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Procedía Engineering 64 (2013) 409 - 418

Procedía Engineering

www.elsevier.com/locate/procedia

International Conference on DESIGN AND MANUFACTURING, IConDM 2013

Optimization of Operating and Design Parameters on Proton Exchange Membrane Fuel Cell by using Taguchi method

P.Karthikeyana*, M.Muthukumarb, S.Vignesh Shanmugamb, P.Pravin Kumarb, Suryanarayanan Muralib, A.P.Senthil Kumarb

a Department of Automobile Engineering, PSG College of Technology, Coimbatore-641004, India b Department of Mechanical Engineering, PSG College of Technology, Coimbatore-641004, India

Abstract

The performance of the Proton Exchange Membrane Fuel Cell (PEMFC) is greatly influenced by the various operating parameters and geometric properties. This paper deals with optimization of both operating and design parameters namely cell temperature, back pressure, anode and cathode inlet velocities, Gas Diffusion Layer (GDL) porosity and thickness, cathode water mass fraction, flow channel dimensions, rib width and porous electrode thickness. The Numerical model of single channel PEM fuel cell was developed and analyzed by using COMSOL Multiphysics 4.2 software package. The optimization of design and operating parameters in software was carried out in two stages using standard orthogonal array of Taguchi method. From the first stage of analysis, it was inferred that back pressure had maximum effect and rib width had least effect on fuel cell performance. In the second stage of analysis, fine tuned optimization was performed on selected factors which caused for 3 % increase in power density and the results were also validated using COMSOL Multiphysics 4.2. © 2013 The Authors. Published by Elsevier Ltd.

Selection and peer-review under responsibilityoftheorganizingandreview committeeoflConDM 2013 Keywords: Optimization; Operating parameters; Geometric properties; Taguchi method; COMSOL Multiphysics 4.2

Nomenclature

P power density (W/cm2)

Pmax maximum power density (W/cm2)

Corresponding author. Tel.: +91 9488850019; fax: +91-422-2573833. E-mail address: apkarthipsg@gmail.com

1877-7058 © 2013 The Authors. Published by Elsevier Ltd.

Selection and peer-review under responsibility of the organizing and review committee of IConDM 2013 doi:10.1016/j.proeng.2013.09.114

Greek symbols T| overall mean

rjopt mean corresponding to optimum combination A difference of values

1. Introduction

With an increasing awareness of environmental concerns and a desire for energy independence, the development of renewable and clean energy sources has become the focus of significant research activity. Hydrogen will play a major role in fulfilling the global energy demands in future. Fuel cell, acting as a transducer, absorbs energy from hydrogen reduction and evolves electrical energy emerged as an ideal choice for use in a wide range power supplies. The PEMFCs are currently under rapid development and promise to become an economically viable commercial power source in many areas, especially for transportation, stationary, portable and automobile applications, because of their high energy density at low operating temperatures and zero emissions [1]. In this effort, many critical issues of PEMFC technology need to be addressed. One of the key issues is the performance enhancement of fuel cell by studying the influence of various operating and design parameters. Dyi-Huey Chang et al. [2] studied the effect of flow channel depth and flow rates on performance of miniature PEMFC. They concluded that optimum flow rate was essential for shallow channel depth to maintain sufficient pressure to force reactant into channel and also to have proper water balance. Shimpalee et al. [3] investigated the effect of number of gas paths on a 200 cm2 serpentine flow field design. They concluded that the 13-channel flow field design gives the best performance for a single cell PEMFC. However, for making a PEMFC stack, the 26-channel flow-field design may be the optimal choice due to more uniform current density distribution on the flow field channel and a lower pressure drop. Also he studied the effect of flow channel dimensions and rib widths for performance studies on PEMFC [4]. Atul Kumar et al. [5] optimized the flow channel dimensions and shape in the flow field of end plates in a single pass serpentine flow field design. The triangular and hemispherical shaped cross section resulted in 9% excess hydrogen consumption in anode side, thus it can influence the enhanced performance of the PEM fuel cell. Wei-Mon Yan et al. [6] studied the effect of flow channel designs on performance of PEMFC and concluded that the interdigitated flow field having 1.4 times better power output than the conventional flow field design. Lin Wang et al. [7] concluded that effect of humidification temperatures is not significant at higher current densities. Also when humidification temperatures are less than cell temperature, the PEMFC performance deteriorates.

