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Optimization of an open-cathode polymer electrolyte fuel cells stack utilizing Taguchi method
Applied Energy xxx (2016) xxx–xxx
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Optimization of an open-cathode polymer electrolyte fuel cells stack utilizing Taguchi method Agus P. Sasmito a,⇑, Jundika C. Kurnia b, Tariq Shamim c, Arun S. Mujumdar a a
Department of Mining and Materials Engineering, McGill University, 3450 University, Frank Dawson Adams Bldg., Montreal, QC H3A0E8, Canada Department of Mechanical Engineering, Universiti Teknologi PETRONAS, 32610 Bandar Seri Iskandar, Perak Darul Ridzuan, Malaysia c Institute Center for Energy (iEnergy), Department of Mechanical and Materials Engineering, Masdar Institute of Science and Technology, Masdar City, Abu Dhabi, United Arab Emirates b
h i g h l i g h t s Design and operating parameters of an open-cathode PEFC stack is optimized. Optimization is carried out with regard to current density and net power. Fuel cell length plays important role on stack performance. Interaction between each parameter is evaluated.
a r t i c l e
i n f o
Article history: Received 27 June 2015 Received in revised form 21 December 2015 Accepted 23 December 2015 Available online xxxx Keywords: Fuel cells stack Open-cathode Net power Optimization Taguchi
a b s t r a c t The design of open-cathode polymer electrolyte fuel cells (PEFC) stacks with forced-convection requires a careful consideration on the geometrical and operating conditions as well as the operating characteristic of PEFC stacks and fan used. This paper evaluates the effect of key geometrical and operating parameters on the stack characteristic and their interactions to the thermal, water and gas managements as well as stack performance. A validated three dimensional model for open-cathode PEFC stack with fan and immediate ambient were solved to evaluate the effect of studied parameters on the stack performance. In tandem, an L27 orthogonal array (OA) of Taguchi matrix of six factors and three level designs to determine the optimum combination of parameters as well as their interactions for high, medium and low voltage operation. The result indicates that fuel cell length plays important role on determining the fuel cell performance in term of system characteristic, current density and net power. Optimum combination of design and operating parameters were obtained with the objective function of maximizing net power generated by stack by taking into account the parasitic loads. Crown Copyright Ó 2015 Published by Elsevier Ltd. All rights reserved.
1. Introduction In order to achieve optimum operating condition of polymer electrolyte fuel cells (PEFC) stacks, it is essential to maintain an efficient gas, water and thermal management. For a PEFC stack with capacity range between 100 and 2000 W, an open cathode design with fans to supply simultaneous air (oxidant) and cooling is desirable due to its less overall system complexity as compared to those with liquid cooling [1,2]. In this design, however, air supply system configurations (fan, blower or compressor) and their operational parameters are critical in determining the performance of PEFC stack as they do not only maintain the optimum tempera⇑ Corresponding author. Tel.: +1 514 398 3788. E-mail address: [email protected] (A.P. Sasmito).
ture (thermal management) but also ensure sufficient reactant air (gas management). Selection of the air supply system usually depends on the system and fan characteristic curves [3]. In PEFC stack, several key factors determining the system characteristic curve (SCC) are overall stack geometry, cathode opening area, cathode flow field type and overall length, stack voltage, and additional coolant channels for separated cooling air. Meanwhile, several factors deciding the fan characteristic curve (FCC) are power rating, type, size and blade. To date, many researchers have been focusing on the opencathode fuel cells stack due to its potential to be used for portable and automotive applications [4]. Strahl et al. [5] experimentally investigated the degradation of open-cathode fuel cell stack. They found that cells located close to the end plates show the biggest performance decay. Huang et al. [6] developed and tested a hybrid
http://dx.doi.org/10.1016/j.apenergy.2015.12.098 0306-2619/Crown Copyright Ó 2015 Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Sasmito AP et al. Optimization of an open-cathode polymer electrolyte fuel cells stack utilizing Taguchi method. Appl Energy (2016), http://dx.doi.org/10.1016/j.apenergy.2015.12.098
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A.P. Sasmito et al. / Applied Energy xxx (2016) xxx–xxx
system with small stack (sub-kW) open-cathode PEM fuel cell stack to simulate vehicle operation with dynamics loading. Liu et al. [7] experimentally improved the membrane electrode assembly of open-cathode fuel cell. Tang et al. [8] developed a hybrid system combining a 2 kW air-blowing open-cathode proton exchange membrane fuel cell (PEMFC) stack and a lead–acid battery pack for a lightweight cruising vehicle. The dynamic performances of this PEMFC system with and without the assistance of the batteries were systematically investigated in a series of laboratory and road tests. The results showed that such a hybrid system was able to dynamically satisfy the vehicular power demand. While most of open-cathode fuel cell design suffers from membrane drying due to lack of humidification, Kong et al. [9] developed a selfhumidifying system by using double gas diffusion backing layers. Obeisun et al. [10] characterized the flow field geometry of opencathode PEMFC using printed circuit boards flow fields and found that circular opening yields lower Ohmic resistance. The mathematical modeling of open-cathode fuel cell started by Sasmito et al. [11] for which the fuel cells stack, fans and immediate ambient is taken into account. Flow reversal concept were introduced to overcome hot-spot at the near outlet region [12], while opencathode with edge-cooling designs were proposed and investigated to improve thermal management of the stack [13,14]. Tadbir et al. [15] developed cell level modeling of the hygrothermal characteristics of open-cathode fuel cells. Ismail et al. developed two-dimensional model for open cathode fuel cell [16] and later developed a simple model of open cathode fuel cell to quantify heat generation from joule heating and entropy generation [17]. Henriques et al. [18] experimentally and numerically investigated approach to improve open-cathode fuel cell efficiency by altering the cathode channel geometry. Recently, Meyer et al. [19] optimized the operating parameters of commercial open-cathode fuel cells using electro-thermal performance map. Despite wide range studies have been conducted worldwide, none of this study has focused on optimizing both design and operating parameters simultaneously which is the theme of this paper. Design of experiments Taguchi method has in recent years become popular tool for engineering optimization due to its simplicity and robustness. Several researchers have implemented Taguchi optimization in fuel cells area. Solehati et al. [20] optimized operating parameters of liquid-cooled fuel cell stack coupled with CHP system. Wu et al. [21] optimized the modified flow field design using Taguchi method. Besseris [22] optimized the fuel cell design using qualimetric engineering (Taguchi) and extremal analysis. They concluded that the proposed technique is simple and practical offering more accuracy, convenience and flexibility when compared with other competing algorithmic schemes. Given the capability of Taguchi method in determining the most significant factor influencing the performance of a fuel cell system, it is therefore of interest to apply this method to assess and evaluate the key parameters affecting the performance of forced-convection open cathode fuel cell and determine the optimum conditions for its operation. Therefore, the
aim of the study presented here is threefold: (i) to investigate the effect of design and operating parameters at different operating cell voltage, i.e. low (0.4 V), medium (0.6 V) and high (0.8 V); (ii) to optimize fuel cell performance based on average current density and net power generated; and (iii) to evaluate interaction between each design and operating factor with regards to the stack performance. The layout of the paper is as follows. First, the model development is introduced; it comprises of two-phase conservation of mass, momentum, species, energy, charge together with its immediate ambient and fan. The pertinent electrochemistry is accounted for by an agglomerate model and Butler–Volmer equation. Taguchi statistical method is then employed to study the sensitivity of each design and operating parameter under various conditions. Interaction between each parameter is evaluated. Optimum design and operating parameters are then calculated based on average current density and net power generated by stack. Finally, conclusions are drawn and extensions of the work are highlighted. 2. Model development 2.1. Mathematical model The mathematical model is based on the validated mathematical framework model developed in previous work [11]. Schematics of the repetitive cell unit a PEFC stack, ambient and fan(s) considered in this study is presented in Fig. 1. The governing equations can be found in Table 1. For the sake of brevity, details on the model derivation and validation are not repeated in this paper. Instead the reader can refer to our previous article [11]. 2.2. Performance evaluation To evaluate the system, net power of the system is calculated as the power generated by the stack minus the parasitic load of the fan and anode humidifier, i.e. Pnet = Pstack Pfan Phum. The power generated by the stack is given by voltage and current density, i.e. Pstack = EcellncellItot. The total current is given by Itot = iaveAcl where iave is the average current density and Acl is the area of the catalyst layer while Ecell is the cell voltage of the repetitive unit. The fan power is obtained from the fan manufacturer specification. 2.3. Taguchi statistical method Developed by Genichi Taguchi, Taguchi statistical method is widely known as a robust and powerful engineering tool for experimental optimization and design method. This method is employed to assess sensitivity of each parameter and determine the optimum combination of the design factors. In this study, six key parameters determining the performance of PEFC system are evaluated; those are fuel cell length, cathode channel height, cathode channel width, flow configuration, fan power and relative humidity at the
Fig. 1. Schematic representations of (a) co-flow, (b) counter-flow and (c) cross-flow forced-convection PEFC system.
