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.     

Simulation and analysis of sintering stress and warpage displacement in anode supported planar solid oxide fuel cells

During the sintering process of solid oxide fuel cells (SOFCs), the mismatch in the thermophysical properties of materials can lead to excessive local thermal stress and warpage. By establishing a 3D multiphysics model, the stress distribution and displacement during sintering are studied. The results show that when the anode and electrolyte thicknesses are 0.2 mm and 0.02 mm, respectively, the maximum sintering stress is 38.8 MPa, which is 48% lower than the maximum value of all simulation results. In this study, when the anode thickness is 0.7 mm and the electrolyte thickness is 0.008 mm, the maximum warpage displacement is the smallest at 0.14 mm. A sintering preparation method for partially coated cells is proposed. These results can be used to optimize the sintering process of SOFCs and greatly reduce the sintering stress and warpage of SOFCs.     

Studies of residual stresses in planar solid oxide fuel cells

Planar solid oxide fuel cells (SOFCs) are composites consisting of porous and dense functional layers as electrodes and electrolyte, respectively. Due to the thermo-elastic mismatch between the individual layers residual stresses develop during manufacturing that result in warping for unconstrained cells. The residual stress of half-cells specimens with oxidized anode has been determined as a function of temperature. Two complementary techniques, X-ray diffraction analyses and measurements of cell curvature were applied. Moreover, changes in electrolyte residual stress associated with cell brazing to a steel interconnect were measured. The joining was carried out with symmetric cell composites having an anode layer sandwiched between two electrolyte layers. In addition to this test the effect of brazing and welding on the stress situation in the electrolyte of a real cell was tested.     

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.     

A model for oxidation-induced stress analysis of Ni-based anode-supported planar solid oxide fuel cell

A critical hurdle in realizing commercially viable anode-supported solid oxide fuel cell (SOFC) is the re-oxidation of cermet anode during the cell abnormal operation. In this paper, the analysis of energy dispersive X-ray spectroscopy on a partially oxidized half-cell demonstrates a particular inhomogeneous oxidation mechanism that a portion of anode near the air/anode interface is oxidized with a graded NiO content, while the remaining region hold a reduced status. Based on this observation, an analytical oxidation-induced stress model is developed to provide in-depth information about the mechanical behavior of the half-cell suffered from various oxidation. The dependences of the mechanical performance of half-cell on the NiO distribution and thickness of oxidation-graded zone are revealed. The results show that an increase in oxidation-graded zone elevates the stress level of electrolyte, but decreases the curvature under the same global degree of oxidation (DoO). In addition, the influence of thickness of oxidation-graded zone on the electrolyte failure probability is also investigated. According to these results, we conclude that the thickness of oxidation-graded zone should be as thin as possible in order to delay the electrolyte cracking.     

Thermal stress analysis of planar solid oxide fuel cell stacks: Effects of sealing design

A three-dimensional multi-cell model based on a prototypical, planar solid oxide fuel cell (pSOFC) stack design using compliant mica-based seal gaskets was constructed in this study to perform comprehensive thermal stress analyses by using a commercial finite element analysis (FEA) code. Effects of the applied assembly load on the thermal stress distribution in the given integrated pSOFC stack with such a compressive sealing design were characterized. A comparison was made with a previous study for a similar comprehensive multi-cell pSOFC stack model but using only a rigid type of glass-ceramic sealant instead. Simulation results indicate that stress distributions in the components such as positive electrode-electrolyte-negative electrode (PEN) plate, PEN-supporting window frame, nickel mesh, and interconnect were mainly governed by the thermal expansion mismatch rather than by the applied compressive load. An applied compressive load of 0.6 MPa could eliminate the bending deformation in the PEN-frame assembly plate leading to a well joined structure. For a greater applied load, the critical stresses in the glass-ceramic and mica sealants were increased to a potential failure level. In this regard, a 0.6 MPa compressive load was considered an optimal assembly load. Changing the seal between the connecting metallic PEN-supporting frame and interconnect from a rigid type of glass-ceramic sealant to a compressive type of mica gasket would significantly influence the thermal stress distribution in the PEN plate. The critical stress in the PEN was favorably decreased at room temperature but considerably increased at operating temperature due to such a change in sealing design. Such differences in the stress distribution could be ascribed to the differences in the constrained conditions at the interfaces of adjacent components under various sealing designs.     

