The analyses of the heat-up process of a planar, anode-supported solid oxide fuel cell using the dual-channel heating strategy

In the present study, a finite-volume (FV) model has been developed to investigate the thermal behavior, the heat-up time and the corresponding temperature gradient for an anode-supported planar SOFC during the heat-up process. A methane burner is employed for the heat-up of the SOFC. Effects of the burner power and the flow configuration on the temperature distribution, the effective maximum-temperature-gradient, the heat-up time and the required energy in the heat-up process are investigated. The numerical results obtained from the present study show that the single-channel mode is impractical for the SOFC heat-up due to the lengthy heat-up time. For a fixed-power burner, the required heat-up time for the counter-flow configuration is about 25% less than that of the co-flow configuration. For the counter-flow configuration, the temperature gradient is averagely about 17% larger than that for the co-flow configuration. The total energy required for the counter-flow configuration is about 20% less than that for the co-flow configuration. The counter-flow configuration is superior to the others as far as the heat-up time and the required energy are concerned, although it yields a relatively higher maximum-temperature-gradient.     

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.     

Control of a solid oxide fuel cell stack based on unmodeled dynamic compensations

To guarantee solid oxide fuel cell (SOFC) safe operation, plenty control strategies have been developed to control stack temperature and voltage within a reasonable range. However, these control approaches ignore unmodeled dynamics of the SOFC system, which may lead to unsatisfactory control results, sometimes even make the system unstable. To overcome this challenge, a unique control strategy which considers unmodeled dynamic compensations of the SOFC system is proposed in this paper. A model of the SOFC system is firstly built, which includes a known linear model and an unmodeled nonlinear dynamic estimation. A nonlinear controller based on the unmodeled dynamic compensation is then developed to force the SOFC to track desired stack temperature and voltage. To evaluate the control performance, the proposed control method is compared with a traditional sliding mode controller. The simulation results show if the unmodeled dynamics have a small effect on the SOFC, both the sliding mode controller and the proposed controller can achieve a precise tracking. If the unmodeled dynamics have a great impact on the SOFC, the temperature and voltage can be well controlled with the proposed control strategy. However, in the sliding mode controller, the temperature and voltage trajectories deviate largely from the reference values.     

The modeling of a standalone solid-oxide fuel cell auxiliary power unit

In this research, a Simulink model of a standalone vehicular solid-oxide fuel cell (SOFC) auxiliary power unit (APU) is developed. The SOFC APU model consists of three major components: a controller model; a power electronics system model; and an SOFC plant model, including an SOFC stack module, two heat exchanger modules, and a combustor module. This paper discusses the development of the nonlinear dynamic models for the SOFC stacks, the heat exchangers and the combustors. When coupling with a controller model and a power electronic circuit model, the developed SOFC plant model is able to model the thermal dynamics and the electrochemical dynamics inside the SOFC APU components, as well as the transient responses to the electric loading changes. It has been shown that having such a model for the SOFC APU will help design engineers to adjust design parameters to optimize the performance. The modeling results of the SOFC APU heat-up stage and the output voltage response to a sudden load change are presented in this paper. The fuel flow regulation based on fuel utilization is also briefly discussed.     

Two-dimensional transient model of a cascaded micro-tubular solid oxide fuel cell fed with methane

A two-dimensional transient simulation model for a cascaded (10 cascades) micro-tubular solid oxide fuel cell (SOFC) and a common micro-tubular SOFC with a preheater tub was developed to calculate the distribution of gas species, the local current, voltage and temperature. The goal was to compare these two different SOFC designs under steady state and load change conditions with respect to power density. Steady state simulation results have shown that the cascaded cell concept is able to operate at higher average cell voltages in principle. Compared to the cascaded cell concept the average ohmic anodic and cathodic resistance of the common cell has to be 84 times lower to reach the same average power density at an average voltage of 0.7 V. The cascaded cell concept gives the opportunity to operate at a higher average voltage than the lowest Nernst voltage offers. This could be interesting to realize high fuel utilization (>85%). Transient simulation results have shown that both cell concepts respond within 10 s on an electrical load change. The cascaded cell concept has shown a lower temporary voltage drop than the common cell concept. This paper describes the theory, solution techniques and results.     

