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Anode flooding characteristics as design boundary for a hydrogen supply system for automotive polymer electrolyte membrane fuel cells
Journal of Power Sources 298 (2015) 249e258
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Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour
Anode flooding characteristics as design boundary for a hydrogen supply system for automotive polymer electrolyte membrane fuel cells Dirk Jenssen a, b, Oliver Berger a, Ulrike Krewer b, * a b
Volkswagen AG, Fuel Cell System Division, Am Krainhop 5, 38550 Isenbüttel, Germany Institute of Energy and Process Systems Engineering, TU Braunschweig, Franz-Liszt-Straße 35, 38106 Braunschweig, Germany
h i g h l i g h t s The critical Reynolds number for water removal from a PEM fuel cell anode is obtained. Various automotive hydrogen supply systems are compared with the resulting requirements. Only active recirculation systems achieve the requirements for all fuel cell load points. Passive systems require a hybridization strategy of the fuel cell system.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 April 2015 Received in revised form 31 July 2015 Accepted 2 August 2015 Available online xxx
An automotive fuel cell is investigated to define the design boundaries for an automotive hydrogen supply system with regard to anode flooding. The flooding characteristics of the fuel cell anode at various operating conditions (hydrogen flow rate, pressure, temperature, current density) are analyzed by in-situ and ex-situ measurements. Stable operation conditions are identified and a relation to the operating conditions is established. For adequate water removal, a minimum Reynolds number in the gas channels has to be adjusted. Using this information, different hydrogen supply system designs are compared in their compliance with the stability requirements. It is shown that passive hydrogen supply systems do not achieve all fuel cell requirements regarding power density, lifetime and robustness. © 2015 Elsevier B.V. All rights reserved.
Keywords: Automotive hydrogen supply system Anode water management Water removal Design process
1. Introduction Electric vehicles powered by fuel cell systems offer high driving ranges with low refueling times. For customer acceptance, the lifetime and reliability of an automotive fuel cell system should be equal or exceed the standards of an internal combustion engine. The U.S. Department of Energy [1] has set a target for the year 2017 for mobile fuel cell systems to reach a lifetime of 5000 h at the costs of 30 US $ per kW. This implies for example that a fuel cell vehicle with this lifetime can drive an overall distance of 250,000 km at an average speed of 50 km per hour. The end of lifetime (EOL) for a fuel cell system can be defined by the voltage degradation of the fuel cell stack, which is in reference to the beginning of life (BOL) voltage. The U.S. Department of Energy sets the voltage degradation
* Corresponding author. http://dx.doi.org/10.1016/j.jpowsour.2015.08.005 0378-7753/© 2015 Elsevier B.V. All rights reserved.
at EOL to 10% of the BOL voltage at rated power output. Among other degradation mechanisms that cause voltage degradation, fuel starvation leads to a significant catalyst degradation [2]. Fuel starvation scenarios occur during freeze starts, aireair starts and poor water management. Water management is important for polymer electrolyte membrane (PEM) fuel cells. The correlation between humidity of the membrane and proton conductivity requires high humidity levels in the membrane to reach the best performance of a PEM fuel cell system. High power densities are essential for integration of a fuel cell system in a vehicle because of the limited space available. As a consequence thin membranes are used and supplied reactant gases are humidified to achieve high membrane humidity levels. Water transport mechanisms in the membrane like electro-osmotic drag and water diffusion lead to a continuous change of water concentration along the gas channels of the anode and cathode. Due to reaction on both electrodes of the fuel cell and low
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temperature operation, water vapor can condense and water droplets block the gas supply to the electrodes. While air starvation is not critical for the lifetime on the cathode side, fuel starvation on the anode side can lead to oxidation of the carbon support of the cathode [2,16]. The oxidized carbon is washed out of the fuel cell, and the fuel cell is irreversible damaged. 1.1. Automotive hydrogen supply system layouts The task of an automotive hydrogen supply system is to prevent fuel starvation and keep the membrane at high humidity level with few, economic and robust system components. The membrane humidity level is also influenced by the air supply system. To prevent fuel starvation on the anode side, water accumulation in the gas distribution channels must be avoided and liquid droplets have to be removed until a maximum tolerable amount of liquid water in the gas channel is reached. A simple layout for a hydrogen supply system is the dead-end design (Fig. 1A), where hydrogen is fed from a storage tank by a pressure controller to the fuel cell. Water droplets in the gas channels and nitrogen, which diffuses through the membrane from the cathode side, are periodically removed by a purge valve. The opening of the purge valve induces a pressure drop over the fuel cell that forces liquid water droplets to movement. A challenge for this design is the equal distribution of hydrogen to all cells in the stack, which is related to the flow characteristics and the manufacturing quality. Chikugo et al. [3] investigated a dead-ended fuel cell system for automotive applications. They used a buffer tank between the anode exhaust and the purge valve. For adequate water removal the hydrogen stream to the fuel cell was pulsed by the pressure controller. These pressure pulses force liquid water and nitrogen into the buffer tank, which is drained regularly. Another operation mode to remove liquid water and nitrogen is to increase the velocity of the hydrogen flow in the gas channels. In
this case, the continuous flow through the fuel cell needs to be sufficiently high to overcome the viscous forces of the water droplets. This operation mode leads to high fuel losses if the exhaust is not recycled. To prevent this, recycling of the exhaust gases is arranged by passing the gases back to the inlet of the fuel cell (Fig. 1B). The advantage of this kind of system layout is that water vapor and nitrogen gas can be recycled. Recycled water vapor can be used to omit a hydrogen humidifier at the fuel cell inlet, and the nitrogen gas increases the flow rate to remove water droplets. A challenge in recycling the exhaust gases is the higher gas pressure level at the inlet of the fuel cell compared to the outlet pressure. To overcome the pressure difference, a recirculation pump is needed. Hydrogen recirculation pumps can be divided in two groups: Active pumps that need an electrical power source for operation, and passive pumps working with fluid energy without electrical power consumption. Different types of fluid flow engines are used for active recirculation. The fluid flow engines need to be compatible to hydrogen and water vapor mixtures. For this reason, regenerative blowers or roots compressors are used in vehicular fuel cell systems [4,5]. Fluid energy pumps work with the principal of momentum transfer from the intake gas to the recirculated gas and need no electrical power supply. They are thus passive recirculation devices. The gas velocity of the intake gas is increased in an orifice to produce low-pressure to suck in the exhaust gas of the fuel cell. These pumps are simple, low cost and maintenance free, but they only function if an intake stream is present [6]. Dehn et al. [7] proposed a near-dead-end hydrogen system with a cascaded fuel cell stack with continuous hydrogen flow. In their concept (Fig. 1C), the fuel cell stack is divided into four anode stages, where the exhaust gas of one stage is the inlet gas of the next stage. The advantage of this near-dead-end design is that each stage gets the hydrogen stream from the following stages, only a small part of the overall supplied hydrogen is exhausted through a
Fig. 1. Hydrogen supply systems: (A) dead-end stack and purge valve; (B) active recirculation and purge valve; (C) cascaded stack on anode side and bleed valve.
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bleed valve and no recirculation pump is required. For the hydrogen supply system layout, liquid water removal from the gas channels sets an essential design boundary.
1.2. Water removal from anode gas channel Water vapor can condense in the gas channels due to operation strategy and high transient load behavior of a fuel cell vehicle. The water forms droplets that accumulate on the surfaces of the channel walls. The gas channel of a fuel cell is typically formed by a bipolar plate and the gas diffusion layer. The shape of the droplet on the surfaces depends on the surface characteristics. Cho et al. [8] investigated the water droplet dynamics of a fuel cell gas channel in detail. Water droplets that cling on the channel walls pose a flow resistance for the gas. The gas flow in each channel performs a drag force Fdrag on the water droplets, while the droplets are clamped by adhesive forces Fdroplet. For adequate water removal, the drag forces Fdrag have to overcome the adhesive forces Fdroplet. The drag force of the gas and the adhesive forces can be merged by the drag coefficient cd. The drag coefficient cd is defined by drag force Fdrag, the projected area of the droplet Adroplet, which represents the flow resistance of the droplet, the density of the gas r and the velocity of the gas ug.
cd ¼
2$Fdrag Adroplet $r$u2g
(1.1)
It is well known, that at incompressible gas flow (Mach number Ma < 0.3), the drag coefficient cd is a function of the Reynolds number Re.
cd ¼ f ðReÞ
(1.2)
Assuming that a certain drag force Fdrag is required to overcome the adhesive forces Fdroplet, a certain Reynolds number Re of the gas flow has to be applied for avoiding fuel starvation in fuel cell systems. Due to consumption of the hydrogen along the gas channel, the gas velocity and therefore the drag force are the lowest at the outlet of the channel [28], thus critical Reynolds numbers are expected at the channel outlet.
1.3. Literature overview Water flooding in PEM fuel cells is mostly attributed to the cathode, because here hydrogen ions and oxygen are recombined to water leading to cathode flooding [15,19], though also flooding may occur at the anode side. Liu et al. [13] investigated the pressure drop characteristics of the anode gas channels under flooding conditions. Ge et al. [18] used a transparent PEM fuel cell to investigate the liquid water formation and transport on the anode side for different surface wettabilities of the gas diffusion layer and channel. O'Rouke et al. [14] proposed an in-situ detection scheme for anode flooding based on impedance measurements at low frequencies. Siegel et al. [21] investigated water accumulation in a PEM fuel cell with a dead-ended anode by neutron imaging. Mench et al. [20] used current distribution measurements for detection of flooding of the cathode of a PEM fuel cell. Jamekhorshid et al. [22] modeled the current distribution for the cathode under flooding conditions. To our knowledge, a systematic analysis of stable anode conditions has not been presented yet. In this paper we investigate anode water flooding conditions to obtain the critical Reynolds number of the gas flow to avoid flooding and compare the results with typical hydrogen supply system layouts. This procedure is essential for designing automotive hydrogen supply systems.
