The effects of operating parameters on the performance of proton exchange membrane fuel cells/Eksploataciniu parametru itaka protonu mainu membranu kuro elementu funkcionavimui.
Dehsara, M. ; Kermani, M.J.
1. Introduction
The wide range of applications from cell phones to new vehicle
generation makes proton exchange membrane fuel cells (PEMFCs) a
distinguished type fuel cells, expected to play a key role in the future
energy system. PEMFCs combine the advantages of running on low operating
temperature, high energy efficiency and low pollution levels. Improving
the performance and reducing the cost of the fuel cells are generally
main development aspects that researchers are working on. Due to PEMFC
especial dimensions, access to inner parts of the cell to measure flow
quantities, is hardly possible. Alternative, another possibility for
detailed study of species concentrations or temperature field through
the components of PEMFC is the use of computational fluid dynamics (CFD)
software packages.
Many researchers have focused on different aspects of PEMFCs by
experimental works. Wang and Liu [1] presented systematic experimental
data on the performance of a proton exchange membrane fuel cell. Their
experiments concentrated on the effects of cell temperature, gas
humidification, cell operating pressure and reactant gas flow rate. And
the results are shown in the form of polarization curves. Jordan et al.
[2] presented the gas diffusion layer parameters effects on polymer
electrolyte fuel cell performances. Sridhar and his colleagues [3]
studied PEMFCs performance by two methods of humidifying. At the same
time many models have been simulated to study PEMFC performance. Gurau
et al. [4] presented mathematical model which enables prediction of
phenomena in entire PEM fuel cell. Sun et al. [5] investigated a
singlephase, cathode side model to account for structural parameters.
COMSOL Multiphysics (FEMLAB) was used to solve all governing equations
in general form. A nonisothermal, single-phase model was presented by
Litster et al. [6]. They addressed heat and mass transfer on the cathode
side of the fuel cell. The model was solved using CFX and the SIMPLEC
algorithm.
Many parameters influence the performance of proton exchange
membrane (PEM) fuel cells such as operating pressure and temperature so
that it is important studies these effects to improve fuel cells'
performance. In this paper, a two-dimensional numerical computation of
steady, compressible, isothermal and single-phase flow of
reactant-product gases mixture in the air side electrode of PEMFC is
performed. The mixture is composed of three species including oxygen,
water vapor and nitrogen. The model presented in this paper is a typical
three-zone that consists of cathode-side gas flow channel, cathode-side
gas diffusion layer and cathode-side catalyst layer. The effects of
operating and geometric parameters on the performance of PEMFCs are
studied. The numerical model of the present paper is validated using the
available experimental data.
2. Numerical modelling
For the present computation the assembly of the software packages
Gambit+Fluent has been used. The geometry employed here is generated
using the software Gambit. Then the problem is run and solved in the
software Fluent using the UDFs developed by the author in the C
programming language.
Fig. 1 shows the schematic of a computational unit of PEM fuel cell
with straight-channel-bed. Layers of the computational unit include
cathode flow channel, gas diffusion layer (GDL), and catalyst layer
(CL).
Structured types of grids (in the form of quad elements) are
applied to each three zones of the computational unit. To solve the
problem, main assumptions considered here are:
* the PEMFC performs under steady-state conditions;
* the reacting gas mixtures are regarded as ideal gases;
* the gas flow is laminar and compressible;
* the GDL and CL are treated as isotropic porous media.
The governing equations used in the present study are given next.
[FIGURE 1 OMITTED]
3. Governing equations
The governing equations of the PEMFCs are described below.
3.1. Conservation equations of mass and momentum
The mixture continuity equation for the present steady computation
is governing by:
[nabla]([epsilon][rho][??]) = 0, (1)
where [epsilon] is the porosity of the GDL and CL (Table 1 for the
values), [??] is the mixture mass averaged velocity and [rho] is the
mixture density which can be defined as:
rho] = 1/[summation] ([y.sub.i]/[[rho].sub.i], (2)
where [y.sub.i] is the mass fraction of the i-th component of the
mixture. The density of each component is determined using the ideal gas
law:
[[rho].sub.i] ([PM.sub.i]/RT, (3)
where P is pressure, [M.sub.i] is molecular mass, T is temperature
and R is the universal gas constant.
