. The existing experimental researches on the PEM fuel cell cold-start phenomenon have been conducted from different perspectives. McDonald et al. [1] focused on the physical and chemical changes in the membrane and the membrane-electrode assembly (MEA) after repetitive freeze/thaw thermal cycling between 80 and −40 ◦ C, and no catastrophic failures were observed in the membranes and MEA, which were assembled in the fuel cell stack under ambient humidity conditions. Cho et al. [2] studied the cell performance degradation after repetitive thermal cycling from 80 to −10 ◦ C, and found that the cell performance could decrease at a rate of 2.3% due to water freezing and melting. To prevent cell performance loss, they [3] proposed the gas-purging and solutionpurging methods, which effectively eliminated cell performance
∗ Tel.: +86 571 87952990; fax: +86 571 87953167. E-mail address: [email protected]. 0013-4686/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2008.04.044
degradation. The research work of Hou et al. [4] investigated the effectiveness of the purging method with low-humidity gases fed into a PEM fuel cell. Instead of focusing on the thermal cycling effects, Kagami et al. [5] directly studied PEM fuel cell cold-start processes from subfreezing temperatures under constant current densities. They found that a successful self-starting without external heating could only be achieved with the startup temperature above −5 ◦ C. This conclusion is consistent with that of Yan et al. [6], who investigated cold-start processes using a PEM fuel cell with a 25 cm2 active area. In order to elucidate the fundamental cold-start characteristics, Oszcipok et al. [7] conducted isothermal potentiostatic single-cell experiments, during which the fuel cell was purged using dry gases and placed inside a constant-temperature environment at −10 ◦ C. They performed statistic analysis of the experimental results and showed that dry membrane and high air flow rates were beneficial for PEM fuel cell cold start. They also concluded that during the cell operation, the product water first increased the membrane humidity; after the membrane was fully hydrated, the product water started to freeze. They [8] further established a simple physical model to aid better understanding of the cold-start processes and the related fundamental mechanisms. Tajiri et al. [9] introduced an experimental procedure of equilibrium purging using partially humidified gases with well-controlled relative humidity to effectively dictate the initial water distribution inside a PEM fuel cell. Based on this method, they studied isothermal cold-start processes under a constant current density from a subzero temperature of −30 ◦ C. They concluded that the membrane played a key role in enhancing the intrinsic capability of PEM fuel
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cell cold start. Tajiri et al. [10] also experimentally investigated the parametric effects on PEM fuel cell cold start, including the purging methods, startup temperatures, current densities, and membrane thicknesses. Aiming to visualize the ice formation mechanisms in a PEM fuel cell during startup from subfreezing temperatures, Ge and Wang [11] developed a transparent cell with a silver mesh used as the cathode gas diffusion layer (GDL) for direct observation of ice formation on the catalyst layer surface. They found that with a startup temperature at −5 ◦ C, water existed in the cathode catalyst layer in gaseous and solid phases, and concluded that the freezing-point depression of water is no larger than 2 ◦ C and thus played a negligible role in cell cold-start applications. Ge and Wang [12] further studied the fundamental characteristics during PEM fuel cell coldstart processes. In addition to narrow down the freezing-point depression of water in the cathode catalyst layer to 1.0 ± 0.5 ◦ C, they suggested that the gas-purging time should be between 90 and 120 s. Ishikawa et al. [13] also observed water generation and freezing phenomena with both visible and infrared images during PEM fuel cell cold start at −10 ◦ C. In contrast to Ge and Wang [11,12], they reported that water generated below the freezing point was in a super-cooled state. Ishikawa et al. [14] made further studies in this area and recently found that the super-cooled liquid water would not exist if the fuel cell was not thoroughly purged, leaving a small amount of liquid water inside the cell before cold start. The remaining liquid water