SOFC Modeling

SOFC performance modeling is impacted by the multi-physic processes taking place on the fuel cell surfaees. Heat transfer together with electrochemical reactions, mass and charge transport are eonducted inside the cell. There are many mathematical models of the SOFC [1], based mainly on mathematical descriptions of these physical, chemical, and electrochemical properties. There are several parameters affecting cell working eonditions, e.g. electrolyte material, electrolyte thickness, cell temperature, inlet and outiet gas compositions at anode and cathode, anode and cathode porosities ete. 

The SOFC models developed thus far are mainly based on the Nernst equation, activation, ohmic, and concentration losses. This approach results in good agreement with experimental data (for which adequate factors were obtained) and poor agreement for other than original experimental working parameters. Moreover, most of the equations used require the addition of numerous factors which are difficult or impossible to determine [2]. Very detailed models (for instance based on finite elements methods) are often characterized by relatively long times needed to find a solution for the used set of equations. Proper identification of all 

Milewski et al.. Advanced Methods of Solid Oxide Fuel Cell Modeling, Green Energy and Technology, DOI 10.1007/978-0-85729-262-9 5, 

Since fuel cell modeling is a multidisciplinary task (see Fig. 5.2), a good scientific background is needed to describe the fuel cell behavior in an appropriate way. As a first step, all known parameters which influence cell characteristics 

Mathematical modeling of any system can be divided into three levels  

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With today s computing power and popular use of CFD codes, SOFC modeling is moving toward multiphysics, electrochemical-transport-coupled, and three-... 

To illustrate typical simulation results from such multiphysics SOFC models, consider a co-flow and a cross-flow electrolyte-supported cell. The cross-flow geometry is of particular interest because of the complex transport phenomena offered in this cell configuration, a configuration able to provide detailed understanding of mass-transfer limitations. Structured, orthogonal meshes were used for all compu-... 

Experimental validation of SOFC models has been quite scarce. Khaleel and Selman °° presented a comparison of 1-D electrochemical model calculations with experimental polarization curves for a range of... 

Campanari S., Iora P., 2004. Definition and sensitivity analysis of a finite volume SOFC model for a tubular cell geometry. Journal of Power Sources 132(1/2), 113-126. 

Todd, B., Young, J.B., 2002. Thermodynamic and transport properties of gases for use in SOFC modeling. Journal of Power Sources 110, 186-200. 

In SOFC modeling the effect of radiation is usually overlooked. We would like to particularly emphasize this important issue in cell/stack modeling. High temperature fuel cells (SOFCs and MCFCs) usually operate at temperatures in the range... 

In contrast to the pseudo 3-D models, tmly multi-dimensional models use, in general, finite element or finite volume CFD (Computational Fluid Dynamics) techniques to solve full 3-D Navier-Stokes equations with appropriate modifications to account for electrochemistry and current distribution. The details of electrochemistry may vary from code to code, but the current density is calculated almost exclusively from Laplace equation for the electric potential (see Equation (5.24)). Inside the electrolyte, the same equation represents the migration of ions (e g. 0= in SOFC), elsewhere it represents the electron/charge transfer. In what follows, we briefly summarize a commonly used multi-dimensional model for PEM fuel cells because of its completeness and of the fact that it also addresses most essential features of SOFC modeling. 

Celik, I.B. and Pakalapati, S.R. (2003) A modular approach to SOFC modeling, Final Report submitted to Oak Ridge Associated Universities (ORAU) Oak Ridge, Tennessee. 

Jiang, W., Fang, R., Khan, J. and Dougal, R. (2006) Parameter setting and analysis of a dynamic tubular SOFC model, Journal of Power Sources 162(1), 316-326. 

Currently, the tendency in SOFC modeling seems to be to take into account all three heat transfer mechanisms. 

The SOFC model introduced in this section only solves the energy equation and the current conservation. The necessary information concerning fluid dynamics and diffusion of species is set through specific assumptions. 

Each hybrid system configuration uses a lumped parameter SOFC model. The SOFC model used in these studies is taken after Berry et al. [4], In this model the activation loss (voltage) is described by ... 

Liese E.A., Smith T.P., Haynes C., Gemmen R.S. (2006) A dynamic bulk SOFC model used in a hybrid turbine controls test facility. In Proceedings of the ASME Turbo Expo, Barcelona, Spain, GT2006-90383. 

Iora P., Aguiar P., Adjiman C.S., Brandon N.P. (2005) Comparison of two IT DIR-SOFC models Impact of variable thermodynamic, physical, and flow properties steady-state and dynamic analysis. Chemical Engineering Science 60, 2963-2975. 

Figure 3.21. Velocity field calculated by a fluid dynamics model for the turning area of the air/oxygen flow in a solid oxide fuel cell at operating temperature. (Reprinted from S. Campanari and P. lora (2004). Definition and sensitivity analysis of a finite volume SOFC model for a tubular cell geometry. /. Power Sources 132,113-126. Used by permission from Elsevier.)...

Morel B, Laurencin J, Bultel Y, Lefebvre-Joud F (2005) Anode-supported SOFC model centered on the direct internal reforming. J Electrochem Soc 152 A1382... 

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