Please cite this article in press as: Sasmito AP et al. Optimization of an open-cathode polymer electrolyte fuel cells stack utilizing Taguchi method. Appl Energy (2016), http://dx.doi.org/10.1016/j.apenergy.2015.12.098
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A.P. Sasmito et al. / Applied Energy xxx (2016) xxx–xxx Table 1 Governing equations. Fuel cell stack
_ H2 O r qðgÞ uðgÞ ¼ Smass m _ H2 O r qðlÞ uðlÞ ¼ m r qðgÞ uðgÞ uðgÞ ¼ r r þ Smom
Mass (gas) Mass (liquid) Momentum
Energy
r qðgÞ C pðgÞ uðgÞ T ¼ r ðkeff rTÞ þ Stemp
Species
r niðgÞ ¼ Si
Membrane water content
r nHðmÞ ¼0 2O
Membrane potential
r iðmÞ ¼ Spot
Solid potential
r iðsÞ ¼ Spot
Stress tensor and fluxes (fuel cells) T r ¼ pðgÞ I þ lðgÞ ruðgÞ þ ðruðgÞ Þ 2=3lðgÞ ðr uðgÞ ÞI ðgÞ
ðgÞ
ðgÞ
¼ qðgÞ uðgÞ xi
ni
ðmÞ
ðmÞ
i
ðgÞ
qðgÞ Di;eff rxi ðmÞ
nH2 O ¼ nd MH2 O =Fi
ði ¼ H2 ; O2 ; H2 O;N2 Þ ðmÞ
qðmÞ =M ðmÞ M H2 O DH2 O;eff rk
ðmÞ
¼ reff r/ðmÞ ðsÞ
¼ reff r/ðsÞ ðgÞ u s ðlÞ u ¼ DðcÞ rs ðsÞ
i
ðffÞ ðgdl; clÞ
Source terms 8 MO MH O ðmÞ > < 4F2 J c þ 2F2 Jc r nH2 O ðcathode clÞ Smass ¼ MH2 J r nðmÞ ðanode clÞ > H2 O : 2F a 0 ðelsewhereÞ 8 M O2 > > ðO2 ; cathode clÞ > 4F J c > > ðmÞ > > þ M H 2 O J c r nH _ H2 O ðH2 O; cathode clÞ m > 2F > 2O < ðmÞ _ ðH2 O; anode clÞ Si ¼ r nH2 O mH2 O > > _ H2 O ðH2 O; gdlÞ > m > > M H2 > > J ðH2 ; anode clÞ > > : 2F a 0 ðelsewhereÞ lðgÞ ðgÞ u ðgdl; clÞ j Smom ¼ 0 ðelsewhereÞ 8 < Jc ðcathode clÞ Spot ¼ Ja ðanode clÞ : 0 ðelsewhereÞ 8 ðmÞ ðmÞ 2 @Erev > > > J c T @T þ jgc j þ reff ðr/ Þ > > ðsÞ ðsÞ 2 > _ > þreff ðr/ Þ þ mH2 O Hvap ðcathode clÞ > > > > > J a g þ rðmÞ ðr/ðmÞ Þ2 þ rðsÞ ðr/ðsÞ Þ2 > > eff eff < _a þmH2 O Hvap ðanode clÞ Stemp ¼ ðmÞ ðmÞ 2 > > reff ð r / Þ ðmÞ > > > 2 > ðsÞ > > reff ðr/ðsÞ Þ þ m_ H2 O Hvap ðgdlÞ > > > ðsÞ > ðsÞ 2 > r ð r / Þ ðspÞ > : eff 0 ðelsewhereÞ Ambient
r qðgÞ uðgÞ ¼ 0 r qðlÞ uðlÞ ¼ 0 ðgÞ ðgÞ ðgÞ ¼rr r q u u
Mass (gas) Mass (liquid) Momentum
Energy
r qðgÞ C pðgÞ uðgÞ T ¼ r ðkeff rTÞ
Species
r niðgÞ ¼ 0
Stress tensor and fluxes (ambient) T r ¼ pðgÞ I þ lðgÞ ruðgÞ þ ðruðgÞ Þ 2=3lðgÞ ðr uðgÞ ÞI ðgÞ
ni u
ðlÞ
ðgÞ
¼ qðgÞ uðgÞ xi ¼u
ðgÞ
ðgÞ
ðgÞ
qðgÞ Di;eff rxi ði ¼ O2 ; H2 O;N2 Þ
s
Fan
Dpfan ¼ C1 ðufan Þ7 þ C2 ðufan Þ6 þ C3 ðufan Þ5 þ C4 ðufan Þ4 þ C5 ðufan Þ3 þ C6 ðufan Þ2 þ C7 ufan þ C8
anode. Three values are evaluated for each parameter, as presented in Table 2. With this variations, more than thousand simulations are needed should each possible combination is evaluated. Therefore, to minimize the required computational time and resources, an L27 orthogonal array is utilized in this computational evaluation, as shown in Table 3.
The objective function of the optimum parameters is based on average current density and net power of the PEFC. Therefore, the signal to noise ratio (S/N) is based on the larger-the-better. The predicted result from Taguchi method is verified with CFD results in term of confidence interval (CI). Both (S/N) and CI are given by
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!
nr 1X 1 ; nr i¼1 Y 2i ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 N CI ¼ F a;v 1 ;v 2 V ep ; where neff ¼ þ : neff r 1 þ DOF opt
S=N ¼ 10log10
ð1Þ
Here, Fa,v1,v2 is the F-ratio required, v1 is the number of degree of freedom of the mean, v2 is the number of degree freedom of the error, Vep is the error of variance, r is the sample size in the confirmation test, N is total number of trials and DOFopt is the total degree of freedom that are associated with items used to estimate gopt. 2.4. Numerics Pre-processor software GAMBITÒ was utilized to draw, mesh and label the computational domain which is illustrated in Fig. 1.
