Numerical study of a flat-tube high power density solid oxide fuel cell: Part II: Cell performance and stack optimization

The flat-tube high power density (HPD) solid oxide fuel cell (SOFC) is a geometry based on a tubular type SOFC, and is being developed by Siemens Westinghouse and other international companies in Japan and Korea. It has increased power density, but still maintains the beneficial feature of secure sealing for a tubular SOFC. In this paper, the electric performance of a flat-tube HPD SOFC is studied. This paper also investigates the effects of the stack chamber number, stack shape, and other stack geometry features on the performance of the flat-tube HPD SOFC. The results show that the performance of a flat-tube HPD SOFC is better than a tubular SOFC with the same active cell surface, and that increasing the number of chambers number can improve the overall performance of a flat-tube HPD SOFC. The height of a flat-tube HPD SOFC and the thickness of the ribs do not have much effect on the performance of the cell as is expected. This study will help to design and optimize the flat-tube HPD SOFC.     

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.     

Numerical study of thermoelectric characteristics of a planar solid oxide fuel cell with direct internal reforming of methane

A three-dimensional mathematical thermo-fluid model coupling the electrochemical kinetics with fluid dynamics was developed to simulate the heat and mass transfer in planar anode-supported solid oxide fuel cell (SOFC). The internal reforming reactions and electrochemical reactions of carbon monoxide and hydrogen in the porous anode layer were analyzed. The temperature, species mole fraction, current density, overpotential loss and other performance parameters of the single cell unit were obtained by a commercial CFD code (Fluent) and external sub-routine. Results show that the current density produced by electrochemical reactions of carbon monoxide cannot be ignored, the cathode overpotential loss is the biggest one among the three overpotential losses, and that the proper decrease of the operating voltage leads to the increase of the current density, PEN structure temperature, fuel utilization factor, fuel efficiency and power output of the SOFC.     

Mechanistic modelling of a cathode-supported tubular solid oxide fuel cell

A two-dimensional mechanistic model of a tubular solid oxide fuel cell (SOFC) considering momentum, energy, mass and charge transport is developed. The model geometry of a single cell comprises an air-preheating tube, air channel, fuel channel, anode, cathode and electrolyte layers. The heat radiation between cell and air-preheating tube is also incorporated into the model. This allows the model to predict heat transfer between the cell and air-preheating tube accurately. The model is validated and shows good agreement with literature data. It is anticipated that this model can be used to help develop efficient fuel cell designs and set operating variables under practical conditions. The transport phenomena inside the cell, including gas flow behaviour, temperature, overpotential, current density and species concentration, are analysed and discussed in detail. Fuel and air velocities are found to vary along flow passages depending on the local temperature and species concentrations. This model demonstrates the importance of incorporating heat radiation into a tubular SOFC model. Furthermore, the model shows that the overall cell performance is limited by O₂ diffusion through the thick porous cathode and points to the development of new cathode materials and designs being important avenues to enhance cell performance.     

Numerical analysis of coupled transport and reaction phenomena in an anode-supported flat-tube solid oxide fuel cell

Heat and mass transfer with electrochemical reaction in an anode-supported flat-tube solid oxide fuel cell (FT-SOFC) is studied by means of three-dimensional numerical simulation. The distributions of the reaction fields in the anode-supported FT-SOFC are found to be similar to those in the planar SOFC with co-flow arrangement. However, in comparison with the latter, the concentration and activation overpotentials of the former can be reduced by additional reactant diffusion through the porous rib of the fuel channel. Parametric survey reveals that, for a fixed activation overpotential model, the output voltage can be improved by increasing the pore size of anode, while the cross-sectional geometry has smaller effect on the cell performance. Based on the results of three-dimensional simulation, we also develop a simplified numerical model of anode-supported FT-SOFC, which takes into account the concentration gradients in the thick anode of complex cross-sectional geometry. The simplified model can sufficiently predict the output voltage as well as the distributions of temperature and current density with very low computational cost. Thus, it can be used as a powerful tool for surveying wide range of anode-supported FT-SOFC design parameters.     

