Influence of gas channel depth in self-humidified miniature PEM fuel cells with dead-ended anode

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Influence of gas channel depth in self-humidified miniature PEM fuel cells with dead-ended anode Denise A. McKahn Picker Engineering Program, Smith College, Ford Hall, 100 Green St, Northampton, MA, 01063, USA

article info

abstract

Article history:

For fuel cells to become a viable power source in low power applications, significant gains

Received 29 September 2014

must be made in maximizing fuel cell specific power density and system specific energy

Received in revised form

density. To reduce complexity, these miniature PEM fuel cells are passively cooled with a

26 February 2015

dead-ended anode. Additionally, dry reactant gases can be supplied, resulting in self-

Accepted 28 February 2015

humidified membranes. Targeting reductions in mass, this work experimentally in-

Available online 27 April 2015

vestigates the influence of flow field channel depth on cell performance. Over the range of 0.457e1.57 mm, the best performance was found at cathode channel depths of 0.813 mm

Keywords:

with no statistically significant difference associated with anode channel depth using static

Fuel cell

polarization curves following anode purges. As a result, an along-the-channel model of

Gas channel

anode nitrogen accumulation identifies the optimal anode channel depth that minimizes

Self-humidified

the system specific energy density given a driving cycle. The anode volumetric leak rate

Low temperature

plays a significant role in the nitrogen frontal evolution and resulting optimal anode

Dead-ended anode

channel depth. If deployed in a multi-cell stack with the recommended channel depths, the

Nitrogen accumulation

PEMFC system would be capable of achieving a specific power density of 45 mW/g and a specific energy density of 680 W h/kg, nearing the specific power density and exceeding the specific energy density of off-the-shelf lithium-ion batteries (approximately 80e100 mW/g and 300 W h/kg). Copyright © 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

Introduction Solid polymer electrolyte membrane fuel cells (PEMFCs) enable rapid transient responses with an ability to startup at ambient, and even freezing [1], conditions. As a result, PEMFC power systems are a suitable candidate for unmanned aerial vehicles (UAVs) and systems [2]. The U.S. Department of Energy Fuel Cell Technologies Research and Development Program has identified portable applications as an early market for PEMFCs, with technical barriers relating to size, weight and thermal and water management [3]. A thorough review of

these barriers was completed for a variety of PEMFC applications and material combinations [4]. A U.S. Department of Defense (DOD) sponsored technology assessment recommended that the DOD establish a near-term 5-yr evaluation and acquisition strategy for fuel cell powered UAVs [2], with significant investment underway in micro aerial vehicles that weigh less than 18 g [5]. A lightweight aerial system must operate at relatively low power (1e300 W); have minimal total system mass, high specific energy density; and tolerate operation at altitude. At both high and low altitude, several hybrid fuel cell power system strategies have been employed, such as hybridizing

E-mail address: [email protected]. http://dx.doi.org/10.1016/j.ijhydene.2015.02.132 0360-3199/Copyright © 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

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fuel cells with photovoltaic panels [6], gas turbines [7], and batteries with or without DC/DC converters [8,9], with electrical architecture and controls analyses completed by Refs. [10,11]. The application of interest here is low altitude, short duration, controlled meteorological (CMET) balloons powered by lithium ion batteries for atmospheric research [12]. Because an entirely different PEMFC design strategy is required for aerial systems [13], a significant operational distinction is made here for CMET balloons as opposed to automotive or other portable applications. For CMETs specifically, the volume of the power system is not as critical as it is for aerial vehicles and portable electronics. Rather, mass poses the limiting constraint. Thus, CMETs have a requirement of high specific energy density (Wh/kg) and specific power (W/kg), as opposed to the typical simultaneous constraints on both mass and volume. In miniature and micro fuel cells designed for low power output (1e50 W), the fuel cell active area approaches 8 cm2 with maximum power densities ranging from 20 to 250 mW/ cm2 [14,15]. This observed performance is nearly an order of magnitude lower than PEMFCs with active areas larger than 100 cm2. This performance discrepancy is the result of the cell operating conditions that come from architectural and cell design differences [16]. The influence of cell operating conditions, such as reactant supply temperatures, pressures and humidities, on fuel cell polarization has been quantified experimentally in miniature PEMFCs [17,18] with results from Ref. [18] connecting these operational variations to gas channel designs. Because the flow fields, used to distribute products and reactants, make up 43% of the total stack mass, their design is critical to necessary stack mass reductions. By reducing channel depth, the flow field plate can be made thinner, resulting in significant weight reductions. When considering channel design, there are three design choices to be resolved, namely channel configuration, orientation and size. An extensive literature review on the influence of channel design was completed by Ref. [19], considering channel configuration, orientation, crosssectional shape, width and height at a range of operating conditions. Few studies investigate miniature fuel cell channel depths in the range of 100e400 mm [14]. When studied, the operating temperature is 50e80
C with humidified reactant supplies in flow through, as opposed to dead-ended, anodes. Under these conditions, it is well established that liquid water flooding occurs on the cathode (and anode if dead-ended), motivating innovative channel shapes. In simulation, when two-phase flow is neglected, improved convective transport is associated with the increased bulk velocity that comes with decreasing the channel cross-sectional area on both the anode and cathode [20,21]. These works lead one to believe that, absent flooding, shallow channels improve performance in cathodes that are not air-breathing. Given the well documented occurrence of cathode flooding, observed at high current density, studies on miniature scale channel depths have therefore focused on liquid water accumulation. Shallow channel depths cause accumulated liquid water to more readily occlude channels, setting a lower constraint on the range of operable current densities [22] as

