The Hydrogen Fuel Cell and Water Electrolyzer Interfaces
The Hydrogen Fuel Cell (fc) and Water Electrolyzer (we) physics interfaces are used to model the different electron and ion-conducting layers of various types of hydrogen fuel cells, or water electrolyzer cells. Optionally, gas phase transport and Darcy’s law for convection in porous media and flow channels may be enabled and also solved for by the interfaces.
The interface supports simulation in 1D, 2D, and 3D as well as for axisymmetric components in 1D and 2D.
Note that once added to a model, the Hydrogen Fuel Cell (fc) and the Water Electrolyzer (we) interfaces are identical in terms of functionality and only differ by some default parameter values (see below), the default name (fc/we), and the icon (/).
The Electrochemistry > Hydrogen Fuel Cell () and the Electrochemistry > Water Electrolyzers () branches in the Model Wizard, or in the Select physics tab, contain a number of different entries for adding either a Hydrogen Fuel Cell (fc) or a Water Electrolyzer (we) physics interface, of different electrolyte types, to a model.
Depending on the selected entry, different species will be included by default in the electrode gas mixtures, and gas phase diffusion will be enabled by default if there are more than one species present a mixture. See also the H2 Gas Mixture and O2 Gas Mixture section below.
The chosen Model Wizard entry will also have an effect on the default stoichiometry and kinetics parameter values used when adding electrode reactions to the model. See the Electrode Reaction Settings below.
Settings at the Interface Level (fc/we)
The Label is the default physics interface name.
The Name is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.
The default Name (for the first physics interface in the model) is fc for the Hydrogen Fuel Cell interface and we for the Water Electrolyzer interface.
Domain Selection
If any part of the model geometry should not partake in the fuel cell/electrolyzer model, remove that part from the selection list.
H2 Gas Mixture and O2 Gas Mixture
These sections specify what the species are present in the Gas Phase domains on the respective sides of the cell. Apart from hydrogen and oxygen, which are always assumed to be present on each side, you may here choose to include one or several of the species H2O, N2, CO2, and CO on each side. The species CH4 may be included on the H2 side. An additional, arbitrarily defined, gaseous species can be included on either side using Auxiliary species. The settings for the auxiliary species are found in the corresponding Gas Phase domain nodes.
If you expect concentration gradients in the gas diffusion electrodes (GDEs), gas diffusion layers (GDLs) or the flow channels, you may choose to Include gas phase diffusion in these sections. Gas phase diffusion can only be enabled if there are more than one species present in the gas mixture.
Use Darcy’s law for momentum transfer for solving for the gas phase pressure using Darcy’s Law in gas phase domains. This can be enabled individually for each gas mixture in these sections. Note, however, that instead of using the built-in Darcy’s law of the fc/we interface, you can instead couple the interface to any Fluid Flow interface, or an analytical expression, by specifying the velocity explicitly in the Gas Phase nodes or by using an Reacting Flow, H2/O2 Gas Phase multiphysics coupling nodes.
If Use H2O(l) in Reaction Stoichiometry is enabled, this will allow for setting the stoichiometric coefficient of liquid water in electrode reactions, which in turn may be used for the built-in calculations of equilibrium and thermoneutral potentials. Unit activity of H2O(l) will be assumed in all expressions.
Electrode Reaction Settings
In this section you can control the default parameter settings that electrode reactions will get when added to the model, and how the potential of the global hydrogen reference electrode will be calculated.
The Charge-carrying ion setting (Proton, Hydroxide, Carbonate, Oxide or Generic) will impact the default stoichiometry of electrode reactions and a built-in hydrogen reference electrode used for the calculation of equilibrium and thermoneutral potentials of the electrode reactions.
For all types except Generic, the Reference hydrogen electrode equilibrium potential, Eeq,RHE (V), will be calculated using an internal database of reaction enthalpies and entropies, in combination with the Reference hydrogen electrode temperature, which should be a global value with no spatial dependency.
The Generic option will add no default stoichiometric coefficients, and for this case the Eeq,RHE and the Charge of the charge-carrying ion will have to be specified explicitly.
Note that the Entropy of the charge-carrying ion has no impact on the equilibrium potentials vs Eeq,RHE, but will have an effect the calculation of the thermoneutral potentials. (See also Calculation of Built-in Equilibrium and Thermoneutral Potentials.)
The following reaction stoichiometry will be used for calculating Eeq,RHE, and as default for the electrode reactions on the H2 and O2 sides, respectively.
Proton:
Hydroxide:
Carbonate:
Oxide:
The Operation mode setting (Fuel cell or Electrolyzer) will impact the default values of the kinetics settings of added electrode reactions. It will also, along with the Charge-carrying ion setting, impact modify the default inlet gas flow settings in H2 Inlet and O2 Inlet. When Fuel cell is chosen, Stoichiometric Feed will be enabled by default. Similarly, when Electrolyzer is chosen and Charge-carrying ion is set to Hydroxide, Carbonate, or Oxide, the H2 Inlet default will be Stoichiometric Feed. When Electrolyzer and Proton are chosen, the O2 Inlet default will be Stoichiometric Feed.