Effect of alumina on the curvature, Young's modulus, thermal expansion coefficient and residual stress of planar solid oxide fuel cells

Planar solid oxide fuel cells (SOFCs) are composites consisting of porous and dense functional layers as electrodes and electrolytes, respectively. Because of the thermo-elastic mismatch between the individual layers, residual stresses develop during manufacturing and cause unconstrained cells to warp. The addition of alumina decreases the thermal expansion coefficient (TEC) of the NiO and yttria-stabilized zirconia (YSZ) anode-support material. Correspondingly, the lower TECs have flattened the half cells during fabrication. In addition, the residual stress at room temperature (RT) for samples with more than 4 wt% alumina is only 20% of the residual stress of the samples without alumina, at approximately 100 MPa. The effects of Al₂O₃ on the curvature, Young's modulus, TEC and residual stress of the SOFC with (NiO-YSZ)_1−x(Al₂O₃)_x (x = 1-5 wt%) anode support are discussed in this work.     

Model-oriented cast ceramic tape seals for planar solid oxide fuel cells

A straight capillary model is developed to estimate the mass leak rate of the cast ceramic tape seals for planar solid oxide fuel cells (SOFCs), which is further rectified with consideration of microstructure complexity including the tortuosity, cross-section variation and cross-link of leak paths. The size distribution of the leak path, effective porosity and the microstructure complexity are the main factors that influence the leak rate of the cast tape seals. According to the model, Al₂O₃ powders are selected for preparation of the seals by tape casting, and the leak rate is evaluated under various compressive stresses and gauge pressures. The results indicate that Al₂O₃ powder with D₅₀ value about 2 μm and specific surface area near 5 m² g⁻¹ can be used for the cast tape seals; and the obtained leak rate can satisfy the allowable leak limit.     

Thermal stress analysis of a planar anode-supported solid oxide fuel cell: Effects of anode porosity

A Fuel cell is a highly efficient device for converting chemical energy in fuels to electrical energy and the electrical efficiency is strongly affected by the porosity in electrodes due to its close couplings with mass transfer and active sites for the electrochemical reactions, which will also cause changes in distribution of thermal stresses inside the electrodes. A three-dimensional computational fluid dynamics (CFD) approach based on the finite element method (FEM) is used to investigate the effects of porosity on polarizations, temperatures and thermal stresses by coupling equations for gas-phase species, heat, momentum, ion and electron transport. It was found that the porosity in the anode remarkably affected the exchange current density and electrical current density, but it had an opposite effect on the anodic activation polarization compared to that in cathode. The first principle stress was enhanced from 0 to 2 MPa to 6–8 MPa by an increased anode porosity from 25% to 40%, and the increased porosity resulted in a decrease of the von mises stress along the main flow direction as well. The conclusions could be used to lay foundations for an improved performance and stabilization by optimizing electrode microstructures and by eliminating the stresses in electrodes.     

Modeling of cooperative defect transport and thermal mismatch in a planar solid oxide fuel cell

Mixed ionic-electronic conducting (MIEC) membranes are widely applied as cathode material in solid oxide fuel cells (SOFCs). Nonetheless, the chemical expansion of an MIEC membrane caused by point defects (oxygen vacancies and small polarons) during oxygen transport induces cell failure. In this study, a multilayer thermo-chemical-mechanical model was proposed to consider defect diffusion under sudden changes in the cathode atmosphere, thermal expansion mismatch, and mechanical bending deformation. Under the set boundary conditions, the overall structural curvature of the multilayer system was relieved when the cathode was subjected to a high tensile stress. The influences of relevant parameters on the transient stress field were also investigated, and the overall stress of the multilayer structure decreased significantly when the oxygen partial pressure in the inlet channel was constrained. Reducing the sintering temperature and chemical expansion coefficient could improve the reliability of the planar SOFC. In addition, the effect of constraints in different directions on the multilayer system stresses is also investigated. This study provides theoretical support for use in designing the stabilities and gas supply strategies of planar solid fuel cells.     

