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Analysis of liquid water formation in polymer electrolyte membrane (PEM) fuel cell flow fields with a dry cathode supply
Journal of Power Sources 306 (2016) 658e665
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Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour
Analysis of liquid water formation in polymer electrolyte membrane (PEM) fuel cell flow fields with a dry cathode supply € nke Go € ßling a, *, Merle Klages b, Jan Haußmann b, Peter Beckhaus a, So Matthias Messerschmidt b, Tobias Arlt c, Nikolay Kardjilov c, Ingo Manke c, Joachim Scholta b, Angelika Heinzel a a b c
Zentrum für BrennstoffzellenTechnik (ZBT), Carl-Benz-Str 201, 47057, Duisburg, Germany Zentrum für Sonnenenergie- und Wasserstoff-Forschung Baden-Württemberg (ZSW), Helmholtzstraße 8, 89081, Ulm, Germany Helmholtz-Zentrum Berlin (HZB), Hahn-Meitner-Platz 1, 14109, Berlin, Germany
h i g h l i g h t s Model to predict the location in PEM fuel cells at which liquid water forms. The Model helps understanding the water management in PEM fuel cells. Diffusion resistance of the GDL is essential for the model and has been included. The model has been validated with neutron images. A special focus of the model is the dry cathode supply.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 July 2015 Received in revised form 13 December 2015 Accepted 16 December 2015 Available online xxx
PEM fuel cells can be operated within a wide range of different operating conditions. In this paper, the special case of operating a PEM fuel cell with a dry cathode supply and without external humidification of the cathode, is considered. A deeper understanding of the water management in the cells is essential for choosing the optimal operation strategy for a specific system. In this study a theoretical model is presented which aims to predict the location in the flow field at which liquid water forms at the cathode. It is validated with neutron images of a PEM fuel cell visualizing the locations at which liquid water forms in the fuel cell flow field channels. It is shown that the inclusion of the GDL diffusion resistance in the model is essential to describe the liquid water formation process inside the fuel cell. Good agreement of model predictions and measurement results has been achieved. While the model has been developed and validated especially for the operation with a dry cathode supply, the model is also applicable to fuel cells with a humidified cathode stream. © 2015 Elsevier B.V. All rights reserved.
Keywords: Dry cathode supply Liquid water Diffusion
1. Introduction Polymer Electrolyte Membrane (PEM) fuel cells are potential power supply solutions for a wide range of applications. Depending
* Corresponding author. Tel.: þ49 1773104041; fax: þ49 20375982222. € ßling), merle. E-mail addresses: [email protected] (S. Go [email protected] (M. Klages), [email protected] (J. Haußmann), p. [email protected] (P. Beckhaus), [email protected] (M. Messerschmidt), [email protected] (T. Arlt), kardjilov@ helmholtz-berlin.de (N. Kardjilov), [email protected] (I. Manke), [email protected] (J. Scholta), [email protected] (A. Heinzel). http://dx.doi.org/10.1016/j.jpowsour.2015.12.060 0378-7753/© 2015 Elsevier B.V. All rights reserved.
on the application, they have to fulfill different requirements with regards to power density, life-time, efficiency and cost, among others. Depending on the requirements there are many different operating strategies for fuel cell systems. As the conductivity of the polymer membrane generally improves with higher water content, the humidity of the gas stream is a very important operating parameter. Especially in applications that require high power densities, external humidification is commonly used [1,2]. The humidification of the inlet gas streams generally results in liquid water formation in the fuel cell. The water produced inside the fuel cell by the electrochemical reaction of hydrogen and oxygen cannot evaporate fully into the gas streams as they reach their saturation point. The remaining liquid water must be transported from the
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Nomenclature VO2 I F S nsp csp cH2 O;el x xlw Msp Vm p psat pamb Dp J
volumetric fraction of oxygen in the air 0:2094 [e] current [A] Faraday constant 96485.3365 [C/mol] stoichiometry [e] molar flow of the species sp [mol/s] concentration of the species sp [g/cm3] concentration of water at the electrode [g/cm3] position along the cathode flow field channel 0 … 1 [e] position of the first visible liquid water 0 … 1 [e] molar mass of the species sp [g/mol] molar volume (@ 273 K and 101300 Pa) 22414 [cm3/ mol] pressure [mbar] saturation pressure of water vapor [mbar] ambient pressure constant for all presented measurements 1030 [mbar] pressure drop in the flow field [mbar] Water flux [g/(cm2 s)]
electrodes through a porous gas diffusion layer (GDL, consisting of the micro porous layer (MPL) and the substrate) to the flow field. The flow fields supply the cell with fuel and oxygen/air and remove the reaction products including the liquid water. The design of such flow fields is a complex task and they are usually optimized for narrow operating ranges. Systems with lower power density requirements on the other hand, can usually be operated without external humidification of the inlet gases. Air with ambient humidity is in many cases sufficient. This is mainly due to the fact that at lower power densities, the ohmic resistance of the polymer membrane affects the cell performance to a much lesser proportion compared to high power applications. The absolute amount of liquid water inside the fuel cell is significantly lower under these operating conditions and the amount of liquid water that must be transported by the flow fields is less. It is therefore possible to design simpler flow fields with lower requirements regarding liquid water transport. Another option is to use flow fields for fully humidified cells, which are likely to ensure a more stable operation of the fuel cell. Although the amount of liquid water is less and fewer droplets occur during non-humidified operation, the water management is not negligible. The aim of this study is to improve the understanding of liquid water management in fuel cells operated without external humidification. For this purpose, a model has been developed, which allows to predict the liquid water formation inside the cell as a function of several operating parameters. Furthermore, experiments have been conducted to analyze the effect of different operating conditions on the liquid water formation. Neutron imaging is a well-established method to investigate the liquid water distribution in a fuel cell during operation ([3e9]). In contrast to X-ray Imaging ([10e13]) the high penetration depth of neutrons into most metals and their high sensitivity to hydrogen ([14e16]) allow for investigation of a whole fuel cell without modifications. Further possible coupling of fuel cell models and neutron imaging has been proven (e.g. Ref. [17]). 2. Model The aim of the model presented in this paper is to predict the location downstream of the cathode inlet, at which liquid water starts to form. When making a number of assumptions, it is possible
dy D Fadj Q_ A U Tel Tfc TGDL DT l l
r v Re L Dh RH
659
diffusion distance [cm] diffusion coefficient [cm2/s] adjusting factor [e] waste heat [W/cm2] area [cm2] cell voltage [V] temperature at the electrode [K] temperature in the flow channel and fuel cell [K] temperature in the GDL, average of Tel and Tfc [K] temperature gradient [K] thermal conductivity [W/(m k)] thickness of the GDL [cm] density [kg/m3] flow velocity [m/s] Reynolds number [e] length of the channel segment [m] hydraulic diameter relative humidity
to approximate the amount of water in the PEM fuel cell cathode flow field channels for steady state operating conditions. The assumptions for the model are as follows: A. The current density and temperature over the active area is assumed to be constant. B. No gradients of the gas properties perpendicular to the membrane plane in the flow field channels are considered. C. The net liquid water transport through the membrane between anode and cathode is neglected, all water that is formed through the reaction remains on the cathode side. D. Liquid water starts to form at that point, where the water concentration in the flow field channel reaches the saturation concentration of vapor water. E. No water in the cathode supply. F. The geometry of the flow field is reduced to one straight channel. Notes to the assumptions: A The current density and the temperature distribution along the cathode channel do have an influence on the point of the first appearance of liquid water in the channel, but the influence is reduced to small deviations of the functions, since the model already works with the averaged value. B A typical flow field channel is much more than 100 times longer than its width or height. The diffusion in the channel is not blocked by material like in the GDL or MPL. The rough surface of the GDL and even possibly edges in the flow field will homogenize the medium in the channel. C The reaction water in PEM fuel cells is produced on the cathode side of the membrane (1). There are two main water transport mechanisms across the membrane: osmotic drag from the anode to the cathode side and diffusion that might take place in both directions. Driven by osmotic drag, additional water can be transported from the anode through the membrane to the cathode. Concentration differences of water between the cathode and anode cause a diffusive transport of water through the membrane. In case of a strong unidirectional water transport through the membrane it has to be considered in the model. For example in the case of very thick membranes where the back
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diffusion of the water from the cathode to the anode is small and where osmotic drag from the anode to the cathode dominates at high current densities. But for state of the art membranes, that usually have a thickness of less than 30 mm, the back diffusion equals the osmotic drag or is even higher [18]. On the other hand the water transport through the membrane has to be considered in case of a dominating back diffusion, where the produced water on the cathode side is transported mainly to the anode side. In principle, depending on the different operating conditions, the anode flow would have the ability to adsorb significant amounts of the produced water of the cathode side. To prevent this, the operating conditions have been chosen in that way, that the amount of water on the anode side stays approximately constant. The operating conditions have been deduced from fuel cells operated with an anode recirculation. Since these systems have no external humidification and only very small amounts of water leave the anode loop via the purge valve, the amount of water in the anode loop reaches a constant level after a short time. The overall water transport through the membrane for the conditions considered in this paper is generally small and is neglected in the following. D Since the microporous layer and the flow field offer a large surface for condensation, it is assumed that liquid water forms at the location where the saturation point is reached in the channel. E The inlet humidity of the cathode gas stream for the performed experiments is close to 0% (dew point measured during fuel cell operation 40.1 C) and has been neglected in this study. F The reduction of multiple channels to one straight channel is tolerable if the geometry of the flow field is based on parallel and similar channels like in the test cell (Fig. 1a). It is not valid in interdigitated flow fields or strongly asymmetric flow fields with complex geometries. The model: The production of water within the fuel cell is governed by the following equation:
O2 þ 4 H þ þ 4e /2H2 O
(1)
At the cathode side of the fuel cell, oxygen is reduced by the electrochemical reaction. For each consumed mole of oxygen 2 mol of water are produced. The stoichiometry S for a specific reactant describes the ratio of the amount of reactant supplied to the fuel cell to the amount consumed. An oxygen stoichiometry of e.g. 3 means, that three times more oxygen is supplied to the fuel cell than is consumed. The variable x describes the path of the air from the cathode inlet (x ¼ 0) to the cathode outlet (x ¼ 1) along the flow field (Fig. 1a, assumption F). The molar flow n of each species at a point x in the channel can be described as:
nO2 ðxÞ ¼
I Sx F 4
nN2 ¼ nO2 ð0Þ
nH2 O ðxÞ ¼
csp ðxÞ ¼
I 1 x F 2 I F
constant and VO2 the volumetric fraction of oxygen in the air. The concentration of a species csp can be calculated using the molar mass Msp and the mole fraction of the species sp and its molar volume Vm.