Electrolyte and Membrane Transport
This section contains two subsections: Electrolyte transport with the option for Solve for electrolyte phase potential and Crossover Species.
By default, Solve for electrolyte phase potential is selected. When selected, the governing equation for electrolyte potential in the electrolyte phase will be solved for by the interface. When cleared, a custom electrolyte phase potential can be entered on the Electrolyte Phase node, allowing for customized ion transport modeling.
The Crossover species allow for enabling of transport of additional species (apart from the charge carrying ion) in Membrane domains. The Crossover species include H2, O2, and N2. Note that the crossover species N2 is available only if species N2 has been selected in both the H2 Gas Mixture and the O2 Gas Mixture.
The option Electroosmotic water drag is available if the species H2O has been selected in both the H2 Gas Mixture and the O2 Gas Mixture and Solve for electrolyte phase potential is selected.
Out-of-Plane Parameter
The out-of-plane geometric parameter is defined here. In 1D, this parameter is the Cross-sectional Area Ac (SI unit: m2); in 1D axisymmetric or 2D geometries, it is the Thickness d (SI unit: m).
Reference Pressure Level
This section is available if the Use Darcy’s law for momentum transport checkbox has been selected. In this section, you specify the Reference pressure level.
Consistent Stabilization
This section is available when Stabilization is selected in the Show More Options dialog shown when the Show More Options button () is selected.
The stabilization settings are applicable separately for the H2 Gas Mixture and the O2 Gas Mixture and are available if the corresponding Include gas phase diffusion checkbox is selected.
In convection-dominated parts of a cell where the mesh is not fine enough to resolve the concentration gradients, for instance in a boundary layer, stabilization may be added in order to avoid spurious oscillations in the solution, and to improve convergence. In fuel cells and electrolyzer cells, stabilization is more likely to be needed in the gas flow channels. In gas diffusion layers and gas diffusion electrodes stabilization is usually not needed due to the lower flow velocities. The stabilization expressions, particularly the crosswind diffusion expressions, may be costly to compute. Therefore, it is recommended to add stabilization only if needed, for instance when spurious gas mass fractions oscillations are observed in a solution.
There are two consistent stabilization methods available — Streamline diffusion (active by default) and Crosswind diffusion (inactive by default). The Residual setting applies to both the consistent stabilization methods. Approximate residual is the default setting and it means that derivatives of the diffusion tensor components are neglected. This setting is usually accurate enough and computationally faster. If required, select Full residual instead.
By default, Streamline diffusion stabilization, using an Approximate residual, is added only to gas flow channels. Crosswind diffusion stabilization, and computation of the Full residual may be turned on as required, in all domains.
Advanced Settings
From the Regularization list, select On (default) or Off. When turned On, regularized mass fractions are selected such that they lie between 0 and 1. The regularized mass fractions are used in the calculation of composition-dependent material properties, such as density.
This section is available when the Advanced Physics Options is selected in the Show More Options dialog shown when the Show More Options button () is selected, in combination with the Include gas phase diffusion checkbox being selected.
Physics vs. Materials Reference Electrode Potential
The Physics vs. Materials Reference Electrode Potential setting on the physics interface node can be used to combine material library data for current densities and equilibrium potentials with an arbitrary reference electrode scale in the physics. The setting affects the electrode potentials used for model input into the materials node as well as all equilibrium potential values output from the materials node.
Note that the setting will only impact how potentials are interpreted in communication between the physics and the Materials node. If the From material option is not in use for equilibrium potentials or electrode kinetics, the setting has no impact.
This section is available when the Advanced Physics Options is selected in the Show More Options dialog shown when the Show More Options button () is selected.
Overview of the Domain Nodes in the Hydrogen Fuel Cell and Water Electrolyzer Interfaces
The following phase nodes are added as default nodes:
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Electrolyte Phase
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Electronic Conducting Phase
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Gas Phase (H2 and O2)
These default phase nodes define the physics in the different phases of the cell, and contain settings for, for instance, electrolyte conductivity and gas diffusion coefficients. Initial Values for the dependent variables defined by the phase nodes are available as subnodes. Boundary conditions for, for instance, potential, current densities, inflow gas compositions, and so on, are added as subnodes to the above phase nodes.
The default phase nodes have their selections locked to all domains, but may have their selections overridden by the following nodes, which may be added by the user:
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Membrane
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Separator
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Current Collector
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Gas Diffusion Electrode (H2 or O2)
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Gas Diffusion Layer (H2 or O2)
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Gas-Electrolyte Compartment (H2 or O2)
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Gas Flow Channel (H2 or O2)
These nodes define properties that do not pertain to the pure electrolyte or gas phases such as porosities, permeabilities, and electronic conductivities. Electrode reactions are added as subnodes to the gas diffusion electrode nodes.