Stress field and failure probability analysis for the single cell of planar solid oxide fuel cells

An analytical model is developed to predict the residual thermal stresses in a single cell of solid oxide fuel cells (SOFCs), which consists of a thick porous 8 mol% Y₂O₃ stabilized zirconia/nickel oxide (8YSZ/NiO) anode, a dense 8YSZ electrolyte and a porous lanthanum strontium manganite (LSM) cathode. The simulated stresses in the cell at room temperature, which are resulted from the contraction mismatch of its components, indicate that the major principal stress in the anode is tensile while the electrolyte and cathode are under compressive stresses. The stress in one component decreases with the increase of its thickness when the thicknesses of the other two components are fixed, and the decrease of the tensile stress in the anode will cause the increase of the compressive stresses in both the cathode and the electrolyte, and vice versa. The analysis also reveals that the anode is the part that is most susceptible to fracture since the tensile thermal stress is so high that it reaches to the fracture strength of the anode material. The Weibull statistic is employed to estimate the failure probability of the anode. The simulation results indicate that the anode failure probability decreases with the increase of the anode thickness and the decrease of the electrolyte thickness. To keep the anode failure probability less than 1E−06, the anode thickness should be greater than 0.7 mm for a cell with an electrolyte thickness of 10 μm and a cathode thickness of 20 μm.     

Integrated thermal management strategy and materials for solid oxide fuel cells

The application of positive temperature coefficient (PTC) thermistors to thermal management of solid oxide fuel cells (SOFCs) is considered. A strategy is proposed for eliminating hotspots and reducing temperature gradients in SOFCs via inclusion of a material that exhibits a dramatic change in resistance near the desired maximum cell temperature. Three PTC thermistor materials with transition temperatures near the maximum desirable SOFC operating temperature are identified and screened for compatibility with common SOFC materials. All are found to be unsuitable because of reaction with the SOFC materials or unacceptably small PTC effect.     

Modeling of thermal stresses and lifetime prediction of planar solid oxide fuel cell under thermal cycling conditions

A typical operating temperature of a solid oxide fuel cell (SOFC) is above 600 °C, which leads to severe thermal stresses caused by the difference in material mechanical properties during thermal cycling. Interfacial shear stress and peeling stress are the two types of thermal stresses that can cause the mechanical failure of the SOFC. Two commonly used SOFC configurations (electrolyte-supported and anode-supported) were considered for this study. The paper developed a mathematical model to estimate the thermal stresses and to predict the lifetime of the cell (Ni/8YSZ-YSZ-LSM). Due to the mismatch of the material mechanical properties of the cell layers, a crack nucleation induced by thermal stresses can be predicted by the crack damage growth rate and the initial damage distribution in the interfacial layer for each thermal cycle. It was found that the interfacial shear stress and peeling stress were more concentrated near the electrode free edge areas. The number of cycles needed for failure decreased with the increase in the porosity of electrode. The number of cycle for failure decreased with increase in electrolyte thickness for both anode- and electrolyte-supported SOFC. The model provides insight into the distribution of interfacial shear stress and peeling stress and can also predict damage evolution in a localized damage area in different SOFC configurations.     

Diagnosis of scale up issues associated with planar solid oxide fuel cells

One of the most important challenges faced by SOFC technology towards the commercialisation lies in the issues related to scale up. In this work, root cause analysis of performance loss in scaled up (1:50) SOFC is carried out. Reduction in actual contact area (6.7% on cathode and 2.5% on the anode) between the metallic interconnects and the cell, and non-uniformity of reactant distribution, are found to play critical roles towards the poor performance of the scaled up cell. Finally, suggestions are made to sustain the performance during the scale up.     