The flow field is uniquely determined by the Navier-Stokes
equations which express the momentum conservation for a Newtonian fluid.
So the mixture momentum equation is given by:
[nabla]([epsilon][rho][??][??]) =
-[epsilon][nabla]P+[nabla]([epsilon][mu][nabla][??])+[S.sub.m], (4)
where [S.sub.m] is the momentum source term taken as [S.sub.m] = 0
in the gas flow channels. For the porous regions the source term
[S.sub.m = -[epsilon.sup.2][mu][??]/K, hence the momentum equation
reduces to Darcy equation: [epsilon][??] = -K[nabla]P/[mu], where [mu]
is the dynamic viscosity of the mixture.
3.2. Species transport equations
The steady state species transport equation is written as follows:
[nabla] ([epsilon][??][[rho].sub.i]) =
[nabla]([D.sup.eff.sub.i][nabla] [[rho].sub.i]) + [S.sub.i), (5)
where [S.sub.i] is the volumetric source terms for the species,
which represents the generation/consumption of species i. [S.sub.i] = 0
for all of the layers except the catalyst layers which possess
generation/consumption of the species:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
where M is the molecular mass of one of the species, F is the
Faraday constant, and i is the current density. [A.sub.g] is the area
from which the species i is generated, and [V.sub.g] is the
computational cell volume that consists sink and source terms.
3.3. Properties
The Bruggemann equation is used for the diffusion of gas species at
the desired temperature, and pressure [7, 8]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
where [D.sup.0.sub.i] is the mass diffusion of species i at
reference temperature and pressure ([T.sub.0], [p.sub.0]),
[[gamma].sub.p] and [[gamma].sub.t], are the reference and constant
values.
3.4. Current calculation
To calculate the fuel cell current, the Butler-Volmer equation is
used [9]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
where [[eta].sub.act] is activation voltage, [[alpha].sub.c] is
load transport coefficient of the cathode side, F is the Faraday
constant, R is the universal gas constant, T is fuel cell operating
temperature,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is oxygen molar
concentration, and [i.sub.o,c] is the value of exchanged current in fuel
cell no-load condition. In PEM fuel cell operating temperature range,
the value of [i.sub.o,c] can be determined from [9]:
[i.sub.o,c] = [10.sup.6.507-4001/T. (10)
The molar concentration of oxygen is obtained using the following
relation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
In the present study, only the activation and ohmic losses are
considered. Therefore the relation between [V.sub.rev] and [V.sub.cell]
can be defined as:
[V.sub.cell] = [V.sub.rev]-i[sigma]-[[eta].sub.act], (12)
where [sigma] is the fuel cell ohmic resistance, [[eta].sub.act] is
the activation voltage loss, [V.sub.cell] is the fuel cell working
voltage, and [V.sub.rev] is the fuel cell open-circuit voltage. The
relation between [V.sub.cell] and the fuel cell working temperature is
obtained using the following relation [9]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)
By combining relations (9) and (12), can be written:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)
Eq. (14) shows the relation among [V.sub.rec], [V.sub.cell], i and
fuel cell internal conditions.
To obtain average current density from current density, the
following relation is used:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)
where i is the current density, [A.sub.g] is the area from which
current density i is generated.
4. Boundary conditions
For the following discussion of boundary conditions, refer to Fig.
1.
* At the boundary location I (channel inlet) where the flow enters
to the cathode channel, mass flow inlet condition is specified.
* At the boundary location II (channel exit) where the flow leaves
the cathode channel, pressure outlet condition is specified.
* At boundary locations III to V, all of the surfaces are set to
stationary walls.
* Cathode flow channel, GDL and CL are set to fluid zones.