(2)
1 VO2 VO2
nO2 ; N2 ; H2 O ðxÞ ¼
Fig. 1. (a) Schematic description of the test cell flow field. The red line describes the mean path from the cathode inlet (x ¼ 0) to the cathode outlet (x ¼ 1). The x coordinates for each corner of the flow field are displayed. (b) Results of the simplified model. If the x-Coordinate, describing the position along the cathode flow field channel, equals xlw, the point of the first formation of liquid water in the cathode channel is predicted by the simplified model as a function of cell temperature (stoichiometry 2.0, dry cathode supply); no diffusion resistance is included. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
S x S 1 VO2 1 þ þ x 4 4 VO2 2
nsp Msp nðxÞ Vm
(6)
(3)
Thus the concentration of water can be calculated using (4), (5) and (6) as:
(4)
cH2 O ðxÞ ¼
(5)
where I is the total electric current of the cell, F is the Faradaic
2x MH2 O þ x Vm
S VO2
(7)
In the model the first formation of liquid water along the xcoordinate coincides with that point, at which the concentration of water exceeds the concentration of a saturated gas cH2 O;sat (assumption D). This point is described by x ¼ xlw.
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cH2 O;sat ðxlw Þ ¼ cH2 O ðxlw Þ
(8)
The saturation concentration can be calculated using the saturation pressure psat of water (calculated using formula of Hyland and Wexler that fits very well in the region between 0 C and 100 C Refs. [19,20]). The pressure in the cathode flow field channel is approximated linearly between the inlet and outlet pressure. The outlet pressure equals the ambient pressure.
cH2 O;sat ðxÞ ¼
psat MH2 O pðxÞ Vm
(9)
pðxÞ ¼ pamb þ Dp Dp,x
(10)
where pamb describes the ambient pressure at the outlet of the cell and Dp the pressure drop between the inlet and the outlet of the cell. Under the given assumptions the concentration of water only depends on the stoichiometry (7). The saturation concentration is a function of temperature and pressure (9). When the stoichiometry and the pressure are prescribed, the coordinate xlw at which liquid water starts to form can be described as a function of the fuel cell temperature alone. xlw can be calculated solving the equation:
psat ðTÞ 2 xlw ¼ pamb þ Dp Dp$xlw VS þ xlw
(11)
O2
The result of the model, with a prescribed stoichiometry of 2 and a pressure drop of 100 mbar is shown in Fig. 1b. The solution of the equation can be found in the Appendix A (A1).
3. Experimental Previous studies proved that it is possible to visualize liquid water in fuel cells in-situ with neutron imaging during actual operation (e.g. Ref. [3,4,21]). To be able to validate the above model predictions a single fuel cell in a standard fuel cell design of ZSW (Zentrum für Sonnenenergie-und Wasserstoff-Forschung BadenWürttemberg, Ulm) with an active area of 100 cm2 is used. Here a three channel meander is used to supply the reactants to the active area (Fig. 1a). The fuel cell is equipped with the same GDLs on anode and cathode side (Sigracet® SGL 25BC) and GORE® PRIMEA® 5761 as the membrane electrode assembly. Anode and cathode channels have both the same nearly rectangular cross-sectional area of 0.91 mm2. The three meander-shaped channels can be considered to have the ability for sufficient condensate removal for state-of-the-art operating conditions. The fuel cell is operated in co-flow configuration, where hydrogen and air both flow from top to bottom to assure a gradual increase of water content as the gases pass through the fuel cell. On the cathode side, a constant stoichiometry of 2 is used for the experiments. An overstoichiometric flow of hydrogen of 2 norm l/min (lambda ¼ 3.6 to 14.3) is employed at the anode to remove all liquid water possibly accumulated on the anode side. The anode gas is humidified using a bubbler with a dew point of 50.3 C, which corresponds to relative gas inlet humidity between 99% and 45% at fuel cell temperature of 50.9 C and 68 C, respectively. The operating conditions are deduced from operating conditions known from recirculated operation. The fuel cell temperature is regulated by a cooling fluid which is guided through two cooling flow fields on the back side of the anode and cathode gas flow field. As a cooling fluid, D2O is used, so that a minor attenuation of the neutron beam is achieved. The flow of the cooling fluid is from bottom to top to avoid accumulation of gas bubbles inside the cooling flow field which can disturb the neutron imaging. The visualization of water transport was performed at the
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neutron facility CONRAD/V7 of the Helmholtz-Zentrum Berlin (BER II research reactor). Details of the experimental setup for visualization with neutrons can be found in Refs. [22,23]. The exposure time was 10 s per radiography with an additional readout-time of 4 s. A lithium scintillator with a thickness of 200 mm was used. The used pixel size was 51.3 mm [24]. The mean pore size of the GDL is smaller than 1 mm [25]. But even with a large number of pores at the size of 20 mm and larger, the pore size is smaller than the limit of the spatial resolution of the used neutron imaging setup of about 100 mm. The spatial resolution was limited by the large size of the fuel cell and the corresponding large pixel size. This is not the general limit of the spatial resolution [26] or water film thickness sensitivity [27] of neutron imaging. However our work is focused on the water distribution in the channels that can be detected with certainty. For the visualization of the point xlw a test series was performed in which current density and fuel cell temperature are varied stepwise to identify the change in water appearance inside the cathode channels. Operating conditions were held constant until no significant change of the liquid water distribution could be detected. The volumetric gas flow of hydrogen is kept constant, whereas the air flow is adjusted in a way to ensure that a constant stoichiometry of the air flow is achieved. The air flow and thus the pressure inside the channels change due to the variation of current density. As the pressure is used as an input for (9), this will be evaluated in detail. The pressure drop is calculated as the actual difference between gas inlet and outlet pressures less the net pressure drop of the balance of plant (BOP) around the fuel cell (pipes, etc.). The pressure drop is recorded at three different current densities (Fig. 2) and for each current density one average pressure drop is calculated for use in the model. The cell voltages have been merged for each current density as well. 4. Results The neutron images obtained in the experiments clearly show the liquid water formation in the fuel cell during operation (Fig. 3). While operated with a dry cathode supply no liquid water can be seen next to the cathode inlet and the area within the channels following the inlet region. Depending on the operating conditions at some point liquid water appears in the neutron images. By overlaying the known geometry of the cathode flow field channels (Fig. 1a), the path of the cathode gas stream can be reconstructed in the neutron images. Liquid water can also be located on the anode side of the cell, but the liquid water on the cathode side dominates. In Fig. 3 the point of the first visible liquid water along the x-coordinate is marked in blue. Since liquid water is initially visible on the neutron images as a gentle shadow and increases to a clearly visible trace, an error bar is used to mark this band. In total 11 neutron pictures have been evaluated. For the post processing of the experimental data, the fuel cell temperature is calculated by averaging the values measured at the cooling inlet and the cooling outlet. The temperature and current density values measured during the experiment are shown in Fig. 4a. The x-coordinates, at which liquid water was observed at different operating temperatures and current densities, are shown in Fig. 4b. The x-coordinates of liquid water formation as predicted by (11) are also presented in Fig. 4b. The curves of the model are adapted to the individual pressure drop of the operating points (i ¼ 0.2 A/cm2 Dp ¼ 61.8 mbar; i ¼ 0.4 A/cm2 Dp ¼ 135.5 mbar; i ¼ 0.8 A/cm2 Dp ¼ 275.8 mbar). A significant discrepancy between the calculated and the observed values for xlw can be seen for all data points. The discrepancy increases for operation points with higher current densities. In all considered operating points, the model predicts
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Fig. 2. Experimentally determined cell voltage U (a) and pressure drop Dp (b) in the testing cell during neutron imaging.