4×4阵列管式固体氧化物燃料电池（SOFC）堆温度场和流场初步分析

通过对实验中管式SOFC堆的数学建模仿真方法,研究实验中的百瓦级4×4管式电池堆内部的流体流动、传热和组分浓度等特性,分析电池参数对电池内部气体流速、温度和浓度分压分布。计算结果和实验测试发现：流场和压力场基本均匀,温度场变化在±34．7K,而阵列电池管开路电压测试值在1．0～1．15vg间,基本满足电堆工作要求。     

Modeling of gas transport through a tubular solid oxide fuel cell and the porous anode layer

A design model is a necessary tool to understand the gas transport phenomena that occurs in a tubular solid oxide fuel cell (SOFC). This paper describes a computational model, which studies the gas flow through an anode-supported tubular SOFC and the subsequent diffusion of gas through its porous anode. The model is a numerical solution for the gas flow through a plug flow reactor with a diffusion layer, which includes the activation, ohmic, and concentration polarizations. Gas diffusion is modeled using the dusty-gas equations which include Knudsen diffusion. Mercury intrusion porosimetry (MIP) is used to experimentally determine micro-structural parameters such as porosity, tortuosity and effective diffusion coefficients, which are used in the diffusion equations for the porous anode layer. It was found that diffusion in the anode plays a key role in the performance of a tubular SOFC. The concentration gradient of hydrogen and water results in a lower concentration of hydrogen and a higher concentration of water at the reactive triple phase boundary (TPB) than in the fuel stream which both lead to a lower cell voltage. The gas diffusion determines the limiting current density of the cell where a higher concentration drop of hydrogen results in a lower limiting current density. The model validates well with experimental data and is used to improve micro-tubular solid oxide fuel cell designs.     

Performance of tubular Solid Oxide Fuel Cell at reduced temperature and cathode porosity

The effect of decreasing the inlet temperature and the cathode porosity of tubular Solid Oxide Fuel Cell (SOFC) with one air channel and one fuel channel is investigated using Computational Fluid Dynamics (CFD) approach. The CFD model was developed using Fluent SOFC to simulate the electrochemical effects. The cathode and the anode of the cell were resolved in the model and the convection and conduction heat transfer modes were included. The results of the CFD model are presented at inlet temperatures of 700 °C, 600 °C and 500 °C and with cathode porosity of 30%, 20% and 10%. It was found that the Fluent-based SOFC model is an effective tool for analyzing the complex and highly interactive three-dimensional electrical, thermal, and fluid flow fields associated with the SOFCs. It is found that the SOFC can operate in the intermediate temperature range and with low porosity cathodes more efficient than at high temperatures given that the transport properties of the cathode, anode and the electrolyte can be kept the same.     

Comparison of heat and mass transfer between planar and MOLB-type SOFCs

A numerical simulation tool for calculating the planar and mono-block layer built (MOLB) type solid oxide fuel cells (SOFC) is described. The tool combines the commercial computational fluid dynamics simulation code with an electrochemical calculation subroutine. Its function is to simulate the heat and mass transfer and to predict the temperature distribution and mass fraction of gaseous species in the SOFC system. The three-dimensional geometry model of SOFC was designed to simulate a co-flow case and counter-flow case. The finite volume method was employed to calculate the conservation equations of mass, momentum and energy. Moreover, the influences of working conditions on the performances of planar and MOLB-type SOFCs were also discussed and compared, such as the delivery rate of gas and the components of fuel gas. Simulation results show that the MOLB-type SOFC has higher fuel utilization than the planar SOFC. For the co-flow case, average temperatures of PEN (positive electrode–electrolyte–negative electrode) in both types of SOFCs rise with the increase in delivery rate and mass fraction of hydrogen. In particular, the temperature of planar SOFC is more sensitive to the working conditions. In order to decrease the average temperatures in SOFC, it is effective to increase the delivery rate of air.     

An analytical model of view factors for radiation heat transfer in planar and tubular solid oxide fuel cells

Radiant heat transfer plays an important role in the distribution of cell temperature and current density in solid oxide fuel cells (SOFC). The objective of this paper is to introduce a mathematical model of view factors for radiation heat exchange in an in-house longitudinally distributed SOFC model. A differential view factor model is first developed for planar and tubular SOFC configurations, but is found invalid when the infinitesimal element size is comparable to the characteristic size. Then, a finite-difference view factor model is developed to solve the problem of discontinuities in the differential view factor model. Starting from a classical problem of convective and radiant heat transfer for a transparent gas flow in a gray-wall tube, a fast and accurate computation is available for the finite-difference view factor model without extra mathematical derivations of the governing equations. Compared to the simple modeling which only takes into account the surface-to-surface radiation exchange between two directly opposed elements, the detailed radiation model based on analytical view factors predicts more uniform distribution of cell temperature and current density in the overall SOFC modeling.     

Effects of transport scale on heat/mass transfer and performance optimization for solid oxide fuel cells

A three-dimensional thermo-fluid–electrochemical model is developed to study the heat/mass transport process and performance of a solid oxide fuel cell (SOFC). The main objectives are to examine the transport channel size effects and to assess the potential of a thin-film-SOFC. A parametric study was performed to evaluate the channel scale effects on the temperature, species concentration, local current density and power density. The results demonstrate that decreasing the height of flow channels can lower the average solid temperature and improve cell efficiency. However, this improvement is rather limited for the smallest channels. Compared with the conventionally sized SOFC, the miniaturized SOFC with a thin-film electrolyte has the advantages of a lower operating temperature and a better performance. Based on our simulation results, the power density of a miniaturized SOFC could reach up to 5.461 W cm⁻³. However, an extremely small structure will lead to severe thermal stress induced by a large temperature gradient, a cell with a thicker rib width would have a higher efficiency and a lower average temperature. Numerical simulation is expected to help optimize the design of a solid oxide fuel cell.     

