Numerical simulation and analysis of thermal stress distributions for a planar solid oxide fuel cell stack with external manifold structure

A three-dimensional numerical model based on the finite element method (FEM) is constructed to calculate the thermal stress distribution in a planar solid oxide fuel cell (SOFC) stack with external manifold structure. The stack is composed of 5 units which include cell, metallic interconnect, seal and anode/cathode current collectors. The temperature profile is described according to measured temperature points in the stack. It can be clearly seen that the maximum stress concentration area appears at the corner of the components when the stack is heated from room temperature (RT) to 780 °C. The effects of stack components on maximum stress concentration have been investigated under the operation temperature, as well as the thermal stress simulation results. It is obvious that the coefficient of thermal expansion (CTE) mismatch between the interconnect and the seal plays an important role in determining the thermal stress distribution in the stack. However, different compressive loads have almost no effect on stress distribution, and the influence of glass-based seal depends on the elastic modulus. The simulation results can be applied for optimizing the structural design of the stack and minimizing the high stress concentration in components.     

Cathode-side electrical contact and contact materials for solid oxide fuel cell stacking: A review

In a planar solid oxide fuel cell (SOFC) stack, a number of individual cells are stacked together to increase the voltage and power output. At both the cathode– and anode–interconnect interfaces, electrical contact layers are applied between the interconnect and electrodes during cell fabrication process or stack assembly to increase the electrode-interconnect contact area and to compensate for dimensional tolerance variation of the contacting components, thus minimizing ohmic contact resistance throughout the stack. As such, electrical contact is an essential component in SOFC stacks. In this paper, we review the cathode-side electrical contact design and contact materials for application in SOFC stacks. Following an introduction of the function and working principles of electrical contact, the material requirements for cathode-side contact layer in SOFC stacks are outlined. The current materials for the cathode–interconnect contact are thoroughly reviewed, including noble metals, conductive ceramics (e.g. perovskites and spinels), composites, and other more complex structures. Several potential directions for cathode–interconnect contact material research and development are also highlighted.     

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.     

Design and analysis of SOFC stack with different types of external manifolds

In this study, a four-cell stack of anode-supported planar solid oxide fuel cells (SOFCs) was designed and simulated to investigate the flow/heat transport phenomena and the performance of the SOFC stack. This SOFC stack was designed based on the external manifold types with one side open toward the cathode inlet and components such as base station, manifold, end plate, press jig, and housing. To investigate the performance of the SOFC stack, a step-by-step heat and flow analysis was conducted. First, the separator, functioning as a current collector and a gas channel, was designed to have repeated convex shapes. As the boundary of the flow passage was periodic in both streamwise and transverse directions, only a small part of the flow channel was simulated. In the case of simple homogeneous porous media, the computational results for flow resistance could be expressed by following Darcy's Law. Subsequently, these calculation results from the separator flow analysis were used in the housing and stack analysis. Second, the flow of the cathode region in the housing of SOFC stack was analyzed to verify the flow uniformity in the cathode channel of the separators. Finally, a stack analysis was executed using the electrochemical reaction model to investigate the performance and transport phenomena of the stack. Owing to the uniformity in flow and temperature, each SOFC cell exhibited similar contours of reactant gases, temperature, and current density. In the case of two different fuel utilizations with different flow rates, the low fuel utilization performed slightly better than the high fuel utilization.     

Model-based development of low-level control strategies for transient operation of solid oxide fuel cell systems

The exploitation of an SOFC-system model to define and test control and energy management strategies is presented. Such a work is motivated by the increasing interest paid to SOFC technology by industries and governments due to its highly appealing potentialities in terms of energy savings, fuel flexibility, cogeneration, low-pollution and low-noise operation.The core part of the model is the SOFC stack, surrounded by a number of auxiliary devices, i.e. air compressor, regulating pressure valves, heat exchangers, pre-reformer and post-burner. Due to the slow thermal dynamics of SOFCs, a set of three lumped-capacity models describes the dynamic response of fuel cell and heat exchangers to any operation change.The dynamic model was used to develop low-level control strategies aimed at guaranteeing targeted performance while keeping stack temperature derivative within safe limits to reduce stack degradation due to thermal stresses. Control strategies for both cold-start and warmed-up operations were implemented by combining feedforward and feedback approaches. Particularly, the main cold-start control action relies on the precise regulation of methane flow towards anode and post-burner via by-pass valves; this strategy is combined with a cathode air-flow adjustment to have a tight control of both stack temperature gradient and warm-up time. Results are presented to show the potentialities of the proposed model-based approach to: (i) serve as a support to control strategies development and (ii) solve the trade-off between fast SOFC cold-start and avoidance of thermal-stress caused damages.     