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.     

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。     

A three-dimensional model for transient performance of a solid oxide fuel cell

This paper presents an analysis of transient behavior of an anode-supported solid oxide fuel cell (SOFC) using a model, which has recently been built for steady state operation. The model is three dimensional (3D), which takes into account heat and mass transport, chemical and electrochemical reactions taking place simultaneously in the cell. The electrochemical processes are assumed to take place in a layer of finite thickness at electrode–electrolyte interfaces. A repeating unit of a planar anode-supported SOFC with co-flow configuration is investigated. Step changes of working voltage and fuel composition are applied to the cell. Results for the dynamic profiles of the temperature, the current density and the activation overpotential distributions in the cell are presented and discussed.     

Dynamic modeling and experimental validation for the electrical coupling in a 5-cell solid oxide fuel cell stack in the perspective of thermal coupling

The electrical coupling in a 5-cell solid oxide fuel cell (SOFC) stack is investigated in this research. The electrical characteristics tests of a single cell and the stack were performed in an electrical furnace. It was found that the single cell with the highest temperature does not give the highest output voltage in the stack test, which is different from the result that the output voltage increases with temperature in the single cell test. A physical interpretation for this phenomenon is given specifically from the standpoint of electrical coupling on the basis of thermal coupling between cells in the stack. Furthermore, a system level electrical coupling dynamic model is developed to characterize the electrical characteristics of the stack by considering the contact resistance between cells. In addition, the electrical coupling dynamic model is calibrated and validated based on the experimental data. The results demonstrate that the electrical coupling dynamic model can depict and predict accurately the electrical characteristics of SOFC stacks. The accurate electrical coupling dynamic model is important for the system level study of SOFCs, such as the optimization of stack structures and the design of peripheral control systems.     

Parametric and transient analysis of non-isothermal, planar solid oxide fuel cells

A multidimensional, model of non-isothermal planar solid oxide fuel cells (SOFCs) including detailed coupled mass and charge transport phenomena, has been developed. The dusty-gas model has been used, in this a comprehensive SOFC model, and has been explicitly written/constructed, for the first time in the COMSOL multiphysics modelling framework to describe mass transport in the porous electrode and detailed charge conservation equations have been taken into account. As we have shown in a recent publication [9] the incorporation of the dusty-gas model results in more accurate predictions of the SOFC behaviour compared to mass transport models based on Fick’s law or Stefan-Maxwell multi-component diffusion. Our model allows prediction of the species composition profiles, temperature profiles, electronic and ionic voltage and current density distributions, and polarisation curves in a single cell. SOFC dynamics have also been considered including responses to step changes in the operating conditions. The model is implemented in two-spatial dimensions, however, the underlying theory is independent of the geometry used. Extensive parametric analysis has been performed and the corresponding SOFC behaviour has been analysed through the resulting polarisation curves. It is shown that SOFCs exhibit higher power outputs at increased operating temperatures and pressures. It was also found that the electrodes’ porosity and tortuosity have a smaller effect on power output. Furthermore, step changes in the inlet temperatures were found to induce slower dynamic behaviours than step changes in the operating voltage.     

