- Email: [email protected]
Performance comparison between airflow-channel and ambient air-breathing PEM fuel cells using three-dimensional computational fluid dynamics models
Renewable Energy 34 (2009) 1812–1824
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Performance comparison between airflow-channel and ambient air-breathing PEM fuel cells using three-dimensional computational fluid dynamics models Maher A.R. Sadiq Al-Baghdadi Mechanical & Energy Department, Higher Institute for Engineering Comprehensive Vocations, Yefren, P.O. Box 65943, Libya
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 May 2008 Accepted 2 December 2008 Available online 3 January 2009
The development of physically representative models that allow reliable simulation of the processes under realistic conditions is essential to the development and optimization of fuel cells, the introduction of cheaper materials and fabrication techniques, and the design and development of novel architectures. Full three-dimensional, multiphase, non-isothermal computational fluid dynamics models of planar airbreathing and airflow-channel PEM fuel cell have been developed. These comprehensive models account for the major transport phenomena in both these types: convective and diffusive heat and mass transfer, electrode kinetics, transport and phase-change mechanism of water, and potential fields. The models are shown to understand the many interacting, complex electrochemical, and transport phenomena that cannot be studied experimentally. Fully three-dimensional results of the species profiles, temperature distribution, potential distribution, and local current density distribution are presented and analyzed with a focus on the physical insight and fundamental understanding for the air-breathing and airflowchannel PEM fuel cells. Ó 2008 Elsevier Ltd. All rights reserved.
Keywords: Ambient air-breathing PEM Fuel cell modelling CFD 3D model
1. Introduction Small fuel cells have provided significant advantages in portable electronic applications over conventional battery systems. However, the typical polymer electrolyte fuel cell system with its heavy reliance on subsystems for cooling, humidification and air supply would not be practical in small applications. The airbreathing PEM fuel cells without moving parts (external humidification instrument, fans or pumps) are one of the most competitive candidates for future portable-power applications. The development of physically representative models that allow reliable simulation of the processes under realistic conditions is essential to the development and optimization of fuel cells, the introduction of cheaper materials and fabrication techniques, and the design and development of novel architectures. The difficult experimental environment of fuel cell systems has stimulated efforts to develop models that could simulate and predict multidimensional coupled transport of reactants, heat and charged species using computational fluid dynamic (CFD) methods. Due to the high activation energy required for the oxygen reduction reaction and the required water management due to condensation, the cathode has been of particular interest in previous computational modelling efforts [1–3]. O’Hayre et al. [1]
E-mail address: [email protected] 0960-1481/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2008.12.002
developed a one-dimensional, non-isothermal model that captures the coupling between water generation, oxygen consumption, self-heating and natural convection at the cathode of an air-breathing fuel cell. Their result confirms the strong effect of self-heating on the water balance within passive air-breathing fuel cells. Litster et al. [2] developed a two-dimensional, singlephase, non-isothermal CFD model of the cathodic electrodes in ambient air-breathing, non-planar, micro-structured PEM fuel cell that increases the surface to volume ratio of the deposited catalyst layer. The model was employed to evaluate the feasibility of these electrodes for use in fuel cells to power small portable consumer electronics. The results of this study indicate that this electrode configuration is feasible and does not suffer from insurmountable mass transfer limitations. Hwang et al. [3] developed a CFD, single-phase, isothermal, three-dimensional model of coupled fluid flow field, mass transport and electrochemistry in an airbreathing cathode of a planar PEM fuel cell. In their results, electrochemical/mass characteristics such as flow velocities, species mass fraction, species flux and current density distributions in a passive cathode have been discussed in detail. These models are very useful because they may include a large portion of the relevant fuel cell physics but at the same time having relatively short solution times. However, this narrowly focused model neglects important parts of the fuel cell making it impossible to get a complete picture of the phenomena governing fuel cell behaviour. Models that include all parts of a fuel cell are
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
Nomenclature a AMEA Ach C Cref Cp D E Ecell F I i iref o,a iref o,c keff kmem Kp _ phase m M
water activity geometrical area of membrane electrode assembly (m2) cross-sectional area of flow channel (m2) local concentration (mol/m3) reference concentration (mol/m3) specific heat capacity (J/kg K) diffusion coefficient (m2/s) equilibrium thermodynamic potential (V) cell operation potential (V) Faraday’s constant ¼ 96 487 (C/mol) cell operating current density (A/m2) local current density (A/m2) anode reference exchange current density cathode reference exchange current density effective electrode thermal conductivity (W/m K) membrane thermal conductivity (W/m K) hydraulic permeability (m2) _ phase ¼ m _ evap Þ and mass transfer: evaporation ðm _ cond Þ (kg/s) _ phase ¼ m condensation ðm molecular weight (kg/mol)
reflecting many of the physical processes occurring within the fuel cell. Entire unit cells have been modelled with the additional complexity of anode and membrane transport in several researches [4–7]. Wang and Ouyang [4] developed a CFD, single-phase model of a channel-type air-breathing PEM fuel cell, in which the air is provided through straight vertical cathode channel open to ambient air at top and bottom. Their model accounts for threedimensional transport processes using non-dimensional heat/mass transfer coefficients. This model was applied to planar channeltype air-breathing fuel cells (which consists of cathode ducts open to atmosphere at top and bottom), rather than planar open-cathode fuel cells (in which the cathode gas diffusion layer (GDL) is completely open to atmosphere). In such cells, performance was shown to depend strongly on the cathode channel geometry [4]. However, the ducted cathode air-breathing PEM fuel cell is the most frequently used design, which consists of cathode ducts open to atmosphere at top and bottom. In addition, this model did not account for phase change, liquid water concentration in the electrodes, and water dissolved in the ion-conducting polymer. An air-breathing PEM fuel cell is considered to be planar if the cathode GDL has a perfectly planar surface without any protrusions or physical disturbances and completely open to atmosphere for absorbing the required oxygen from air. Litster and Djilali [5] developed a single-phase one-dimensional semi-analytical model of the membrane electrode assembly of planar air-breathing PEM fuel cells for portable devices. Their study suggests that improved performance of air-breathing fuel cells can be achieved by increasing the heat removal rate and thus promoting higher relative humidity levels in the GDL. Rajani and Kolar [6] developed a single-phase two-dimensional model for a planar air-breathing PEM fuel cell that considered both heat and mass transfer. Their results showed that the maximum power density and the corresponding current density increase with decreasing height of the fuel cell, decreasing ambient temperature and increasing ambient relative humidity. In all these models [1–6], multiphase transport in the cell is not considered; they do not account for phase change, liquid water concentration in the electrodes, and water dissolved in the
NW nd ne P Pc q_ R s sat T u xi yi
aa ac 3 h le lm m r s x
1813
net water flux across the membrane (kg/m2 s) electro-osmotic drag coefficient number of electrons transfer pressure (Pa) capillary pressure (Pa) heat generation (W/m2) universal gas constant ¼ 8.314 (J/mol K) specific entropy (J/mol K) saturation temperature (K) velocity vector (m/s) mole fraction mass fraction charge transfer coefficient, anode side charge transfer coefficient, cathode side porosity overpotential (V) electrode electronic conductivity (S/m) membrane ionic conductivity (S/m) viscosity (kg/m s) density (kg/m3) surface tension (N/m) stoichiometric flow ratio
ion-conducting polymer; that is, single phase is assumed. Besides diffusion mass transfer, transport of liquid water can be important in the gas diffusion layers, catalyst layers, and membrane of airbreathing PEM fuel cells. Paquin and Frechette [7] developed a simple multiphase one-dimensional model of a free convection planar air-breathing PEM fuel cell that couples heat and mass transfer with the electrochemical reaction of a small air-breathing PEM fuel cell to analyse water management. The simplifications that used in this model regarding heat transfer did not allow an exact agreement between experimental and model results, so a correction factor was used to get a better match between temperatures. Models that include all parts of a fuel cell are typically two- or three-dimensional and reflect many of the physical processes occurring within the fuel cell. However, in a real PEM fuel cell geometry, the GDLs are used to enhance the reaction area accessible by the reactants. The effect of using these diffusion layers is to allow a spatial distribution in the current density on the membrane in both the direction of bulk flow and the direction orthogonal to the flow but parallel to the membrane. This twodimensional distribution cannot be modelled with the well-used two-dimensional models where the mass-transport limitation is absent in the third direction. The objective of the present work is to numerically study the transport phenomena in a passive mode PEM fuel cell that operates without external forced flows. Multiphase, multi-component flow, non-isothermal, three-dimensional CFD model of complete parts of an ambient air-breathing PEM fuel cell, which work in still, or slowly moving air has been developed and presented in detail. The porous cathode is attached to a perforated current collector. It breathes the fresh air through the perforations and routes out the electric current through its solid counterpart. A comparison study between the performances of the planar air-breathing PEM fuel cell with the airflow-channel PEM fuel cell is also presented. The informative results obtained by the present study can help in understanding of the local gas transports and electrochemical characteristics in both designs of the fuel cells. In addition, they can provide a solid basis for optimizing the geometry of the passive PEM fuel cell stack.