would freeze and serve as seed ice to initiate the ice formation process of the product water during the cell cold start. Therefore, the super-cooled liquid water could only exist with thorough purging of the cell before its cold-start, removing all the liquid water and consequently the potential seed ice. Even with the existence of the super-cooled liquid water, the cell performance degradation was still dictated by the ice formation at the GDL/MEA interface during the cell cold start. More research work is still needed in this area to further clarify this issue. Thompson et al. [15] investigated low-temperature proton transport inside the Nafion membrane. They observed a crossover in the activation energy for proton transport with temperature coinciding with water phase transition, and concluded that water phase transition inside the membrane would affect proton transport mechanisms. Their results contradicted those of Tajiri et al. [9], who concluded that no water phase transition occurred inside the membrane. Therefore, more research work is apparently required in this area, as well. Thompson et al. [16] also developed an experimental procedure to study the electrochemical kinetics of the oxygen reduction reaction (ORR) in a PEM fuel cell operating at subfreezing temperatures, and they found no fundamental change in reaction mechanism. In parallel to experimental studies, numerical modeling and simulation of the PEM fuel cell cold-start phenomenon has also been conducted. Mao and Wang [17] and Wang [18] both developed analytic models to gain fundamental understandings of the coldstart behaviors of PEM fuel cells, and they investigated the effects of a number of key parameters, including the initial membrane water content and the startup temperature, on the cell cold-start processes. Ahluwalia and Wang [19] developed a two-dimensional model, considering the through-membrane and along-channel directions, to determine the electric field, current distribution, species concentration, and ice formation and melting in a PEM fuel cell starting up from subfreezing temperatures. They made parametric studies to determine optimized conditions for achieving rapid self-start. Mao and Wang [20] developed a three-dimensional PEM fuel cell model based on a single-domain framework, considering ice formation in the cathode catalyst layer and GDL. They applied the numerical model for predicting cell performance and revealing
three-dimensional distributions of current density, temperature, membrane water content, and ice fraction in a PEM fuel cell undergoing isothermal cold start. Meng [21] recently 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 [22–25], which has been used for solving two-phase transient phenomena. The numerical model has been applied for elucidating fuel cell isothermal cold-start processes at a subfreezing temperature of −20 ◦ C under both constant current and constant cell voltage conditions. Numerical results indicated that the cold-start process of a PEM fuel cell with an initial low water content inside the membrane would experience a two-stage evolution, including an initial cell performance increase attributable to membrane hydration by the product water and an subsequent performance drop due to ice formation in the cathode catalyst layer, which would block oxygen transport and cover up the active catalyst surface. The trend is consistent with the experimental results of Oszcipok et al. [7,8] and Tajiri et al. [9,10]. In this paper, the PEM fuel cell model for cold-start simulations developed by Meng [21] are applied in a two-dimensional cross section for parametric studies of the isothermal cold-start phenomenon, focusing on the effects of many key parameters, including the initial membrane water content, the air flow rate in the cathode gas channel, the startup temperature, the current density, and the cell voltage, on the startup processes and the related intrinsic mechanisms. 2. Theoretical formulation The transient multi-phase multi-dimensional PEM fuel cell model for cold-start simulations have been presented in an earlier publication [21], and thus are only briefly described in this paper. The transient conservation equations in the gaseous phase are Mass conservation: ∂[ε(1 − sice )] ) = Sm + ∇ · (u ∂t
(1)
Momentum conservation: ) ∂(u 1 1 + ∇ (u u ) = −∇p + ∇ · + Su ε(1 − sice ) ∂t ε2 (1 − sice )2
(2)
Species conservation: ∂[εeff (1 − sice )ci ] ci ) = ∇ · (Dieff ∇ci ) + Si + ∇ · (u ∂t
(3)