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2. Methods In this section, the setup and operating conditions for the experimental investigation of anode flooding of an automotive fuel cell are described. Furthermore, on the modeling part equations for calculating the Reynolds number of the gas flow and typical automotive hydrogen supply system models are presented. 2.1. Experimental Water build-up experiments are done using a single low temperature automotive PEM fuel cell. Some hundreds of these fuel cells are used in a stack for integration in a fuel cell vehicle system. At rated electric current Imax of 400 A, a single fuel cell provides a maximum electric power Pmax of about 250 W. A typical automotive fuel cell stack with maximum power Pmax of 100 kW hence needs about 400 fuel cells. The fuel cell is operated on a test bench for single cells (FuelCon), which consists of three main functional groups: gas supply and conditioning, electric load and cooling. The gas supply unit controls the mass flow, pressure, temperature and humidification of the reactant gases. For the anode supply, hydrogen with a purity of 99.999%, and for the cathode supply compressed air is used. The electric load runs in galvano static mode. The accuracy of the fuel cell voltage measurement is about 10 mV. A cooling system controls the inlet coolant temperature Tcell,in to 343.15 K. The outlet coolant temperature warms up due to heat generation depending on the electric load adjusted. Air and coolant are fed in co-flow to the fuel cell, while the hydrogen is fed in counter flow. In this operating mode, the inlet temperature of the hydrogen adapts the temperature of the coolant outlet, because of rapid heat transfer through the bipolar plates. The bipolar plates have a flowfield with parallel gas channels for the anode and cathode. Fuel cell voltage is measured directly between both bipolar plates at the hydrogen outlet. For detection of water flooding in the cell, a current density measurement board (Sþþ) is used. The measurement board is mounted below the cathode of the fuel cell. The board consists of 840 segments that measure the local currents using the Hall Effect. With the effective area of each element the local current density is calculated. 2.2. Operating mode and conditions For the investigation of flooding and adequate water removal on the anode side, fuel cell operating conditions are set to high humidification levels and low hydrogen flow rates to obtain condensate in the flow field. The hydrogen inlet flow rate of the fuel cell is expressed as hydrogen excess ratio lH2 , defined as the ratio of the hydrogen mass flow m_ an;H2 ;in to the consumed hydrogen mass flow m_ an;H2 ;F on the anode side of the fuel cell.
lH2 ¼
m_ an;H2 ;in m_ an;H2 ;F
(2.1)
Hydrogen is fully humidified at the inlet of the fuel cell and the flow rate of hydrogen is lowered until flooding is detected by the current density distribution measurement. Air is fed with high flow rate according to an air excess ratio of lair ¼ 2 to prevent flooding or air starvation on the cathode, which leads to changes in the current density distribution. Dry out of the membrane, that also influences the current density distribution, is avoided by feeding the air fully humidified. The parameters for the experimental investigation are listed in Table 1. Flooding on the anode is detected when in more than two elements of the measurement board a decreasing current is detected. This procedure is repeated for different loads with
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stream.
Table 1 Operating parameters.
M psat $ H2 O $ m_ an:H2 ;out þ m_ an;N2 ;out pan;out psat Mg
Parameter
Unit
Value
m_ an;v;out ¼
lH2
e e K MPa % % e
2.01.1 2.0 343.15 0.1370.2 100 100 0.151
The viscosity of the gas mixture hm, consisting of up to 3 components, is calculated according to Wilke [9] with the viscosity of each component hi, the mole fraction xi and a dimensionless number f,
lair Tcell,in pH2 ;in r:h:H2 r.h.air I/Imax
hm ¼
k X i¼1
1þ
increasing gas pressure at the inlet.
1 xi
hi Pj¼k
(2.7)
xi fij
j¼1
(2.6)
jsi
with:
1. mass flow and hydrogen consumption is the same for all channels 2. no nitrogen and hydrogen crossover over the membrane 3. the gas flow at the outlet of each channel is water vapor saturated 4. steady flow operation For the calculation of the Reynolds number of the gas flow at the anode gas channel outlet, the mass flow m_ an;g;out, the gas viscosity hm and the perimeter of the channel U (1.75 * 103 m) is required.
Re ¼
m_ an;g;out $4 hm $U
(2.2)
The gaseous mass flow at the anode gas channel outlet is calculated with the mass flows of hydrogen, nitrogen and water vapor:
m_ an;g;out ¼ m_ an;H2 ;out þ m_ an;N2 ;out þ m_ an;v;out
(2.3)
The hydrogen mass flow at the outlet is the difference between the inlet hydrogen mass flow and the consumed hydrogen mass flow.
m_ an;H2 ;out ¼ m_ an;H2 ;in m_ an;H2 ;F
(2.4)
The nitrogen mass flow at the outlet is the nitrogen mass flow at the inlet.
m_ an;N2 ;out ¼ m_ an;N2 ;in
(2.5)
The water vapor flow is calculated with the equation for water loading of a dry gas mass flow (2.6), where psat is the saturation pressure of water and Mg is the average molar mass of the dry gas
" .pffiffiffi
4 2 1þ
Mj Mi
(2.8)
!#1 2 =
2.3.1. Gas channel conditions The Reynolds number of the gas flow at the anode gas channel outlet is not measured directly and needs to be calculated by a model using gas flow properties. The minimum Reynolds number is obtained, when critical operating conditions are applied to the fuel cell and water flooding occurs. It is assumed that in each gas channel the same mass flow is present. For the calculations the following assumptions are made.
1þ fij ¼
!1 2 1 4 2 =
The modeling work of the gas channel conditions is used to determine the Reynolds number of the gas flow at the outlet of an anode gas channel based on measurement data. Water vapor saturated hydrogen mass flow at the outlet of four different automotive hydrogen supply systems is calculated to determine the hydrogen excess ratio lH2 of each system to compare these with a stack requirement curve, illustrated as hydrogen excess ratio lH2 .
hi hj
=
2.3. Modeling
Mi Mj
For illustration of a stack requirement curve based on minimum Reynolds number at the gas channel outlet, the hydrogen excess ratio lH2 according to Equation (2.1) is used. 2.3.2. Hydrogen supply system layouts Stable fuel cell stack operation requires a minimum mass flow at the outlet of the fuel gas channel for adequate water removal. The hydrogen supply system has to feed sufficient hydrogen for reaction and an excess to ensure a remaining mass flow for all operating conditions of the fuel cell. In this section, four typical hydrogen supply system models are used to calculate the remaining mass flow at the outlet of the gas channels. This information is used to calculate the hydrogen excess ratio lH2 and to compare the compliance of hydrogen supply system with the requirement curve of a 100 kW fuel cell stack. In a dead-end hydrogen supply system, the supplied hydrogen mass flow corresponds to the required mass flow for reaction:
m_ an;H2 ;in;DE ¼ m_ an;H2 ;F
(2.9)
At the outlet of the fuel gas channel no mass flow is present. In a near-dead-end hydrogen supply system with a cascaded stack, the supplied hydrogen mass flow flows through a number of stages k and each stage consumes hydrogen. The last stage is open to environment and a small fraction of the total supplied hydrogen is exhausted.
m_ an;H2 ;NDE;k ¼ m_ an;H2 ;in
k1 X
m_ H2 ;i;F
(2.10)
i¼1
For example, a stack with a total number of 400 cells can be divided in 4 stages, where the first stage has 270 cells, the second has 90 cells, the third has 30 cells and the last stage has 10 cells. If the outlet hydrogen mass flow is only 1.25% of the required mass flow for reaction, each stage has a hydrogen excess ratio of lH2 ¼ 1.5. In a hydrogen supply system with active recirculation, the supplied hydrogen mass flow corresponds to the required mass flow for reaction and the recirculated hydrogen mass flow e.g. by a regenerative blower, which is schematically shown in Fig. 2A.
m_ an;H2 ;in;AR ¼ m_ an;H2 ;F þ yH2 $m_ an;rec;bl
(2.11)
The advantage of a hydrogen supply system with a blower is, that the impeller revolution n can be controlled to pump the
D. Jenssen et al. / Journal of Power Sources 298 (2015) 249e258
253
Fig. 2. Recirculation pumps: (A) regenerative blower; (B) jet pump.
recirculated mass flow m_ an;rec;bl. It is calculated with the recirculated mass flow m_ an;rec;bl, a flow coefficient 4, which depends on the head coefficient j, the cross section of the blower side channel Ac, the diameter of the blower D and the gas inlet density r.
n¼
m_ an;rec;bl 4ðjÞ$AC $p$D$r
(2.12)
In this work the recirculated mass flow of the blower m_ an;rec;bl corresponds with the required mass flow for adequate water removal, which is determined by the experimental work and scaled for a 100 kW automotive fuel cell stack. Constructive parameters of the blower used in this work are listed in Table 2. The dependency of the flow coefficient 4 from the head coefficient j is related to the flow characteristics in a blower. Badami et al. [10] presented a model for a regenerative blower for automotive fuel cell application at various operating conditions. Badami et al. found the following relation:
j ¼ 6:61$42 10:2$4 þ 10:35
(2.13)
The head coefficient j is not a constant but itself a function of the differential pressure of the gas Dp, the gas inlet density r, the diameter of the impeller D and the unknown blower revolution n.
j¼
Dp
(2.14)
1$r$ðp$D$nÞ2 2
The required impeller revolution n is finally calculated by combining equations (2.12), (2.13) and (2.14):
0
1 @ 10:2 m_ an;rec;bl $ $ n¼ p$D 2$10:35 AC $r vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !ffi1 u 2 u _ 2an;rec;bl _ 6:61$ m m 10:2 2$Dp an;rec;bl A $ þt þ þ 2$10:35 AC $r 10:35$r 10:35$r2 $A2C
It is assumed that the blower only has to overcome the fuel cells pressure drop, which is determined by the experimental work. In a hydrogen supply system with passive recirculation, the supplied hydrogen mass flow m_ an;H2 ;in; PR is composed of the required mass flow for reaction m_ an;H2 ;F and the recirculated hydrogen mass flow yH2 $m_ an;rec;jp e.g. by a jet pump.