1814
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
2. Model description The present work presents a comprehensive three-dimensional, multiphase, non-isothermal model of an airflow-channel/airbreathing PEM fuel cell that incorporates the significant physical processes and the key parameters affecting fuel cell performance. The following assumptions are made: (i) The fuel cell operates under steady-state conditions. This is because the start-up or stop or any transient process of a fuel cell is not considered in this model. (ii) The ionic conductivity of the membrane is constant. The conductivity of the membrane is a function of hydration, which is expressed as the number of water molecules per sulfonate group. Membrane conductivity increases with membrane water content. If
the membrane is drying, a rising resistance (protonic overpotential) will reveal this [8]. (iii) The membrane is impermeable to gases and cross-over of reactant gases is neglected. The highly diffusive hydrogen can cross the membrane and recombine with the oxygen at the cathode side without being oxidized at the anode catalyst layer, which results in a loss of fuel [9]. (iv) The GDL is homogeneous and isotropic. This assumption asserts that the porosity is a constant in the whole region of the gas diffusers. The porosity of the GDL affects the performance of the fuel cell in two aspects: a higher void fraction provides less resistance for the reactant gases to reach the catalyst layer on one hand, but in turn it leads to a higher contact resistance [10]. (v) The produced water is in the vapour phase. (vi) Two-phase flow inside the porous media.
Fig. 1. Three-dimensional computational domains of PEM fuel cells used in this work: (a) ambient air-breathing design and (b) airflow-channel design.
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
(vii) Both phases occupy a certain local volume fraction inside the porous media and their interaction is accounted for through a multi-fluid approach. The model accounts for both gas and liquid phase in the same computational domain, and thus allows for the implementation of phase change inside the gas diffusion layers. The model includes the transport of gaseous species, liquid water, protons, energy, and water dissolved in the ion-conducting polymer. Water transport inside the porous gas diffusion layer and catalyst layer is described by two physical mechanisms: viscous drag and capillary pressure forces, and is described by advection within the gas channels. Water transport across the membrane is also described by two physical mechanisms: electro-osmotic drag and diffusion. Water is assumed to be exchanged among three phases; liquid, vapour, and dissolved, and equilibrium among these phases is assumed.
2.1. Computational domain
1815
Table 2 Geometrical and operational parameters for base case operating conditions. Parameter
Symbol
Value
Unit
Channel length Channel height Channel width Gas diffusion layer thickness Wet membrane thickness (NafionÒ 117) Catalyst layer thickness Hydrogen reference mole fraction Oxygen reference mole fraction Fuel pressure Air pressure Fuel stoichiometric flow ratio
L H W
0.05 1e3 1e3 0.26e3 0.23e3 0.0287e3 0.84639 0.17774 1 1 2
m m
dGDL dmem dCL xref H2 xref O2 Pa Pc
xa
2 V$ rg ug 5ug mg Vug ¼ Vrg P þ mg V$ug 3 h T i þ V$ mg Vug
m m m – – atm atm –
(3)
The full computational domains for the air-breathing and airflow-channel PEM fuel cell consist of anode gas-flow field, cathode, and the membrane electrode assembly as shown in Fig. 1.
and
2.2. Model equations
The mass balance is described by the divergence of the mass flux through diffusion and convection. Multiple species are considered in the gas phase only, and the species conservation equation in multi-component, multiphase flow can be written in the following expression for species i;
2.2.1. Air and fuel gas flow In natural convection region, the transport equations solved in the ambient air include continuity, momentum, energy and masstransport equations. In the fuel channel, the gas-flow field is obtained by solving the steady-state Navier–Stokes equations, i.e. the continuity equation, the mass conservation equation for each phase yields the volume fraction (r) and along with the momentum equations the pressure distribution inside the channel. The continuity equation for the gas phase inside the channel is given by;
V$ rg rg ug ¼ 0
(1)
and for the liquid phase inside the channel becomes;
V$ðrl rl ul Þ ¼ 0
h i 2 V$ðrl ul 5ul ml Vul Þ ¼ Vrl P þ ml V$ul þ V$ ml ðVul ÞT 3
2
VP VM Vyj þ yj þ xj yj M P j¼1 3 VT 5 ¼ 0 þ rg rg yi $ug þ DTi T
V$4 rg rg yi
N X
Dij
M Mj
Two sets of momentum equations are solved in the channel, and they share the same pressure field. Under these conditions, it can be shown that the momentum equations becomes; Table 1 Electrode and membrane properties and parameters. Symbol
Value
Unit
Electrode porosity Electrode electronic conductivity Membrane ionic conductivity (humidified NafionÒ 117) Transfer coefficient, anode side Transfer coefficient, cathode side Cathode reference exchange current density Anode reference exchange current density Electrode thermal conductivity Membrane thermal conductivity Electrode hydraulic permeability Entropy change of cathode side reaction Heat transfer coefficient between solid and gas phase Fuel cell temperature Relative humidity Protonic diffusion coefficient Fixed-charge concentration Fixed-site charge Electro-osmotic drag coefficient
3 le lm
0.4 100 17.1223
– S/m S/m
aa ac
b
0.5 1 1.8081e3 2465.598 1.3 0.455 1.76e11 326.36 4e6
– – A/m2 A/m2 W/m K W/m K m2 J/mol K W/m3
Tcell R DHþ cf zf nd
353.15 100 4.5e9 1200 1 2.5
K % m2/s mol/m3 – –
iref o,c iref o,a keff kmem Kp DS
(5)
where the subscript i denotes hydrogen and j is water vapour. The Maxwell–Stefan diffusion coefficients of any two species are dependent on temperature and pressure. They can be
(2)
Parameter
(4)
Fig. 2. Comparison of the models and the experimental polarization curves.
1816
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
calculated according to the empirical relation based on kinetic gas theory [11];
" #1=2 T 1:75 103 1 1 Dij ¼ " !1=3 !1=3 #2 M þ M i j P P P Vki þ Vkj k
(6)
k
In this equation, pressure is in [atm] and the binary diffusion P coefficient is in [cm2/s]. The values for ( Vki) are given by Fuller et al. [11]. The temperature field is obtained by solving the convective energy equation;
V$ rg rg Cpg ug T kg VT ¼ 0
(7)
The gas phase and the liquid phase are assumed to be in thermodynamic equilibrium; hence the temperature of the liquid water is the same as the gas phase temperature.
2.2.2. Gas diffusion layers The physics of multiple phases through a porous medium is further complicated here with phase change and the sources and sinks associated with the electrochemical reaction. The equations used to describe transport in the gas diffusion layers are given below. _ phase > 0Þ and Mass transfer in the form of evaporation ðm _ phase < 0Þ is assumed, so that the mass balance condensation ðm equations for both phases are;
_ phase V$ ð1 satÞrg 3ug ¼ m
(8)
and
_ phase V$ðsat$rl 3ul Þ ¼ m
(9)
The momentum equation for the gas phase reduces to Darcy’s law, which is, however, based on the relative permeability for the gas phase (Kp). The relative permeability accounts for the reduction
Fig. 3. Oxygen molar fraction distribution: (a) ambient air-breathing and (b) airflow-channel.
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
in pore space available for one phase due to the existence of the second phase [12]. The momentum equation for the gas phase inside the gas diffusion layer becomes;
ug ¼ ð1 satÞ
Kp VP
(10)
mg
Two liquid water transport mechanisms are considered; shear, which drags the liquid phase along with the gas phase in the direction of the pressure gradient, and capillary forces, which drive liquid water from high to low saturation regions [12]. Therefore, the momentum equation for the liquid phase inside the gas diffusion layer becomes;
Pc ¼ s
3
Kp
1817
1=2 1:417ð1 satÞ
2:12ð1 satÞ2 þ1:263ð1 satÞ3
(12)
The liquid phase consists of pure water, while the gas phase has multi-components. The transport of each species in the gas phase is governed by a general convection–diffusion equation in conjunction which the Stefan–Maxwell equations to account for multispecies diffusion;
2
(11)
VP VM þ xj yj Vyj þ yj M P j¼1 3 VT 5 _ phase þ ð1 satÞrg 3yi $ug þ 3DTi ð13Þ ¼ m T
The functional variation of capillary pressure with saturation is calculated as [12];
where the subscript i denotes oxygen at the cathode side and hydrogen at the anode side, and j is water vapour in both cases. Nitrogen is the third species at the cathode side.
sat$Kp sat$Kp vPc ul ¼ VP þ Vsat ml ml vsat
V$4 ð1 satÞrg 3yi
N X
Dij
M Mj
Fig. 4. Hydrogen molar fraction distribution: (a) ambient air-breathing and (b) airflow-channel.
