Hydrogen Fuel Cell
In the first part of the tutorial, a secondary (not concentration dependent) current distribution is modeled. Diffusion is hence disabled in the H2 and O2 gas phase mixtures. The default gas species are hydrogen and water on the anode side, and oxygen, nitrogen, and water on the cathode side.
1
In the Model Builder window, under Component 1 (comp1) click Hydrogen Fuel Cell (fc).
2
In the Settings window for Hydrogen Fuel Cell, locate the H2 Gas Mixture section, and in the Transport mechanisms subsection, clear the Include gas phase diffusion checkbox.
3
Similarly, locate the O2 Gas Mixture section and check the Use Darcy’s Law for momentum transport checkbox here.
A number of domain nodes, defining the different phases present in the model were added by default. The active selection of these nodes are locked, but may be controlled by adding additional domain nodes (such as Membrane, and so on). Start by adding these additional nodes, and make the corresponding selections on the geometry.
Membrane
1
In the Physics toolbar, click  Domains and choose Membrane.
2
In the Settings window for Membrane, locate the Domain Selection section.
3
From the Selection list, choose Membrane.
H2 Gas Diffusion Electrode
1
In the Physics toolbar, click  Domains and choose H2 Gas Diffusion Electrode.
2
In the Settings window for H2 Gas Diffusion Electrode, locate the Domain Selection section.
3
From the Selection list, choose Anode Gas Diffusion Electrode.
O2 Gas Diffusion Electrode
1
In the Physics toolbar, click  Domains and choose O2 Gas Diffusion Electrode.
2
In the Settings window for O2 Gas Diffusion Electrode, locate the Domain Selection section.
3
From the Selection list, choose Cathode Gas Diffusion Electrode.
Electrolyte Phase
The Electrolyte Phase node should now be active on all three domains. Define the conductivity in the Electrolyte Phase node by using the Fuel Cell and Electrolyzer material library, which contains conductivity data for some common electrolytes.
Add Electrolyte Material
1
In the Home toolbar, click Add Material.
2
Go to the Add Material window. In the tree, select Fuel Cell and Electrolyzer > Polymer Electrolytes > Nafion, EW 1100, Vapor Equilibrated, Protonated, and choose Add to Component.
3
In the Home toolbar, click Add Material to close the Add Material window.
The polymer electrolyte conductivity depends on the temperature and the relative humidity. Specify the temperature globally in the Default Model Inputs node. The temperature defined in the Default Model Inputs node may be accessed by multiple physics nodes in the model (such as the Nernst and Butler-Volmer equations that will be set later).
Set Temperature in Default Model Inputs
1
In the Model Builder window, under Global Definitions click Default Model Inputs.
2
In the Settings window for Default Model Inputs, locate the Browse Model Inputs section.
3
In the tree, select General > Temperature (K) - minput.T.
4
Find the Expression for remaining selection subsection. In the Temperature text field, type T.
Membrane
Also specify the relative humidity for the membrane electrolyte in the Membrane node.
1
In the Model Builder window, under Component 1 > Hydrogen Fuel Cell, click Membrane 1.
2
In the Settings window for Membrane, locate the Electrolyte Water Activity for Material Model Input section.
3
In the aw text field, type RH.
Note that the water activity in the polymer of the gas diffusion electrodes (GDEs) is approximated to be in equilibrium with the adjacent gas phase in the pores, and is hence automatically set equal to the relative humidity in the GDEs.
H2 Gas Phase
The H2 Gas Phase node should be active in domain 1 only.
Set up the composition of the H2 gas phase mixture using the Humidified mixture option.
1
In the Model Builder window, click H2 Gas Phase 1.
2
In the Settings window for H2 Gas Phase, locate the Composition section.
3
From the Mixture specification list, choose Humidified mixture.
4
In the RHhum text field, type RH.
5
In the Thum text field, type T.
O2 Gas Phase
The O2 Gas Phase node should be active in domain 3 only.
Similarly, set up the initial composition of the O2 gas phase mixture using the Humidified air option.
1
In the Model Builder window, click O2 Gas Phase 1.
2
In the Settings window for O2 Gas Phase, locate the Composition section.
3
From the Mixture specification list, choose Humidified air.
4
In the RHhum text field, type RH.
5
In the Thum text field, type T.
H2 Gas Diffusion Electrode
Next set up the properties of the H2 Gas Diffusion Electrode node. Note that the electrolyte volume fraction is used to calculate the effective electrolyte conductivity in the porous gas diffusion electrode.
1
In the Model Builder window, click H2 Gas Diffusion Electrode 1.
2
In the Settings window for H2 Gas Diffusion Electrode, locate the Electrode Charge Transport section.
3
In the σs text field, type sigma_s.
4
Locate the Effective Electrolyte Charge Transport section. In the εl text field, type eps_l.
H2 Gas Diffusion Electrode Reaction
The thermodynamics and kinetics of the hydrogen oxidation reaction are set in the child node that is added by default. Note that the reference equilibrium potential is calculated automatically when the default Built in option is used.
1
In the Model Builder window, click H2 Gas Diffusion Electrode Reaction 1.
2
In the Settings window for H2 Gas Diffusion Electrode Reaction, locate the Electrode Kinetics section.
3
From the Kinetics expression type list, choose Linearized Butler-Volmer.
4
In the i0,ref(T) text field, type i0_ref_H2.
5
Locate the Active Specific Surface Area section. In the av text field, type Av.
O2 Gas Diffusion Electrode
Set up the properties of the O2 Gas Diffusion Electrode node in the same way.
1
In the Model Builder window, click O2 Gas Diffusion Electrode 1.
2
In the Settings window for O2 Gas Diffusion Electrode, locate the Electrode Charge Transport section.
3
In the σs text field, type sigma_s.
O2 Gas Diffusion Electrode Reaction
The thermodynamics and kinetics of the oxygen reduction reaction are similarly set in the child node that is added by default. Note that the reference equilibrium potential is calculated automatically when the default Built in option is used.
1
In the Model Builder window, click O2 Gas Diffusion Electrode Reaction 1.
2
In the Settings window for O2 Gas Diffusion Electrode Reaction, locate the Electrode Kinetics section.
3
In the i0,ref(T) text field, type i0_ref_O2.
4
Locate the Active Specific Surface Area section. In the av text field, type Av.
Ground Boundary Condition on the Anode Side
Finalize the secondary current distribution model by setting up the boundary conditions for the potentials in the electronic conducting phase.
1
In the Model Builder window, click Electronic Conducting Phase 1.
2
In the Physics toolbar, click  Attributes and choose Electric Ground.
3
Select Boundary 3 only.
Potential Boundary Condition on the Cathode Side
1
In the Model Builder window, click Electronic Conducting Phase 1.
2
In the Physics toolbar, click  Attributes and choose Electric Potential.
3
Select Boundary 10 only.
4
In the Settings window for Electric Potential, locate the Electric Potential section, and in the ϕs,bnd text field, type E_cell.