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Effects of modified flow field on optimal parameters estimation and cell performance of a PEM fuel cell with the Taguchi method
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 6 1 3 e1 6 2 7
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Effects of modified flow field on optimal parameters estimation and cell performance of a PEM fuel cell with the Taguchi method Horng-Wen Wu*, Hui-Wen Ku Department of System and Naval Mechatronic Engineering, National Cheng Kung University, 1 Ta-Hsueh Road, Tainan 701, Taiwan, ROC
article info
abstract
Article history:
The study applies a three-dimensional model simulating the transport phenomenon and
Received 1 July 2011
electrochemical reactions of full scale serpentine channels to determine the best
Received in revised form
arrangement of cuboid rows at the axis in the anode and cathode channels. With the best
8 September 2011
arrangement of the cuboid rows in the channels, the Taguchi methodology is used in the
Accepted 27 September 2011
experiment to obtain the optimal operating parameters for three objectives with the
Available online 24 October 2011
minimum pressure drops in anode and cathode channels, and maximum electrical power. The results show that the interactions of flow fields between each cuboid and the current
Keywords:
collector surface generate less overall deflection effect and force more reactant gases into
Proton exchange membrane fuel cell
the catalyst layer to have more uniform current density distributions. The electrical power
Modified flow field
is 30% greater for the three objectives optimization than for minimum pressure drops
Cuboid rows
optimization and the pressure drops 275% less for the three objectives optimization than
Full scale serpentine channels
for maximum electrical power optimization.
Taguchi method
Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
In recent years, proton exchange membrane (PEM) fuel cells have been considered as a promising alternative power source for various applications because of their low operating temperature, high power density, quick start-up capability, and high efficiency [1]. Nevertheless, design of the flow channel in bipolar plates is one of the important factors for the cell performance of a PEM fuel cell system [2]. Numerous past studies have therefore endeavored to analyze various flow channels in PEM fuel cell systems, such as the arrangements of the serpentine channel, multiple channels in parallel type, and interdigitated channels. The flow field design has been understood to be a deterministic role on mass transport and thermal management, and then great efforts have been made
for the optimum design of flow field to achieve a high and stable cell performance. Several researchers have studied how flow field design affected PEM fuel cell performance [3e10]. Shimpalee and Van Zee [3] showed that the local temperature, water content, and current density distributions became more uniform for serpentine flow field designs with shorter path lengths or larger number of channels. Sun et al. [4] applied a twodimensional cross-the-channel model to investigate how gas diffusion layer (GDL) properties and flow field geometry influenced the local reaction rate in the PEM fuel cell cathode catalyst layer. Xu and Zhao [5] presented a re-patterning conventional single serpentine flow fields design to improve system efficiency. Jeon et al. [6] developed a computer simulation to investigate the effect of different configurations of
* Corresponding author. E-mail address: [email protected] (H.-W. Wu). 0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.09.115
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Nomenclature ANOVA C Cp Di,eff F i j M P Ru S S/N T / u V Y
analysis of variance mole concentration, mol m3 Mixture-averaged specific heat capacity, J kg1 K1 diffusivity of species i, m2 s1 Fraday’s constant, 96,478 C mol1 current density, A m2 exchange current density, A m3 molecular weight, kg mol1 pressure of system, Pa gas constant, 8.314 J mol1 K1 source term signal-to-noise ratio, dB temperature, K velocity voctors, m s1 voltage, V mass fraction
serpentine flow fields. They analyzed polarization, local current density distribution, and membrane water content for these flow fields of single channel, double channel, and cyclic single at each humidity condition. Detailed descriptions of the inlet regions and local current density profiles were also provided. Yoon et al. [7] studied how gas diffusion and electric conduction affected the performance of a polymer electrolyte membrane fuel cell in an effort to optimize the channel configurations of flow field plates. Their results showed that, the performance of a cell was improved in the narrower the rib width. Jang et al. [8] explored the performance and transport phenomena in PEMFC with the numerical models for conventional flow field designs (parallel flow field, Z-type flow field, and serpentine flow field). Liu et al. [9] and Soong et al. [10] applied the baffle-blocked flow channels to enhance reactant transport and cell performance of PEMFC. They used two-dimensional half cell model to investigate the effects of the blockage with various gap ratios and numbers of the baffle plates. Perng and Wu [11,12] used a two-dimensional finite element analysis to find that a transverse installation of a baffle plate on the channel wall and a rectangular block at the axis in the flow channel effectively enhanced the local cell performance. In addition, the effect of a rectangular block was more than that of a baffle plate on the overall cell performance because the deflecting effect arising from the gas flow out of the GDL was reduced by the gas flow through the passageway between the current collector and the block. The Taguchi method of experimental design has been widely used in the industry for finding factors that are essential for achieving objectives with the reduction in number of experimental runs using orthogonal arrays and reliable quality control. Using the Taguchi method optimizes qualitative characteristics through the setting of design parameters and reduces the sensitivity of the system performance to sources of variation of a single characteristic. The application of the Taguchi method to PEM fuel cell systems has not received much attention in quality analysis until recently [13e18]. Yu et al. [13] employed the method of the design of experiments (DOE) to obtain the optimum combination of the six primary
a b ε r m keff z h j
electric conductivity, U1 m1 heat transfer coefficient, W K1m3 porosity density of gas, kg m3 viscosity, m s2 effective thermal conductivity, W K1 m1 stoichiometric flow ratio overpotential phase potential, V
Superscript s current conductor s coefficient of Bruggeman Subscript a anode c cathode i, j species
operating parameters. They determined the optimal combination of factors for a fuel cell applying the L27 (313) orthogonal array of the Taguchi method. Wu et al. [14] used the dynamic Taguchi method for experiment to acquire the primary optimum setting of the operating parameters in PEM fuel cells. The relationship between control factors and responses in the PEMFC stack was determined with a neural network. Kayta lu and Akyalc¸ın [15] determined optimum working condikog tions for maximum power density of a PEM fuel cell with the Taguchi’s orthogonal array (OA) L9 (34). Chang et al. [16] presented a new approach to estimate the optimal performance of an unknown physical PEMFC employing a generic numerical PEMFC model combined with the Taguchi method. Dante et al. [17] developed a fractional experimental design supported by a statistical methodology to analyze how four parameters affected the electric power output of a stack. Wu and Gu [18] conducted experiments with the Taguchi method to determine the optimal combination of six primary operating parameters of PEM fuel cells. The transport phenomenon via a two-dimensional simulation model was also realized for the fuel cell at optimal operating conditions. Some papers have been conducted on how single baffle plate, single rectangular block, and a row of baffle plates influenced the performance using a two-dimensional cathodic half cell model of a PEM fuel cell. However, there is no study on how the overall deflecting effect and the performance enhancement become for a row of cuboids and the row arrangements at the axis in the anode and cathode channels of PEM fuel cells. In addition, the design of PEM fuel cells and the complete tests with all probable parameters is a complex problem. A large number of samples and experiments are required for statistical credibility, which is financially unfeasible and extremely time consuming. This paper therefore applies a three-dimensional simulation and the Taguchi design of experiment methodology to analyze the transport phenomenon and electrochemical reactions modifying flow field by cuboid rows installed transversely at the axis in the full scale serpentine channels of PEM fuel cells. In the past, one quality characteristic in the
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 6 1 3 e1 6 2 7
Taguchi method has been used to enhance the cell performance in the PEM fuel cell systems. However, the flow field designers in the bipolar plate have considered more crucial factors to enhance the cell performance and to decrease the pressure drop. The higher pressure drop needs more pumping power for delivering the fuel. If more than one characteristic is simultaneously considered for the same process, the method may not produce a unique optimal combination of parameters. This study then applies the Taguchi’s orthogonal array L27 (313) to determine the optimum operating condition of these operating parameters, which integrates three objectives with the minimum pressure drops in anode and cathode channels, and maximum electrical power before comparing the enhancement between no cuboids and cuboid rows installed transversely at the axis in the anode and cathode channels of PEM fuel cells. The results of this paper may be of interest to engineers attempting to optimize the PEM fuel cell performance and to researchers interested in the transport phenomenon of the internal flow modification corresponding to the optimization condition in the PEM fuel cell.
Where ε is porosity of electrodes and r the density of gas P mixture; r ¼ i Yi ri .
2.1.2.
Momentum conservation equation
/ / / / mu V$ðεru u Þ ¼ εVp þ V$ εmeff Vu b
2.1.3.
Mathematical description
The system of proton exchange membrane fuel cell is the sophisticated multiple-physics coupling one. The computational fluid dynamic model of full scale three-dimensional fuel cells includes the flow momentum, energy, mass species transport, electrochemical reactions, and current transfer within seven distinct sub-regions: anode gas channel, anode gas diffusion layer, anode catalyst layer, membrane, cathode catalyst layer, cathode gas diffusion layer, and cathode flow channel. Several assumptions on the model are made as follows. (a) The flow in the channels is considered laminar base on small gas pressure gradient and low Reynolds number. (b) A PEM fuel cell operates under steady-state conditions. (c) Both the fuel and oxidant gases are considered as ideal gas mixtures. (d) Porous properties of electrodes and membrane are homogeneous and isotropic. (e) Gravity effect is ignored. (f) Ohmic potential resistance between solid layers as flow channel, diffusion layer, catalyst layer and exchange membranes is overlooked. (g) BultereVolmer equation is used to compute the fuel and oxidant electrochemical reactions in the catalyst layers.
2.1.
Governing equation
The governing equations assumptions are written as
2.1.1. /
under
the
above-mentioned
/
V$ðεu HÞ ¼ εkeff V$ðVTÞ
(3)
Where H is the total enthalpy and keff is the effective thermal conductivity.
2.1.4.
Species transport equation
/
V$ðεru Yi Þ ¼ V$Ji þ Si
(4)
Where X rYi eff DM X eff D VM rYi Deff Dj Yj j VYj rYi M i M j i
(5)
Following the Bruggeman correlation to account for the effects of porosity and tortuosity in porous electrodes and membrane, this study modifies the effective mass diffusion coefficient as ¼ Di ε1:5 Deff i
(6)
Where the diffusion coefficient of species is a function of temperature and pressure, i.e., Di ðT; pÞ ¼ Do;i
1:5 T po p To
(7)
The Si is the mass generation source term which is ja MH2 =2F for hydrogen, jc MO2 =4F for oxygen, and jc MH2 O =2F for water vapor. The ja and jc are the exchange current density on anode side and cathode side, calculated from BultereVolmer expression [19]: ja ¼ airef o
a
jc ¼ airef o
c
CH2 Cref H2
!12
exp aaa F=RT ha exp aac F=RT ha
! CO2 exp aca F=RT hc exp acc F=RT hc Cref O2
(8)
(9)
For PEM fuel cell operation, the second specie on anode side and cathode side is water vapor, which is assumed to exist at the saturation pressure. The molar fraction of water vapor is expressed as xw;v ¼
Psat w ðTÞ pg
(10)
Where saturation pressure Psat w is a function of temperature and is given by
Mass conservation equation
V$ðεru Þ ¼ 0
(2)
Energy conservation equation
Ji ¼ rDeff i VYi þ
2.
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(1)
2 3 log10 Psat w ðTÞ ¼ 2:1794 þ 0:02953T 9:1837T þ 1:4454T
(11)
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where T is the temperature in K. The sum of all mass fractions is notably equal to unity X
Yi ¼ 1
2.2.
