Wei Jiang Ruixian Fang Department of Mechanical Engineering, University of South Carolina, Columbia, SC 29208 Roger A. Dougal Department of Electrical Engineering, University of South Carolina, Columbia, SC 29208 Jamil A. Khan Department of Mechanical Engineering, University of South Carolina, Columbia, SC 29208 Thermoelectric Model of a Tubular SOFC for Dynamic Simulation A one-dimensional transient model of a tubular solid oxide fuel cell stack is proposed in this paper. The model developed in the virtual test bed (VTB) computational environment is capable of dynamic system simulation. This model is based on the electrochemical and thermal modeling, accounting for the voltage losses and temperature dynamics. The single cell is discretized using a finite volume method where all the governing equations are solved for each finite volume. The temperature, the current density, and the gas concentration distribution along the axial direction of the cell are presented. The dy- namic behavior of electrical characteristics and temperature under the variable load is simulated and analyzed. For easy implementation in the VTB platform, the nonlinear governing equations are discretized in resistive companion form. The developed model is validated with experimental results and can be used for dynamic performance evaluation and design optimization of the cell under variable operating conditions and geometric condition. DOI: 10.1115/1.2906114 Keywords: solid oxide fuel cell, SOFC, dynamic model, simulation, virtual test bed 1 Introduction Research in solid oxide fuel cell SOFC is gaining momentum because of its distinct advantages over other energy conversion methods. It has the distinct advantages of high energy conversion efficiency, low environmental impact, and flexibility of usable fuel type. The high operating temperature 800°C allows the direct reformation of the natural gas. The hydrogen is electrochemically converted producing electrical power and high quality by-product heat for cogeneration or other cycle. So far, a 47% net SOFC electrical efficiency has been achieved as demonstrated in Ref. 1. Furthermore, the integration of a pressurized SOFC stack lends itself to the possibility of hybrid power generation, where the stack gases can be used to operate a gas turbine. One such power system in operation today Siemens-Westinghouse Power Corporation achieves an efficiency of 55% 2. It is apparent that the SOFC has the potential to play a significant role in the electric utility. Several models, with different levels of detailed description, have been developed and tested in the past couple of years to study the design and operating conditions of SOFC stack. Most models, however, are steady state models 3,4 and can validly work for only the specific operating points. Padulles et al. 5 developed a SOFC model with species dynamic, but temperature and heat transfer dynamics were not considered in their model. A dynamic transient SOFC model has been developed by Sedghisi- garchi 6; however, their model is based on lumped capacitance model where the spatial distributions of temperature, current den- sity, and species concentration are not investigated. In this paper, a one-dimensional dynamic model of a tubular SOFC with internal reforming, complying with the discussed characteristics and capable of system integration, is presented. This model, based on the electrical quantities, chemical reaction equilibrium, and energy balance, can predict the SOFC character- istics at the steady states and also at transient operating states. The accuracy and reliability of the model are demonstrated by com- parisons with experimental data from the literature. Furthermore, the temperature, current density, and gas concentration distribu- tion along the axial length of the cell are individually analyzed. The distinctive feature of the current model is that the model takes into consideration the variation of variables in the axial direction. As a result, it can predict the cell performance more accurately. In addition, the simulation developed from the model is dynamic in nature. As a result, this can be used for performance evaluation and design optimization of the cell under variable operating con- ditions and geometric conditions, respectively 7. To the best of the knowledge of the authors, such a model is the first of its kind. The virtual test bed VTB, a software developed at the Univer- sity of South Carolina, provides an effective computational envi- ronment to simulate the dynamic performance of the SOFC stack 8,9. The nonlinear model equations based on electrochemical and thermodynamics are discretized in resistive companion RC form for effective implementation in the VTB platform. The de- tailed RC model formulation is presented in Sec. 3. Details of the capabilities of VTB can be found elsewhere in Ref. 10. The remainder of this paper is organized as follows. The SOFC model description is presented in Sec. 2. The RC model formula- tion is derived in Sec. 3. The simulation results, distribution analy- sis, and discussion of dynamic behavior under the variable load condition are presented in Sec. 4. Conclusions are made in Sec. 5. 2 SOFC Model Description The proposed model employs the internal reforming mecha- nism. In this study, a one-dimensional transient model of the tu- bular SOFC stack is developed, and then the model is programed into a dynamic simulation mode in VTB. This model focuses on the electrochemical processes and the associated thermodynamic aspects of the cell operation. Given that all the cells are identical, the performance of the fuel cell is evaluated. Figure 1 shows the SOFC stack model icon, where all the cells are enveloped into a single model icon. The simulation software allows the users to easily connect this model into a larger system with all the features of the SOFC included in this model. The model icon comprises an air inlet port, a fuel inlet port, an outlet port, and an electrical power output port. Fuel cell parameters employed for the present study are shown in Table 1. Contributed by the Advanced Energy Systems Division for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received April 14, 2006; final manuscript received January 30, 2007; published online May 16, 2008. Review conducted by Dan Flowers. Journal of Energy Resources Technology JUNE 2008, Vol. 130 / 022601-1 Copyright © 2008 by ASME Downloaded 08 Feb 2010 to 129.252.23.139. 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