1818
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
In order to account for geometric constraints of the porous media, the diffusivities are corrected using the Bruggemann correction formula [13,14]; 1:5 Deff ij ¼ Dij 3
(14)
The heat transfer in the gas diffusion layers is governed by the energy equation as follows;
V$ ð1 satÞ rg 3Cpg ug T keff;g 3VT _ phase DHevap ¼ 3bðTsolid TÞ 3m
(15)
where the term (3b(Tsolid T)), on the right hand side, accounts for the heat exchange to and from the solid matrix of the GDL. The gas phase and the liquid phase are assumed to be in thermodynamic equilibrium, i.e., the liquid water and the gas phase are at the same temperature. The potential distribution in the gas diffusion layers is governed by;
V$ðle VfÞ ¼ 0
(16)
In order to account for the magnitude of phase change inside the GDL, expressions are required to relate the level of over- and undersaturation as well as the amount of liquid water present to the amount of water undergoing phase change. In the present work, the procedure of the current author in his previous paper [15] was used to account for the magnitude of phase change inside the GDL. 2.2.3. Catalyst layers The catalyst layer is treated as a thin interface, where sink and source terms for the reactants are implemented. Due to the infinitesimal thickness, the source terms are actually implemented in the last grid cell of the porous medium. At the cathode side, the sink term for oxygen is given by;
SO2 ¼
MO2 ic 4F
(17)
whereas the sink term for hydrogen is specified as;
MH SH2 ¼ 2 ia 2F
Fig. 5. Local current density distribution: (a) ambient air-breathing and (b) airflow-channel.
(18)
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
The production of water is modelled as a source term, and hence can be written as;
S H2 O ¼
MH2 O ic 2F
(19)
The generation of heat in the cell is due to entropy changes as well as irreversibilities due to the activation overpotential [16];
q_ ¼
TðDsÞ þ hact;c ic ne F
(20)
The local current density distribution in the catalyst layers is modelled by the Butler–Volmer equation [13,14];
0
1 aa F ac F ref @ CO2 A h h þ exp ic ¼ io;c exp RT act;c RT act;c C ref
(21)
1819
2.2.4. Membrane The balance between the electro-osmotic drag of water from anode to cathode and back diffusion from cathode to anode yields the net water flux through the membrane;
i NW ¼ nd MH2 O V$ðrDW VcW Þ F
(23)
The water diffusivity in the polymer can be calculated as follows [17];
1 1 DW ¼ 1:3 1010 exp 2416 303 T
(24)
The variable cW represents the number of water molecules per sulfonic acid group (i.e. mol H2O/equivalent SO1 3 ). The water content in the electrolyte phase is related to water vapour activity via [18];
O2
0
11=2
@ CH2 A ia ¼ iref o;a ref CH 2
exp
aa F RT
hact;a
ac F hact;a þ exp RT
(22)
cW
8 2 3 > <0:043 þ 17:81a 39:85a þ 36:0a ð0 < a 1Þ ¼ 14:0 þ 1:4ða 1Þ ð1 < a 3Þ > : 16:8 ða 3Þ
Fig. 6. Temperature distribution inside the cell: (a) ambient air-breathing and (b) airflow-channel.
(25)
1820
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
The water vapour activity is given by;
x P a ¼ W Psat
(26)
Heat transfer in the membrane is governed by;
V$ðkmem $VTÞ ¼ 0
(27)
The potential loss in the membrane is due to resistance to proton transport across membrane, and is governed by;
V$ðlm VfÞ ¼ 0
(28)
2.2.5. Cell potential Useful work (electrical energy) is obtained from a fuel cell only when a current is drawn, but the actual cell potential (Ecell) is decreased from its equilibrium thermodynamic potential (E) because of irreversible losses. The cell potential is obtained by subtracting all overpotentials (losses) from the equilibrium thermodynamic potential as the following expression;
Ecell ¼ E hact hohm hmem hDiff
(29)
The equilibrium potential is determined using the Nernst equation [15];
E ¼ 1:229 0:83 103 ðT 298:15Þ þ 4:3085 1 105 T ln PH2 þ ln PO2 2
(30)
The anode and cathode activation overpotentials are calculated from Butler–Volmer equation ((21) and (22)). The ohmic overpotentials in GDLs and protonic overpotential in membrane are calculated from the potential equations (16) and (28) respectively. The anode and cathode diffusion overpotentials are calculated from the following equations [15];
hDiff;c ¼
RT ic ln 1 iL;c 2F
(31)
hDiff;a ¼
RT ia ln 1 2F iL;a
(32)
Fig. 7. Activation overpotential distribution at the cathode sites: (a) ambient air-breathing and (b) airflow-channel.
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
iL;c ¼
iL;a ¼
2FDO2 CO2
(33)
dGDL 2FDH2 CH2
(34)
dGDL
3. Results and discussion The governing equations were discretized using a finite volume method and solved using the commercial CFD code FEMLAB-2.3. Stringent numerical tests were performed to ensure that the solutions were independent of the grid size. The coupled set of equations was solved iteratively, and the solution was considered to be convergent when the relative error in each field between two consecutive iterations was less than 1.0 106 (convergence error less than 0.5%). The calculations presented here have all been obtained on a Pentium IV PC (3 GHz, 2 GB RAM) using Windows XP operating system. The values of the electrochemical transport parameters for the base case operating conditions are taken from Ref. [15] and are
1821
listed in Table 1. The geometric and the base case operating conditions are listed in Table 2. Performance curves of the ambient air-breathing and airflow-channel PEM fuel cells were compared with the experimental results provided by Wang et al. [19] for the airflow-channel PEM fuel cell in the same operating conditions (Fig. 2). Polarization curves of the two models clearly show that higher cell potentials are achieved with the airbreathing design mainly because of lower activation and diffusion potentials. Better gas replenishment at the catalyst sites in air-breathing design results in lower activation and diffusion potentials. The lower cell potentials of the airflow-channel design are due to the oxygen concentration decreases gradually from the inflow channel to the outflow channel due to the consumption of oxygen at the catalyst layer. The lower diffusivity of the oxygen along with the low concentration of oxygen in ambient air results in noticeable oxygen depletion near outflow channel and also under the land areas. Moreover, fresh air coming from the inflow channel has a longer distance to diffuse through to reach these areas. The ambient air-breathing fuel cell does not seem to have higher mass-transport losses. The linear behaviour of the voltage–current curve for the ambient air-breathing fuel cell
Fig. 8. Ohmic overpotential distribution in the anode and cathode GDLs: (a) ambient air-breathing and (b) airflow-channel.
1822
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
suggests that the overall overpotential is driven mainly by ohmic losses. In order to gain some insight into why the polarization curve is better in the case of the ambient air-breathing PEM fuel cell, the oxygen and hydrogen distribution, local current densities, temperature distribution, and potential distribution are plotted in Figs. 3–10, respectively, for a fixed nominal current density of 0.8 A cm2. The detailed distribution of oxygen molar fraction for both designs is shown in Fig. 3. In the GDL of the airflow-channel design, oxygen concentration under the land area is smaller than that under the air inlet area. The concentration of oxygen at the catalyst layer is balanced by the oxygen that is being consumed and the amount of oxygen that diffuses towards the catalyst layer driven by the concentration gradient. The lower diffusivity of the oxygen along with the low concentration of oxygen in ambient air results in noticeable oxygen depletion under the land areas. The airbreathing design gives more even distribution of the molar oxygen fraction at the catalyst layer. At air-breathing design, the oxygen mole fraction variation is low enough not to cause diffusive limitations, whereas at airflow-channel design the concentration of oxygen under the land areas has already reached near-zero values.
The molar oxygen fraction at the catalyst layer increases with more even distribution with air-breathing design. This is because of a better gas replenishment at the catalyst sites, which results in quite uniform distribution for the oxygen to reach the catalyst layer. Due to the relatively low diffusivity of the oxygen compared with that of the hydrogen, the cathode operation conditions usually determine the limiting current density. This is because an increase in current density corresponds to an increase in oxygen consumption. The hydrogen molar fraction distribution in the anode side is shown in Fig. 4 for both designs. In general, the hydrogen concentration decreases from inlet to outlet as it is being consumed. However, the decrease is quite small along the channel and the decrease in molar concentration of the hydrogen under the land areas is smaller than for the oxygen in cathode side due to the higher diffusivity of the hydrogen. Fig. 5 shows the local current density (in A cm2) distribution at the cathode side catalyst layer for both designs. The local current density of the cathode side reaction depends directly on the oxygen concentration. The diffusion of the oxygen towards the catalyst layer is the main impediment for reaching high current densities. Therefore, it can be seen that for air-breathing design, the distribution of the local current density is quite uniform. This is changed
Fig. 9. Membrane overpotential distribution across the membrane: (a) ambient air-breathing and (b) airflow-channel.