(12)
Boundary conditions
The boundary conditions are required only at the external surfaces of the computational domain due to the singledomain formulation used. The fuel and oxidant flow rates are described by a stoichiometric flow ratio, z, defined as the amount of reactant fed in the chamber gas divided by the amount required by the electrochemical reaction. That is za ¼ Xa ya;in
2F Pa ; Iref Sa Ru T
zc ¼ Xc yc;in
4F Pc Iref Sa Ru T
Gas diffusion thickness Anode catalyst layer thickness Cathode catalyst layer thickness Membrane thickness Cell open-circuit voltage Electronic conductivity Membrane permeability Diffusion and catalyst layers permeability Diffusion and catalyst layers porosity Membrane porosity Operating pressure Anode transfer coefficient Cathode transfer coefficient
0.3 mm 0.01 mm 0.01 mm 0.035 mm 1.0 V 570 S/m 1.8 1018 m2 1.76 1011 m2 0.4 0.28 1 atm 0.5 1
(13)
Where y is the inlet volumetric flow rate of a gas channel, P and T the pressure and temperature, Ru and F the universal gas constant and Faraday’s constant, Iref the reference current density, and Sa the electrode surface area. The subscript a denotes the cathode side and the subscript c anode side. For convenience, the stoichiometric flow ratios defined in Eq. (13) refers to the current density of 1 A cm2 here, and the ratios are considered as dimensionless flow rates of the fuel and oxidant. Both outlets of the module have ambient static pressures and the pressures are extrapolated from the flow in the interior. For the interface between fluid domain and solid domain, the flux of species is equal to zero, no-slip applied to velocity condition and the coupled boundary condition set for temperature. The temperature on the external surface of the bipolar plate refers to cell operation environment temperature in this paper.
2.3.
Table 1 e Channel geometry and physical properties parameters.
Numerical method
Table 1 lists the geometry and physical properties as well as parameters of fuel cell’s components. The full scale three-dimensional flow fields considered in this work are divided into two types, schematic description of no cuboids channel and a row of cuboids installed transversely at the axis in the flow channel of PEM fuel cell. Fig. 1 shows the geometric configuration of the PEM fuel cell with a cuboid used for the numerical model and experiment. The geometrical relations in this study are set forth: H/H1 ¼ 1.5, H2/H1 ¼ 0.5, H3/H1 ¼ 0.6; where H is the collector width, H1 the collector height, H2 the gas channel width and height, and H3 the cuboid height. The no cuboids and locations of cuboid rows, which are regarded as the designed variables, are plotted in Fig. 2. Jeon et al. [6] showed that the reactant gases at the middle and near outlet of the channel had lower concentrations from the distribution of the reactant gases from the inlet toward the outlet. Therefore, this design applied a row of cuboids at the middle and near outlet of the full scale channel to force the reactant gases to move into the catalyst layer. Fig. 2(a) shows the no cuboids arrangement. In Fig. 2(b), in case (a), the cuboids are uniformly located at the central position of 9th channel. In case (b), the cuboids are uniformly located at the positions
of 17th channel from the inlet. In case (c), the cuboids are uniformly located at the positions of 9th and 17th channel from the inlet. In case (d), the cuboids are uniformly located at the positions of 1st, 9th, and 17th channel from the inlet. The conservation equations including mass, momentum, species, charges, and energy were converted to a finite-volume method. An orthogonal uniform grid for computational discretion was employed in this work. The solutions of the velocity component equations are obtained in a staggered control volume. The SIMPLE (semi-implicit method for pressure-linked equations) scheme [20] was adopted for the pressure correction. The species equations are calculated following the velocity vector coupled with calculation of the potentials by electrochemical reaction kinetics. The coupled set of equations was solved iteratively until the relative error in each field reached to the specific convergent standard (usually106). All the calculations have been performed by using a PENTIUM 4 4.0G PC. After a series of test runs, a quadrilateral mesh (620,000 grids) was chosen in all cases. Further refinement changed the current density less than 0.1%. The other two meshes tested were 540,000 grids and 780,000 grids as illustrated in Fig. 3.
3.
Experimental system
A schematic drawing of the experimental apparatus employed in this study is shown in Fig. 4. The apparatus includes fuel supply system, flow rate control system, temperature control system, humidifying system, and electronic load system. The active surface area of the signal PEM fuel cell used in this study is 5 5 cm2. The membraneelectrode-assembly (MEA) of the fuel cell has a five-layer structure combining a proton exchange membrane with a catalyst layer and gas diffusion layer. The single serpentine channel width and the rib width of the flow fields were 1.5 mm and tested on both the anode and cathode sides. This study employs the Taguchi method for integrating three objectives with the minimum pressure drops in anode and cathode channels, and maximum electrical power in the experiment with different PEM fuel cell operating conditions. More crucial factors as enhancing the cell performance and
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Fig. 1 e Model geometry with a cuboid.
decreasing the pressure drop have been considered for the flow field design in the bipolar plate. It is necessary to optimize operating parameters at the flow field design for the multiple objectives problem. The steps of the Taguchi method are described as follows.
3.1. Design of experiments and describe quality characteristics The temperature of fuel cell, anode humidification temperature, cathode humidification temperature, stoichiometric flow ratio of hydrogen, and stoichiometric flow ratio of oxygen are chosen as the five control factors. The Taguchi optimization procedure begins with selection of orthogonal array with a distinct number of levels (L) defined for each of the factors. The minimum number of trials in the array is
N ¼ ðL 1Þ F þ 1
(14)
where F ¼ number of factors ¼ 5. In this paper, as the overall degree of freedom (DOF) for the single parameters and interactions being 22, Taguchi orthogonal array L27 is the most suitable for the DOE. Thus, 27 experiments were conducted for the electrical power and pressure drops were measured. To observe the data reliably on this experiment, this study repeated each one four times with same conditions. Quality characteristics selected to be the optimization criteria are divided into three categories, the larger-the-best, the smaller-the-best, and the nominal-the-best. The quality characteristics of this study are the maximum electrical power of PEM fuel cell and minimum pressure drops, which belong to a larger-the-best characteristic and a smaller-thebest, and are calculated by using
Fig. 2 e The (a) no cuboids and (b) locations of cuboid rows as designed variables.
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3.2. Analyze the results to determine the optimum conditions The results of the Taguchi experiments are analyzed in a standard series of phases. First, the main effects are evaluated and the influences of the factors are determined in qualitative terms. The optimum condition and performance at the optimum condition are also determined from the factorial effects. In the next phase, analysis of variance (ANOVA) is performed on the experimental data. ANOVA study identifies the relative effect of the factors in discrete terms.
3.3. Run a confirmatory test using the optimum conditions
Fig. 3 e Comparison of prediction results for various grid systems.
In order to test the predicted result, the authors have conducted confirmation experiment by running another four replications at the optimal settings of the process parameters determined from the analysis. From the analyses of S/N ratio and the mean response characteristic, the optimum levels of the control factors are determined as shown in the reference [21]. ^ opt ¼ Tm þ SN
n X ðTi Tm Þ
(17)
i¼1
n S 1 X 1 ¼ 10log N n i¼1 y2i
n S 1 X y2 ¼ 10log N n i¼1 i
! (15)
! (16)
Where yi is the value of quality characteristic measured from the trial, the unit of S/N dB, and n the number of the tests in a trial.
Fig. 4 e Experimental apparatus.
Where Tm is the total S/N average for all experiment data. Ti are the average values of the S/N with process parameters at their respective optimal levels. An important step in Taguchi’s optimization technique is to conduct confirmation experiments for validating the predicted results by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1 1 þ CI ¼ F a; 1; fe Ve Neff R And
Fig. 5 e Comparison of the results between the present prediction and experiment without cuboids.
(18)
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Neff ¼
N 1 þ TDOF
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(19)
Where Fða; 1; fe Þ is the Feratio required for 100 (1ea) percent confidence intervals, fe DOF for error, Ve error variance, R number of replications for confirmation experiment, and Neff effective number of replications. N the total numbers of experiments and TDOF the total degrees of freedom for the estimate of mean optimum.
Fig. 6 e Comparison of the polarization curves and power density curves among the prototypical flow field without cuboids and four designs with cuboid rows.
4.
Results and discussion
4.1.
Effects of the cuboid positions
Numerical predictions of the performance of the fuel cell by the present direct problem solver are needed to agree with the experimental data. The values of the physical and electrochemical parameters adopted in the direct problem solution model are calibrated with the help of the experimental data. The polarization curves between the experimental and the present numerical methods are compared on the basis of the
Fig. 7 e Effects of the cuboid rows positions on the local current density distributions at Vcell [ 0.4 V along (a) 1st, (b) 9th, (c) 17th, and (d) full scale channel.
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same group of parameters, and the values of the physical and electrochemical parameters of the solution model are tuned continuously toward the agreement between the numerical predictions and the experimental data. Fig. 5 depicts the polarization curves obtained from the model and the measured polarization curves for without cuboids. The simulated polarization curves with three-dimensional full scale model have the same trends with the experimental ones. This paper first numerically examines how the arrangements of cuboid rows affect the cell performance and the polarization curves for four types of cuboid rows with various positions as indicated in Fig. 6 at a cell temperature of 333 K, an anode humidification temperature of 333 K, a cathode humidification temperature of 333 K, a hydrogen stoichiometric flow ratio of 1.9, and an oxygen stoichiometric flow ratio of 1.9. At the high voltages, above 0.5 V, the overall cell performance is found to vary slightly with various locations of cuboid rows compared with no cuboids. At the low voltage, below 0.5 V, however, various locations of cuboid rows greatly change the polarization curves. It is very significant to examine how cuboid rows locations influence the local transport characteristics of the PEMFC, especially at low voltages. In addition, as seen from Fig. 6, the PEM fuel cells with a row of cuboids located at the positions of case(c) (as indicated in Fig. 2(b)) flow field perform better than those with other positions flow field and prototypical flow field with no cuboids. Fig. 7 shows how various locations of cuboid rows affect the local current density distributions with the axial direction y at the low voltage (Vcell ¼ 0.4 V). The profiles of local current density in the 1st, 9th, 17th and full scale channel from the inlet along the interface between the gas diffuser layer (GDL) and catalyst layer (CL) are plotted in Fig. 7 (a), (b), (c), and (d) respectively. The no cuboids design has higher local current density in the 1st, 9th channel than the others, but has lower local current density in the 17th channel. For no cuboids design, the reactant gases at the middle and near outlet of the channel have lower concentrations from the distribution of the reactant gases from the inlet toward the outlet. For each cuboid, the similar observation of local current density distribution from a single cuboid has been gained in a numerical study by Perng and Wu [11]. In addition, each hump region for each cuboid is caused by the interactions of flow fields between each cuboid and the current collector surface generating less overall deflection effect and forcing more the reactant gases into the catalyst layer to have more uniform current density distributions. In Fig. 7, the peak values of the current density, from the inlet toward the outlet, with no cuboids design and case (a) are rapidly reduced to approximately 1.0 A cm2, where as the current density with the cases (b), (c), (d) is still retained larger than 2.0 A cm2. However, the overall current densities and power densities are all higher in the cases (b), (c), and (d) designs than for no cuboids design. Among all cases, case (c) has the maximum cell performance because one row of cuboids at the middle and the other row of cuboids near outlet of the full scale channel generates less overall deflection effect and forces more reactant gases to move into the catalyst layer, and has more uniform current density distributions.