Cool-down time of solid oxide fuel cells intended for transpotation application

To provide answers to the concern as to how quickly the temperature of solid oxide fuel cells (SOFCs) for transportation application will drop, a thermal analysis of the cool-down time of an SOFC stack during vehicle idle or stand-by has been carried out. Because a large amount of thermal energy is stored in high-temperature SOFC stacks, it is important to select suitable thermal insulations to reduce heat loss. Three typical kinds of thermal insulating materials have been selected in the present calculations. The results indicate that a high-performance, vacuum-multifoil thermal insulation can be applied to significantly reduce heat loss and to maintain temperature uniformity across a cell stack. Consequently, the cool-down time from 1000 to 800°C is extended from 2 h (with a 5 cm thick conventional material) to about 31 h (with a 1 cm thick high-performance material).     

Three-dimensional computational analysis of gas and heat transport phenomena in ducts relevant for anode-supported solid oxide fuel cells

Various transport phenomena occurring in an anode duct of medium temperature solid oxide fuel cell (SOFC) have been simulated and analyzed by a fully three-dimensional calculation method. The considered composite duct consists of a thick porous layer, the gas flow duct and solid current interconnector. Unique fuel cell boundary and interfacial conditions, such as the combined thermal boundary conditions on solid walls, mass transfer associated with the electrochemical reaction and gas permeation across the interface, were applied in the analysis. Based on three characteristic ratios proposed in this study, gas flow and heat transfer were investigated and presented in terms of friction factors and Nusselt numbers. It was revealed that, among various parameters, the duct configuration and properties of the porous anode layer have significant effects on both gas flow and heat transfer of anode-supported SOFC ducts. The results from this study can be applied in fuel cell overall modeling methods, such as those considering unit/stack level modeling.     

Global failure criteria for positive/electrolyte/negative structure of planar solid oxide fuel cell

Due to mismatch of the coefficients of thermal expansion of various layers in the positive/electrolyte/negative (PEN) structures of solid oxide fuel cells (SOFC), thermal stresses and warpage on the PEN are unavoidable due to the temperature changes from the stress-free sintering temperature to room temperature during the PEN manufacturing process. In the meantime, additional mechanical stresses will also be created by mechanical flattening during the stack assembly process. In order to ensure the structural integrity of the cell and stack of SOFC, it is necessary to develop failure criteria for SOFC PEN structures based on the initial flaws occurred during cell sintering and stack assembly. In this paper, the global relationship between the critical energy release rate and critical curvature and maximum displacement of the warped cells caused by the temperature changes as well as mechanical flattening process is established so that possible failure of SOFC PEN structures may be predicted deterministically by the measurement of the curvature and displacement of the warped cells.     

Performance analysis and temperature gradient of solid oxide fuel cell stacks operated with bio-oil sorption-enhanced steam reforming

A high temperature gradient within a solid oxide fuel cell (SOFC) stack is considered a major challenge in SOFC operations. This study investigates the effects of the key parameters on SOFC system efficiency and temperature gradient within a SOFC stack. A 40-cell SOFC stack integrated with a bio-oil sorption-enhanced steam reformer is simulated using MATLAB and DETCHEM. When the air-to-fuel ratio and steam-to-fuel ratio increase, the stack average temperature and temperature gradient decrease. However, a decrease in the stack temperature steadily reduces the system efficiency owing to the tradeoff between the stack performance and thermal balance between heat recovered and consumed by the system. With an increase in the bio-oil flow rate, the system efficiency decreases because of the lower resident time for the electrochemical reaction. This is not, however, beneficial to the maximum temperature gradient. To minimize the temperature gradient of the SOFC stack, a decrease in the bio-oil flow rate is the most effective way. The maximum temperature gradient can be reduced to 14.6 K cm⁻¹ with the stack and system efficiency of 76.58 and 65.18%, respectively, when the SOFC system is operated at an air-to-fuel ratio of 8, steam-to-fuel ratio of 6, and bio-oil flow rate of 0.0041 mol s⁻¹.     