m_ an;H2 ;in;PR ¼ m_ an;H2 ;F þ yH2 $m_ an;rec;jp
(2.16)
In jet pumps the mass flow m_ an;H2 ;F is routed through a nozzle, where the velocity of the flow increases and the pressure decreases. This low-pressure is used to suck in and accelerate the secondary flow, which is in case of a fuel cell application the exhaust gas of the anode m_ an;rec;jp . In the mixing chamber the two flows intermix with each other and leave the jet pump through a diffusor, where the velocity decreases and static pressure is regained. A typical sketch for a jet pump is shown in Fig. 2B. Thermodynamical and constructive parameters of the jet pump determine the velocity increase of the secondary flow and thereby the efficiency of the pumping process. Zhu et al. [11] developed a model for a convergent nozzle ejector for fuel cell operation to calculate the recirculated mass flow of a jet pump. They introduced an exponential function for velocity pattern of the secondary flow in Section 2 of the jet pump using an exponent nv. The secondary flow m_ an;rec;jp is calculated with the velocity of the primary flow uP,2, the density of the recirculated gas r, the geometrical radius of the jet pump at Section 2 R2, the radius of the primary flow at Section 2 RP,2 and the velocity exponent nv.
m_ an;rec;jp ¼
2$p$r$uP;2 $ R2 RP;2 R2 þ RP;2 þ nv RP;2 ðnv þ 1Þðnv þ 2Þ
(2.17)
The velocity of the primary flow uP,2 is calculated with the Mach number at Section 2 Mp,2 and the sonic velocity of the primary gas flow.
uP;2 ¼ MP;2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kRg TP;2
(2.18)
(2.15) The Mach number Mp,2 is calculated with the primary pressure pP, the secondary pressure pS and the isentropic coefficient k. Table 2 Blower parameters. Parameter
Unit
Value
External diameter of the vane, D Side channel area, Ac Range of blower revolution, n
mm mm2 rpm
138 353 5000e20,000
MP;2
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u k=ðk1Þ u u pP 1 u pS t ¼ ðk 1Þ
(2.19)
The temperature of the primary flow at Section 2 TP,2 is calculated with the inlet temperature of the primary flow TP and the
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Mach number MP,2:
TP;2 ¼
1þ
TP 2 1ÞMP;2
1 ðk 2
(2.20)
The radius of the primary gas flow at Section 2 RP,2 is calculated with:
RP;2
#ðkþ1Þ=ð4ðk1ÞÞ " 2 Dt Mt 0:5 2 þ ðk 1ÞMP;2 ¼ $ 2$xexp MP;2 2 þ ðk 1ÞMt2
(2.21)
(2.22)
with the pressure quotient
bP ¼
p0:8 S
(2.23)
p1:1 P
(ps and pP in bar) and the diameter quotient
bD ¼
Dm Dt
(2.24)
The recirculated mass flow of the ejector in Equation (2.17) is thus dependent of the primary pressure pP and temperature of the primary flow TP, the diameter of the nozzle Dt and the pressure of the secondary flow pS. The primary pressure pP and the Mach number in the nozzle throat Mt can be calculated with the nozzle equation. The primary pressure pP has to be adjusted such that the primary mass flow m_ an;P;jp corresponds with the hydrogen mass flow for reaction m_ an;H2 ;F . The primary mass flow m_ an;P;jp is calculated in dependency of the operating mode of the ejector, which is defined by the critical pressure ratio ycr. The critical pressure ratio ycr of a nozzle is:
ycr ¼
2 kþ1
k=ðk1Þ (2.25)
When the primary pressure pP is higher than pS/ycr, the primary flow reaches sonic conditions and the primary mass flow is m_ an;P;jp calculated with:
m_ an;P;jp ¼ pP At
sffiffiffiffiffiffiffiffiffiffi ðkþ1Þ=ð2ðk1ÞÞ jp k 2 Rg TP k þ 1
(2.28)
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i u h u2 1 ðps =pP Þðk1Þ=k t
(2.29)
ðk 1Þ
Jet pump parameters that are used for the calculations in this paper are listed in Table 3. The nozzle diameter Dt is conform with the requirement of an 100 kW automotive fuel cell system, that needs a hydrogen mass flow for reaction of about 1.66 g s1 at about 8 bar primary pressure at the jet pump inlet.
3. Results and discussion The difference between operating conditions leading to stable or instable cell operation is illustrated by a comparison of the voltage output and the associated current density distribution for a stable condition and instable flooding condition, both at 65% of rated fuel cell current. In Fig. 3, voltage signals are plotted as a function of time for each condition. The average cell voltage of the flooding condition is lower than from the stable operation at same fuel cell current, because the fuel cell runs in higher current density due to partially flooded active area. The higher current density increases the transport losses, which lowers the cell voltage. The voltage signal for stable operation is almost constant with some smaller deviation from the average voltage. This deviation from the mean value is 0.004 V, which is in range of the accuracy of the measurement hardware. The voltage signal under flooding conditions shows strong fluctuations. The deviation from the average value is significant with a maximum of 0.021 V. Voltage fluctuations therefore are an indicator for flooding. Fig. 4 shows pictures from the current density distribution for flooding condition. The data for the pictures have been recorded starting with the left picture at 521 s, the middle at 531 s and the right at 541 s according to the voltage signal in Fig. 3. Hydrogen flows from the right top corner to the left bottom corner of each picture. On the upper left corner at the hydrogen outlet, the current density periodically decreased to almost zero current. The local drop of current density is related to drop in cell voltage, because the fuel cell runs in a higher average current density, which lowers the cell voltage. As the cathode is fed with a constant high flow rate and the gases are fed in counter flow, the observed local stagnation of the current at the anode outlet is attributed to a water build-up in the anode gas channels. This caused the resistance for the gas flow to increase and parts of the active area did not get sufficient hydrogen for reaction, so that local current decreases. Fig. 5 shows the current density for stable operation of the fuel cell. The current density distribution shows no variation over time
(2.26) Table 3 Jet pump parameters.
and the Mach number in the nozzle throat Mt is:
Mt ¼ 1
Rg TP ðk 1Þ
and the Mach number in the nozzle throat Mt is:
Mt ¼
with the diameter of the nozzle throat Dt, the Mach number of the primary flow in the nozzle throat Mt and a correction coefficient xexp, that considers the frictional losses of the mixing process of the primary and secondary flow. Zhu et al. [11] used the computational fluid dynamics method to get a function for the velocity exponent nv in dependency of different gas conditions and different ejector geometries. They found the following dependency:
bP þ 0:456bD þ 0:1668 nv ¼ 1:393$104 exp 0:05
m_ an;P;jp ¼ pP At
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i h u u2jp k ðps =pP Þ2=k ðps =pP Þð1þkÞ=k t
(2.27)
When the primary pressure pP is less than pS/ycr, the primary flow is subsonic and the primary mass flow is calculated with:
Parameter
Unit
Value
Nozzle diameter, Dt Mixing chamber diameter, Dm Temperature of primary flow, TP Isentropic coefficient of primary flow, jp
mm mm K e
2.1 5.2 298.15 0.9
D. Jenssen et al. / Journal of Power Sources 298 (2015) 249e258
Fig. 3. Voltage response of the fuel cell at 65% of rated current for stable condition (lH2 ¼ 1.3) and for flooding conditions (lH2 ¼ 1.1), Tcell,in ¼ 343.15 K, pH2 ;in ¼ 0.18 MPa.
pan;out
8 I I > > 13530$lH2 $ > < 130000 þ 12490$I Imax max ¼ > I > > : 128570 1557$lH2 þ 75110$ Imax
for for
and only small variations in space. Both temporal and spatial changes in current density thus are representative for identifying stable fuel cell operation. For the evaluated operating conditions, that lead to stable and flooding conditions of the fuel cell, the related Reynolds numbers Re at the gas channel outlets are calculated according to Equation (2.2). For this calculation the water vapor flow is required, which is a function of temperature and pressure. It is assumed that the gas has the same temperature as the coolant. The outlet pressure varies according to the pressure drop over the fuel cell, which is a function of the gas flow rate in the gas channel. The gas flow rate changes with gas pressure and hydrogen consumption along the channel. The outlet pressure is measured and averaged for each variation of hydrogen excess ratio and load point of the fuel cell. The dependency of the outlet pressure from the load of the fuel cell takes into account, that the gas pressure is increased with the fuel cell current and more hydrogen is consumed. For the calculation of the pressure at anode outlet, an empirical function is obtained from averaged measurement data for current ratios I=Imax from 0.15 to 1. For current ratios below 0.15 another function is used to consider a constant inlet hydrogen pressure in these load points. This leads to the following empirical formula:
I < 0:15 Imax I Imax
255
in Pa
(3.1)
0:15
Fig. 4. Current density distribution at 65% of rated fuel cell current under flooding conditions with lH2 ¼ 1.1, Tcell,in ¼ 343.15 K, pH2 ;in ¼ 0.18 MPa, current density according to legend, time ¼ 521 s (left), 531 s (middle), 541 s (right).
Fig. 5. Current density distribution at 65% of rated fuel cell current under stable operation with lH2 ¼ 1.3, Tcell,in ¼ 343.15 K, pH2 ;in ¼ 0.18 MPa, current density according to legend, time ¼ 300 s (left), 310 s (middle), 320 s (right).
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Fig. 6 shows the calculated gas channel outlet Reynolds numbers for different excess ratios as a function of the fuel cell load. The black markers represent stable operation points, while the white markers represent non-stable operation points. The gaps between the calculated Reynolds numbers at constant current are smaller at low loads of the fuel cell, while the resolution of the measurement grid decreases at higher loads. For determination of a critical Reynolds number, the lower load points of the fuel cell provide apparently the best accuracy. The critical Reynolds number at the outlet for adequate water removal can be extracted from the transition between stable operation and non-stable operation points. The outlet Reynolds numbers for stable operation at loads from 15 to 45% of the rated fuel cell current show an almost constant value of between Re ¼ 6.5 to 8 with a mean value of Re z 7.5. Outlet Reynolds numbers below this value were found only for operating conditions, where risk of flooding is present. At loads above 45% of rated current, the calculated Reynolds numbers for stable operation confirm this critical Reynolds number. These results show that a certain force described by the Reynolds number is required to effectively remove water droplets from the flow channels. 3.1. Calculation of minimum hydrogen excess ratio From Fig. 6, knowledge of the required minimum Reynolds number for stable operation at the gas channel outlet can be extracted. This value is important for dimensioning a hydrogen supply system and deciding for an operation strategy. The hydrogen supply system has to feed so much mass flow to the fuel cell that a certain amount is left after reacting in the fuel cell. The required hydrogen mass flow at the inlet of the fuel cell to achieve a Reynolds number of Re ¼ 7.5 at the outlet of the gas channel, illustrated as the hydrogen excess ratio, is shown in Fig. 7. It is inversely proportional to fuel cell load and as such increases strongly at low load operation, e.g. at 10% of rated fuel cell current 3.5 times the electrochemically required hydrogen flow rate has to be supplied to the fuel cell to achieve adequate water removal.
