Analyzing and Modeling of Water Transport Phenomena in Open-Cathode Polymer Electrolyte Membrane Fuel Cell
Abstract
:1. Introduction
2. Mathematical Description
Electrochemical Model
3. Results
3.1. Gas Diffusion Layer
3.2. Catalyst Layers
3.3. Water Transport in Membrane
3.4. Source Terms
3.5. Boundary Conditions and Initial Values
4. Mathematical Description
5. Results and Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Abbreviations | |
ACL | Anode catalyst layer |
CCL | Cathode catalyst layer |
CL | Catalyst layer |
EW | Equivalent weight |
GC | Gas channel |
GDE | Gas-diffusion electrode |
GDL | Gas diffusion layer |
HOR | Hydrogen oxidation reaction |
MEA | Membrane-electrode assembly |
MPL | Microporous layer |
ORR | Oxygen reduction reaction |
PEM | Polymer electrolyte membrane |
PDE | Partial differential equation |
Symbols | |
C | Total interstitial gas concentration [mol/m3] |
Cv,an | Water concentration on the surface area of the membrane at the anode side [mol/m3] |
Cv,ca | Water concentration on the surface area of the membrane at the cathode side [mol/m3] |
Di | Diffusivity of O2, H2, and H2O in the gas mixture [m2/s] |
Di,ref | Diffusivity of i at reference conditions [m2/s] |
Dcl | Knudsen diffusion coefficient [m2/s] |
Dλ | Diffusion coefficient of dissolved water [m2/s] |
Dw | Water diffusion coefficient related to the water activity [m2/s] |
F | Faraday’s constant (96,485 C mol−1) |
Had | Water ab-/desorption enthalpy [J/mol] |
Hec | Evaporation/condensation enthalpy [J/mol] |
J | Flux [A/m2] |
L | Layer thickness [m] |
Mw | Molar mass of water [kg/mol] |
Mm,dry | Molar mass of water [kg/mol] |
Nelectro | The net transport water caused by electro-osmotic drag [mol/(s∙cm2)] |
Ndiffusion | The net transport water caused by back-diffusion [mol/(s∙cm2)] |
P | Absolute gas pressure [Pa] |
Pref | Reference pressure (1 atm, 101,325 Pa) |
Psat | Saturation water vapor pressure [Pa] |
Pa | Gas pressure in anode gas channel [Pa] |
Pc | Gas pressure in cathode gas channel [Pa] |
R | Gas constant (8.31446 J/mol K) |
RH | Relative gas humidity [–] |
RHa | Relative humidity in anode gas channel [–] |
RHc | Relative humidity in cathode gas channel [–] |
SH2O | Source term of hydrogen |
SO2 | Source term of oxygen |
Selectron | Source term of electrons |
Sproton | Source term of protons |
Swater | Source term of water |
Sλ | Dissolved water reaction rate [mol/m3s] |
ST | Heat source [W/m3] |
Sred | Reduced liquid water saturation [–] |
T | Absolute temperature [K] |
Tref | Reference temperature [K] |
Tst | Stack temperature [K] |
Ta | Temperature of anode plate and GC [K] |
Tc | Temperature of cathode plate and GC [K] |
U | Open voltage of single fuel cell [V] |
VW | Molar volume of liquid water [m3/mol] |
Vm | Acid equivalent volume of membrane [m3/mol] |
a | Active surface area density [1/m] |
alg | Liquid–gas interfacial area density prefactor [1/m] |
i | Electrochemical reaction rate [A/m3] |
i0 | Exchange current density [A/m2] |
ki | Water absorption/desorption transfer coefficient [m/s] |
ke | Water evaporation transfer coefficient [m/s] |
kc | Water condensation transfer coefficient [m/s] |
nd | Electro-osmotic drag coefficient |
Equivalent capillary radius [m] | |
s | Liquid water saturation [–] |
