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Solid Oxide Fuel Cells Modeling

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Advances in Medium and High Temperature Solid Oxide Fuel Cell Technology

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 574))

Abstract

A solid oxide fuel cell (SOFC) is a complex system consisting of different components, in which interconnected physical phenomena occur simultaneously and contribute to determine the global thermo-electrochemical response of the system. The simulation and prediction of the response of an SOFC are of paramount importance for the analysis of possible applications without resorting to extensive experimental investigations. Simulating the SOFC response requires to develop reliable models that can describe the significant phenomena occurring in the system. Different approaches can be followed for the SOFC modeling, depending on the goals of the model. This chapter will provide an introduction to SOFC modeling focusing on a macroscopic, physically based approach.

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Abbreviations

a :

Thermodynamic activity

B p :

Permeability (m2)

C f :

Drag constant

C p :

Specific heat at constant pressure (J kg−1 K−1)

d :

Molecule, particle, pore diameter (m, μm)

D :

Diffusion coefficient (m2 s−1, cm2 s−1)

D T :

Thermal diffusion coefficient (kg m−1 s−1)

E :

Equilibrium, electrode potential (V)

E act :

Activation energy (J mol−1)

E b :

Emissive power of black body (W m−2)

f :

Volume fraction of ionic/electronic phase in the electrode

f :

Body forces acting on the fluid (m s−2)

F :

Faraday’s constant (C mol−1)

F :

Volume force (N m−3)

F i−j :

View factor between i and j surface elements

\(\bar{g}\) :

Molar Gibbs free energy variation (J mol−1)

\(\bar{h}\) :

Molar enthalpy (J mol−1)

H 0 :

Incident irradiation (W m−2)

i :

Current density (A m−2)

i 0 :

Exchange current density (A m−2)

i v :

Volumetric current density (A m−3)

i TPB :

Current per unit of TPB length (A m−1)

I :

Current (A)

\(\vec{j}\) :

Mass flux (kg m−2 s−1)

k :

Thermal conductivity (W m−1 K−1)

k B :

Boltzmann constant (J K−1)

K r :

Equilibrium constant of r reaction

L p :

Characteristic size of the pore (m)

M n :

Molecular weight (kg mol−1)

n :

Number of electrons involved in redox reactions

p :

Pressure (Pa, bar)

P :

Percolation probability

q :

Rate of charge-transfer reaction (mol m−1 s−1)

\(\vec{q}\) :

Heat flux (W m−2)

Q :

Volumetric heat source (W m−3)

r :

Reaction rate (mol m−3 s−1)

R :

Ideal gas constant (J mol−1 K−1)

R con :

Contact resistance (Ω cm2)

\(\bar{s}\) :

Molar entropy (J mol−1 K−1)

\(\dot{s}_{k}\) :

Molar rate of k species (mol cm−2 s−1)

S :

Mass source term (kg m−3 s−1)

t :

Time (s)

T :

Temperature (K)

u :

Fluid velocity vector (m s−1)

\(\bar{\varvec{u}}\) :

Superficial velocity (m s−1)

V :

Cell voltage (V)

V a :

Atomic diffusion volumes (cm3 mol−1)

x :

Mass fraction

[X]:

Molar concentration (mol m−3, mol m−2)

y :

Molar fraction

α :

Symmetry coefficient of Butler–Volmer equation

β :

Symmetry coefficient of charge-transfer reaction

\(\beta_{\text{e}}\) :

Extinction coefficient of the medium (m−1)

γ :

Pre-exponential activation parameter (A cm−2)

\(\gamma_{\text{s}}\) :

Scaling factor (1 or m−1)

\(\gamma_{0i}\) :

Sticking coefficient of i-reaction

Γ :

Surface site density (mol cm−2)

ε :

Porosity

η :

Overpotential (V)

\(\theta_{k}\) :

Surface coverage of k species

λ :

Mean free path (m)

\(\lambda_{\text{TPB}}\) :

Volumetric TPB density (m−2)

μ :

Gas viscosity (Pa s)

v :

Stoichiometric coefficient

ξ :

Surface emissivity

ρ :

Density (kg m−3)

σ :

Electronic, ionic conductivity (S m−1)

\(\sigma_{\text{B}}\) :

Stefan–Boltzmann constant (W m−2 K−4)

\(\sigma_{k}\) :

Coordination number of k species

\(\sigma_{\alpha \beta }\) :

Average collision diameter (Å)

\(\tau_{\text{g}}\) :

Tortuosity

\({\vec{\tau }}\) :

Stress tensor (Pa)

\(\phi\) :

Electronic, ionic potential (V)

\(\phi_{\text{v}}\) :

Viscous dissipation (kg m−1 s−3)

\(\chi\) :

Volumetric charge density (C m−3)

\(\psi\) :

Volumetric charge source (C s−1 m−3)

\(\varOmega_{\alpha \beta }\) :

Collision integral

act:

Activation

adv:

Advection

an:

Anode

cat:

Cathode

chem:

Chemical

con:

Contact

conc:

Concentration

diff:

Diffusion

eff:

Effective

eq:

Equilibrium

irr:

Irreversible

mol:

Molecular

oc:

Open-circuit

ohm:

Ohmic

rad:

Radiative

react:

Reaction

res:

Resistance

rev:

Reversible

BV:

Butler–Volmer

DGM:

Dusty gas model

SMM:

Stefan–Maxwell model

SOFC:

Solid oxide fuel cell

SRU:

Stack repeating unit

TPB:

Three phase boundary

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Authors and Affiliations

  1. Energy Department, Polytechnic of Turin, Turin, Italy

    Domenico Ferrero, Andrea Lanzini & Massimo Santarelli

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  1. Domenico Ferrero
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  2. Andrea Lanzini
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Correspondence to Massimo Santarelli .

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  1. University of Udine , Udine, Italy

    Marta Boaro

  2. Institute for Advances Energy Technologies (ITAE), National Research Council (CNR), Messina, Italy

    Aricò Antonino Salvatore

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Ferrero, D., Lanzini, A., Santarelli, M. (2017). Solid Oxide Fuel Cells Modeling. In: Boaro, M., Salvatore, A. (eds) Advances in Medium and High Temperature Solid Oxide Fuel Cell Technology. CISM International Centre for Mechanical Sciences, vol 574. Springer, Cham. https://doi.org/10.1007/978-3-319-46146-5_8

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