Page 318 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

294 High Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications

small-size, laboratory-scale cell, by fitting an appropriate model, can yield input
parameters for the performance of a larger cell or stack. This cell or stack
simulation can be used to determine the effects of various design and operating
parameters on the power generated, fuel conversion efficiency, maximum cell
temperature reached, stresses caused by temperature gradients, and the effects of
thermal expansion for electrolytes, electrodes, and interconnects.
Thus, modelling is an important tool in design optimisation, helping to answer
important practical questions such as what air and fuel flow rates must be used
to avoid excessive temperature or pressure drop. On the other hand, by providing
answers to questions such as how much the electrical properties of the cell
materials must be improved, simulations at the cell and electrode level can guide
the development of new and improved materials. Mathematical simulation,
therefore, has the potential to guide technology development, test the
significance of various design features, assess the effectiveness of developments
in materials or fabrication procedures, and select optimum operating conditions
from a set of feasible parameters.
Various modelling approaches exist. The modelling may focus on individual
thermal-mechanical, flow, chemical, and electrochemical subsystems or on
coupled integrated systems. Because the subsystems are typically characterised
by different length scales, modelling may also take place on different levels,
ranging from the atomistic/molecuIar-level via the cell component-level, the cell-
level to the stack-level, and finally to the system-level performance simulations.
This chapter discusses SOFC modelling primarily from the viewpoint of cells
and stacks, although some information on system modelling and more extensive
information on electrode modelling are also presented. After an introductory
discussion of modelling levels, the SOFC cell and stack are first examined from the
viewpoint of fluid dynamics and transport phenomena (SOFC as a heat and mass
exchanger). This is followed in Section 11.3 by an exposition of electrochemical
modelling at the ‘continuum level’, suitable for integration into modelling of
full-scale stacks (SOFC as an electrochemical generator). In Section 11.4, the
chemical reactions depending on fuel composition and the heat effects associated
with their electrochemical conversion are discussed in detail (SOFC as a chemical
reactor). Section 11.5 discusses cell- and stack-level modelling; and Section 11.6
briefly describes major approaches in SOFC system modelling (SOFC as a system
component): Section 11.7 links the thermal analysis of the SOFC cell and stack
with the modelling of thermal stresses: and Section 11.8 discusses in more detail
the electrochemical modelling at the pm level suitable for electrode design and
microstructure. Finally, Section 11.9 sketches possible approaches of molecular
modelling suitable for elucidating kinetic and mechanistic issues relevant to
SOFC performance.

11.2 Flow and Thermal Models
In a fuel cell operation, the flow, thermal, chemical, and electrochemical systems
are intrinsically coupled. Heat generation and absorption affect the temperature