tm | Membrane thickness |
ΔE | Galvani potential difference [V] |
ΔE0 | Reversible potential difference [V] |
ΔG | Gibbs free energy difference [J/mol] |
ΔH | Enthalpy of formation of liquid water [J/mol] |
ΔSHOR | Hydrogen oxidation reaction entropy [J/mol K] |
ΔSORR | Oxygen reduction reaction entropy [J/mol K] |
Greek letters | |
αH2 | Mole fraction of hydrogen in dry fuel gas [–] |
αO2 | Mole fraction of oxygen in dry oxidant gas [–] |
β | Half-reaction symmetry factor [–] |
γi | Water evaporation/condensation rate [1/s] |
σe | Electric conductivity [S/m] |
σp | Protonic conductivity [S/m] |
εP | Porosity of the GDLs [–] |
η | Activation overpotential [V] |
κ | Hydraulic permeability [m2] |
λ | Ionomer water content [–] |
λan | Ionomer water content in anode [–] |
λca | Ionomer water content in cathode [–] |
λeq | Equilibrium ionomer water content [–] |
μ | Dynamic viscosity of liquid water [Pa s] |
ξ | Electro-osmotic drag coefficient [–] |
π | Ratio of circumference to diameter [–] |
ρm,dry | Dry density of membrane [kg m−3] |
ϕe | Electrode phase potential [V] |
ϕp | Electrolyte phase potential [V] |
Water vapor mole fraction [–] | |
Saturation water vapor mole fraction [–] | |
Hydrogen mole fraction in anode GC [–] | |
Water vapor mole fraction in anode GC [–] | |
Oxygen mole fraction in cathode GC [–] | |
Water vapor mole fraction in cathode GC [–] | |
ψ | Empirical coefficient |
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Description | Symbol | Flux Equation | Continuity Equation |
---|---|---|---|
Fourier’s heat conduction | |||
Water transport in ionomer | |||
Ohm’s law of electrons | |||
Ohm’s law of proton | |||
Fickian oxygen diffusion | |||
Fickian hydrogen diffusion | |||
Fickian water vapor diffusion | |||
Liquid water transport (Darcy’s law) |
Symbol | Explanation | AGDL&CGDL | ACL&CCL | PEM |
---|---|---|---|---|
L | Layer thickness | 160 μm | 10 μm | 25 μm |
Symbol | Explanation | Value |
---|---|---|
RHC | Relative humidity in cathode GC | 20% |
SC | Liquid saturation at CGDL/GC interface | 0.12 |
TA | Temperature of anode plate and GC | 60 °C |
TC | Temperature of cathode plate and GC | 58 °C |
αH2 | Hydrogen mole fraction in dry fuel gas | 1.00 |
αO2 | Oxygen mole fraction in dry oxidant gas | 0.21 |
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Yuan, W.-W.; Ou, K.; Jung, S.; Kim, Y.-B. Analyzing and Modeling of Water Transport Phenomena in Open-Cathode Polymer Electrolyte Membrane Fuel Cell. Appl. Sci. 2021, 11, 5964. https://doi.org/10.3390/app11135964
Yuan W-W, Ou K, Jung S, Kim Y-B. Analyzing and Modeling of Water Transport Phenomena in Open-Cathode Polymer Electrolyte Membrane Fuel Cell. Applied Sciences. 2021; 11(13):5964. https://doi.org/10.3390/app11135964
Chicago/Turabian StyleYuan, Wei-Wei, Kai Ou, Seunghun Jung, and Young-Bae Kim. 2021. "Analyzing and Modeling of Water Transport Phenomena in Open-Cathode Polymer Electrolyte Membrane Fuel Cell" Applied Sciences 11, no. 13: 5964. https://doi.org/10.3390/app11135964
APA StyleYuan, W. -W., Ou, K., Jung, S., & Kim, Y. -B. (2021). Analyzing and Modeling of Water Transport Phenomena in Open-Cathode Polymer Electrolyte Membrane Fuel Cell. Applied Sciences, 11(13), 5964. https://doi.org/10.3390/app11135964