Fig. 4. (a) Fuel cell current and temperature during the neutron imaging (b) Experimental and simple model starting point of liquid water in the cathode channel; relation between cell temperature and path length (stoichiometry 2.0, dry cathode supply). At a specific temperature (e.g. 58 C) the model calculates the starting point of liquid water in the cathode channel later (92%) than the liquid water appears in the measurements (73%).
4.1. Derivation of the optimized model In stoichiometric air supply operation the correlation between produced water and the cathode gas stream is constant, but the absolute amount of produced water increases proportional to the current density. The water must be transported from the electrode, where the electrochemical reaction takes place, to the cathode flow field channel, passing through the gas diffusion layer (GDL) that consists of layers of different porosities (MPL and substrate). As long as no liquid water is present in the flow field channels, the water transport to the channel takes place in the gaseous phase. The GDL can be considered as a diffusion resistance for the gaseous water transport and Fick's law is a good approximation of the real diffusion processes within a fuel cell.
J¼D
Fig. 3. Neutron image at 0.2 A cm-2 and 51 C fuel cell temperature; mean cathode path and path length overlaid; starting point of liquid water in the cathode channel at 50.0% of path length.
condensation to occur closer to the outlet of the cathode flow channels than observed during the experiments. In the following, the discrepancy between the theoretically predicted and the observed condensation is analyzed.
dc ; dy
(12)
where J is the diffusion flow, D a material specific diffusion, dc the concentration gradient of the species and dy the diffusion distance. The driving force for the gaseous water diffusion through the GDL is the concentration gradient of water between the electrode and the cathode flow field channel. Fig. 5 schematically describes the situation for the water transport in the cell. The concentration in the flow channel can be described by (7) as a function of the electrochemical reaction rate alone, if the assumptions A, B and C are applied. Condensation is only expected if the partial pressure of gaseous water reaches the saturation pressure and it is evaporated when the saturation pressure is not
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reached. The not optimized model depends only on the temperature and stoichiometry. Since the experiments showed condensation at a point along the x-coordinate, which is well before the point at which the model predicted the saturation pressure to be reached, the validity of the assumption D, liquid water forms at the location where the saturation point is reached, must be questioned. Before the first appearance of liquid water, the transport mechanism for water is the diffusion process (12). Since the water concentration in the flow field channel can be calculated by (7), the concentration at the electrode cH2 O;el can as well be calculated via the diffusion as:
cH2 O;el ðxÞ ¼
J,dy þ cH2 O ðxÞ D
(13)
Assumption If the concentration of water at the electrode exceeds the maximal possible concentration of gaseous water, i.e. the saturation pressure, liquid water appears and is transported in the liquid phase to the channel. This point ðx ¼ xlw Þ is visible in the neutron images.
cH2 O;el ðxlw Þ ¼ cH2 O;sat ðxlw Þ
(14)
Once the water is produced at the electrode in the liquid phase, it will not be evaporated again within the GDL and is transported in the liquid phase to the flow field. This is not a valid assumption for an equilibrium state after an infinite time but it seem acceptable for the short times and diffusion paths in fuel cell operation. That means, that after this point the pure gaseous water transport in the fuel cell is complemented by liquid water transport like described by Kimball “Liquid is driven by a hydraulic pressure from the membrane/cathode interface through the largest pores while gas moves from the gas flow channel to the membrane/cathode interface through smaller, but more plentiful, pores” [28]. Based on this assumption the point of the first appearance of liquid water ðx ¼ xlw Þ can be calculated by solving the equation for xlw :
J,dy cH2 O;sat ðxlw ; Tel Þ cH2 O xlw ; Tfc ¼ D
663
The coefficient has been measured at 25 C and 1014 mbar. Since the diffusion coefficient is temperature and pressure dependent an adaption to the operating conditions is calculated (17). The adaption is based on the general temperature and pressure dependency Hirschfelder et al. have developed [31]. For the calculations of the diffusion coefficient the average temperature and pressure of the channel is used. Calculating with this diffusion coefficient in (15) the calculated points of the first visible liquid water are shown in Fig. 6.
Dlit ¼ 0:0630
D ¼ Dlit
pDlit p
cm2 s T TDlit
(16)
3 2
(17)
Where pDlit and TDlit are the conditions where LaManna has measured the coefficient. The description of the points of the first visible liquid water including diffusion using the diffusion coefficient of (16) from literature does not fit the experimental results. The mechanical installation situation of the GDL and MPL in the experimental setup for the measurement of the diffusion coefficient differs at some points from the installation situation in the fuel cell. The compression of the material and the channel and landing situation is different and will influence the effective diffusion coefficient significantly, as discussed in chapter 5, discussion. By using an additional adjusting coefficient Fadj ¼ 3:2 (Fig. 7), used in Eq. (18), to effectively increase the diffusion
(15)
Note, that the temperature at the electrode Tel differs from the temperature in the flow field channel Tfc and thus differ the saturation concentrations. The temperature gradient is caused by the waste heat of the fuel cell, that is also transported through the GDL. The calculation for the temperature gradient can be found in the Appendix B. For the used GDL (SGL25BC, assembly of an MPL and substrate) a diffusion coefficient D can be found in the literature [29,30],(16).
Fig. 6. Experimental and theoretical points of the first appearance of liquid water in the cathode channel calculated with a diffusion coefficient of 0.063 cm2/s; relation between cell temperature and path length (stoichiometry 2.0, dry cathode supply).
Fig. 5. Schematic diagram showing the diffusion process in the fuel cell cathode.
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resistance and adapt the model for the special cell, a good agreement between predictions and measurements can be achieved:
J,dy ,Fadj cH2 O;sat ðxlw ; Tel Þ cH2 O xlw ; Tfc ¼ D
(18)
The complete solution of the equation can be found in the Appendix A (A2).
5. Discussion Assuming that the assumption (14) is correct, the diffusion of gaseous water through the GDL seems to be much slower than the diffusion is described in literature. The necessary adjusting might be caused mainly by two reasons. Firstly, the bipolar plates consist of numerous flow channels and landings. Whereas the water is produced on the whole surface of the electrode, it can only enter the gas stream in the channels. This causes an increased diffusion path under the landings. Further the amount of transported water concentrates in the regions under the landings close to the channels. This is exactly the area (the intersection of the channel to the landing) where the lowest temperatures are usually simulated [32], since most of the waste heat of the electrode is transported through the landings out of the fuel cell, and the first droplets in the channel are usually visible [33]. In Fig. 8 a schematic description of the area between the channels and the electrode is shown. Additionally, only one reference is known for the diffusion coefficient of the GDL SGL 25BC (16) ([29,30]). In the conclusion of his master's thesis LaManna writes: “It is desirable to know if water vapor diffusion coefficients change with GDL compression” [30]. Till now it is not clear what effect the compression of the GDL has on the diffusion coefficient. The GDLs in the testing fuel cell of ZSW should be compressed to roughly 83% of their initial thickness. This will differ from the compression of LaManna, but so far the influence of compression is not clear. The compression might change the diffusion coefficient. Especially the region under the landings, where the first droplets in the channel are usually visible [33], is most compressed. If the adjusting factor is only applied to the diffusion coefficient a corrected diffusion coefficient determined by iteration of (19) results.