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well as a tradeoff between space constraints and water management [23]. Moreover, the Peclet numbers are not sufficient for liquid water detachment through convection [24], a serious limitation for air breathing fuel cells [22]. As a result, in miniature channels, when the cathode is flooded, there is little benefit in water management to selecting a particular channel orientation [25], variable depth along the channel [26], or configuration [27]. In addition to water flooding, both modeling and experimental evidence have established that nitrogen [28e31] accumulates in the anode of dead-ended PEMFCs as a result of the concentration gradient across the membrane when air (containing nitrogen) is supplied to the cathode. The presence of nitrogen decreases the molar fraction and partial pressure of hydrogen, creating a “blanket” which prevents hydrogen from reaching catalyst sites. This reduction in catalytic activity locally increases current density which reduces terminal cell voltage. An equilibrium condition is achieved when the nitrogen concentration on the anode is equal to that on the cathode, corresponding to the minimal hydrogen molar fraction [32], and setting a lower bound on cell performance. The larger the anode volume, the longer it takes to fill the anode with nitrogen. Thus, not only does anode channel depth impact stack mass, it is related to cell performance as a result of nitrogen accumulation. In summary, there is limited experimental data on the influence of channel depth in PEMFCs with small active areas of less than 5 cm2 [19]. When studies were conducted, these PEMFCs were operated at temperatures commonly seen in large format stacks (50e80
C) with fully humidified reactants and flow through anode operation. The work presented here aims to fill a gap in analysis of both anode and cathode channel depth with dead-ended anodes and dry reactant supply for miniature PEMFCs. In particular we target system specific energy density, a critical metric not commonly considered. First we present the experimental hardware. Then we examine the expected variability in cell performance to find the statistically significant impacts associated with gas channel depth. Finally, we calibrate an along-the-channel model of nitrogen accumulation in dead-ended anodes to explore the impact of the anode natural leak rate and channel depth on system specific energy density.

Experimental hardware This section presents the CMET application, bench hardware and stack materials. A detailed discussion of the choices made in material selection, system design and architecture is provided in Ref. [16].

Stack and cell materials Each cell was comprised of a flow field plate, Buna-N gaskets, gas diffusion layers (GDL), and a membrane electrode assembly (MEA). A summary table of the component masses is provided in Table 1, with a total single cell stack mass of 48.00 g.

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Table 1 e Cell component masses. Part

Mass (g)

Cathode and anode graphite flow fields Buna-N gaskets Acrylic endplates PTFE fittings PTFE tie-rods and nuts GDLs and MEA Total single cell stack mass

20.52 2.54 20.96 1.88 1.69 0.41 48.00

Fig. 2 e Fuel cell experimental hardware.

Fig. 1 e Separator plate design.

Fig. 1 displays the flow patterns used for both the anode and cathode flow fields. The anode and cathode flow fields were made of 3.18 mm GM10 grade Graphtek® graphite blanks. Each channel was machined to a width of 1.17 mm. The channel lands (ribs) and grooves were evenly spaced and parallel. The channels were placed in a cross-flow pattern with the anode oriented vertically and the cathode horizontally. The fuel cell utilizes standard commercially available Nafion® 212 MEAs, purchased from Ion Power®, with an active area of 4.84 cm2, a catalyst layer of 0.3 mg/cm2 Pt/C on the anode and cathode with no integrated gaskets. A non-woven SGL Sigracet® 10BC GDL was chosen with an uncompressed thickness of 0.38 mm. Four tie-rods were used to hold the cell materials together and tightened sufficiently to avoid material displacement on handling. Stack compression was then maintained as described in the Test bench hardware section.

Test bench hardware As previously mentioned, the CMET application is a significant deviation from standard PEMFC test conditions. The system design and architecture decisions are thoroughly detailed in Ref. [16]. Here, we present the physical test bench hardware deployed to evaluate the influence of electrode channel depths in test conditions designed to mimic in-flight hardware. A schematic of the major system components used for experimental analysis is provided in Fig. 2. When the fuel cell is deployed in a CMET, the air compressor, air storage tank and mass flow controller are replaced with a miniature air pump and the supply and exhaust valves are removed. It is not typically recommended that the anode and cathode be operated under dry conditions [33]. Therefore it is

important to highlight the lack of reactant pre-treatment (humidification) in this work. A consequential system architecture decision is made here to decrease system mass by removing the gas humidifiers, a common design choice in micro, low-power applications [34,35]. While studies have clearly shown increased performance associated with electrode water injection [33], the specific power and energy density is not improved when accounting for the mass of the related equipment for miniature PEMFC systems. To directly control and measure the clamping pressure applied to the endplates, each fuel cell stack was placed under a compressive load using an Instron® 5542 Electromechanical Test Instrument with a 500 N frame. Steel block standoffs with a contact area of 514 mm2 (0.797 in2), centered on the active area, were used to transfer this load to the fuel cell endplates, resulting in applied pressures of up to 9.6 bar (140 psi). Prescale® pressure paper was used to confirm relatively uniform compression across the active area. Dry pure hydrogen is pressure regulated at the anode inlet to 1.8 psig (1.14 bar). This pressure regulation system replenishes the hydrogen consumed in the chemical reaction. The hydrogen stream is dead-ended. Using a purge valve located downstream of the anode, hydrogen can be momentarily purged through the anode to remove water and gases that accumulate. Dry air is delivered by a mass flow controller to the cathode from a stream of oil-less air. The cathode is operated as flow through and the cathode exhaust gases are vented. No cooling equipment is used with the miniature fuel cells in this work. An experimentally validated thermal model of this miniature PEMFC design was developed in Ref. [36]. With the multi-cell stack required to power the CMET, active cooling is not required. This result is confirmed in other studies on the cooling needs and temperature effects in miniature low power applications [37]. In fact, low thermal conductivity materials have been considered in order to retain heat within miniature air-breathing PEMFCs [38]. A DynaLoad® programmable electronic load is used to mimic driving cycles. Both current and voltage output from the PEMFC stack are measured independently from the load.

