A Mixed Wettability Pore Size Distribution Based Mathematical Model for Analyzing Two-Phase Flow in Porous Electrodes

Abstract

A multi-dimensional, non-isothermal, two-phase membrane electrode assembly (MEA) numerical model is developed where the micro-structure of the porous layers is characterized by a mixed wettability pore size distribution (PSD). The PSD model is used to predict local water saturation based on gas and liquid pressures, and can be used to study the effect of varying pore size and wettability. The MEA model accounts for gas transport via molecular and Knudsen diffusion, liquid water transport, sorbed water transport by back-diffusion, electro-and thermo-osmosis, and heat generation and transport. Multi-step kinetic models are used to predict anode and cathode electrochemical reactions. Local transport losses are accounted for using a local transport resistance. The PSD model is used to predict capillary pressure vs. saturation and saturation vs. relative liquid permeability curves based on PSDs from several GDLs obtained using mercury intrusion porosimetry. The PSD-based MEA model electrochemical performance predictions are also compared to experimental data from the literature. Results show that the numerical model is able to capture the performance changes associated with varying temperate and the introduction of a micro-porous layer. Improving the performance of polymer electrolyte fuel cells (PEFCs) at high current density is critical for reducing stack size, cost and weight in automobile applications. Water accumulation in the electrode however, limits fuel cell performance at high current densities. [1][2][3] In order to mitigate the excessive water buildup in the cell, which hinders mass transport, gas diffusion layer (GDL) and catalyst layer (CL) microstructures and wettabilities must be advanced to achieve sufficient water retention in the electrolyte, reject excess water in vapor form and alleviate complete flooding of the electrode. For example, by modifying the weight percentage (wt%) of the hydrophobic content in the GDL, Wang et al. 4 reported a 10%-20% increase in performance. To understand fuel cell behavior in the two-phase region and optimize the design of GDL and CL, a two-phase model which includes microstructural information of the porous layers is needed.Two approaches have commonly been used to study liquid water transport in fuel cells. The first approach involves the solution of a saturation equation obtained by replacing liquid pressure by saturation in Darcy's law. [5][6][7] In this approach the Levertt J-function is commonly used to relate saturation with capillary pressure. The Leverett J-function is however, an empirically measured curve for a given material and it is obtained from porous media structure analysis. Thus, it is difficult to optimize the structure of the porous layers using Leverett J-functions. The second approach, known as the multi-phase approach, involves solving mass and momentum equations for gas and liquid phases independently and then relating the capillary pressure to saturation using a closure equation based on micro-structural information such as a pore size dist...

A Mixed Wettability Pore Size Distribution Based Mathematical Model for Analyzing Two-Phase Flow in Porous Electrodes

“…1 Due to the more anisotropic capillary pressure distribution in Toray 090, a greater change in saturation between the channel and the rib regions is observed in Figure 12g as compared to the SGL 34BA. The oxygen molar fraction distributions for two GDLs are plotted in Figures 12h and 12i.…”

“…All the water fluxes and PCI flow in the MEA are shown in Figure 3. The normalized water flux reported in the plots is defined as, [1] where N H2O is the water flux evaluated at the boundary in g/(cm 2 · s), F is Faraday's constant, j is the current density and M H2O is the water molar mass. The positive values in Figure 3a represent a flux leaving the MEA.…”

Virtual Liquid Water Intrusion in Fuel Cell Gas Diffusion Media

“…Agreement at lower saturations in the GDL would be more beneficial for the prediction of transport parameters during in-situ fuel cell operation 79 because the liquid intrusion would be governed by the underlying catalyst layer or micro-porous layer and proceed until breakthrough of the liquid water into the channels at saturations of 8-25%. [79][80][81] In this study, however, the objective was only to evaluate the accuracy of the CFM model to predict liquid water distributions and transport properties. A major difference between the CFM and μ-CT water distributions, was the appearance of smaller and discrete liquid water clusters compared to the larger water clusters in the μ-CT reconstructions.…”

Free open reference implementation of a two-phase PEM fuel cell model

“…Historically, simple Dirichlet BCs for s are often used [19,29,30]. Conditional unidirectional flux conditions have later been proposed as a more realistic replacement [31,32], but solving these numerically can be a challenge [33]. We use here a Dirichlet BC for s at the CGDL/GC interface-the simplest common denominator in two-phase MEA modeling-bearing its limitations in mind.…”