Fig. 7. Required hydrogen excess ratio at the inlet of the fuel cell with different nitrogen concentrations for stable fuel cell operation, 343.15 K of coolant temperature at hydrogen outlet, r. h. ¼ 100% of recirculated gas, pan,out according to Equation (3.1).
In case of using a recirculation pump, nitrogen that diffuses through the membrane, is recirculated as well. Nitrogen flow can be used to lower the required hydrogen mass flow to achieve adequate water removal. The impact of nitrogen level in the hydrogen is shown in Fig. 7. The benefit is stronger at low loads of the fuel cell. For example at 10% of rated fuel cell current, a 30 vol.% nitrogen level in the outlet hydrogen flow decreases the necessary hydrogen mass flow at the inlet from 2.25 to 1.5 times the required mass flow for reaction. On the other hand, nitrogen in the recirculation loop of the anode decreases the cell voltage of the stack and therefore the power output of the fuel cell system [27]. The desired nitrogen level in the recirculation loop is therefore a trade-off between water removal advantages, hydrogen losses during purging and stack power losses. At higher loads the required hydrogen excess ratio for water removal decreases and is below the value of lH2 < 1.2, even at pure hydrogen and water vapor mass flow. Due to non-uniform distribution in an automotive full stack and rapid load changes of the fuel cell current, fuel starvation in some cells occurs, when the hydrogen excess ratio drops below lH2 < 1 in these cells. A practical solution is that a minimum excess ratio could be defined, e.g. Ref. lH2 ;min ¼ 1.5. 3.2. System layout comparison
Fig. 6. Calculated Reynolds numbers at anode gas channel outlet for hydrogen excess ratios from Ref. lH2 ¼ 1.1e2.0 in dependency of the rated fuel cell current, Tcell,in ¼ 343.15 K, pan,out according to Equation (3.1); stable operation points are represented with black markers, instable points with white markers.
The last session highlighted the need to supply a flow rate which is higher than the minimum flow rate corresponding to a certain Reynolds number at the channel outlet, in this case Re ¼ 7.5. In Fig. 8, the required minimum hydrogen flow rate is compared with operating curves of hydrogen supply system designs. In dead-end design, the fuel cell stack runs mostly with hydrogen excess ratio of one, as hydrogen is not recycled. As shown in Fig. 8, the flow rate in the dead-ended system is insufficient to assure adequate water removal from the stack for all currents. During purging, the hydrogen excess ratio is temporarily increased and liquid water can be removed, but during normal operation the fuel cell is endangered for flooding.
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almost equal to a passive recirculation system. Both systems, passive recirculation and near-dead-end require an increasing mass flow at low fuel cell currents. A chance of using a near-dead-end system or a passive recirculation for automotive applications is to hybridize the power train of the vehicle and the fuel cell is only active above the critical currents. 4. Conclusions
Fig. 8. Comparison between required hydrogen excess ratio of the rated current of the fuel cell and modeled operating curves for hydrogen supply system designs, 343.15 K coolant temperature at hydrogen outlet, r. h. ¼ 100% of recirculated gas, pan,out according to Equation (3.1), numbers are calculated blower rpm.
A near-dead-end system with a cascaded stack may have a constant local hydrogen excess ratio of lH2 ¼ 1.5 in each stage for every current of the fuel cell. The required minimum hydrogen excess ratio and as such stable operation is reached only above 25% of the rated fuel cell current. Below 25%, the hydrogen excess ratio is insufficient to ensure liquid water removal. In this operation mode, where hydrogen is not recycled, no significant nitrogen gas flow is available to lower the required hydrogen excess ratio. Passive recirculation devices such as jet pumps can be designed for nominal pumping mass flow rates. Besides the nominal mass flow rates, the pumping efficiency is lower. Jet pump parameters have been selected so that the jet pump starts recycling above 8% of rated fuel cell current. However, the entrainment of the primary flow to the secondary flow is small. Below 8% of rated fuel cell current, the ejector works even in back flow mode. At about 32% of the rated current the ejector achieves the required hydrogen excess ratio. Below 45% of the rated current the ejector works in subcritical mode, above 45% it works in critical mode and reaches a maximum hydrogen recirculation ratio at about 50% of the rated current. When the ejector works in critical mode, the secondary mass flow is limited, and hence the hydrogen excess ratio decreases with increasing fuel cell current. In hydrogen supply systems with an active recirculation like a blower, the hydrogen excess ratio can be controlled by the turning speed of the blower. It is shown in Fig. 8 that the operating curve of the blower follows the stack requirement curve and therefore fulfills the stack requirement even at low loads. For all load points the required revolutions per minute is between 5200 and 6400. The blower has a range of 5000e20,000 revolutions per minute, which indicates that there are reserves to supply a higher flow rate, or a smaller blower could be integrated to the system. The comparison of the different hydrogen supply systems shows that only active recirculation fulfills the stack requirements. The use of passive recirculation is limited by the fluid dynamics of the jet pump especially when the pump works in subcritical mode. A neardead-end system with cascaded stack in this configuration is
An automotive PEM fuel cell has been investigated experimentally and by modeling to compare the fuel cells requirements to anode water management with typical automotive hydrogen supply system layouts. The fuel cell was operated under anode flooding conditions to measure the required operation conditions. Flooding on the anode of the fuel cell was detected by measuring the cell voltage at the anode outlet and by fluctuations of the current density distribution in the fuel cell. By modeling the gas conditions at the outlet of each gas channel, it was found that the gas outlet conditions for stable operation of the fuel cell were always above a certain Reynolds number. For the here investigated fuel cell, a Reynolds number of about Re z 7.5 at the gas channel outlet was identified as adequate for water removal and thus, stable operation. This information was found to be essential to evaluate the suitability of different operation strategies and designing a hydrogen supply system for the fuel cell. Different hydrogen supply systems were evaluated in terms of compliance with the required flow conditions. An active hydrogen recirculation system for increasing the flow rate in the fuel cell is the only device to meet the requirements for each power level of the fuel cell from 0 to 100%. In contrast, passive recirculation systems or cascaded stack designs need to be designed carefully to meet the requirements of the fuel cell. A support for the use of passive recirculation components is a hybridization strategy of the fuel cell system with a battery system. Appendix A. Nomenclature
Latin symbols Ac side channel cross section area of blower, mm2 Adroplet projected area of a water droplet, m2 cD drag coefficient D diameter of the impeller of the blower, mm Dm diameter of jet pump mixing chamber, mm Dt diameter of jet pump nozzle throat, mm F Faraday constant, 96485.3 C mol1 Fdrag drag force, N Fdroplet adhesive force, N I current, A m_ mass flow, kg s1 M molar mass, kg mol1 MP,2 Mach number of primary flow at Section 2 Mt Mach number in jet pump throat n revolutions of blower, min1 nv velocity exponent P power, W p pressure, Pa Q volumetric flow rate of the blower, m3 s1 r, R radius, m rc side channel mean radius, m Rg gas constant, J kg1 K1 r. h. relative humidity, % T absolute temperature, K u velocity, m s1
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U x y
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gas channel perimeter, m mole fraction mass fraction
Greek symbols bD diameter ratio bP pressure ratio ycr critical pressure ratio h dynamic viscosity, Pa s k isentropic coefficient l excess ratio r gas density, kg m3 4 dimensionless flow coefficient j dimensionless head coefficient jp isentropic coefficient of primary flow f dimensionless parameter according to Wilke [9]. Subscripts air air an anode AR active recirculation bl blower cell fuel cell DE dead-end F Faraday g gas H2 hydrogen H2O gaseous water i, j, k counting numbers in inlet jp jetpump m mixture max maximum N2 nitrogen NDE near-dead-end out outlet P primary PR passive recirculation rec recirculated S secondary sat saturated t nozzle throat v water vapor References [1] U.S. Department of Energy, The Department of Energy Hydrogen and Fuel
Cells Program Plan, 2011, pp. 60e61. [2] W. Gu, P.T. Yu, R.N. Carter, R. Makharia, H.A. Gasteiger, Modeling of membrane-electrode-assembly degradation in proton exchange-membrane fuel cells e local H2 starvation and start-stopp induced carbon-support corrosion, Model. Diagn. Polym. Electrol. Fuel Cells (2010) 45e87. [3] H. Chikugo, Y. Ichikawa, K. Ikezoe, Low-Cost FC System Concept with Fewer Parts and Adoption of Low-cost Components, SAE Technical Paper 2012-01-1222 (2012). [4] J. Blaszczyk, In-situ anode recirculation rate measurement method, in: Fuel Cell Seminar & Exposition Conference, Orlando, 2011. [5] Y.-H. Kim, S.-H. Kang, Performance evaluation of a regenerative blower for hydrogen recirculation application in fuel cell vehicles, in: ASME Joint U.S. e European Fluids Engineering Summer Meeting, 2006. [6] A.Y. Karnik, J. Sun, J.H. Buckland, Control analysis of an ejector based fuel cell anode recirculation system, in: Proceedings of the 2006 American Control Conference, 2006, pp. 484e489. [7] S. Dehn, M. Woehr, A. Heinzel, Development of a near-dead-ended fuel cell stack operation in an automotive drive system, in: IEEE Vehicle Power and Propulsion Conference, Chicago, 2011. [8] S.C. Cho, Y. Wang, K.S. Chen, Droplet dynamics in a polymer electrolyte fuel cell gas flow channel: forces, deformation and detachment. I: theoretical and numerical analyses, J. Power Sources 206 (2012), 199e128. [9] C. Wilke, A viscosity equation for gas mixtures, J. Chem. Phys. 18 (1950) 517e519. [10] M. Badami, M. Mura, Theoretical model with experimental validation of a regenerative blower for hydrogen recirculation in a PEM fuel cell system, Energy Convers. Manag. 51 (2010) 553e560. [11] Y. Zhu, Y. Li, New theoretical model for convergent nozzle ejector in the proton exchange membrane fuel cell system, J. Power Sources 191 (2009) 510e519. [13] X. Liu, H. Guo, F. Ye, C.F. Ma, Water flooding and pressure drop characteristics in flow channels of proton exchange membrane fuel cells, Electrochem. Acta 52 (2007) 3607e3614. [14] J. O'Rourke, M. Ramani, M. Arcak, In situ detection of anode flooding of a PEM fuel cell, Int. J. Hydrogen Energy 34 (2009) 6765e6770. [15] H. Li, Y. Tang, Z. Wang, Z. Shi, S. Wu, D. Song, J. Zhang, K. Fatih, J. Zhang, H. Wang, Z. Liu, R. Abouatallah, A. Mazza, A review of water flooding issues in the proton exchange membrane fuel cell, J. Power Sources 178 (2008) 103e117. [16] X.-G. Yang, Q. Ye, P. Cheng, In-plane transport effects on hydrogen depletion and carbon corrosion induced by anode flooding in proton exchange membrane fuel fells, Int. J. Heat Mass Transf. 55 (2012) 4754e4765. [18] S. Ge, C.-Y. Wang, Liquid water formation and transport in the PEFC anode, J. Electrochem. Soc. 154 (2007) 998e1005. [19] F.Y. Zhang, X.G. Yang, C.Y. Wang, Liquid water removal from a polymer electrolyte fuel cell, J. Electrochem. Soc. 153 (2006) 225e232. [20] M.M. Mench, C.Y. Wang, M. Ishikawa, In situ current distribution measurements in polymer electrolyte fuel cells, J. Electrochem. Soc. 150 (2003) 1052e1059. [21] J.B. Siegel, et al., Measurement of liquid water accumulation in a PEMFC with dead-ended anode, J. Electrochem. Soc. 155 (2008) 1168e1178. [22] A. Jamekhorshid, G. Karimi, X. Li, Current distribution in a polymer electrolyte membrane fuel cell under flooding conditions, in: ASME 7th International Conference on Fuel Cell Science, Engineering and Technology, 2009, pp. 387e393. [27] R.K. Ahluwalia, X. Wang, Buildup of nitrogen in direct hydrogen polymerelectrolyte fuel cell stacks, J. Power Sources 171 (2007) 63e71. [28] E.J. See, S.G. Kandlikar, A two-phase pressure drop model incorporating local water balance and reactant consumption in PEM fuel cell gas channels, ECS Trans. 50 (2012) 99e111.