In Eq. (1), the source term, Sm , arises from the coupling of the flow-field and the species transport processes, including the phase-change effect, and the details have been discussed in a previous publication [23]. It should be noted that in the present two-dimensional calculations, since the convective effect can be neglected, this mass source term would not exert any influence on the numerical results. The above equations are established in a mixed-domain framework [22–25]. The effect of ice formation on the effective gaseous species diffusion is considered by the following expression: Dieff = Di ε1.5 (1 − sice )1.5
(4)
In addition, ice coverage of the active catalyst surface is modeled as aeff = (1 − sice )a
(5)
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Table 1 Electrochemical and physical relationships Description
Expression
1/2
˛a + ˛c ·F · RT ˛c ref j = aeff j0,c ·F · exp − RT cO2 ,ref in anode side = s − e = s − e − U0 in cathode side 1.23 − 0.9 × 10−3 (T − 298) U0 = 1.0 for ≤ 14 nd = 1.5/8( − 14) + 1.0 otherwise ref j = aeff j0,a
Transfer current density [29] (A/m3 )
Over potential (V) [29,30] Open-circuit potential (V) [26,30] Electro-osmotic drag coefficient [30]
cH2
cHc2 ,ref O2
in anode side in cathode side
C w Ru T psat
Water activity
a=
Water saturation pressure (atm) [29] Partial pressure of water vapor (Pa)
log10 psat = −2.1794 + 0.02953(T − 273.15) − 9.1837 × 10−5 (T − 273.15)2 + 1.4454 × 10−7 (T − 273.15)3 pv = C w Ru T 3.1 × 10−7 (e0.28 − 1) · e[−2346/T ] 0<≤3 m = Dw 4.17 × 10−8 (1 + 161e− ) · e[−2346/T ] otherwise m m D = EW Dw
Membrane water diffusivity (m2 /s) [30] Water content diffusivity (mol m−1 s−1 )
= (0.5139 − 0.326) exp 1268
Proton conductivity (S/m) [29,30]
where the effective surface area, aeff , is related to the electrochemical kinetics. A transient conservation equation of the ice phase, which is formed by direct water vapor desublimation, is derived as ∂(εice sice ) = Svi Ww ∂t
(6)
where the parameter, sice , is the ice fraction, defined as the ratio of the volume of ice to the pore volume in the porous materials sice =
Vice Vp
(7)
The volumetric desublimation rate in Eq. (6), Svi , is expressed in the following form: Svi = hpc (pv − psat )
(8)
where the desublimation parameter is defined as hpc
kc ε(1 − sice )xv = 2Ru T
|pv − psat | 1+ v p − psat
(9)
More details concerning these expressions can be found in reference [21]. A transient water content conservation equation is solved inside the membrane ∂ ∂t
m EW
= ∇ · (D ∇) + S
(10)
A transient conservation equation of energy is provided in the following form: ∂ T ) = ∇ · (keff ∇T ) + ST [(Cp )eff T ] + ∇ · (Cp u ∂t
(11)
where the source term considering the heat of desublimation can be derived as [21,26]
ST = j + T
dU0 dT
+
i2 + hvi Ww Svi cond
(12)
The conservation equations of proton and electron transport are solved in the following steady-state form because of rapid electric charging/discharging processes [27,28]: Proton transport:
∇ ( eff ∇e ) + Se = 0
(13)
Electron transport:
∇ ( eff ∇s ) + Ss = 0
(14)
1 303
−
1 T
The relevant expressions for the electrochemical and physical relationships are listed in Table 1. The source terms and definitions of boundary conditions can be found in the earlier publications [21,24]. The physicochemical parameters employed for the present numerical studies are provided in Table 2. The temperature effect on physicochemical and transport parameters has been considered in the present numerical model, but it is noteworthy that because of the lack of sufficient experimental data and also existing uncertainties in the experimental studies, some of the expressions could be further improved specifically for cold-start simulations. They are, however, sufficient for the present qualitative parametric studies. In the present numerical model, the influence of the possible super-cooled liquid water during the cold-start process is neglected but could be incorporated once the issue is finally clarified. This PEM fuel cell model for cold-start simulations has been applied in a two-dimensional cross section, as shown in Fig. 1, for parametric studies of the isothermal cold-start phenomenon under both constant current and constant cell voltage conditions, focusing on the effects of many key parameters on the startup processes and the related intrinsic mechanisms. Table 2 Physicochemical parameters Anode volumetric exchange current density, aj0 (A/m3 ) [30] Cathode volumetric exchange current density, aj0 (A/m3 ) [30] Reference hydrogen concentration, CH2 (mol/m3 ) [30] Reference oxygen concentration, CO2 (mol/m3 ) [30] Anode transfer coefficients [30] Cathode transfer coefficient [30] Faraday constant, F (C/mol) GDL porosity Porosity of catalyst layer Volume fraction of ionomer in catalyst layer GDL permeability (m2 ) Catalyst layer permeability (m2 ) Equivalent weight of ionomer (kg/mol) [30] Dry membrane density (kg/m3 ) [30] Effective electronic conductivity in CL/GDL (S/m) [30] Operation pressure (atm) Desublimation rate coefficient (s−1 ) Thermal conductivity of GDL (W m−1 K−1 ) [26] Thermal conductivity of CL (W m−1 K−1 ) [26] Thermal conductivity of the membrane (W m−1 K−1 ) [26] Enthalpy of desublimation (J/kg) [21] Density of carbon material (kg m−3 ) [28] Density of ice (kg m−3 ) [21] Heat capacity of carbon material (J kg−1 K−1 ) [28] Heat capacity of membrane material (J kg−1 K−1 ) [28] Heat capacity of ice (J kg−1 K−1 ) [21]
1.0E+9 1.0E+4 40 40 ˛a = ˛c = 1 ˛c = 1 96,487 0.6 0.2 0.4 1.0E−12 1.0E−13 1.1 1980 5000 2 3.0E+7 1.5 1.5 0.5 2.64E+6 2200 900 1050 1050 2100
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Fig. 1. A two-dimensional cross section of a PEM fuel cell.
Fig. 2. Time evolution of cell voltage with different water vapor concentrations defined at boundary 2.
3. Result and discussion The cell geometry and the geometric parameters for the present numerical studies are provided in Fig. 1 and Table 3, respectively. Unless otherwise stated, the PEM fuel cell is operated at 2 atm on both the anode and cathode sides; the cell stoichiometry number is two on both sides with a reference current density at 50 mA/cm2 . Present studies simulate isothermal cold-start phenomena by fixing the cell boundary temperature. The initial water content in the membrane is controlled by equilibrium gas-purging and is assumed to be uniformly distributed. The initial ice fraction inside the cell is neglected in the present numerical studies. Dry hydrogen and dry air are fed into the anode and cathode side, respectively. The numerical model applied in the present numerical studies has been previously developed for elucidating the isothermal cold-start mechanisms of a PEM fuel cell at a constant boundary temperature of −20 ◦ C [21]. Numerical results from the previous calculations showed consistent trend with the experimental data, i.e. the two-stage evolution of the cell performance under both constant current and constant cell voltage conditions. Detailed discussions could be found in reference [21]. The numerical model has been employed in this paper for extensive parametric studies to gain fundamental understandings of the roles played by many key parameters on fuel cell cold-start characteristics. These important parameters include the water vapor concentration in the cathode gas channel, which is closely related to the air flow rate, the initial membrane water content, the startup temperature or boundary temperature, the current density under a constant current condition, and the cell voltage under a constant cell voltage condition.
3.1. Effect of water vapor concentration in the cathode gas channel In the present numerical model, based on the experimental observations of Ge et al. [11,12], ice is assumed to form by desublimation directly from water vapor in the cathode catalyst layer. Since the water vapor concentration at boundary 2, an interface between the GDL and gas channel on the cathode side, influences the water vapor distribution inside the catalyst layer, it would affect ice precipitation and growth inside the fuel cell. The effect of the water vapor concentration in the cathode gas channel on ice formation and cell performance is investigated by specifying different water vapor concentrations at boundary 2, which could represent different downstream locations along the flow direction as the water vapor concentration increases in this direction or different air flow rates in the gas channel as high gas flow in the channel reduces the overall water vapor concentration, especially in the section close to the cathode inlet. Under a constant current density at 50 mA/cm2 and a constant cell boundary temperature of −20 ◦ C, numerical calculations are conducted with two different water vapor concentrations of
Table 3 Cell geometric parameters Fuel cell geometry (mm) Layer thickness Diffusion Catalyst Membrane Land width Channel width Computational cell numbers
0.3 0.01 0.025 0.5 1.0 ∼1600
Fig. 3. Time evolution of cell voltage under different relative humidity of the purging gas.