Modeling of a planar solid oxide fuel cell based on proton‐conducting electrolyte

A 2D computational fluid dynamics (CFD) model is developed to study the performance of an advanced planar solid oxide fuel cell based on proton conducting electrolyte (SOFC‐H). The governing equations are solved with the finite volume method (FVM). Simulations are conducted to understand the transport phenomena and electrochemical reaction involved in SOFC‐H operation as well as the effects of operating/structural parameters on SOFC‐H performance. In an SOFC based on oxygen ion conducting electrolyte (SOFC‐O), mass is transferred from the cathode side to the anode side. While in an SOFC‐H, mass is transferred from the anode to the cathode, which causes different velocity fields of the fuel and oxidant gas channels and influences the distributions of temperature and gas composition in the cell. It is also found that increasing the inlet gas velocity leads to an increase in the local current density and a slight decrease in the SOFC‐H temperature due to stronger cooling effect of the gas species at a higher velocity. Another finding is that the electrode structure does not significantly affect the heat and mass transfer in an SOFC‐H at typical operating voltages. Copyright © 2009 John Wiley & Sons, Ltd.     

Artificial intelligence based structural optimization of solid oxide fuel cell with three-dimensional reticulated trapezoidal flow field

Three-dimensional Reticulated trapezoidal flow field (RTFF) is promising in improving the performance and durability of the solid oxide fuel cell (SOFC). However, the structural complexity makes it challenging for the geometry configuration of the splitter and mixer. To this end, an intelligent optimization framework is proposed by coupling artificial neural network (ANN) and non-dominated sorting genetic algorithm-II (NSGA-II), in order to maximize the net power density and oxygen uniformity simultaneously. The ANN prediction model is trained to obtain the computationally efficient surrogate model of the computational fluid dynamics (CFD) numerical simulation. NSGA-II is used for the multi-objective optimization of the RTFF structural parameters. The results illustrate that the prediction model is of high prediction precision and generalization capability. In comparison to SOFC with conventional parallel flow fields (CPFF), the degree of the performance improvement of SOFC with optimized RTFF depends on the working condition, i.e., fuel and air flow rates and operating temperatures. The SOFC with the optimal RTFF achieves a higher molar concentration of oxygen and a more uniform distribution of oxygen and current density than the CPFF SOFC. The proposed optimization framework provides an efficient design method for the development of the next-generation SOFC flow field.     

Effects of operations and structural parameters on the one-cell stack performance of planar solid oxide fuel cell

A three-dimensional mathematical model coupling the electrochemical kinetics with fluid dynamics is developed to simulate the heat and mass transfer in the one-cell stack of planar solid oxide fuel cells (SOFCs). Based on flow uniformity analysis, the distributions of temperature, current density, overpotential loss and other performance parameters in various operating parameters are obtained using a commercial CFD code (Fluent) coupled with the external subroutines programmed by VC++. Numerical flow data are observed in good agreement with experimental results reported in the literature. Results show that the one-cell stack in counter flow case has the advantages in better uniform current density and temperature distributions of PEN (Positive/Electrolyte/Negative) structure in the width direction, higher power output, fuel utilization factor and fuel efficiency than that in co-flow case. For counter flow case, better thermoelectric characteristics are observed in the temperature gradient, power output, fuel utilization factor and fuel efficiency with the decrease in the fuel inlet flow rate or the anode porosity. Increasing the air inlet flow rate and decreasing the fuel inlet temperature will reduce the temperature gradient; power output, fuel utilization factor and fuel efficiency are enhanced with the increase of the air inlet temperature and the decrease of the anode pore size and thickness.     

A transient analysis of a micro-tubular solid oxide fuel cell (SOFC)

A two-dimensional, axisymmetric transient computational fluid dynamics model is developed for an intermediate temperature micro-tubular solid oxide fuel cell (SOFC), which incorporates mass, species, momentum, energy, ionic and electronic charge conservation. In our model we also take into account internal current leak which is a common problem with ceria based electrolytes. The current density response of the SOFC as a result of step changes in voltage is investigated. Time scales associated with mass transfer and heat transfer are distinguished in our analysis while discussing the effect of each phenomenon on the overall dynamic response. It is found that the dynamic response is controlled by the heat transfer. Dynamic behavior of the SOFC as a result of failure in fuel supply is also investigated, and it is found that the external current drops to zero in less than 1 s.     