Contents lists available at ScienceDirect
Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour
Anode flooding characteristics as design boundary for a hydrogen supply system for automotive polymer electrolyte membrane fuel cells Dirk Jenssen a, b, Oliver Berger a, Ulrike Krewer b, * a b
Volkswagen AG, Fuel Cell System Division, Am Krainhop 5, 38550 Isenbüttel, Germany Institute of Energy and Process Systems Engineering, TU Braunschweig, Franz-Liszt-Straße 35, 38106 Braunschweig, Germany
h i g h l i g h t s The critical Reynolds number for water removal from a PEM fuel cell anode is obtained. Various automotive hydrogen supply systems are compared with the resulting requirements. Only active recirculation systems achieve the requirements for all fuel cell load points. Passive systems require a hybridization strategy of the fuel cell system.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 April 2015 Received in revised form 31 July 2015 Accepted 2 August 2015 Available online xxx
An automotive fuel cell is investigated to define the design boundaries for an automotive hydrogen supply system with regard to anode flooding. The flooding characteristics of the fuel cell anode at various operating conditions (hydrogen flow rate, pressure, temperature, current density) are analyzed by in-situ and ex-situ measurements. Stable operation conditions are identified and a relation to the operating conditions is established. For adequate water removal, a minimum Reynolds number in the gas channels has to be adjusted. Using this information, different hydrogen supply system designs are compared in their compliance with the stability requirements. It is shown that passive hydrogen supply systems do not achieve all fuel cell requirements regarding power density, lifetime and robustness. © 2015 Elsevier B.V. All rights reserved.
Keywords: Automotive hydrogen supply system Anode water management Water removal Design process
1. Introduction Electric vehicles powered by fuel cell systems offer high driving ranges with low refueling times. For customer acceptance, the lifetime and reliability of an automotive fuel cell system should be equal or exceed the standards of an internal combustion engine. The U.S. Department of Energy [1] has set a target for the year 2017 for mobile fuel cell systems to reach a lifetime of 5000 h at the costs of 30 US $ per kW. This implies for example that a fuel cell vehicle with this lifetime can drive an overall distance of 250,000 km at an average speed of 50 km per hour. The end of lifetime (EOL) for a fuel cell system can be defined by the voltage degradation of the fuel cell stack, which is in reference to the beginning of life (BOL) voltage. The U.S. Department of Energy sets the voltage degradation
* Corresponding author. http://dx.doi.org/10.1016/j.jpowsour.2015.08.005 0378-7753/© 2015 Elsevier B.V. All rights reserved.
at EOL to 10% of the BOL voltage at rated power output. Among other degradation mechanisms that cause voltage degradation, fuel starvation leads to a significant catalyst degradation [2]. Fuel starvation scenarios occur during freeze starts, aireair starts and poor water management. Water management is important for polymer electrolyte membrane (PEM) fuel cells. The correlation between humidity of the membrane and proton conductivity requires high humidity levels in the membrane to reach the best performance of a PEM fuel cell system. High power densities are essential for integration of a fuel cell system in a vehicle because of the limited space available. As a consequence thin membranes are used and supplied reactant gases are humidified to achieve high membrane humidity levels. Water transport mechanisms in the membrane like electro-osmotic drag and water diffusion lead to a continuous change of water concentration along the gas channels of the anode and cathode. Due to reaction on both electrodes of the fuel cell and low
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temperature operation, water vapor can condense and water droplets block the gas supply to the electrodes. While air starvation is not critical for the lifetime on the cathode side, fuel starvation on the anode side can lead to oxidation of the carbon support of the cathode [2,16]. The oxidized carbon is washed out of the fuel cell, and the fuel cell is irreversible damaged. 1.1. Automotive hydrogen supply system layouts The task of an automotive hydrogen supply system is to prevent fuel starvation and keep the membrane at high humidity level with few, economic and robust system components. The membrane humidity level is also influenced by the air supply system. To prevent fuel starvation on the anode side, water accumulation in the gas distribution channels must be avoided and liquid droplets have to be removed until a maximum tolerable amount of liquid water in the gas channel is reached. A simple layout for a hydrogen supply system is the dead-end design (Fig. 1A), where hydrogen is fed from a storage tank by a pressure controller to the fuel cell. Water droplets in the gas channels and nitrogen, which diffuses through the membrane from the cathode side, are periodically removed by a purge valve. The opening of the purge valve induces a pressure drop over the fuel cell that forces liquid water droplets to movement. A challenge for this design is the equal distribution of hydrogen to all cells in the stack, which is related to the flow characteristics and the manufacturing quality. Chikugo et al. [3] investigated a dead-ended fuel cell system for automotive applications. They used a buffer tank between the anode exhaust and the purge valve. For adequate water removal the hydrogen stream to the fuel cell was pulsed by the pressure controller. These pressure pulses force liquid water and nitrogen into the buffer tank, which is drained regularly. Another operation mode to remove liquid water and nitrogen is to increase the velocity of the hydrogen flow in the gas channels. In
this case, the continuous flow through the fuel cell needs to be sufficiently high to overcome the viscous forces of the water droplets. This operation mode leads to high fuel losses if the exhaust is not recycled. To prevent this, recycling of the exhaust gases is arranged by passing the gases back to the inlet of the fuel cell (Fig. 1B). The advantage of this kind of system layout is that water vapor and nitrogen gas can be recycled. Recycled water vapor can be used to omit a hydrogen humidifier at the fuel cell inlet, and the nitrogen gas increases the flow rate to remove water droplets. A challenge in recycling the exhaust gases is the higher gas pressure level at the inlet of the fuel cell compared to the outlet pressure. To overcome the pressure difference, a recirculation pump is needed. Hydrogen recirculation pumps can be divided in two groups: Active pumps that need an electrical power source for operation, and passive pumps working with fluid energy without electrical power consumption. Different types of fluid flow engines are used for active recirculation. The fluid flow engines need to be compatible to hydrogen and water vapor mixtures. For this reason, regenerative blowers or roots compressors are used in vehicular fuel cell systems [4,5]. Fluid energy pumps work with the principal of momentum transfer from the intake gas to the recirculated gas and need no electrical power supply. They are thus passive recirculation devices. The gas velocity of the intake gas is increased in an orifice to produce low-pressure to suck in the exhaust gas of the fuel cell. These pumps are simple, low cost and maintenance free, but they only function if an intake stream is present [6]. Dehn et al. [7] proposed a near-dead-end hydrogen system with a cascaded fuel cell stack with continuous hydrogen flow. In their concept (Fig. 1C), the fuel cell stack is divided into four anode stages, where the exhaust gas of one stage is the inlet gas of the next stage. The advantage of this near-dead-end design is that each stage gets the hydrogen stream from the following stages, only a small part of the overall supplied hydrogen is exhausted through a
Fig. 1. Hydrogen supply systems: (A) dead-end stack and purge valve; (B) active recirculation and purge valve; (C) cascaded stack on anode side and bleed valve.
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bleed valve and no recirculation pump is required. For the hydrogen supply system layout, liquid water removal from the gas channels sets an essential design boundary.