5. Solution method
The representation of the mesh generation and geometry creation in
the present computation are given in Fig. 2. As it can be seen, the grid
network consists of three zones of cathode channel, GDL and CL that
their interior surfaces are shown with the blue lines. A control volume
method within the environment of software package Fluent has been used
to solve the governing equations and perform the parametric studies in
the present paper. The SIMPLE algorithm is taken for computation with 1
x [10.sup.-5] precision. The model consists of several user-defined
functions (UDFs) to incorporate the formulations, source terms and other
model parameters that are written by authors. Multigrid cycle is also
set to F-Cycle for all the equations. Stabilization method is changed to
BCGSTAB (bi-conjugate gradient stabilized method) for species
concentrations. Also maximum number of cycles was increased for 50. The
under-relaxation factors for the governing equations are set as follows:
for pressure to 0.45, for density to 1, for body forces to 0.9, for
momentum to 0.3, for species concentration to 0.9, for energy to 0.2.
The discretization method was changed to second order (leading to more
precise solutions) for all equations [10].
[FIGURE 2 OMITTED]
6. Results and discussion
In this paper, a two-dimensional numerical computation of steady,
compressible, isothermal and singlephase flow of reactant-product gases
in the air side electrode of PEMFC is performed. The effects of
operating and geometric parameters on the performance of PEMFCs are
studied. The PEM fuel cell operates at 80[degrees]C temperature, 5 atm
pressure and relative humidity of 100%. Table 1 shows the physical
parameters used in the present computation.
Fig. 3 depicts a comparison between the simulation results and the
experimental data of Ticianelli et al. [11]. As it can be seen in Fig.
3, there is a good agreement between the polarization curves of
numerical and experimental results, which confirms the validity of the
present paper model.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
Fig. 4 shows the variations of local current density with respect
to operating pressure. As is can be observed, the local current
generation increases with the increase of fuel cell pressure. The
increase of pressure causes the increase of reacting gasses diffusion
from GDL to the catalyst layer, and consequently the reaction rate in
catalyst layer, which is the reaction site, increases. As a result,
higher local current is generated.
The variations of oxygen sink term with respect to the fuel cell
operating pressure are shown in Fig. 5. It can be seen that the oxygen
consumption rate in catalyst layer increases with the increase of
operating pressure. The in crease of pressure causes the increase of
oxygen diffusion in catalyst layer, which is the reaction site, and
therefore the oxygen consumption rate increases due to the oxygen higher
presence in reaction site.
[FIGURE 5 OMITTED]
Fig. 6 shows the characteristic curves of PEM fuel cells which
include fuel cell polarization and output power density. As it can be
seen, the fuel cell characteristic curves shift positively with the
increase of pressure.
As it was observed in Fig. 5, the increase of pressure increases
the oxygen consumption rate in the cathode catalyst layer. Therefore
according to the Faraday law, the local current generation rate
increases. As a result, the PEM fuel cell output current density
increases, which can obviously be seen in Fig. 6.
[FIGURE 6 OMITTED]
Fig. 7 demonstrates the variations of fuel cell local current
density with respect to the operating temperature. As it can be
observed, the generated local current density increases with the
increase of operating temperature. The increase of temperature causes
the increase of exchanged current density, and consequently the
improvement of mass transport properties in catalyst layer, which is the
reaction site. Therefore the local current generation is boosted.
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
Fig. 8 shows the variations of oxygen sink term with respect to the
PEM fuel cell operating temperature. Higher oxygen consumption rate can
be seen in cathode side catalyst layer with the increase of fuel cell
operating temperature, which shows the increase of local current
generation rate. The variations of the PEM fuel cell characteristic
curves with respect to the fuel cell operating temperature are shown in
Fig. 9. As it was also observed in Fig. 8, the temperature increase
causes the increase of oxygen consumption rate in cathode side catalyst
layer, and therefore the PEM fuel cell output current density increases.
Fig. 10 depicts the fuel cell local current density with respect to the
cathode exchange coefficient. The increase of cathode exchange
coefficient causes the reduction of the fuel cell voltage loss, and
therefore the local current density in fuel cell increases.
