A Two-Fluid Mathematical Model for Two-Phase Flow in PEM Fuel Cells
Authors: Chan Shih-Hung , Tong Timothy W. , Abou-Ellail Mohsen , Beshay Karam R. 
Published: October 2008

The proton-exchange membrane (PEM) fuel cell works under low temperatures and hence is suitable for the automotive industry. The produced water vapor in the vicinity of the membrane may condense into liquid water, if the water mass fraction is higher than the saturation value corresponding to the local temperature. In this case the flowing fluid inside the layers of the PEMFC is a 2-phase flow. The locally homogeneous flow (LHF) model has been previously used for modeling the 2-phase flow in PEM fuel cells, with limited success. This model could not predict the blocking effect of the liquid phase, since both phases flow locally with the same velocity, according to the LHF model. In contrast to complete coupling of the two phases, assumed by the LHF model, a blocking model was used by some investigators where the liquid is totally uncoupled to the gas phase. This assumption causes the liquid to become essentially stationary inside the pores of the GDL and catalyst layers and hence only the gas phase equations need to be considered. Both of these extreme models were only successful to a limited extent. The present work considers a two-fluid mathematical model for the gas-liquid flow in PEM fuel cells. One fluid represents the continuous gas phase flow through the layers of the fuel cell. For this fluid, the governing equations of momentum, energy, mass continuity and species mass fractions, are considered with additional inter-fluid exchange source terms. The second fluid represents the dispersed liquid phase that is formed from the condensed water vapor inside the layers of the PEM fuel cell. For this fluid only the momentum, energy and mass continuity equations need to be included, as no electrochemical reactions are essentially possible. The dispersed fluid is made up of small droplets in the gas channel. However, in the porous layers of the fuel cell, the flowing layers of water represent the dispersed fluid over the solid matrix. The thickness of the creeping water layers is controlled by the wetability of the solid matrix of the porous layers of the PEM fuel cell. Numerical computations are carried out for a typical proton exchange membrane fuel cell that has experimental data. In order to obtain complete performance results, the computations are repeated for increasing fuel cell electric current densities until the limiting current is reached. The obtained two-fluid and single-phase simulations are compared with the corresponding experimental and numerical data available in the literature. The 2-fluid model shows that the blocking effect of the liquid phase starts to dominate, for cell voltage less than 0.65 V; in this case, the flowing 2-phase flow produces faster drop in cell voltage as the loading electric current increases. This phenomenon was partially hindered by the LHF model but essentially completely bypassed by the single-phase simulations. The 2-fluid simulations show that most of the liquid dispersed phase is concentrated in the cathode, reaching maximum value near the cathode catalyst layer- membrane interface. This behavior results from the lack of mobility of the liquid water inside the pores.