The cell performance of the PEM fuel cell with various cuboid rows arrangements increases when the electrical power rises from 25.2 to 26.6 W at 0.4 V in Fig. 8(a). This confirms that the presence of blockage effect due to cuboids in the flow channel enhances the fuel gas transport and, and then augments the cell performance. However, the flow field design influences not only the cell performance but also the pressure drop in the fuel cell. Larger pressure drops in the fuel cell mean that more power is needed to pump the reactants. Thus, the pressure drop is a significant issue to be considered in choosing the flow field designs in addition to the polarization curves. Fig. 8(b) presents how the arrangement of cuboid rows affects the pressure drop across the fuel channel, DP0 ¼ P0in P0out . The intrusion of the cuboids causes larger pressure loss and needs higher pumping power for delivering fuel. The pressure drop has been converted to a power using [22]. Wp ¼ DP0 Acnannel uin where Wp represents the pressure drop loss, DP’ the total pressure drop in the fuel cell, Acnannel the cross-sectional flow inlet area, and uin the fuel velocity at the inlet. The calculated net power, the cell output power deducting pumping loss power, for the no cuboids and various cuboid rows arrangements are shown in Fig. 8(c). As the number of cuboid rows increases, the total pressure drops and pressure drop losses
a
b
c
Fig. 8 e Comparison of (a) the electrical power, (b) pressure drop, (c) the net power on the cathode side among prototypical flow field without cuboids and four designs with cuboid rows.
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increase, but the pressure drop losses are far less than the cell output power. In all cases, the case (c) has the maximum net power, Wnet, and the pressure drop of the case (c) only is 0.053 bar larger than that of the no cuboids design on the cathode side. From these results in the present study, the transverse cuboids used in all cases enhance the overall cell performance of a PEMFC system, and the flow channel designs are practicable in a real PEMFC system.
4.2. Reactant gas and temperature distribution inside the flow field The distributions of hydrogen and oxygen have to be observed to comprehend how the internal flow modification influences the cell performance. Fig. 9 reveals how no cuboids (left) and
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case(c) (right) affect the contours of (a) hydrogen and (b) oxygen concentrations inside the gas channel and catalyst layers at 0.4 V. The depletion of the reactant gases is clearly illustrated from the inlet toward the outlet as well as the distribution of the reactant gases inside the gas channels and catalyst layers. A larger amount of reactant gases is forced to move into the catalyst layer around the region on more numbers of cuboids by installing two rows of cuboids, and a strong reaction and higher consumption of reactant gases occur in this region. Fig. 9(c) shows the temperature distributions of no cuboids (left) and case(c) (right) for Vcell ¼ 0.4 V at the catalyst layer on cathode sides at a cell temperature of 333 K, an anode humidification temperature of 333 K, a cathode humidification temperature of 333 K, a hydrogen stoichiometric flow
Fig. 9 e The local (a) hydrogen, (b) oxygen concentration, and (c) temperature distributions of no cuboids (left) and case(c) (right) for Vcell [ 0.4 V at the catalyst layer.
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ratio of 1.9, and an oxygen stoichiometric flow ratio of 1.9. The stronger effect of case(c) is seen to generate a lower and more uniform temperature distribution in the fuel flow channel; i.e., the stronger effect of case(c) obtains a better heat transfer performance of the PEM fuel cell and reduces the cell reaction temperature. In general, the improvement obtained in the convection heat transfer performance in the fuel flow channel may be caused by an increasing flow interruption, a reduction in the thermal boundary layer near the catalyst layer.
4.3. Comparison between the numerical and experimental data for the design model of case (c) Other than the model validation for no cuboids in Section 4.1, the experiment was conducted to verify the numerical model in case(c) (as indicated in Fig. 2) at a cell temperature of 313 K, an anode humidification temperature of 313 K, a cathode humidification temperature of 313 K, a hydrogen stoichiometric flow ratio of 1.2, and an oxygen stoichiometric flow ratio of 1.2. In the experiment, the serpentine flow field plates with the cuboids were made by electrical discharge machining to verify the numerical results. The polarization curves obtained from the design model in the case(c) are depicted in Fig. 10, together with the measured polarization curves. This design is improving the cell performance and making it possible to compare experimental results with those obtained in three-dimensional simulations at the same conditions (A1B1C1D1E1). This comparison shows that the numerical and experimental results are in close agreement.
4.4.
Experimental results of the Taguchi method
According to the numerical results of the arrangement of cuboid rows affecting the cell performance and pressure drop in Section 4.1, the authors choose case (c) (in Fig. 2) as a channel design and find the optimum conditions conducting
the experimentation with the Taguchi method. It is important quality objective to enhance the cell performance and decrease the pressure drops in the flow field design for PEM fuel cell. The experimental design factors considered are (A) temperature of fuel cell, (B) anode humidification temperature, (C) cathode humidification temperature, (D) stoichiometric flow ratio of hydrogen, and (E) stoichiometric flow ratio of oxygen each changed for three levels (Table 2). This experiment was supposed to be conducted 35 ¼ 243 times using one factor-at-a-time experiments or full-factorial experiments; however, it just runs 27 times employing the Taguchi method of experimental design. Besides these parameters, interactions between three important parameters such as temperature of fuel cell, anode and cathode humidification temperature are involved in the investigation. The results of electrical power, pressure drop in the anode and cathode channels, the relatively S/N ratios are shown in Table 3 after conducting the experimentation and applying Taguchi analysis. The average S/N ratios of all parameters are derived from the factors at three levels from Table 3 as shown in Fig. 11. The order of graphs in Fig. 11 prepared for the experiments is used according to how the parameters influence the performance characteristics. The optimal level of a process parameter for fuel cell performance characteristic in obtaining the maximum electrical power is the level with the highest S/N value calculated by Eq. (15) and the minimum pressure drops in the both anode and cathode channels are the level with the smaller S/N value calculated by Eq. (16). For the quality characteristic of electrical power, pressure drop in the anode and cathode channels, the greatest S/N from these levels obtained is the initial optimal combination of the control factor levels, A2B3C3D2E2, A1B1C1D1E1, and A1B1C1D3E1, respectively, as Fig. 11(a)e(c). The optimal combination of process parameters are predicted with the ANOVA on the performance characteristics. The results of variance analysis for the experiment are listed in Table 4. The F-test of statistics is used to decide which parameters of the fuel cell greatly alter the quality characteristics. When the F-test values of factors and interactions between the factors are smaller than 95% confidence interval, these values are classified as insignificant factors and are regarded as errors. Therefore, the control factors with the significant effect for acquiring the maximal electrical power are A, B, and C at the 90% confidence interval as Table 4(a). Furthermore, since the effects of the interactions between
Table 2 e Control factors and levels for the L27 (313) design. Factor A B C D
Fig. 10 e Comparison of the polarization curves between the numerical and experimental results for case (c).
E
Parameters Temperature of fuel cell (K) Anode humidification temperature (K) Cathode humidification temperature (K) Stoichiometric flow ratio of hydrogen Stoichiometric flow ratio of oxygen
Level 1
Level 2
Level 3
313
333
353
313
333
353
313
333
353
1.2
1.9
2.7
1.2
1.9
2.7
Table 3 e The numerical results obtained at cell potential of 0.4 V for the L27 (313) design.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3
1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3
1 1 1 2 2 2 3 3 3 2 2 2 3 3 3 1 1 1 3 3 3 1 1 1 2 2 2
1 1 1 2 2 2 3 3 3 3 3 3 1 1 1 2 2 2 2 2 2 3 3 3 1 1 1
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 1 2 3 2 3 1 2 3 1 2 3 1 3 1 2 3 1 2 3 1 2
1 2 3 1 2 3 1 2 3 3 1 2 3 1 2 3 1 2 2 3 1 2 3 1 2 3 1
1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2
1 2 3 2 3 1 3 1 2 2 3 1 3 1 2 1 2 3 3 1 2 1 2 3 2 3 1
1 2 3 2 3 1 3 1 2 3 1 2 1 2 3 2 3 1 2 3 1 3 1 2 1 2 3
1 2 3 3 1 2 2 3 1 1 2 3 3 1 2 2 3 1 1 2 3 3 1 2 2 3 1
1 2 3 3 1 2 2 3 1 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1 1 2 3
1 2 3 3 1 2 2 3 1 3 1 2 2 3 1 1 2 3 2 3 1 1 2 3 3 1 2
Power (W) 14.87 17.16 16.99 16.75 17.64 17.75 18.47 17.57 19.17 16.39 17.49 19.38 16.29 17.30 19.75 22.13 22.64 22.69 16.85 18.44 17.94 20.21 16.40 19.33 21.60 18.78 20.74
14.87 17.18 17.01 16.77 17.68 17.80 18.48 17.59 19.23 16.41 17.47 19.38 16.24 17.27 19.77 22.10 22.68 22.74 16.84 18.42 18.03 19.81 16.24 19.35 21.34 18.43 20.65
14.88 17.14 17.01 16.79 17.72 17.76 18.54 17.62 19.27 16.43 17.46 19.39 16.24 17.25 19.77 22.09 22.70 22.81 16.84 18.33 18.01 19.54 16.52 19.38 21.18 19.20 20.45
14.91 17.19 17.03 16.81 17.73 17.78 18.56 17.64 19.29 16.42 17.47 19.40 16.25 17.26 19.85 22.09 22.73 22.74 16.74 18.25 18.00 19.38 16.48 19.40 21.59 19.32 20.39
MSD
S/N
0.0045 0.0034 0.0035 0.0036 0.0032 0.0032 0.0029 0.0032 0.0027 0.0037 0.0033 0.0027 0.0038 0.0034 0.0026 0.0020 0.0019 0.0019 0.0035 0.0030 0.0031 0.0026 0.0037 0.0027 0.0022 0.0028 0.0024
23.45 24.69 24.61 24.49 24.95 24.99 25.35 24.91 25.68 24.30 24.85 25.75 24.22 24.75 25.93 26.89 27.12 27.14 24.52 25.28 25.10 25.90 24.30 25.74 26.62 25.54 26.26
Pressure drop in the cathode (bar) 0.05 0.09 0.16 0.09 0.15 0.07 0.15 0.05 0.11 0.13 0.06 0.11 0.06 0.10 0.20 0.14 0.25 0.08 0.10 0.21 0.07 0.20 0.07 0.15 0.09 0.15 0.25
0.05 0.09 0.15 0.09 0.15 0.07 0.16 0.06 0.11 0.13 0.05 0.11 0.06 0.10 0.20 0.14 0.25 0.08 0.10 0.21 0.07 0.19 0.08 0.15 0.09 0.15 0.24
0.05 0.09 0.15 0.09 0.15 0.06 0.16 0.05 0.11 0.13 0.06 0.11 0.06 0.09 0.20 0.14 0.25 0.08 0.10 0.20 0.07 0.19 0.08 0.15 0.08 0.15 0.25
0.06 0.09 0.16 0.08 0.15 0.06 0.15 0.06 0.11 0.13 0.05 0.11 0.06 0.10 0.21 0.14 0.25 0.07 0.10 0.21 0.07 0.19 0.08 0.15 0.08 0.14 0.25
MSD
S/N
0.0027 0.0082 0.0239 0.0071 0.0222 0.0045 0.0242 0.0033 0.0131 0.0173 0.0029 0.0123 0.0037 0.0098 0.0409 0.0194 0.0627 0.0058 0.0096 0.0433 0.0048 0.0377 0.0062 0.0228 0.0070 0.0221 0.0597
25.66 20.85 16.22 21.48 16.54 23.47 16.15 24.81 18.83 17.63 25.33 19.10 24.36 20.09 13.89 17.11 12.02 22.38 20.20 13.63 23.17 14.24 22.09 16.42 21.53 16.56 12.24
Pressure drop in the anode (bar) 0.01 0.04 0.07 0.04 0.07 0.01 0.11 0.03 0.08 0.05 0.07 0.03 0.07 0.01 0.06 0.08 0.13 0.20 0.07 0.03 0.06 0.04 0.07 0.15 0.19 0.23 0.05
0.01 0.04 0.07 0.04 0.07 0.01 0.11 0.02 0.08 0.05 0.07 0.03 0.07 0.02 0.07 0.07 0.12 0.24 0.07 0.04 0.06 0.04 0.06 0.15 0.17 0.20 0.06
0.01 0.04 0.07 0.04 0.07 0.02 0.10 0.03 0.08 0.05 0.07 0.03 0.06 0.02 0.07 0.07 0.11 0.23 0.07 0.03 0.06 0.04 0.07 0.16 0.15 0.26 0.05
0.01 0.04 0.07 0.04 0.07 0.01 0.11 0.02 0.09 0.05 0.08 0.02 0.06 0.02 0.06 0.06 0.10 0.21 0.07 0.04 0.06 0.03 0.08 0.15 0.16 0.22 0.05
MSD
S/N
0.0001 0.0016 0.0044 0.0018 0.0049 0.0002 0.0119 0.0007 0.0072 0.0023 0.0056 0.0006 0.0042 0.0003 0.0039 0.0051 0.0134 0.0496 0.0050 0.0012 0.0038 0.0013 0.0047 0.0227 0.0281 0.0522 0.0027
40.55 28.01 23.53 27.46 23.10 36.47 19.23 31.34 21.45 26.38 22.49 32.05 23.74 35.29 24.10 22.91 18.74 13.05 23.00 29.07 24.17 28.83 23.30 16.44 15.51 12.82 25.62
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Exp A B A B A B C A C A C B C D E B C e e
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Fig. 11 e S/N responses for three quality characteristics of (a) electrical power, (b) pressure drop on the anode side, and (c) pressure drop on the cathode side.
