4.3 Solid Oxide Fuel Cell With Unresolved Electrolyte Module Set Up Procedure

The following describes an overview of the procedure required in order to use the SOFC With Unresolved Electrolyte Model in ANSYS FLUENT.

1.   Start ANSYS FLUENT.

You must start ANSYS FLUENT in 3d double-precision mode. Note that the SOFC With Unresolved Electrolyte Model is only available in 3d.

2.   Read the case file.

File $\rightarrow$ Read $\rightarrow$ Case...

3.   Scale the mesh.

General Scale...

4.   Define various model parameters for the simulation.

(a)   Check the solver settings.

General

i.   In the Solver group box, enable Pressure Based under Type.

ii.   Enable Implicit under Formulation.

iii.   Enable Steady under Time.

iv.   Enable Absolute under Velocity Formulation.

(b)   Open the Energy dialog and enable the Energy option (if it is not already enabled).

Models Energy Edit...

Enable the Energy Equation option, if it is not already enabled.

(c)   Open the Viscous Model dialog and enable the Laminar option.

Models Viscous Edit...

Enable the Laminar option, if it is not already enabled.

(d)   Open the Species Model dialog.

Models Species Edit...

i.   Enable the Species Transport option.

ii.   Enable the Volumetric option under Reactions.

iii.   Disable the Inlet Diffusion option under Options.

iv.   Enable the Diffusion Energy Source option under Options.

v.   Enable the Full Multicomponent Diffusion option under Options.

vi.   Enable the Thermal Diffusion option under Options.

(e)   Open the SOFC Model dialog to set the parameters for the SOFC With Unresolved Electrolyte Model.

Models SOFC Model (Unresolved Electrolyte) Edit...

Enable the SOFC Model option.

Open the Model Parameters tab.

i.   Set the Current Underrelaxation Factor to a value of either 0.3 or 0.4.

ii.   Set the Electrochemical and Electrical Parameters according to your problem specification.

(f)   Set the electrochemistry parameters.

Open the Electrochemistry tab of the SOFC Model dialog.

i.   Enter values for the Constant Exchange Current Densities for the anode and the cathode. These are the $i_0$ values in the Butler-Volmer equation for the anodic and cathodic reactions. By default, the Anode Exchange Current Density is set to 1000 Amps and the Cathode Exchange Current Density is set to 100 Amps.

ii.   Enter values for the Mole Fraction Reference Values.

These are the species concentrations at which the exchange current densities were taken. These are used to adjust the $i_0$ values of reactant species that are depleted. By default, the H2 Reference Value is set to 0.8 moles/moles, the 02 Reference Value is set to 0.21 moles/moles, and the H2O Reference Value is set to 0.2 moles/moles.

iii.   Enter values for the Stoichiometric Exponents by setting values for the H2 Exponent, the H20 Exponent, and the O2 Exponent (defaulted to 0.5). These are the stoichiometric factors in the electrochemical reaction equation. They are used as exponents as part of the $i_0$ scaling.

iv.   Enter values for the Butler-Volmer Transfer Coefficients by setting values for the Anodic Transfer Coefficient and the Cathode Transfer Coefficient for both the anode reaction and the cathode reaction (defaulted to 0.5). These are the alpha values in the Butler-Volmer equation. They represent the forward and backward rates of reaction at both the anode and cathode.

v.   Enter a values for the Temperature Dependent Exchange Current Density by turning on the Enable Temperature Dependent I_0 option and setting values for A and B. These two coefficients allow the $i_0$ for the cathode to vary as a function of temperature.

(g)   Set the anode interface components for the SOFC With Unresolved Electrolyte Model.

Open the Electrode and Tortuosity tab of the SOFC Model dialog.

i.   Under Anode Electrolyte, specify a zone in the Zone(s) list.

ii.   Enable Anode Interface if it is applicable.

(h)   Set the cathode interface components for the SOFC With Unresolved Electrolyte Model.

Open the Electrode and Tortuosity tab of the SOFC Model dialog.

i.   Under Cathode Electrolyte, specify a zone in the Zone(s) list.

ii.   Enable Cathode Interface if it is applicable.

(i)   Set the tortuosity parameters for the SOFC With Unresolved Electrolyte Model.

Open the Electrode and Tortuosity tab of the SOFC Model dialog.

i.   Under Tortuosity Zone, specify a zone in the Zone(s) list.

ii.   Turn on Enable Tortuosity if it is applicable.

(j)   Set the parameters for the electric field model.

Open the Electric Field tab of the SOFC Model dialog.

i.   Specify up to 5 conductive regions.

ii.   Specify up to 3 contact surfaces.

iii.   Specify a voltage tap surface.

iv.   Specify a current tap surface.

5.   Define material properties.

(a)   Define a user-defined scalar.

i.   Open the User-Defined Scalars dialog.

Define $\rightarrow$ User-Defined $\rightarrow$ Scalars...

ii.   Change the Number of User-Defined Scalars to 1.

iii.   Indicate none as the Flux Function and click OK to close the User-Defined Scalars dialog.

(b)   Define 14 user-defined memory locations.

i.   Open the User-Defined Memory dialog.

Define $\rightarrow$ User-Defined $\rightarrow$ Memory...

ii.   Change the Number of User-Defined Memory Locations to 14.

iii.   Click OK to close the User-Defined Memory dialog.

(c)   Define user-defined function hooks.

i.   Open the User-Defined Function Hooks dialog.