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Several measurements are taken as indicated in Fig. 2. In the gas plumbing external to the fuel cell stack, the anode inlet and the cathode inlet total pressures are measured. Inside the fuel cell stack, in the cathode exhaust manifold, the cathode outlet temperature is measured. These measurements are acquired using off-the-shelf data acquisition and signal conditioning equipment. Signals are amplified using 5B Series signal conditioning modules with a 4 Hz filter. Signals are acquired using a National Instruments® USB-6212 multifunction data acquisition board and processed using LabVIEW®.

Experimental results First, we establish a testing protocol, then we characterize the expected variability in cell polarization at a single set of operating conditions and channel depths. Then we examine the influence of channel depth on cell performance.

Testing protocol At each new channel depth a new fuel cell stack was assembled and tested under the same conditions and compared at the same point in membrane life. A testing protocol was established with variable current density and air mass flow, as shown in Fig. 3. Polarization curves were taken at different times throughout the test. This driving cycle was designed to mimic the observed variability in load during a flight campaign [39]. The cathode inlet temperature is influenced by the compressor conditions and remains between 23 and 27oC throughout all experiments. As expected, the cathode outlet

Fig. 3 e Fuel cell driving cycle and stack inputs. The subplots display current density, air mass flow rate, and cathode inlet temperature.

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temperature is influenced by stack heat production and removal, in turn functions of current density and air mass flow. Throughout the experiments, the cathode outlet temperature remains between 23 and 35oC. It is important to note that the stack temperature (cathode outlet temperature) is relatively low for an operating PEM fuel cell in comparison to the typical 60e80oC range common for active areas greater than 100 cm2. At these lower temperatures, it was expected that liquid water flooding would be more pronounced due to the decreased amount of water entrained in the cathode exhaust gas. However, the relatively low current density and the lack of supply gas humidification may result in less flooding than typically expected for low temperature PEM fuel cells and will be further explored in this work.

Cell variability To ensure that any performance differences are the result of the change in channel depth, we first examine the expected variability in cell performance at one channel depth. Four different fuel cell stacks were assembled, each with a new MEA and GDLs, and with flow channels that were 1.17 mm wide and deep. Tests were conducted following the protocol established in the Testing protocol section. The voltage output for each of the four stacks were compared for each polarization curve along with the standard deviation from the mean cell voltage, shown in Fig. 4. As is well established in literature [40], the open circuit voltage was observed to be a function of the oxygen partial pressure through the fixed air mass flow rate, with little variation from one test to the next. For a given air mass flow rate, there was relatively little cell voltage variability in the activation region of the polarization curve (<50 mA/cm2), indicating that oxygen partial pressure regulation was consistent from one experiment to the next. Greater variability in cell voltage was observed in the ohmic region of

Fig. 4 e Standard deviation in voltage as a function of current density for the first five polarization curves taken following the testing protocol. Polarization curves are taken at fixed air mass flow rates of either 40, 100, and 300 sccm.

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the polarization curve, which is well known to be sensitive to membrane water content [40,41]. There is little variation in the cathode air outlet temperature throughout testing for each stack, indicating that membrane water content is likely the contributing factor for the observed variability in ohmic resistance from one fuel cell stack to the next. Liquid water droplet detachment at the GDL to channel interface is a function of the fluid velocity [42,43]. Liquid water that accumulates in the gas channels is, therefore, less likely to be entrained in the gas stream and removed from the cell at low flow. To assess whether liquid water accumulation occurred, the cells were periodically surged with air, resulting in a rapid but unsustained increase in cell voltage due to the increased oxygen partial pressures. Earlier dynamic studies with neutron radiography have clearly demonstrated the voltage signature during cathode surge and anode purge events when liquid water is present [44]. As a result, it was determined that the cells were not operating under flooded cathode conditions in these tests. While neutron radiography has confirmed that anode flooding occurs and dominates at low current density in stacks with well humidified cathodes [44], the anode is not flooded in miniature cathodes supplied with dry air [18]. As with cathode surges, anode purges do not result in the sustained voltage recovery typical of flooded anodes. Thus, observed differences in ohmic loss are not thought to be influenced by a resistance to mass transport associated with liquid water accumulation. Similar membrane hysteresis [45], the standard deviation in voltage is a function of current density and the order in which the polarization curve was taken as a result of the membrane state of hydration. The smallest standard deviation in voltage was observed in the first polarization curve and the largest standard deviation in voltage seen in the last polarization curve. The standard deviation in cell voltage generally increases as a function of current density with the smallest deviations of 6e11 mV typically seen near 50 mA/ cm2. Interestingly, beyond approximately 150 mA/cm2, the increase in the standard deviation in voltage is a relatively constant function of current density. The main rationale for assessing cell variability in this work was to identify the polarization curve for which the least variability in cell voltage is expected in order to compare the influence of channel depth on cell performance. While the first polarization curve has the smallest observed standard deviation in cell voltage, the fourth polarization curve has the smallest mean standard deviation across the range of current densities tested. Thus, for this particular testing protocol and set of operating conditions, it is recommended that the fourth polarization curve be used in comparing the influence of design variables or operating conditions on cell voltage. More importantly, we argue that an assessment of expected cell variability be made any time that design parameters are experimentally evaluated. Fig. 5 displays three standard deviations from the mean cell voltage along with the 5% and 95% confidence intervals for the fourth polarization curve. Clearly, the standard deviation, s, increases as current density increases, with a mean across all current densities of s ¼ 18 mV and a s ¼ 26 mV at 250 mA/ cm2.

Fig. 5 e Descriptive statistics. One, two and three standard deviations about the mean cell voltage for the fourth polarization curve shown in Fig. 4.