Apart from the effect of flow field design and operating parameters, the performance of the PEM fuel cells is greatly influenced by the water management issue. Adequate water-vapour must be available to maintain high electrolyte ionic-conductivity for ensuring suitable performance. However, if excessive water is present in the liquid phase, it can block pores in the catalyst and GDLs, which hinders the transport of reactants to the catalyst. Karthikeyan et al. investigated the water impact on performance of PEMFC with porous flow channels [8]. They concluded that the porous flow channels had 48% more power output than non porous flow channels due to water accumulation in non porous flow channels. Thus, proper water management is absolutely essential for enhanced fuel cell performance. Also, water and thermal management issues were severely affected by proper selection of design and operating parameters.

Hence, it is clearly evident that there is an exigent need of analyzing the simultaneous influence of operating and design parameters using mathematical tool and to optimize the same for better performance of the PEMFC by using Taguchi method. Thus, this paper concerns with the optimization of ten different operating and design parameters using Taguchi method. Using standard orthogonal arrays, optimal combinations of all the considered input parameters at its corresponding levels were found and the operating parameters were optimized [9]. But, one of the main limitation of the Taguchi technique is that not more than six factors can be optimized for 4-level and 5-level designs. Hence the high level design will yield better optimized results. For the sake of adopting such high levels into the design of experiments, the Taguchi technique was implemented in two stages in this study to analyse ten factors with a 3-level design per stage and finally arriving at better optimized results.

Though few works in literature arena were based on the application of Taguchi method in optimizing fuel cell parameters, not more than five factors were simultaneously analysed for hierarchical influence in the performance

of PEMFC. This is because many factors such as rib width of the flow channel and porosity are not easy to change for each trial, while running experiments. In order to study the combined effect of all such factors, due to the constraints posed with experimentation, the numerical modeling was chosen as a platform for analysis. The proposed work focusing on implementation of Taguchi method for optimizing operating and design parameters for performance enhanced studies on PEM fuel cell has been addressed. Also, the combined effect of those parameters has been addressed in this paper.

2. Modelling in software

A five layered Proton Exchange Membrane fuel cell was modelled using commercial finite element software (COMSOL Multiphysics 4.2). The five layers under consideration were electrolyte membrane, anode and cathode porous electrodes in which catalyst would be embedded, anode and cathode gas diffusion layers. Assumptions considered while modelling the PEMFC are steady, laminar and incompressible flow with isothermal, all material properties being homogeneous and isotropic in nature, and adoption of Darcy's law with negligence of gravitational field effect and contact resistance [10].

A single fuel cell with the flow channel length of 125 mm and Nafion 117 (with thickness of 183 microns) electrolyte was chosen for this analysis. Though lower electrolyte thickness gives better performance, in order to withstand a back pressure of 1.5 bar, Nafion 117 was chosen. The other design and operating parameters, which are to be optimized, were changed for every trial corresponding to orthogonal array of Taguchi method. The corresponding modules necessary for the analysis were selected in the software. Free and subsurface flow module, current distribution module and species transport module were included in the analysis. The flow module involves the flow of the species according to given boundary conditions like pressure, velocity etc. The species transport module deals with the chemical reactions taking place for the given diffusivity matrix. Current distribution module determines the amount of current density generated corresponding to reaction taking place. Thus, a coupled analysis of all these three modules were performed in the software and the power density was deduced from the polarization curve.

2.1 Adoption of the Taguchi method

In order to study the combined effect of multiple factors affecting the performance of fuel cell, all those factors with the considered levels in each are to be involved when formulating the design of experiments. But, by doing this, the number of experiments shoots up to a practically impossible level. Hence, in order to avoid this constrain, the Taguchi method can be used to reduce the number of experiments to a practically feasible level without any sacrifice in considering any factor or even any one of its level. This is leading to the formulation of a fractional factorial design of experiments. Hence, this method can also be used to find out the most optimum combination among the input parameters which will result in getting the maximum possible output which cause in the performance enhancement of PEMFC. For the research being reported, ten different factors with three levels were considered. A 3-level design was selected to find the significance of these factors taking into consideration of low, high and middle range values. In full factorial design, it was found that 59049 runs were to be performed to find the combined significant effect of each factor. For a 3-level design, L27 standard orthogonal array is used in the analysis for a maximum of 13 factors in Taguchi method. When this orthogonal array is used, significance of factors and optimum combination would be found in 27 runs itself.

