Numerical Simulation on Impacts of Thickness of Nafion Series Membranes and Relative Humidity on PEMFC Operated at 363 K and 373 K
Abstract
:1. Introduction
2. Numerical Modeling
2.1. Model Description and Governing Equations
2.2. Model Assumption
- (i)
- The distributions of the inlet gas flow rate at the anode side and cathode side are uniform, respectively.
- (ii)
- The pressure of the outlet of the gas channel is the atmospheric pressure.
- (iii)
- No slip on the gas channel wall excluding the inlet and the outlet of the gas channel is considered.
- (iv)
- The cell voltage obtained by the power generation experiment is set at the cathode electrode and the earth ground is set at the anode electrode. The in-plane distribution of cell voltage at the cathode electrode is uniform.
- (v)
- Reactant gases are treated as an ideal gas and incompressible Newton fluid.
- (vi)
- H2O is treated as a vapor.
- (vii)
- The cell temperature is uniform and the outside boundary of the 3D model is set at Tini.
- (viii)
- The effective porosity and the permeability of the porous media are isotropic. The conductivity in the porous media is also isotropic.
3. Results and Discussion
3.1. In-Plane Distribution of Mass and Current Density on the Interface between Nafion Membrane and Anode Catalyst Layer or the Interface between Nafion Membrane and Cathode Catalyst Layer
3.2. Quantitative Evaluation along with the Gas Flow through the Gas Channel on Mass and Current Density on the Interface between Nafion Membrane and Cathode Catalyst Layer
4. Conclusions
- (i).
- The molar concentration of H2 and O2 decreases along with the gas flow through the gas channel, irrespective of the Nafion membrane thickness and Tini.
- (ii).
- The O2 consumption in the fuel cell is the largest at Tini = 353 K, irrespective of Nafion membrane thickness.
- (iii).
- The molar concentration of H2O increases along with the gas flow through the gas channel, irrespective of the Nafion membrane thickness and Tini, which can be explained by the O2 reduction reaction at cathode.
- (iv).
- The current density decreases along with the gas flow through the gas channel, irrespective of Nafion membrane thickness and Tini. The current density is the largest at Tini = 353 K, irrespective of the Nafion membrane thickness.
- (v).
- The molar concentration of H2O increases when the relative humidity of the supply gas increases, irrespective of the Nafion membrane thickness and Tini. The molar concentration of H2O is the largest with A80%RH&C80% RH, while it is the smallest with A40%RH&C40%RH.
- (vi).
- The molar concentration of H2O generally decreases when the thickness of the Nafion membrane increases. The molar concentration of H2O for Nafion 115, whose thickness is 127 μm, is much smaller than that for the other thin Nafion membranes.
- (vii).
- It is revealed that the largest molar concentration of H2O is 15.1 mol/m3 near the outlet in the case of using Nafion NRE-211 at Tini = 353 K with A80%RH&C80%RH among the conditions investigated in this study.
- (viii).
- The current density is the highest at Tini = 353 K.
- (ix).
- The current density increases when the relative humidity of the supply gas increases, irrespective of the Nafion membrane thickness and Tini, which indicates that the power generation performance is enhanced with the increase in relative humidity due to the promotion of proton conductivity of the Nafion membrane.
- (x).
- The current density increases with the decrease in the Nafion membrane thickness since the H2O flux of the Nafion membrane as well as the conductivity of the Nafion membrane is promoted with the thinner Nafion membrane.
- (xi).
- It is revealed that the largest current density is 0.336 A/mm2 near the inlet in the case of using Nafion NRE-211 at Tini = 353 K with A80%RH&C80%RH among the conditions investigated in this study.
- (xii).
- This study reveals that the thinner Nafion membrane under well-humidified conditions is more desirable to obtain a higher power generation performance at higher temperatures, i.e., 363 K and 373 K. Thinner Nafion membranes can provide a uniform distribution of current density as well.
- (xiii).