Dadj ¼
Dlit cm2 ¼ 0:0197 3:2 s
(19)
A combination of the two reasons is also conceivable.
Fig. 8. Lengthened diffusion path and concentrated water diffusion under the landings.
6. Conclusion In this study a PEM fuel cell model is presented which aims to predict the location in the flow field at which liquid water forms at the cathode. It is validated with neutron images of a PEM fuel cell visualizing the locations at which liquid water forms in the fuel cell flow field channels. It seems that diffusion limited gaseous water transport, calculated with the Fick's law, is capable to describe the point of the first appearance of liquid water in the flow field channels of the cathode. That means that if the limit of diffusion from the electrode to the channel is reached, liquid water appears at the electrode. This water does not evaporate again but is rather transported in liquid phase through the GDL to the channel. To adapt the diffusion by Fick's law to the performed measurements an adjusting factor of 3.2 for the coefficient is necessary. Good agreement of model predictions and measurement results has been achieved. This adjusting is argumentable by geometric flow field reasons or by a necessary diffusion coefficient correction. The simplifications A (homogeneous temperature and current density distribution), B (no gradients perpendicular to the membrane plane in the flow field channels) and C (no net liquid water transport through the membrane) might cause some small deviations but will not change the basic results. Presumably both reasons (landing/channel and compression) are relevant and the adjusting must be split between them. The calculation is based on the assumption of (14). Yet the results are not fully proving our theory, but they strongly support the explanations described above. Further test have to be done to fully prove the theory. Acknowledgments This work was supported by the Federal Ministry of Economics and Technology, Germany (funding number 03ET2007, “Entwicklung von Lebensdauerprognosemodellen von Brennstoffzellen in realen Anwendungen”). Appendix A Solutions for (11)
Fig. 7. Results of the enlarged model. Experimental and theoretical points of the first appearance of liquid water in the cathode channel calculated with a diffusion coefficient of 0.063 cm2/s and an adjusting factor of 3.2; relation between cell temperature and path length (stoichiometry 2.0, dry cathode supply).
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u S u psat þ 2ðpamb þ DpÞ t psat þ 2ðpamb þ DpÞ 2 psat VO2 xlw ¼ 4,Dp 4,Dp 2,Dp (A1) Solution for (17)
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J Ddy,Dp,V S
xlw ¼
MH O 2 Vm
O2
665
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi v0 12 J dy u ,ðpamb þDpÞ,V S u J Ddy,Dp,VOS J dy D ,ðp þDpÞ O amb S u 2 þ psat þ 2ðpamb þ DpÞ uB MH O 2 þ D MH O psat þ 2ðpamb þ DpÞC psat VO MH O 2 2 2 2 C uB Vm Vm Vm C B u 0 0 1 1 uB J dy C ,Dp D A J dy J dy u@ 2,Dp MH O ,Dp ,Dp t 2 2@ 2,Dp DMH O A 2@ 2,Dp DMH O A Vm J dy ,ðpamb þDpÞ D MH O 2 Vm
2 Vm
2 Vm
(A2)
Appendix B Calculation of the temperature gradient through the cathode GDL The temperature of the flow field side of the GDL is assumed to be equal to the cell temperature because of its greater proximity to the fuel cell temperature sensor. An estimation for the temperature gradient between the electrode and the flow field channel has been done on the basis of the thermal conductivity of the GDL and a waste heat calculation using a theoretical open cell voltage of 1.253 V. The calculations are based on the lower heating value, since the calculations describes the limit of the gaseous water transport. Since most of the heat is produced at the cathode electrode and the way for the heat transport to the flow field channels through the membrane and the anode GDL is longer than only through the cathode GDL, the fraction of the total waste heat that is transported through the cathode side of the fuel cell is greater than 50%. But a fraction of the heat is also transported through the anode, since the membrane has only a thickness of 18 mm. It is assumed, that the cathode fraction of the waste heat transport is 55%.
Q_ ¼ ð1:253 V UÞ,i,55 %; A
(A3)
where Q_ is the waste heat, A the reference surface, U the cell voltage and i the current density. When the GDL is compressed with 0.75 MPa, the thickness l of the GDL is approximately 190 mm and the thermal conductivity l of the used GDL is reported in literature [34]. The temperature gradient can then be calculated using the Fourier's law as:
DT ¼
Q_ l A l
(A4)
References [1] B. James, et al., Mass Production Cost Estimation for Direct H2 PEM Fuel Cell Systems for Transportation Applications: 2014 Update, Report to the DOE Fuel Cell Technologies Program, Nov 05, 2015. [2] B. Blunier, A. Miraoui, Proton exchange membrane fuel cell air management in automotive applications, J. Fuel Cell Sci. Technol. 7 (4) (Apr 06, 2010) 041007. €tter, I. Manke, R. Kuhn, T. Arlt, N. Kardjilov, M.P. Hentschel, [3] H. Marko A. Kupsch, A. Lange, C. Hartnig, J. Scholta, J. Banhart, J. Power Sources 219 (2012) 120e125. € tzke, I. Manke, A. Hilger, G. Choinka, N. Kardjilov, T. Arlt, H. Markotter, [4] C. To A. Schroder, K. Wippermann, D. Stolten, C. Hartnig, P. Kruger, R. Kuhn, J. Banhart, J. Power Sources 196 (2011) 4631e4637. [5] A. Turhan, S. Kim, M. Hatzell, M.M. Mench, Electrochim. Acta 55 (2010) 2734e2745. [6] D.S. Hussey, D.L. Jacobson, M. Arif, J.P. Owejan, J.J. Gagliardo, T.A. Trabold,