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Fig. 4. Time evolution of ice fraction in the cathode catalyst layer: (a) with the purging gas relative humidity at 0.5, and (b) with the purging gas relative humidity at 0.75.
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0.074 and 0.033 mol/m3 at boundary 2, representing 100% relative humidity and 45% relative humidity in the cathode gas channel, respectively. The fuel cell is purged to an equilibrium condition using a dry gas with 25% relative humidity on both the anode and cathode sides prior to its cold start. Transient variations of the cell voltage are shown in Fig. 2. Both curves in Fig. 2 clearly show two-stage evolutions, namely an initial voltage recovery period owing to the membrane hydration by the product water, and an voltage drop-down period caused by ice formation and its subsequent blockage of oxygen transport and coverage of the active catalyst surface. This trend is consistent with the experimental observation of Tajiri et al. [9,10]. With a higher water vapor concentration, i.e. 0.074 mol/m3 , specified at boundary 2, the fuel cell cold-start operation shuts down sooner at around 200 s, since in this case the water vapor concentration inside the cathode catalyst layer and GDL reaches its saturation value and start to freeze earlier. This result clearly indicates that high gas flow rates on the cathode side could increase the fuel cell operation time and benefit the cold-start process, a conclusion consistent with the experimental result of Oszcipok et al. [7]. More detailed discussion concerning this issue could be found in an earlier publication [21].
Fig. 5. Transient variation of water content in the middle of the membrane: (a) with the purging gas relative humidity at 0.5, and (b) with the purging gas relative humidity at 0.75.
3.2. Effect of initial membrane water content The initial water content inside the membrane could be wellcontrolled by the relative humidity of the purging gas prior to the cell startup using an equilibrium purging method discussed by Tajiri et al. [9]. The initial membrane water content or the relative humidity of the purging gas significantly affects the cold-start characteristics of a PEM fuel cell, as clearly illustrated in Fig. 3, in which the relative humidity of the purging gas at 0.25, 0.5, and 0.75 corresponds to the initial membrane water content at 2.57, 3.49, and 6.17, respectively. Numerical calculations are performed under a subfreezing boundary temperature of −20 ◦ C and a constant operating current density at 50 mA/cm2 . For all the three cases, the water vapor concentration inside the cathode gas channel and defined at the boundary 2 are at a fully humidified value at −20 ◦ C, i.e. 0.074 mol/m3 . Results in Fig. 3 indicate that with a higher initial membrane water content, the cell shows a better performance once started, as expected, but the cell operation also shuts down sooner. The two curves corresponding to the relative humidity of the purging gas at 0.25 and 0.5 clearly show two-stage evolutions, a phenomenon discussed in detail in the preceding section. The third curve corresponding to a relative humidity of the purging gas at 0.75 also shows a two-stage evolution, but the first stage of performance increase becomes very short, around 25 s, and the cell performance only increases slightly. After an initial short period, the third curve starts to move slowly downslope due to ice precipitation, as illustrated in Fig. 4b. As explained in the earlier publications [7,20,21], the membrane plays a crucial role for a PEM fuel cell cold-start process. A drier membrane would initially absorb more water produced during the cell operation, thus delaying the ice precipitation in the cathode catalyst layer. The time evolutions of the ice formation in the cathode catalyst layer are illustrated in Fig. 4 for the two cases corresponding to the relative humidity of the purging gas at 0.5 and 0.75. The pictures corresponding to the third case, with a lower initial membrane water content or relative humidity of the purging gas, was provided in an earlier publication [21]. These figures clearly indicate that with a higher initial membrane water content, ice precipitation inside the cell starts sooner. In addition, ice grows faster under the current-collecting land and at the interface between the catalyst layer and GDL.
Fig. 6. Time evolution of cell voltage under different cell boundary temperatures.
