Page 323 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Cell. Stack and System Modelling 299

element and depending on the mismatch in coefficients of thermal expansion
between cell components. The configuration of the manifolds and overall cell
dimensions can be modified based on the thermal stress results. The simulation
can also be used to optimise the stack geometry for flow uniformity.

'111.3 Continuum-Level Electrochemistry Model
One of the most important aspects of SOFC design is the voltage and current
distribution in the PEN. This couples with the temperature distribution from the
flow model and also with the electrochemical reactions at the electrodes. The
electrochemical process generates electrical power and heat, but excessive heat
generation must be avoided since it may cause thermal stresses affecting the
structural stability of the SOFC.
At the effective property or continuum level, the simulation of electrode and
cell performance basically requires only a parameterised electrochemical model.
Such an electrochemical model is usually described as a current-voltage
relation, or I-V curve, for a single cell, in terms of parameters that are effective
cell properties and operational parameters. The I-V relation describes the
voltage (potential) loss at a specified current with respect to the ideal
thermodynamic performance, which is called overpotential or polarisation (q).
This cell I-V curve is specific for the materials, structural characteristics, and
operational parameters (gas compositions, pressure, temperature) of a given
PEN element.
As an analogy to mass and energy balances, one can write a potential balance
of the fuel cell as follows [lo]:

v(i) = Eeq - iRi - Vc - VA = Eeq - iRi - VCa - VCc - VAa - VAc (7)

Here E,, is the equilibrium (open circuit) voltage, or emf (electromotive force) of
the cell, i is the current density, iRi is the ohmic potential drop, and qc and qA
are the polarisation of the cathode and the anode, respectively. As shown
in Eq. (7) each of the polarisation may be further split in an activation-
related contribution (subscript a) and a concentration (i.e., diffusion) related
contribution (subscript c).
The thermodynamic cell potential, Eeq, depends on reactant and product
partial pressures as well as temperature. For example, for the hydrogen/oxygen
fuel cell

where R is the gas constant, T is the temperature, and F is the Faraday constant.
AG" is the standard free-energy change of the reaction Hz + 1/202 --f H20; Le.,
the free-energy change when reacting species and products are all at the
standard pressure of 1 atm. The first term on the right-hand side of Eq. (gat,