Influence of anode channel depth To examine the influence of the anode channel depth on cell performance, single cell stacks were assembled of varying anode channel depth at a cathode channel width and depth of 1.17 mm and an anode channel width of 1.17 mm. Each stack was tested according to the protocol discussed in the Testing protocol section. The results for the second, fourth and fifth polarization tests, at cathode air flows of 40 sccm, 100 sccm and 300 sccm, respectively, are shown in Fig. 6. The 95% confidence interval around an anode channel depth of 1.17 mm is plotted in light green as an indication of the expected variability in cell performance. The polarization curves taken at all three cathode air mass flow rates fell within or were very close to the 95% confidence interval. As a result, there is little statistical significance in the voltage deviations for anode channel depths of 0.457e1.57 mm and these operating conditions. This result is not surprising given that the anode is deadended. The anode inlet total pressure is regulated and the gas velocities are relatively slow compared with the cathode. If no other constituents accumulate in the anode, the hydrogen partial pressure should not change with anode channel depth. Of greater interest, is any improvement in the specific power density resulting from reductions in the graphite plate thickness for shallower anode channel depths. Given the CMET application of interest, with a nominal 3.7 V PEMFC output voltage, a 6-cell PEMFC stack is needed. Assuming the average cell voltage in a 6-cell stack performs the same as the single cell tested, the specific power density of a 6-cell stack is estimated as a function of anode channel depth, shown in Fig. 6. The shallowest anode channel depth results in the highest specific power density at current densities < 200 mA/ cm2, it does not result in the maximum specific power density at all current densities. However, it is important to recall that the polarization curve differences were not statistically

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Fig. 6 e Influence of anode channel depth, d, on cell performance. The right y-axis displays the estimated specific power density if this single cell were assembled into a 6 cell stack with a cathode channel depth of 1.17 mm. The subplots contain, from top to bottom, pol. curve 2 at 40 sccm, pol. curve 4 at 100 sccm, and pol. curve 5 at 300 sccm. The 95% confidence intervals are plotted in light green. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

significant. Therefore, it is recommended that the shallowest anode channel depth tested, corresponding to the smallest graphite plate mass, be used.

Influence of cathode channel depth The influence of the cathode channel depth was assessed with an anode channel width and depth of 1.17 mm and a cathode channel width of 1.17 mm. Each stack was tested according to the protocol discussed in the Testing protocol section. The results for the second, fourth and fifth polarization tests, at

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Fig. 7 e Influence of cathode channel depth, d, on cell polarization. The subplots contain, from top to bottom, pol. curve 2 at 40 sccm, pol. curve 4 at 100 sccm, and pol. curve 5 at 300 sccm. The 95% confidence intervals are plotted in light green. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

40 sccm, 100 sccm and 300 sccm, respectively, are shown in Fig. 7. Unlike with the anode, the cathode channel depth does have a statistically significant influence on cell polarization. Additionally, the cell polarization resulting in the best performance is a function of the fixed air mass flow rate. At 40 sccm, generally the cell polarization improves as cathode channel depth increases, with the greatest performance with the deepest cathode channels. At this flow rate, there is little difference in performance between 1.17 mm and 1.57 mm as well as little difference between 0.64 mm and 0.46 mm. It is important to note, that these results while statistically significant, lie just outside the 95% confidence interval. As the air mass flow rate increases, the shallow channel depths appreciably degrade performance in both the activation and ohmic regions of the polarization curves. As the

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cathode channel depth increases, the channel cross sectional area increases. When operating under fixed air mass flow rates, this increased channel cross sectional area results in lower air velocities and oxygen partial pressures at a given current density. As discussed with varying the anode channel depth, in these tests it is not expected that either anode or cathode liquid water flooding occurs due to the dry reactant gases supplied. Thus, it was expected that shallower cathode channels would result in reduced activation losses (greater oxygen partial pressures), which was not consistent with the observed results. The ohmic losses are a function of the membrane humidity, bulk and contact resistances, presuming that the cell temperature is relatively constant. For a given cathode channel depth, the contact and bulk electrical resistance should not be a function of air mass flow rate. Thus, any sensitivity to air mass flow rate indicates that membrane humidity might be the driving factor influencing the differences in ohmic losses observed at high flow. For a given channel depth, as air mass flow rate increases, the membrane humidity decreases and ohmic losses increase. As with the anode channel depth, it is also expected that increased cathode channel depths result in increased bulk ohmic resistance. Thus, the ohmic slope is not fixed from one cathode channel depth to the next, as observed. The estimated specific power density for a 6 cell stack with varying cathode plate thicknesses is shown in Fig. 8. At an air mass flow rate of 40 sccm, the specific power density is greatest for the shallowest cathode channel depth of 0.46 mm. However, this performance significantly degrades as the air mass flow rate is increased. At 100 and 300 sccm, the best specific power density was observed for a depth of 0.81 mm. Due to the range of current densities of interest, the stack will operate at air mass flow rates between 50 and -240 sccm/ cell, with the most significant amount of time spent at higher flow. As a result, the recommended cathode channel depth is 0.81 mm. If the estimated 6 cell stack specific power density was adjusted to the recommended 0.457 mm anode channel depth and 0.813 mm cathode channel depth, given the 0.813 mm cathode channel polarization performance, a maximum specific power density of 51 mW/g could be achieved.

Designing for nitrogen accumulation In the Influence of anode channel depth section, it was shown that with dry reactant feed streams, at low temperature, liquid water does not accumulate in the anode gas channel and there is no statistically significant difference in cell performance as a function of the anode gas channel depth under the operating conditions and range of channel depths considered. However, these experimental results were taken from polarization curves in which the anode was first purged of nitrogen. As a result, we next consider nitrogen accumulation, and its impact on cell performance as a guide for channel design and purge scheduling. Our goal here is to evaluate the degree to which cell performance is impacted by nitrogen accumulation at different anode channel depths.

