Evaluating the Results
Compare the Polarization Curves
Modify the Polarization Curve as follows to compare the concentration independent and concentration dependent solutions.
1
In the Model Builder window, expand the Polarization Curve node, then click Probe Table Graph 1.
2
In the Settings window for Table Graph, type Probe Table Graph: Limited O2 gas phase transport in the Label text field.
3
Click to expand the Legends section. From the Legends list, choose Manual.
4
In the table, enter the following settings:
Legends
Limited O2 gas phase transport
5
Right-click Probe Table Graph: Limited O2 gas phase transport and choose Duplicate.
6
In the Settings window for Table Graph, type Probe Table Graph: Unlimited O2 gas phase transport in the Label text field.
7
Locate the Data section. From the Table list, choose Unlimited O2 gas phase transport.
8
Locate the Legends section. In the table, enter the following settings:
Legends
Unlimited O2 gas phase transport
9
In the Model Builder window, click Polarization Curve, and in the Polarization Curve toolbar, click  Plot.
Mole Fraction, O2, Streamline
The mole fractions of the different species are plotted by default at the cell potential of 0.5 V. Modify the O2 plots as follows to plot at the cell potential of 0.7 V.
1
In the Model Builder window, click Mole Fraction, O2, Streamline (fc).
2
In the Settings window for 3D Plot Group, locate the Data section.
3
From the Parameter value (E_cell (V)) list, choose 0.7.
Note the direction of the arrows. Oxygen flows from the inlet hole into the porous cathode to react to form water.
Mole Fraction, O2, Surface
1
In the Model Builder window, click Mole Fraction, O2, Surface (fc).
2
In the Settings window for 3D Plot Group, locate the Data section.
3
From the Parameter value (E_cell (V)) list, choose 0.7.
The oxygen mole fraction gets low far away from the inlet hole.
Pressure
The Darcy pressure with velocity streamlines is also plotted by default at the cell potential of 0.5 V. Modify as follows to plot at the cell potential of 0.7 V.
1
In the Model Builder window, click Pressure (fc).
2
In the Settings window for 3D Plot Group, locate the Data section.
3
From the Parameter value (E_cell (V)) list, choose 0.7.Click Plot.
The direction of the net velocity is toward the inlet hole, that is, opposite to the oxygen flux. This a result of the production of two water molecules per consumed oxygen molecule in the cathode.
Overpotential in Cathode
Finally, create some additional plots for the activation overpotential and local volumetric current density in the cathode gas diffusion electrode, and the current density at the anode gas diffusion electrode boundary.
1
In the Home toolbar, click  Add Plot Group and choose 3D Plot Group.
2
In the Settings window for 3D Plot Group, type Overpotential in Cathode in the Label text field.
3
Locate the Data section. From the Parameter value (E_cell (V)) list, choose 0.7.
Now add a Surface Plot as follows:
1
Right-click Overpotential in Cathode and choose Surface.
1
In the Settings window for Surface, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1) > Hydrogen Fuel Cell > Electrode kinetics > fc.eta_o2gder1 - Overpotential - V.
2
In the Overpotential in Cathode toolbar, click  Plot.
Generally, the highest overpotentials (in magnitude) are found in the region facing the Membrane domain. Since the overpotential is the driving force for the electrochemical reactions, this is the region were we can expect higher reaction rates.
Local Volumetric Current Density in Cathode
1
In the Home toolbar, click  Add Plot Group and choose 3D Plot Group.
2
In the Settings window for 3D Plot Group, type Local Volumetric Current Density in Cathode in the Label text field.
3
Locate the Data section. From the Parameter value (E_cell (V)) list, choose 0.7.
Also here add a Surface plot as follows:
1
Right-click Local Volumetric Current Density in Cathode and choose Surface.
2
In the Settings window for Surface, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1) > Hydrogen Fuel Cell > Electrode kinetics > fc.iv_o2gder1 - Local current source - A/m³.
3
In the Local Volumetric Current Density in Cathode toolbar, click  Plot.
As for the overpotentials, the highest current density magnitudes are found close to the Membrane domain.
Current Density at Anode Boundary
1
In the Home toolbar, click  Add Plot Group and choose 3D Plot Group.
2
In the Settings window for 3D Plot Group, type Current Density at Anode Boundary in the Label text field.