factors A and B are attempted to evaluate, the interaction plot for the mean S/N ratios is used. The interactions of A B response plot are displayed in Fig. 12. The error as listed in Table 4 is from the empty column in the orthogonal array in Table 3. Factors without a significant effect are pooled as error. The 95% confidence interval of the predicted optimal power is thus obtained as 27.42 0.61 dB after substituting these values in Eqs. (17) and (18). In order to test the predicted result, the authors have conducted confirmation experiment by running another four times at the optimal settings of the process parameters determined from the analysis. The S/N of the mean power from the confirmation experiments is 26.99 dB, which falls within the predicted 95% confidence interval. Therefore, the predictions made by Taguchi’s parameter design technique were in good agreement with the confirmation results. In the Taguchi method, the factors without any significant effects on the reaction of the PEM fuel cell are set as constants with a favorable level for the fuel cell; the levels of the insignificant factors A and B are thus set as A2 and B3 for the maximal
electric power. For minimal pressure drop on the anode side, the control factors are A, B, and, D at the 95% confidence interval as listed in Table 4(b). Correspondingly, for minimal pressure drop on the cathode side, the control factors are A, B, C, and, E as listed in Table 4(c). An analysis of variance (ANOVA) was decided to perform to determine which of the factor effects has a significant impact on the multiple objectives performance statistic. To compare the Table 4(b) and (c) indicates that D and E are significant factors for affecting the pressure drops in the anode and cathode channels and their contribution larger than the others. Therefore, when fixing the significant factors, the primary optimal combination factor is A2B3C1D1E1 to achieve the objective of maximum electrical power and minimum pressure drops in the both anode and cathode channels.
4.5. The optimum condition obtained with three objectives A case study of maximizing electrical power and minimizing pressure drops in the anode and cathode channels is
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Table 4 e ANOVA for the L27 (313) design: (a) electrical power, (b) pressure drop in the anode side, and (c) pressure drop in the cathode side. (a) Factor
SS
DOF
3.73 10.35 1.98 0.12 0.95 2.18 1.51 1.66 0.30 1.38 22.79
2 2 2 2 2 4 4 4 4 8 26
SS
DOF
155.32 303.01 6.67 641.00 9.99 21.76 9.43 25.09 9.93 82.87 1182.21
2 2 2 2 2 4 4 4 4 20 26
A B C D E AB AC BC e Error Total
Var
F
1.86 10.80 5.17 29.95 0.99 5.74 0.06 0.36 0.48 2.76 0.55 3.16 0.38 2.19 0.41 2.40 0.08 0.44 0.17 S ¼ 0.42 dB at least 90% confidence
F0.1
SS0
Contribution
3.11 3.11 3.11 3.11 3.11 2.81 2.81 2.81 2.81
3.38 10.00 1.64 e e 1.49 e e e 6.28 22.79
14.85% 43.88% 7.18% e e 6.55% e e e 27.53% 100.00%
F0.05
SS0
Contribution
3.49 3.49 3.49 3.49 3.49 2.87 2.87 2.87 2.87
147.03 294.73 e 632.71 e e e e e 107.73 1182.21
12.44% 24.93% e 53.52% e e e e e 9.11% 100.00%
F0.05
SS0
Contribution
3.55 3.55 3.55 3.55 3.55 2.93 2.93 2.93 2.93
30.25 20.97 7.33 e 356.40 e e e e 20.53 435.47
6.95% 4.82% 1.68% e 81.84% e e e e 4.71% 100.00%
(b) Factor A B C D E AB AC BC e Error Total
Var
F
77.66 18.74 151.51 36.56 3.34 0.81 320.50 77.35 4.99 1.20 5.44 1.31 2.36 0.57 6.27 1.51 2.48 0.60 4.14 S ¼ 2.04 dB at least 95% confidence
(c) Factor A B C D E AB AC BC e Error Total
SS
DOF
31.83 22.55 8.91 0.85 357.98 5.51 1.06 3.33 3.47 14.21 435.47
2 2 2 2 2 4 4 4 4 18 26
Var
15.92 20.16 11.27 14.28 4.45 5.64 0.42 0.54 178.99 226.72 1.38 1.74 0.26 0.34 0.83 1.06 0.87 1.10 0.79 S ¼ 0.89 dB at least 95% confidence
Interaction between A and B 28
A1
27
A2
S/N
26
A3
25 24 23 22
B1
B2
F
B3
Fig. 12 e S/N response for the interaction between A and B (as listed in Table 2) for the quality characteristic of electrical power.
presented to demonstrate the potential of the Taguchi methodology. In the Fig. 13, the experimental result displays the polarization curves compared with different the optimum conditions for augmenting the electrical power (A2B3C3D2E3), for decreasing the pressure drops in the anode and cathode channels (A1B1C1D1E1), and for the three objectives of augmenting the electrical power and decreasing the pressure drops (A2B3C1D1E1). The maximal electrical power is higher at the condition A2B3C3D2E3 of 22.36 W than at the condition A2B3C1D1E1 of 21.83 W, and than at the condition A1B1C1D1E1 of 16.85 W with 0.4 V. However, the minimal pressure drop on the cathode side is lower at the condition A1B1C1D1E1 of 0.033 bar than at the condition A2B3C1D1E1 of 0.071 bar, and than at the condition A2B3C3D2E3 of 0.27 bar with 0.4 V. The minimal pressure drop on the anode side is lower at the condition A1B1C1D1E1 of 0.039 bar than at the condition A2B3C1D1E1 of 0.074 bar, and than at the condition
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of maximum electrical power and minimum pressure drops in limited experiments. Therefore, the optimum result presents to augment the electrical power by 30% and to reduce the pressure drops by 275%.
Acknowledgment The authors would like to acknowledge the financial support of this work by the National Science Council, ROC through the Contract 97-2221-E-006-270-MY3.
references
Fig. 13 e Comparison of the polarization curves with parametric optimization of three objectives with the minimum pressure drops (A1B1C1D1E1), maximum electrical power (A2B3C3D2E3), and all above (A2B3C1D1E1).
A2B3C3D2E3 of 0.12 bar with 0.4 V. The results indicate that pressure drops at the anode and cathode channels greatly vary with the hydrogen and oxygen stoichiometric flow ratios. This comparison shows that the electrical power is 30% larger for the optimal condition A2B3C1D1E1 of the three objectives optimization than for the condition A1B1C1D1E1, and the pressure drops 275% less for the optimal condition A2B3C1D1E1 with the three objectives optimization than for the condition A2B3C3D2E3.
5.
Conclusion
This paper illustrates how the hydrogen concentration, oxygen concentration, and operating temperature distributions around cuboid rows influence the performance of PEM fuel cells. The best arrangement of cuboid rows is one row of cuboids at the middle and the other row of cuboids near outlet of the full scale channel due to less overall deflection effect to force more reactant gases into the catalyst layer and has more uniform current density distributions. This study then optimizes the operating parameters affecting the performance with the best arrangement of cuboid rows installed transversely in the serpentine channel PEM fuel cell. In this way, the three objectives optimization approach is presented by integrating the contributions of individual factors influential to the flow channels with cuboid rows installed transversely in a PEM fuel cell. The primary optimal combination factor is a cell temperature of 333 K, an anode humidification temperature of 333 K, a cathode humidification temperature of 313 K, a hydrogen stoichiometric flow ratio of 1.2, and an oxygen stoichiometric flow ratio of 1.2 to achieve the objective
[1] Basu Suddhasatwa. Recent trends in fuel cell science and technology. New York: Springer; 2007. [2] Barbir Frano. PEM fuel cells: theory and practice. Elsevier Academic Press; 2005. [3] Shimpalee S, Van Zee JW. Numerical study on rib/channel dimension of flow-field on PEMFC performance. J Hydrogen Energy 2007;32:842e56. [4] Sun Wei, Peppley Brant A, Karan Kunal. Modeling the influence of GDL and flow-field plate parameters on the reaction distribution in the PEMFC cathode catalyst layer. J Power Sources 2005;144:42e53. [5] Xu C, Zhao TS. A new flow field design for polymer electrolyte-based fuel cells. Electrochem Commun 2007;9: 497e503. [6] Jeon DH, Greenway S, Shimpalee S, Van Zee JW. The effect of serpentine flow-field designs on PEM fuel cell performance. Int J Hydrogen Energy 2008;33:1052e66. [7] Yoon Young-Gi, Lee Won-Yong, Park Gu-Gon, Yang TaeHyun, Kim Chang-Soo. Effects of channel and rib widths of flow-field plates on the performance of a PEMFC. Int J Hydrogen Energy 2005;30:1363e6. [8] Jang Jer-Huan, Yan Wei-Mon, Li Hung-Yi, Tsai Wei-Che. Three-dimensional numerical study on cell performance and transport phenomena of PEM fuel cells with conventional flow fields. Int J Hydrogen Energy 2008;33: 156e64. [9] Liu Hui-Chung, Yan Wei-Mon, Soong Chyi-Yeou, Chen Falin. Effects of baffle-blocked flow channel on reactant transport and cell performance of a proton exchange membrane fuel cell. J Power Sources 2005;142:125e33. [10] Soong CY, Yan Wei-Mon, Tseng C-Y, Liu HC, Falin Chen, Chu HS. Analysis of reactant gas transport in a PEM fuel cell with partially blocked fuel flow channels. J Power Sources 2005;143:36e47. [11] Perng Shiang-Wuu, Wu Horng-Wen. Effects of internal flow modification on the cell performance enhancement of a PEM fuel cell. J Power Sources 2008;175:806e16. [12] Perng Shiang-Wuu, Wu Horng-Wen, Jue Tswen-Chyuan, Cheng Kuo-Chih. Numerical predictions of a PEM fuel cell performance enhancement by a rectangular Cylinder installed transversely in the flow channel. Appl Energy 2009; 86:1541e54. [13] Yu Wei-Lung, Wu Sheng-Ju, Shah Sheau-Wen. Parametric analysis of the proton exchange membrane fuel cell performance using design of experiments. Int J Hydrogen Energy 2008;33:2311e22. [14] Yu Wei-Lung, Wu Sheng-Ju, Shah Sheau-Wen. Experimental analysis of dynamic characteristics on the PEM fuel cell stack by using Taguchi approach with neural networks. Int J Hydrogen Energy 2011;35:11138e47.
