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

(20–87)

where 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 Fuel Cell and Electrolysis user defined functions (UDF) as,

(20–88)

In addition to Equation 20–87, the Ansys Fluent Fuel Cell and Electrolysis 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):

(20–89)

where is the effective gas species diffusivity, is the porosity of the porous medium, 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 the Fuel Cell and Electrolysis Model. in Equation 20–89 is used to model the effect of tortuosity. While this is implemented as the default method in the Fuel Cell and Electrolysis Model, 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

For SOFC and high-temperature Electrolysis, the ionic conductivity in the electrolyte is modeled as a function of temperature, and, by default, is defined as:

(20–90)

This is valid for temperatures ranging from 1073 K to 1373 K. You can implement your own models in the user-customizable UDF function Electrolyte_Conductivity in pem_user.c.

For high-temperature PEMFC, the electrolyte (also called the membrane) phase conductivity is a user-specified constant.

For low-temperature PEMFC, the electrolyte (also called the membrane) phase conductivity is modeled as:

(20–91)

where is the water content. Two model constants, and are introduced in Ansys Fluent for generality. Equation 20–91 becomes the original correlation from [627] when .

Osmotic Drag Coefficient (low-temperature PEMFC)

(20–92)

Back Diffusion Flux (low-temperature PEMFC)

(20–93)

where and are the density and the equivalent weight of the dry membrane, respectively.

Membrane Water Diffusivity (low-temperature PEMFC)

(20–94)

Water Content (low-temperature PEMFC)

The water content, , that appears in the preceding property computations are obtained using Springer et al’s correlation [627],

(20–95)

here is the water activity that is defined as,

(20–96)

where and are the water vapor pressure and the saturation pressure, respectively.

Water Vapor Pressure

The water vapor pressure is computed based upon the vapor molar fraction and the local pressure,

(20–97)

Saturation Pressure

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

(20–98)

It is noted here that in [627], water activity is defined on the basis of total water or super-saturated water vapor. With phase change being invoked in the present two-phase model, is added to the original formulation as suggested by [156].