1.2. Water removal from anode gas channel Water vapor can condense in the gas channels due to operation strategy and high transient load behavior of a fuel cell vehicle. The water forms droplets that accumulate on the surfaces of the channel walls. The gas channel of a fuel cell is typically formed by a bipolar plate and the gas diffusion layer. The shape of the droplet on the surfaces depends on the surface characteristics. Cho et al. [8] investigated the water droplet dynamics of a fuel cell gas channel in detail. Water droplets that cling on the channel walls pose a flow resistance for the gas. The gas flow in each channel performs a drag force Fdrag on the water droplets, while the droplets are clamped by adhesive forces Fdroplet. For adequate water removal, the drag forces Fdrag have to overcome the adhesive forces Fdroplet. The drag force of the gas and the adhesive forces can be merged by the drag coefficient cd. The drag coefficient cd is defined by drag force Fdrag, the projected area of the droplet Adroplet, which represents the flow resistance of the droplet, the density of the gas r and the velocity of the gas ug.
cd ¼
2$Fdrag Adroplet $r$u2g
(1.1)
It is well known, that at incompressible gas flow (Mach number Ma < 0.3), the drag coefficient cd is a function of the Reynolds number Re.
cd ¼ f ðReÞ
(1.2)
Assuming that a certain drag force Fdrag is required to overcome the adhesive forces Fdroplet, a certain Reynolds number Re of the gas flow has to be applied for avoiding fuel starvation in fuel cell systems. Due to consumption of the hydrogen along the gas channel, the gas velocity and therefore the drag force are the lowest at the outlet of the channel [28], thus critical Reynolds numbers are expected at the channel outlet.
1.3. Literature overview Water flooding in PEM fuel cells is mostly attributed to the cathode, because here hydrogen ions and oxygen are recombined to water leading to cathode flooding [15,19], though also flooding may occur at the anode side. Liu et al. [13] investigated the pressure drop characteristics of the anode gas channels under flooding conditions. Ge et al. [18] used a transparent PEM fuel cell to investigate the liquid water formation and transport on the anode side for different surface wettabilities of the gas diffusion layer and channel. O'Rouke et al. [14] proposed an in-situ detection scheme for anode flooding based on impedance measurements at low frequencies. Siegel et al. [21] investigated water accumulation in a PEM fuel cell with a dead-ended anode by neutron imaging. Mench et al. [20] used current distribution measurements for detection of flooding of the cathode of a PEM fuel cell. Jamekhorshid et al. [22] modeled the current distribution for the cathode under flooding conditions. To our knowledge, a systematic analysis of stable anode conditions has not been presented yet. In this paper we investigate anode water flooding conditions to obtain the critical Reynolds number of the gas flow to avoid flooding and compare the results with typical hydrogen supply system layouts. This procedure is essential for designing automotive hydrogen supply systems.
251
2. Methods In this section, the setup and operating conditions for the experimental investigation of anode flooding of an automotive fuel cell are described. Furthermore, on the modeling part equations for calculating the Reynolds number of the gas flow and typical automotive hydrogen supply system models are presented. 2.1. Experimental Water build-up experiments are done using a single low temperature automotive PEM fuel cell. Some hundreds of these fuel cells are used in a stack for integration in a fuel cell vehicle system. At rated electric current Imax of 400 A, a single fuel cell provides a maximum electric power Pmax of about 250 W. A typical automotive fuel cell stack with maximum power Pmax of 100 kW hence needs about 400 fuel cells. The fuel cell is operated on a test bench for single cells (FuelCon), which consists of three main functional groups: gas supply and conditioning, electric load and cooling. The gas supply unit controls the mass flow, pressure, temperature and humidification of the reactant gases. For the anode supply, hydrogen with a purity of 99.999%, and for the cathode supply compressed air is used. The electric load runs in galvano static mode. The accuracy of the fuel cell voltage measurement is about 10 mV. A cooling system controls the inlet coolant temperature Tcell,in to 343.15 K. The outlet coolant temperature warms up due to heat generation depending on the electric load adjusted. Air and coolant are fed in co-flow to the fuel cell, while the hydrogen is fed in counter flow. In this operating mode, the inlet temperature of the hydrogen adapts the temperature of the coolant outlet, because of rapid heat transfer through the bipolar plates. The bipolar plates have a flowfield with parallel gas channels for the anode and cathode. Fuel cell voltage is measured directly between both bipolar plates at the hydrogen outlet. For detection of water flooding in the cell, a current density measurement board (Sþþ) is used. The measurement board is mounted below the cathode of the fuel cell. The board consists of 840 segments that measure the local currents using the Hall Effect. With the effective area of each element the local current density is calculated. 2.2. Operating mode and conditions For the investigation of flooding and adequate water removal on the anode side, fuel cell operating conditions are set to high humidification levels and low hydrogen flow rates to obtain condensate in the flow field. The hydrogen inlet flow rate of the fuel cell is expressed as hydrogen excess ratio lH2 , defined as the ratio of the hydrogen mass flow m_ an;H2 ;in to the consumed hydrogen mass flow m_ an;H2 ;F on the anode side of the fuel cell.
lH2 ¼
m_ an;H2 ;in m_ an;H2 ;F
(2.1)
Hydrogen is fully humidified at the inlet of the fuel cell and the flow rate of hydrogen is lowered until flooding is detected by the current density distribution measurement. Air is fed with high flow rate according to an air excess ratio of lair ¼ 2 to prevent flooding or air starvation on the cathode, which leads to changes in the current density distribution. Dry out of the membrane, that also influences the current density distribution, is avoided by feeding the air fully humidified. The parameters for the experimental investigation are listed in Table 1. Flooding on the anode is detected when in more than two elements of the measurement board a decreasing current is detected. This procedure is repeated for different loads with
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stream.
Table 1 Operating parameters.
M psat $ H2 O $ m_ an:H2 ;out þ m_ an;N2 ;out pan;out psat Mg
Parameter
Unit
Value
m_ an;v;out ¼
lH2
e e K MPa % % e
2.01.1 2.0 343.15 0.1370.2 100 100 0.151
The viscosity of the gas mixture hm, consisting of up to 3 components, is calculated according to Wilke [9] with the viscosity of each component hi, the mole fraction xi and a dimensionless number f,
lair Tcell,in pH2 ;in r:h:H2 r.h.air I/Imax
hm ¼
k X i¼1
1þ
increasing gas pressure at the inlet.
1 xi
hi Pj¼k
(2.7)
xi fij
j¼1
(2.6)
jsi
with:
1. mass flow and hydrogen consumption is the same for all channels 2. no nitrogen and hydrogen crossover over the membrane 3. the gas flow at the outlet of each channel is water vapor saturated 4. steady flow operation For the calculation of the Reynolds number of the gas flow at the anode gas channel outlet, the mass flow m_ an;g;out, the gas viscosity hm and the perimeter of the channel U (1.75 * 103 m) is required.
Re ¼
m_ an;g;out $4 hm $U
(2.2)
The gaseous mass flow at the anode gas channel outlet is calculated with the mass flows of hydrogen, nitrogen and water vapor:
m_ an;g;out ¼ m_ an;H2 ;out þ m_ an;N2 ;out þ m_ an;v;out
(2.3)
The hydrogen mass flow at the outlet is the difference between the inlet hydrogen mass flow and the consumed hydrogen mass flow.
m_ an;H2 ;out ¼ m_ an;H2 ;in m_ an;H2 ;F
(2.4)
The nitrogen mass flow at the outlet is the nitrogen mass flow at the inlet.
m_ an;N2 ;out ¼ m_ an;N2 ;in
(2.5)
The water vapor flow is calculated with the equation for water loading of a dry gas mass flow (2.6), where psat is the saturation pressure of water and Mg is the average molar mass of the dry gas
" .pffiffiffi
4 2 1þ
Mj Mi
(2.8)
!#1 2 =
2.3.1. Gas channel conditions The Reynolds number of the gas flow at the anode gas channel outlet is not measured directly and needs to be calculated by a model using gas flow properties. The minimum Reynolds number is obtained, when critical operating conditions are applied to the fuel cell and water flooding occurs. It is assumed that in each gas channel the same mass flow is present. For the calculations the following assumptions are made.
1þ fij ¼
!1 2 1 4 2 =
The modeling work of the gas channel conditions is used to determine the Reynolds number of the gas flow at the outlet of an anode gas channel based on measurement data. Water vapor saturated hydrogen mass flow at the outlet of four different automotive hydrogen supply systems is calculated to determine the hydrogen excess ratio lH2 of each system to compare these with a stack requirement curve, illustrated as hydrogen excess ratio lH2 .
hi hj
=
2.3. Modeling
Mi Mj
For illustration of a stack requirement curve based on minimum Reynolds number at the gas channel outlet, the hydrogen excess ratio lH2 according to Equation (2.1) is used. 2.3.2. Hydrogen supply system layouts Stable fuel cell stack operation requires a minimum mass flow at the outlet of the fuel gas channel for adequate water removal. The hydrogen supply system has to feed sufficient hydrogen for reaction and an excess to ensure a remaining mass flow for all operating conditions of the fuel cell. In this section, four typical hydrogen supply system models are used to calculate the remaining mass flow at the outlet of the gas channels. This information is used to calculate the hydrogen excess ratio lH2 and to compare the compliance of hydrogen supply system with the requirement curve of a 100 kW fuel cell stack. In a dead-end hydrogen supply system, the supplied hydrogen mass flow corresponds to the required mass flow for reaction:
m_ an;H2 ;in;DE ¼ m_ an;H2 ;F
(2.9)
At the outlet of the fuel gas channel no mass flow is present. In a near-dead-end hydrogen supply system with a cascaded stack, the supplied hydrogen mass flow flows through a number of stages k and each stage consumes hydrogen. The last stage is open to environment and a small fraction of the total supplied hydrogen is exhausted.
m_ an;H2 ;NDE;k ¼ m_ an;H2 ;in
k1 X
m_ H2 ;i;F
(2.10)
i¼1
For example, a stack with a total number of 400 cells can be divided in 4 stages, where the first stage has 270 cells, the second has 90 cells, the third has 30 cells and the last stage has 10 cells. If the outlet hydrogen mass flow is only 1.25% of the required mass flow for reaction, each stage has a hydrogen excess ratio of lH2 ¼ 1.5. In a hydrogen supply system with active recirculation, the supplied hydrogen mass flow corresponds to the required mass flow for reaction and the recirculated hydrogen mass flow e.g. by a regenerative blower, which is schematically shown in Fig. 2A.