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
1823
Fig. 10. Diffusion overpotential distribution at the cathode sites: (a) ambient air-breathing and (b) airflow-channel.
for airflow-channel design, where under the land areas a noticeable decrease takes place. It can be seen that for airflow-channel design, a high fraction of the current is generated at the catalyst layer that lies beneath the air inlet area, leading to under-utilization of the catalyst under the land areas. This can lead to local hot spots inside the membrane electrode assembly. These hot spots can lead to a further drying out of the membrane, thus increasing the electric resistance, which in turn leads to more heat generation and can lead to a failure of the membrane. Thus, it is important to keep the current density relatively even throughout the cell. For optimal fuel cell performance, a uniform current density generation is desirable, and this could only be achieved with a non-uniform catalyst distribution, possibly in conjunction with non-homogeneous gas diffusion layers. The temperature distribution inside the fuel cell has important effects on nearly all transport phenomena, and knowledge of the magnitude of temperature increases due to irreversibilities might help preventing failure [15]. Fig. 6 shows the distribution of the temperature (in K) inside the cell for both designs. The result of the both designs shows that the increase in temperature can exceed several Kelvin near the catalyst layer regions, where the
electrochemical activity is highest. The temperature peak appears in the cathode catalyst layer, implying that major heat generation takes place in the region. In general, the temperature at the cathode side is higher than that at the anode side; this is due to the reversible and irreversible entropy production. The air-breathing design results in more even distribution of the local current density with low fraction than airflow-channel design. Therefore, the maximum temperature gradient appears in the airflow-channel design as can be seen in Fig. 6. For an optimum fuel cell performance, and in order to avoid large temperature gradients inside the fuel cell, it is desirable to achieve a uniform current density distribution inside the cell. Activation overpotential (in V) distribution for both designs is shown in Fig. 7. The activation overpotential profile correlates with the local current density. For the airflow-channel design, fresh air coming from the air inlet area has a longer distance to diffuse through to reach the land areas. This fact results in a diminished oxygen concentration at the catalyst sites under the land areas of the airflow-channel design. Therefore, the airflow-channel design fuel cell leads to a distribution where the maximum is located under the centre of the air inlet area and coincides with the highest
1824
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
reactant concentrations. Better gas replenishment at the catalyst sites in the air-breathing design results in lower activation potentials with quite uniform distribution. To perform a comprehensive comparison study for each component of the cell, two types of ohmic losses that occur in MEA are characterized. These are potential losses due to electron transport through electrodes and potential loss due to proton transport through the membrane. Ohmic overpotential is the loss associated with resistance to electron transport in the GDLs. For a given nominal current density, the magnitude of this overpotential is dependent on the path of the electrons. The potential field (in V) in the cathodic and the anodic gas diffusion electrodes is shown in Fig. 8 for both designs. The potential distributions are normal to the flow inlet, fuel and air, and the side walls. For airflow-channel design, there is a gradient into the land areas where electrons flow into the bipolar plate. The distributions exhibit gradients in both x and z directions due to the non-uniform local current production and show that ohmic losses are larger in the area of the catalyst layer under the fuel and air inlet. The potential loss in the membrane is due to resistance to proton transport across the membrane from anode catalyst layer to cathode catalyst layer. The distribution pattern of the protonic overpotential is dependent on the path travelled by the protons and the activities in the catalyst layers. Fig. 9 shows the potential loss distribution (in V) in the membrane for both designs. It can be seen that the potential drop is more uniformly distributed across the membrane. This is because of the smaller gradient of the hydrogen concentration distribution at the anode catalyst layer due to the higher diffusivity of the hydrogen. The variation of the cathode diffusion overpotentials (in V) is shown in Fig. 10 for both designs. Air-breathing design improves the mass transport within the cell and this leads to reducing the mass-transport loss. Better gas replenishment at the catalyst sites results in lower and quite uniform distribution of diffusion potentials. For airflow-channel design, there is a much stronger distribution of diffusion potentials at the catalyst sites, with higher values under the air inlet area. This is due to the reduction of the molar oxygen fraction at the catalyst layer under the land areas. 4. Conclusions Full three-dimensional computational fluid dynamics models of airflow-channel and air-breathing PEM fuel cell have been developed. The results show that higher power densities are achieved with the air-breathing design mainly because of lower activation and diffusion overpotentials. Better gas replenishment at the catalyst sites in air-breathing design results in lower and quite uniform distribution of activation and diffusion potentials. An airbreathing design evens out the local current density distribution. For an airflow-channel design a much higher fraction of the total current is generated under the air inlet area. Therefore, the maximum temperature gradient appears in the air-breathing
design. The models are shown to be able to: (1) understand the many interacting, complex electrochemical and transport phenomena that cannot be studied experimentally; (2) identify limiting steps and components; and (3) provide a computer-aided tool for the design and optimization of future fuel cells to improve their lifetime with a much higher power density and lower cost. The analysis offers valuable physical insight towards design of a cell and a cell stack, to be considered in a future study.
Acknowledgements This project was supported by International Technological University (ITU), London, UK.
References [1] O’Hayre R, Fabian T, Litster S, Prinz FB, Santiago JG. Engineering model of a passive planar air breathing fuel cell cathode. J Power Sources 2007;167(1): 118–29. [2] Litster S, Pharoah JG, McLean G, Djilali N. Computational analysis of heat and mass transfer in a micro-structured PEMFC cathode. J Power Sources 2006; 156(2):334–44. [3] Hwang JJ, Wu SD, Pen RG, Chen PY, Chao CH. Mass/electron co-transports in an air-breathing cathode of a PEM fuel cell. J Power Sources 2006;160(1):18–26. [4] Wang Y, Ouyang M. Three-dimensional heat and mass transfer analysis in an air-breathing proton exchange membrane fuel cell. J Power Sources 2007; 164(2):721–9. [5] Litster S, Djilali N. Mathematical modelling of ambient air-breathing fuel cells for portable devices. Electrochim Acta J 2007;52(11):3849–62. [6] Rajani BPM, Kolar AK. A model for a vertical planar air breathing PEM fuel cell. J Power Sources 2007;164(1):210–21. [7] Paquin M, Frechette L. Understanding cathode flooding and dry-out for water management in air breathing PEM fuel cells. J Power Sources 2008;180(1): 440–51. [8] Wang CY. Fundamental models for fuel cell engineering. Chem Rev 2004; 104(10):4727–65. [9] Barbir F. PEM fuel cellsdtheory and practice. London: Elsevier Academic Press; 2005. [10] Weber AZ, Newman J. Modeling transport in polymer-electrolyte fuel cells. Chem Rev 2004;104(10):4679–726. [11] Fuller EN, Schettler PD, Giddings JC. A new method for prediction of binary gas-phase diffusion coefficients. Ind Eng Chem 1966;58(5):18–27. [12] Berning T, Djilali N. A 3D, multi-phase, multicomponent model of the cathode and anode of a PEM fuel cell. J Electrochem Soc 2003;150(12):A1589–98. [13] Berning T, Lu DM, Djilali N. Three-dimensional computational analysis of transport phenomena in a PEM fuel cell. J Power Sources 2002;106(1–2): 284–94. [14] Nguyen PT, Berning T, Djilali N. Computational model of a PEM fuel cell with serpentine gas flow channels. J Power Sources 2004;130(1–2):149–57. [15] Al-Baghdadi MARS, Al-Janabi HAKS. Modeling optimizes PEM fuel cell performance using three-dimensional multi-phase computational fluid dynamics model. Energy Convers Manag 2007;48(12):3102–19. [16] Lampinen MJ, Fomino M. Analysis of free energy and entropy changes for half-cell reactions. J Electrochem Soc 1993;140(12):3537–46. [17] Siegel NP, Ellis MW, Nelson DJ, Spakovsky MR von. A two-dimensional computational model of a PEMFC with liquid water transport. J Power Sources 2004;128(2):173–84. [18] Hu M, Gu A, Wang M, Zhu X, Yu L. Three dimensional, two phase flow mathematical model for PEM fuel cell. Part I. Model development. Energy Convers Manag 2004;45(11–12):1861–82. [19] Wang L, Husar A, Zhou T, Liu H. A parametric study of PEM fuel cell performances. Int J Hydrogen Energy 2003;28(11):1263–72.
