- freely available
Sensors 2009, 9(11), 9104-9121; doi:10.3390/s91109104
2. Numerical Models
2.1. Model Assumptions
- The gas mixture is incompressible, ideal fluid;
- The flow in the flow channel is laminar (Reynolds number <900 at anode and cathode relative humidity 100%);
- Isothermal condition;
- Butler-Volmer kinetics for electrochemical reaction rate.
2.2. Governing Equations
- Mass conservation equation:
- Momentum conservation equationThe fluid flow in the fuel cell can be described by the general equation as:
- Species conservation equationThe species conservation equation for the gas mixture is:Here, k denotes chemical species that include hydrogen, oxygen, nitrogen and water. is the effective diffusion coefficient. Source term Sk denotes:
2.3. Water Transport Equation
- Electro-osmotic drag fluxElectro-osmotic water flux through the membrane can be calculated from the proton flux through the membrane, given by the specified current density and Faraday's law:
- Back diffusion fluxThe water formation at the cathode results in a gradient in the water content between the cathode side and anode side of the membrane. For PEMFC, this gradient causes a water flux back to the anode side which is superimposed to the electro-osmotic flux. This back diffusion is expressed as following water flux:Dw is water diffusion coefficient which is strongly dependent on water content as follows:
- Current density and membrane ion ConductivityI(x,y,z) is current density generated by electrochemical reaction, which can be expressed as:
2.4. Numerical Simulation Model
- The computed polarization curve is in good agreement with the experimental polarization curve at low and moderate current density. At high current density, the effects of two phase flow should be considered.
- The oxygen and water concentration on the centerline surface of the micro parallel channel and gas diffusion layer under different relative humidity at cathode side was changed greatly due to electrochemical reaction and electro osmotic drag and back diffusion.
- The highest average current density was noticeable at 100% humidity at the anode side and at 60% humidity at the cathode side. Although the hydrogen ion can smoothly move from the anode side to the cathode side due to high ion conductivity in the membrane from 100% humidity at anode and the cathode relative humidity, the performance of fuel cell was not expected to be best because of the increased water concentration at cathode side resulting to the decreased oxygen concentration at cathode side.
- It is found that there is trade-off between performance gain by increase of high ion conductivity due to high humidity and performance loss by reduction of oxygen due to high water concentration by electro osmotic drag and back diffusion in order to make best performance of fuel cell.
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|Channel length (mm) (mm)||40||Anode, Cathode side pressure (atm)||1|
|Channel width (μm)||762||Cell temperature (K)||353.15|
|Channel height (μm)||762||Anode stoichiometric number||1.5|
|GDL thickness (μm)||254||Cathode stoichiometric number||2.0|
|GDL porosity||0.7||O2/N2 ratio||0.21/0.79|
|Wet Membrane thickness (μm)||230||Anode side Humidification (%)||100|
|Catalyst layer thickness (μm)||28.7||Cathode side Humidification (%)||0-100|
|Experimental MEA Parameters|
|Membrane||Nafion 117||Pt catalyst loading (mg/cm2)||0.4|
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