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Fig. 7. Time evolution of ice fraction in the cathode catalyst layer under a cell boundary temperature of −10 ◦ C.
Transient variations of the water content in the middle of the membrane for the two cases corresponding to the relative humidity of the purging gas at 0.5 and 0.75 are shown in Fig. 5. Again, the figure for the third case was provided earlier [21]. The water content inside the membrane initially distributes uniformly in the lateral direction, and it increases continuously during the entire cold-start process. However, the increasing rate becomes slower as time elapses, indicating that less water is absorbed in the membrane and more water becomes frozen. The water content inside the membrane shows higher value directly under the currentcollecting land since the water vapor concentration is higher in this region. 3.3. Effect of startup cell temperature The effect of the startup cell temperature on PEM fuel cell cold start is numerically investigated by defining different boundary temperatures at the boundaries 3 and 4. Again, numerical calculations are performed under a constant operating current density at 50 mA/cm2 . It is noteworthy that for the present calculations, the water vapor inside the cathode gas channel is defined to be fully humidified, with different concentrations corresponding to different startup cell temperatures. In fact, unless otherwise stated, the numerical studies performed in the following sections in this paper are all under the fully humidified water vapor condition at boundary 2. As discussed in an earlier publication [21], the temperature inside the fuel cell increases only slightly from the boundary temperature, i.e. less than 0.2 ◦ C, and therefore the boundary temperature could be considered as the startup cell temperature, leading to essentially an isothermal cold-start process. As shown in Fig. 6, with a higher startup cell temperature, the cell performs much better, since the electrochemical kinetics and ionic
conductivity inside the membrane increase with an increasing cell temperature. Furthermore, with a higher startup cell temperature, the cold-start time could be significantly prolonged, because the saturation water vapor concentration increases with an increasing cell temperature and ice precipitation only starts after the water vapor becomes saturated. Under a startup temperature of −5 ◦ C, the cold-start operation could last more than 500 s, still showing no noticeable performance deterioration. In fact, in this case, cell performance decreases at around 400 s, but the decreasing pace is very slow and thus negligible within 500 s. The ice distribution and evolution with a startup cell temperature of −10 ◦ C are displayed in Fig. 7. Comparing with the results at a startup cell temperature of −20 ◦ C presented earlier [21], it is clear that with a higher startup cell temperature, ice precipitation is significantly delayed. For example, ice starts to appear at around 50 s at a startup cell temperature of −20 ◦ C [21] while it only does so at around 150 s at −10 ◦ C. In addition, higher startup cell temperature influences the ice formation and distribution directly under the gas channel, resulting in very low and quite uniform ice fraction in this region before 250 s, as illustrated in Fig. 7. 3.4. Effect of current density Increasing the operating current would produce more water and drastically reduce the isothermal cold-start time of a PEM fuel cell, as indicated in Fig. 8. This figure shows that increasing the operating current density from 50 to 75 mA/cm2 decreases the cell voltage, as expected. In addition, under a relatively higher current density of 75 mA/cm2 , the initial rate of cell performance increase becomes much faster, and the transition stage between cell voltage increase and decrease disappears, resulting in a cold-start time just slightly longer than 100 s.
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Fig. 8. Time evolution of cell voltage under different operating current densities at a subfreezing boundary temperature of −20 ◦ C.
Fig. 10. Time evolution of current density under different operation cell voltages at a subfreezing boundary temperature of −20 ◦ C.
The time evolution of the water content distribution in the middle of the membrane under a constant current density of 75 mA/cm2 and a startup cell temperature at −20 ◦ C is presented in Fig. 9. As discussed in an earlier section, the water content inside the membrane increases continuously during the startup process owing to product water absorption, but the increasing rate slows down as time elapses. Under a relatively higher current density of 75 mA/cm2 , the membrane does not become as well hydrated as in the case under a lower current density of 50 mA/cm2 . At the end of the cold-start process, the highest water content in the middle of the membrane in Fig. 9 reaches less than 8 while it is close to 9.5 in the earlier case under a lower current density of 50 mA/cm2 [21]. 3.5. Effect of cell voltage Under a constant cell voltage conditions, decreasing the operating cell voltage of a PEM fuel cell would increase the output current density, as shown in Fig. 10. The result in this figure indicates that at a relatively low cell voltage of 0.5 V, the initial increase of the Fig. 11. Transient variation of water content in the middle of the membrane under a constant cell voltage of 0.5 V.