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Performance comparison between airflow-channel and ambient air-breathing PEM fuel cells using three-dimensional computational fluid dynamics models Maher A.R. Sadiq Al-Baghdadi Mechanical & Energy Department, Higher Institute for Engineering Comprehensive Vocations, Yefren, P.O. Box 65943, Libya
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 May 2008 Accepted 2 December 2008 Available online 3 January 2009
The development of physically representative models that allow reliable simulation of the processes under realistic conditions is essential to the development and optimization of fuel cells, the introduction of cheaper materials and fabrication techniques, and the design and development of novel architectures. Full three-dimensional, multiphase, non-isothermal computational fluid dynamics models of planar airbreathing and airflow-channel PEM fuel cell have been developed. These comprehensive models account for the major transport phenomena in both these types: convective and diffusive heat and mass transfer, electrode kinetics, transport and phase-change mechanism of water, and potential fields. The models are shown to understand the many interacting, complex electrochemical, and transport phenomena that cannot be studied experimentally. Fully three-dimensional results of the species profiles, temperature distribution, potential distribution, and local current density distribution are presented and analyzed with a focus on the physical insight and fundamental understanding for the air-breathing and airflowchannel PEM fuel cells. Ó 2008 Elsevier Ltd. All rights reserved.
Keywords: Ambient air-breathing PEM Fuel cell modelling CFD 3D model
1. Introduction Small fuel cells have provided significant advantages in portable electronic applications over conventional battery systems. However, the typical polymer electrolyte fuel cell system with its heavy reliance on subsystems for cooling, humidification and air supply would not be practical in small applications. The airbreathing PEM fuel cells without moving parts (external humidification instrument, fans or pumps) are one of the most competitive candidates for future portable-power applications. The development of physically representative models that allow reliable simulation of the processes under realistic conditions is essential to the development and optimization of fuel cells, the introduction of cheaper materials and fabrication techniques, and the design and development of novel architectures. The difficult experimental environment of fuel cell systems has stimulated efforts to develop models that could simulate and predict multidimensional coupled transport of reactants, heat and charged species using computational fluid dynamic (CFD) methods. Due to the high activation energy required for the oxygen reduction reaction and the required water management due to condensation, the cathode has been of particular interest in previous computational modelling efforts [1–3]. O’Hayre et al. [1]
E-mail address: [email protected] 0960-1481/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2008.12.002
developed a one-dimensional, non-isothermal model that captures the coupling between water generation, oxygen consumption, self-heating and natural convection at the cathode of an air-breathing fuel cell. Their result confirms the strong effect of self-heating on the water balance within passive air-breathing fuel cells. Litster et al. [2] developed a two-dimensional, singlephase, non-isothermal CFD model of the cathodic electrodes in ambient air-breathing, non-planar, micro-structured PEM fuel cell that increases the surface to volume ratio of the deposited catalyst layer. The model was employed to evaluate the feasibility of these electrodes for use in fuel cells to power small portable consumer electronics. The results of this study indicate that this electrode configuration is feasible and does not suffer from insurmountable mass transfer limitations. Hwang et al. [3] developed a CFD, single-phase, isothermal, three-dimensional model of coupled fluid flow field, mass transport and electrochemistry in an airbreathing cathode of a planar PEM fuel cell. In their results, electrochemical/mass characteristics such as flow velocities, species mass fraction, species flux and current density distributions in a passive cathode have been discussed in detail. These models are very useful because they may include a large portion of the relevant fuel cell physics but at the same time having relatively short solution times. However, this narrowly focused model neglects important parts of the fuel cell making it impossible to get a complete picture of the phenomena governing fuel cell behaviour. Models that include all parts of a fuel cell are
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
Nomenclature a AMEA Ach C Cref Cp D E Ecell F I i iref o,a iref o,c keff kmem Kp _ phase m M
water activity geometrical area of membrane electrode assembly (m2) cross-sectional area of flow channel (m2) local concentration (mol/m3) reference concentration (mol/m3) specific heat capacity (J/kg K) diffusion coefficient (m2/s) equilibrium thermodynamic potential (V) cell operation potential (V) Faraday’s constant ¼ 96 487 (C/mol) cell operating current density (A/m2) local current density (A/m2) anode reference exchange current density cathode reference exchange current density effective electrode thermal conductivity (W/m K) membrane thermal conductivity (W/m K) hydraulic permeability (m2) _ phase ¼ m _ evap Þ and mass transfer: evaporation ðm _ cond Þ (kg/s) _ phase ¼ m condensation ðm molecular weight (kg/mol)
reflecting many of the physical processes occurring within the fuel cell. Entire unit cells have been modelled with the additional complexity of anode and membrane transport in several researches [4–7]. Wang and Ouyang [4] developed a CFD, single-phase model of a channel-type air-breathing PEM fuel cell, in which the air is provided through straight vertical cathode channel open to ambient air at top and bottom. Their model accounts for threedimensional transport processes using non-dimensional heat/mass transfer coefficients. This model was applied to planar channeltype air-breathing fuel cells (which consists of cathode ducts open to atmosphere at top and bottom), rather than planar open-cathode fuel cells (in which the cathode gas diffusion layer (GDL) is completely open to atmosphere). In such cells, performance was shown to depend strongly on the cathode channel geometry [4]. However, the ducted cathode air-breathing PEM fuel cell is the most frequently used design, which consists of cathode ducts open to atmosphere at top and bottom. In addition, this model did not account for phase change, liquid water concentration in the electrodes, and water dissolved in the ion-conducting polymer. An air-breathing PEM fuel cell is considered to be planar if the cathode GDL has a perfectly planar surface without any protrusions or physical disturbances and completely open to atmosphere for absorbing the required oxygen from air. Litster and Djilali [5] developed a single-phase one-dimensional semi-analytical model of the membrane electrode assembly of planar air-breathing PEM fuel cells for portable devices. Their study suggests that improved performance of air-breathing fuel cells can be achieved by increasing the heat removal rate and thus promoting higher relative humidity levels in the GDL. Rajani and Kolar [6] developed a single-phase two-dimensional model for a planar air-breathing PEM fuel cell that considered both heat and mass transfer. Their results showed that the maximum power density and the corresponding current density increase with decreasing height of the fuel cell, decreasing ambient temperature and increasing ambient relative humidity. In all these models [1–6], multiphase transport in the cell is not considered; they do not account for phase change, liquid water concentration in the electrodes, and water dissolved in the
NW nd ne P Pc q_ R s sat T u xi yi
aa ac 3 h le lm m r s x
1813
net water flux across the membrane (kg/m2 s) electro-osmotic drag coefficient number of electrons transfer pressure (Pa) capillary pressure (Pa) heat generation (W/m2) universal gas constant ¼ 8.314 (J/mol K) specific entropy (J/mol K) saturation temperature (K) velocity vector (m/s) mole fraction mass fraction charge transfer coefficient, anode side charge transfer coefficient, cathode side porosity overpotential (V) electrode electronic conductivity (S/m) membrane ionic conductivity (S/m) viscosity (kg/m s) density (kg/m3) surface tension (N/m) stoichiometric flow ratio
ion-conducting polymer; that is, single phase is assumed. Besides diffusion mass transfer, transport of liquid water can be important in the gas diffusion layers, catalyst layers, and membrane of airbreathing PEM fuel cells. Paquin and Frechette [7] developed a simple multiphase one-dimensional model of a free convection planar air-breathing PEM fuel cell that couples heat and mass transfer with the electrochemical reaction of a small air-breathing PEM fuel cell to analyse water management. The simplifications that used in this model regarding heat transfer did not allow an exact agreement between experimental and model results, so a correction factor was used to get a better match between temperatures. Models that include all parts of a fuel cell are typically two- or three-dimensional and reflect many of the physical processes occurring within the fuel cell. However, in a real PEM fuel cell geometry, the GDLs are used to enhance the reaction area accessible by the reactants. The effect of using these diffusion layers is to allow a spatial distribution in the current density on the membrane in both the direction of bulk flow and the direction orthogonal to the flow but parallel to the membrane. This twodimensional distribution cannot be modelled with the well-used two-dimensional models where the mass-transport limitation is absent in the third direction. The objective of the present work is to numerically study the transport phenomena in a passive mode PEM fuel cell that operates without external forced flows. Multiphase, multi-component flow, non-isothermal, three-dimensional CFD model of complete parts of an ambient air-breathing PEM fuel cell, which work in still, or slowly moving air has been developed and presented in detail. The porous cathode is attached to a perforated current collector. It breathes the fresh air through the perforations and routes out the electric current through its solid counterpart. A comparison study between the performances of the planar air-breathing PEM fuel cell with the airflow-channel PEM fuel cell is also presented. The informative results obtained by the present study can help in understanding of the local gas transports and electrochemical characteristics in both designs of the fuel cells. In addition, they can provide a solid basis for optimizing the geometry of the passive PEM fuel cell stack.