Fig. 8 e The influence of cathode channel depth, d, on specific power density if the cell were assembled into a 6 cell stack with an anode channel depth of 1.17 mm. Power was calculated using the polarization data from Fig. 7 with subplots containing data, top to bottom, from polarization curve 2 at 40 sccm, polarization curve 4 at 100 sccm, and polarization curve 5 at 300 sccm.

Along-the-channel model of nitrogen accumulation To predict nitrogen accumulation along the gas channel in a dead-ended anode under dry conditions, we leverage an existing isothermal, one-dimensional (along-the-channel) model of the anode that was developed and experimentally validated in Ref. [28]. Here, the critical equations are summarized for clarity. The reader is encouraged to review the original presentation of the model in Ref. [28] for details

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Table 2 e Model nomenclature: variables as well as standard, calibrated and identified model parameters. Symbol

Value

E hCh I k

Description Max theoretical cell voltage [V] Channel depth [m] Stack current [A] Permeability coefficient [mol/(m3 s)] Cathode O2 partial pressure [Pa] Time [s] Velocity [m/s] Terminal cell voltage [V] Channel location [m] Molar fraction [-]

pCa O2 t u V x y R F M H2 To Dh Ds po , pH 2 O

8.3145 96,485 2.016e-3 273.15 241980 44.43 101,325

Ideal gas constant [J/mol/K] Faraday constant [A s] Molar weight, H2 [kg/mol] Standard temperature [K] Enthalpy change, [J/mol] Entropy change, [J/(mol K)] Standard and water pressure [Pa]

tm LCh wCh wR nCh nCells

0.0000381 0.0324 0.00117 0.00117 9 6

Membrane thickness [m] Channel length [m] Channel width [m] Rib width [m] Number of channels per FC [-] Number of fuel cells [-]

yH2 ;An;starv yAir N2 yAir O2 T ɸmb T pCa pAn ɸAn,In ɸCa Ec iloss e f g h

0.01 0.78 0.21 283 0.5 283 101,400 113,400 0 0.01 6600 0.001 0.0080 0.0670 0.1018 0.1266

H2 molar fraction when blocked [-] O2 molar fraction in air [-] N2 molar fraction in air [-] Cell operating temperature [K] Membrane relative humidity [-] Fuel cell temperature [K] Cathode pressure [Pa] Anode pressure [Pa] RH at anode inlet [-] RH at cathode [-] Activation energy [J/mol] Loss current density [A/cm2] Mb. conductivity param [53]. Mb. conductivity param [53]. Mb. conductivity param [53]. Mb. conductivity param [53].

K1 K2 K3 K4 · VAn;Out · VAn;Out

2.66 1.00 12.0 704 1.92  109 1.00  107

voltage parameter 1 voltage parameter 2 voltage parameter 3 voltage parameter 4 Leak rate out anode [m3/s] Purge rate out anode [m3/s]

regarding discretization and implementation. Table 2 defines model variables and parameter values. Given the small channel lengths used in these miniature cells (32 mm), we assume that anode temperature and total pressure are constant in time and space and that mass transport occurs primarily due to convection, as opposed to the StefaneMaxwell formulation used in Ref. [30] for combined diffusion and convection. Applying a mass balance on a control volume in the anode channel yields a partial differential equation (PDE) for the mass of each component i2 {H2,N2,H2O} of the gas stream traveling with velocity u(x,t). The resulting mass balance can be expressed with respect to molar fraction, yAn i ðx; tÞ,

 · An v An v
y ðx; tÞ ¼  uðx; tÞyAn i ðx; tÞ þ yi ðx; tÞ: vt i vx

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(1)

Since the molar fractions of a gas mixture sum to one P ð yAn i ðx; tÞ ¼ 1Þ, the mass balance for the gas mixture yields i



X v
 X · An uðx; tÞyAn yi ðx; tÞ ¼ 0: i ðx; tÞ þ vx i i

(2)

While (1) describes the variation of the molar fractions of the gas mixture over time and along the channels, the overall balance in (2) can be used to determine the flow speed of the gas mixture. · An The source terms yi ðx; tÞ in (1) and (2) reflect the component production/consumption rates quantified in Ref. [46]. The consumption rate of hydrogen can be expressed as  · An R T wCh þ wR kH2 An kO $ y ðx; tÞpAn þ 2 2 pCa yH2 ðx; tÞ ¼  $ pAn wCh hCh tm H2 tm O 2  1 iapp ðtÞ : þ 2F

(3)

This consumption rate is valid only when and where hydrogen is available, yAn H2 ðx; tÞ > 0, and describes the losses of hydrogen due to crossover to the cathode, reaction with oxygen that transfers through the membrane from the cathode, and consumption due to the desired electrochemical reaction. The hydrogen and oxygen permeation coefficients, kH2 and kO2 , are functions of temperature as described in Ref. [28]. The diffusion of nitrogen to the anode from the cathode is expressed as · An

yN2 ðx; tÞ ¼

 R T wCh þ wR kN2  Ca pN2  yAn $ $ N2 ðx; tÞpAn : pAn wCh hCh d

(4)

The permeation coefficient of nitrogen, kN2 , is assumed to be constant. From (1), the production/consumption rate of water vapor is described by · An

yH2 O ðx; tÞ ¼ yAn H2 O $

v uðx; tÞ; vx

(5)

where yAn H2 O ¼ 4An psat ðTÞ=pAn . Given the low humidity application, we assume that the anode relative humidity and membrane water content are constant in time and space. Initial and boundary conditions for the PDEs (1) and (2) must be defined. The initial mole fractions of H2, N2, and H2 O in the anode channels, form the initial conditions for the convection equation (1). The initial mole fractions are defined as the conditions just after a purge event, where no nitrogen An exists in the anode channel, therefore yAn H2 ðx; 0Þ ¼ 1  yH2 O . The boundary conditions of the convection equations (1) and (2) are given by the molar composition at the anode inlet and flow speed at the anode outlet (Dirichlet conditions) as uðLCh ; tÞ ¼ uOut An