The analysis was performed in two stages namely: coarse optimization of factors and refinement of coarsely optimized factors. In the first stage of analysis, in order to find the significance of each factor, levels were selected such that full operating range was covered for each factor. The factors considered for this study were operating cell temperature, back pressure, GDL porosity and thickness, flow channel dimensions and rib width, porous electrode thickness, anode and cathode inlet velocities and cathode inlet water content.

The levels for GDL porosity and thickness were decided based on the work done by Jer-Huan Jang et al. [11]. They proposed that the performance of the fuel cell has been increase with the increasing of GDL porosity and decreasing of GDL thickness in their operating range. Young Gi Yoon et al. [12] discussed the effects of rib width and flow channel dimensions, and they proposed that these design parameters in the range of 0.5 to 3 mm shows the best performance of PEMFC.

Biao Zhou et al. [13] used a steady state, 2D mathematical model to investigate the effect of water content on a PEM fuel cell. They concluded that the proper liquid water injection in cathode inlet in the range of 50% to 100% does not improve the cell performance. Hence the levels for this analysis were selected in the range of 10% to 70% to investigate its effect on fuel cell performance. Summarizing all the data acquired as mentioned earlier, the levels were chosen in the full operating range as shown in Table 1 for this proposed work.

Table 1. Selection of factors and levels

Factors Level 1 Level 2 Level 3

Back pressure (bar) 0.5 1 1.5

Cell temperature (K) 303 323 343

GDL porosity (%) 40 60 80

Flow channel depth and width (mm) 1x1 2x1 2x2

Cathode inlet water content (%) 10 40 70

Electrode thickness (microns) 50 60 70

GDL thickness (microns) 250 325 400

Rib width (mm) 1.2 1.5 1.8

Anode inlet velocity (m/s) 0.2 0.5 0.8

Cathode inlet velocity (m/s) 0.5 1.0 1.2

The combinations of these levels were derived using MINITAB 16 software for standard L27 orthogonal array. Thus, a single fuel cell with the flow channel length of 125 mm modelled using a commercial finite element analysis package (COMSOL Multiphysics 4.2), was applied with boundary conditions as per the L27 orthogonal array combinations. The layers under consideration were electrolyte, porous electrodes embedded with catalyst; and gas diffusion layers. The flow channel dimensions under consideration were rib width, width and height of the flow channel. As per L27 orthogonal array, the inputs were given to the analysis software and having all other parameters constant. The power density from polarisation curve was found for all 27 runs and corresponding S/N ratios were shown in Table 2. The S/N ratio was calculated using the formula -10 log10(1/P2), where 'P' is the power density.

Table 2. Power density and S/N ratio for 27 runs

Trial Power-density S/N ratio Trial Power-density S/N ratio

1 0.174460 -15.16608 15 0.182655 -14.76737

2 0.171820 -15.29853 16 0.179603 -14.91375

3 0.162195 -15.79925 17 0.175093 -15.13465

4 0.168465 -15.46981 18 0.158500 -15.99887

5 0.163983 -15.70405 19 0.197940 -14.06911

6 0.150315 -16.45995 20 0.189805 -14.43385

7 0.168850 -15.44998 21 0.180140 -14.85411

8 0.157795 -16.03814 22 0.198110 -14.06187

9 0.155513 -16.16469 23 0.184745 -14.66855

10 0.187055 -14.56061 24 0.182050 -14.79619

11 0.181198 -14.83696 25 0.198605 -14.04020

12 0.175148 -15.13192 26 0.196295 -14.14182

13 0.185488 -14.63371 27 0.196103 -14.15034

14 0.189530 -14.44644

The analysis was performed for "Larger the Better" type, since power output of PEMFC must be maximised. The analysis results were based on Signal/Noise (S/N) ratios which was the ratio of controlled and uncontrolled factors. The mean of S/N ratios corresponding to their levels was shown in Table 3. It was calculated by estimating mean of the S/N ratios of all the trials corresponding to that level of the factor. For example, mean of S/N ratio corresponding to 0.5 bar of back pressure was calculated by taking mean of first nine trials of L27 combinations, mean of S/N ratio corresponding to 1.5 bar of back pressure was calculated by taking mean of last nine trials of L27 combinations and so on for other factors. In other words, S/N ratio corresponding to that level of a factor was calculated by taking the mean value of all those trials containing that level.

