Comparative Studies of Time-stepping Schemes for the Treatment of the Darcy Drag Term of the Momentum Equation

Abstract

A numerical comparison of time-stepping schemes for the solution of the conservation equations of mass and momentum of polymer electrolyte fuel cells (PEFCs) is presented. Darcy drag force is the dominating term for the fluid flow inside the gas diffusion layer (GDL). Permeability of the GDL is usually very small. Convergence of continuity is a major problem for the fluid flow through the GDL, and the situation becomes critical in lower-permeability cases. To overcome this kind of severe situation, an implicit scheme is used to obtain not only faster convergence but also a more accurate continuity condition. Explicit, implicit and semi-implicit treatment of the Darcy drag term is considered, and the schemes are compared for various physical parameters of the GDL, e.g., the Darcy number and the porosity parameter, by one dimensional numerical simulation. Influence of strict convergence on the secondary flow effect and on the pressure loss is described and the superiority of implicit scheme is confirmed for three-dimensional numerical simulation of PEFC channel flow.

Numerical Study of Pressure Drop Mechanism and Cross Flow Behavior in the Gas Channel and Porous Medium of a Polymer Electrolyte Membrane Fuel Cell

“…The fractional-step algorithm was developed by considering an implicit treatment of the Darcy drag term with attention to strict mass conservation. Details of the advantages of this algorithm have been described previously [28], and the algorithm is incorporated in our simulation code FrontFlow/Red PEFC version. This simulation code already has been validated by means of small-scale calculations on deformation of the GDL [29].…”

“…The details of this developed method and advantage was discussed in the previous paper by Saha et al [28] and it is used to carry out our present simulation. It is obviously important to notice that the error level change from 0.05% to 0.1% causes the change in the pressure drop which cannot be allowed as sometimes comparable the pressure drop obtained for two different order of permeability was reported in the study of Saha et al Using this improved method, the pressure drop mechanism was predicted with considering the complex situation of GDL deformation and validated the results with experimental work by Saha et al [29].…”

Numerical Investigation of Cross Flow on the Performance of Polymer Electrolyte Fuel Cell

“…The fractional-step algorithm was developed by considering an implicit treatment of the Darcy drag term with attention to strict mass conservation. Details of the advantages of this algorithm have been described previously [40], and the algorithm was incorporated in our FrontFlow/red (for PEFC) simulation code. This simulation code previously was validated using small-scale calculations on the deformation of the GDL [41].…”

“…The present model is developed to investigate the effect of gas flow phenomena on the electrochemical reaction. In order to treat the complex flow situation such as cross flow, it was previously developed a numerical method [40] focusing the mass conservation strictly which is incorporated to their [33,35] three dimensional single phase model to investigate the coupled flow, species transport and electrochemical aspects in a PEFCs. To check the feasibility of our developed model we intently designed such a complex flow in a polymer electrolyte fuel cell.…”