3
Locate the Data section. From the Parameter value (E_cell (V)) list, choose 0.7.
Use a boundary selection to plot the current density at the anode boundary only.
1
Expand Selection section.
2
Select Boundary at the Geometry entity level.
3
Select Boundary 6 only.
Add a Surface plot as follows:
1
Right-click Current Density at Anode Boundary and choose Surface.
2
In the Settings window for Surface, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1) > Hydrogen Fuel Cell > fc.nIl - Normal electrolyte current density - A/m².
3
Locate the Expression section. In the Expression text field, type abs(fc.nIl).
The abs() is an operator which will return the absolute (positive) value of the argument.
4
Select the Description checkbox.
5
In the associated text field, type Current density.
6
In the Current Density at Anode Boundary toolbar, click  Plot.
The region of the highest current densities is located below the quarter circular edge of the inlet hole. In this area the combined effects of the ohmic and mass transfer losses in the gas diffusion electrode are at a minimum.
Power Losses
Finally, we will plot the different sources of power losses in the cell.
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Power Losses in the Label text field.
Create a plot of a Global variable as follows:
1
Right-click Power Losses and choose Global.
2
In the Settings window for Global, click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp 1) > Hydrogen Fuel Cell > Power losses > Feature-node integrated > fc.o2gde1.o2gder1.P_loss_act - Kinetic activation power loss - W.
3
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp 1) > Hydrogen Fuel Cell > Power losses > Cell integrated > fc.P_loss_l - Electrolyte transport power loss - W.
4
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp 1) > Hydrogen Fuel Cell > Cell integrated > fc.P_loss_s - Electron conduction power loss - W.
5
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp 1) > Hydrogen Fuel Cell > Power losses > Cell integrated > fc.P_loss_gas - Gas transport power loss - W.
6
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp 1) > Hydrogen Fuel Cell > Power losses > Feature-node integrated > fc.h2gde1.h2gder1.P_loss_act - Kinetic activation power loss - W.
7
Locate the y-Axis Data section. In the table, enter the following settings:
Expression
Unit
Description
fc.o2gde1.o2gder1.P_loss_act
W
Kinetic activation, O2
fc.P_loss_l
W
Electrolyte transport
fc.P_loss_s
W
Electron conduction
fc.P_loss_gas
W
Gas transport
fc.h2gde1.h2gder1.P_loss_act
W
Kinetic activation, H2
8
Locate the x-Axis Data section. From the Parameter list, choose Expression.
9
In the Expression text field, type I_avg.
10
In the Unit field, type A/cm^2.
Power Losses
1
In the Model Builder window, click Power Losses.
2
In the Settings window for 1D Plot Group, locate the Plot Settings section.
3
Select the x-axis label checkbox. In the associated text field, type Average cell current density (A/cm<sup>2</sup>).
4
Select the y-axis label checkbox. In the associated text field, type Power Loss (W).
5
Locate the Legend section. From the Position list, choose Upper left.
6
In the Power Losses toolbar, click  Plot.
Cell-Averaged Overpotentials
By dividing the integrated power losses of the cell by the cell current we can also compute corresponding overpotentials for the whole cell.
1
Right-click Power Losses and choose Duplicate.
2
In the Settings window for 1D Plot Group, type Cell-Averaged Overpotentials in the Label text field.
Modify the plot of a Global variable as follows:
1
In the Model Builder window, expand the Cell-Averaged Overpotentials node, then click Global 1.
2
In the Settings windows for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
fc.o2gde1.o2gder1.P_loss_act/(I_avg*A_cell)
V
Kinetic activation, O2
fc.P_loss_l/(I_avg*A_cell)
V
Electrolyte transport
fc.P_loss_s/(I_avg*A_cell)
V
Electron conduction
fc.P_loss_gas/(I_avg*A_cell)
V
Gas transport
fc.h2gde1.h2gder1.P_loss_act/(I_avg*A_cell)
V
Kinetic activation, H2
Cell-Averaged Overpotentials
1
In the Model Builder window, click Cell-Averaged Overpotentials.
2
In the Settings window for 1D Plot Group, locate the Plot Settings section.
3
In y-axis label text field, type Cell-averaged overpotential (V).
4
In the Cell-Averaged Overpotentials toolbar, click  Plot.