After mesh independence study, the computational domain was resolved with 105 elements. The governing equations together with constitutive relations and appropriate boundary conditions are solved by using a finite volume solver, FLUENT 6.3. FLUENT with user-defined function and scalars were incorporated to solve the model. 500 MB of random access memory (RAM) and 200–500 iteration which take 1–2 h computational time is needed for typical simulation with convergence criteria of 106 on a workstation with a quad core 2.68 GHz processor. The Taguchi statistical analysis to the key operating parameters was conducted by employing MINITAB 14 software. To evaluate the sensitivity of each parameter, determine the optimum combination of operating parameters and examine the confidence levels between Taguchi prediction and CFD results a variance analysis (ANOVA) was performed in this study.
(a)
(b)
(c)
Fig. 2. S/N response graph and interaction graph of various parameters with respect to stack performance (average current density) for (a) Ecell 0.4 V, (b) Ecell 0.6 V and (c) Ecell 0.8 V.
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A.P. Sasmito et al. / Applied Energy xxx (2016) xxx–xxx Table 2 Combinations of each parameters and levels.
A B C D E F
3. Results and discussion
Parameters
Level 1
Level 2
Level 3
Fuel cell length (length) Cathode channel height (height) Cathode channel width (width) Flow channel configuration (configuration) Fan power (Pfan) Anode relative humidity (RHa)
2 cm 1 mm 1 mm Coflow 4.5 W 0%
4 cm 2 mm 2 mm Counterflow 12.2 W 50%
8 cm 4 mm 3 mm Crossflow 30 W 100%
Table 3 Orthogonal array for L27 with six parameters and three levels experimental design and the corresponding numerical results. No
Length
Height
width
configuration
Pfan
RHa
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
2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 8 8 8 8 8 8 8 8 8
1 1 1 2 2 2 4 4 4 1 1 1 2 2 2 4 4 4 1 1 1 2 2 2 4 4 4
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
Co Co Co Counter Counter Counter Cross Cross Cross Cross Cross Cross Co Co Co Counter Counter Counter Counter Counter Counter Cross Cross Cross Co Co Co
4.5 12.2 30 4.5 12.2 30 4.5 12.2 30 4.5 12.2 30 4.5 12.2 30 4.5 12.2 30 4.5 12.2 30 4.5 12.2 30 4.5 12.2 30
0 50 100 0 50 100 0 50 100 50 100 0 50 100 0 50 100 0 100 0 50 100 0 50 100 0 50
Simulations were carried out for typical conditions found in an open-cathode PEFC with forced-air convection cooling. Details on the operating and geometrical parameters can be found in [11]. Sensitivity analysis of each operating parameter is investigated from the response of signal-to-noise ratio of orthogonal array (OA) for various conditions; optimum design and operating parameters are then examined based on average current density and net power generated. 3.1. Average current density The current study evaluates the average density based on OA of Taguchi method which is tabulated in Table 4. Analysis of variance (ANOVA) is then implemented to analyze the sensitivity of each parameter. The signal to noise (S/N) ratio for each parameter is presented in Fig. 2 (left side). As can be seen, shorter fuel cell is more desirable. Longer stack imposes higher friction to the air flowing through the stack. Higher pressure drop is therefore required to drive the air flow. On the other hand, high fan power and anode relative humidity is beneficial to the performance of the fuel cell stack. The reason for the former is affirmative, higher fan power drives more air to the stack increasing oxygen supply for the fuel cell operation and maintain the temperature of fuel cell at optimum condition. Higher fan power, however, leads to higher parasitic load; more discussion on it will be presented in the later section. As for the anode relative humidity, this finding is consistent with the finding from previous study [20] where high relative humidity plays an important role in determining the performance of the fuel cell. On the flow channel configuration, it is found that cross-flow offers the highest performance while counter flow is the worst. This can be explained by the fact that cross-flow configuration provides better heat, mass and ionics transport. Looking at the cathode geometrical design, interestingly, the optimum cathode channel height and width are at 2 mm (level 2) for both factors: too small leads to high flow resistance which hinder oxygen transport; conversely, too large causes excessive flow rate which dried out the membrane and increase membrane protonic resistance.
Table 4 Numerical results of various combinations of operating parameters. No
iave 0.4 V (A/m2)
iave 0.6 V (A/m2)
iave 0.8 V (A/m2)
Pnet 0.4 V (W)
Pnet 0.6 V (W)
Pnet 0.8 V (W)
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
4708 5822 7098 5037 6545 8767 5804 7691 9575 7615 8659 6010 4395 5658 6054 4715 5861 5239 2942 2966 3515 9102 6346 8490 4780 4961 7353
3379 4478 5171 3603 4654 5823 3804 5058 6318 5161 5809 3894 3660 4396 4113 3831 4407 3528 2254 2460 3108 6217 4100 5530 4074 3903 5012
1558 1916 2229 1579 1916 2400 1502 1932 2539 2000 2601 1542 1713 1928 1679 1780 1912 1574 1484 1422 1629 2891 1539 2044 1918 1711 1983
139 164 183 115 142 175 89 111 122 456 507 336 203 253 258 147 174 140 348 349 395 847 592 772 300 309 442
150 191 204 124 153 176 88 110 122 465 513 326 255 298 264 180 199 141 403 437 535 873 573 755 387 367 454
90 104 105 71 79 83 44 50 51 238 302 158 158 170 130 110 111 72 354 334 365 541 281 358 242 209 226
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A.P. Sasmito et al. / Applied Energy xxx (2016) xxx–xxx
(a)
(b)
(c)
Fig. 3. S/N response graph and interaction graph of various parameters with respect to net stack performance (net power) at (a) Ecell 0.4 V, (b) Ecell 0.6 V and (c) Ecell 0.8 V.