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of a proton exchange membrane fuel cell using the Taguchi method. J Power Sources 2010;195:3621e30. Costamagna P, Honegger K. Modeling of solid oxide heat exchanger integrated stacks and simulation at high fuel utilization. J Electrochem Soc 1998;145:3995e4007. Oran Elaine S, Boris Jay P. Numerical simulation of reactive flow. Cambridge University Press; 2001. Roy Ranjit K. A primer on the Taguchi method. Society of Manufacturing Engineers; 1990. Venkatraman M, Shimpalee S, Van Zee JW, Moon Sung In, Extrand CW. Estimates of pressure gradients in PEMFC gas channels due to blockage by static liquid drops. Int J Hydrogen Energy 2009;34:5522e8.
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Effects of modified flow field on optimal parameters estimation and cell performance of a PEM fuel cell with the Taguchi method Horng-Wen Wu*, Hui-Wen Ku Department of System and Naval Mechatronic Engineering, National Cheng Kung University, 1 Ta-Hsueh Road, Tainan 701, Taiwan, ROC
article info
abstract
Article history:
The study applies a three-dimensional model simulating the transport phenomenon and
Received 1 July 2011
electrochemical reactions of full scale serpentine channels to determine the best
Received in revised form
arrangement of cuboid rows at the axis in the anode and cathode channels. With the best
8 September 2011
arrangement of the cuboid rows in the channels, the Taguchi methodology is used in the
Accepted 27 September 2011
experiment to obtain the optimal operating parameters for three objectives with the
Available online 24 October 2011
minimum pressure drops in anode and cathode channels, and maximum electrical power. The results show that the interactions of flow fields between each cuboid and the current
Keywords:
collector surface generate less overall deflection effect and force more reactant gases into
Proton exchange membrane fuel cell
the catalyst layer to have more uniform current density distributions. The electrical power
Modified flow field
is 30% greater for the three objectives optimization than for minimum pressure drops
Cuboid rows
optimization and the pressure drops 275% less for the three objectives optimization than
Full scale serpentine channels
for maximum electrical power optimization.
Taguchi method
Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
In recent years, proton exchange membrane (PEM) fuel cells have been considered as a promising alternative power source for various applications because of their low operating temperature, high power density, quick start-up capability, and high efficiency [1]. Nevertheless, design of the flow channel in bipolar plates is one of the important factors for the cell performance of a PEM fuel cell system [2]. Numerous past studies have therefore endeavored to analyze various flow channels in PEM fuel cell systems, such as the arrangements of the serpentine channel, multiple channels in parallel type, and interdigitated channels. The flow field design has been understood to be a deterministic role on mass transport and thermal management, and then great efforts have been made
for the optimum design of flow field to achieve a high and stable cell performance. Several researchers have studied how flow field design affected PEM fuel cell performance [3e10]. Shimpalee and Van Zee [3] showed that the local temperature, water content, and current density distributions became more uniform for serpentine flow field designs with shorter path lengths or larger number of channels. Sun et al. [4] applied a twodimensional cross-the-channel model to investigate how gas diffusion layer (GDL) properties and flow field geometry influenced the local reaction rate in the PEM fuel cell cathode catalyst layer. Xu and Zhao [5] presented a re-patterning conventional single serpentine flow fields design to improve system efficiency. Jeon et al. [6] developed a computer simulation to investigate the effect of different configurations of
* Corresponding author. E-mail address: [email protected] (H.-W. Wu). 0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.09.115
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Nomenclature ANOVA C Cp Di,eff F i j M P Ru S S/N T / u V Y
analysis of variance mole concentration, mol m3 Mixture-averaged specific heat capacity, J kg1 K1 diffusivity of species i, m2 s1 Fraday’s constant, 96,478 C mol1 current density, A m2 exchange current density, A m3 molecular weight, kg mol1 pressure of system, Pa gas constant, 8.314 J mol1 K1 source term signal-to-noise ratio, dB temperature, K velocity voctors, m s1 voltage, V mass fraction
serpentine flow fields. They analyzed polarization, local current density distribution, and membrane water content for these flow fields of single channel, double channel, and cyclic single at each humidity condition. Detailed descriptions of the inlet regions and local current density profiles were also provided. Yoon et al. [7] studied how gas diffusion and electric conduction affected the performance of a polymer electrolyte membrane fuel cell in an effort to optimize the channel configurations of flow field plates. Their results showed that, the performance of a cell was improved in the narrower the rib width. Jang et al. [8] explored the performance and transport phenomena in PEMFC with the numerical models for conventional flow field designs (parallel flow field, Z-type flow field, and serpentine flow field). Liu et al. [9] and Soong et al. [10] applied the baffle-blocked flow channels to enhance reactant transport and cell performance of PEMFC. They used two-dimensional half cell model to investigate the effects of the blockage with various gap ratios and numbers of the baffle plates. Perng and Wu [11,12] used a two-dimensional finite element analysis to find that a transverse installation of a baffle plate on the channel wall and a rectangular block at the axis in the flow channel effectively enhanced the local cell performance. In addition, the effect of a rectangular block was more than that of a baffle plate on the overall cell performance because the deflecting effect arising from the gas flow out of the GDL was reduced by the gas flow through the passageway between the current collector and the block. The Taguchi method of experimental design has been widely used in the industry for finding factors that are essential for achieving objectives with the reduction in number of experimental runs using orthogonal arrays and reliable quality control. Using the Taguchi method optimizes qualitative characteristics through the setting of design parameters and reduces the sensitivity of the system performance to sources of variation of a single characteristic. The application of the Taguchi method to PEM fuel cell systems has not received much attention in quality analysis until recently [13e18]. Yu et al. [13] employed the method of the design of experiments (DOE) to obtain the optimum combination of the six primary
a b ε r m keff z h j
electric conductivity, U1 m1 heat transfer coefficient, W K1m3 porosity density of gas, kg m3 viscosity, m s2 effective thermal conductivity, W K1 m1 stoichiometric flow ratio overpotential phase potential, V
Superscript s current conductor s coefficient of Bruggeman Subscript a anode c cathode i, j species
operating parameters. They determined the optimal combination of factors for a fuel cell applying the L27 (313) orthogonal array of the Taguchi method. Wu et al. [14] used the dynamic Taguchi method for experiment to acquire the primary optimum setting of the operating parameters in PEM fuel cells. The relationship between control factors and responses in the PEMFC stack was determined with a neural network. Kayta lu and Akyalc¸ın [15] determined optimum working condikog tions for maximum power density of a PEM fuel cell with the Taguchi’s orthogonal array (OA) L9 (34). Chang et al. [16] presented a new approach to estimate the optimal performance of an unknown physical PEMFC employing a generic numerical PEMFC model combined with the Taguchi method. Dante et al. [17] developed a fractional experimental design supported by a statistical methodology to analyze how four parameters affected the electric power output of a stack. Wu and Gu [18] conducted experiments with the Taguchi method to determine the optimal combination of six primary operating parameters of PEM fuel cells. The transport phenomenon via a two-dimensional simulation model was also realized for the fuel cell at optimal operating conditions. Some papers have been conducted on how single baffle plate, single rectangular block, and a row of baffle plates influenced the performance using a two-dimensional cathodic half cell model of a PEM fuel cell. However, there is no study on how the overall deflecting effect and the performance enhancement become for a row of cuboids and the row arrangements at the axis in the anode and cathode channels of PEM fuel cells. In addition, the design of PEM fuel cells and the complete tests with all probable parameters is a complex problem. A large number of samples and experiments are required for statistical credibility, which is financially unfeasible and extremely time consuming. This paper therefore applies a three-dimensional simulation and the Taguchi design of experiment methodology to analyze the transport phenomenon and electrochemical reactions modifying flow field by cuboid rows installed transversely at the axis in the full scale serpentine channels of PEM fuel cells. In the past, one quality characteristic in the
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Taguchi method has been used to enhance the cell performance in the PEM fuel cell systems. However, the flow field designers in the bipolar plate have considered more crucial factors to enhance the cell performance and to decrease the pressure drop. The higher pressure drop needs more pumping power for delivering the fuel. If more than one characteristic is simultaneously considered for the same process, the method may not produce a unique optimal combination of parameters. This study then applies the Taguchi’s orthogonal array L27 (313) to determine the optimum operating condition of these operating parameters, which integrates three objectives with the minimum pressure drops in anode and cathode channels, and maximum electrical power before comparing the enhancement between no cuboids and cuboid rows installed transversely at the axis in the anode and cathode channels of PEM fuel cells. The results of this paper may be of interest to engineers attempting to optimize the PEM fuel cell performance and to researchers interested in the transport phenomenon of the internal flow modification corresponding to the optimization condition in the PEM fuel cell.
Where ε is porosity of electrodes and r the density of gas P mixture; r ¼ i Yi ri .
2.1.2.
Momentum conservation equation
/ / / / mu V$ðεru u Þ ¼ εVp þ V$ εmeff Vu b
2.1.3.
Mathematical description
The system of proton exchange membrane fuel cell is the sophisticated multiple-physics coupling one. The computational fluid dynamic model of full scale three-dimensional fuel cells includes the flow momentum, energy, mass species transport, electrochemical reactions, and current transfer within seven distinct sub-regions: anode gas channel, anode gas diffusion layer, anode catalyst layer, membrane, cathode catalyst layer, cathode gas diffusion layer, and cathode flow channel. Several assumptions on the model are made as follows. (a) The flow in the channels is considered laminar base on small gas pressure gradient and low Reynolds number. (b) A PEM fuel cell operates under steady-state conditions. (c) Both the fuel and oxidant gases are considered as ideal gas mixtures. (d) Porous properties of electrodes and membrane are homogeneous and isotropic. (e) Gravity effect is ignored. (f) Ohmic potential resistance between solid layers as flow channel, diffusion layer, catalyst layer and exchange membranes is overlooked. (g) BultereVolmer equation is used to compute the fuel and oxidant electrochemical reactions in the catalyst layers.
2.1.
Governing equation
The governing equations assumptions are written as
2.1.1. /
under
the
above-mentioned
/
V$ðεu HÞ ¼ εkeff V$ðVTÞ
(3)
Where H is the total enthalpy and keff is the effective thermal conductivity.
2.1.4.
