Parameter optimization for tubular solid oxide fuel cell stack based on the dynamic model and an improved genetic algorithm

The tubular solid oxide fuel cell (SOFC) stack has important parameters that need to be identified and optimized for the control of high performance. In this paper, a simple SOFC electrochemical model which its parameters need to be optimized is introduced to implement stack control for high output power. A dynamic SOFC model is built based on three sub-models to provide a large numbers simulated data and different condition for optimization. Unlike the traditional parameter optimization method--simple genetic algorithm (SGA), an improved genetic algorithm (IGA) is introduced. The proposed method shows more accuracy and validity by comparing the different results using SGA and IGA methods, the simulated data, and experimental data. The models and IGA method are adapted to control processes.     

Model based evaluation of the electrochemical reaction sites in solid oxide fuel cell electrodes

The electrode microstructure plays an important role in determining the performance of the Solid Oxide Fuel Cells (SOFCs). The conventional SOFC electrodes are based on two kinds of particles, one electron conducting and another ion conducting. Over the years, electrodes with alternative microstructures have been proposed for performance enhancement based on the developments in materials and fabrication techniques. Analytical models for the microstructure offer the scope of quick evaluation of the effect of various microstructural parameters on important microstructural properties like the triple phase boundary densities. However, validation of these models in the light of the experimental data is seldom reported. In this work, the microstructural data derived from image-based reconstruction of the electrodes is used to calibrate and validate an analytical model for the conventional SOFC electrode microstructure revealing insights into the model's applicability. This model forms the basis for the models of other modified microstructures studied in this work. Designing of improved SOFC microstructures require an understanding of the effect of controllable parameters on the reaction sites. Model based evaluation of the electrochemical reaction sites in five different SOFC microstructures is performed in this work. The results and insights will enable the selection of microstructural parameters for tailoring the electrode microstructure to achieve improved performance.     

Numerical modeling and parametric analysis of solid oxide fuel cell button cell testing process

In laboratory studies of solid oxide fuel cell (SOFC), performance testing is commonly conducted upon button cells because of easy implementation and low cost. However, the comparison of SOFC performance testing results from different labs is difficult because of the different testing procedures and configurations used. In this paper, the SOFC button cell testing process is simulated. A 2‐D numerical model considering the electron/ion/gas transport and electrochemical reactions inside the porous electrodes is established, based on which the effects of different structural parameters and configurations on SOFC performance testing results are analyzed. Results show that the vertical distance (H) between the anode surface and the inlet of the anode gas channel is the most affecting structure parameter of the testing device, which can lead to up to 18% performance deviation and thus needs to be carefully controlled in SOFC button cell testing process. In addition, the current collection method and the configuration of gas tubes should be guaranteed to be the same for a reasonable and accurate comparison between different testing results. This work would be helpful for the standardization of SOFC button cell testing.     

A mathematical model of a tubular solid oxide fuel cell with specified combustion zone

A numerical model has been developed to simulate the effect of combustion zone geometry on the steady state and transient performance of a tubular solid oxide fuel cell (SOFC). The model consists of an electrochemical submodel and a thermal submodel. In the electrochemical model, a network circuit of a tubular SOFC was adopted to model the dynamics of Nernst potential, ohmic polarization, activation polarization, and concentration polarization. The thermal submodel simulated heat transfers by conduction, convention, and radiation between the cell and the air feed tube. The developed model was applied to simulate the performance of a tubular solid oxide fuel cell at various operating parameters, including distributions of circuits, temperature, and gas concentrations inside the fuel cell. The simulations predicted that increasing the length of the combustion zone would lead to an increase of the overall cell tube temperature and a shorter response time for transient performance. Enlarging the combustion zone, however, makes only a negligible contribution to electricity output properties, such as output voltage and power. These numerical results show that the developed model can reasonably simulate the performance properties of a tubular SOFC and is applicable to cell stack design.     

Performance comparison of cocurrent and countercurrent flow solid oxide fuel cells

Solid oxide fuel cell (SOFC) is a complicated system with heat and mass transfer as well as electrochemical reactions. The flowing configuration of fuel and oxidants in the fuel cell will greatly affect the performance of the fuel cell stack. Based on the developed mathematical model of direct internal reforming SOFC, this paper established a distributed parameters simulation model for cocurrent and countercurrent types of SOFC based on the volume-resistance characteristic modeling method. The steady-state distribution characteristics and dynamic performances were compared and were analyzed for cocurrent and countercurrent types of SOFCs. The results indicate that the cocurrent configuration of SOFC is more suitable with regard to performance and safety.     