Mini CHP based on the electrochemical generator and impeded fluidized bed reactor for methane steam reforming

The paper presents a configuration of mini CHP with the methane reformer and planar solid oxide fuel cell (SOFC) stacks. This mini CHP may produce electricity and superheated steam as well as preheat air and methane for the reformer along with cathode air used in the SOFC stack as an oxidant. Moreover, the mathematical model for this power plant has been created. The thermochemical reactor with impeded fluidized bed for autothermal steam reforming of methane (reformer) considered as the basis for the synthesis gas (syngas) production to fuel SOFC stacks has been studied experimentally as well. A fraction of conversion products has been oxidized by the air fed to the upper region of the impeded fluidized bed in order to carry out the endothermic methane steam reforming in a 1:3 ratio as well as to preheat products of these reactions. Studies have shown that syngas containing 55% of hydrogen could be produced by this reactor. Basic dimensions of the reactor as well as flow rates of air, water and methane for the conversion of methane have been adjusted through mathematical modelling.The paper provides heat balances for the reformer, SOFC stack and waste heat boiler (WHB) intended for generating superheated water steam along with preheating air and methane for the reformer as well as the preheated cathode air. The balances have formed the basis for calculating the following values: the useful product fraction in the reformer; fraction of hydrogen oxidized at SOFC anode; gross electric efficiency; anode temperature; exothermic effect of syngas hydrogen oxidation by air oxygen; excess entropy along with the Gibbs free energy change at standard conditions; electromotive force (EMF) of the fuel cell; specific flow rate of the equivalent fuel for producing electric and heat energy. Calculations have shown that the temperature of hydrogen oxidation products at SOFC anode is 850 °C; gross electric efficiency is 61.0%; EMF of one fuel cell is 0.985 V; fraction of hydrogen oxidized at SOFC anode is 64.6%; specific flow rate of the equivalent fuel for producing electric energy is 0.16 kg of eq.f./(kW·h) while that for heat generation amounts to 44.7 kg of eq.f./(GJ). All specific parameters are in agreement with the results of other studies.     

Effect of air flow rate distribution and flowing direction on the thermal stress of a solid oxide fuel cell stack with cross-flow configuration

This study investigates the effect of non-uniform distribution of the air inlet flow rate and change of air flowing direction on the thermal stress of a solid oxide fuel cell stack with cross-flow configuration. This study considers three patterns of air inlet flow rate in the transverse direction of each stack, and five patterns of air inlet flow rate in the stacking direction. The software package for simulation is reliable through an accuracy comparison, and it analyzes the current density, temperature, and thermal stress distribution of a SOFC stack with 20 layers. The results show that the progressively increasing profile of the air inlet flow rate along the x direction drops the cell thermal stress of a SOFC unit. Moreover, the non-uniform profile of air inlet flow rate in the stacking direction affects the position of the region with high thermal stress of the SOFC stack, and changing flow direction of the air obviously drops down the thermal stress without affecting the power generation of the SOFC stack.     

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。     

Performance analysis for the part-load operation of a solid oxide fuel cell–micro gas turbine hybrid system

In this paper, the performance evaluation of a solid oxide fuel cell (SOFC)–micro gas turbine (MGT) hybrid power generation system under the part-load operation was studied numerically. The present analysis code includes distributed parameters model of the cell stack module. The conversions of chemical species for electrochemical process and fuel reformation process are considered. Besides the temperature distributions of the working fluids and each solid part of cell module by accounting heat generation and heat transfers, are taken into calculation. Including all of them, comprehensive energy balance in the cell stack module is calculated. The variable MGT rotational speed operation scheme is adopted for the part-load operation. It will be made evident that the power generation efficiency of the hybrid system decreases together with the power output. The major reason for the performance degradation is the operating temperature reduction in the SOFC module, which is caused by decreasing the fuel supply and the heat generation in the cells. This reduction is also connected to the air flow rate supplement. The variable MGT rotational speed control requires flexible air flow regulations to maintain the SOFC operating temperature. It will lead to high efficient operation of the hybrid system.     