J. Power Sources 172 (2007) 225e228. [7] K.T. Cho, M.M. Mench, Phys. Chem. Chem. Phys. 14 (2012) 4296e4302. [8] R.J. Bellows, M.Y. Lin, M. Arif, A.K. Thompson, D. Jacobson, J. Electrochem. Soc. 146 (1999) 1099e1103. [9] M.A. Hickner, N.P. Siegel, K.S. Chen, D.S. Hussey, D.L. Jacobson, M. Arif, J. Electrochem. Soc. 155 (2008) B427eB434. [10] R. Kuhn, J. Scholta, P. Krueger, C. Hartnig, W. Lehnert, T. Arlt, I. Manke, J. Power Sources 196 (2011) 5231e5239. [11] T. Sasabe, P. Deevanhxay, S. Tsushima, S. Hirai, Electrochem. Commun. 13 (2011) 638e641. € tter, R. Alink, J. Haussmann, K. Dittmann, T. Arlt, F. Wieder, C. Totzke, [12] H. Marko M. Klages, C. Reiter, H. Riesemeier, J. Scholta, D. Gerteisen, J. Banhart, I. Manke, Int. J. Hydrogen Energy 37 (2012) 7757e7761. [13] J. Haussmann, H. Markotter, R. Alink, A. Bauder, K. Dittmann, I. Manke, J. Scholta, J. Power Sources 239 (2013) 611e622. [14] N. Kardjilov, I. Manke, A. Hilger, M. Strobl, J. Banhart, Mater. Today 14 (2011) 248e256. [15] L. Gondek, N.B. Selvaraj, J. Czub, H. Figiel, D. Chapelle, N. Kardjilov, A. Hilger, I. Manke, Int. J. Hydrogen Energy 36 (2011) 9751e9757. [16] A. Griesche, E. Dabah, T. Kannengiesser, N. Kardjilov, A. Hilger, I. Manke, Acta Mater. 78 (2014) 14e22. [17] A. Iranzo, P. Boillat, P. Oberholzer, J. Guerra, Energy 68 (2014) 971e981. [18] G. Hinds, M. Stevens, J. Wilkinson, M. de Podesta, S. Bell, J. Power Sources 186 (2009) 52e57. [19] R.W. Hyland, A. Wexler, ASHRAE Trans. 89(2A) 500e519. [20] R.W. Hyland, A. Wexler, ASHRAE Trans. 89(2A) 520e535. [21] M. Klages, S. Enz, H. Markotter, I. Manke, N. Kardjilov, J. Scholta, J. Power Sources 239 (2013) 596e603. [22] N. Kardjilov, A. Hilger, I. Manke, M. Strobl, M. Dawson, S. Williams, J. Banhart, Nuclear instruments and methods in physics research section A: accelerators, spectrometers, Detect. Assoc. Equip. 651 (2011) 47e52. [23] N. Kardjilov, A. Hilger, I. Manke, M. Strobl, M. Dawson, J. Banhart, Nuclear instruments and methods in physics research section A: accelerators, spectrometers, Detect. Assoc. Equip. 605 (2009) 13e15. [24] N. Kardjilov, M. Dawson, A. Hilger, I. Manke, M. Strobl, D. Penumadu, K.H. Kim, F. Garcia-Moreno, J. Banhart, Nuclear instruments and methods in physics research section A: accelerators, spectrometers, Detect. Assoc. Equip. 651 (2011) 95e99. [25] A. El-kharouf, T. Mason, D. Brett, B. Pollet, Ex-situ characterisation of gas diffusion layers for proton exchange membrane fuel cells, J. Power Sources 218 (2012) 393e404. [26] S.H. Williams, A. Hilger, N. Kardjilov, I. Manke, M. Strobl, P.A. Douissard, T. Martin, H. Riesemeier, J. Banhart, J. Instrum. 7 (2012). P02014. [27] J.R. Bunn, D. Penumadu, R. Woracek, N. Kardjilov, A. Hilger, I. Manke, S. Williams, Appl. Phys. Lett. 102 (2013) 234102. [28] E. Kimball, T. Whitaker, Y.G. Kevrekidis, J.B. Benziger, AIChE J. 54 (2008) 1313e1332. [29] J.M. LaManna, S.G. Kandlikar, Int. J. Hydrogen Energy 36 (8) (2011) 5021e5029. [30] J.M. LaManna, Determination of Effective Water Vapor Diffusion Coefficient in Pemfc Gas Diffusion Layers, Master's Thesis, Department of Mechanical Engineering Rochester Institute of Technology, June, 2010. [31] J.O. Hirschfelder, C.F. Curtiss, R.B. Bird, Molecular Theory of Gases and Liquids (Chemistry), John Wiley & Sons, January 1966. [32] S. Shimpalee, J.W. Van Zee, Numerical Studies on Rib & Channel Dimension of Flow-field on PEMFC Performance, Department of Chemical Engineering, University of South Carolina, Columbia, November 2006. [33] I. Manke, C. Hartnig, M. Grunerbel, W. Lehnert, N. Kardjilov, A. Haibel, A. Hilger, J. Banhart, H. Riesemeier, Appl. Phys. Lett. 90 (2007) 174105S. [34] A. Radhakrishnan, Thermal Conductivity Measurement of Gas Diffusion Layer Used in PEMFC, Master's thesis, Department of Mechanical Engineering Rochester Institute of Technology, November 2009.
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Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour
Analysis of liquid water formation in polymer electrolyte membrane (PEM) fuel cell flow fields with a dry cathode supply € nke Go € ßling a, *, Merle Klages b, Jan Haußmann b, Peter Beckhaus a, So Matthias Messerschmidt b, Tobias Arlt c, Nikolay Kardjilov c, Ingo Manke c, Joachim Scholta b, Angelika Heinzel a a b c
Zentrum für BrennstoffzellenTechnik (ZBT), Carl-Benz-Str 201, 47057, Duisburg, Germany Zentrum für Sonnenenergie- und Wasserstoff-Forschung Baden-Württemberg (ZSW), Helmholtzstraße 8, 89081, Ulm, Germany Helmholtz-Zentrum Berlin (HZB), Hahn-Meitner-Platz 1, 14109, Berlin, Germany
h i g h l i g h t s Model to predict the location in PEM fuel cells at which liquid water forms. The Model helps understanding the water management in PEM fuel cells. Diffusion resistance of the GDL is essential for the model and has been included. The model has been validated with neutron images. A special focus of the model is the dry cathode supply.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 July 2015 Received in revised form 13 December 2015 Accepted 16 December 2015 Available online xxx
PEM fuel cells can be operated within a wide range of different operating conditions. In this paper, the special case of operating a PEM fuel cell with a dry cathode supply and without external humidification of the cathode, is considered. A deeper understanding of the water management in the cells is essential for choosing the optimal operation strategy for a specific system. In this study a theoretical model is presented which aims to predict the location in the flow field at which liquid water forms at the cathode. It is validated with neutron images of a PEM fuel cell visualizing the locations at which liquid water forms in the fuel cell flow field channels. It is shown that the inclusion of the GDL diffusion resistance in the model is essential to describe the liquid water formation process inside the fuel cell. Good agreement of model predictions and measurement results has been achieved. While the model has been developed and validated especially for the operation with a dry cathode supply, the model is also applicable to fuel cells with a humidified cathode stream. © 2015 Elsevier B.V. All rights reserved.
Keywords: Dry cathode supply Liquid water Diffusion
1. Introduction Polymer Electrolyte Membrane (PEM) fuel cells are potential power supply solutions for a wide range of applications. Depending
* Corresponding author. Tel.: þ49 1773104041; fax: þ49 20375982222. € ßling), merle. E-mail addresses: [email protected] (S. Go [email protected] (M. Klages), [email protected] (J. Haußmann), p. [email protected] (P. Beckhaus), [email protected] (M. Messerschmidt), [email protected] (T. Arlt), kardjilov@ helmholtz-berlin.de (N. Kardjilov), [email protected] (I. Manke), [email protected] (J. Scholta), [email protected] (A. Heinzel). http://dx.doi.org/10.1016/j.jpowsour.2015.12.060 0378-7753/© 2015 Elsevier B.V. All rights reserved.