1814
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
2. Model description The present work presents a comprehensive three-dimensional, multiphase, non-isothermal model of an airflow-channel/airbreathing PEM fuel cell that incorporates the significant physical processes and the key parameters affecting fuel cell performance. The following assumptions are made: (i) The fuel cell operates under steady-state conditions. This is because the start-up or stop or any transient process of a fuel cell is not considered in this model. (ii) The ionic conductivity of the membrane is constant. The conductivity of the membrane is a function of hydration, which is expressed as the number of water molecules per sulfonate group. Membrane conductivity increases with membrane water content. If
the membrane is drying, a rising resistance (protonic overpotential) will reveal this [8]. (iii) The membrane is impermeable to gases and cross-over of reactant gases is neglected. The highly diffusive hydrogen can cross the membrane and recombine with the oxygen at the cathode side without being oxidized at the anode catalyst layer, which results in a loss of fuel [9]. (iv) The GDL is homogeneous and isotropic. This assumption asserts that the porosity is a constant in the whole region of the gas diffusers. The porosity of the GDL affects the performance of the fuel cell in two aspects: a higher void fraction provides less resistance for the reactant gases to reach the catalyst layer on one hand, but in turn it leads to a higher contact resistance [10]. (v) The produced water is in the vapour phase. (vi) Two-phase flow inside the porous media.
Fig. 1. Three-dimensional computational domains of PEM fuel cells used in this work: (a) ambient air-breathing design and (b) airflow-channel design.
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
(vii) Both phases occupy a certain local volume fraction inside the porous media and their interaction is accounted for through a multi-fluid approach. The model accounts for both gas and liquid phase in the same computational domain, and thus allows for the implementation of phase change inside the gas diffusion layers. The model includes the transport of gaseous species, liquid water, protons, energy, and water dissolved in the ion-conducting polymer. Water transport inside the porous gas diffusion layer and catalyst layer is described by two physical mechanisms: viscous drag and capillary pressure forces, and is described by advection within the gas channels. Water transport across the membrane is also described by two physical mechanisms: electro-osmotic drag and diffusion. Water is assumed to be exchanged among three phases; liquid, vapour, and dissolved, and equilibrium among these phases is assumed.
2.1. Computational domain
1815
Table 2 Geometrical and operational parameters for base case operating conditions. Parameter
Symbol
Value
Unit
Channel length Channel height Channel width Gas diffusion layer thickness Wet membrane thickness (NafionÒ 117) Catalyst layer thickness Hydrogen reference mole fraction Oxygen reference mole fraction Fuel pressure Air pressure Fuel stoichiometric flow ratio
L H W
0.05 1e3 1e3 0.26e3 0.23e3 0.0287e3 0.84639 0.17774 1 1 2
m m
dGDL dmem dCL xref H2 xref O2 Pa Pc
xa
2 V$ rg ug 5ug mg Vug ¼ Vrg P þ mg V$ug 3 h T i þ V$ mg Vug
m m m – – atm atm –
(3)
The full computational domains for the air-breathing and airflow-channel PEM fuel cell consist of anode gas-flow field, cathode, and the membrane electrode assembly as shown in Fig. 1.
and
2.2. Model equations
The mass balance is described by the divergence of the mass flux through diffusion and convection. Multiple species are considered in the gas phase only, and the species conservation equation in multi-component, multiphase flow can be written in the following expression for species i;
2.2.1. Air and fuel gas flow In natural convection region, the transport equations solved in the ambient air include continuity, momentum, energy and masstransport equations. In the fuel channel, the gas-flow field is obtained by solving the steady-state Navier–Stokes equations, i.e. the continuity equation, the mass conservation equation for each phase yields the volume fraction (r) and along with the momentum equations the pressure distribution inside the channel. The continuity equation for the gas phase inside the channel is given by;
V$ rg rg ug ¼ 0
(1)
and for the liquid phase inside the channel becomes;
V$ðrl rl ul Þ ¼ 0
h i 2 V$ðrl ul 5ul ml Vul Þ ¼ Vrl P þ ml V$ul þ V$ ml ðVul ÞT 3
2
VP VM Vyj þ yj þ xj yj M P j¼1 3 VT 5 ¼ 0 þ rg rg yi $ug þ DTi T
V$4 rg rg yi
N X
Dij
M Mj
Two sets of momentum equations are solved in the channel, and they share the same pressure field. Under these conditions, it can be shown that the momentum equations becomes; Table 1 Electrode and membrane properties and parameters. Symbol
Value
Unit
Electrode porosity Electrode electronic conductivity Membrane ionic conductivity (humidified NafionÒ 117) Transfer coefficient, anode side Transfer coefficient, cathode side Cathode reference exchange current density Anode reference exchange current density Electrode thermal conductivity Membrane thermal conductivity Electrode hydraulic permeability Entropy change of cathode side reaction Heat transfer coefficient between solid and gas phase Fuel cell temperature Relative humidity Protonic diffusion coefficient Fixed-charge concentration Fixed-site charge Electro-osmotic drag coefficient
3 le lm
0.4 100 17.1223
– S/m S/m
aa ac
b
0.5 1 1.8081e3 2465.598 1.3 0.455 1.76e11 326.36 4e6
– – A/m2 A/m2 W/m K W/m K m2 J/mol K W/m3
Tcell R DHþ cf zf nd
353.15 100 4.5e9 1200 1 2.5
K % m2/s mol/m3 – –
iref o,c iref o,a keff kmem Kp DS
(5)
where the subscript i denotes hydrogen and j is water vapour. The Maxwell–Stefan diffusion coefficients of any two species are dependent on temperature and pressure. They can be
(2)
Parameter
(4)
Fig. 2. Comparison of the models and the experimental polarization curves.
1816
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
calculated according to the empirical relation based on kinetic gas theory [11];
" #1=2 T 1:75 103 1 1 Dij ¼ " !1=3 !1=3 #2 M þ M i j P P P Vki þ Vkj k
(6)
k
In this equation, pressure is in [atm] and the binary diffusion P coefficient is in [cm2/s]. The values for ( Vki) are given by Fuller et al. [11]. The temperature field is obtained by solving the convective energy equation;
V$ rg rg Cpg ug T kg VT ¼ 0
(7)
The gas phase and the liquid phase are assumed to be in thermodynamic equilibrium; hence the temperature of the liquid water is the same as the gas phase temperature.
2.2.2. Gas diffusion layers The physics of multiple phases through a porous medium is further complicated here with phase change and the sources and sinks associated with the electrochemical reaction. The equations used to describe transport in the gas diffusion layers are given below. _ phase > 0Þ and Mass transfer in the form of evaporation ðm _ phase < 0Þ is assumed, so that the mass balance condensation ðm equations for both phases are;
_ phase V$ ð1 satÞrg 3ug ¼ m
(8)
and
_ phase V$ðsat$rl 3ul Þ ¼ m
(9)
The momentum equation for the gas phase reduces to Darcy’s law, which is, however, based on the relative permeability for the gas phase (Kp). The relative permeability accounts for the reduction
Fig. 3. Oxygen molar fraction distribution: (a) ambient air-breathing and (b) airflow-channel.
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
in pore space available for one phase due to the existence of the second phase [12]. The momentum equation for the gas phase inside the gas diffusion layer becomes;
ug ¼ ð1 satÞ
Kp VP
(10)
mg
Two liquid water transport mechanisms are considered; shear, which drags the liquid phase along with the gas phase in the direction of the pressure gradient, and capillary forces, which drive liquid water from high to low saturation regions [12]. Therefore, the momentum equation for the liquid phase inside the gas diffusion layer becomes;
Pc ¼ s
3
Kp
1817
1=2 1:417ð1 satÞ
2:12ð1 satÞ2 þ1:263ð1 satÞ3
(12)
The liquid phase consists of pure water, while the gas phase has multi-components. The transport of each species in the gas phase is governed by a general convection–diffusion equation in conjunction which the Stefan–Maxwell equations to account for multispecies diffusion;
2
(11)
VP VM þ xj yj Vyj þ yj M P j¼1 3 VT 5 _ phase þ ð1 satÞrg 3yi $ug þ 3DTi ð13Þ ¼ m T
The functional variation of capillary pressure with saturation is calculated as [12];
where the subscript i denotes oxygen at the cathode side and hydrogen at the anode side, and j is water vapour in both cases. Nitrogen is the third species at the cathode side.
sat$Kp sat$Kp vPc ul ¼ VP þ Vsat ml ml vsat
V$4 ð1 satÞrg 3yi
N X
Dij
M Mj
Fig. 4. Hydrogen molar fraction distribution: (a) ambient air-breathing and (b) airflow-channel.