Closer inspection reveals that as the operating voltage increases, fuel cell length becomes less significant parameter affecting the performance; similarly, height, width, flow configuration and fan power becomes less significant, on the other hand, anode humidification plays significant role at high operating voltage. Fig. 2 (right side) shows interaction plot for each factor for which parallel plot denotes no interaction while crossing indicates significant interaction. Here, several features are apparent; foremost among them is the interaction of fuel cell length which shows the most significant influence to other factors, followed by channel height which has significant influence to the channel width and flow configuration. Fan power, on the other hand, yields less interaction to other factors, but length. 3.2. Net power In general, high stack performance is measured by power density generated from electrochemical reaction; however, this
may not be true as high power density stack may require sophisticated supporting system which imposes high parasitic loads. Hence, a careful balance should be taken between the stack performance and parasitic loads. In light of this, we examine the sensitivity of operating parameters with regard to the net power generated by the system which is defined as the power generated by the stack minus the parasitic load of the fan and humidification power. Fig. 3 (left side) presents the signal to noise (S/N) ratio for each parameter to the net power. For instance, fuel cell length plays key role for high net power generated; however, in contrast to average current density, the longer the length, the higher the net power generated. This can be adequately explained by the fact that longer channel represents larger active catalyst area; thus, although the average current density is smaller, the total power generated is higher due to larger active area. Similarly, lower cathode channel height gives rise to the net power due to more number of cells that fits at a given stack volume. Cross-flow configuration also offers better performance than others, while cathode channel width, fan power
Please cite this article in press as: Sasmito AP et al. Optimization of an open-cathode polymer electrolyte fuel cells stack utilizing Taguchi method. Appl Energy (2016), http://dx.doi.org/10.1016/j.apenergy.2015.12.098
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A.P. Sasmito et al. / Applied Energy xxx (2016) xxx–xxx Table 5 Optimum combination of operating parameters; the optimum values are highlighted in bold. Parameter
Ecell 0.4 V
Ecell 0.6 V
iave
Pnet
iave
Pnet
iave
Pnet
Length (cm) Height (mm) Width (mm) Configuration Pfan (W) RHa (%) iave (A/m2) Pnet (W) CL (%)
2 2 2 Cross-flow 30 100 10,900 – 94.7%
8 2 2 Cross-flow 30 100 – 863 96.4%
2 2 2 Cross-flow 30 100 6915 – 93.8%
8 1 2 Cross-flow 30 100 – 878 94.1%
2 2 2 Cross-flow 30 100 2980 – 95.6%
8 1 2 Cross-flow 4.5 100 – 545 94.8%
and anode humidification has marginal effect to the net power. As the operating voltage increases, there is no significant difference on the Taguchi S/N ratio trend; however, at high operating voltage, lower fan power is recommended as it constitutes to lower parasitic load and thus higher net power generated. Looking at the interaction of each factor in Fig. 3 (right side), it is found that significant interaction is shown between fuel cell length and height, width and configuration. Cathode channel height interacts significantly with cathode channel width and flow configuration and cathode channel width gives large interaction with the flow configuration. It is also noted that anode humidification interacts with fan power significantly. 3.3. Optimization Thus far we have shown the Taguchi S/N results and interaction between parameters, now we look further to the optimum combination of design and operating parameters for optimum average current density and net power generated by stack. Table 5 depicts the optimum performance for three different operating voltage. It is noted that the maximum average current density of 10,900, 6915 and 2980 A/m2 is achieved for operating voltage of 0.4 V, 0.6 V and 0.8 V respectively. The best combination of design and operating parameters are 2 cm fuel cell length, 2 mm cathode channel height, 2 mm cathode channel width, cross-flow channel configuration, 30 W fan power and 100% anode relative humidity. However, when the performance is optimized with regard to net power, the best combination of design and operating parameter are 8 cm fuel cell length due to the fact that longer fuel cell length produced larger active catalyst area; 1 mm cathode channel height since shorter height fits more cell at a given stack geometry, 2 mm cathode channel width, cross-flow channel configuration, 4.5 W fan power as it reduces parasitic load and 100% anode relative humidity for high operating voltage (0.8 V). At medium operating voltage (0.6 V) the best combination of parameters is similar to high operating voltage, but the fan power required is at maximum (30 W) due to the fact that lower operating voltage produces higher current which requires more oxidant and cooling from fans. At low operating voltage (0.4 V), the best combination of parameters similar to medium operating voltage, but with increasing cathode height of 2 mm. This can be adequately explained as higher current density is generated which requires more oxidant, and at the same time, more heat is generated which requires more cooling. Thus, increasing cathode height leads to enhanced heat and mass transfer. To ensure the confidence level of Taguchi optimization, confirmatory test was carried out by using the developed fuel cell model with design and operating parameters listed in Table 5. The results suggest that the level of confidence from Taguchi prediction is around 95% which indicates that Taguchi
Ecell 0.8 V
statistical method is a robust method to determine the optimum combination of operating parameters. 4. Concluding remarks A computational study of an open-cathode fuel cells stack with forced-air convection cooling has been carried out together with Taguchi statistical method to evaluate the significance of key design and operating parameters with regards to the average current density, stack power and net power generated by the fuel cell system. Significance of individual factors were evaluated and interaction between factors were also carried out. It was found that fuel cell length plays important role on determining fuel cell performance: for optimizing average current density, shorter fuel cell length (2 cm) is preferred, while for net stack power, longer fuel cell length of 8 cm is recommended. From this study, it can be highlighted that the developed three-dimensional fuel cell model together with Taguchi method is promising to be used as optimization tools for design and operating parameters of fuel cells for high performance operation. Future work shall be conducted to incorporate more detail statistical analysis to include stochastic analysis of design and operating parameters to arrive at more optimum fuel cell design. References [1] Dhathathreyan KS, Rajalakshmi N. Polymer electrolyte membrane fuel cell, book chapter. In: Basu S, editor. Recent trends in fuel cell science and technology. New Delhi: Anamaya Publisher; 2007. [2] Larminie J, Dicks A. Fuel cell systems explained. 2nd ed. Singapore: Wiley; 2003. [3] Sasmito AP, Birgersson E, Lum KW, Mujumdar AS. Fan selection and stack design for open-cathode polymer electrolyte fuel cell stacks. Renew Energy 2012;37:325–32. [4] Sasmito AP, Birgersson E, Mujumdar AS. Numerical evaluation of various thermal management strategies for polymer electrolyte fuel cell stacks. Int J Hydrogen Energy 2011;36:12991–3007. [5] Strahl S, Gasamans N, Llorca J, Husar A. Experimental analysis of a degraded open-cathode PEM fuel cell stack. Int J Hydrogen Energy 2014; 39:5378–87. [6] Huang ZM, Su A, Liu YC. Development and testing of a hybrid system with a sub-kW open-cathode type PEM (proton exchange membrane) fuel cell stack. Energy 2014;72:547–53. [7] Liu W, Wan L, Liu J, Zhao M, Zou Z. Performance improvement of the opencathode proton exchange membrane fuel cell by optimizing membrane electrode assemblies. Int J Hydrogen Energy 2015;40:7159–67. [8] Tang Y, Yuan W, Pan M, Wan Z. Experimental investigation on the dynamic performance of a hybrid PEM fuel cell/battery system for lightweight electric vehicle application. Appl Energy 2011;88:68–76. [9] Kong IM, Choi JW, Kim SI, Lee ES, Kim MS. Experimental study on the selfhumidification effect in proton exchange membrane fuel cells containing double gas diffusion backing layer. Appl Energy 2015;145:345–53. [10] Obeisun OA, Meyer Q, Robinson J, Gibbs CW, Kucernak AR, Shearing PR, et al. Development of open-cathode polymer electrolyte fuel cells using printed circuit board flow-field plates: flow geometry characterization. Int J Hydrogen Energy 2014;39:18326–36.
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[11] Sasmito AP, Lum KW, Birgersson E, Mujumdar AS. Computational study of forced air-convection in open-cathode polymer electrolyte fuel cells stacks. J Power Sources 2010;195:5550–63. [12] Sasmito AP, Birgersson E, Mujumdar AS. A novel flow reversal concept for improved thermal management in polymer electrolyte fuel cell stacks. Int. J. Therm. Sci. 2012;54:242–52. [13] Sasmito AP, Shamim T, Birgersson E, Mujumdar AS. Computational study of edge cooling for open-cathode polymer electrolyte fuel cell stacks. ASME J Fuel Cell Sci Technol 2012;9(6):061008. [14] Sasmito AP, Shamim T, Birgersson E, Mujumdar AS. Numerical investigation of water and temperature distributions for open-cathode polymer electrolyte fuel cell stack with edge cooling. ASME J Fuel Cell Sci Technol 2013;10 (6):061003. [15] Tadbir MA, Desouza A, Bahrami M, Kjeang E. Cell level modeling of the hygrothermal characteristics of open cathode polymer electrolyte membrane fuel cells. Int J Hydrogen Energy 2014;39:14993–5004. [16] Ismail MS, Ingham DB, Hughes KJ, Ma L, Pourkashanian M. Thermal modelling of the cathode in air-breathing PEM fuel cells. Appl Energy 2013;111:529–37.
