A Mass Transport Model for Flows in Channels and Porous Media of Fuel Cells
Authors: Jarauta Alex , Zingan Valentin , Minev Peter , Secanell Marc 
Published: May 2020

Low-temperature fuel cells are a promising alternative technology to conventional energy systems such as internal combustion engines. However, their large-scale commercialization is still limited due to several challenges, such as mass transport losses at high power densities [1]. Estimation of gas transport properties in porous materials of fuel cells, such as gas diffusion layers (GDLs), is therefore critical. Several experimental studies in literature estimated the permeability of different GDL samples using a one-dimensional model, which does not account for channel effects [1-6]. Some authors in literature have assumed that the flow is incompressible in their numerical studies [7-10]. This hypothesis is not justified because the error in permeability estimation with an incompressible fluid flow model compared to the estimation with a compressible fluid flow model can be as high as 20% [2]. Numerical models for channels and porous media require volume-averaged formulations, and an in-depth discussion on the physical meaning of density and velocity in these models is seldom found in literature. Also, most of the existing numerical studies neglect the anisotropic nature of GDLs.
In this work, a volume-averaged form of the steady-state, compressible, and isothermal Navier-Stokes equations for flows in channels and porous materials is developed and implemented in the open-source framework OpenFCST [11]. Particular attention is given to flows in channels and GDLs of polymer electrolyte fuel cells. The fluid flow model in porous materials is derived by means of the method of volume averaging [12]. A continuous Galerkin finite element method is used to discretize and numerically solve the resulting system of governing equations in the framework of a single domain approach. The coupling boundary conditions at the internal interface between channels and porous media are discussed and a stable non-oscillatory pair of solution variables in the porous domain is obtained. The study reveals that for volume-averaged formulations, the permeability obtained in experiments has to be corrected with the sample porosity. The model is used to estimate in-plane and through-plane permeabilities of fuel cell diffusion media, which is compared to experimental data. Three-dimensional simulations show that channel effects cannot be neglected and therefore one-dimensional models for permeability estimation are limited. Assuming that the fluid is incompressible is only valid for through-plane permeability, and a compressible formulation should be used for in-plane simulations, even at moderate gas flow rates. The suitability of the mathematical model for fuel cell applications is illustrated by estimating the change in pressure drop in a serpentine channel in contact with either a solid wall or a gas diffusion media. An interdigitated channel design is also considered in order to compare the pressure drop and the velocity in the GDL with the results observed with a serpentine channel.

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