Effect of inlet flow maldistribution in the stacking direction on the performance of a solid oxide fuel cell stack

This study examines the performance of a ten-cell solid oxide fuel cell (SOFC) stack with a non-uniform flow rate in the stacking direction. The author develops a two-dimensional numerical method to solve the electrochemical, mass and energy equations one stack at a time. The energy equations couple the heat exchange between the interconnector and both the cell and the flowing gas of adjacent cells. Moreover, this paper considers two boundary conditions, adiabatic and constant temperature, on the top and bottom faces of the SOFC. The results show that the non-uniform inlet flow rate of the fuel dominates the current density distribution; it causes the cell voltage to vary by over 13% for both boundary conditions. In addition, the constant temperature condition in this study can produce 3% more power than with the adiabatic condition. On the other hand, the air dominates the temperature field of a SOFC, and the non-uniform inlet flow rate of the air produces a variation of 3% in the average cell temperature of the cells when the boundary condition is adiabatic. This non-uniform effect on the electrical performance of each stack is apparently larger than in the transverse direction, which has been examined in our previous research.     

Investigate the multi-physics performance of a new fuel cell stack by a 3D large-scale model basing on realistic structures

There are great interactions between the multi-physics fields distributing characteristics and the key structure factors within the solid oxide fuel cell (SOFC) stack. Understanding these secrets are important for the development of stack technologies referring to performance and duration. In this paper, the 3D large scale multi-physics model basing on the realistic solid, space and porous structures of a special designed 24-cells stack is successful developed with 15,656,579 specially designed meshes. The research result show that: i) adopting the 3-paralleled serpentine rib channels and discrete cylindrical rib channels for the anodic and cathodic surfaces, respectively, can well ensure relevant high fuel pressure and reactants distributing uniformities over the electrolyte surfaces; ii) the even and odd numbered interconnect plates are designed to have same structures and placed in different directions, which contribute to one fuel flow path and two separated 2in3out air flow paths. Each air flow path will in charge of the air feeding for half of the stack; iii) the trapezoidal distributor will feed the sub-inlet manifolds of each air flow path with similar mass flow rates. The corresponding fuel and air flows, hydrogen and oxygen, and temperature uniformities on both stack and single cell levels are calculated and analyzed.     

Performance of a proton exchange membrane fuel cell stack with thermally conductive pyrolytic graphite sheets for thermal management

This work experimentally investigates the effects of the pyrolytic graphite sheets (PGS) on the performance and thermal management of a proton exchange membrane fuel cell (PEMFC) stack. These PGS with the features of light weight and high thermal conductivity serve as heat spreaders in the fuel cell stack for the first time to reduce the volume and weight of cooling systems, and homogenizes the temperature in the reaction areas. A PEMFC stack with an active area of 100 cm² and 10 cells in series is constructed and used in this research. Five PGS of thickness 0.1 mm are cut into the shape of flow channels and bound to the central five cathode gas channel plates. Four thermocouples are embedded on the cathode gas channel plates to estimate the temperature variation in the stack. It is shown that the maximum power of the stack increase more than 15% with PGS attached. PGS improve the stack performance and alleviate the flooding problem at low cathode flow rates significantly. Results of this study demonstrate the feasibility of application of PGS to the thermal management of a small-to-medium-sized fuel cell stack.     

Three-dimensional simulation of solid oxide fuel cell with metal foam as cathode flow distributor

In this study, the use of metal foam as a flow distributor at cathode is evaluated numerically by a comprehensive three-dimensional solid oxide fuel cell (SOFC) model. The results show that the adoption of metal foam improves the power density by 13.74% at current density of 5000 A m⁻² in comparison with conventional straight channel design. It is found that electronic overpotential, oxygen concentration and reaction rates distribute more uniformly without the restriction of ribs. The effects of cathode thickness on the two different flow distributors are compared. Compared with conventional straight channel, the metal foam is found to be more suitable as a distributor for anode supported SOFC with thin cathode gas diffusion layer. Moreover, when metal foam is applied to the fuel cell with a larger reaction area, a more uniform velocity distribution and a lower temperature distribution can be achieved. It is also found that an appropriate permeability coefficient should offer a reasonable pressure drop, which is beneficial for the fuel cell system performance improvement.     