[17] Ismail MS, Ingham DB, Hughes KJ, Ma L, Pourkashanian M. An efficient mathematical model for air-breathing PEM fuel cells. Appl Energy 2014;135:490–503. [18] Henriques T, César B, Costa Branco PJ. Increasing the efficiency of a portable PEM fuel cell by altering the cathode channel geometry: a numerical and experimental study. Appl Energy 2010;87:1400–9. [19] Meyer Q, Ronaszegi K, Pei-June G, Curnick O, Ashton S, Reisch T, et al. Optimisation of air cooled, open-cathode fuel cells: current of lowest resistance and electro-thermal performance mapping. J Power Sources 2015;291:261–9. [20] Solehati N, Bae J, Sasmito AP. Optimization of operating parameters for liquidcooled PEM fuel cell stacks using Taguchi method. J Ind Eng Chem 2012;18 (3):1039–50. [21] Wu HW, Ku HW. Effects of modified flow field on optimal parameters estimation and cell performance of a PEM fuel cell with the Taguchi method. Int J Hydrogen Energy 2012;37:1613–27. [22] Besseris GJ. Using qualimetric engineering and extremal analysis to optimize a proton exchange membrane fuel cell stack. Appl Energy 2014;128:15–26.
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Optimization of an open-cathode polymer electrolyte fuel cells stack utilizing Taguchi method Agus P. Sasmito a,⇑, Jundika C. Kurnia b, Tariq Shamim c, Arun S. Mujumdar a a
Department of Mining and Materials Engineering, McGill University, 3450 University, Frank Dawson Adams Bldg., Montreal, QC H3A0E8, Canada Department of Mechanical Engineering, Universiti Teknologi PETRONAS, 32610 Bandar Seri Iskandar, Perak Darul Ridzuan, Malaysia c Institute Center for Energy (iEnergy), Department of Mechanical and Materials Engineering, Masdar Institute of Science and Technology, Masdar City, Abu Dhabi, United Arab Emirates b
h i g h l i g h t s Design and operating parameters of an open-cathode PEFC stack is optimized. Optimization is carried out with regard to current density and net power. Fuel cell length plays important role on stack performance. Interaction between each parameter is evaluated.
a r t i c l e
i n f o
Article history: Received 27 June 2015 Received in revised form 21 December 2015 Accepted 23 December 2015 Available online xxxx Keywords: Fuel cells stack Open-cathode Net power Optimization Taguchi
a b s t r a c t The design of open-cathode polymer electrolyte fuel cells (PEFC) stacks with forced-convection requires a careful consideration on the geometrical and operating conditions as well as the operating characteristic of PEFC stacks and fan used. This paper evaluates the effect of key geometrical and operating parameters on the stack characteristic and their interactions to the thermal, water and gas managements as well as stack performance. A validated three dimensional model for open-cathode PEFC stack with fan and immediate ambient were solved to evaluate the effect of studied parameters on the stack performance. In tandem, an L27 orthogonal array (OA) of Taguchi matrix of six factors and three level designs to determine the optimum combination of parameters as well as their interactions for high, medium and low voltage operation. The result indicates that fuel cell length plays important role on determining the fuel cell performance in term of system characteristic, current density and net power. Optimum combination of design and operating parameters were obtained with the objective function of maximizing net power generated by stack by taking into account the parasitic loads. Crown Copyright Ó 2015 Published by Elsevier Ltd. All rights reserved.
1. Introduction In order to achieve optimum operating condition of polymer electrolyte fuel cells (PEFC) stacks, it is essential to maintain an efficient gas, water and thermal management. For a PEFC stack with capacity range between 100 and 2000 W, an open cathode design with fans to supply simultaneous air (oxidant) and cooling is desirable due to its less overall system complexity as compared to those with liquid cooling [1,2]. In this design, however, air supply system configurations (fan, blower or compressor) and their operational parameters are critical in determining the performance of PEFC stack as they do not only maintain the optimum tempera⇑ Corresponding author. Tel.: +1 514 398 3788. E-mail address: [email protected] (A.P. Sasmito).
ture (thermal management) but also ensure sufficient reactant air (gas management). Selection of the air supply system usually depends on the system and fan characteristic curves [3]. In PEFC stack, several key factors determining the system characteristic curve (SCC) are overall stack geometry, cathode opening area, cathode flow field type and overall length, stack voltage, and additional coolant channels for separated cooling air. Meanwhile, several factors deciding the fan characteristic curve (FCC) are power rating, type, size and blade. To date, many researchers have been focusing on the opencathode fuel cells stack due to its potential to be used for portable and automotive applications [4]. Strahl et al. [5] experimentally investigated the degradation of open-cathode fuel cell stack. They found that cells located close to the end plates show the biggest performance decay. Huang et al. [6] developed and tested a hybrid
http://dx.doi.org/10.1016/j.apenergy.2015.12.098 0306-2619/Crown Copyright Ó 2015 Published by Elsevier Ltd. All rights reserved.
