FEM Based Solution of Thermo Fluid Dynamic Phenomena in Solid Oxide Fuel Cells (SOFCS)

Computer models have become a common tool for the analysis of engineering problems such as energy conversion systems. In fact, these models, based on the numerical solution of the set of equations that describe the physical problem give the possibility to reduce costs and time needed to perform experiments. For instance in system optimization, it is only necessary to validate through experiments the optimal solution chosen based on numerical data. Furthermore, computational models can provide detailed information on complex phenomena, such as those occurring in energy conversion processes, that can otherwise be extremely difficult to obtain from measurements. Numerical methods can also be used to design and analyse experiments, in order to estimate systematic errors. Fuel cells represent a very interesting example of complex engineering application. Among other energy conversion systems, fuel cells have gained popularity due to the high efficiency, low emissions and potentially cost-effective supply of electric power. Solid Oxide Fuel Cells (SOFCs) are considered particularly interesting thanks to their modularity, fuel adaptability and low levels of NOx and SOx emissions. Furthermore, high operating temperatures allows cogeneration, making SOFC technology particularly suitable for stationary power generation. Nowadays, despite the intensive research and significant progress, SOFCs are still not ready for commercialization, due to high manufacturing and operating costs and low reliability, compared to more traditional energy conversion systems. To make SOFCs commercially competitive, it is necessary to better understand some of the fundamentals of these systems, and optimize design and operation. All these objectives can be achieved through efficient numerical tools. Several phenomena (mass, energy and charge transport, chemical and electrochemical reactions) take place in a fuel cell and need to be clearly understood. These phenomena occur simultaneously, and are strongly coupled, making a physically representative prediction of fuel cells operating conditions extremely complex. The complexity of the phenomena occurring in SOFCs, the presence of electrodes that can be modelled as porous media with very low permeability and the necessity to accurately describe multispecies gas diffusion and eventually reforming chemical reactions, make it necessary to develop accurate and flexible numerical codes for detailed description of fuel cells operation. As a consequence, the development of fast, stable, flexible and robust proprietary codes is still extremely important to predict SOFCs performance. Based on this idea, the authors have developed a novel Artificial Compressibility (AC) Characteristic Based Split (CBS) algorithm for the solution of thermo fluid-dynamic problems in composite domains and in presence of large source terms. Based on such a novel numerical scheme, a detailed model has been developed and employed for the effective numerical simulation of SOFC. The matrix inversion free procedure, the stability of the solution process and the use of single domain approach enormously increase the flexibility of the present code. In this chapter, the main models available for the description of SOFCs operating principles are reviewed, from the initial and significant attempts to the more recent multi-dimensional models for fuel cells. The numerical procedure developed by the authors, based on the Finite Element Method (FEM), is presented together with the results obtained for an anode supported SOFC.