Modeling Of Gaseous Flows Within Proton Exchange Membrane Fuel Cells

Kirk R. Weisbrod, Nicholas E. Vandcrborgh Energy and Process Engineering Group Los Alamos National Laboratory, Los Alamos,New Mexico- 87545

Stephen A. Grot Delphi Energy and Engine Management Systems Rochester, NY 14602


Development of a comprehensive mechanistic model has been helpful to understand PEM fuel cell performance. Both through-the-electrode and down-the-channel models have been developed to support our experimental effort to enhance fuel cell design and operation (1).

The through-the-electrode model was described previously. This code describes the known transport properties and dynamic processes that occur within a membrane and electrode assembly (1). Key parameters include transport through the backing layers, water diffusion and electro-osmotic transport in the membrane, and reaction elcctrochcmical kinetics within the cathode catalyst layer. In addition, two geometric regions within the cathode layer arc represented, the first region below saturation and second with liquid water present. Although processes at high gas stoichiometry are well represented by more simple codes, moderate stoichiomctry processes require a two dimensional representation that include the gaseous composition and temperature along flow channel. Although usually-PEM hardware utilizes serpentine flow channels, this code does not include such geometric features and thus the flow can be visualized along a single channel.

This paper describes the "down-lhe-channel model" which also incorporates all components of the earlier through-the-electrode model. The model proceeds by solving localized "through the electrode model" arithmetic, and uses those new conditions to set initial conditions for the next cell "down the channel." The model is first validated by comparison to a series of single cell tests under varying conditions. The effect of membrane thickness is explored. The impact of anode and cathode gas humidification, operating temperature and pressure are predicted.

Model Description

The model calculates the water and gas fluxes in the membane electrode assembly (MEA) and obtains the current density at each step along the flow channel. Components of the through-the-membrane model are summarized first, followed by the down-the-channel formulation.

Primary components of the model include gas transport, water and ionic transport in the membrane, and catalytic layer diffusion and reaction.

1. The transport of all gaseous components are represented by the Stefan-Maxwell equation. Often, at some location in the cathode backing, liquid water from the cathode catalyst layer is vaporized and travels to the cathode channel as vapor. For the region where liquid water is present, the effective diffusion coefficient is decreased further because some porosity in the backing layer is water filled.

2. Net water transport through the membrane is the sum of electro-osmotic drag and diffusion processes. It is defined as positive from anode to cathode. Depending upon conditions in the anode and cathode channels, diffusion may be transporting water either toward or away from the anode catalyst layer. The model assumes liquid water is not transported through the anode backing. Because of this vapor transport, at the anode catalyst layer - membrane interface the membrane is at equilibrium with saturated vapor as long as liquid water is present (two phase) in the anode channel. Relationships for the expansion of the membrane as a function of water content are also included. Membrane transport rates, water diffusion and proton conductivity, agree with those published previously (2).

3. Oxygen reduction in the cathode catalyst layer is described by four main equations, (a) Butler-Volmer reaction kinetics are used with reaction coefficients derived from Parthasarathy et al. (3,4).

(b) Potential drop through the porous catalyst layer was calculated by ohms law with an effective resistivity dependent upon bulk conductivity at a given water saturation and porosity of the layer.

(c) Flux of oxygen is related to local current density, (d) Finally, the change in oxygen concentration with position is related to oxygen flux and the effective oxygen diffusion coefficient. As in other models, it is assumed that the cathode dynamics are rate limiting, and thus hydrogen oxidation rate terms are not included. In anode-limited electrochemical cases other models would be required.

The down the channel section of the model solves for the change in gas temperature and compositions for the anode and cathode channels. In the calculations shown here, that anode and cathode gases flow in parallel. While the gas streams can enter at any temperature, all solid components including backing layers are at uniform temperature at any one point along the flow channel. The differential equations used to describe the down the channel behavior are similar to those given by Nguyen et al (5). Ten equations are solved for the following 10 unknowns: five at the anode

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