Fig. 11 shows the variations of oxygen sink term with respect to
the cathode exchange coefficient. As it can be seen, the increase of
cathode exchange coefficient, for the sake of reaction rate boosting,
increases the oxygen consumption rate. Fig. 12 shows the variations of
fuel cell polarization and output power density with respect to the
cathode exchange coefficient. As it was observed in Figs. 10 and 11, the
increase of cathode exchange coefficient increases the oxygen
consumption rate, and therefore, according to the Faraday law, the fuel
cell local current generation increases. As a result, the PEM fuel cell
output current density increases. The ohmic losses in fuel cell are due
to the resistances in electrodes and various internal connections in the
flow path of electrons and also due to the resistances in the transport
path of positive ions in electrolyte. Fig. 13 shows the variations of
local current density with respect to the fuel cell overall ohmic
resistance. It is seen that with the increase of ohmic resistance, the
fuel cell output current density reduces due to the higher resistances
in the transport path of positive ions.
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
The variations of oxygen sink term with respect to the PEM fuel
cell ohmic resistance is depicted in Fig. 14. The oxygen consumption
rate in cathode catalyst layer increases with the increase of ohmic
resistance.
Fig. 15 demonstrates the PEM fuel cell performance curves with
respect to the overall ohmic resistance. When the ohmic resistances
increase, the resistance to the electron and proton transport in fuel
cell increases. Therefore the fuel cell output power density decreases.
The results of the parameter study are summarized in Table 2 in terms of
the range, optimum value, and sensitivity for each parameter considered.
The parameters are also ranked from 1 to 12 in order of their
importance, with the rank 1 for [sigma] indicating that it is the
structural parameter that has the most significant influence on PEMFC
performance.
[FIGURE 11 OMITTED]
[FIGURE 12 OMITTED]
[FIGURE 13 OMITTED]
[FIGURE 14 OMITTED]
[FIGURE 15 OMITTED]
7. Conclusions
A two-dimensional computational proton exchange membrane fuel cell
(PEMFC) model is presented to investigate the effects of operating
parameters such as overall ohmic resistance, cathode side charge
transfer coefficient, operating pressure, and fuel cell temperature on
PEMFCs. A single phase, compressible and isothermal flow of
reactant-product mixture in the air-side electrode of PEMFC with
straight gas channel is considered. The modeling results are illustrated
using local current density curve, oxygen sink curve and performance
curves. The results show that the net transport of reacting species
through porous layers toward the catalyst layer and also the performance
of PEMFC can be enhanced by increasing cathode side charge transfer
coefficient, operating pressure and operating temperature. Also, [sigma]
(overall ohmic resistance) is the structural parameter that has the most
significant influence on PEMFC performance.
Nomenclature
[A.sub.g] - generation area, [m.sup.2]; [MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE IN ASCII] - reference Oxygen concentration,
mol/[m.sup.3]; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] -
reference diffusivity of [O.sub.2], [m.sup.2]/s; [MATHEMATICAL
EXPRESSION NOT REPRODUCIBLE IN ASCII] - reference diffusivity of
[H.sub.2]O, [m.sub.2]/s; F - Faraday number; [h.sub.ch] - channel
height, m; [h.sub.GDL] - gas diffusion layer (GDL) height, m; [h.sub.CL]
- catalyst layer (CL) height, m; i - current density, A/[m.sup.2]; j -
diffusion mass flux, kg/[m.sup.2].s; K - hydraulic permeability of GDL
and CL, [m.sup.2]; [L.sub.ch] - channel length, m; M - molecular mass,
kg/mol; P - pressure vector, Pa; R - universal gas constant, J/(kg mol
K); S - source term; T - temperature, K; [??] - velocity, m/s;
[V.sub.cell] - fuel cell working voltage, V; [V.sub.g] - computational
cell volume, [m.sup.3]; [V.sub.oc] - open-circuit voltage, V; y - mass
fraction. Greek symbols: [[alpha].sub.c] - cathode exchange coefficient;
[[epsilon].sub.CL] - porosity of CL; [[epsilon].sub.GDL] - porosity of
GDL; [[eta].sub.act] - activation voltage, V; [rho] - mixture density,
kg/[m.sup.3]; [sigma] - Ohmic resistance, [m.sup.2]. Subscripts: act -
activation; CL - catalyst layer; GDL - gas diffusion layer; i -
component of the mixture.