Three-dimensional computational fluid dynamics modeling of anode-supported planar SOFC

Modeling plays a very important role in the development of fuel cells and fuel cell systems. The aim of this work is to investigate the electrochemical processes of a Solid Oxide Fuel Cell (SOFC) and to evaluate the performance of the proposed SOFC design. For this aim a three-dimensional Computational Fluid Dynamics (CFD) model has been developed for an anode-supported planar SOFC with corrugated bipolar plates serving as gas channels and current collector. The conservation of mass, momentum, energy and species is solved by using the commercial CFD code FLUENT in the developed model. The add-on FLUENT SOFC module is implemented for modeling the electrochemical reactions, loss mechanisms and related electric parameters throughout the cell. The distributions of temperature, flow velocity, pressure and gaseous (fuel and air) concentrations through the cell structure and gas channels is investigated. The relevant fuel cell variables such as the potential and current distribution over the cell and fuel utilization are calculated and studied. The modeling results indicate that, for the proposed SOFC design, reasonably uniform distributions of current density over the active cell area can be achieved. The geometry of the cathode gas channel has a substantial effect on the oxygen distribution and thus the overall cell performance. Methods for arriving at improved cell designs are discussed.     

Single solid oxide fuel cell modeling and optimization

In this paper a dynamic model of a single solid oxide fuel cell (SOFC) is developed using a volume element methodology. It consists of a set of algebraic and ordinary differential equations derived from physical laws (e.g., the first law of thermodynamics, Fick's law, and Fourier's law), which allow for the prediction of the temperature and pressure spatial distribution inside the single SOFC, as functions of geometric and operating parameters. The thermodynamic model is coupled with an electrochemical model that is capable of determining the voltage, current, and power output. Based on the simulation results, the internal configuration (structure of the positive electrode-electrolyte-negative electrode assembly) and the operating conditions (air stoichiometric ratio and fuel utilization factor), as well as their impact on the performance of the single SOFC are discussed. Optimal geometric and operating parameters are obtained so that electrical power of the single SOFC at the nominal operating point is maximized. The method used is general and the fundamental optimization results are sharp, showing up to a 357% single SOFC performance variation within the studied parameters’ range, therefore these findings show the potential to use the model as a tool for future SOFC design, simulation and optimization.     

Optimization of single SOFC structural design for maximum power

This paper improves previously published models by the authors for a single solid oxide fuel cell (SOFC), and introduces a procedure to optimize its external configuration and operating conditions, so that the net power is maximized. The previous models are hereby improved to include: i) a constant offset overpotential in total potential drop; ii) heat generation associated with all the potential losses; iii) temperature-dependent thermo-physical properties of fuel and air, and iv) pumping power to maximize fuel cell performance. The thermodynamic model is derived from physical laws (e.g., the first law of thermodynamics, Fick's law, Fourier's law) to obtain the temperature and pressure spatial distribution in the SOFC. The electrochemical model is validated by direct comparison with experimental data from the Pacific Northwest National Laboratory (PNNL), and allows for the computation of the SOFC voltage, current, and power output. Based on the simulation results, the structural design, the active three phase boundaries regions at the electrodes and the fuel utilization factor, and their impact on the SOFC performance are discussed. Subjected to fixed total volume, the optimal geometric and operating parameters are pursued so that the net power of the SOFC is maximized through a 4-way-optimization procedure. The method used is general and the numerically obtained maxima are sharp, taking into account that up to a 631% single SOFC performance variation was observed within the studied parameters' range. The fixed volume constraint was then relaxed, and the effect of total volume variation on performance was investigated, delivering the general optimal parameters for the 4-way maximized SOFC net power output within the studied total dimensionless fuel cell volume range. These findings show the potential to use the model as a tool for future SOFC design, simulation and optimization.     

Performance analysis of a SOFC button cell using a CFD model

In this study, a 2-D numerical model is investigated to predict and evaluate the performance of an anode-supported SOFC button cell. The flow field is calculated using 2D Navier–Stokes equations. Heat and mass transfer equations are solved to calculate species and temperature distribution in the cell body and in fuel and air channels. The electrical and electrochemical processes are simulated coupled with the heat and mass transfer model. A discretized network circuit is adopted to the cell geometry for considering the ohmic losses and joule heating of the current that passes through the cell body. The model predicts the cell output voltage, the local EMF and the state variables pressure, temperature and species concentrations. The local electrical parameters are calculated based on the local pressure, temperature and concentration of the species. The numerical results are compared with the experimental data and good agreement is observed. The simulation is carried out for different input fuel flow rates and humidification. The results show how the input fuel mass flow rate and humidification level affects the button cell SOFC performance. In addition, influences of the anode thickness on cell performance through the ohmic over potential are investigated.