Define $\rightarrow$ User-Defined $\rightarrow$ Function Hooks...

ii.   Change the Adjust function to adjust_function.

iii.   Click OK to close the User-Defined Function Hooks dialog.

(d)   Create or re-define new solid materials as appropriate for the anode, the cathode, and the electrolyte according to your problem specification.

Note that since the ANSYS FLUENT SOFC With Unresolved Electrolyte Model does not currently support the shell conduction model, you cannot use it to take into account the transversal conductive heat inside the membrane.

(e)   Edit the mixture-template mixture material.

Materials Create/Edit...

i.   In the Create/Edit Materials dialog, click Fluent Database... to open the Fluent Database Materials dialog.

ii.   In the Fluent Database Materials dialog, make a copy of the h2 fluid material.

iii.   In the Create/Edit Materials dialog, change the Material Type to mixture and click Edit... for the Mixture Species.

iv.   In the Species dialog, arrange the materials under Selected Species in the following order: h2o, o2, h2, and n2.

v.   In the Create/Edit Materials dialog, change the Thermal Conductivity and the Viscosity to ideal-gas-mixing-law.

vi.   Change the Mass Diffusivity to user-defined and select diffusivity::sofc as the corresponding user-defined function.

vii.   Change the UDS Diffusivity to user-defined and select E_Conductivity::sofc as the corresponding user-defined function.

viii.   Retain the default values for the other parameters and click Change/Create.

6.   Set the operating conditions.

General Operating Conditions...

Retain the default values..

7.   Set the boundary conditions.

Boundary Conditions

Define the conditions at the anode, the cathode, the interface between the anode and current collector, the interface between the cathode and the current collector, the anode inlet, and the cathode inlet boundaries according to your problem specification.

Note that sources only need to be hooked to the mass, species, and energy equation in a single fluid zone in order for the ANSYS FLUENT SOFC With Unresolved Electrolyte Model to function properly (but can be hooked to all zones if you so choose). ANSYS FLUENT does not rely on cell or thread referencing in the sources in order to cover the solution domain.

8.   Set the multigrid control parameters.

Solution Controls Advanced...

  

(a)   In the Multigrid tab of the Advanced Solution Controls dialog, set the cycle type for h2, h2o, and o2 to V-cycle. For serial calculations, set the cycle type for Energy and User-defined Scalar-0 to W-cycle or F-cycle. For parallel calculations, select the F-cycle option for both.

(b)   Set the Max Cycles to 50.

(c)   Retain the default values for the rest of the parameters.

9.   Define the convergence criteria.

Monitors Residuals Edit...

In the Residual Monitors dialog, set the Convergence Criterion for all equations to 1e-08.

10.   Initialize the flow field.

Solution Initialization Initialize

Retain the default values for all parameters.

11.   In the Define SOFC Model Parameters dialog, turn on the ANSYS FLUENT SOFC With Unresolved Electrolyte Model by activating the Enable SOFC Model option, the Enable Surface Energy Source option, the Enable Species Source option, and the Disable CO Electrochemistry option.

If the electrolyte resistivity changes as a function of temperature, then turn on the Enable Electrolyte Conductivity Submodel option. If there is CO in the fuel line, then you should turn off the Disable CO Electrochemistry option.

12.   Run the simulation until all residuals are decreasing.

13.   Turn on the Enable Volumetric Energy Source option and continue the simulation until convergence is achieved.

14.   Save the case and data files.

15.   Perform post-processing using standard quantities and by using the user-defined memory allocations. By default, the ANSYS FLUENT SOFC With Unresolved Electrolyte Model defines the following user-defined memory allocations:

Table 4.3.1: User-Defined Memory Allocations

UDM-0	Interface Current Density (A/m $^2$)
UDM-1	Nernst Potential (Volts)
UDM-2	Activation Overpotentail (Volts)
UDM-3	Volumetric Ohmic Source (W/m $^3$)
UDM-4	x Component of the Current Density (A/m $^2$)
UDM-5	y Component of the Current Density (A/m $^2$)
UDM-6	z Component of the Current Density (A/m $^2$)
UDM-7	Electrolyte Voltage Jump
UDM-8	Electrolyte Resistivity (Ohm-m)
UDM-9	Effective Electric Resistance
UDM-10	Anode Activation
UDM-11	Cathode Activation
UDM-12	Electrochemical Source (W/m $^3$)
UDM-13	Magnitude of Current Density (A/m $^2$)

Note that UDM-7 and UDM-8 are the linearized values that ANSYS FLUENT uses to solve the potential field and electrochemical coupling. They are necessary to the calculations but do not contain any real physical meaning.

Note that UDM-10 and UDM-11 contain the disaggregated activation polarizations at the anode and cathode.

The current density in UDM-0 is a conservative flux of electricity ( $A/{m^2}$). Performing an area integral over the electrolyte surface will sum to the total current ( $A$). That value is computed at the electrolyte faces during the electric field solution. The values in UDM-4 - UDM-6 contain cell-centered values of the current density vector. These are not, and cannot be, conservative, so depending on the material conductivity and the geometric configuration, these can sometimes unavoidably produce values that do not match the UDM values. The same issues exist when interpolating velocity values to obtain the mass fluxes.

Note that, by default, the ANSYS FLUENT SOFC With Unresolved Electrolyte Model defines a single user-defined scalar:

Table 4.3.2: User-Defined Scalar Allocations

UDS-0

Electric Potential (Volts)