[cross.sup.ref] http://dx.doi.org/10.5755/j01.mech.19.6.5989
Acknowledgement
Financial support from the Renewable Energy Organization of Iran
(SUNA) is acknowledged.
Received September 19, 2012
Accepted November 11, 2013
References
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M. Dehsara, Department of Mechanical Engineering, Amirkabir
University of Technology (Tehran Polytechnic), 424 Hafez Avenue, P.O.
Box, 15875-4413 Tehran, Iran, E-mail: bm_dehsara@aut.ac.ir
M.J. Kermani, Energy Conversion Research Laboratory, and The New
Technologies Research Center, Department of Mechanical Engineering,
Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez
Avenue, P.O. Box, 15875-4413 Tehran, Iran, E-mail: mkermai@aut.ac.ir
Table 1
Physical properties and parameters
Symbol Property Value/Reference
[L.sub.ch] Channel length 7.112 cm
[h.sub.ch] Channel height 0.0762 cm
[h.sub.GDL] Gas diffusion layer 0.0254 cm
height
[h.sub.CL] Catalyst layer height 0.00127 cm
[[epsilon].sub.GDL] Porosity of GDL 0.4 [12]
K Hydraulic permeability 1.76 x [10.sup.-11]
of GDL and CL [m.sup.2] [13]
[V.sub.oc] Open circuit voltage 0.0025T + 0.2329
V [10]
[[alpha].sub.c] Cathode exchange 1 [14]
coefficient
[MATHEMATICAL Reference diffusivity 2.06 x [10.sup.-5]
EXPRESSION NOT of [O.sub.2] [m.sup.2]/s
REPRODUCIBLE IN ASCII]
[MATHEMATICAL Reference diffusivity 2.56 x [10.sup.-5]
EXPRESSION NOT of [H.sub.2]O [m.sup.2]/s
REPRODUCIBLE IN ASCII]
[[epsilon].sub.CL] Porosity of CL 0.25 [12]
[sigma] Ohmic resistance 0.55 [ohm]
[cm.sup.2] [8]
[MATHEMATICAL Reference oxygen 1.2 x [10.sup.-6]
EXPRESSION NOT concentration mol [cm.sup.-3]
REPRODUCIBLE IN ASCII] [14]
Table 2
The results for parametric study ([V.sub.cell] = 0.5 V,
i [approximately equal to] 0.696 A [cm.sup.2])
Rank Parameter Ranges studied Optimum value
1 [sigma] 0.55-0.85 0.55 [ohm]
[cm.sup.2]
2 [[alpha].sub.c] 0.9-1.2 1.2
3 P 2-5 5 atm
4 T 50-80 80[degrees]C
5 [[epsilon].sub.GDL] 0.2-0.5 0.5
6 [U.sub.in] 0.1-0.7 0.7 m [s.sup.-1]
7 [H.sub.GDL] 0.0127-0.0508 0.0127 cm
8 [H.sub.channel] 0.0381-0.1524 0.1524 cm
9 [[epsilon].sub.CL] 0.15-0.45 0.45
10 [H.sub.CL] 0.000635-0.00254 0.000635 cm
11 [K.sub.GDL] 1.76 x [10.sup.-10] 1.76 x
-1.76 x [10.sup.-10]
[10.sup.-12] [m.sup.2]
12 [K.sub.CL] 1.76 x [10.sup.-10] 1.76 x
-1.76 x [10.sup.-10]
[10.sup.-12] [m.sup.2]
Rank Sensitivity [??]i, Sensitivity [??]P,
A [cm.sup.-2] W [cm.sup.-2]
1 0.227354386 0.113677193
2 0.108425761 0.054212881
3 0.055977878 0.027988939
4 0.037486234 0.018743117
5 0.019534051 0.009767026
6 0.019380243 0.009690121
7 0.01205766 0.00602883
8 0.007391903 0.003695952
9 0.000695248 0.000347624
10 0.000447686 0.000223843
11 5.9284E-05 2.9642E-05
12 2.64E-07 1.32E-07