- Since the current density at high temperatures of 363 K and 373 K, which are 0.237 A/mm2 and 0.107 A/mm2, respectively, is still low, even using Nafion NRE-211 with A80%RH&C80%RH, this study suggests the optimization of catalyst layer, MPL, and gas channel flow of gas separator in order to control the mass and heat transfer phenomena as well as to improve the electrochemical reaction.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Components | Size | Characteristics |
---|---|---|
PEM | 50.0 mm × 50.0 mm × 0.127 mm (for Nafion 115), 0.051 mm (for Nafion NRE-212) and 0.025 mm (for Nafion NRE-211) | Nafion 115, Nafion NRE-212, Nafion NRE-211 (manufactured by Du Pont Corp.) |
Catalyst layer | 50.0 mm × 50.0 mm × 0.01 mm | Pt/C (Pt: 20 wt%) |
MPL | 50.0 mm × 50.0 mm × 0.003 mm | PTFE + carbon black |
GDL | 50.0 mm × 50.0 mm × 0.19 mm | TGP-H-060 (manufactured by Toray Corp.) |
Gas separator | 50.0 mm × 50.0 mm × 2.00 mm (thickness of rib: 1.00 mm) (width of gas channel and rib: 1.0 mm, thickness of gas channel: 1.0 mm) | Carbon graphite, serpentine |
Parameter Name | Value |
---|---|
Density of H2 (kg/m3) | 7.10 × 10−2 (353 K), 6.89 × 10−2 (363 K), 6.69 × 10−2 (373 K) [32] |
Density of O2 (kg/m3) | 1.11 (353 K), 1.08 (363 K), 1.05 (373 K) [32] |
Density of H2O (kg/m3) | 2.95 × 10−1 (353 K), 4.26 × 10−1 (363 K), 6.01 × 10−1 (373 K) [32] |
Viscosity of H2 (Pa s) | 9.96 × 10−6 (353 K), 1.02 × 10−5 (363 K), 1.03 × 10−5 (373 K) [32] |
Viscosity of O2 (Pa s) | 2.35 × 10−5 (353 K), 2.40 × 10−5 (363 K), 2.45 × 10−5 (373 K) [32] |
Viscosity of H2O (Pa s) | 1.16 × 10−5 (353 K), 1.19 × 10−5 (363 K), 1.23 × 10−5 (373 K) [32] |
Binary diffusion coefficient between H2 and H2O (m2/s) | 9.27 × 10−5 [33] |
Binary diffusion coefficient between O2 and H2O (m2/s) | 3.57 × 10−5 [33] |
Porosity of catalyst layer ( ) | 0.78 [17,22,29,30,31] |
Permeability of catalyst layer (m2) | 8.69 × 10−12 [17,22,29,30,31] |
Porosity of MPL ( ) | 0.60 [17,22,29,30,31] |
Permeability of MPL (m2) | 1.00 × 10−13 [17,22,29,30,31] |
Porosity of GDL ( ) | 0.78 [17,22,29,30,31] |
Permeability of GDL (m2) | 8.69 × 10−12 [17,22,29,30,31] |
Conductivity of Nafion series membrane (S/m) | 10 [34] |
Conductivity of catalyst layer (S/m) | 53 [35] |
Conductivity of MPL (S/m) | 1000 [36] |
Conductivity of GDL (S/m) | 1250 [37] |
Anode reference equilibrium potential (V) | 0 |
Cathode reference equilibrium potential (V) | 1.229 |
Anode reference exchange current density (A/m2) | 1000 [38] |