m_ an;H2 ;in;AR ¼ m_ an;H2 ;F þ yH2 $m_ an;rec;bl
(2.11)
The advantage of a hydrogen supply system with a blower is, that the impeller revolution n can be controlled to pump the
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253
Fig. 2. Recirculation pumps: (A) regenerative blower; (B) jet pump.
recirculated mass flow m_ an;rec;bl. It is calculated with the recirculated mass flow m_ an;rec;bl, a flow coefficient 4, which depends on the head coefficient j, the cross section of the blower side channel Ac, the diameter of the blower D and the gas inlet density r.
n¼
m_ an;rec;bl 4ðjÞ$AC $p$D$r
(2.12)
In this work the recirculated mass flow of the blower m_ an;rec;bl corresponds with the required mass flow for adequate water removal, which is determined by the experimental work and scaled for a 100 kW automotive fuel cell stack. Constructive parameters of the blower used in this work are listed in Table 2. The dependency of the flow coefficient 4 from the head coefficient j is related to the flow characteristics in a blower. Badami et al. [10] presented a model for a regenerative blower for automotive fuel cell application at various operating conditions. Badami et al. found the following relation:
j ¼ 6:61$42 10:2$4 þ 10:35
(2.13)
The head coefficient j is not a constant but itself a function of the differential pressure of the gas Dp, the gas inlet density r, the diameter of the impeller D and the unknown blower revolution n.
j¼
Dp
(2.14)
1$r$ðp$D$nÞ2 2
The required impeller revolution n is finally calculated by combining equations (2.12), (2.13) and (2.14):
0
1 @ 10:2 m_ an;rec;bl $ $ n¼ p$D 2$10:35 AC $r vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !ffi1 u 2 u _ 2an;rec;bl _ 6:61$ m m 10:2 2$Dp an;rec;bl A $ þt þ þ 2$10:35 AC $r 10:35$r 10:35$r2 $A2C
It is assumed that the blower only has to overcome the fuel cells pressure drop, which is determined by the experimental work. In a hydrogen supply system with passive recirculation, the supplied hydrogen mass flow m_ an;H2 ;in; PR is composed of the required mass flow for reaction m_ an;H2 ;F and the recirculated hydrogen mass flow yH2 $m_ an;rec;jp e.g. by a jet pump.
m_ an;H2 ;in;PR ¼ m_ an;H2 ;F þ yH2 $m_ an;rec;jp
(2.16)
In jet pumps the mass flow m_ an;H2 ;F is routed through a nozzle, where the velocity of the flow increases and the pressure decreases. This low-pressure is used to suck in and accelerate the secondary flow, which is in case of a fuel cell application the exhaust gas of the anode m_ an;rec;jp . In the mixing chamber the two flows intermix with each other and leave the jet pump through a diffusor, where the velocity decreases and static pressure is regained. A typical sketch for a jet pump is shown in Fig. 2B. Thermodynamical and constructive parameters of the jet pump determine the velocity increase of the secondary flow and thereby the efficiency of the pumping process. Zhu et al. [11] developed a model for a convergent nozzle ejector for fuel cell operation to calculate the recirculated mass flow of a jet pump. They introduced an exponential function for velocity pattern of the secondary flow in Section 2 of the jet pump using an exponent nv. The secondary flow m_ an;rec;jp is calculated with the velocity of the primary flow uP,2, the density of the recirculated gas r, the geometrical radius of the jet pump at Section 2 R2, the radius of the primary flow at Section 2 RP,2 and the velocity exponent nv.
m_ an;rec;jp ¼
2$p$r$uP;2 $ R2 RP;2 R2 þ RP;2 þ nv RP;2 ðnv þ 1Þðnv þ 2Þ
(2.17)
The velocity of the primary flow uP,2 is calculated with the Mach number at Section 2 Mp,2 and the sonic velocity of the primary gas flow.
uP;2 ¼ MP;2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kRg TP;2
(2.18)
(2.15) The Mach number Mp,2 is calculated with the primary pressure pP, the secondary pressure pS and the isentropic coefficient k. Table 2 Blower parameters. Parameter
Unit
Value
External diameter of the vane, D Side channel area, Ac Range of blower revolution, n
mm mm2 rpm
138 353 5000e20,000
MP;2
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u k=ðk1Þ u u pP 1 u pS t ¼ ðk 1Þ
(2.19)
The temperature of the primary flow at Section 2 TP,2 is calculated with the inlet temperature of the primary flow TP and the
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D. Jenssen et al. / Journal of Power Sources 298 (2015) 249e258
Mach number MP,2:
TP;2 ¼
1þ
TP 2 1ÞMP;2
1 ðk 2
(2.20)
The radius of the primary gas flow at Section 2 RP,2 is calculated with:
RP;2
#ðkþ1Þ=ð4ðk1ÞÞ " 2 Dt Mt 0:5 2 þ ðk 1ÞMP;2 ¼ $ 2$xexp MP;2 2 þ ðk 1ÞMt2
(2.21)
(2.22)
with the pressure quotient
bP ¼
p0:8 S
(2.23)
p1:1 P
(ps and pP in bar) and the diameter quotient
bD ¼
Dm Dt
(2.24)
The recirculated mass flow of the ejector in Equation (2.17) is thus dependent of the primary pressure pP and temperature of the primary flow TP, the diameter of the nozzle Dt and the pressure of the secondary flow pS. The primary pressure pP and the Mach number in the nozzle throat Mt can be calculated with the nozzle equation. The primary pressure pP has to be adjusted such that the primary mass flow m_ an;P;jp corresponds with the hydrogen mass flow for reaction m_ an;H2 ;F . The primary mass flow m_ an;P;jp is calculated in dependency of the operating mode of the ejector, which is defined by the critical pressure ratio ycr. The critical pressure ratio ycr of a nozzle is:
ycr ¼
2 kþ1
k=ðk1Þ (2.25)
When the primary pressure pP is higher than pS/ycr, the primary flow reaches sonic conditions and the primary mass flow is m_ an;P;jp calculated with:
m_ an;P;jp ¼ pP At
sffiffiffiffiffiffiffiffiffiffi ðkþ1Þ=ð2ðk1ÞÞ jp k 2 Rg TP k þ 1
(2.28)
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i u h u2 1 ðps =pP Þðk1Þ=k t
(2.29)
ðk 1Þ
Jet pump parameters that are used for the calculations in this paper are listed in Table 3. The nozzle diameter Dt is conform with the requirement of an 100 kW automotive fuel cell system, that needs a hydrogen mass flow for reaction of about 1.66 g s1 at about 8 bar primary pressure at the jet pump inlet.
3. Results and discussion The difference between operating conditions leading to stable or instable cell operation is illustrated by a comparison of the voltage output and the associated current density distribution for a stable condition and instable flooding condition, both at 65% of rated fuel cell current. In Fig. 3, voltage signals are plotted as a function of time for each condition. The average cell voltage of the flooding condition is lower than from the stable operation at same fuel cell current, because the fuel cell runs in higher current density due to partially flooded active area. The higher current density increases the transport losses, which lowers the cell voltage. The voltage signal for stable operation is almost constant with some smaller deviation from the average voltage. This deviation from the mean value is 0.004 V, which is in range of the accuracy of the measurement hardware. The voltage signal under flooding conditions shows strong fluctuations. The deviation from the average value is significant with a maximum of 0.021 V. Voltage fluctuations therefore are an indicator for flooding. Fig. 4 shows pictures from the current density distribution for flooding condition. The data for the pictures have been recorded starting with the left picture at 521 s, the middle at 531 s and the right at 541 s according to the voltage signal in Fig. 3. Hydrogen flows from the right top corner to the left bottom corner of each picture. On the upper left corner at the hydrogen outlet, the current density periodically decreased to almost zero current. The local drop of current density is related to drop in cell voltage, because the fuel cell runs in a higher average current density, which lowers the cell voltage. As the cathode is fed with a constant high flow rate and the gases are fed in counter flow, the observed local stagnation of the current at the anode outlet is attributed to a water build-up in the anode gas channels. This caused the resistance for the gas flow to increase and parts of the active area did not get sufficient hydrogen for reaction, so that local current decreases. Fig. 5 shows the current density for stable operation of the fuel cell. The current density distribution shows no variation over time
(2.26) Table 3 Jet pump parameters.
and the Mach number in the nozzle throat Mt is:
Mt ¼ 1
Rg TP ðk 1Þ
and the Mach number in the nozzle throat Mt is:
Mt ¼
with the diameter of the nozzle throat Dt, the Mach number of the primary flow in the nozzle throat Mt and a correction coefficient xexp, that considers the frictional losses of the mixing process of the primary and secondary flow. Zhu et al. [11] used the computational fluid dynamics method to get a function for the velocity exponent nv in dependency of different gas conditions and different ejector geometries. They found the following dependency:
bP þ 0:456bD þ 0:1668 nv ¼ 1:393$104 exp 0:05
m_ an;P;jp ¼ pP At
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i h u u2jp k ðps =pP Þ2=k ðps =pP Þð1þkÞ=k t
(2.27)
When the primary pressure pP is less than pS/ycr, the primary flow is subsonic and the primary mass flow is calculated with:
Parameter
Unit
Value
Nozzle diameter, Dt Mixing chamber diameter, Dm Temperature of primary flow, TP Isentropic coefficient of primary flow, jp
mm mm K e
2.1 5.2 298.15 0.9
D. Jenssen et al. / Journal of Power Sources 298 (2015) 249e258
Fig. 3. Voltage response of the fuel cell at 65% of rated current for stable condition (lH2 ¼ 1.3) and for flooding conditions (lH2 ¼ 1.1), Tcell,in ¼ 343.15 K, pH2 ;in ¼ 0.18 MPa.
pan;out
8 I I > > 13530$lH2 $ > < 130000 þ 12490$I Imax max ¼ > I > > : 128570 1557$lH2 þ 75110$ Imax
for for
and only small variations in space. Both temporal and spatial changes in current density thus are representative for identifying stable fuel cell operation. For the evaluated operating conditions, that lead to stable and flooding conditions of the fuel cell, the related Reynolds numbers Re at the gas channel outlets are calculated according to Equation (2.2). For this calculation the water vapor flow is required, which is a function of temperature and pressure. It is assumed that the gas has the same temperature as the coolant. The outlet pressure varies according to the pressure drop over the fuel cell, which is a function of the gas flow rate in the gas channel. The gas flow rate changes with gas pressure and hydrogen consumption along the channel. The outlet pressure is measured and averaged for each variation of hydrogen excess ratio and load point of the fuel cell. The dependency of the outlet pressure from the load of the fuel cell takes into account, that the gas pressure is increased with the fuel cell current and more hydrogen is consumed. For the calculation of the pressure at anode outlet, an empirical function is obtained from averaged measurement data for current ratios I=Imax from 0.15 to 1. For current ratios below 0.15 another function is used to consider a constant inlet hydrogen pressure in these load points. This leads to the following empirical formula:
I < 0:15 Imax I Imax
255
in Pa
(3.1)
0:15
Fig. 4. Current density distribution at 65% of rated fuel cell current under flooding conditions with lH2 ¼ 1.1, Tcell,in ¼ 343.15 K, pH2 ;in ¼ 0.18 MPa, current density according to legend, time ¼ 521 s (left), 531 s (middle), 541 s (right).
