Appendix: User Field Function and Parameters Properties

Names, dimensions, definitions, and formulation of the user-defined field functions and parameters that are used in the Solid Oxide Fuel Cell tutorial.

Global Parameters

Faraday Constant: Dimensions: ElectricCharge/Quantity; Value: $F = 9.6485 \times 10^{7} [s A / k m o l]$
UniversalGasConstant: Dimensions: Energy/(Temperature Quantity); Value: $R_{u} = 8314.4621 [J / k m o l K]$

User-Defined Field Functions

Exchange Current Densities

Description: The exchange current densities of the anode and cathode, as required by the Butler-Volmer equation.

Dimensions: Current/Length^2

AnodeExchangeCurrent: Formulation:
Figure 17. EQUATION_DISPLAY

$j_{0, a} = \frac{j_{0, a}^{*}}{{[({X T O C}_{a} \cdot 0.8) ({X T O C}_{a} \cdot 0.2)]}^{0.5}}$
(5305); Definition: 7746 / pow($AnodeXToCconversion * $AnodeXToCconversion * .8 * .2,.5); (Where 0.8 and 0.2 correspond to the reference concentrations of H₂ and H₂O respectively, from measurement, according to literature.)
CathodeExchangeCurrent: Formulation:
Figure 18. EQUATION_DISPLAY

$j_{0, c} = \frac{j_{0, c}^{*}}{{({X T O C}_{c} \cdot 0.21)}^{0.5}}$
(5306); Definition: 10010 / pow($CathodeXToCconversion * .21,.5); (Where 0.21 corresponds to the reference concentration of O₂ from measurement, according to literature.)

Mass Fluxes

Description: Mass fluxes of hydrogen, nitrogen, oxygen, and water.

Dimensions: Mass/Length^2-Time

Mass Flux H2: Formulation:
Figure 19. EQUATION_DISPLAY

${\dot{m}}_{H_{2}} = W_{H_{2}} \frac{υ_{H_{2}} j}{n F} = Y_{H_{2}} \dot{m}$
(5307); Definition: ${MassFractionH2} * ${MassFlux}
Mass Flux N2: Formulation:
Figure 20. EQUATION_DISPLAY

${\dot{m}}_{N_{2}} = W_{N_{2}} \frac{υ_{N_{2}} j}{n F} = Y_{N_{2}} \dot{m}$
(5308); Definition: ${MassFractionN2} * ${MassFlux}
Mass Flux O2: Formulation:
Figure 21. EQUATION_DISPLAY

${\dot{m}}_{O_{2}} = W_{O_{2}} \frac{υ_{O_{2}} j}{n F} = Y_{O_{2}} \dot{m}$
(5309); Definition: ${MassFractionO2} * ${MassFlux}
Mass Flux H2O: Formulation:
Figure 22. EQUATION_DISPLAY

${\dot{m}}_{H_{2} O} = W_{H_{2} O} \frac{υ_{H_{2} O} j}{n F} = Y_{H_{2} O} \dot{m}$
(5310); Definition: ${MassFractionH2O} * ${MassFlux}

Conversion Factors

Description: The conversion factors (XTOC) from mole fraction to molar concentration (required by Simcenter STAR-CCM+) for the species in the respective mixture.

Dimensions: Quantity/Length^3

AnodeXToCconversion: Formulation:
Figure 23. EQUATION_DISPLAY

${X T O C}_{a} = \frac{ρ}{X_{H_{2}} W_{H_{2}} + X_{H_{2} O} W_{H_{2} O}}$
(5311); Definition: $Density / (${MoleFractionH2} * $MolecularWeightH2 + $MoleFractionH2O * $MolecularWeightH2O)
CathodeXToCconversion: Formulation:
Figure 24. EQUATION_DISPLAY

${X T O C}_{c} = \frac{ρ}{X_{N_{2}} W_{N_{2}} + X_{O_{2}} W_{O_{2}}}$
(5312); Definition: $Density / ($MoleFractionN2 * $MolecularWeightN2 + $MoleFractionO2 * $MolecularWeightO2)

ElectricPowerFlux: Description: Electric power.; Dimensions: Power/Length^2; Formulation:
Figure 25. EQUATION_DISPLAY

$P = U I$
(5313); Definition: ${ElectricPotential} * ${BoundarySpecificElectricCurrent}

ElectrolyteConductivity: Description: The conductivity of the solid oxide electrolyte.; Dimensions: ElectricConductance/Length; Formulation:
Figure 26. EQUATION_DISPLAY

$σ_{m} = \frac{1}{(0.3685 + 0.002838 \times e^{\frac{10300}{T}})} \cdot 100$
(5314); Definition: 1. / ((0.3685 + 0.002838 * exp(10300 / $Temperature)) / 100.0)

SOFC Tutorial Nomenclature


Nomenclature	Description
$C_{p}$	Heat capacity
$E_{e q}$	Equilibrium potential
$E_{0}$	Nernst standard potential
$F$	Faraday constant, 96485339.924 C/kmol
$H$	Enthalpy
$I$	Total current that is available to the external circuit, J
$j$	Reaction current density, A/m²
${\dot{m}}_{i}$	Mass flux of species $i$
$p$	Pressure, Pa
$p_{a t m}$	Reference pressure at which the thermodynamic data was measured, 101325 Pa
$P$	Power, J/s
$R_{u}$	Universal gas constant, 8314.4621 J / kmol K
$ρ$	Density
$σ$	Conductivity, S/m
$S$	Entropy
$T$	Temperature, K
$U$	Anode-cathode potential difference
$υ_{i}$	Stoichiometric coefficient of species $i$
$W$	Molecular weight
$X$	Mole fraction
$X T O C$	Conversion factor
$Y$	Mass fraction