Cathode reference exchange current density (A/m2) | 1 [38] |
Anode charge transfer coefficient ( ) | 0.5 [39] |
Cathode charge transfer coefficient ( ) | 0.5 [40] |
Each Condition | Value | |
---|---|---|
The initial temperature of cell (Tini) (K) | 353, 363, 373 | |
Cell voltage (V) | Experimental data are used [16,17] | |
Supply gas condition | ||
Anode | Cathode | |
Gas type | H2 | O2 |
Temperature of supply gas at inlet (K) | 353, 363, 373 | 353, 363, 373 |
Relative humidity of supply gas (%RH) | 40, 80 | 40, 80 |
Pressure of supply gas at inlet (absolute) (MPa) | 0.4 | 0.4 |
Flow rate of supply gas at inlet [NL/min] (Stoichiometric ratio ( )) | 0.210 (1.5) | 0.105 (1.5) |
A | B | C | D | E | F | G | H | I | J | K | |
---|---|---|---|---|---|---|---|---|---|---|---|
353 K | |||||||||||
115 | 0.721 | 2.07 | 3.14 | 4.27 | 5.22 | 6.25 | 7.12 | 8.05 | 8.85 | 9.61 | 10.3 |
212 | 0.793 | 2.87 | 4.46 | 6.10 | 7.46 | 8.88 | 10.1 | 11.3 | 12.4 | 13.3 | 14.2 |
211 | 0.813 | 3.08 | 4.81 | 6.57 | 8.02 | 9.53 | 10.8 | 12.1 | 13.2 | 14.2 | 15.1 |
363 K | |||||||||||
115 | 0.955 | 2.23 | 3.23 | 4.28 | 5.18 | 6.13 | 6.96 | 7.84 | 8.59 | 9.31 | 9.93 |
212 | 0.979 | 2.49 | 3.67 | 4.89 | 5.92 | 7.02 | 7.96 | 8.94 | 9.78 | 10.6 | 11.3 |
211 | 0.981 | 2.51 | 3.70 | 4.93 | 5.97 | 7.08 | 8.02 | 9.01 | 9.85 | 10.6 | 11.3 |
373 K | |||||||||||
115 | 1.17 | 1.58 | 1.91 | 2.27 | 2.58 | 2.93 | 3.23 | 3.56 | 3.85 | 4.13 | 4.38 |
212 | 1.19 | 1.77 | 2.24 | 2.74 | 3.17 | 3.65 | 4.06 | 4.52 | 4.91 | 5.29 | 5.63 |
211 | 1.20 | 1.86 | 2.39 | 2.95 | 3.45 | 3.98 | 4.45 | 4.95 | 5.40 | 5.82 | 6.20 |
A | B | C | D | E | F | G | H | I | J | K | |
---|---|---|---|---|---|---|---|---|---|---|---|
353 K | |||||||||||
115 | 0.425 | 1.68 | 2.68 | 3.73 | 4.62 | 5.59 | 6.41 | 7.30 | 8.05 | 8.77 | 9.40 |
212 | 0.477 | 2.28 | 3.68 | 5.13 | 6.35 | 7.63 | 8.71 | 9.85 | 10.8 | 11.7 | 12.5 |
211 | 0.492 | 2.44 | 3.96 | 5.52 | 6.81 | 8.17 | 9.31 | 10.5 | 11.5 | 12.5 | 13.3 |
363 K | |||||||||||
115 | 0.527 | 1.46 | 2.21 | 3.01 | 3.69 | 4.44 | 5.07 | 5.77 | 6.36 | 6.94 | 7.44 |
212 | 0.557 | 1.80 | 2.78 | 3.81 | 4.68 | 5.63 | 6.43 | 7.29 | 8.02 | 8.72 | 9.33 |
211 | 0.575 | 2.00 | 3.12 | 4.28 | 5.27 | 6.32 | 7.21 | 8.16 | 8.97 | 9.73 | 10.4 |
373 K | |||||||||||
115 | 0.644 | 1.02 | 1.33 | 1.66 | 1.95 | 2.28 | 2.56 | 2.87 | 3.14 | 3.40 | 3.64 |
212 | 0.664 | 1.25 | 1.72 | 2.23 | 2.67 | 3.16 | 3.57 | 4.03 | 4.43 | 4.82 | 5.16 |
211 | 0.675 | 1.37 | 1.92 | 2.52 | 3.15 | 3.60 | 4.08 | 4.61 | 5.07 | 5.51 | 5.91 |
