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.     

Thermal stress modeling of anode supported micro-tubular solid oxide fuel cell

An anode-supported micro-tubular solid oxide fuel cell (SOFC) is analyzed by a two-dimensional axisymmetric numerical model, which is validated with the experimental I-V data. The temperature distribution generated by the thermo-electrochemical model is used to calculate the thermal stress field in the tubular SOFC. The results indicate that the current transport in the anode is the same at every investigated position. The stress of the micro-tubular cell occurs mainly because of the residual stress due to the mismatch between the coefficients of thermal expansion of the materials of the membrane electrode assembly. The micro-tubular cell can operate safely, but if there is an interfacial defect or a high enough tensile stress applied at the electrolyte, a failure can arise.     

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.     

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.     

Three-dimensional thermo-fluid and electrochemical modeling of anode-supported planar solid oxide fuel cell

This paper presents a three-dimensional model of an anode-supported planar solid oxide fuel cell with corrugated bipolar plates serving as gas channels and current collector above the active area of the cell. Conservation equations of mass, momentum, energy and species are solved incorporating the electrochemical reactions. Heat transfer due to conduction, convection and radiation is included. An empirical equation for cell resistance with measured values for different parameters is used for the calculations. Distribution of temperature and gas concentrations in the PEN (positive electrode/electrolyte/negative electrode) structure and gas channels are investigated. Variation of current density over the cell is studied. Furthermore, the effect of radiation on the temperature distribution is studied and discussed. Modeling results show that the relatively uniform current density is achieved at given conditions for the proposed design and the inclusion of thermal radiation is required for accurate prediction of temperature field in the single cell unit.     

Three dimensional stress analysis of solid oxide fuel cell anode micro structure

One of the most common problems in solid oxide fuel cells (SOFCs) is the delamination and thus the degradation of electrode/electrolyte interface which occurs in the consequences of the stresses generated within the different layers of the cell. Nowadays, the modeling of this problem under certain conditions is one of the main issues for the researchers. The structural and thermo-physical properties of the cell materials (i.e. porosity, density, Young's modulus etc.) are usually assumed to be homogenous in the mathematical modeling of solid oxide fuel cells at macro-scale. However, during the real operation, the stresses created in the multiphase porous layers might be very different than those at macro-scale. Therefore, micro-level modeling is required for an accurate estimation of the real stresses and the performance of SOFCs. This study presents a microstructural characterization and a finite element analysis of the delamination and the degradation of porous solid oxide fuel cell anode and electrode/electrolyte interface under various operating temperatures, compressing forces and material compositions by using the synthetically generated microstructures. A multi physics computational package (COMSOL) is employed to calculate the Von Misses stresses in the anode microstructures. The maximum thermal stress in the electrode/electrolyte interface and three phase boundaries is found to exceed the yield strength at 900 °C while 800 °C is estimated as a critical temperature for the delamination and micro cracks due to thermal stress generated. The thermal stress decreases in the grain boundaries with increasing content of one of the phases (either Ni or YSZ) and the porosity of the electrode. A clamping load higher than 5 kg cm⁻² is also found to exceed the shear stress limit.     

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.     

Thermal imaging of solid oxide fuel cell anode processes

A Si-charge-coupled device (CCD), camera-based, near-infrared imaging system is demonstrated on Ni/yttria-stabilized zirconia (YSZ) fragments and the anodes of working solid oxide fuel cells (SOFCs). NiO reduction to Ni by H₂ and carbon deposition lead to the fragment cooling by 5 ± 2 °C and 16 ± 1 °C, respectively. When air is flowed over the fragments, the temperature rises 24 ± 1 °C as carbon and Ni are oxidized. In an operational SOFC, the decrease in temperature with carbon deposition is only 4.0 ± 0.1 °C as the process is moderated by the presence of oxides and water. Electrochemical oxidation of carbon deposits results in a ΔT of +2.2 ± 0.2 °C, demonstrating that electrochemical oxidation is less vigorous than atmospheric oxidation. While the high temperatures of SOFCs are challenging in many respects, they facilitate thermal imaging because their emission overlaps the spectral response of inexpensive Si-CCD cameras. Using Si-CCD cameras has advantages in terms of cost, resolution, and convenience compared to mid-infrared thermal cameras. High spatial (0.1 mm) and temperature (0.1 °C) resolutions are achieved in this system. This approach provides a convenient and effective analytical technique for investigating the effects of anode chemistry in operating SOFCs.     