on the application, they have to fulfill different requirements with regards to power density, life-time, efficiency and cost, among others. Depending on the requirements there are many different operating strategies for fuel cell systems. As the conductivity of the polymer membrane generally improves with higher water content, the humidity of the gas stream is a very important operating parameter. Especially in applications that require high power densities, external humidification is commonly used [1,2]. The humidification of the inlet gas streams generally results in liquid water formation in the fuel cell. The water produced inside the fuel cell by the electrochemical reaction of hydrogen and oxygen cannot evaporate fully into the gas streams as they reach their saturation point. The remaining liquid water must be transported from the
ۧling et al. / Journal of Power Sources 306 (2016) 658e665 S. Go
Nomenclature VO2 I F S nsp csp cH2 O;el x xlw Msp Vm p psat pamb Dp J
volumetric fraction of oxygen in the air 0:2094 [e] current [A] Faraday constant 96485.3365 [C/mol] stoichiometry [e] molar flow of the species sp [mol/s] concentration of the species sp [g/cm3] concentration of water at the electrode [g/cm3] position along the cathode flow field channel 0 … 1 [e] position of the first visible liquid water 0 … 1 [e] molar mass of the species sp [g/mol] molar volume (@ 273 K and 101300 Pa) 22414 [cm3/ mol] pressure [mbar] saturation pressure of water vapor [mbar] ambient pressure constant for all presented measurements 1030 [mbar] pressure drop in the flow field [mbar] Water flux [g/(cm2 s)]
electrodes through a porous gas diffusion layer (GDL, consisting of the micro porous layer (MPL) and the substrate) to the flow field. The flow fields supply the cell with fuel and oxygen/air and remove the reaction products including the liquid water. The design of such flow fields is a complex task and they are usually optimized for narrow operating ranges. Systems with lower power density requirements on the other hand, can usually be operated without external humidification of the inlet gases. Air with ambient humidity is in many cases sufficient. This is mainly due to the fact that at lower power densities, the ohmic resistance of the polymer membrane affects the cell performance to a much lesser proportion compared to high power applications. The absolute amount of liquid water inside the fuel cell is significantly lower under these operating conditions and the amount of liquid water that must be transported by the flow fields is less. It is therefore possible to design simpler flow fields with lower requirements regarding liquid water transport. Another option is to use flow fields for fully humidified cells, which are likely to ensure a more stable operation of the fuel cell. Although the amount of liquid water is less and fewer droplets occur during non-humidified operation, the water management is not negligible. The aim of this study is to improve the understanding of liquid water management in fuel cells operated without external humidification. For this purpose, a model has been developed, which allows to predict the liquid water formation inside the cell as a function of several operating parameters. Furthermore, experiments have been conducted to analyze the effect of different operating conditions on the liquid water formation. Neutron imaging is a well-established method to investigate the liquid water distribution in a fuel cell during operation ([3e9]). In contrast to X-ray Imaging ([10e13]) the high penetration depth of neutrons into most metals and their high sensitivity to hydrogen ([14e16]) allow for investigation of a whole fuel cell without modifications. Further possible coupling of fuel cell models and neutron imaging has been proven (e.g. Ref. [17]). 2. Model The aim of the model presented in this paper is to predict the location downstream of the cathode inlet, at which liquid water starts to form. When making a number of assumptions, it is possible
dy D Fadj Q_ A U Tel Tfc TGDL DT l l
r v Re L Dh RH
659
diffusion distance [cm] diffusion coefficient [cm2/s] adjusting factor [e] waste heat [W/cm2] area [cm2] cell voltage [V] temperature at the electrode [K] temperature in the flow channel and fuel cell [K] temperature in the GDL, average of Tel and Tfc [K] temperature gradient [K] thermal conductivity [W/(m k)] thickness of the GDL [cm] density [kg/m3] flow velocity [m/s] Reynolds number [e] length of the channel segment [m] hydraulic diameter relative humidity
to approximate the amount of water in the PEM fuel cell cathode flow field channels for steady state operating conditions. The assumptions for the model are as follows: A. The current density and temperature over the active area is assumed to be constant. B. No gradients of the gas properties perpendicular to the membrane plane in the flow field channels are considered. C. The net liquid water transport through the membrane between anode and cathode is neglected, all water that is formed through the reaction remains on the cathode side. D. Liquid water starts to form at that point, where the water concentration in the flow field channel reaches the saturation concentration of vapor water. E. No water in the cathode supply. F. The geometry of the flow field is reduced to one straight channel. Notes to the assumptions: A The current density and the temperature distribution along the cathode channel do have an influence on the point of the first appearance of liquid water in the channel, but the influence is reduced to small deviations of the functions, since the model already works with the averaged value. B A typical flow field channel is much more than 100 times longer than its width or height. The diffusion in the channel is not blocked by material like in the GDL or MPL. The rough surface of the GDL and even possibly edges in the flow field will homogenize the medium in the channel. C The reaction water in PEM fuel cells is produced on the cathode side of the membrane (1). There are two main water transport mechanisms across the membrane: osmotic drag from the anode to the cathode side and diffusion that might take place in both directions. Driven by osmotic drag, additional water can be transported from the anode through the membrane to the cathode. Concentration differences of water between the cathode and anode cause a diffusive transport of water through the membrane. In case of a strong unidirectional water transport through the membrane it has to be considered in the model. For example in the case of very thick membranes where the back
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660
diffusion of the water from the cathode to the anode is small and where osmotic drag from the anode to the cathode dominates at high current densities. But for state of the art membranes, that usually have a thickness of less than 30 mm, the back diffusion equals the osmotic drag or is even higher [18]. On the other hand the water transport through the membrane has to be considered in case of a dominating back diffusion, where the produced water on the cathode side is transported mainly to the anode side. In principle, depending on the different operating conditions, the anode flow would have the ability to adsorb significant amounts of the produced water of the cathode side. To prevent this, the operating conditions have been chosen in that way, that the amount of water on the anode side stays approximately constant. The operating conditions have been deduced from fuel cells operated with an anode recirculation. Since these systems have no external humidification and only very small amounts of water leave the anode loop via the purge valve, the amount of water in the anode loop reaches a constant level after a short time. The overall water transport through the membrane for the conditions considered in this paper is generally small and is neglected in the following. D Since the microporous layer and the flow field offer a large surface for condensation, it is assumed that liquid water forms at the location where the saturation point is reached in the channel. E The inlet humidity of the cathode gas stream for the performed experiments is close to 0% (dew point measured during fuel cell operation 40.1 C) and has been neglected in this study. F The reduction of multiple channels to one straight channel is tolerable if the geometry of the flow field is based on parallel and similar channels like in the test cell (Fig. 1a). It is not valid in interdigitated flow fields or strongly asymmetric flow fields with complex geometries. The model: The production of water within the fuel cell is governed by the following equation:
O2 þ 4 H þ þ 4e /2H2 O
(1)
At the cathode side of the fuel cell, oxygen is reduced by the electrochemical reaction. For each consumed mole of oxygen 2 mol of water are produced. The stoichiometry S for a specific reactant describes the ratio of the amount of reactant supplied to the fuel cell to the amount consumed. An oxygen stoichiometry of e.g. 3 means, that three times more oxygen is supplied to the fuel cell than is consumed. The variable x describes the path of the air from the cathode inlet (x ¼ 0) to the cathode outlet (x ¼ 1) along the flow field (Fig. 1a, assumption F). The molar flow n of each species at a point x in the channel can be described as:
nO2 ðxÞ ¼
I Sx F 4
nN2 ¼ nO2 ð0Þ
nH2 O ðxÞ ¼
csp ðxÞ ¼
I 1 x F 2 I F
constant and VO2 the volumetric fraction of oxygen in the air. The concentration of a species csp can be calculated using the molar mass Msp and the mole fraction of the species sp and its molar volume Vm.
(2)
1 VO2 VO2
nO2 ; N2 ; H2 O ðxÞ ¼
Fig. 1. (a) Schematic description of the test cell flow field. The red line describes the mean path from the cathode inlet (x ¼ 0) to the cathode outlet (x ¼ 1). The x coordinates for each corner of the flow field are displayed. (b) Results of the simplified model. If the x-Coordinate, describing the position along the cathode flow field channel, equals xlw, the point of the first formation of liquid water in the cathode channel is predicted by the simplified model as a function of cell temperature (stoichiometry 2.0, dry cathode supply); no diffusion resistance is included. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
S x S 1 VO2 1 þ þ x 4 4 VO2 2
nsp Msp nðxÞ Vm
(6)
(3)
Thus the concentration of water can be calculated using (4), (5) and (6) as:
(4)
cH2 O ðxÞ ¼
(5)
where I is the total electric current of the cell, F is the Faradaic
2x MH2 O þ x Vm
S VO2
(7)
In the model the first formation of liquid water along the xcoordinate coincides with that point, at which the concentration of water exceeds the concentration of a saturated gas cH2 O;sat (assumption D). This point is described by x ¼ xlw.
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cH2 O;sat ðxlw Þ ¼ cH2 O ðxlw Þ
(8)
The saturation concentration can be calculated using the saturation pressure psat of water (calculated using formula of Hyland and Wexler that fits very well in the region between 0 C and 100 C Refs. [19,20]). The pressure in the cathode flow field channel is approximated linearly between the inlet and outlet pressure. The outlet pressure equals the ambient pressure.
cH2 O;sat ðxÞ ¼
psat MH2 O pðxÞ Vm
(9)
pðxÞ ¼ pamb þ Dp Dp,x
(10)
where pamb describes the ambient pressure at the outlet of the cell and Dp the pressure drop between the inlet and the outlet of the cell. Under the given assumptions the concentration of water only depends on the stoichiometry (7). The saturation concentration is a function of temperature and pressure (9). When the stoichiometry and the pressure are prescribed, the coordinate xlw at which liquid water starts to form can be described as a function of the fuel cell temperature alone. xlw can be calculated solving the equation:
psat ðTÞ 2 xlw ¼ pamb þ Dp Dp$xlw VS þ xlw
(11)
O2
The result of the model, with a prescribed stoichiometry of 2 and a pressure drop of 100 mbar is shown in Fig. 1b. The solution of the equation can be found in the Appendix A (A1).