A | B | C | D | E | F | G | H | I | J | K | |
---|---|---|---|---|---|---|---|---|---|---|---|
353 K | |||||||||||
115 | 0.706 | 1.91 | 2.86 | 3.87 | 4.73 | 5.67 | 6.46 | 7.31 | 8.05 | 8.74 | 9.36 |
212 | 0.758 | 2.49 | 3.83 | 5.23 | 6.40 | 7.64 | 8.69 | 9.79 | 10.7 | 11.6 | 12.4 |
211 | 0.773 | 2.65 | 4.10 | 5.60 | 6.85 | 8.17 | 9.27 | 10.4 | 11.4 | 12.3 | 13.1 |
363 K | |||||||||||
115 | 0.915 | 1.80 | 2.51 | 3.26 | 3.91 | 4.62 | 5.23 | 5.89 | 6.46 | 7.01 | 7.49 |
212 | 0.945 | 2.12 | 3.05 | 4.03 | 4.86 | 5.76 | 6.53 | 7.35 | 8.06 | 8.73 | 9.32 |
211 | 0.954 | 2.21 | 3.21 | 4.25 | 5.13 | 6.08 | 6.89 | 7.76 | 8.50 | 9.20 | 9.82 |
373 K | |||||||||||
115 | 1.16 | 1.41 | 1.62 | 1.85 | 2.05 | 2.27 | 2.46 | 2.68 | 2.87 | 3.05 | 3.22 |
212 | 1.18 | 1.70 | 2.11 | 2.55 | 2.94 | 3.37 | 3.74 | 4.15 | 4.50 | 4.85 | 5.15 |
211 | 1.19 | 1.80 | 2.28 | 2.81 | 3.26 | 3.76 | 4.19 | 4.66 | 5.07 | 5.46 | 5.82 |
A | B | C | D | E | F | G | H | I | J | K | |
---|---|---|---|---|---|---|---|---|---|---|---|
353 K | |||||||||||
115 | 0.368 | 1.01 | 1.54 | 2.11 | 2.59 | 3.13 | 3.60 | 4.11 | 4.56 | 4.99 | 5.37 |
212 | 0.438 | 1.83 | 2.93 | 4.09 | 5.06 | 6.12 | 7.00 | 7.96 | 8.77 | 9.53 | 10.2 |
211 | 0.453 | 2.00 | 3.22 | 4.50 | 5.56 | 6.71 | 7.67 | 8.70 | 9.57 | 10.4 | 11.1 |
363 K | |||||||||||
115 | 0.464 | 0.727 | 0.944 | 1.18 | 1.39 | 1.62 | 1.82 | 2.04 | 2.24 | 2.43 | 2.60 |
212 | 0.529 | 1.09 | 2.25 | 3.06 | 3.75 | 4.51 | 5.16 | 5.86 | 6.47 | 7.05 | 7.55 |
211 | 0.539 | 1.59 | 2.43 | 3.32 | 4.08 | 4.90 | 5.61 | 6.37 | 7.02 | 7.64 | 8.18 |
373 K | |||||||||||
115 | 0.615 | 0.693 | 0.757 | 0.828 | 0.890 | 0.960 | 1.02 | 1.09 | 1.15 | 1.21 | 1.26 |
212 | 0.650 | 1.09 | 1.45 | 1.84 | 2.18 | 2.56 | 2.88 | 3.24 | 3.55 | 3.86 | 4.13 |
211 | 0.657 | 1.16 | 1.57 | 2.01 | 2.40 | 2.82 | 3.19 | 3.60 | 3.90 | 4.29 | 4.59 |
A | B | C | D | E | F | G | H | I | J | K | |
---|---|---|---|---|---|---|---|---|---|---|---|
353 K | |||||||||||
115 | 0.197 | 0.194 | 0.192 | 0.190 | 0.187 | 0.185 | 0.182 | 0.180 | 0.178 | 0.175 | 0.173 |
212 | 0.307 | 0.300 | 0.293 | 0.289 | 0.281 | 0.277 | 0.270 | 0.265 | 0.259 | 0.254 | 0.250 |
211 | 0.336 | 0.328 | 0.320 | 0.314 | 0.305 | 0.299 | 0.291 | 0.286 | 0.277 | 0.272 | 0.266 |
363 K | |||||||||||
115 | 0.197 | 0.193 | 0.191 | 0.189 | 0.186 | 0.184 | 0.181 | 0.179 | 0.176 | 0.174 | 0.172 |
212 | 0.234 | 0.230 | 0.226 | 0.223 | 0.218 | 0.215 | 0.211 | 0.208 | 0.204 | 0.200 | 0.198 |
211 | 0.237 | 0.232 | 0.228 | 0.225 | 0.220 | 0.217 | 0.212 | 0.209 | 0.205 | 0.201 | 0.198 |
