1.5 Liquid Water Formation, Transport, and its Effects (PEMFC Only)

Since PEM fuel cells operate under relatively low temperature ( $<$100 $^\circ$C), the water vapor may condense to liquid water, especially at high current densities. While the existence of the liquid water keeps the membrane hydrated, it also blocks the gas diffusion passage, reduces the diffusion rate and the effective reacting surface area and hence the cell performance. To model the formation and transport of liquid water, ANSYS FLUENT uses a saturation model based on [ 7],[ 5]. In this approach, the liquid water formation and transport is governed by the following conservation equation for the volume fraction of liquid water, $s$, or the water saturation,

where the subscript $l$ stands for liquid water, and $r_{\rm w}$ is the condensation rate that is modeled as,

where $-r_{\rm w}$ is added to the water vapor equation, as well as the pressure correction (mass source). This term is not applied inside the membrane. The condensation rate constant is hardwired to $c_{\rm r} = 100 s^{-1}$. It is assumed that the liquid velocity, $V_{\rm l}$, is equivalent to the gas velocity inside the gas channel (i.e., a fine mist). Inside the highly-resistant porous zones, the use of the capillary diffusion term allows us to replace the convective term in Equation  1.5-1:

Depending on the wetting phase, the capillary pressure is computed as a function of $s$ (the Leverett function),

where $\varepsilon$ is the porosity, $\sigma$ is the surface tension (N/m $^2$), $\theta_c$ is the contact angle and $K$ the absolute permeability.

Equation  1.5-1 models various physical processes such as condensation, vaporization, capillary diffusion, and surface tension.

The clogging of the porous media and the flooding of the reaction surface are modeled by multiplying the porosity and the active surface area by $(1-s)$, respectively.