Gas Phase Species Diffusivity

Gas phase species diffusivities can be computed either by using the dilute approximation method or by using the full multicomponent method. With the dilute approximation method, we have

(20–45)

where is the porosity of the porous medium, is the mass diffusivity of species at reference temperature and pressure (, ) [663]. These reference values and the exponents () as well as the exponent of pore blockage () are defined in the PEMFC user-defined functions (UDF) as,

(20–46)

In addition to Equation 20–45, the Ansys Fluent PEMFC model also contains a method to compute the gas phase species diffusion (a full multicomponent diffusion method with corrections to account for the porous media tortuosity):

(20–47)

where is the effective gas species diffusivity, is the gas species mass diffusivity computed by the full multicomponent diffusion method (see Full Multicomponent Diffusion in the Fluent Theory Guide), and is the Knudsen diffusivity computed from Equation 20–105. Note that the Knudsen diffusion plays an important role in determining the gas diffusivity because the average pore size in the porous media can be on the same order as the mean free path in PEMFC.

Note that in Equation 20–47 is used to model the effect of tortuosity. While this is implemented as the default method in the PEMFC, you can overwrite it with your own correction methods by using the user-modifiable routines that are provided.

Properties such as electrolyte phase electrical conductivity, water diffusivity, and the osmotic drag coefficient are evaluated as functions of the water content, using various correlations as suggested by [627]. To capture the relevant physics of the problem, various properties of the membrane are incorporated into the model as default options. You can, however, directly incorporate your own formulations and data for these properties by editing the functions defined in the provided source code file called pem_user.c and compiling the code yourself. For more information, see User-Accessible Functions.

Electrolyte Phase (Ionic) Conductivity

The electrolyte (also called the membrane) phase conductivity is modeled based upon [627]:

(20–48)

where is the water content, and is the activation energy for the temperature correction term. The is calculated as ([586]):

(20–49)

Two model constants, and are introduced in Ansys Fluent for generality. Equation 20–48 becomes the original correlation from [627] when .

Diffusivity of Water Content

The diffusivity coefficient in the water content (dissolved phase) transport equation is computed as follows:

(20–50)

where is a user-specified coefficient for generality, and the function can be computed from Wu et al. [718] or Wang and Wang [691]:

Osmotic Drag Coefficient

(20–53)

where is a user-specified coefficient for generality with the default value of 1.0. The default formulation for is:

This formulation can be changed using the provided user-accessible function code file pemfc_user.c.

Saturation Pressure

The saturation pressure is calculated, in terms of , as,

(20–54)

Ansys Fluent allows you to provide a custom formulation by modifying the user-accessible function code file pemfc_user.c.