Performance simulation for an anode-supported SOFC using Star-CD code

Experimental activities and computational fluid dynamics (CFD) simulation are presented in this paper for investigating the performance of an anode-supported solid oxide fuel cell (SOFC). The goal of this work is to assess a commercial CFD code, Star-CD with es-sofc module, to simulate the current–voltage (I–V) characteristics with respect to the experimental data. Compiled with the geometry of cell test housing, a 3D numerical model and test conditions were established to analyze the anode-supported cell (ASC) performance including current density and temperature distributions, fuel concentration, and fuel utilization. After adjusting parameters in the electrochemical model, the simulation results showed good agreements with the experimental data. The results also revealed that the power density increased while the fuel utilization decreased as the fuel flow rate increased.     

Performance analysis of a solid oxide fuel cell with reformed natural gas fuel

In the present study a two‐dimensional model of a tubular solid oxide fuel cell operating in a stack is presented. The model analyzes electrochemistry, momentum, heat and mass transfers inside the cell. Internal steam reforming of the reformed natural gas is considered for hydrogen production and Gibbs energy minimization method is used to calculate the fuel equilibrium species concentrations. The conservation equations for energy, mass, momentum and voltage are solved simultaneously using appropriate numerical techniques. The heat radiation between the preheater and cathode surface is incorporated into the model and local heat transfer coefficients are determined throughout the anode and cathode channels. The developed model has been compared with the experimental and numerical data available in literature. The model is used to study the effect of various operating parameters such as excess air, operating pressure and air inlet temperature and the results are discussed in detail. The results show that a more uniform temperature distribution can be achieved along the cell at higher air‐flow rates and operating pressures and the cell output voltage is enhanced. It is expected that the proposed model can be used as a design tool for SOFC stack in practical applications. Copyright © 2009 John Wiley & Sons, Ltd.     

Multi-physics modeling of a symmetric flat-tube solid oxide fuel cell with internal methane steam reforming

Methane is regarded as one of the ideal fuels for solid oxide fuel cells (SOFCs) due to its huge reserves and transportation properties. In this study, a 3D numerical model coupling with chemical reaction, electrochemical reaction, mass transfer, charge transfer, and heat transfer is developed to understand the heat and mass transfer processes of methane steam direct internal reforming based on double-sided cathodes (DSC) SOFC. After the model verification, the parametric simulations are performed to study the effects of operating voltage, inlet temperature, and steam to carbon (S/C) ratio on the performance of a DSC. It is found that the non-uniform distribution of flow rate among channels results in the non-uniform distribution of each physical field. Increasing the inlet temperature significantly enhances the performance of DSC, however, when the temperature is above 1073 K, the concentration loss and the temperature gradient of DSC increase, which is not conducive to the long-term operation of the DSC. In addition, we revealed the effect of the S/C ratios on the heat and mass transfer process. This study provides an insight into the heat and mass transfer process of SOFC with a mixture of steam and methane and operating conditions for enhancing the performance.     

连接体结构对固体氧化物燃料电池性能影响的数值分析

固体氧化物燃料电池（SOFC）中连接体结构对电池性能有重要影响。为探究连接体结构对固体氧化物燃料电池性能的影响，建立了传统直通、圆柱形、矩形和凹形4种不同连接体结构SOFC的三维数值模型，并对其流体流动、组分传递、电化学反应和固体流体传热的多物理场耦合过程进行了数值模拟。结果表明，在一定条件下，圆柱形、矩形和凹形连接体结构有利于电池中气体的传输，使电池的电流密度和输出功率均有所提升，其中凹形连接体结构的提升效果最明显，圆柱形、矩形连接体结构的次之。不同孔隙率下圆柱形、矩形和凹形连接体结构均优于传统直通连接体结构，在阴极孔隙率较小时其优势更加明显。     

Novel gas distributors and optimization for high power density in fuel cells

A novel gas distributor for fuel cells is proposed. It has three-dimensional current-collecting elements distributed in gas-delivery fields for effective current collection and heat/mass transfer enhancement. An analysis model has been developed in order to understand the performance of the output power density when the dimensions and distributive arrangement of the current collectors are different. Optimization analysis for a planar-type SOFC was conducted in order to outline the approach in optimizing a gas-delivery field when adopting three-dimensional current-collecting elements in a fuel cell. Experimental test of a proton exchange membrane (PEM) fuel cell adopting the novel gas distributor was conducted for verification of the new approach. Significant improvement of power output was obtained for the proposed new PEM fuel cells compared to the conventional ones under the same conditions except for the different gas distributors. Both the experimental results and modeling analysis are of great significance to the design of fuel cells of high power density.