3. Experimental Previous studies proved that it is possible to visualize liquid water in fuel cells in-situ with neutron imaging during actual operation (e.g. Ref. [3,4,21]). To be able to validate the above model predictions a single fuel cell in a standard fuel cell design of ZSW (Zentrum für Sonnenenergie-und Wasserstoff-Forschung BadenWürttemberg, Ulm) with an active area of 100 cm2 is used. Here a three channel meander is used to supply the reactants to the active area (Fig. 1a). The fuel cell is equipped with the same GDLs on anode and cathode side (Sigracet® SGL 25BC) and GORE® PRIMEA® 5761 as the membrane electrode assembly. Anode and cathode channels have both the same nearly rectangular cross-sectional area of 0.91 mm2. The three meander-shaped channels can be considered to have the ability for sufficient condensate removal for state-of-the-art operating conditions. The fuel cell is operated in co-flow configuration, where hydrogen and air both flow from top to bottom to assure a gradual increase of water content as the gases pass through the fuel cell. On the cathode side, a constant stoichiometry of 2 is used for the experiments. An overstoichiometric flow of hydrogen of 2 norm l/min (lambda ¼ 3.6 to 14.3) is employed at the anode to remove all liquid water possibly accumulated on the anode side. The anode gas is humidified using a bubbler with a dew point of 50.3 C, which corresponds to relative gas inlet humidity between 99% and 45% at fuel cell temperature of 50.9 C and 68 C, respectively. The operating conditions are deduced from operating conditions known from recirculated operation. The fuel cell temperature is regulated by a cooling fluid which is guided through two cooling flow fields on the back side of the anode and cathode gas flow field. As a cooling fluid, D2O is used, so that a minor attenuation of the neutron beam is achieved. The flow of the cooling fluid is from bottom to top to avoid accumulation of gas bubbles inside the cooling flow field which can disturb the neutron imaging. The visualization of water transport was performed at the
661
neutron facility CONRAD/V7 of the Helmholtz-Zentrum Berlin (BER II research reactor). Details of the experimental setup for visualization with neutrons can be found in Refs. [22,23]. The exposure time was 10 s per radiography with an additional readout-time of 4 s. A lithium scintillator with a thickness of 200 mm was used. The used pixel size was 51.3 mm [24]. The mean pore size of the GDL is smaller than 1 mm [25]. But even with a large number of pores at the size of 20 mm and larger, the pore size is smaller than the limit of the spatial resolution of the used neutron imaging setup of about 100 mm. The spatial resolution was limited by the large size of the fuel cell and the corresponding large pixel size. This is not the general limit of the spatial resolution [26] or water film thickness sensitivity [27] of neutron imaging. However our work is focused on the water distribution in the channels that can be detected with certainty. For the visualization of the point xlw a test series was performed in which current density and fuel cell temperature are varied stepwise to identify the change in water appearance inside the cathode channels. Operating conditions were held constant until no significant change of the liquid water distribution could be detected. The volumetric gas flow of hydrogen is kept constant, whereas the air flow is adjusted in a way to ensure that a constant stoichiometry of the air flow is achieved. The air flow and thus the pressure inside the channels change due to the variation of current density. As the pressure is used as an input for (9), this will be evaluated in detail. The pressure drop is calculated as the actual difference between gas inlet and outlet pressures less the net pressure drop of the balance of plant (BOP) around the fuel cell (pipes, etc.). The pressure drop is recorded at three different current densities (Fig. 2) and for each current density one average pressure drop is calculated for use in the model. The cell voltages have been merged for each current density as well. 4. Results The neutron images obtained in the experiments clearly show the liquid water formation in the fuel cell during operation (Fig. 3). While operated with a dry cathode supply no liquid water can be seen next to the cathode inlet and the area within the channels following the inlet region. Depending on the operating conditions at some point liquid water appears in the neutron images. By overlaying the known geometry of the cathode flow field channels (Fig. 1a), the path of the cathode gas stream can be reconstructed in the neutron images. Liquid water can also be located on the anode side of the cell, but the liquid water on the cathode side dominates. In Fig. 3 the point of the first visible liquid water along the x-coordinate is marked in blue. Since liquid water is initially visible on the neutron images as a gentle shadow and increases to a clearly visible trace, an error bar is used to mark this band. In total 11 neutron pictures have been evaluated. For the post processing of the experimental data, the fuel cell temperature is calculated by averaging the values measured at the cooling inlet and the cooling outlet. The temperature and current density values measured during the experiment are shown in Fig. 4a. The x-coordinates, at which liquid water was observed at different operating temperatures and current densities, are shown in Fig. 4b. The x-coordinates of liquid water formation as predicted by (11) are also presented in Fig. 4b. The curves of the model are adapted to the individual pressure drop of the operating points (i ¼ 0.2 A/cm2 Dp ¼ 61.8 mbar; i ¼ 0.4 A/cm2 Dp ¼ 135.5 mbar; i ¼ 0.8 A/cm2 Dp ¼ 275.8 mbar). A significant discrepancy between the calculated and the observed values for xlw can be seen for all data points. The discrepancy increases for operation points with higher current densities. In all considered operating points, the model predicts
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Fig. 2. Experimentally determined cell voltage U (a) and pressure drop Dp (b) in the testing cell during neutron imaging.
Fig. 4. (a) Fuel cell current and temperature during the neutron imaging (b) Experimental and simple model starting point of liquid water in the cathode channel; relation between cell temperature and path length (stoichiometry 2.0, dry cathode supply). At a specific temperature (e.g. 58 C) the model calculates the starting point of liquid water in the cathode channel later (92%) than the liquid water appears in the measurements (73%).
4.1. Derivation of the optimized model In stoichiometric air supply operation the correlation between produced water and the cathode gas stream is constant, but the absolute amount of produced water increases proportional to the current density. The water must be transported from the electrode, where the electrochemical reaction takes place, to the cathode flow field channel, passing through the gas diffusion layer (GDL) that consists of layers of different porosities (MPL and substrate). As long as no liquid water is present in the flow field channels, the water transport to the channel takes place in the gaseous phase. The GDL can be considered as a diffusion resistance for the gaseous water transport and Fick's law is a good approximation of the real diffusion processes within a fuel cell.
J¼D
Fig. 3. Neutron image at 0.2 A cm-2 and 51 C fuel cell temperature; mean cathode path and path length overlaid; starting point of liquid water in the cathode channel at 50.0% of path length.
condensation to occur closer to the outlet of the cathode flow channels than observed during the experiments. In the following, the discrepancy between the theoretically predicted and the observed condensation is analyzed.
dc ; dy
(12)
where J is the diffusion flow, D a material specific diffusion, dc the concentration gradient of the species and dy the diffusion distance. The driving force for the gaseous water diffusion through the GDL is the concentration gradient of water between the electrode and the cathode flow field channel. Fig. 5 schematically describes the situation for the water transport in the cell. The concentration in the flow channel can be described by (7) as a function of the electrochemical reaction rate alone, if the assumptions A, B and C are applied. Condensation is only expected if the partial pressure of gaseous water reaches the saturation pressure and it is evaporated when the saturation pressure is not
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reached. The not optimized model depends only on the temperature and stoichiometry. Since the experiments showed condensation at a point along the x-coordinate, which is well before the point at which the model predicted the saturation pressure to be reached, the validity of the assumption D, liquid water forms at the location where the saturation point is reached, must be questioned. Before the first appearance of liquid water, the transport mechanism for water is the diffusion process (12). Since the water concentration in the flow field channel can be calculated by (7), the concentration at the electrode cH2 O;el can as well be calculated via the diffusion as:
cH2 O;el ðxÞ ¼
J,dy þ cH2 O ðxÞ D
(13)
Assumption If the concentration of water at the electrode exceeds the maximal possible concentration of gaseous water, i.e. the saturation pressure, liquid water appears and is transported in the liquid phase to the channel. This point ðx ¼ xlw Þ is visible in the neutron images.
cH2 O;el ðxlw Þ ¼ cH2 O;sat ðxlw Þ
(14)
Once the water is produced at the electrode in the liquid phase, it will not be evaporated again within the GDL and is transported in the liquid phase to the flow field. This is not a valid assumption for an equilibrium state after an infinite time but it seem acceptable for the short times and diffusion paths in fuel cell operation. That means, that after this point the pure gaseous water transport in the fuel cell is complemented by liquid water transport like described by Kimball “Liquid is driven by a hydraulic pressure from the membrane/cathode interface through the largest pores while gas moves from the gas flow channel to the membrane/cathode interface through smaller, but more plentiful, pores” [28]. Based on this assumption the point of the first appearance of liquid water ðx ¼ xlw Þ can be calculated by solving the equation for xlw :
J,dy cH2 O;sat ðxlw ; Tel Þ cH2 O xlw ; Tfc ¼ D
663
The coefficient has been measured at 25 C and 1014 mbar. Since the diffusion coefficient is temperature and pressure dependent an adaption to the operating conditions is calculated (17). The adaption is based on the general temperature and pressure dependency Hirschfelder et al. have developed [31]. For the calculations of the diffusion coefficient the average temperature and pressure of the channel is used. Calculating with this diffusion coefficient in (15) the calculated points of the first visible liquid water are shown in Fig. 6.
