Development of a Fully Explicit Matrix Inversion Free Finite Element Algorithm for the Simulation of High Temperature Fuel Cells
Mauro, Alessandro (2009) Development of a Fully Explicit Matrix Inversion Free Finite Element Algorithm for the Simulation of High Temperature Fuel Cells. [Tesi di dottorato] (Inedito)
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In this work of thesis, a new, detailed and complete proprietary non-commercial model, for two- and three- dimensional accurate and efficient fuel cells and thermo fluid dynamic problems simulation, has been developed. The Artificial Compressibility (AC) matrix inversion free version of the Characteristic Based Split (CBS) algorithm has been specifically implemented, for the first time, to simulate heat and mass transfer phenomena in free fluid channels and porous electrodes of an anode-supported planar Solid Oxide Fuel Cell (SOFC), in order to reduce computing requirements and allow easy parallelization procedure. The generalized porous medium model has been adopted to describe heat and fluid flow in domains containing simultaneously a porous and a free fluid layer. The Finite Element Method (FEM) has been employed, for the spatial discretization of the governing partial differential equations (PDEs) over the computational domain, in order to allow multidisciplinary applications. A single domain approach, for the whole fuel cell, has been successfully used, in order to increase to flexibility of the algorithm. A stability analysis for the AC-CBS scheme has been specifically carried out, in order to stabilize and speed up the solution process. The algorithm has been applied to many complex engineering problems simulation, both in two and three dimensions, related to isothermal and non-isothermal incompressible flows, flow through saturated porous media, flow through interfaces between saturated porous media and free fluids and SOFCs. All the results obtained by using the present algorithm have been undergone a Verification and Validation (VV) procedure against analytical, experimental and numerical data available from the literature, in order to ensure their accuracy. The present work of thesis can be involved in the more general survey of energy saving. This issue is becoming significant due to increasing power demand, instability of the rising oil prices and environmental problems. Among the various renewable energy sources, fuel cells are gaining more popularity due to their high efficiency, cleanliness and cost-effective supply of power demanded by the consumers. SOFCs are considered particularly interesting thanks to their modularity, fuel adaptability and very low levels of NOx and SOx emissions. Furthermore, because of their high operating temperature (≈800°C), natural gas fuel can be reformed within the cell stack eliminating the need for an expensive external reformer and also less expensive catalyst materials can be used. The high operating temperature also 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 the traditional energy conversion systems. To make SOFCs commercially competitive, more research effort is required to better understand some of the fundamental aspects of these systems. Under operating conditions, several phenomena (mass, energy and charge transport; chemical and electrochemical reactions) take place in different parts of the fuel cell. Such phenomena occur simultaneously, and are strongly coupled to each other. Therefore, a physically representative prediction of the fuel cells operating conditions is not an easy objective to achieve. In the author’s opinion, the development of flexible and detailed proprietary codes is still extremely important in order to simulate the complex physical phenomena evolving in SOFCs, predict their overall performances and face future challenges effectively. In particular, more efficient, accurate and stable algorithms are needed to solve the strongly coupled PDEs governing fuel cells operation. In fact, many commercial and proprietary codes can fail in finding the solution of such complex thermo fluid dynamic problems, mainly because of instability issues. For example, the presence of large source terms, due to both porous domains with very low permeability and high buoyancy forces, is one of the main causes of numerical instability. The present model has been specifically developed to overcome such difficulties and produce a fast, efficient and accurate solution for complex thermo fluid dynamic and SOFC problems. The thesis is structured as follows: the first chapter presents an overview of fuel cells technology; chapter two describes the analytical model proposed for SOFCs simulation; the third chapter presents the numerical model employed to solve the governing PDEs; chapter four shows the VV procedure for the thermo fluid dynamic model, adopted to ensure the correctness of the results obtained by using the present algorithm; finally, chapter five presents the results obtained for the simulation of an anode-supported planar SOFC, in different operating conditions, while some conclusions are drawn at the end of the thesis, together with the description of the future developments of this work.
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