(6a)

An An yAn H2 ð0; tÞ ¼ 1  yH2 O ð0; tÞ  yN2 ð0; tÞ

(6b)

An An where yAn N2 ð0; tÞ ¼ 0 and yH2 O ð0; tÞ ¼ yH2 O . Hence the initial and boundary conditions depend on the model input variables 4An,

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· Out

pAn, T and VAn . The anode outlet flow speed can be calculated from the specified volumetric flow rate at the anode outlet, · Out VAn , as · Out

uOut An

¼

nCells

VAn : nCh wCh hCh

(7)

The anode outlet volumetric flow is included to examine the impact of anode purges as well as the natural leak rate. To relate the predicted accumulation of nitrogen to cell performance, we now examine the fuel cell voltage output equation. It is well established [40] that the terminal cell voltage, V, is a function of the maximum theoretical cell voltage, E, and the activation and ohmic over voltages, Vact and Vohm, such that VðtÞ ¼ EðtÞ  Vact ðtÞ  Vohm ðtÞ:

(8)

We neglect concentration losses that dominate at high current density as a result of the moderate current densities expected during flight. The maximum theoretical open circuit voltage is found by modifying the Nernst equation such that Gibbs free energy is a function of temperature [40], resulting in 0  0:5 1 An Ca Dh Ds RTðtÞ BpH2 ðtÞ pO2 C ðTðtÞ  To Þ þ ln@ EðtÞ ¼  þ A 2F 2F 2F pH2 0

(9)

where T is the cell temperature, R is the universal ideal gas constant, F is Faraday's constant, pAn H2 is the anode hydrogen is the cathode oxygen partial pressure, partial pressure, pCa O2 and pH2 O is the product water vapor partial pressure. The activation overvoltage has been described a number of ways depending upon the expected cell operating conditions. Because these miniature PEMFCs, when operated under dry conditions, have high activation losses of (50e100 mA/cm2), the modified form of the Butler-Volmer equation [40,47] is used, Vact ðtÞ ¼

   iapp ðtÞ þ iloss RT ln ; 2F io

(10)

where iapp(t) is the time-varying apparent current density, io is the tunable exchange current density, and iloss is the tunable loss current density due to hydrogen cross-over. Other common relations for the activation overvoltage include the Tafel equation [40] and a continuous functional fit to the modified ButlereVolmer equation [48] that is more widely used for control applications. Regardless of the functional form used to specify the activation overvoltage, the sensitivity of voltage to , takes the same shape. apparent current density, vivV app In a worst case scenario, the anode originally contains pure hydrogen (just following an anode purge) and is then depleted to the minimal amount, a maximal change in pAn H2 . This minimal hydrogen partial pressure corresponds to a hydrogen molar fraction of yAn H2 ¼ 0.22, or nitrogen molar fraction of yAn N2 ¼ 0.78 (the maximal amount of nitrogen that can be contained on the anode as a result of Fickian diffusion from the cathode). The resulting deviation in terminal cell voltage is DV ¼ 0.010 V, arguably a rather small change in voltage given the large change in hydrogen partial pressure. It is important to note that this result is not a function of the

cell materials or channel design. Rather, it is a function of the cell operating temperature and expected deviations in hydrogen partial pressure. Given this relatively small sensitivity, it is a reduction in cell active area, or apparent area, due to the nitrogen frontal evolution that results in voltage degradation [30]. The notion of apparent current density was first proposed and experimentally validated in Ref. [49] with subsequent articles [47,50,44] relating accumulation of liquid water to a reduction in cell active area. The definition of apparent current density was used to investigate local fuel starvation due to nitrogen accumulation [28]. The time varying apparent current density, iapp(t), active area, Aapp(t), and channel length, Lapp(t), are related through  iapp ðtÞ ¼ IðtÞ Aapp ðtÞ; Aapp ðtÞ ¼ nnCh ðwch þ wr Þ LApp ðtÞ; o Lapp ðtÞ ¼ x yAn H2 ðx; tÞ > yH2 ;an;starv ;

(11)

where I(t) is the nominal stack current and yH2 ;an;starv is the molar fraction at which the electrode is assumed to be blocked. The ohmic overvoltage is a function of the ionic conductivity of the membrane, s, and the membrane thickness, tm [40], such that Vohm ¼ tsm iapp . The relationship between water conductivity and water content or membrane humidity is a function of water uptake properties and temperature. The exact basis function used to describe this relation at a particular temperature can be as simple as the linear relation for Nafion®117 described by Ref. [51] or could be a fifth order polynomial [52]. The ohmic overvoltage under sub-saturated conditions is Vohm ðtÞ ¼

tm iapp ðtÞ e þ f fmb þ gf2mb þ hf3mb

(12)

where ɸmb is the membrane relative humidity, and e, f, g, and h are temperature sensitive experimentally identified parameters found in Ref. [53] for the membrane used in this work. Our intent here, is to determine the optimal anode channel depth. Channel dimensions impact hydrogen molar fraction. From (11), it is the hydrogen mole fraction that impacts apparent gas channel length, in turn impacting the apparent area and apparent current density. Fig. 9 illustrates the exact mapping from channel depth to apparent current density.

Fig. 9 e Symbolic mapping from gas channel depth to cell apparent current density when nitrogen accumulates in dead-ended anodes under dry conditions.