Performance evaluation of different configurations of biogas-fuelled SOFC micro-CHP systems for residential applications

Three configurations of solid oxide fuel cell (SOFC) micro-combined heat and power (micro-CHP) systems are studied with a particular emphasis on the application for single-family detached dwellings. Biogas is considered to be the primary fuel for the systems studied. In each system, a different method is used for processing the biogas fuel to prevent carbon deposition over the anode of the cells used in the SOFC stack. The anode exit gas recirculation, steam reforming, and partial oxidation are the methods employed in systems I–III, respectively. The results predicted through computer simulation of these systems confirm that the net AC electrical efficiency of around 42.4%, 41.7% and 33.9% are attainable for systems I–III, respectively. Depending on the size, location and building type and design, all the systems studied are suitable to provide the domestic hot water and electric power demands for residential dwellings. The effect of the cell operating voltage at different fuel utilization ratios on the number of cells required for the SOFC stack to generate around 1 kW net AC electric power, the thermal-to-electric ratio (TER), the net AC electrical and CHP efficiencies, the biogas fuel consumption, and the excess air required for controlling the SOFC stack temperature is also studied through a detailed sensitivity analysis. The results point out that the cell design voltage is higher than the cell voltage at which the minimum number of cells is obtained for the SOFC stack.     

固体氧化物燃料电池的神经模糊控制策略研究

固体氧化物燃料电池(Solid Oxide Fuel Cell,SOFC)具有多输入多输出、强耦合的特点,为了使其输出电压稳定设计了高效控制器,采用神经模糊控制方法对其输出电压进行控制。通过机理分析和实验数据拟合方法分别建立SOFC的机理模型和神经网络模型,在此基础上采用模糊控制策略对SOFC的输出电压进行控制,并应用神经模糊控制方法进一步提高了控制精度。通过MATLAB/Simulink仿真实验发现,SOFC神经网络模型得到的预测电压与实际电压之间的误差小于0.008 V,较其机理模型更加准确,所提出的控制策略能有效控制SOFC的输出电压。     

Feedback control of solid oxide fuel cell spatial temperature variation

A high performance feedback controller has been developed to minimize SOFC spatial temperature variation following significant load perturbations. For thermal management, spatial temperature variation along SOFC cannot be avoided. However, results indicate that feedback control can be used to manipulate the fuel cell air flow and inlet fuel cell air temperature to maintain a nearly constant SOFC electrode electrolyte assembly temperature profile. For example temperature variations of less than 5 K are obtained for load perturbations of ±25% from nominal. These results are obtained using a centralized control strategy to regulate a distributed temperature profile and manage actuator interactions. The controller is based on H-infinity synthesis using a physical based dynamic model of a single co-flow SOFC repeat cell. The model of the fuel cell spatial temperature response needed for control synthesis was linearized and reduced from nonlinear model of the fuel cell assembly. A single 11 state feedback linear system tested in the full nonlinear model was found to be effective and stable over a wide fuel cell operating envelope (0.82-0.6 V). Overall, simulation of the advanced controller resulted in small and smooth monotonic temperature response to rapid and large load perturbations. This indicates that future SOFC systems can be designed and controlled to have superb load following characteristic with less than previously expected thermal stresses.     

Simulation of creep and damage in the bonded compliant seal of planar solid oxide fuel cell

Planar solid oxide fuel cell (SOFC) operates at high temperature and requires a good creep strength to ensure the structure integrity. This paper presents a creep and damage analysis of a bonded compliant seal (BCS) structure of a planar SOFC considering the effect of as-bonded residual stress and thermal stress, as well as the effect of filler metal and foil thickness. A modified continuum creep-damage model is used in the finite element simulation. It demonstrates that the BCS structure meets the requirement of the long-term operation at the high temperature of 600 °C with an appropriate braze bonding process. The results show that the failure location is not in the region of maximum creep deformation due to the effect of high level multi-axial stress which drastically decreases the multi-axial ductility. Reasonably reducing the thickness of filler metal and foil can decrease the damage of the BCS structure. Based on the consideration of creep and damage, it is proposed that the thickness of filler metal and foil should not exceed 0.1 and 0.05 mm, respectively.     