Table 3. Mean S/N ratios for each level of factors

Factors Level 1 Level 2 Level 3

Back pressure -15.7278 -14.9360 -14.3573

Cell temperature -14.9056 -15.0009 -15.1147

GDL porosity -15.0931 -14.9440 -14.9842

Flow channel dimensions -14.7160 -15.2265 -15.0788

Cathode water content -14.7072 -14.9670 -15.3470

Electrode thickness -15.0254 -14.9944 -15.0015

GDL thickness -14.9227 -15.0122 -15.0862

Rib width -15.0149 -15.0054 -15.0009

Anode inlet velocity -14.9780 -14.9954 -15.0478

Cathode inlet velocity -15.1885 -14.9369 -14.8958

The S/N ratio plot for the same were deduced and the level with maximum S/N ratio gives better performance as the analysis is based on "Larger the Better". As shown in the Fig. 1(a), the back pressure with level 3 gives better performance. Thus 1.5 bar was considered to be the optimum back pressure. It was clear from the figure that the effect of back pressure was significant due to the S/N ratio. Fig. 1(b) infers that the cell temperature with level 1 gives better performance. Thus 303 K was considered to be the optimum cell temperature. Fig. 2(a) shows that the GDL porosity with level 2 gives better performance. Thus 60% was considered to be the optimum GDL porosity. From Fig. 2(b), it was inferred that the flow channel dimensions with level 1 give better performance. Thus, 1 mm x 1mm was considered to be the optimum flow channel dimensions (depth and width).

Fig. 1. S/N ratio plot for (a) back pressure; (b) temperature.

As shown in the Fig. 3(a), the cathode inlet water content with level 1 gives enhanced performance. Thus, 10% was considered to be the optimum cathode inlet water content. From Fig. 3(b), it was inferred that, though there was no significant effect on the performance of fuel cell, the electrode thickness with level 3 gives enhanced performance. Thus, 70 microns was considered to be the optimum porous electrode thickness. Fig. 4 (a) infers that the GDL thickness with level 1 gives enhanced performance. Thus, 250 microns was considered to be the optimum GDL thickness. Its effect on performance of fuel cell was moderate. From Fig. 4 (b), it was inferred that there is no effect for rib width on performance of fuel cell. But when observed at the accurate level, it was found that 1.8 mm rib width gives enhanced performance. Fig. 5(a) shows that the anode velocity has no effect till 0.5 m/s. Then, the performance decreases. Thus, 0.5 m/s was considered to be the optimum anode inlet velocity. Fig. 5(b) infers that the cathode inlet velocity with level 3 gives enhanced performance. Thus, 1.2 m/s was considered to be the optimum cathode inlet velocity.

Anode inlet velocity

* -t-Senesl

Fig. 5. S/N ratio plot for (a) anode inlet velocity; (b) cathode inlet velocity.

The next step was to find the significance of each factor by ranking them according to their significance. The ranking was based on the delta value. Delta value was calculated as the difference of highest and lowest mean S/N ratio values of each factor from Table 3. The factor with highest delta value indicates higher significance. This analysis was performed in the MINITAB 16 software itself and the results were shown in Table 4. It was found that back pressure was the predominant factor affecting the performance of fuel cell. The other parameters influencing the output to a considerable extent were cathode inlet water content and flow channel dimensions. As shown in Fig. 1-5, back pressure affects the performance to the highest level. Factors such as flow channel dimensions, temperature and cathode inlet velocity have moderate effect on performance of fuel cell. But factors such as electrode thickness, anode inlet velocity and rib width had no significant effect on the performance of fuel cell.

