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# A Two-Fluid Mathematical Model for Gas-Liquid Flows in PEM Fuel Cells

[+] Author Affiliations
Shih-Hung Chan

Yuan Ze University, Taiwan

Timothy W. Tong, Mohsen Abou-Ellail

George Washington University, Washington, D.C.

Karam R. Beshay

Cairo University, Cairo, Egypt

Paper No. FUELCELL2006-97003, pp. 1-12; 12 pages
doi:10.1115/FUELCELL2006-97003
From:
• ASME 2006 4th International Conference on Fuel Cell Science, Engineering and Technology
• ASME 2006 Fourth International Conference on Fuel Cell Science, Engineering and Technology, Parts A and B
• Irvine, California, USA, June 19–21, 2006
• ISBN: 0-7918-4247-9 | eISBN: 0-7918-3780-7

## abstract

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 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. The mean droplet diameter can be computed from a balance equation of the forces acting on the emerging liquid water from the pores of the GDL into the gas channels. The droplet diameters are found to range between 150 and 170 microns for the present PEM fuel cell at 0.8 V. In the present work, the full momentum conservation equations are invoked, in the layers of the fuel cell, for the two fluids. 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 a modified SIMPLE algorithm, for the two fluids. One solution domain is superimposed over all the layers 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 gas diffusion layers and simultaneously insuring a non-singular matrix of finite-difference coefficients. The obtained two-fluid and single-phase numerical 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 previous LHF model results and essentially completely bypassed by the single-phase simulations.

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