Thesis for degree: Licentiate of Engineering

Figure 2.2: Characteristic time and length scales for various modeling methods. Data is taken from [1].
At macroscale, homogeneity is assumed throughout the model, which subsequently can cause
errors during the loop of the modeling algorithm. Several models are based on the assumption
that the porous structure is isotropic and can be described by a few experimentally estimated
parameters [4, 8]. Porosity, tortuosity, and surface area to volume ratio are examples of
parameters that are affected by assumptions concerning homogeneity at all scales. Note that
these microstructural parameters are known to have a significant influence on the cell
performance and durability [9]. As the available computational power increases, it opens up
for a more sophisticated and deeper understanding of the physical processes and effects of
chemical reactions within the porous microstructure. This makes it possible to address the
microstructural uncertainties to improve cell performance, as these are limiting the SOFC
progress [10].
Multiphysics modeling takes into account the interaction between several physical processes,
which can be described by partial differential equations. A good computational design
considers the physical processes and the system at both a microscale and a macroscale level.
Some of the limitations are the lack of material structure and test data in the literature to
validate the models [11, 12]. The results of a numerical simulation cannot guarantee of how
well the cell actually will operate in reality. Because of the numerical approximations and
arbitrary unknowns implemented in the model, there will most likely be a number of errors
and inaccurate results [11]. Still, the use of numerical modeling as a predictive tool can be
validated through careful consideration of results and comparisons of numerical and
experimental data. A great deal of computational modeling research, where the results are
obtained from numerical codes, has achieved sufficient accuracy both in comparison with
other different numerical modeling approaches and with experimental data [10-11].
Fuel cell modeling is complicated due to the interaction of physical and chemical processes,
such as multicomponent gas flow with heat and mass transfer, electrochemical and reforming
reactions [10-11]. To model SOFCs, it is common to handle the governing equations in
differential forms by deriving them in forms of discretized equations. These equations are
solved numerically by the Gaussian-elimination method or the Tri-diagonal matrix algorithm.
There are several approaches to solve these by numerical methods. For macroscale, in a
simplified manner, one may say that the methods differ in the sense of how the flow variables
are approximated. The commercial software which is currently available is mainly based on
the Finite Difference Method (FDM), the Finite Element Method (FEM) and the Finite
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