373 K | |||||||||||
115 | 0.066 | 0.065 | 0.065 | 0.065 | 0.064 | 0.064 | 0.063 | 0.063 | 0.062 | 0.062 | 0.062 |
212 | 0.094 | 0.093 | 0.092 | 0.092 | 0.091 | 0.090 | 0.089 | 0.088 | 0.088 | 0.087 | 0.086 |
211 | 0.107 | 0.106 | 0.105 | 0.104 | 0.103 | 0.102 | 0.101 | 0.100 | 0.099 | 0.098 | 0.097 |
A | B | C | D | E | F | G | H | I | J | K | |
---|---|---|---|---|---|---|---|---|---|---|---|
353 K | |||||||||||
115 | 0.175 | 0.172 | 0.170 | 0.168 | 0.166 | 0.164 | 0.162 | 0.160 | 0.158 | 0.156 | 0.154 |
212 | 0.253 | 0.248 | 0.244 | 0.240 | 0.235 | 0.231 | 0.226 | 0.223 | 0.218 | 0.214 | 0.211 |
211 | 0.276 | 0.270 | 0.246 | 0.260 | 0.253 | 0.249 | 0.243 | 0.239 | 0.233 | 0.229 | 0.225 |
363 K | |||||||||||
115 | 0.135 | 0.133 | 0.132 | 0.131 | 0.129 | 0.128 | 0.127 | 0.125 | 0.124 | 0.123 | 0.122 |
212 | 0.180 | 0.178 | 0.175 | 0.173 | 0.170 | 0.168 | 0.165 | 0.163 | 0.160 | 0.158 | 0.156 |
211 | 0.208 | 0.204 | 0.201 | 0.198 | 0.194 | 0.191 | 0.187 | 0.185 | 0.181 | 0.178 | 0.176 |
373 K | |||||||||||
115 | 0.057 | 0.056 | 0.056 | 0.055 | 0.055 | 0.055 | 0.054 | 0.054 | 0.054 | 0.053 | 0.053 |
212 | 0.088 | 0.087 | 0.086 | 0.086 | 0.085 | 0.084 | 0.083 | 0.083 | 0.082 | 0.081 | 0.081 |
211 | 0.104 | 0.103 | 0.102 | 0.101 | 0.100 | 0.099 | 0.098 | 0.097 | 0.096 | 0.095 | 0.094 |
A | B | C | D | E | F | G | H | I | J | K | |
---|---|---|---|---|---|---|---|---|---|---|---|
353 K | |||||||||||
115 | 0.175 | 0.173 | 0.171 | 0.169 | 0.167 | 0.165 | 0.163 | 0.161 | 0.159 | 0.157 | 0.155 |
212 | 0.254 | 0.249 | 0.245 | 0.241 | 0.236 | 0.233 | 0.228 | 0.225 | 0.220 | 0.216 | 0.213 |
211 | 0.277 | 0.270 | 0.265 | 0.261 | 0.255 | 0.251 | 0.245 | 0.241 | 0.235 | 0.231 | 0.227 |
363 K | |||||||||||
115 | 0.136 | 0.134 | 0.133 | 0.132 | 0.130 | 0.132 | 0.128 | 0.127 | 0.125 | 0.124 | 0.123 |
212 | 0.181 | 0.178 | 0.176 | 0.174 | 0.171 | 0.170 | 0.167 | 0.165 | 0.162 | 0.160 | 0.159 |
211 | 0.195 | 0.192 | 0.189 | 0.187 | 0.183 | 0.181 | 0.178 | 0.176 | 0.173 | 0.170 | 0.168 |
373 K | |||||||||||
115 | 0.041 | 0.041 | 0.041 | 0.041 | 0.040 | 0.040 | 0.040 | 0.040 | 0.039 | 0.039 | 0.039 |
212 | 0.083 | 0.082 | 0.082 | 0.081 | 0.080 | 0.080 | 0.079 | 0.079 | 0.078 | 0.077 | 0.077 |
211 | 0.098 | 0.097 | 0.096 | 0.096 | 0.095 | 0.094 | 0.093 | 0.092 | 0.091 | 0.091 | 0.090 |
A | B | C | D | E | F | G | H | I | J | K | |
---|---|---|---|---|---|---|---|---|---|---|---|
353 K | |||||||||||
115 | 0.089 | 0.088 | 0.088 | 0.087 | 0.086 | 0.086 | 0.085 | 0.085 | 0.084 | 0.083 | 0.083 |