The effect of porosity gradient in a Nickel/Yttria Stabilized Zirconia anode for an anode-supported planar solid oxide fuel cell

In this paper, a graded Ni/YSZ cermet anode, an 8 mol.%YSZ electrolyte, and a lanthanum strontium manganite (LSM) cathode were used to fabricate a solid oxide fuel cell (SOFC) unit. An anode-supported cell was prepared using a tape casting technique followed by hot pressing lamination and a single step co-firing process, allowing for the creation of a thin layer of dense electrolyte on a porous anode support. To reduce activation and concentration overpotential in the unit cell, a porosity gradient was developed in the anode using different percentages of pore former to a number of different tape-slurries, followed by tape casting and lamination of the tapes. The unit cell demonstrated that a concentration distribution of porosity in the anode increases the power in the unit cell from 76 mW cm⁻² to 101 mW cm⁻² at 600 °C in humidified hydrogen. Although the results have not been optimized for good performance, the effect of the porosity gradient is quite apparent and has potential in developing superior anode systems.     

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.     

Performance of anode-supported solid oxide fuel cell using novel ceria electrolyte

The potential of a novel co-doped ceria material Sm_0.075Nd_0.075Ce_0.85O_2−δ as an electrolyte was investigated under fuel cell operating conditions. Conventional colloidal processing was used to deposit a dense layer of Sm_0.075Nd_0.075Ce_0.85O_2−δ (thickness 10 μm) over a porous Ni-gadolinia doped ceria anode. The current-voltage performance of the cell was measured at intermediate temperatures with 90 cm³ min⁻¹ of air and wet hydrogen flowing on cathode and anode sides, respectively. At 650 °C, the maximum power density of the cell reached an exceptionally high value of 1.43 W cm⁻², with an area specific resistance of 0.105 Ω cm². Impedance measurements show that the power density decrease with decrease in temperature is mainly due to the increase in electrode resistance. The results confirm that Sm_0.075Nd_0.075Ce_0.85O_2−δ is a promising alternative electrolyte for intermediate temperature solid oxide fuel cells.     

Transient modeling of anode-supported solid oxide fuel cells

An isothermal 2-D transient model is developed for an anode-supported solid oxide fuel cell. The model takes into account the transient effects of both charge migration and species transport in PEN assembly. Due to the lack of transient experimental data, the transient model, under steady state operating conditions, is validated using experimental results from open literature. Numerical results show that the cell can obtain very quick transient current response when subjected to a step voltage change, followed by a slow current transient period due to species diffusion effects within porous electrodes. It is also found that the transient response of the cell current is sensitive to oxygen concentration change at cathode/channel interface, whereas the current response is slow when step change of hydrogen concentration is applied at anode/channel interface. The cell transient performance can be improved by increasing porosity or decreasing tortuosity of electrodes.     

Effect of anode thickness on impedance response of anode-supported solid oxide fuel cells

This study examines effects of the anode functional layer thickness on the performance of anode-supported solid oxide fuel cells (SOFCs). The SOFCs with different AFL thicknesses (8 μm, 19 μm, and 24 μm) exhibit similar power densities at the measured current density range (0–2 A cm⁻²), but show different impedance responses. Further investigation on the spectra using the CNLS fitting method based on DRT-based equivalent circuit model helps us pinpoint two electrochemical processes directly affected by the AFL thickness changes, the charge transfer reaction in the AFL as well as the diffusion-coupled charge transfer reaction in the AFL. The combined effects of these two electrochemical processes probably forged a minimal impact on the overall fuel cell performance by offsetting each other, which offers a reasonable explanation of the seemingly little influence of the AFL thickness on the SOFC performance.     

Basic properties of a liquid tin anode solid oxide fuel cell

An unconventional high temperature fuel cell system, the liquid tin anode solid oxide fuel cell (LTA-SOFC), is discussed. A thermodynamic analysis of a solid oxide fuel cell with a liquid metal anode is developed. Pertinent thermochemical and thermophysical properties of liquid tin in particular are detailed. An experimental setup for analysis of LTA-SOFC anode kinetics is described, and data for a planar cell under hydrogen indicated an effective oxygen diffusion coefficient of 5.3 × 10⁻⁵ cm² s⁻¹ at 800 °C and 8.9 × 10⁻⁵ cm² s⁻¹ at 900 °C. This value is similar to previously reported literature values for liquid tin. The oxygen conductivity through the tin, calculated from measured diffusion coefficients and theoretical oxygen solubility limits, is found to be on the same order of that of yttria-stabilized zirconia (YSZ), a traditional SOFC electrolyte material. As such, the ohmic loss due to oxygen transport through the tin layer must be considered in practical system cell design since the tin layer will usually be at least as thick as the electrolyte.     