3D modeling of anode-supported planar SOFC with internal reforming of methane

Deposition of carbon on conventional anode catalysts and formation of large temperature gradients along the cell are the main barriers for implementing internal reforming in solid oxide fuel cell (SOFC) systems. Mathematical modeling is an essential tool to evaluate the effectiveness of the strategies to overcome these problems. In the present work, a three-dimensional model for a planar internal reforming SOFC is developed. A co-flow system with no pre-reforming, methane fuel utilization of 75%, voltage of 0.7 V and current density of 0.65 A cm⁻² was used as the base case. The distributions of both temperature and gas composition through the gas channels and PEN (positive electrode/electrolyte/negative electrode) structure were studied using the developed model. The results identified the most susceptible areas for carbon formation and thermal stress according to the methane to steam ratio and temperature gradients, respectively. The effects of changing the inlet gas composition through recycling were also investigated. Recycling of the anode exhaust gas, at an optimum level of 60% for the conditions studied, has the potential to significantly decrease the temperature gradients and reduce the carbon formation at the anode, while maintaining a high current density.     

A 2D transient numerical model combining heat/mass transport effects in a tubular solid oxide fuel cell

The purpose of this study is to present a 2D transient numerical model to predict the dynamic behavior of a tubular SOFC. In this model, the transient conservation equations (momentum, species and energy equations) are solved numerically and electrical and electrochemical outputs are calculated with an equivalent electrical circuit for the cell. The developed model determines the cell electrical and thermal responses to the variation of load current. Also it predicts the local EMF, state variables (pressure, temperature and species concentration) and cell performance for different cell load currents. Using this comprehensive model the dynamic behavior of Tubular SOFC is studied. First an initial steady state operating condition is set for the SOFC model and then the time response of the fuel cell to changes of some interested input parameters (like electrical load) is analyzed. The simulation starts when the cell is at the steady state in a specific output load. When the load step change takes place, the solution continues to reach to the new steady state condition. Then the cell transient behavior is analyzed. The results show that when the load current is stepped up, the output voltage decreases to a new steady state voltage in about 67 min.     

Analysis of a SOFC energy generation system fuelled with biomass reformate

Biomass reformation is an interesting path for hydrogen production and its use for efficient energy generation. The main target is the fully exploitation of the potential of renewable fuels. To this aim, the coupling a biomass reformer together with a high temperature solid oxide fuel cell (SOFC) stack shows some advantages for the similar operating temperature of the two processes and the internal reforming capability of the SOFC. The latter further allows less stringent composition requirements of the feed gas from a gasifier and internal cooling of the SOFC.In this work, a complete model of a SOFC coupled with a biomass gasifier is used to identify the main effects of the operating conditions on the fuel cell performance.The gasification process has been simulated by an equilibrium model able to compute the reformate composition under different operating conditions, whereas a 3D fluid dynamics simulation (FLUENT) coupled with an external model for the electrochemical reactions has been used to predict the fuel cell performance in terms of electrical response and mass-energy fluxes.A 14 kW integrated SOFC-gasifier system has been analysed with this model to address the response of a planar SOFC as a function of the gasifier operating conditions.     

Effect of holding time in brazing cooling process on creep life of the solid oxide fuel cell with bonded compliant seal

In present paper, effect of holding time at 600 °C during the brazing cooling process on creep life of solid oxide fuel cell (SOFC) with bonded compliant seal (BCS) is investigated by the finite element method. The research indicates that creep crack initiation time in BCS structure increases significantly with the holding time increasing. Compared with that the traditional cooling method during the brazing process, the creep crack initiation time can be prolonged more than twice by the holding time of 150 h with the operating temperature of 600 °C, it increases from 14,949 h to 31,911 h. When the operating temperature is 800 °C, the creep crack initiation time of SOFC can hardly be affected if the holding time exceeds 10 h. Based on the creep damage analysis and considering the cost of the SOFC manufacturing process, it is recommended that the holding time should not be exceeded 300 h if the operating temperature is below 750 °C. And when the operating temperature is 800 °C, the recommended holding time should not be longer than 10 h. The research of the present paper can provide theoretical guidance for the long life manufacturing and reliability operation of SOFC.     

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.