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system with small stack (sub-kW) open-cathode PEM fuel cell stack to simulate vehicle operation with dynamics loading. Liu et al. [7] experimentally improved the membrane electrode assembly of open-cathode fuel cell. Tang et al. [8] developed a hybrid system combining a 2 kW air-blowing open-cathode proton exchange membrane fuel cell (PEMFC) stack and a lead–acid battery pack for a lightweight cruising vehicle. The dynamic performances of this PEMFC system with and without the assistance of the batteries were systematically investigated in a series of laboratory and road tests. The results showed that such a hybrid system was able to dynamically satisfy the vehicular power demand. While most of open-cathode fuel cell design suffers from membrane drying due to lack of humidification, Kong et al. [9] developed a selfhumidifying system by using double gas diffusion backing layers. Obeisun et al. [10] characterized the flow field geometry of opencathode PEMFC using printed circuit boards flow fields and found that circular opening yields lower Ohmic resistance. The mathematical modeling of open-cathode fuel cell started by Sasmito et al. [11] for which the fuel cells stack, fans and immediate ambient is taken into account. Flow reversal concept were introduced to overcome hot-spot at the near outlet region [12], while opencathode with edge-cooling designs were proposed and investigated to improve thermal management of the stack [13,14]. Tadbir et al. [15] developed cell level modeling of the hygrothermal characteristics of open-cathode fuel cells. Ismail et al. developed two-dimensional model for open cathode fuel cell [16] and later developed a simple model of open cathode fuel cell to quantify heat generation from joule heating and entropy generation [17]. Henriques et al. [18] experimentally and numerically investigated approach to improve open-cathode fuel cell efficiency by altering the cathode channel geometry. Recently, Meyer et al. [19] optimized the operating parameters of commercial open-cathode fuel cells using electro-thermal performance map. Despite wide range studies have been conducted worldwide, none of this study has focused on optimizing both design and operating parameters simultaneously which is the theme of this paper. Design of experiments Taguchi method has in recent years become popular tool for engineering optimization due to its simplicity and robustness. Several researchers have implemented Taguchi optimization in fuel cells area. Solehati et al. [20] optimized operating parameters of liquid-cooled fuel cell stack coupled with CHP system. Wu et al. [21] optimized the modified flow field design using Taguchi method. Besseris [22] optimized the fuel cell design using qualimetric engineering (Taguchi) and extremal analysis. They concluded that the proposed technique is simple and practical offering more accuracy, convenience and flexibility when compared with other competing algorithmic schemes. Given the capability of Taguchi method in determining the most significant factor influencing the performance of a fuel cell system, it is therefore of interest to apply this method to assess and evaluate the key parameters affecting the performance of forced-convection open cathode fuel cell and determine the optimum conditions for its operation. Therefore, the
aim of the study presented here is threefold: (i) to investigate the effect of design and operating parameters at different operating cell voltage, i.e. low (0.4 V), medium (0.6 V) and high (0.8 V); (ii) to optimize fuel cell performance based on average current density and net power generated; and (iii) to evaluate interaction between each design and operating factor with regards to the stack performance. The layout of the paper is as follows. First, the model development is introduced; it comprises of two-phase conservation of mass, momentum, species, energy, charge together with its immediate ambient and fan. The pertinent electrochemistry is accounted for by an agglomerate model and Butler–Volmer equation. Taguchi statistical method is then employed to study the sensitivity of each design and operating parameter under various conditions. Interaction between each parameter is evaluated. Optimum design and operating parameters are then calculated based on average current density and net power generated by stack. Finally, conclusions are drawn and extensions of the work are highlighted. 2. Model development 2.1. Mathematical model The mathematical model is based on the validated mathematical framework model developed in previous work [11]. Schematics of the repetitive cell unit a PEFC stack, ambient and fan(s) considered in this study is presented in Fig. 1. The governing equations can be found in Table 1. For the sake of brevity, details on the model derivation and validation are not repeated in this paper. Instead the reader can refer to our previous article [11]. 2.2. Performance evaluation To evaluate the system, net power of the system is calculated as the power generated by the stack minus the parasitic load of the fan and anode humidifier, i.e. Pnet = Pstack Pfan Phum. The power generated by the stack is given by voltage and current density, i.e. Pstack = EcellncellItot. The total current is given by Itot = iaveAcl where iave is the average current density and Acl is the area of the catalyst layer while Ecell is the cell voltage of the repetitive unit. The fan power is obtained from the fan manufacturer specification. 2.3. Taguchi statistical method Developed by Genichi Taguchi, Taguchi statistical method is widely known as a robust and powerful engineering tool for experimental optimization and design method. This method is employed to assess sensitivity of each parameter and determine the optimum combination of the design factors. In this study, six key parameters determining the performance of PEFC system are evaluated; those are fuel cell length, cathode channel height, cathode channel width, flow configuration, fan power and relative humidity at the
Fig. 1. Schematic representations of (a) co-flow, (b) counter-flow and (c) cross-flow forced-convection PEFC system.
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A.P. Sasmito et al. / Applied Energy xxx (2016) xxx–xxx Table 1 Governing equations. Fuel cell stack
_ H2 O r qðgÞ uðgÞ ¼ Smass m _ H2 O r qðlÞ uðlÞ ¼ m r qðgÞ uðgÞ uðgÞ ¼ r r þ Smom
Mass (gas) Mass (liquid) Momentum
Energy
r qðgÞ C pðgÞ uðgÞ T ¼ r ðkeff rTÞ þ Stemp
Species
r niðgÞ ¼ Si
Membrane water content
r nHðmÞ ¼0 2O
Membrane potential
r iðmÞ ¼ Spot
Solid potential
r iðsÞ ¼ Spot
Stress tensor and fluxes (fuel cells) T r ¼ pðgÞ I þ lðgÞ ruðgÞ þ ðruðgÞ Þ 2=3lðgÞ ðr uðgÞ ÞI ðgÞ
ðgÞ
ðgÞ
¼ qðgÞ uðgÞ xi
ni
ðmÞ
ðmÞ
i
ðgÞ
qðgÞ Di;eff rxi ðmÞ
nH2 O ¼ nd MH2 O =Fi
ði ¼ H2 ; O2 ; H2 O;N2 Þ ðmÞ
qðmÞ =M ðmÞ M H2 O DH2 O;eff rk
ðmÞ
¼ reff r/ðmÞ ðsÞ
¼ reff r/ðsÞ ðgÞ u s ðlÞ u ¼ DðcÞ rs ðsÞ
i
ðffÞ ðgdl; clÞ
Source terms 8 MO MH O ðmÞ > < 4F2 J c þ 2F2 Jc r nH2 O ðcathode clÞ Smass ¼ MH2 J r nðmÞ ðanode clÞ > H2 O : 2F a 0 ðelsewhereÞ 8 M O2 > > ðO2 ; cathode clÞ > 4F J c > > ðmÞ > > þ M H 2 O J c r nH _ H2 O ðH2 O; cathode clÞ m > 2F > 2O < ðmÞ _ ðH2 O; anode clÞ Si ¼ r nH2 O mH2 O > > _ H2 O ðH2 O; gdlÞ > m > > M H2 > > J ðH2 ; anode clÞ > > : 2F a 0 ðelsewhereÞ lðgÞ ðgÞ u ðgdl; clÞ j Smom ¼ 0 ðelsewhereÞ 8 < Jc ðcathode clÞ Spot ¼ Ja ðanode clÞ : 0 ðelsewhereÞ 8 ðmÞ ðmÞ 2 @Erev > > > J c T @T þ jgc j þ reff ðr/ Þ > > ðsÞ ðsÞ 2 > _ > þreff ðr/ Þ þ mH2 O Hvap ðcathode clÞ > > > > > J a g þ rðmÞ ðr/ðmÞ Þ2 þ rðsÞ ðr/ðsÞ Þ2 > > eff eff < _a þmH2 O Hvap ðanode clÞ Stemp ¼ ðmÞ ðmÞ 2 > > reff ð r / Þ ðmÞ > > > 2 > ðsÞ > > reff ðr/ðsÞ Þ þ m_ H2 O Hvap ðgdlÞ > > > ðsÞ > ðsÞ 2 > r ð r / Þ ðspÞ > : eff 0 ðelsewhereÞ Ambient
r qðgÞ uðgÞ ¼ 0 r qðlÞ uðlÞ ¼ 0 ðgÞ ðgÞ ðgÞ ¼rr r q u u
Mass (gas) Mass (liquid) Momentum
Energy
r qðgÞ C pðgÞ uðgÞ T ¼ r ðkeff rTÞ
Species
r niðgÞ ¼ 0
Stress tensor and fluxes (ambient) T r ¼ pðgÞ I þ lðgÞ ruðgÞ þ ðruðgÞ Þ 2=3lðgÞ ðr uðgÞ ÞI ðgÞ
ni u
ðlÞ
ðgÞ
¼ qðgÞ uðgÞ xi ¼u
ðgÞ
ðgÞ
ðgÞ
qðgÞ Di;eff rxi ði ¼ O2 ; H2 O;N2 Þ
s
Fan
Dpfan ¼ C1 ðufan Þ7 þ C2 ðufan Þ6 þ C3 ðufan Þ5 þ C4 ðufan Þ4 þ C5 ðufan Þ3 þ C6 ðufan Þ2 þ C7 ufan þ C8
anode. Three values are evaluated for each parameter, as presented in Table 2. With this variations, more than thousand simulations are needed should each possible combination is evaluated. Therefore, to minimize the required computational time and resources, an L27 orthogonal array is utilized in this computational evaluation, as shown in Table 3.