Table 4. Significance of factors

Factors Delta Rank Factors Delta Rank

Back pressure 1.370 1 Electrode thickness 0.031 9

Cell temperature 0.209 5 GDL thickness 0.164 6

GDL porosity 0.149 7 Rib width 0.014 10

Flow channel 0.510 3 Anode inlet velocity 0.070 8

dimensions Cathode inlet 0.293 4

Cathode inlet water 0.640 2 velocity

content

3. Optimization of operating and design parameters:

The optimum operating and design parameters were found from Table 3. Generally, the factors which have least effect on the response would be pooled off and neglected for further analysis. But in this analysis, all the factors were considered irrespective of their significance to get accurate results with better performance on PEMFC. The level with highest S/N ratio was considered to be optimum level and optimum combination of operating and design parameters was found to be A3B1C2D1E1F2G1H3I2J3. The maximum power for this combination found using Taguchi calculation was 0.2148 W/cm2 as shown by equation (1).

S/N ratio for optimum combination, riopt = ti +AA3 +AB1+AC2+AD1+AE1+AF2+AG1 + AH3+AI2+AJ3 (1)

(AA3 corresponds to the difference of overall S/N ratio mean and S/N ratio mean corresponding to level 3 of factor A in Table 3 and so on; T| corresponds to overall mean of S/N ratio in Table 2)

T|opt = -15.0071 + 0.649764 + 0.10149 + 0.063139 + 0.291131 + 0.299865 + 0.01272 + 0.084373 + 0.006184 + 0.029062 + 0.111326 = -13.358 = -10log10(1/Pmax2) Pmax = 0.2148 W/cm2

In order to validate this, the optimum combination of parameters was given as input to COMSOL and the power density was found to be 0.218 W/cm2. This was in close agreement with power density obtained from Taguchi calculation with a percentage of deviation of 1.5. Thus, through the methodology developed, the single channel PEMFC gives best performance when operated at back pressure of 1.5 bar, cell temperature of 303 K, GDL porosity of 60%, flow channel's depth and width of 1mm x 1mm, rib width of 1.8 mm, electrode thickness of 60 microns, GDL thickness of 250 microns, anode and cathode inlet velocities of 0.5 m/s and 1.2 m/s respectively, and cathode inlet water content of 10%.

4. Refinement of coarsely optimized parameters

As the levels chosen for first stage of analysis covered full possible range of operating parameters, the levels obtained as optimum were not considered to be accurate. Thus, further optimization was required to find the optimized parameters close to actual value. Out of the ten parameters, optimum levels corresponding to temperature, GDL thickness, inlet cathode water content and GDL porosity were considered to be relatively less accurate due to their wide operating range and rib width and electrode thickness had least significance. So, second stage of Taguchi analysis was performed for four parameters alone with standard L9 orthogonal array with three different levels. These levels were chosen close to the optimum levels found in the first stage to refine them as shown in Table 5. All the nine combinations were run by keeping all the other six factors constant, with optimum levels found in the first stage.

Table 5. Factors and levels for second stage of analysis

Factors Level 1 Level 2 Level 3

Cell temperature 298 303 313

GDL thickness 235 250 275

Cathode inlet water content 5 10 15

GDL porosity 55 60 65

Thus, giving nine combinations as input to software, the maximum power was obtained from the polarisation curve for each trial. The combinations were based on standard L9 orthogonal array. The power density and S/N ratio values were shown in Table 6. As stated earlier, the S/N ratio was calculated using the formula -10 log10(1/P2), where 'P' is the power density.

Table 6. Power density and S/N ratio of fine tuned parameters for 9 runs

Trial Power density S/N ratio Trial Power density S/N ratio

1 0.220715 -13.1234 6 0.218845 -13.1973

2 0.219010 -13.1907 7 0.215160 -13.3448

3 0.216810 -13.2784 8 0.218213 -13.2224

4 0.218900 -13.1951 9 0.214995 -13.3514

5 0.216040 -13.3093

Using these S/N ratio values, the mean of the S/N ratios for each level of all four factors were calculated and presented in Table 7. It was calculated by estimating mean of the S/N ratios of all the trials corresponding to that level of the factor. For example, mean of S/N ratio corresponding to 298 K of temperature was calculated by taking mean of first three trials of L9 combinations, mean of S/N ratio corresponding to 313 K of temperature was calculated by taking mean of last three trials of L9 combinations and so on for other factors. In other words, S/N ratio corresponding to that level of a factor was calculated by taking the mean value of all those trials containing that level.