1818
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
In order to account for geometric constraints of the porous media, the diffusivities are corrected using the Bruggemann correction formula [13,14]; 1:5 Deff ij ¼ Dij 3
(14)
The heat transfer in the gas diffusion layers is governed by the energy equation as follows;
V$ ð1 satÞ rg 3Cpg ug T keff;g 3VT _ phase DHevap ¼ 3bðTsolid TÞ 3m
(15)
where the term (3b(Tsolid T)), on the right hand side, accounts for the heat exchange to and from the solid matrix of the GDL. The gas phase and the liquid phase are assumed to be in thermodynamic equilibrium, i.e., the liquid water and the gas phase are at the same temperature. The potential distribution in the gas diffusion layers is governed by;
V$ðle VfÞ ¼ 0
(16)
In order to account for the magnitude of phase change inside the GDL, expressions are required to relate the level of over- and undersaturation as well as the amount of liquid water present to the amount of water undergoing phase change. In the present work, the procedure of the current author in his previous paper [15] was used to account for the magnitude of phase change inside the GDL. 2.2.3. Catalyst layers The catalyst layer is treated as a thin interface, where sink and source terms for the reactants are implemented. Due to the infinitesimal thickness, the source terms are actually implemented in the last grid cell of the porous medium. At the cathode side, the sink term for oxygen is given by;
SO2 ¼
MO2 ic 4F
(17)
whereas the sink term for hydrogen is specified as;
MH SH2 ¼ 2 ia 2F
Fig. 5. Local current density distribution: (a) ambient air-breathing and (b) airflow-channel.
(18)
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
The production of water is modelled as a source term, and hence can be written as;
S H2 O ¼
MH2 O ic 2F
(19)
The generation of heat in the cell is due to entropy changes as well as irreversibilities due to the activation overpotential [16];
q_ ¼
TðDsÞ þ hact;c ic ne F
(20)
The local current density distribution in the catalyst layers is modelled by the Butler–Volmer equation [13,14];
0
1 aa F ac F ref @ CO2 A h h þ exp ic ¼ io;c exp RT act;c RT act;c C ref
(21)
1819
2.2.4. Membrane The balance between the electro-osmotic drag of water from anode to cathode and back diffusion from cathode to anode yields the net water flux through the membrane;
i NW ¼ nd MH2 O V$ðrDW VcW Þ F
(23)
The water diffusivity in the polymer can be calculated as follows [17];
1 1 DW ¼ 1:3 1010 exp 2416 303 T
(24)
The variable cW represents the number of water molecules per sulfonic acid group (i.e. mol H2O/equivalent SO1 3 ). The water content in the electrolyte phase is related to water vapour activity via [18];
O2
0
11=2
@ CH2 A ia ¼ iref o;a ref CH 2
exp
aa F RT
hact;a
ac F hact;a þ exp RT
(22)
cW
8 2 3 > <0:043 þ 17:81a 39:85a þ 36:0a ð0 < a 1Þ ¼ 14:0 þ 1:4ða 1Þ ð1 < a 3Þ > : 16:8 ða 3Þ
Fig. 6. Temperature distribution inside the cell: (a) ambient air-breathing and (b) airflow-channel.
(25)
1820
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
The water vapour activity is given by;
x P a ¼ W Psat
(26)
Heat transfer in the membrane is governed by;
V$ðkmem $VTÞ ¼ 0
(27)
The potential loss in the membrane is due to resistance to proton transport across membrane, and is governed by;
V$ðlm VfÞ ¼ 0
(28)
2.2.5. Cell potential Useful work (electrical energy) is obtained from a fuel cell only when a current is drawn, but the actual cell potential (Ecell) is decreased from its equilibrium thermodynamic potential (E) because of irreversible losses. The cell potential is obtained by subtracting all overpotentials (losses) from the equilibrium thermodynamic potential as the following expression;
Ecell ¼ E hact hohm hmem hDiff
(29)
The equilibrium potential is determined using the Nernst equation [15];
E ¼ 1:229 0:83 103 ðT 298:15Þ þ 4:3085 1 105 T ln PH2 þ ln PO2 2
(30)
The anode and cathode activation overpotentials are calculated from Butler–Volmer equation ((21) and (22)). The ohmic overpotentials in GDLs and protonic overpotential in membrane are calculated from the potential equations (16) and (28) respectively. The anode and cathode diffusion overpotentials are calculated from the following equations [15];
hDiff;c ¼
RT ic ln 1 iL;c 2F
(31)
hDiff;a ¼
RT ia ln 1 2F iL;a
(32)
Fig. 7. Activation overpotential distribution at the cathode sites: (a) ambient air-breathing and (b) airflow-channel.
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
iL;c ¼
iL;a ¼
2FDO2 CO2
(33)
dGDL 2FDH2 CH2
(34)
dGDL
3. Results and discussion The governing equations were discretized using a finite volume method and solved using the commercial CFD code FEMLAB-2.3. Stringent numerical tests were performed to ensure that the solutions were independent of the grid size. The coupled set of equations was solved iteratively, and the solution was considered to be convergent when the relative error in each field between two consecutive iterations was less than 1.0 106 (convergence error less than 0.5%). The calculations presented here have all been obtained on a Pentium IV PC (3 GHz, 2 GB RAM) using Windows XP operating system. The values of the electrochemical transport parameters for the base case operating conditions are taken from Ref. [15] and are
1821
listed in Table 1. The geometric and the base case operating conditions are listed in Table 2. Performance curves of the ambient air-breathing and airflow-channel PEM fuel cells were compared with the experimental results provided by Wang et al. [19] for the airflow-channel PEM fuel cell in the same operating conditions (Fig. 2). Polarization curves of the two models clearly show that higher cell potentials are achieved with the airbreathing design mainly because of lower activation and diffusion potentials. Better gas replenishment at the catalyst sites in air-breathing design results in lower activation and diffusion potentials. The lower cell potentials of the airflow-channel design are due to the oxygen concentration decreases gradually from the inflow channel to the outflow channel due to the consumption of oxygen at the catalyst layer. The lower diffusivity of the oxygen along with the low concentration of oxygen in ambient air results in noticeable oxygen depletion near outflow channel and also under the land areas. Moreover, fresh air coming from the inflow channel has a longer distance to diffuse through to reach these areas. The ambient air-breathing fuel cell does not seem to have higher mass-transport losses. The linear behaviour of the voltage–current curve for the ambient air-breathing fuel cell
Fig. 8. Ohmic overpotential distribution in the anode and cathode GDLs: (a) ambient air-breathing and (b) airflow-channel.
1822
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
suggests that the overall overpotential is driven mainly by ohmic losses. In order to gain some insight into why the polarization curve is better in the case of the ambient air-breathing PEM fuel cell, the oxygen and hydrogen distribution, local current densities, temperature distribution, and potential distribution are plotted in Figs. 3–10, respectively, for a fixed nominal current density of 0.8 A cm2. The detailed distribution of oxygen molar fraction for both designs is shown in Fig. 3. In the GDL of the airflow-channel design, oxygen concentration under the land area is smaller than that under the air inlet area. The concentration of oxygen at the catalyst layer is balanced by the oxygen that is being consumed and the amount of oxygen that diffuses towards the catalyst layer driven by the concentration gradient. The lower diffusivity of the oxygen along with the low concentration of oxygen in ambient air results in noticeable oxygen depletion under the land areas. The airbreathing design gives more even distribution of the molar oxygen fraction at the catalyst layer. At air-breathing design, the oxygen mole fraction variation is low enough not to cause diffusive limitations, whereas at airflow-channel design the concentration of oxygen under the land areas has already reached near-zero values.
The molar oxygen fraction at the catalyst layer increases with more even distribution with air-breathing design. This is because of a better gas replenishment at the catalyst sites, which results in quite uniform distribution for the oxygen to reach the catalyst layer. Due to the relatively low diffusivity of the oxygen compared with that of the hydrogen, the cathode operation conditions usually determine the limiting current density. This is because an increase in current density corresponds to an increase in oxygen consumption. The hydrogen molar fraction distribution in the anode side is shown in Fig. 4 for both designs. In general, the hydrogen concentration decreases from inlet to outlet as it is being consumed. However, the decrease is quite small along the channel and the decrease in molar concentration of the hydrogen under the land areas is smaller than for the oxygen in cathode side due to the higher diffusivity of the hydrogen. Fig. 5 shows the local current density (in A cm2) distribution at the cathode side catalyst layer for both designs. The local current density of the cathode side reaction depends directly on the oxygen concentration. The diffusion of the oxygen towards the catalyst layer is the main impediment for reaching high current densities. Therefore, it can be seen that for air-breathing design, the distribution of the local current density is quite uniform. This is changed
Fig. 9. Membrane overpotential distribution across the membrane: (a) ambient air-breathing and (b) airflow-channel.