212 | 0.195 | 0.191 | 0.189 | 0.186 | 0.183 | 0.181 | 0.178 | 0.176 | 0.173 | 0.170 | 0.168 |
211 | 0.218 | 0.214 | 0.210 | 0.207 | 0.203 | 0.200 | 0.196 | 0.194 | 0.190 | 0.190 | 0.184 |
363 K | |||||||||||
115 | 0.038 | 0.037 | 0.037 | 0.037 | 0.037 | 0.037 | 0.037 | 0.036 | 0.036 | 0.036 | 0.036 |
212 | 0.138 | 0.136 | 0.135 | 0.133 | 0.132 | 0.130 | 0.129 | 0.128 | 0.126 | 0.125 | 0.123 |
211 | 0.153 | 0.151 | 0.149 | 0.147 | 0.145 | 0.143 | 0.141 | 0.140 | 0.138 | 0.136 | 0.135 |
373 K | |||||||||||
115 | 0.012 | 0.012 | 0.012 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 | 0.011 |
212 | 0.066 | 0.066 | 0.065 | 0.065 | 0.064 | 0.064 | 0.064 | 0.063 | 0.062 | 0.062 | 0.062 |
211 | 0.076 | 0.075 | 0.075 | 0.074 | 0.074 | 0.073 | 0.072 | 0.072 | 0.072 | 0.071 | 0.070 |
A80%RH&C80%RH | |||||||||
Tini [K] | 353 | 363 | 373 | ||||||
Nafion type | 115 | 212 | 211 | 115 | 212 | 211 | 115 | 212 | 211 |
Voltage [V] | 0.581 | 0.631 | 0.636 | 0.601 | 0.611 | 0.606 | 0.461 | 0.501 | 0.516 |
A80%RH&C40%RH | |||||||||
Tini [K] | 353 | 363 | 373 | ||||||
Nafion type | 115 | 212 | 211 | 115 | 212 | 211 | 115 | 212 | 211 |
Voltage [V] | 0.561 | 0.601 | 0.606 | 0.541 | 0.571 | 0.586 | 0.441 | 0.481 | 0.511 |
A40%RH&C80%RH | |||||||||
Tini [K] | 353 | 363 | 373 | ||||||
Nafion type | 115 | 212 | 211 | 115 | 212 | 211 | 115 | 212 | 211 |
Voltage [V] | 0.561 | 0.601 | 0.606 | 0.541 | 0.571 | 0.576 | 0.401 | 0.481 | 0.501 |
A40%RH&C40%RH | |||||||||
Tini [K] | 353 | 363 | 373 | ||||||
Nafion type | 115 | 212 | 211 | 115 | 212 | 211 | 115 | 212 | 211 |
Voltage [V] | 0.461 | 0.561 | 0.571 | 0.371 | 0.531 | 0.541 | 0.291 | 0.451 | 0.466 |
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Nishimura, A.; Toyoda, K.; Kojima, Y.; Ito, S.; Hu, E. Numerical Simulation on Impacts of Thickness of Nafion Series Membranes and Relative Humidity on PEMFC Operated at 363 K and 373 K. Energies 2021, 14, 8256. https://doi.org/10.3390/en14248256
Nishimura A, Toyoda K, Kojima Y, Ito S, Hu E. Numerical Simulation on Impacts of Thickness of Nafion Series Membranes and Relative Humidity on PEMFC Operated at 363 K and 373 K. Energies. 2021; 14(24):8256. https://doi.org/10.3390/en14248256
Chicago/Turabian StyleNishimura, Akira, Kyohei Toyoda, Yuya Kojima, Syogo Ito, and Eric Hu. 2021. "Numerical Simulation on Impacts of Thickness of Nafion Series Membranes and Relative Humidity on PEMFC Operated at 363 K and 373 K" Energies 14, no. 24: 8256. https://doi.org/10.3390/en14248256