P. Karthikeyan et al. /Procedia Engineering 64 (2013) 409 - 418 Table 7. Factors and levels for second stage of analysis

Factors Level 1 Level 2 Level 3

Cell temperature -13.197 -13.233 -13.306

GDL thickness -13.221 -13.240 -13.275

Cathode water content -13.181 -13.245 -13.310

GDL porosity -13.261 -13.244 -13.232

After completing analysis in software, S/N ratio plots for the same were deduced. These plots were used for optimization. The level with highest S/N ratio was considered as the optimum value. The plots were derived for "Larger the Better". Plots for S/N ratio were generated using MINITAB 16 as explained in section 3. It was found that A1B1C1D3 was the optimum level with highest S/N ratio. Thus, the refined optimized parameters were found to be cell temperature of 298 K, cathode inlet water content of 5%, GDL porosity of 65% and GDL thickness of 235 microns. As this analysis was concerned with the fine tune of optimized parameters, ranking of parameters according to their significance was not carried out. As per the calculations from equation (2), maximum power density for this optimum combination was found to be 0.2214 W/cm2.

S/N ratio for optimum combination, T|opt = T| + AA1 + AB1 + AC1 + AD3 (2)

(AA1 corresponds to the difference of overall S/N ratio mean and S/N ratio mean corresponding to level 1 of factor A in Table 7 and so on; T| corresponds to overall mean of S/N ratio in Table 6)

Hopt = -13.2459 + 0.048401 + 0.024828 + 0.064887 + 0.013931 = -13.0938 = -10log10(1/Pmax2) Pmax = 0.2214 W/cm2

When the refined optimum combination for four factors was given to the CFD software as input with all the other six factors same as found in first stage, the maximum power found from polarisation curve was 0.22143 W/cm2. The deviation in result was 0.01% indicating that Taguchi results were in good agreement with software results. Hence, it is proved here that by increasing the number of levels through the usage of two-stage optimization, the error is getting reduced. Hence, it means that the model is determining the results to a more accurate level. Thus the refined optimized combination of input parameters was found to be back pressure of 1.5 bar, cell temperature of 298 K, GDL porosity of 65%, channel's depth and width of 1mm x 1mm, rib width of 1.8 mm, porous electrode thickness of 60 microns, GDL thickness of 235 microns, anode inlet velocity of 0.5 m/s, cathode inlet velocity of 1.2 m/s and inlet water content in cathode of 5%. On refining the parameters to a more accurate level, the power density increased by 3%. When cell temperature is higher than humidification temperature, the performance of the PEMFC decreases [8]. As the anode and cathode humidification temperatures in this analysis is low (293 K) corresponding to cell temperature, 298 K gives better performance.

5. Inferences

• Refinement of optimized parameters yielded improved performance of fuel cell. More number of stages of optimization with refinement yields high accuracy results.

• Refining yielded 3% increase in power density. Also, deviation error decreased from 1.5% to 0.01%.

• More number of factors (>6) with high level design (>5) can be analyzed with a multi stage optimization of parameters using Taguchi method.

• Combined effect of all the parameters showed a different response compared to their individual effects.

• The effect of operating parameters affected the performance of fuel cell more significantly than the flow channel dimensions.

• The maximum power density corresponding to Taguchi calculations was in good agreement to those software results indicating the compatibility of Taguchi method for fuel cell application [14].

6. Future Scope

This work enables the analysis of more number of factors with accuracy in optimization of factors. Also Taguchi method proved to be one of the best tools for optimization. Thus, fine tuned optimization with Taguchi method is a new technique which gives better performance of fuel cell as compared to conventional optimization. This work also proved the compatibility of Taguchi method for fuel cell application and hence refined optimization can also be applied to experiments. Taguchi method when applied to experiments with fine tuned optimization is expected to give better results. In real time applications, fuel cell must be worked with these optimum design and operating parameters to get enhanced performance.

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