Three-dimensional Simulations of Transient Response of Pem Fuel Cells

Transients have utmost importance in the lifetime and performance degradation of PEM fuel cells. Recent studies show that cyclic transients can induce hygro-thermal fatigue. In particular, the amount of water in the membrane varies significantly during transients, and determines the ionic conductivity and the structural properties of the membrane. In this work, we present three-dimensional time-dependent simulations and analysis of the transport in PEM fuel cells. U-sections of anode and cathode serpentine flow channels, anode and cathode gas diffusion layers, and the membrane sandwiched between them are modeled using incompressible Navier-Stokes equations in the gas flow channels, Maxwell-Stefan equations in the channels and gas diffusion layers, advection-diffusion-type equation for water transport in the membrane and Ohm’s law for ionic currents in the membrane and electric currents in gas diffusion electrodes. Transient responses to step changes in load, pressure and the relative humidity of the cathode are obtained from simulations, which are conducted by means of a third party finite-element package, COMSOL. INTRODUCTION Modeling and analysis of transport of reactants and flow in PEM fuel cells improve our understanding of PEM operation under normal conditions, transients and failure. In particular, membrane electron assembly has mechanical, electrical and transport properties that depend strongly on hydration and temperature which can be computed by transport models. Due to decreasing cost of computation power and memory, 3D transient models of transport in full active area of a single PEM fuel cell with serpentine flow channels are readily available [1,2]. Moreover, in addition to relative success in tackling of the geometric complexity, modeling the physical complexity of PEM fuel cells remains a challenge; especially those related to multi-scale computational modeling of multiphase flow and transport in PEM fuel cells are addressed by Djilali [3]. Water transport in PEM fuel cell membranes consists of two important mechanisms: diffusion and drag. Both mechanisms are well-known and can be modeled in different ways. Springer et al. [4] use a one-dimensional diffusive model, which is based on the activity of water in the membrane, and empirical electro-osmotic drag. Springer model incorporates Fick’s Law with a modified diffusion coefficient, and an empirical electroosmotic drag coefficient, which is a linear function of the water concentration; thus leading to a transport mechanism that is similar to advection-diffusion equation, in which the advection velocity is the ionic currents of the membrane. Springer’s governing equations are widely used in modeling of the water transport in the membrane with small variations in the diffusion coefficient, and in the empirical electro-osmotic drag terms. More elaborate water transport models include the use of twoseparate diffusion equations for liquid water and hydronium ions by Berg et al. [5], using Maxwell-Stefan equations to model the diffusion of hydronium ions and water molecules in the solid matrix by Baschuk and Li [6]. In Springer model, boundary conditions are Dirichlet-type, and evaluated based on the absorption values at the catalystlayers. However, due to significant response times that are observed for the membrane’s water intake, several authors suggest that Neumann boundary conditions would be more appropriate in the transient analysis [5-7]. Here, we present time-dependent three-dimensional isothermal single-phase model of: − Water transport in the membrane based on the Springer model subject to Neumann boundary conditions; − Transport of species in gas channels and gas diffusion layers by Maxwell-Stefan equations; − Flow in gas channels by Navier-Stokes equations; − Darcy’s flow in anode gas-diffusion layer; − Conservation of charge in the membrane and gas diffusion layers in a U-section of a PEMFC with serpentine flow fields as shown in Fig. 1. The model is essentially similar to our previous twodimensional model [8].