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Model calibration There are four types of model parameters that must be determined. The final parameter values are listed in Table 2, alongside a listing of model variables. The top most portion of Table 2 lists the symbols used to detail model variables. The second portion of the table lists parameters that are general reference values commonly published in literature. The third portion of the model parameters in Table 2 are calibrated for a particular fuel cell based on material properties and stack geometry. The values used in this work are taken for the miniature fuel cell described in the Stack and cell materials section. Most importantly, the number of cells, ncells, in the PEMFC stack is six to satisfy the expected voltage needs for the CMET balloon. The group of model parameters that are second from the bottom in Table 2 represent operating conditions that are held constant, such as cell operating temperature and cathode inlet relative humidity, and are taken based on the expected operating conditions of the CMET balloon [39]. Based on the model structure, these operating conditions could be treated as dynamic inputs but were held constant in this work. The bottom most portion of the model parameters in Table 2 require identification using experimental data. These identified parameters relate to the terminal cell voltage, the volumetric flow rate of hydrogen leaving the anode during a purge event, and the anode natural leak rate. There are two different values for the volumetric flow of hydrogen out of the anode, V_ An;Out ; one value relates to the nominal flow rate between purges (natural leak rate) and the other value relates to the average flow rate during a purge event. By measuring the hydrogen mass flow rate supplied to the anode under operation, the hydrogen volumetric flow rates leaving the anode between purges (natural leak rate) and during a purge were determined at the specified anode inlet total pressure. To tune the voltage output estimation from (8e12), tunable parameters were deployed such that the voltage equation was linear in the coefficient [47],

With a model of the temporal evolution in cell voltage as nitrogen accumulates, the optimal anode channel depth can be assessed. The optimal anode channel depth is defined as that which produces the highest specific energy density (Wh/g) over the duration of a test flight. To estimate the specific energy density, the mass of the fuel cell stack, hydrogen storage and air delivery systems were specified and are detailed here. To determine the mass of hydrogen required for a 15 h test flight, the anode was assumed to be operating with no purges. The total hydrogen mass is then the sum of the mass of hydrogen required for the reaction and that lost due to leaks, described by mH2 ¼

 · Ii Po MH2 nCells þ Van;out;i ðti  ti1 Þ ; 2FMH2 RTo

n  X i¼1

(15)

model data

0.85 5 0.8 8

where the four tunable parameters, K1-K4 must be experimentally identified. Using the experimental data collected for assessing cell variability, from the Cell variability section, at an anode channel depth of hCh ¼ 1.17 mm, the first polarization curve from each of the four experiments was used to minimize the sum of the squared residuals between the measured and estimated cell voltage using the cost function, (14)

b i is the where Vi is the measured terminal cell voltage and V estimated cell voltage over the n data points collected. To esb i , the apparent current density, cell operating timate V

Cell Voltage (V)

0.75 5

(13)

2 n  1X Vi  c Vi n i¼1

Optimal anode channel depths

0.9



  RT b ¼ E  K1 RT log iapp þ iloss þ Ec 1  1  K1 logðK2 Þ V 2F 2F R T To ! Ca p RT tm O2  K1 K3 log iapp  K4 2F po e þ f fmb þ gf2mb þ hf3mb

J¼

temperature, cathode oxygen partial pressure, anode hydrogen partial pressure and membrane relative humidity must be known. In order to specify these variables, the membrane relative humidity was assumed to be ɸmb ¼ 0.5. The cathode outlet temperature was measured, and assumed to be equal to the cell operating temperature, T. The oxygen partial pressure was estimated by assuming that the cathode channel total pressure was half of the difference between the inlet and outlet total pressures. The hydrogen partial pressure was estimated to be equal to the hydrogen inlet total pressure, given that the anode purge valve was closed and nitrogen had been removed from the anode volume due to a purge event. The resulting four voltage parameters, K1K4, are presented in Table 2. Fig. 10 displays the experimental data consisting of the first polarization curve taken during the Testing Protocol for each of the four assembled cells in comparison to the model estimates. The mean and standard deviation between the measured and estimated voltage is 0.010 V and 0.014 V.

0.7 7 0.65 5 0.6 6 0.55 5 0.5 5 0.45 5 0.4 4 0

0.05

0.1 0.15 0.2 Current Density (A/cm2)

0.25

0.3

Fig. 10 e Measured and estimated cell voltage. Measured data are taken from the first polarization curve of the four assembled stacks used to assess cell variability from the Cell variability section. Cell temperature ¼ 299 K, ɸmb ¼ 0.5, and anode and cathode channel depth ¼ 1.17 mm.

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where n is the number of data points during the flight duration · from initial time t1 to the final time tn, VAn;Out;i is the total volumetric flow out of the anode (natural leak rate) at time ti, Ii is the nominal PEMFC current at time ti, and temperature and pressure are taken at standard state. To estimate fuel cell stack mass, the cathode channel depth was specified to be the optimal 0.813 mm found in the Experimental results section and the anode channel depth is variable. The density of graphite was found to be 82.08 g/in of flow field plate thickness. Note, the flow field plate surface area does not vary, nor does the number of bipolar plates. Rather, it is only the flow field plate thickness that changes with channel depth. The mass of the graphite was then estimated as a function of channel depth. The remaining stack components which include the MEA, GDL, gaskets, endplates and plumbing fittings do not vary as a function of channel depth and were measured to be 35.2 g. The mass of the air delivery system was estimated based on the mass of widely available Parker miniature diaphragm air pumps. These pumps were tested and found to produce the required air mass flow rate under the expected range of cathode back pressures, with a mass of 10 g. The mass of the hydrogen delivery system, including the hydrogen, a pressure regulator, and required tubing is 18 g. Neglected here is the anode purge valve given that the cell will not be purged during this relatively short duration flight. The total system mass, msys, is msys ¼ mfc þ mH2 þ mH2 ;sys þ mair;sys ;

(16)

where mfc is the variable PEMFC stack mass, mH2 is the stored hydrogen fuel mass shown in (15), and mH2 ;sys and mair,sys are the mass of the hydrogen and air delivery systems. The mass of micro-controllers needed for onboard monitoring and control is neglected assuming that the existing data collection system onboard the CMET will be adequate.