The objective function of the optimum parameters is based on average current density and net power of the PEFC. Therefore, the signal to noise ratio (S/N) is based on the larger-the-better. The predicted result from Taguchi method is verified with CFD results in term of confidence interval (CI). Both (S/N) and CI are given by
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!
nr 1X 1 ; nr i¼1 Y 2i ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 N CI ¼ F a;v 1 ;v 2 V ep ; where neff ¼ þ : neff r 1 þ DOF opt
S=N ¼ 10log10
ð1Þ
Here, Fa,v1,v2 is the F-ratio required, v1 is the number of degree of freedom of the mean, v2 is the number of degree freedom of the error, Vep is the error of variance, r is the sample size in the confirmation test, N is total number of trials and DOFopt is the total degree of freedom that are associated with items used to estimate gopt. 2.4. Numerics Pre-processor software GAMBITÒ was utilized to draw, mesh and label the computational domain which is illustrated in Fig. 1.
After mesh independence study, the computational domain was resolved with 105 elements. The governing equations together with constitutive relations and appropriate boundary conditions are solved by using a finite volume solver, FLUENT 6.3. FLUENT with user-defined function and scalars were incorporated to solve the model. 500 MB of random access memory (RAM) and 200–500 iteration which take 1–2 h computational time is needed for typical simulation with convergence criteria of 106 on a workstation with a quad core 2.68 GHz processor. The Taguchi statistical analysis to the key operating parameters was conducted by employing MINITAB 14 software. To evaluate the sensitivity of each parameter, determine the optimum combination of operating parameters and examine the confidence levels between Taguchi prediction and CFD results a variance analysis (ANOVA) was performed in this study.
(a)
(b)
(c)
Fig. 2. S/N response graph and interaction graph of various parameters with respect to stack performance (average current density) for (a) Ecell 0.4 V, (b) Ecell 0.6 V and (c) Ecell 0.8 V.
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A.P. Sasmito et al. / Applied Energy xxx (2016) xxx–xxx Table 2 Combinations of each parameters and levels.
A B C D E F
3. Results and discussion
Parameters
Level 1
Level 2
Level 3
Fuel cell length (length) Cathode channel height (height) Cathode channel width (width) Flow channel configuration (configuration) Fan power (Pfan) Anode relative humidity (RHa)
2 cm 1 mm 1 mm Coflow 4.5 W 0%
4 cm 2 mm 2 mm Counterflow 12.2 W 50%
8 cm 4 mm 3 mm Crossflow 30 W 100%
Table 3 Orthogonal array for L27 with six parameters and three levels experimental design and the corresponding numerical results. No
Length
Height
width
configuration
Pfan
RHa
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
2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 8 8 8 8 8 8 8 8 8
1 1 1 2 2 2 4 4 4 1 1 1 2 2 2 4 4 4 1 1 1 2 2 2 4 4 4
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
Co Co Co Counter Counter Counter Cross Cross Cross Cross Cross Cross Co Co Co Counter Counter Counter Counter Counter Counter Cross Cross Cross Co Co Co
4.5 12.2 30 4.5 12.2 30 4.5 12.2 30 4.5 12.2 30 4.5 12.2 30 4.5 12.2 30 4.5 12.2 30 4.5 12.2 30 4.5 12.2 30
0 50 100 0 50 100 0 50 100 50 100 0 50 100 0 50 100 0 100 0 50 100 0 50 100 0 50
Simulations were carried out for typical conditions found in an open-cathode PEFC with forced-air convection cooling. Details on the operating and geometrical parameters can be found in [11]. Sensitivity analysis of each operating parameter is investigated from the response of signal-to-noise ratio of orthogonal array (OA) for various conditions; optimum design and operating parameters are then examined based on average current density and net power generated. 3.1. Average current density The current study evaluates the average density based on OA of Taguchi method which is tabulated in Table 4. Analysis of variance (ANOVA) is then implemented to analyze the sensitivity of each parameter. The signal to noise (S/N) ratio for each parameter is presented in Fig. 2 (left side). As can be seen, shorter fuel cell is more desirable. Longer stack imposes higher friction to the air flowing through the stack. Higher pressure drop is therefore required to drive the air flow. On the other hand, high fan power and anode relative humidity is beneficial to the performance of the fuel cell stack. The reason for the former is affirmative, higher fan power drives more air to the stack increasing oxygen supply for the fuel cell operation and maintain the temperature of fuel cell at optimum condition. Higher fan power, however, leads to higher parasitic load; more discussion on it will be presented in the later section. As for the anode relative humidity, this finding is consistent with the finding from previous study [20] where high relative humidity plays an important role in determining the performance of the fuel cell. On the flow channel configuration, it is found that cross-flow offers the highest performance while counter flow is the worst. This can be explained by the fact that cross-flow configuration provides better heat, mass and ionics transport. Looking at the cathode geometrical design, interestingly, the optimum cathode channel height and width are at 2 mm (level 2) for both factors: too small leads to high flow resistance which hinder oxygen transport; conversely, too large causes excessive flow rate which dried out the membrane and increase membrane protonic resistance.
Table 4 Numerical results of various combinations of operating parameters. No
iave 0.4 V (A/m2)
iave 0.6 V (A/m2)
iave 0.8 V (A/m2)
Pnet 0.4 V (W)
Pnet 0.6 V (W)
Pnet 0.8 V (W)
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
4708 5822 7098 5037 6545 8767 5804 7691 9575 7615 8659 6010 4395 5658 6054 4715 5861 5239 2942 2966 3515 9102 6346 8490 4780 4961 7353
3379 4478 5171 3603 4654 5823 3804 5058 6318 5161 5809 3894 3660 4396 4113 3831 4407 3528 2254 2460 3108 6217 4100 5530 4074 3903 5012
1558 1916 2229 1579 1916 2400 1502 1932 2539 2000 2601 1542 1713 1928 1679 1780 1912 1574 1484 1422 1629 2891 1539 2044 1918 1711 1983
139 164 183 115 142 175 89 111 122 456 507 336 203 253 258 147 174 140 348 349 395 847 592 772 300 309 442
150 191 204 124 153 176 88 110 122 465 513 326 255 298 264 180 199 141 403 437 535 873 573 755 387 367 454
90 104 105 71 79 83 44 50 51 238 302 158 158 170 130 110 111 72 354 334 365 541 281 358 242 209 226
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A.P. Sasmito et al. / Applied Energy xxx (2016) xxx–xxx
(a)
(b)
(c)
Fig. 3. S/N response graph and interaction graph of various parameters with respect to net stack performance (net power) at (a) Ecell 0.4 V, (b) Ecell 0.6 V and (c) Ecell 0.8 V.