Fig. 5. Current density distribution at 65% of rated fuel cell current under stable operation with lH2 ¼ 1.3, Tcell,in ¼ 343.15 K, pH2 ;in ¼ 0.18 MPa, current density according to legend, time ¼ 300 s (left), 310 s (middle), 320 s (right).
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Fig. 6 shows the calculated gas channel outlet Reynolds numbers for different excess ratios as a function of the fuel cell load. The black markers represent stable operation points, while the white markers represent non-stable operation points. The gaps between the calculated Reynolds numbers at constant current are smaller at low loads of the fuel cell, while the resolution of the measurement grid decreases at higher loads. For determination of a critical Reynolds number, the lower load points of the fuel cell provide apparently the best accuracy. The critical Reynolds number at the outlet for adequate water removal can be extracted from the transition between stable operation and non-stable operation points. The outlet Reynolds numbers for stable operation at loads from 15 to 45% of the rated fuel cell current show an almost constant value of between Re ¼ 6.5 to 8 with a mean value of Re z 7.5. Outlet Reynolds numbers below this value were found only for operating conditions, where risk of flooding is present. At loads above 45% of rated current, the calculated Reynolds numbers for stable operation confirm this critical Reynolds number. These results show that a certain force described by the Reynolds number is required to effectively remove water droplets from the flow channels. 3.1. Calculation of minimum hydrogen excess ratio From Fig. 6, knowledge of the required minimum Reynolds number for stable operation at the gas channel outlet can be extracted. This value is important for dimensioning a hydrogen supply system and deciding for an operation strategy. The hydrogen supply system has to feed so much mass flow to the fuel cell that a certain amount is left after reacting in the fuel cell. The required hydrogen mass flow at the inlet of the fuel cell to achieve a Reynolds number of Re ¼ 7.5 at the outlet of the gas channel, illustrated as the hydrogen excess ratio, is shown in Fig. 7. It is inversely proportional to fuel cell load and as such increases strongly at low load operation, e.g. at 10% of rated fuel cell current 3.5 times the electrochemically required hydrogen flow rate has to be supplied to the fuel cell to achieve adequate water removal.
Fig. 7. Required hydrogen excess ratio at the inlet of the fuel cell with different nitrogen concentrations for stable fuel cell operation, 343.15 K of coolant temperature at hydrogen outlet, r. h. ¼ 100% of recirculated gas, pan,out according to Equation (3.1).
In case of using a recirculation pump, nitrogen that diffuses through the membrane, is recirculated as well. Nitrogen flow can be used to lower the required hydrogen mass flow to achieve adequate water removal. The impact of nitrogen level in the hydrogen is shown in Fig. 7. The benefit is stronger at low loads of the fuel cell. For example at 10% of rated fuel cell current, a 30 vol.% nitrogen level in the outlet hydrogen flow decreases the necessary hydrogen mass flow at the inlet from 2.25 to 1.5 times the required mass flow for reaction. On the other hand, nitrogen in the recirculation loop of the anode decreases the cell voltage of the stack and therefore the power output of the fuel cell system [27]. The desired nitrogen level in the recirculation loop is therefore a trade-off between water removal advantages, hydrogen losses during purging and stack power losses. At higher loads the required hydrogen excess ratio for water removal decreases and is below the value of lH2 < 1.2, even at pure hydrogen and water vapor mass flow. Due to non-uniform distribution in an automotive full stack and rapid load changes of the fuel cell current, fuel starvation in some cells occurs, when the hydrogen excess ratio drops below lH2 < 1 in these cells. A practical solution is that a minimum excess ratio could be defined, e.g. Ref. lH2 ;min ¼ 1.5. 3.2. System layout comparison
Fig. 6. Calculated Reynolds numbers at anode gas channel outlet for hydrogen excess ratios from Ref. lH2 ¼ 1.1e2.0 in dependency of the rated fuel cell current, Tcell,in ¼ 343.15 K, pan,out according to Equation (3.1); stable operation points are represented with black markers, instable points with white markers.
The last session highlighted the need to supply a flow rate which is higher than the minimum flow rate corresponding to a certain Reynolds number at the channel outlet, in this case Re ¼ 7.5. In Fig. 8, the required minimum hydrogen flow rate is compared with operating curves of hydrogen supply system designs. In dead-end design, the fuel cell stack runs mostly with hydrogen excess ratio of one, as hydrogen is not recycled. As shown in Fig. 8, the flow rate in the dead-ended system is insufficient to assure adequate water removal from the stack for all currents. During purging, the hydrogen excess ratio is temporarily increased and liquid water can be removed, but during normal operation the fuel cell is endangered for flooding.
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almost equal to a passive recirculation system. Both systems, passive recirculation and near-dead-end require an increasing mass flow at low fuel cell currents. A chance of using a near-dead-end system or a passive recirculation for automotive applications is to hybridize the power train of the vehicle and the fuel cell is only active above the critical currents. 4. Conclusions
Fig. 8. Comparison between required hydrogen excess ratio of the rated current of the fuel cell and modeled operating curves for hydrogen supply system designs, 343.15 K coolant temperature at hydrogen outlet, r. h. ¼ 100% of recirculated gas, pan,out according to Equation (3.1), numbers are calculated blower rpm.
A near-dead-end system with a cascaded stack may have a constant local hydrogen excess ratio of lH2 ¼ 1.5 in each stage for every current of the fuel cell. The required minimum hydrogen excess ratio and as such stable operation is reached only above 25% of the rated fuel cell current. Below 25%, the hydrogen excess ratio is insufficient to ensure liquid water removal. In this operation mode, where hydrogen is not recycled, no significant nitrogen gas flow is available to lower the required hydrogen excess ratio. Passive recirculation devices such as jet pumps can be designed for nominal pumping mass flow rates. Besides the nominal mass flow rates, the pumping efficiency is lower. Jet pump parameters have been selected so that the jet pump starts recycling above 8% of rated fuel cell current. However, the entrainment of the primary flow to the secondary flow is small. Below 8% of rated fuel cell current, the ejector works even in back flow mode. At about 32% of the rated current the ejector achieves the required hydrogen excess ratio. Below 45% of the rated current the ejector works in subcritical mode, above 45% it works in critical mode and reaches a maximum hydrogen recirculation ratio at about 50% of the rated current. When the ejector works in critical mode, the secondary mass flow is limited, and hence the hydrogen excess ratio decreases with increasing fuel cell current. In hydrogen supply systems with an active recirculation like a blower, the hydrogen excess ratio can be controlled by the turning speed of the blower. It is shown in Fig. 8 that the operating curve of the blower follows the stack requirement curve and therefore fulfills the stack requirement even at low loads. For all load points the required revolutions per minute is between 5200 and 6400. The blower has a range of 5000e20,000 revolutions per minute, which indicates that there are reserves to supply a higher flow rate, or a smaller blower could be integrated to the system. The comparison of the different hydrogen supply systems shows that only active recirculation fulfills the stack requirements. The use of passive recirculation is limited by the fluid dynamics of the jet pump especially when the pump works in subcritical mode. A neardead-end system with cascaded stack in this configuration is
An automotive PEM fuel cell has been investigated experimentally and by modeling to compare the fuel cells requirements to anode water management with typical automotive hydrogen supply system layouts. The fuel cell was operated under anode flooding conditions to measure the required operation conditions. Flooding on the anode of the fuel cell was detected by measuring the cell voltage at the anode outlet and by fluctuations of the current density distribution in the fuel cell. By modeling the gas conditions at the outlet of each gas channel, it was found that the gas outlet conditions for stable operation of the fuel cell were always above a certain Reynolds number. For the here investigated fuel cell, a Reynolds number of about Re z 7.5 at the gas channel outlet was identified as adequate for water removal and thus, stable operation. This information was found to be essential to evaluate the suitability of different operation strategies and designing a hydrogen supply system for the fuel cell. Different hydrogen supply systems were evaluated in terms of compliance with the required flow conditions. An active hydrogen recirculation system for increasing the flow rate in the fuel cell is the only device to meet the requirements for each power level of the fuel cell from 0 to 100%. In contrast, passive recirculation systems or cascaded stack designs need to be designed carefully to meet the requirements of the fuel cell. A support for the use of passive recirculation components is a hybridization strategy of the fuel cell system with a battery system. Appendix A. Nomenclature
Latin symbols Ac side channel cross section area of blower, mm2 Adroplet projected area of a water droplet, m2 cD drag coefficient D diameter of the impeller of the blower, mm Dm diameter of jet pump mixing chamber, mm Dt diameter of jet pump nozzle throat, mm F Faraday constant, 96485.3 C mol1 Fdrag drag force, N Fdroplet adhesive force, N I current, A m_ mass flow, kg s1 M molar mass, kg mol1 MP,2 Mach number of primary flow at Section 2 Mt Mach number in jet pump throat n revolutions of blower, min1 nv velocity exponent P power, W p pressure, Pa Q volumetric flow rate of the blower, m3 s1 r, R radius, m rc side channel mean radius, m Rg gas constant, J kg1 K1 r. h. relative humidity, % T absolute temperature, K u velocity, m s1
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gas channel perimeter, m mole fraction mass fraction
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