cell performance, or current density, becomes very rapid, i.e. the current density rising from around 75 to 130 mA/cm2 in 30 s. Since a higher current leads to more product water, ice starts to form in the cathode catalyst layer sooner and grows faster, causing a very sharp decrease of the cell performance in the second stage of the two-stage evolution of the cell performance. The PEM fuel cell shuts down its operation at around 60 s in this case. The time evolution and distribution of the water content in the middle of the membrane under a constant cell voltage of 0.5 V are presented in Fig. 11. Since the fuel cell shuts down its operation very quickly, there is no sufficient time for the membrane to become well hydrated, leaving the highest water content in the middle of the membrane at around 6 at the end of the cold-start process. 4. Conclusions
Fig. 9. Transient variation of water content in the middle of the membrane under a constant current density of 75 mA/cm2 .
In this paper, a previously established PEM fuel cell model for cold-start simulations has been employed for numerical investigations of the isothermal startup characteristics under subfreezing
H. Meng / Electrochimica Acta 53 (2008) 6521–6529
cell temperatures, focusing on the effects of many key parameters on cold-start mechanisms, including the water vapor concentration or the gas flow rate in the cathode gas channel, the initial membrane water content, the startup cell temperature, the current density under the constant current condition, and the cell voltage under the constant cell voltage condition. Based on the present parametric studies, the following conclusions can be summarized: - Increasing the gas flow rate in the cathode gas channel is beneficial for the cold-start process, since it would decrease the water vapor concentration inside the channel, which in turn influences water vapor distribution and thus ice precipitation and growth in the cathode catalyst layer. - An initial drier membrane would absorb more product water and therefore delay ice formation and consequently prolong the coldstart process. - Operating a PEM fuel cell under a lower current density or higher cell voltage would produce less water and consequently prolong the cold-start process. However, in practical applications, in order to achieve the fastest startup from a subfreezing temperature, the operation current or cell voltage should be optimized to generate the most amount of waste heat in a desired startup time. - Increasing the startup cell temperature would significantly delay ice formation, which would then lead to longer cold-start time. Therefore, various internal and external heating sources should be considered in the PEM fuel cell design scheme for successful cold-start processes.
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Greek letters ˚ phase potential (V) mole fraction ε porosity fraction of the membrane phase in the catalyst layer εm over-potential (V) proton conductivity (S/m) water content viscosity (kg m−1 s−1 ) gaseous density (kg/m3 )
electronic conductivity (S/m) viscous stress tensor Superscripts cl catalyst layer eff effective value sat saturation value v vapor phase Subscripts cl catalyst layer e electrolyte or energy i species m membrane s electron or solid phase sat saturation value vi water vapor to ice phase w water
Appendix A. Nomenclature
a c cond Cp D D EW F hvi i j k kc K nd p Ru sice S t T u U0 V Vcell W
water activity or surface area molar concentration (mol/m3 ) proton or electron conductivity (S/m) constant-pressure heat capacity (J kg−1 K−1 ) mass diffusivity (m2 /s) water content diffusivity (mol m−1 s−1 ) equivalent weight of the membrane (kg/mol) Faraday constant 96,487 C/mol enthalpy of desublimation (J/kg) current density (A/m2 ) transfer current density (A/m3 ) thermal conductivity (W m−1 K−1 ) desublimation rate coefficient (s−1 ) permeability (m2 ) electro-osmotic drag coefficient gas-phase pressure (Pa) universal gas constant (J mol−1 K−1 ) ice fraction source term time (s) temperature (K) gas-phase velocity (m/s) open-circuit potential (V) volume (m3 ) cell voltage (V) molecular weight (kg/mol)
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