Species transport equation
/
V$ðεru Yi Þ ¼ V$Ji þ Si
(4)
Where X rYi eff DM X eff D VM rYi Deff Dj Yj j VYj rYi M i M j i
(5)
Following the Bruggeman correlation to account for the effects of porosity and tortuosity in porous electrodes and membrane, this study modifies the effective mass diffusion coefficient as ¼ Di ε1:5 Deff i
(6)
Where the diffusion coefficient of species is a function of temperature and pressure, i.e., Di ðT; pÞ ¼ Do;i
1:5 T po p To
(7)
The Si is the mass generation source term which is ja MH2 =2F for hydrogen, jc MO2 =4F for oxygen, and jc MH2 O =2F for water vapor. The ja and jc are the exchange current density on anode side and cathode side, calculated from BultereVolmer expression [19]: ja ¼ airef o
a
jc ¼ airef o
c
CH2 Cref H2
!12
exp aaa F=RT ha exp aac F=RT ha
! CO2 exp aca F=RT hc exp acc F=RT hc Cref O2
(8)
(9)
For PEM fuel cell operation, the second specie on anode side and cathode side is water vapor, which is assumed to exist at the saturation pressure. The molar fraction of water vapor is expressed as xw;v ¼
Psat w ðTÞ pg
(10)
Where saturation pressure Psat w is a function of temperature and is given by
Mass conservation equation
V$ðεru Þ ¼ 0
(2)
Energy conservation equation
Ji ¼ rDeff i VYi þ
2.
1615
(1)
2 3 log10 Psat w ðTÞ ¼ 2:1794 þ 0:02953T 9:1837T þ 1:4454T
(11)
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where T is the temperature in K. The sum of all mass fractions is notably equal to unity X
Yi ¼ 1
2.2.
(12)
Boundary conditions
The boundary conditions are required only at the external surfaces of the computational domain due to the singledomain formulation used. The fuel and oxidant flow rates are described by a stoichiometric flow ratio, z, defined as the amount of reactant fed in the chamber gas divided by the amount required by the electrochemical reaction. That is za ¼ Xa ya;in
2F Pa ; Iref Sa Ru T
zc ¼ Xc yc;in
4F Pc Iref Sa Ru T
Gas diffusion thickness Anode catalyst layer thickness Cathode catalyst layer thickness Membrane thickness Cell open-circuit voltage Electronic conductivity Membrane permeability Diffusion and catalyst layers permeability Diffusion and catalyst layers porosity Membrane porosity Operating pressure Anode transfer coefficient Cathode transfer coefficient
0.3 mm 0.01 mm 0.01 mm 0.035 mm 1.0 V 570 S/m 1.8 1018 m2 1.76 1011 m2 0.4 0.28 1 atm 0.5 1
(13)
Where y is the inlet volumetric flow rate of a gas channel, P and T the pressure and temperature, Ru and F the universal gas constant and Faraday’s constant, Iref the reference current density, and Sa the electrode surface area. The subscript a denotes the cathode side and the subscript c anode side. For convenience, the stoichiometric flow ratios defined in Eq. (13) refers to the current density of 1 A cm2 here, and the ratios are considered as dimensionless flow rates of the fuel and oxidant. Both outlets of the module have ambient static pressures and the pressures are extrapolated from the flow in the interior. For the interface between fluid domain and solid domain, the flux of species is equal to zero, no-slip applied to velocity condition and the coupled boundary condition set for temperature. The temperature on the external surface of the bipolar plate refers to cell operation environment temperature in this paper.
2.3.
Table 1 e Channel geometry and physical properties parameters.
Numerical method
Table 1 lists the geometry and physical properties as well as parameters of fuel cell’s components. The full scale three-dimensional flow fields considered in this work are divided into two types, schematic description of no cuboids channel and a row of cuboids installed transversely at the axis in the flow channel of PEM fuel cell. Fig. 1 shows the geometric configuration of the PEM fuel cell with a cuboid used for the numerical model and experiment. The geometrical relations in this study are set forth: H/H1 ¼ 1.5, H2/H1 ¼ 0.5, H3/H1 ¼ 0.6; where H is the collector width, H1 the collector height, H2 the gas channel width and height, and H3 the cuboid height. The no cuboids and locations of cuboid rows, which are regarded as the designed variables, are plotted in Fig. 2. Jeon et al. [6] showed that the reactant gases at the middle and near outlet of the channel had lower concentrations from the distribution of the reactant gases from the inlet toward the outlet. Therefore, this design applied a row of cuboids at the middle and near outlet of the full scale channel to force the reactant gases to move into the catalyst layer. Fig. 2(a) shows the no cuboids arrangement. In Fig. 2(b), in case (a), the cuboids are uniformly located at the central position of 9th channel. In case (b), the cuboids are uniformly located at the positions
of 17th channel from the inlet. In case (c), the cuboids are uniformly located at the positions of 9th and 17th channel from the inlet. In case (d), the cuboids are uniformly located at the positions of 1st, 9th, and 17th channel from the inlet. The conservation equations including mass, momentum, species, charges, and energy were converted to a finite-volume method. An orthogonal uniform grid for computational discretion was employed in this work. The solutions of the velocity component equations are obtained in a staggered control volume. The SIMPLE (semi-implicit method for pressure-linked equations) scheme [20] was adopted for the pressure correction. The species equations are calculated following the velocity vector coupled with calculation of the potentials by electrochemical reaction kinetics. The coupled set of equations was solved iteratively until the relative error in each field reached to the specific convergent standard (usually106). All the calculations have been performed by using a PENTIUM 4 4.0G PC. After a series of test runs, a quadrilateral mesh (620,000 grids) was chosen in all cases. Further refinement changed the current density less than 0.1%. The other two meshes tested were 540,000 grids and 780,000 grids as illustrated in Fig. 3.
3.
Experimental system
A schematic drawing of the experimental apparatus employed in this study is shown in Fig. 4. The apparatus includes fuel supply system, flow rate control system, temperature control system, humidifying system, and electronic load system. The active surface area of the signal PEM fuel cell used in this study is 5 5 cm2. The membraneelectrode-assembly (MEA) of the fuel cell has a five-layer structure combining a proton exchange membrane with a catalyst layer and gas diffusion layer. The single serpentine channel width and the rib width of the flow fields were 1.5 mm and tested on both the anode and cathode sides. This study employs the Taguchi method for integrating three objectives with the minimum pressure drops in anode and cathode channels, and maximum electrical power in the experiment with different PEM fuel cell operating conditions. More crucial factors as enhancing the cell performance and
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Fig. 1 e Model geometry with a cuboid.
decreasing the pressure drop have been considered for the flow field design in the bipolar plate. It is necessary to optimize operating parameters at the flow field design for the multiple objectives problem. The steps of the Taguchi method are described as follows.
3.1. Design of experiments and describe quality characteristics The temperature of fuel cell, anode humidification temperature, cathode humidification temperature, stoichiometric flow ratio of hydrogen, and stoichiometric flow ratio of oxygen are chosen as the five control factors. The Taguchi optimization procedure begins with selection of orthogonal array with a distinct number of levels (L) defined for each of the factors. The minimum number of trials in the array is
N ¼ ðL 1Þ F þ 1
(14)
where F ¼ number of factors ¼ 5. In this paper, as the overall degree of freedom (DOF) for the single parameters and interactions being 22, Taguchi orthogonal array L27 is the most suitable for the DOE. Thus, 27 experiments were conducted for the electrical power and pressure drops were measured. To observe the data reliably on this experiment, this study repeated each one four times with same conditions. Quality characteristics selected to be the optimization criteria are divided into three categories, the larger-the-best, the smaller-the-best, and the nominal-the-best. The quality characteristics of this study are the maximum electrical power of PEM fuel cell and minimum pressure drops, which belong to a larger-the-best characteristic and a smaller-thebest, and are calculated by using
Fig. 2 e The (a) no cuboids and (b) locations of cuboid rows as designed variables.
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3.2. Analyze the results to determine the optimum conditions The results of the Taguchi experiments are analyzed in a standard series of phases. First, the main effects are evaluated and the influences of the factors are determined in qualitative terms. The optimum condition and performance at the optimum condition are also determined from the factorial effects. In the next phase, analysis of variance (ANOVA) is performed on the experimental data. ANOVA study identifies the relative effect of the factors in discrete terms.
3.3. Run a confirmatory test using the optimum conditions
Fig. 3 e Comparison of prediction results for various grid systems.
In order to test the predicted result, the authors have conducted confirmation experiment by running another four replications at the optimal settings of the process parameters determined from the analysis. From the analyses of S/N ratio and the mean response characteristic, the optimum levels of the control factors are determined as shown in the reference [21]. ^ opt ¼ Tm þ SN
n X ðTi Tm Þ
(17)
i¼1
n S 1 X 1 ¼ 10log N n i¼1 y2i
n S 1 X y2 ¼ 10log N n i¼1 i
! (15)
! (16)
Where yi is the value of quality characteristic measured from the trial, the unit of S/N dB, and n the number of the tests in a trial.
Fig. 4 e Experimental apparatus.
Where Tm is the total S/N average for all experiment data. Ti are the average values of the S/N with process parameters at their respective optimal levels. An important step in Taguchi’s optimization technique is to conduct confirmation experiments for validating the predicted results by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1 1 þ CI ¼ F a; 1; fe Ve Neff R And
Fig. 5 e Comparison of the results between the present prediction and experiment without cuboids.
(18)
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 6 1 3 e1 6 2 7
Neff ¼
N 1 þ TDOF
1619
(19)
Where Fða; 1; fe Þ is the Feratio required for 100 (1ea) percent confidence intervals, fe DOF for error, Ve error variance, R number of replications for confirmation experiment, and Neff effective number of replications. N the total numbers of experiments and TDOF the total degrees of freedom for the estimate of mean optimum.
Fig. 6 e Comparison of the polarization curves and power density curves among the prototypical flow field without cuboids and four designs with cuboid rows.
4.
Results and discussion
4.1.
Effects of the cuboid positions
Numerical predictions of the performance of the fuel cell by the present direct problem solver are needed to agree with the experimental data. The values of the physical and electrochemical parameters adopted in the direct problem solution model are calibrated with the help of the experimental data. The polarization curves between the experimental and the present numerical methods are compared on the basis of the
Fig. 7 e Effects of the cuboid rows positions on the local current density distributions at Vcell [ 0.4 V along (a) 1st, (b) 9th, (c) 17th, and (d) full scale channel.
