An Efficient Two-grid Method for a Two-phase Mixed-domain Model of Polymer Exchange Membrane Fuel Cell

AbstractIn this paper, an efficientandfast numerical methodis studiedand implementedfora simplifiedtwo-phasemixed domain model of polymer exchange membrane fuel cell (PEMFC), which fully incorporates both the anode and cathode sides, including the conservation equations of mass, momentum, water vapor concentration, liquid water saturationandwater content.Theproposed numericalalgorithmisbasedonthetwo-grid discretization technique,the combined finite element-upwind finitevolume method and some other appropriate linearization schemes. The original nonlinear partial differential equations are only solved on the coarse grid while the fine grid approximation solution is obtained linearly. Therefore the computational time can be reduced tremendously compared with the traditional one-grid method. Numerical experiments of the two-grid method and conventional method for a two-phase mixed domain fuel cell model are carried out, showing that the presented method is effective and accurate for the numerical simulation of PEMFC

Numerical Analysis of Finite Element Method for a Transient Two-phase Transport Model of Polymer Electrolyte Fuel Cell

AbstractIn this paper, we study a 2D transient two-phase transport model for water species in the cathode gas diffusion layer of hydrogen polymer electrolyte fuel cell (PEFC), the reformulation of water concentration equation is described by using Kirchhoff transformation, and its numerical efficiency is demonstrated by successfully dealing with the discontinuous and degenerate water diffusivity. The semi-discrete and fully discrete finite element approximations with Crank-Nicolson scheme are developed for the present model and the optimal error estimate in H1 norm and the sub-optimal error estimate in L2 norm are established for both finite element schemes

Modeling studies and numerical analyses of coupled PDEs system in electrohydrodynamics

Electrohydrodynamics (EHD) is the term used for the hydrodynamics coupled with electrostatics, whose governing equations consist of the electrostatic potential (Poisson) equation, the ionic concentration (Nernst-Planck) equations, and Navier-Stokes equations for an incompressible, viscous dielectric liquid. In this dissertation, we focus on a specic application of EHD - fuel cell dynamics - in the eld of renewable and clean energy, study its traditional model and attempt to develop a new fuel cell model based on the traditional EHD model. Meanwhile, we develop a series of ecient and robust numerical methods for these models, and carry out their numerical analyses on the approximation accuracy. In particular, we analyze the error estimates of nite element method for a simplied 2D isothermal steady state two-phase transport model of Proton Exchange Membrane Fuel Cell (PEMFC) as well as its transient version. On the aspect of hydrodynamics arising in the fuel cell system, the fluid flow through the open channels and porous media at the same time, both Navier-Stokes equations and Darcy\u27s law are involved in the fluid domains, leading to a Navier-Stokes-Darcy coupling problem. In this dissertation, we study a one-continuum model approach, so-called Brinkman model, to overcome this problem in a more ecient way. To develop a new fuel cell model based on EHD theory, in addition to the two-phase transport model of fuel cells, we carry out numerical analyses for Poisson-Nernst-Planck (PNP) equations using both standard FEM and mixed FEM, which are the essential governing equations involved by EHD model. Finally, we are able to further extend the traditional fuel cell model to more general cases in view of EHD characteristics, and develop a new fuel cell model by appropriately combining PNP equations with the traditional fuel cell model. We conduct the error analysis for PNP-Brinkman system in this dissertation