Gas Phase Theory

When gas phase diffusion is enabled, the gas phase nodes solve for a set of mass fraction variables, ωi, where i is the index of the species. The governing equations are defined using the Maxwell–Stefan set of equations, as described in Theory for the Transport of Concentrated Species Interface.

Darcy’s Law

When Darcy’s law is enabled, the gas phase nodes solve for a pressure variable p (Pa).

The Darcy’s law equations are documented in Theory for the Darcy’s Law Interface.

Built-in Binary Diffusion Coefficients

The calculation of the built-in binary diffusion coefficients is done using the Fuller–Schettler–Giddings (FGS) model (Ref. 2):

(3-5)

where T denotes the temperature (K), Mi the molecular weight of species i (g/mol), P is the pressure (Pa), and vi are the atomic diffusion volumes (Fuller diffusion volume) (cm3).

Table 3-1: Diffusion volumes used for calculating binary diffusion coefficients.
Species	Fuller Diffusion Volume
H2	6.12
O2	16.3
H2O	13.1
N2	18.5
CO	18
CO2	26.9
CH4	25.15

Built-in Dynamic Viscosity

The built-in mixture viscosity of the gas phase is based on kinetic theory by Brokaw (Ref. 3):

where

(3-6)

and the interaction parameter is defined as

(3-7)

with

(3-8)

where ηi,v is the vapor viscosity of each individual species, and Mi are the molecular weights.

Built-in Thermal Conductivity

The gas phase mixture thermal conductivity, which may be used in heat transfer simulations, is calculated by the Hydrogen Fuel Cell and Water Electrolyzer interfaces according to (Ref. 4)

(3-9)

(3-10)

In the above formula, the summations are done for all active species, where λi,v and ηi,v are the individual vapor thermal conductivity and dynamic viscosity correlations as a functions of temperature for the pure gases, respectively. The normal boiling points Tb,i and the species molecular weights are also considered. The factor Sij equals 0.773 if either i or j represents the index of water (steam). For all other cases Sij =1.

Since the above equation relies on the individual species viscosities, the thermal conductivity is only calculated in gas phase domains using built-in (non-user defined) dynamic viscosities.

Built-in Heat Capacity

The Hydrogen Fuel Cell and Water Electrolyzer interfaces also calculate the heat capacity of the gas mixture which may be used in heat transfer simulations. The heat capacity is calculated as

where Cp,mix is the heat capacity of the fluid mixture in J/(kg·K), cp,i is the species heat capacity in J/(mol·K).