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same group of parameters, and the values of the physical and electrochemical parameters of the solution model are tuned continuously toward the agreement between the numerical predictions and the experimental data. Fig. 5 depicts the polarization curves obtained from the model and the measured polarization curves for without cuboids. The simulated polarization curves with three-dimensional full scale model have the same trends with the experimental ones. This paper first numerically examines how the arrangements of cuboid rows affect the cell performance and the polarization curves for four types of cuboid rows with various positions as indicated in Fig. 6 at a cell temperature of 333 K, an anode humidification temperature of 333 K, a cathode humidification temperature of 333 K, a hydrogen stoichiometric flow ratio of 1.9, and an oxygen stoichiometric flow ratio of 1.9. At the high voltages, above 0.5 V, the overall cell performance is found to vary slightly with various locations of cuboid rows compared with no cuboids. At the low voltage, below 0.5 V, however, various locations of cuboid rows greatly change the polarization curves. It is very significant to examine how cuboid rows locations influence the local transport characteristics of the PEMFC, especially at low voltages. In addition, as seen from Fig. 6, the PEM fuel cells with a row of cuboids located at the positions of case(c) (as indicated in Fig. 2(b)) flow field perform better than those with other positions flow field and prototypical flow field with no cuboids. Fig. 7 shows how various locations of cuboid rows affect the local current density distributions with the axial direction y at the low voltage (Vcell ¼ 0.4 V). The profiles of local current density in the 1st, 9th, 17th and full scale channel from the inlet along the interface between the gas diffuser layer (GDL) and catalyst layer (CL) are plotted in Fig. 7 (a), (b), (c), and (d) respectively. The no cuboids design has higher local current density in the 1st, 9th channel than the others, but has lower local current density in the 17th channel. For no cuboids design, the reactant gases at the middle and near outlet of the channel have lower concentrations from the distribution of the reactant gases from the inlet toward the outlet. For each cuboid, the similar observation of local current density distribution from a single cuboid has been gained in a numerical study by Perng and Wu [11]. In addition, each hump region for each cuboid is caused by the interactions of flow fields between each cuboid and the current collector surface generating less overall deflection effect and forcing more the reactant gases into the catalyst layer to have more uniform current density distributions. In Fig. 7, the peak values of the current density, from the inlet toward the outlet, with no cuboids design and case (a) are rapidly reduced to approximately 1.0 A cm2, where as the current density with the cases (b), (c), (d) is still retained larger than 2.0 A cm2. However, the overall current densities and power densities are all higher in the cases (b), (c), and (d) designs than for no cuboids design. Among all cases, case (c) has the maximum cell performance because one row of cuboids at the middle and the other row of cuboids near outlet of the full scale channel generates less overall deflection effect and forces more reactant gases to move into the catalyst layer, and has more uniform current density distributions.
The cell performance of the PEM fuel cell with various cuboid rows arrangements increases when the electrical power rises from 25.2 to 26.6 W at 0.4 V in Fig. 8(a). This confirms that the presence of blockage effect due to cuboids in the flow channel enhances the fuel gas transport and, and then augments the cell performance. However, the flow field design influences not only the cell performance but also the pressure drop in the fuel cell. Larger pressure drops in the fuel cell mean that more power is needed to pump the reactants. Thus, the pressure drop is a significant issue to be considered in choosing the flow field designs in addition to the polarization curves. Fig. 8(b) presents how the arrangement of cuboid rows affects the pressure drop across the fuel channel, DP0 ¼ P0in P0out . The intrusion of the cuboids causes larger pressure loss and needs higher pumping power for delivering fuel. The pressure drop has been converted to a power using [22]. Wp ¼ DP0 Acnannel uin where Wp represents the pressure drop loss, DP’ the total pressure drop in the fuel cell, Acnannel the cross-sectional flow inlet area, and uin the fuel velocity at the inlet. The calculated net power, the cell output power deducting pumping loss power, for the no cuboids and various cuboid rows arrangements are shown in Fig. 8(c). As the number of cuboid rows increases, the total pressure drops and pressure drop losses
a
b
c
Fig. 8 e Comparison of (a) the electrical power, (b) pressure drop, (c) the net power on the cathode side among prototypical flow field without cuboids and four designs with cuboid rows.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 6 1 3 e1 6 2 7
increase, but the pressure drop losses are far less than the cell output power. In all cases, the case (c) has the maximum net power, Wnet, and the pressure drop of the case (c) only is 0.053 bar larger than that of the no cuboids design on the cathode side. From these results in the present study, the transverse cuboids used in all cases enhance the overall cell performance of a PEMFC system, and the flow channel designs are practicable in a real PEMFC system.
4.2. Reactant gas and temperature distribution inside the flow field The distributions of hydrogen and oxygen have to be observed to comprehend how the internal flow modification influences the cell performance. Fig. 9 reveals how no cuboids (left) and
1621
case(c) (right) affect the contours of (a) hydrogen and (b) oxygen concentrations inside the gas channel and catalyst layers at 0.4 V. The depletion of the reactant gases is clearly illustrated from the inlet toward the outlet as well as the distribution of the reactant gases inside the gas channels and catalyst layers. A larger amount of reactant gases is forced to move into the catalyst layer around the region on more numbers of cuboids by installing two rows of cuboids, and a strong reaction and higher consumption of reactant gases occur in this region. Fig. 9(c) shows the temperature distributions of no cuboids (left) and case(c) (right) for Vcell ¼ 0.4 V at the catalyst layer on cathode sides at a cell temperature of 333 K, an anode humidification temperature of 333 K, a cathode humidification temperature of 333 K, a hydrogen stoichiometric flow
Fig. 9 e The local (a) hydrogen, (b) oxygen concentration, and (c) temperature distributions of no cuboids (left) and case(c) (right) for Vcell [ 0.4 V at the catalyst layer.
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ratio of 1.9, and an oxygen stoichiometric flow ratio of 1.9. The stronger effect of case(c) is seen to generate a lower and more uniform temperature distribution in the fuel flow channel; i.e., the stronger effect of case(c) obtains a better heat transfer performance of the PEM fuel cell and reduces the cell reaction temperature. In general, the improvement obtained in the convection heat transfer performance in the fuel flow channel may be caused by an increasing flow interruption, a reduction in the thermal boundary layer near the catalyst layer.
4.3. Comparison between the numerical and experimental data for the design model of case (c) Other than the model validation for no cuboids in Section 4.1, the experiment was conducted to verify the numerical model in case(c) (as indicated in Fig. 2) at a cell temperature of 313 K, an anode humidification temperature of 313 K, a cathode humidification temperature of 313 K, a hydrogen stoichiometric flow ratio of 1.2, and an oxygen stoichiometric flow ratio of 1.2. In the experiment, the serpentine flow field plates with the cuboids were made by electrical discharge machining to verify the numerical results. The polarization curves obtained from the design model in the case(c) are depicted in Fig. 10, together with the measured polarization curves. This design is improving the cell performance and making it possible to compare experimental results with those obtained in three-dimensional simulations at the same conditions (A1B1C1D1E1). This comparison shows that the numerical and experimental results are in close agreement.
4.4.
Experimental results of the Taguchi method
According to the numerical results of the arrangement of cuboid rows affecting the cell performance and pressure drop in Section 4.1, the authors choose case (c) (in Fig. 2) as a channel design and find the optimum conditions conducting
the experimentation with the Taguchi method. It is important quality objective to enhance the cell performance and decrease the pressure drops in the flow field design for PEM fuel cell. The experimental design factors considered are (A) temperature of fuel cell, (B) anode humidification temperature, (C) cathode humidification temperature, (D) stoichiometric flow ratio of hydrogen, and (E) stoichiometric flow ratio of oxygen each changed for three levels (Table 2). This experiment was supposed to be conducted 35 ¼ 243 times using one factor-at-a-time experiments or full-factorial experiments; however, it just runs 27 times employing the Taguchi method of experimental design. Besides these parameters, interactions between three important parameters such as temperature of fuel cell, anode and cathode humidification temperature are involved in the investigation. The results of electrical power, pressure drop in the anode and cathode channels, the relatively S/N ratios are shown in Table 3 after conducting the experimentation and applying Taguchi analysis. The average S/N ratios of all parameters are derived from the factors at three levels from Table 3 as shown in Fig. 11. The order of graphs in Fig. 11 prepared for the experiments is used according to how the parameters influence the performance characteristics. The optimal level of a process parameter for fuel cell performance characteristic in obtaining the maximum electrical power is the level with the highest S/N value calculated by Eq. (15) and the minimum pressure drops in the both anode and cathode channels are the level with the smaller S/N value calculated by Eq. (16). For the quality characteristic of electrical power, pressure drop in the anode and cathode channels, the greatest S/N from these levels obtained is the initial optimal combination of the control factor levels, A2B3C3D2E2, A1B1C1D1E1, and A1B1C1D3E1, respectively, as Fig. 11(a)e(c). The optimal combination of process parameters are predicted with the ANOVA on the performance characteristics. The results of variance analysis for the experiment are listed in Table 4. The F-test of statistics is used to decide which parameters of the fuel cell greatly alter the quality characteristics. When the F-test values of factors and interactions between the factors are smaller than 95% confidence interval, these values are classified as insignificant factors and are regarded as errors. Therefore, the control factors with the significant effect for acquiring the maximal electrical power are A, B, and C at the 90% confidence interval as Table 4(a). Furthermore, since the effects of the interactions between
Table 2 e Control factors and levels for the L27 (313) design. Factor A B C D
Fig. 10 e Comparison of the polarization curves between the numerical and experimental results for case (c).