Dlit ¼ 0:0630
D ¼ Dlit
pDlit p
cm2 s T TDlit
(16)
3 2
(17)
Where pDlit and TDlit are the conditions where LaManna has measured the coefficient. The description of the points of the first visible liquid water including diffusion using the diffusion coefficient of (16) from literature does not fit the experimental results. The mechanical installation situation of the GDL and MPL in the experimental setup for the measurement of the diffusion coefficient differs at some points from the installation situation in the fuel cell. The compression of the material and the channel and landing situation is different and will influence the effective diffusion coefficient significantly, as discussed in chapter 5, discussion. By using an additional adjusting coefficient Fadj ¼ 3:2 (Fig. 7), used in Eq. (18), to effectively increase the diffusion
(15)
Note, that the temperature at the electrode Tel differs from the temperature in the flow field channel Tfc and thus differ the saturation concentrations. The temperature gradient is caused by the waste heat of the fuel cell, that is also transported through the GDL. The calculation for the temperature gradient can be found in the Appendix B. For the used GDL (SGL25BC, assembly of an MPL and substrate) a diffusion coefficient D can be found in the literature [29,30],(16).
Fig. 6. Experimental and theoretical points of the first appearance of liquid water in the cathode channel calculated with a diffusion coefficient of 0.063 cm2/s; relation between cell temperature and path length (stoichiometry 2.0, dry cathode supply).
Fig. 5. Schematic diagram showing the diffusion process in the fuel cell cathode.
ۧling et al. / Journal of Power Sources 306 (2016) 658e665 S. Go
664
resistance and adapt the model for the special cell, a good agreement between predictions and measurements can be achieved:
J,dy ,Fadj cH2 O;sat ðxlw ; Tel Þ cH2 O xlw ; Tfc ¼ D
(18)
The complete solution of the equation can be found in the Appendix A (A2).
5. Discussion Assuming that the assumption (14) is correct, the diffusion of gaseous water through the GDL seems to be much slower than the diffusion is described in literature. The necessary adjusting might be caused mainly by two reasons. Firstly, the bipolar plates consist of numerous flow channels and landings. Whereas the water is produced on the whole surface of the electrode, it can only enter the gas stream in the channels. This causes an increased diffusion path under the landings. Further the amount of transported water concentrates in the regions under the landings close to the channels. This is exactly the area (the intersection of the channel to the landing) where the lowest temperatures are usually simulated [32], since most of the waste heat of the electrode is transported through the landings out of the fuel cell, and the first droplets in the channel are usually visible [33]. In Fig. 8 a schematic description of the area between the channels and the electrode is shown. Additionally, only one reference is known for the diffusion coefficient of the GDL SGL 25BC (16) ([29,30]). In the conclusion of his master's thesis LaManna writes: “It is desirable to know if water vapor diffusion coefficients change with GDL compression” [30]. Till now it is not clear what effect the compression of the GDL has on the diffusion coefficient. The GDLs in the testing fuel cell of ZSW should be compressed to roughly 83% of their initial thickness. This will differ from the compression of LaManna, but so far the influence of compression is not clear. The compression might change the diffusion coefficient. Especially the region under the landings, where the first droplets in the channel are usually visible [33], is most compressed. If the adjusting factor is only applied to the diffusion coefficient a corrected diffusion coefficient determined by iteration of (19) results.
Dadj ¼
Dlit cm2 ¼ 0:0197 3:2 s
(19)
A combination of the two reasons is also conceivable.
Fig. 8. Lengthened diffusion path and concentrated water diffusion under the landings.
6. Conclusion In this study a PEM fuel cell model is presented which aims to predict the location in the flow field at which liquid water forms at the cathode. It is validated with neutron images of a PEM fuel cell visualizing the locations at which liquid water forms in the fuel cell flow field channels. It seems that diffusion limited gaseous water transport, calculated with the Fick's law, is capable to describe the point of the first appearance of liquid water in the flow field channels of the cathode. That means that if the limit of diffusion from the electrode to the channel is reached, liquid water appears at the electrode. This water does not evaporate again but is rather transported in liquid phase through the GDL to the channel. To adapt the diffusion by Fick's law to the performed measurements an adjusting factor of 3.2 for the coefficient is necessary. Good agreement of model predictions and measurement results has been achieved. This adjusting is argumentable by geometric flow field reasons or by a necessary diffusion coefficient correction. The simplifications A (homogeneous temperature and current density distribution), B (no gradients perpendicular to the membrane plane in the flow field channels) and C (no net liquid water transport through the membrane) might cause some small deviations but will not change the basic results. Presumably both reasons (landing/channel and compression) are relevant and the adjusting must be split between them. The calculation is based on the assumption of (14). Yet the results are not fully proving our theory, but they strongly support the explanations described above. Further test have to be done to fully prove the theory. Acknowledgments This work was supported by the Federal Ministry of Economics and Technology, Germany (funding number 03ET2007, “Entwicklung von Lebensdauerprognosemodellen von Brennstoffzellen in realen Anwendungen”). Appendix A Solutions for (11)
Fig. 7. Results of the enlarged model. Experimental and theoretical points of the first appearance of liquid water in the cathode channel calculated with a diffusion coefficient of 0.063 cm2/s and an adjusting factor of 3.2; relation between cell temperature and path length (stoichiometry 2.0, dry cathode supply).
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u S u psat þ 2ðpamb þ DpÞ t psat þ 2ðpamb þ DpÞ 2 psat VO2 xlw ¼ 4,Dp 4,Dp 2,Dp (A1) Solution for (17)
ۧling et al. / Journal of Power Sources 306 (2016) 658e665 S. Go
J Ddy,Dp,V S
xlw ¼
MH O 2 Vm
O2
665
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi v0 12 J dy u ,ðpamb þDpÞ,V S u J Ddy,Dp,VOS J dy D ,ðp þDpÞ O amb S u 2 þ psat þ 2ðpamb þ DpÞ uB MH O 2 þ D MH O psat þ 2ðpamb þ DpÞC psat VO MH O 2 2 2 2 C uB Vm Vm Vm C B u 0 0 1 1 uB J dy C ,Dp D A J dy J dy u@ 2,Dp MH O ,Dp ,Dp t 2 2@ 2,Dp DMH O A 2@ 2,Dp DMH O A Vm J dy ,ðpamb þDpÞ D MH O 2 Vm
2 Vm
2 Vm
(A2)
Appendix B Calculation of the temperature gradient through the cathode GDL The temperature of the flow field side of the GDL is assumed to be equal to the cell temperature because of its greater proximity to the fuel cell temperature sensor. An estimation for the temperature gradient between the electrode and the flow field channel has been done on the basis of the thermal conductivity of the GDL and a waste heat calculation using a theoretical open cell voltage of 1.253 V. The calculations are based on the lower heating value, since the calculations describes the limit of the gaseous water transport. Since most of the heat is produced at the cathode electrode and the way for the heat transport to the flow field channels through the membrane and the anode GDL is longer than only through the cathode GDL, the fraction of the total waste heat that is transported through the cathode side of the fuel cell is greater than 50%. But a fraction of the heat is also transported through the anode, since the membrane has only a thickness of 18 mm. It is assumed, that the cathode fraction of the waste heat transport is 55%.
Q_ ¼ ð1:253 V UÞ,i,55 %; A
(A3)
where Q_ is the waste heat, A the reference surface, U the cell voltage and i the current density. When the GDL is compressed with 0.75 MPa, the thickness l of the GDL is approximately 190 mm and the thermal conductivity l of the used GDL is reported in literature [34]. The temperature gradient can then be calculated using the Fourier's law as:
DT ¼
Q_ l A l
(A4)
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