Crack propagation of planar and corrugated solid oxide fuel cells during cooling process

The corrugated solid oxide fuel cell (SOFC) can effectively improve energy density and transformation efficiency compared with conventional planar SOFC, but its stability and durability have not been systematically analyzed. The residual stress of SOFC may lead to crack initiation and propagation during cooling process, so stress distributions of planar and corrugated SOFCs are simulated to analyze the location of crack initiation. The materials of electrolyte, anode, and cathode in this paper are yttria‐stabilization zirconia (YSZ), Ni‐YSZ, and strontium‐doped lanthanum manganite (LSM), respectively. The result shows that the edge of cell is more prone to cracking. Therefore, precracks including edge crack and middle crack are introduced into anode‐electrolyte interfaces to investigate crack propagation of two types of SOFCs during cooling process. For corrugated SOFC, the cracks propagate more slowly, and the cell is less prone to interfacial delamination compared with planar SOFC. In addition, the interface energy release rates are obtained to further analyze crack propagation of two types of SOFCs, and the corrugated SOFC has lower energy release rate. The research in this paper provides guidance for stability analysis and lays a foundation for future mechanical analysis of corrugated SOFC.     

Investigation of external compression in scaling up of planar solid oxide fuel cells

The effect of contact pressure on the performance of electrolyte supported planar solid oxide fuel cells (SOFCs) are experimentally investigated in this study by varying the pressure applied on the push rod. For this purpose, cells with 1 cm², 9 cm², 16 cm², 81 cm² and 150 cm² active areas are manufactured and tested under different external compression pressures. Maximum power densities of 0.486 W/cm², 0.308 W/cm² and 0.231 W/cm² are obtained from the cells with an active area of 1 cm², 9 cm² and 16 cm², respectively, under the same contact pressure. When the impedance results are considered, it is seen that under the same compression pressure, the cell resistance increases nonlinearly with the cell size. However, when the pressure is adjusted according to the active area, a similar power density of approximately 0.4 W/cm² is obtained from these three cells. Moreover, very similar performances are measured from all cells when a portion of cells with 1 cm² active is cut and tested under the same contact pressure of 0.2 MPa. The overall results indicate that the external load should be adjusted according to the cell size, but there is no linear relationship between the active area and the applied external pressure.     

Three-dimensional modeling of planar solid oxide fuel cells and the rib design optimization

Three-dimensional (3D) multi-physics models of co-, counter- and cross-flow planar solid oxide fuel cell (SOFC) stack units are described. The models consider electronic conduction in the electrodes, ionic conduction in the electrolyte, mass transport in the porous electrodes and electrochemical reactions on the three phase boundaries. Based on the analysis of the ionic conducting equation for the thin electrolyte layer, a mathematically equivalent method is proposed to scale the electrolyte thickness with the corresponding change in the ionic conductivity to moderate the thin film effect in the meshing step and decrease the total number of degrees of freedom in the 3D numerical models. Examples of applications are given with typical physical fields illustrated and the characteristic features discussed for co-, counter- and cross-flow designs. The 3D models are also used to optimize the rib widths in SOFC stacks as a function of interconnect–electrode contact resistance.     

Thermal stress and thermo-electrochemical analysis of a planar anode-supported solid oxide fuel cell: Effects of anode porosity

A 3D integrated numerical model is constructed to evaluate the thermal-fluid behavior and thermal stress characteristics of a planar anode-supported solid oxide fuel cell (SOFC). Effects of anode porosity on performance, temperature gradient and thermal stress are investigated. Using commercial Star-CD software with the es-sofc module, simulations are performed to obtain the current-voltage (I-V) characteristics of a fuel cell as a function of the anode porosity and the temperature distribution within the fuel cell under various operating conditions. The temperature field is then imported into the MARC finite element analysis (FEA) program to analyze thermal stresses induced within the cell. The numerical results are found to be in good agreement with the experimental data. It is shown that the maximum principal stress within the positive electrode-electrolyte-negative electrode (PEN) increases at a higher current and a higher temperature gradient. It is recommended that the temperature gradient should be limited to less than 10.6 °C mm⁻¹ to maintain the structural integrity of the PEN.