E
Parameters Temperature of fuel cell (K) Anode humidification temperature (K) Cathode humidification temperature (K) Stoichiometric flow ratio of hydrogen Stoichiometric flow ratio of oxygen
Level 1
Level 2
Level 3
313
333
353
313
333
353
313
333
353
1.2
1.9
2.7
1.2
1.9
2.7
Table 3 e The numerical results obtained at cell potential of 0.4 V for the L27 (313) design.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3
1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3
1 1 1 2 2 2 3 3 3 2 2 2 3 3 3 1 1 1 3 3 3 1 1 1 2 2 2
1 1 1 2 2 2 3 3 3 3 3 3 1 1 1 2 2 2 2 2 2 3 3 3 1 1 1
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 1 2 3 2 3 1 2 3 1 2 3 1 3 1 2 3 1 2 3 1 2
1 2 3 1 2 3 1 2 3 3 1 2 3 1 2 3 1 2 2 3 1 2 3 1 2 3 1
1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2
1 2 3 2 3 1 3 1 2 2 3 1 3 1 2 1 2 3 3 1 2 1 2 3 2 3 1
1 2 3 2 3 1 3 1 2 3 1 2 1 2 3 2 3 1 2 3 1 3 1 2 1 2 3
1 2 3 3 1 2 2 3 1 1 2 3 3 1 2 2 3 1 1 2 3 3 1 2 2 3 1
1 2 3 3 1 2 2 3 1 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1 1 2 3
1 2 3 3 1 2 2 3 1 3 1 2 2 3 1 1 2 3 2 3 1 1 2 3 3 1 2
Power (W) 14.87 17.16 16.99 16.75 17.64 17.75 18.47 17.57 19.17 16.39 17.49 19.38 16.29 17.30 19.75 22.13 22.64 22.69 16.85 18.44 17.94 20.21 16.40 19.33 21.60 18.78 20.74
14.87 17.18 17.01 16.77 17.68 17.80 18.48 17.59 19.23 16.41 17.47 19.38 16.24 17.27 19.77 22.10 22.68 22.74 16.84 18.42 18.03 19.81 16.24 19.35 21.34 18.43 20.65
14.88 17.14 17.01 16.79 17.72 17.76 18.54 17.62 19.27 16.43 17.46 19.39 16.24 17.25 19.77 22.09 22.70 22.81 16.84 18.33 18.01 19.54 16.52 19.38 21.18 19.20 20.45
14.91 17.19 17.03 16.81 17.73 17.78 18.56 17.64 19.29 16.42 17.47 19.40 16.25 17.26 19.85 22.09 22.73 22.74 16.74 18.25 18.00 19.38 16.48 19.40 21.59 19.32 20.39
MSD
S/N
0.0045 0.0034 0.0035 0.0036 0.0032 0.0032 0.0029 0.0032 0.0027 0.0037 0.0033 0.0027 0.0038 0.0034 0.0026 0.0020 0.0019 0.0019 0.0035 0.0030 0.0031 0.0026 0.0037 0.0027 0.0022 0.0028 0.0024
23.45 24.69 24.61 24.49 24.95 24.99 25.35 24.91 25.68 24.30 24.85 25.75 24.22 24.75 25.93 26.89 27.12 27.14 24.52 25.28 25.10 25.90 24.30 25.74 26.62 25.54 26.26
Pressure drop in the cathode (bar) 0.05 0.09 0.16 0.09 0.15 0.07 0.15 0.05 0.11 0.13 0.06 0.11 0.06 0.10 0.20 0.14 0.25 0.08 0.10 0.21 0.07 0.20 0.07 0.15 0.09 0.15 0.25
0.05 0.09 0.15 0.09 0.15 0.07 0.16 0.06 0.11 0.13 0.05 0.11 0.06 0.10 0.20 0.14 0.25 0.08 0.10 0.21 0.07 0.19 0.08 0.15 0.09 0.15 0.24
0.05 0.09 0.15 0.09 0.15 0.06 0.16 0.05 0.11 0.13 0.06 0.11 0.06 0.09 0.20 0.14 0.25 0.08 0.10 0.20 0.07 0.19 0.08 0.15 0.08 0.15 0.25
0.06 0.09 0.16 0.08 0.15 0.06 0.15 0.06 0.11 0.13 0.05 0.11 0.06 0.10 0.21 0.14 0.25 0.07 0.10 0.21 0.07 0.19 0.08 0.15 0.08 0.14 0.25
MSD
S/N
0.0027 0.0082 0.0239 0.0071 0.0222 0.0045 0.0242 0.0033 0.0131 0.0173 0.0029 0.0123 0.0037 0.0098 0.0409 0.0194 0.0627 0.0058 0.0096 0.0433 0.0048 0.0377 0.0062 0.0228 0.0070 0.0221 0.0597
25.66 20.85 16.22 21.48 16.54 23.47 16.15 24.81 18.83 17.63 25.33 19.10 24.36 20.09 13.89 17.11 12.02 22.38 20.20 13.63 23.17 14.24 22.09 16.42 21.53 16.56 12.24
Pressure drop in the anode (bar) 0.01 0.04 0.07 0.04 0.07 0.01 0.11 0.03 0.08 0.05 0.07 0.03 0.07 0.01 0.06 0.08 0.13 0.20 0.07 0.03 0.06 0.04 0.07 0.15 0.19 0.23 0.05
0.01 0.04 0.07 0.04 0.07 0.01 0.11 0.02 0.08 0.05 0.07 0.03 0.07 0.02 0.07 0.07 0.12 0.24 0.07 0.04 0.06 0.04 0.06 0.15 0.17 0.20 0.06
0.01 0.04 0.07 0.04 0.07 0.02 0.10 0.03 0.08 0.05 0.07 0.03 0.06 0.02 0.07 0.07 0.11 0.23 0.07 0.03 0.06 0.04 0.07 0.16 0.15 0.26 0.05
0.01 0.04 0.07 0.04 0.07 0.01 0.11 0.02 0.09 0.05 0.08 0.02 0.06 0.02 0.06 0.06 0.10 0.21 0.07 0.04 0.06 0.03 0.08 0.15 0.16 0.22 0.05
MSD
S/N
0.0001 0.0016 0.0044 0.0018 0.0049 0.0002 0.0119 0.0007 0.0072 0.0023 0.0056 0.0006 0.0042 0.0003 0.0039 0.0051 0.0134 0.0496 0.0050 0.0012 0.0038 0.0013 0.0047 0.0227 0.0281 0.0522 0.0027
40.55 28.01 23.53 27.46 23.10 36.47 19.23 31.34 21.45 26.38 22.49 32.05 23.74 35.29 24.10 22.91 18.74 13.05 23.00 29.07 24.17 28.83 23.30 16.44 15.51 12.82 25.62
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Exp A B A B A B C A C A C B C D E B C e e
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1624
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Fig. 11 e S/N responses for three quality characteristics of (a) electrical power, (b) pressure drop on the anode side, and (c) pressure drop on the cathode side.
factors A and B are attempted to evaluate, the interaction plot for the mean S/N ratios is used. The interactions of A B response plot are displayed in Fig. 12. The error as listed in Table 4 is from the empty column in the orthogonal array in Table 3. Factors without a significant effect are pooled as error. The 95% confidence interval of the predicted optimal power is thus obtained as 27.42 0.61 dB after substituting these values in Eqs. (17) and (18). In order to test the predicted result, the authors have conducted confirmation experiment by running another four times at the optimal settings of the process parameters determined from the analysis. The S/N of the mean power from the confirmation experiments is 26.99 dB, which falls within the predicted 95% confidence interval. Therefore, the predictions made by Taguchi’s parameter design technique were in good agreement with the confirmation results. In the Taguchi method, the factors without any significant effects on the reaction of the PEM fuel cell are set as constants with a favorable level for the fuel cell; the levels of the insignificant factors A and B are thus set as A2 and B3 for the maximal
electric power. For minimal pressure drop on the anode side, the control factors are A, B, and, D at the 95% confidence interval as listed in Table 4(b). Correspondingly, for minimal pressure drop on the cathode side, the control factors are A, B, C, and, E as listed in Table 4(c). An analysis of variance (ANOVA) was decided to perform to determine which of the factor effects has a significant impact on the multiple objectives performance statistic. To compare the Table 4(b) and (c) indicates that D and E are significant factors for affecting the pressure drops in the anode and cathode channels and their contribution larger than the others. Therefore, when fixing the significant factors, the primary optimal combination factor is A2B3C1D1E1 to achieve the objective of maximum electrical power and minimum pressure drops in the both anode and cathode channels.
4.5. The optimum condition obtained with three objectives A case study of maximizing electrical power and minimizing pressure drops in the anode and cathode channels is
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Table 4 e ANOVA for the L27 (313) design: (a) electrical power, (b) pressure drop in the anode side, and (c) pressure drop in the cathode side. (a) Factor
SS
DOF
3.73 10.35 1.98 0.12 0.95 2.18 1.51 1.66 0.30 1.38 22.79
2 2 2 2 2 4 4 4 4 8 26
SS
DOF
155.32 303.01 6.67 641.00 9.99 21.76 9.43 25.09 9.93 82.87 1182.21
2 2 2 2 2 4 4 4 4 20 26
A B C D E AB AC BC e Error Total
Var
F
1.86 10.80 5.17 29.95 0.99 5.74 0.06 0.36 0.48 2.76 0.55 3.16 0.38 2.19 0.41 2.40 0.08 0.44 0.17 S ¼ 0.42 dB at least 90% confidence
F0.1
SS0
Contribution
3.11 3.11 3.11 3.11 3.11 2.81 2.81 2.81 2.81
3.38 10.00 1.64 e e 1.49 e e e 6.28 22.79
14.85% 43.88% 7.18% e e 6.55% e e e 27.53% 100.00%
F0.05
SS0
Contribution
3.49 3.49 3.49 3.49 3.49 2.87 2.87 2.87 2.87
147.03 294.73 e 632.71 e e e e e 107.73 1182.21
12.44% 24.93% e 53.52% e e e e e 9.11% 100.00%
F0.05
SS0
Contribution
3.55 3.55 3.55 3.55 3.55 2.93 2.93 2.93 2.93
30.25 20.97 7.33 e 356.40 e e e e 20.53 435.47
6.95% 4.82% 1.68% e 81.84% e e e e 4.71% 100.00%
(b) Factor A B C D E AB AC BC e Error Total
Var
F
77.66 18.74 151.51 36.56 3.34 0.81 320.50 77.35 4.99 1.20 5.44 1.31 2.36 0.57 6.27 1.51 2.48 0.60 4.14 S ¼ 2.04 dB at least 95% confidence
(c) Factor A B C D E AB AC BC e Error Total
SS
DOF
31.83 22.55 8.91 0.85 357.98 5.51 1.06 3.33 3.47 14.21 435.47
2 2 2 2 2 4 4 4 4 18 26
Var
15.92 20.16 11.27 14.28 4.45 5.64 0.42 0.54 178.99 226.72 1.38 1.74 0.26 0.34 0.83 1.06 0.87 1.10 0.79 S ¼ 0.89 dB at least 95% confidence
Interaction between A and B 28
A1
27
A2
S/N
26
A3
25 24 23 22
B1
B2
F
B3
Fig. 12 e S/N response for the interaction between A and B (as listed in Table 2) for the quality characteristic of electrical power.
presented to demonstrate the potential of the Taguchi methodology. In the Fig. 13, the experimental result displays the polarization curves compared with different the optimum conditions for augmenting the electrical power (A2B3C3D2E3), for decreasing the pressure drops in the anode and cathode channels (A1B1C1D1E1), and for the three objectives of augmenting the electrical power and decreasing the pressure drops (A2B3C1D1E1). The maximal electrical power is higher at the condition A2B3C3D2E3 of 22.36 W than at the condition A2B3C1D1E1 of 21.83 W, and than at the condition A1B1C1D1E1 of 16.85 W with 0.4 V. However, the minimal pressure drop on the cathode side is lower at the condition A1B1C1D1E1 of 0.033 bar than at the condition A2B3C1D1E1 of 0.071 bar, and than at the condition A2B3C3D2E3 of 0.27 bar with 0.4 V. The minimal pressure drop on the anode side is lower at the condition A1B1C1D1E1 of 0.039 bar than at the condition A2B3C1D1E1 of 0.074 bar, and than at the condition
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of maximum electrical power and minimum pressure drops in limited experiments. Therefore, the optimum result presents to augment the electrical power by 30% and to reduce the pressure drops by 275%.
Acknowledgment The authors would like to acknowledge the financial support of this work by the National Science Council, ROC through the Contract 97-2221-E-006-270-MY3.
references
Fig. 13 e Comparison of the polarization curves with parametric optimization of three objectives with the minimum pressure drops (A1B1C1D1E1), maximum electrical power (A2B3C3D2E3), and all above (A2B3C1D1E1).
A2B3C3D2E3 of 0.12 bar with 0.4 V. The results indicate that pressure drops at the anode and cathode channels greatly vary with the hydrogen and oxygen stoichiometric flow ratios. This comparison shows that the electrical power is 30% larger for the optimal condition A2B3C1D1E1 of the three objectives optimization than for the condition A1B1C1D1E1, and the pressure drops 275% less for the optimal condition A2B3C1D1E1 with the three objectives optimization than for the condition A2B3C3D2E3.
5.
Conclusion
This paper illustrates how the hydrogen concentration, oxygen concentration, and operating temperature distributions around cuboid rows influence the performance of PEM fuel cells. The best arrangement of cuboid rows is one row of cuboids at the middle and the other row of cuboids near outlet of the full scale channel due to less overall deflection effect to force more reactant gases into the catalyst layer and has more uniform current density distributions. This study then optimizes the operating parameters affecting the performance with the best arrangement of cuboid rows installed transversely in the serpentine channel PEM fuel cell. In this way, the three objectives optimization approach is presented by integrating the contributions of individual factors influential to the flow channels with cuboid rows installed transversely in a PEM fuel cell. The primary optimal combination factor is a cell temperature of 333 K, an anode humidification temperature of 333 K, a cathode humidification temperature of 313 K, a hydrogen stoichiometric flow ratio of 1.2, and an oxygen stoichiometric flow ratio of 1.2 to achieve the objective
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