Specific Energy Density (Wh/g)

0.4

0.35

0.3

0.25

0.2 0.3 1

0.2 0.8

0.6

han,ch (mm)

0.4

0.1 0.2

0

0

V

an,out

(cm3/s)

Fig. 11 e Surface representation of the optimal anode channel depth and resulting specific energy density for a given anode leak rate. Simulations were conducted at a constant current of 1.00 A (0.21 A/cm2) for a time interval of 15 h.

The specific energy density of the PEMFC system is shown · as a function of the natural anode leak rate, Van;out , and the anode channel depth in Fig. 11 at a constant stack current of 1.00 A and a 15 h flight. Nitrogen accumulates in the anode channel until it achieves a mole fraction equal to that on the cathode, at which point an equilibrium condition is achieved and the flux of nitrogen from the cathode to the anode is zero [54]. When nitrogen no longer accumulates on the anode, the apparent current density remains constant. As a result, the anode natural leak rate significantly impacts the system specific energy density by shifting the location of the nitrogen front. Smaller leak rates correspond to increased apparent current density, which decreases cell voltage and reduces the system specific energy density. As the natural leak rate increases, nitrogen no longer accumulates in the anode in significant concentration, resulting in little impact in the system specific energy density. Under these testing conditions, the natural leak rate at which nitrogen accumulation no longer significantly impacts system specific energy density is approximately 0.05 cm3/s for all anode channel depths. By adjusting endplate compression and gasket hardness, this volumetric flow rate could be experimentally tuned, resulting in significant gains in system specific energy density. While an increased anode leak rate would result in lower hydrogen utilization efficiencies, the increased hydrogen mass is insignificant compared with the gains associated with reducing nitrogen accumulation. For a given anode natural leak rate, specific energy density increases as anode channel depth decreases. While the anode channel depth also impacts the location of the nitrogen front, specific energy density gains are achieved through the reduced system mass that occurs due to shallower channels. The evidence suggesting a monotonically increasing performance associated with shallower channels is not new [21,55]; however, has never been assessed with respect to system specific energy density, arguably a very different metric than cell polarization alone. These results indicate that the optimal anode channel depth occurs at the shallowest depth that can be achieved without suffering GDL intrusion into the gas channels under compression. It is important to note that this result neglects liquid water accumulation given this CMET application. Should liquid water accumulate in the anode gas channels, simultaneous predictions of nitrogen and liquid water accumulation and removal can be made as in Ref. [56]. Fig. 12 displays the system specific energy density as a function of a constant stack current and anode leak rate at an anode channel depth of 0.03 mm for a 15 h flight. At shallow channel depths, moderate current densities and a small anode leak rate, the location of the nitrogen front is close enough to the anode inlet to cause the apparent current density to increase beyond that which results in a stable cell voltage, and thus a positive specific energy density. As a result, while it may be tempting to operate at the very shallow anode depths seen in micro-PEMFC designs, for CMETs with dead-ended operation and no anode purges (short duration), channel depths less than 0.03 mm are not recommended. Finally, it is important to note that the 6-cell PEMFC system design presented here has an estimated specific energy density that exceeds the U.S. Department of Energy Fuel Cell Technologies Research and Development Program 2015 target

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 0 ( 2 0 1 5 ) 7 1 6 8 e7 1 8 1

7179

density of 45 W/kg and energy density of 678Wh/kg, nearing and exceeding the performance of off-the-shelf lithium ion batteries, at approximately 80e100 W/kg and 300 Wh/kg.

0.4

Specific Energy Density (Wh/g)

0.35 0.3

Acknowledgments

0.25 0.2

We gratefully acknowledge Dale Renfrow and Eric Jensen in the Smith College Center for Design and Fabrication for their generous guidance and support in fabricating the fuel cell materials used in this work.

0.15 0.1 0.05 0 0.5

0.4 0.3

0.4 0.3

0.2

0.2

0.1

0.1 2

i (A/cm )

references

0

0

V

an,out

(cm3/s)

Fig. 12 e PEMFC system specific energy density as a function of the anode leak rate as well as the nominal constant stack current density. Simulations were conducted at an anode channel depth of 0.03 mm for a time interval of 15 h.

for the specific energy density of portable PEMFC power systems that operate at less than 2 W [3]. The nominal system specific power density is 45.2 W/kg, with a specific energy density of 678 W h/kg, placing these PEMFC system in direct competition with Lithium-ion batteries. However, this CMET balloon application is unique in that there is not a significant volumetric penalty associated with hydrogen storage. The volumetric energy density of this system still falls well below the technical targets.

Conclusions Using Nafion®212 MEAs and SGL® Sigracet 10BC GDLs, expected cell variability was analyzed under dry conditions and dead-ended anode operation. Cathode and anode channel depths were compared experimentally, with the best performance using the minimal anode channel depth tested, 0.457 mm, and a cathode channel depth of 0.813 mm. The anode channel depth does not have a statistically significant impact on cell performance. An along-the-channel model of nitrogen accumulation was then calibrated to estimate cell performance during a 15 h CMET balloon flight. The anode natural leak rate has a significant impact on PEMFC system specific energy density, with anode channel depth influencing the location of the nitrogen front and the resultant apparent current density. Given the expected range in system current, this methodology could be used to identify the optimal anode channel depth. Additionally, the anode natural leak rate can be tuned in design to minimize the impact of nitrogen accumulation. If deployed in a multicell stack with thinner flow fields, this same performance would translate to a system specific power

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