A Two-Phase Flow Mathematical Model for Proton Exchange Membrane Fuel Cells With Enhanced Geometry
Authors: Chan Shih-Hung , Tong Timothy , Abou-Ellail Mohsen , Beshay Karam R. 
Published: November 2008

The produced water vapor in the vicinity of the membrane, of a proton exchange membrane fuel cell (PEMFC), 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 present mathematical model is based on the locally homogeneous flow model (LHFM) where the slip velocity between the two phases is assumed negligibly small. Therefore, the governing gas-phase and liquid-phase, for each dependent variable, can be economically added together. The resulting equations contain a ‘mixture density’, which is a function of the void fraction, species mass fractions, pressure and temperature. The resulting governing equations for u, v, T and species mass fractions together with the electric potential and mass continuity equations are solved iteratively using the SIMPLE algorithm. One solution domain is superimposed over all the layers of the PEMFC with appropriate boundary conditions applied at inlet, exit and sidewalls of the fuel cell. Special care is devoted to the electric potential, ‘Poisson-type’, equation boundary condition to prevent any escape of protons through the two diffuser layers and simultaneously insuring a non-singular matrix of finite-difference coefficients. This is because Poisson equation is notoriously known for having problems with zero gradient boundary condition. 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 voltage vanishes. The obtained 2-phase and 1-phase simulations are compared with the corresponding experimental and numerical data available in the literature. Systematically, the 1-phase current density is under predicted especially for values of the cell potential less than 0.8 V. On the other hand, the two-phase simulation current density, of the parallel geometry FC, is in very good agreement with the corresponding experiment data. The 2-phase flow simulations show that most of the liquid phase is concentrated in the cathode, reaching maximum value near the cathode catalyst layer-membrane interface. A new design of the serpentine PEMFC is suggested and is tested numerically. The new design involves blocking the outlet sections, either partially or fully, of the anode and/or the cathode gas channels to force the flowing fluids to diffuse into the catalyst layers at rates higher than a typical parallel geometry PEMFC. The new serpentine PEMFC design is expected to increase the concentrations of the hydrogen fuel and the oxidant in the catalyst layers and hence increase the transfer current densities. In order to obtain full simulation of the enhanced geometry of the fuel cell, the end boundary condition of the gas channels is adjusted using zero porosity to prevent any flow through the blocked area which automatically reduces the local velocity to zero value. The two-phase flow numerical results, for the modified serpentine PEMFC, indicate that the performance of the fuel cell could be enhanced appreciably.