Development of 1 kW class solid oxide fuel cell stack using anode-supported planar cells

We have developed a 1 kW class solid oxide fuel cell (SOFC) stack composed of 50 anode-supported planar 120-mm-diameter SOFCs. Intermediate plates, which exhibited negligible deformation under operating conditions, were placed in the stack to cancel out the cumulative error related to the position and angle of the stack parts. The stack provided an electrical conversion efficiency of 54% (based on the lower heating value (LHV) of the methane used as a fuel) and an output of 1120 W when the fuel utilization, current density, and operating temperature were 67%, 0.28 A cm⁻², and 1073 K, respectively. The stack operated stably for almost 700 h.     

Numerical investigation of flow/heat transfer and structural stress in a planar solid oxide fuel cell

The present work investigates the effects of the temperature and thermal stress distributions in a planar solid oxide fuel cell (SOFC) unit cell. A computational fluid dynamic (CFD) analysis of a planar anode-supported SOFC that considers electrochemical reactions is performed, and the thermal stresses are calculated. The static friction coefficients are assumed to range from 0.05 to 0.3, and conservatively, a perfectly bonded condition is assumed. The results show that the electrolyte is the weakest component and has the maximum stress because the electrolyte is the thinnest and the Young modulus is the highest. Thus, the contact between the anode electrode and the electrolyte, and between the cathode electrode and the electrolyte, would be the perfectly bonded condition. As a result, this research showed that the stresses induced by constraint forces with various contact conditions were dominant for the structural stability in a SOFC. Therefore, static friction coefficients on operative high temperature conditions are important to predict the structural integrity in a SOFC, and they will be investigated in future works in order to improve the structural stability in a stack design as well as in a SOFC.     

Multi-scale design simulation of a novel intermediate-temperature micro solid oxide fuel cell stack system

This paper presents a multi-scale simulation technique for designing a novel intermediate-temperature planar-type micro solid oxide fuel cell (mSOFC) stack system. This multi-scale technique integrates the fundamentals of molecular dynamics (MD) and computational fluid dynamics (CFD). MD simulations are carried out to determine the optimal composition of a potential electrolyte that is capable of operation in the intermediate-temperature region without sacrifice in performance. A commercial CFD package plus a self-written computational electrochemistry code are employed to design the fuel and air flow systems in a planar five-cell stack, including the preheating manifold. Different samarium-doped ceria (SDC) electrolyte compositions and operating temperatures from 673 K to 1023 K are investigated to identify the maximum ionic conductivity. The electrochemical performance simulation using an available 5-cell yittria-stablized-zirconia (YSZ) mSOFC stack shows good agreement with our experimental results. The same stack design is used to predict a novel SDC-mSOFC performance. Feasibiulity studies of this intermediate-temperature stack are presented using this multi-scale technique.     

Fabrication and operation of a 6 kWe class interconnector-type anode-supported tubular solid oxide fuel cell stack

A 6 kW class interconnector-type anode-supported tubular solid oxide fuel cell (ICT SOFC) stack is fabricated and operated in this study. An optimized current-collection method, which the method for current collection at the cathode using the winding method and is the method for the connection between cells using interconnect, is suggested to enhance the performance of the fabricated cell. That method can increase the current collection area because of usage of winding method for cell and make the connection between cells easy. The performance of a single cell with an effective electrode area of 205 cm² exhibits 51 W at 750 °C and 0.7 V. To assemble a 1 kW class stack, the prepared ICT SOFC cells are connected in series to 20 cells connected in parallel (20 cells in series × two in parallel, 20S2P). Four modules are assembled for a 6 kWe class stack. For one module, the prepared ICT SOFC cells are connected in series to 48 cells, in which one unit bundle consists of two cells connected in parallel. The performance of the stack in 3% humidified H₂ and air at 750 °C exhibits the maximum electrical power of 7425 W.