Influence of stack arrangement on performance of multiple-stack solid oxide fuel cells with non-uniform potential operation

The performance of multiple-stack solid oxide fuel cells (SOFCs) with different stack arrangements is compared with respect to the presence of an in-stack pressure drop. It was demonstrated in our previous work that when a multiple-stack SOFC is arranged in series and the operating voltages are allowed to vary among the different stacks, an improved performance over a conventional SOFC (stacks arranged in parallel and operated under the same operating voltage) can be realized. Nevertheless, the differences in pressure drop and the required power for compression among the different operations were not taken into account. In the study reported here, it is demonstrated that the pressure drop in the stack depends not only on the feed rate and operating voltage, but also on the stack arrangement. The pressure drop in the anode channels is about half that in the cathode channels. The configuration of stacks in series with compressors installed only at the inlets of the first stack is the best option as it shows the highest electrical power generation. The pressure drops in the anode and cathode channels are about 4.7 and 3.75 times those in the corresponding channels of the conventional case with the stacks arranged in parallel. In addition, when considering the net obtained electrical power, it appears that multiple-stack SOFCs with stacks arranged in series are not as attractive as the conventional SOFC because they require much higher compression power. Therefore, it is suggested that a new stack design with a low pressure drop is required for the concept of multiple-stack SOFC with non-uniform potential operation to become practical.     

Analytical modelling of boiling phase change phenomenon in high-temperature proton exchange membrane fuel cells during warm-up process

This paper investigates the thermal and water balance as well as the electro-kinetics during the warm-up process of a Hydrogen/Oxygen high-temperature proton exchange membrane fuel cell (HT-PEMFC) from room temperature up to the desired temperature of 180 °C. The heating strategy involves the extraction of constant current from the fuel cell, while an external heating source with a constant heat input rate is applied at the end plates of the cell simultaneously. A simple analytical unsteady model is derived addressing the boiling phase changing phenomenon in the cathode catalyst layer (CCL) and cathode gas diffusion layer (CGDL) of the cathode that occurs when the temperature of the fuel cell reaches the boiling temperature of water. Parameters such as the heat input rate, extracted current, cathode pressure and cathode stoichiometric flow ratio are varied and their effects on the temperature, liquid water fraction and most importantly, the voltage profiles with respect to time, are explored. A comparison between other existing heating strategies using the model suggests that there is insignificant improvement in warm-up time when current is extracted from room temperature considering a single cell. However, considering the solution for a typical 1-kW stack suggests that reductions in warm-up time and energy consumption can be expected. In addition, the results show that boiling phase change is found to be a key factor that affects the level of water saturation in the porous media such as the CCL and CGDL during the warm-up process, when current is extracted from the start of the process i.e. room temperature. However, the energy consumption due to boiling phase change is found to be negligible as compared to external heating input rate. The parametric studies show that the variation of heat input rate, extracted current and cathode pressure have significant effect on the cell voltage that is strongly dominated by the liquid water fraction in the porous media. On the other hand, the variation of cathode stoichiometric flow ratio is found to have minimal effect on the output cell voltage. The parametric studies also indicate that boiling phase change is present for a significant period of time under typical operating conditions.     

Application of adaptive neuro-fuzzy inference system techniques and artificial neural networks to predict solid oxide fuel cell performance in residential microgeneration installation

This study applies adaptive neuro-fuzzy inference system (ANFIS) techniques and artificial neural network (ANN) to predict solid oxide fuel cell (SOFC) performance while supplying both heat and power to a residence. A microgeneration 5 kW_el SOFC system was installed at the Canadian Centre for Housing Technology (CCHT), integrated with existing mechanical systems and connected in parallel to the grid. SOFC performance data were collected during the winter heating season and used for training of both ANN and ANFIS models. The ANN model was built on back propagation algorithm as for ANFIS model a combination of least squares method and back propagation gradient decent method were developed and applied. Both models were trained with experimental data and used to predict selective SOFC performance parameters such as fuel cell stack current, stack voltage, etc.