Closer inspection reveals that as the operating voltage increases, fuel cell length becomes less significant parameter affecting the performance; similarly, height, width, flow configuration and fan power becomes less significant, on the other hand, anode humidification plays significant role at high operating voltage. Fig. 2 (right side) shows interaction plot for each factor for which parallel plot denotes no interaction while crossing indicates significant interaction. Here, several features are apparent; foremost among them is the interaction of fuel cell length which shows the most significant influence to other factors, followed by channel height which has significant influence to the channel width and flow configuration. Fan power, on the other hand, yields less interaction to other factors, but length. 3.2. Net power In general, high stack performance is measured by power density generated from electrochemical reaction; however, this
may not be true as high power density stack may require sophisticated supporting system which imposes high parasitic loads. Hence, a careful balance should be taken between the stack performance and parasitic loads. In light of this, we examine the sensitivity of operating parameters with regard to the net power generated by the system which is defined as the power generated by the stack minus the parasitic load of the fan and humidification power. Fig. 3 (left side) presents the signal to noise (S/N) ratio for each parameter to the net power. For instance, fuel cell length plays key role for high net power generated; however, in contrast to average current density, the longer the length, the higher the net power generated. This can be adequately explained by the fact that longer channel represents larger active catalyst area; thus, although the average current density is smaller, the total power generated is higher due to larger active area. Similarly, lower cathode channel height gives rise to the net power due to more number of cells that fits at a given stack volume. Cross-flow configuration also offers better performance than others, while cathode channel width, fan power
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A.P. Sasmito et al. / Applied Energy xxx (2016) xxx–xxx Table 5 Optimum combination of operating parameters; the optimum values are highlighted in bold. Parameter
Ecell 0.4 V
Ecell 0.6 V
iave
Pnet
iave
Pnet
iave
Pnet
Length (cm) Height (mm) Width (mm) Configuration Pfan (W) RHa (%) iave (A/m2) Pnet (W) CL (%)
2 2 2 Cross-flow 30 100 10,900 – 94.7%
8 2 2 Cross-flow 30 100 – 863 96.4%
2 2 2 Cross-flow 30 100 6915 – 93.8%
8 1 2 Cross-flow 30 100 – 878 94.1%
2 2 2 Cross-flow 30 100 2980 – 95.6%
8 1 2 Cross-flow 4.5 100 – 545 94.8%
and anode humidification has marginal effect to the net power. As the operating voltage increases, there is no significant difference on the Taguchi S/N ratio trend; however, at high operating voltage, lower fan power is recommended as it constitutes to lower parasitic load and thus higher net power generated. Looking at the interaction of each factor in Fig. 3 (right side), it is found that significant interaction is shown between fuel cell length and height, width and configuration. Cathode channel height interacts significantly with cathode channel width and flow configuration and cathode channel width gives large interaction with the flow configuration. It is also noted that anode humidification interacts with fan power significantly. 3.3. Optimization Thus far we have shown the Taguchi S/N results and interaction between parameters, now we look further to the optimum combination of design and operating parameters for optimum average current density and net power generated by stack. Table 5 depicts the optimum performance for three different operating voltage. It is noted that the maximum average current density of 10,900, 6915 and 2980 A/m2 is achieved for operating voltage of 0.4 V, 0.6 V and 0.8 V respectively. The best combination of design and operating parameters are 2 cm fuel cell length, 2 mm cathode channel height, 2 mm cathode channel width, cross-flow channel configuration, 30 W fan power and 100% anode relative humidity. However, when the performance is optimized with regard to net power, the best combination of design and operating parameter are 8 cm fuel cell length due to the fact that longer fuel cell length produced larger active catalyst area; 1 mm cathode channel height since shorter height fits more cell at a given stack geometry, 2 mm cathode channel width, cross-flow channel configuration, 4.5 W fan power as it reduces parasitic load and 100% anode relative humidity for high operating voltage (0.8 V). At medium operating voltage (0.6 V) the best combination of parameters is similar to high operating voltage, but the fan power required is at maximum (30 W) due to the fact that lower operating voltage produces higher current which requires more oxidant and cooling from fans. At low operating voltage (0.4 V), the best combination of parameters similar to medium operating voltage, but with increasing cathode height of 2 mm. This can be adequately explained as higher current density is generated which requires more oxidant, and at the same time, more heat is generated which requires more cooling. Thus, increasing cathode height leads to enhanced heat and mass transfer. To ensure the confidence level of Taguchi optimization, confirmatory test was carried out by using the developed fuel cell model with design and operating parameters listed in Table 5. The results suggest that the level of confidence from Taguchi prediction is around 95% which indicates that Taguchi
Ecell 0.8 V
statistical method is a robust method to determine the optimum combination of operating parameters. 4. Concluding remarks A computational study of an open-cathode fuel cells stack with forced-air convection cooling has been carried out together with Taguchi statistical method to evaluate the significance of key design and operating parameters with regards to the average current density, stack power and net power generated by the fuel cell system. Significance of individual factors were evaluated and interaction between factors were also carried out. It was found that fuel cell length plays important role on determining fuel cell performance: for optimizing average current density, shorter fuel cell length (2 cm) is preferred, while for net stack power, longer fuel cell length of 8 cm is recommended. From this study, it can be highlighted that the developed three-dimensional fuel cell model together with Taguchi method is promising to be used as optimization tools for design and operating parameters of fuel cells for high performance operation. Future work shall be conducted to incorporate more detail statistical analysis to include stochastic analysis of design and operating parameters to arrive at more optimum fuel cell design. References [1] Dhathathreyan KS, Rajalakshmi N. Polymer electrolyte membrane fuel cell, book chapter. In: Basu S, editor. Recent trends in fuel cell science and technology. New Delhi: Anamaya Publisher; 2007. [2] Larminie J, Dicks A. Fuel cell systems explained. 2nd ed. Singapore: Wiley; 2003. [3] Sasmito AP, Birgersson E, Lum KW, Mujumdar AS. Fan selection and stack design for open-cathode polymer electrolyte fuel cell stacks. Renew Energy 2012;37:325–32. [4] Sasmito AP, Birgersson E, Mujumdar AS. Numerical evaluation of various thermal management strategies for polymer electrolyte fuel cell stacks. Int J Hydrogen Energy 2011;36:12991–3007. [5] Strahl S, Gasamans N, Llorca J, Husar A. Experimental analysis of a degraded open-cathode PEM fuel cell stack. Int J Hydrogen Energy 2014; 39:5378–87. [6] Huang ZM, Su A, Liu YC. Development and testing of a hybrid system with a sub-kW open-cathode type PEM (proton exchange membrane) fuel cell stack. Energy 2014;72:547–53. [7] Liu W, Wan L, Liu J, Zhao M, Zou Z. Performance improvement of the opencathode proton exchange membrane fuel cell by optimizing membrane electrode assemblies. Int J Hydrogen Energy 2015;40:7159–67. [8] Tang Y, Yuan W, Pan M, Wan Z. Experimental investigation on the dynamic performance of a hybrid PEM fuel cell/battery system for lightweight electric vehicle application. Appl Energy 2011;88:68–76. [9] Kong IM, Choi JW, Kim SI, Lee ES, Kim MS. Experimental study on the selfhumidification effect in proton exchange membrane fuel cells containing double gas diffusion backing layer. Appl Energy 2015;145:345–53. [10] Obeisun OA, Meyer Q, Robinson J, Gibbs CW, Kucernak AR, Shearing PR, et al. Development of open-cathode polymer electrolyte fuel cells using printed circuit board flow-field plates: flow geometry characterization. Int J Hydrogen Energy 2014;39:18326–36.
Please cite this article in press as: Sasmito AP et al. Optimization of an open-cathode polymer electrolyte fuel cells stack utilizing Taguchi method. Appl Energy (2016), http://dx.doi.org/10.1016/j.apenergy.2015.12.098
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Please cite this article in press as: Sasmito AP et al. Optimization of an open-cathode polymer electrolyte fuel cells stack utilizing Taguchi method. Appl Energy (2016), http://dx.doi.org/10.1016/j.apenergy.2015.12.098