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
1823
Fig. 10. Diffusion overpotential distribution at the cathode sites: (a) ambient air-breathing and (b) airflow-channel.
for airflow-channel design, where under the land areas a noticeable decrease takes place. It can be seen that for airflow-channel design, a high fraction of the current is generated at the catalyst layer that lies beneath the air inlet area, leading to under-utilization of the catalyst under the land areas. This can lead to local hot spots inside the membrane electrode assembly. These hot spots can lead to a further drying out of the membrane, thus increasing the electric resistance, which in turn leads to more heat generation and can lead to a failure of the membrane. Thus, it is important to keep the current density relatively even throughout the cell. For optimal fuel cell performance, a uniform current density generation is desirable, and this could only be achieved with a non-uniform catalyst distribution, possibly in conjunction with non-homogeneous gas diffusion layers. The temperature distribution inside the fuel cell has important effects on nearly all transport phenomena, and knowledge of the magnitude of temperature increases due to irreversibilities might help preventing failure [15]. Fig. 6 shows the distribution of the temperature (in K) inside the cell for both designs. The result of the both designs shows that the increase in temperature can exceed several Kelvin near the catalyst layer regions, where the
electrochemical activity is highest. The temperature peak appears in the cathode catalyst layer, implying that major heat generation takes place in the region. In general, the temperature at the cathode side is higher than that at the anode side; this is due to the reversible and irreversible entropy production. The air-breathing design results in more even distribution of the local current density with low fraction than airflow-channel design. Therefore, the maximum temperature gradient appears in the airflow-channel design as can be seen in Fig. 6. For an optimum fuel cell performance, and in order to avoid large temperature gradients inside the fuel cell, it is desirable to achieve a uniform current density distribution inside the cell. Activation overpotential (in V) distribution for both designs is shown in Fig. 7. The activation overpotential profile correlates with the local current density. For the airflow-channel design, fresh air coming from the air inlet area has a longer distance to diffuse through to reach the land areas. This fact results in a diminished oxygen concentration at the catalyst sites under the land areas of the airflow-channel design. Therefore, the airflow-channel design fuel cell leads to a distribution where the maximum is located under the centre of the air inlet area and coincides with the highest
1824
M.A.R. Sadiq Al-Baghdadi / Renewable Energy 34 (2009) 1812–1824
reactant concentrations. Better gas replenishment at the catalyst sites in the air-breathing design results in lower activation potentials with quite uniform distribution. To perform a comprehensive comparison study for each component of the cell, two types of ohmic losses that occur in MEA are characterized. These are potential losses due to electron transport through electrodes and potential loss due to proton transport through the membrane. Ohmic overpotential is the loss associated with resistance to electron transport in the GDLs. For a given nominal current density, the magnitude of this overpotential is dependent on the path of the electrons. The potential field (in V) in the cathodic and the anodic gas diffusion electrodes is shown in Fig. 8 for both designs. The potential distributions are normal to the flow inlet, fuel and air, and the side walls. For airflow-channel design, there is a gradient into the land areas where electrons flow into the bipolar plate. The distributions exhibit gradients in both x and z directions due to the non-uniform local current production and show that ohmic losses are larger in the area of the catalyst layer under the fuel and air inlet. The potential loss in the membrane is due to resistance to proton transport across the membrane from anode catalyst layer to cathode catalyst layer. The distribution pattern of the protonic overpotential is dependent on the path travelled by the protons and the activities in the catalyst layers. Fig. 9 shows the potential loss distribution (in V) in the membrane for both designs. It can be seen that the potential drop is more uniformly distributed across the membrane. This is because of the smaller gradient of the hydrogen concentration distribution at the anode catalyst layer due to the higher diffusivity of the hydrogen. The variation of the cathode diffusion overpotentials (in V) is shown in Fig. 10 for both designs. Air-breathing design improves the mass transport within the cell and this leads to reducing the mass-transport loss. Better gas replenishment at the catalyst sites results in lower and quite uniform distribution of diffusion potentials. For airflow-channel design, there is a much stronger distribution of diffusion potentials at the catalyst sites, with higher values under the air inlet area. This is due to the reduction of the molar oxygen fraction at the catalyst layer under the land areas. 4. Conclusions Full three-dimensional computational fluid dynamics models of airflow-channel and air-breathing PEM fuel cell have been developed. The results show that higher power densities are achieved with the air-breathing design mainly because of lower activation and diffusion overpotentials. Better gas replenishment at the catalyst sites in air-breathing design results in lower and quite uniform distribution of activation and diffusion potentials. An airbreathing design evens out the local current density distribution. For an airflow-channel design a much higher fraction of the total current is generated under the air inlet area. Therefore, the maximum temperature gradient appears in the air-breathing
design. The models are shown to be able to: (1) understand the many interacting, complex electrochemical and transport phenomena that cannot be studied experimentally; (2) identify limiting steps and components; and (3) provide a computer-aided tool for the design and optimization of future fuel cells to improve their lifetime with a much higher power density and lower cost. The analysis offers valuable physical insight towards design of a cell and a cell stack, to be considered in a future study.
Acknowledgements This project was supported by International Technological University (ITU), London, UK.
References [1] O’Hayre R, Fabian T, Litster S, Prinz FB, Santiago JG. Engineering model of a passive planar air breathing fuel cell cathode. J Power Sources 2007;167(1): 118–29. [2] Litster S, Pharoah JG, McLean G, Djilali N. Computational analysis of heat and mass transfer in a micro-structured PEMFC cathode. J Power Sources 2006; 156(2):334–44. [3] Hwang JJ, Wu SD, Pen RG, Chen PY, Chao CH. Mass/electron co-transports in an air-breathing cathode of a PEM fuel cell. J Power Sources 2006;160(1):18–26. [4] Wang Y, Ouyang M. Three-dimensional heat and mass transfer analysis in an air-breathing proton exchange membrane fuel cell. J Power Sources 2007; 164(2):721–9. [5] Litster S, Djilali N. Mathematical modelling of ambient air-breathing fuel cells for portable devices. Electrochim Acta J 2007;52(11):3849–62. [6] Rajani BPM, Kolar AK. A model for a vertical planar air breathing PEM fuel cell. J Power Sources 2007;164(1):210–21. [7] Paquin M, Frechette L. Understanding cathode flooding and dry-out for water management in air breathing PEM fuel cells. J Power Sources 2008;180(1): 440–51. [8] Wang CY. Fundamental models for fuel cell engineering. Chem Rev 2004; 104(10):4727–65. [9] Barbir F. PEM fuel cellsdtheory and practice. London: Elsevier Academic Press; 2005. [10] Weber AZ, Newman J. Modeling transport in polymer-electrolyte fuel cells. Chem Rev 2004;104(10):4679–726. [11] Fuller EN, Schettler PD, Giddings JC. A new method for prediction of binary gas-phase diffusion coefficients. Ind Eng Chem 1966;58(5):18–27. [12] Berning T, Djilali N. A 3D, multi-phase, multicomponent model of the cathode and anode of a PEM fuel cell. J Electrochem Soc 2003;150(12):A1589–98. [13] Berning T, Lu DM, Djilali N. Three-dimensional computational analysis of transport phenomena in a PEM fuel cell. J Power Sources 2002;106(1–2): 284–94. [14] Nguyen PT, Berning T, Djilali N. Computational model of a PEM fuel cell with serpentine gas flow channels. J Power Sources 2004;130(1–2):149–57. [15] Al-Baghdadi MARS, Al-Janabi HAKS. Modeling optimizes PEM fuel cell performance using three-dimensional multi-phase computational fluid dynamics model. Energy Convers Manag 2007;48(12):3102–19. [16] Lampinen MJ, Fomino M. Analysis of free energy and entropy changes for half-cell reactions. J Electrochem Soc 1993;140(12):3537–46. [17] Siegel NP, Ellis MW, Nelson DJ, Spakovsky MR von. A two-dimensional computational model of a PEMFC with liquid water transport. J Power Sources 2004;128(2):173–84. [18] Hu M, Gu A, Wang M, Zhu X, Yu L. Three dimensional, two phase flow mathematical model for PEM fuel cell. Part I. Model development. Energy Convers Manag 2004;45(11–12):1861–82. [19] Wang L, Husar A, Zhou T, Liu H. A parametric study of PEM fuel cell performances. Int J Hydrogen Energy 2003;28(11):1263–72.