Effect of the geometrical size on time dependent failure probability of the solid oxide fuel cell

The time dependent failure probabilities (TDFP) of solid oxide fuel cell (SOFC) under different geometrical sizes are analyzed by a creep and damage related probability prediction constitutive model. The results demonstrate that sealant is the most possible failure component of the SOFC under different geometrical sizes. Increasing the sealant thickness or width can decrease the TDFP of the sealant. While the cathode thickness and electrolyte thickness have little effect on the TDFP of SOFC components. Decreasing the anode thickness, frame thickness can reduce the TDFP of the sealant. The sealant thickness and frame thickness can greatly affect the life of the SOFC stack. Based on the TDFP analysis of SOFC, it recommends that the sealant thickness should not be smaller than 0.1 mm, the frame thickness should not be less than 0.4 mm considering the stiffness requirement.     

Thermal stress and probability of failure analyses of functionally graded solid oxide fuel cells

Thermal stresses and probability of failure of a functionally graded solid oxide fuel cell (SOFC) are investigated using graded finite elements. Two types of anode-supported SOFCs with different cathode materials are considered: NiO-YSZ/YSZ/LSM and NiO-YSZ/YSZ/GDC-LSCF. Thermal stresses are significantly reduced in a functionally graded SOFC as compared with a conventional layered SOFC when they are subject to spatially uniform and non-uniform temperature loads. Stress discontinuities are observed across the interfaces between the electrodes and the electrolyte for the layered SOFC due to material discontinuity. The total probability of failure is also computed using the Weibull analysis. For the regions of graded electrodes, we considered the gradation of mechanical properties (such as Young’s modulus, the Poisson’s ratio, the thermal expansion coefficient) and Weibull parameters (such as the characteristic strength and the Weibull modulus). A functionally graded SOFC showed the least probability of failure based on the continuum mechanics approach used herein.     

Long-term evolution of mechanical performance of solid oxide fuel cell stack and the underlying mechanism

Mechanical performance analysis is important for ensuring the long-term reliability of solid oxide fuel cells (SOFCs). Thermal-mechanical models are constructed to conduct time-dependent mechanical performance analysis of SOFC stack with temperature field obtained by multiphysics modeling. The volume-averaged temperature field is used as comparison. The creep strains are examined with a time step of 10 h for 10,000 h. It reveals: (1) Uniform temperature significantly decreases the stresses, strains, failure probabilities of all stack components. (2) The failure probability of sealant reduced rapidly and the sealant becomes mechanically safer for long-term operation. (3) Creep strain is dominant for anode/sealant/interconnect, but negligible for electrolyte/cathode. All components are predictably safe against strain failure for 100,000 h (4) Creep strains of stack components interact with each other. Coupled analysis of creep strains of anode/sealant/interconnect is mandatory, but the creep strains of electrolyte/cathode may be neglected for studying mechanical evolutions.     

Mismatch effect of material creep strength on creep damage and failure probability of planar solid oxide fuel cell

The constraint effect with material parameters mismatch between every parts of planar solid oxide fuel cell (SOFC) plays an important role in the operation life. In this study, the mismatch effect of material creep strength coefficient on creep damage and failure probability of planar SOFC was investigated by finite element method. The results show that the maximum equivalent creep strain and failure probability of SOFC are located in the outer corner of sealant layer. With the increase of the creep strength coefficient of the sealant layer, the maximum creep damage, damage area and failure probability of the sealant layer all increase gradually. The creep strength coefficient of the sealant layer is suggested to be smaller than that of the frame material, which will improve service life of SOFC.     

Thermal stress analysis of a planar SOFC stack

The aim of this study is, by using finite element analysis (FEA), to characterize the thermal stress distribution in a planar solid oxide fuel cell (SOFC) stack during various stages. The temperature profiles generated by an integrated thermo-electrochemical model were applied to calculate the thermal stress distributions in a multiple-cell SOFC stack by using a three-dimensional (3D) FEA model. The constructed 3D FEA model consists of the complete components used in a practical SOFC stack, including positive electrode–electrolyte–negative electrode (PEN) assembly, interconnect, nickel mesh, and gas-tight glass-ceramic seals. Incorporation of the glass-ceramic sealant, which was never considered in previous studies, into the 3D FEA model would produce more realistic results in thermal stress analysis and enhance the reliability of predicting potential failure locations in an SOFC stack. The effects of stack support condition, viscous behavior of the glass-ceramic sealant, temperature gradient, and thermal expansion mismatch between components were characterized. Modeling results indicated that a change in the support condition at the bottom frame of the SOFC stack would not cause significant changes in thermal stress distribution. Thermal stress distribution did not differ significantly in each unit cell of the multiple-cell stack due to a comparable in-plane temperature profile. By considering the viscous characteristics of the glass-ceramic sealant at temperatures above the glass-transition temperature, relaxation of thermal stresses in the PEN was predicted. The thermal expansion behavior of the metallic interconnect/frame had a greater influence on the thermal stress distribution in the PEN than did that of the glass-ceramic sealant due to the domination of interconnect/frame in the volume of a planar SOFC assembly.     

Predicting Young's modulus of glass/ceramic sealant for solid oxide fuel cell considering the combined effects of aging,micro-voids and self-healing

We study the temperature dependent Young's modulus for the glass/ceramic seal material used in solid oxide fuel cells (SOFCs). With longer heat treatment or aging time during operation, further devitrification may reduce the residual glass content in the seal material while boosting the ceramic crystalline content. In the meantime, micro-voids induced by the cooling process from the high operating temperature to room temperature can potentially degrade the mechanical properties of the glass/ceramic sealant. Upon reheating to the SOFC operating temperature, possible self-healing phenomenon may occur in the glass/ceramic sealant which can potentially restore some of its mechanical properties. A phenomenological model is developed to model the temperature dependent Young's modulus of glass/ceramic seal considering the combined effects of aging, micro-voids, and possible self-healing. An aging time-dependent crystalline content model is first developed to describe the increase of the crystalline content due to the continuing devitrification under high operating temperature. A continuum damage mechanics (CDM) model is then adapted to model the effects of both cooling induced micro-voids and reheating induced self-healing. This model is applied to model the glass–ceramic G18, a candidate SOFC seal material previously developed at PNNL. Experimentally determined temperature-dependent Young's modulus is used to validate the model predictions.     

High temperature creep strength design and optimization of solid oxide fuel cell

In order to improve product design efficiency and guarantee the high temperature structural integrity during the long-term creep of solid oxide fuel cell (SOFC), the creep strength design method is studied by using the finite element method (FEM) and the response surface method (RSM) with considering the interaction between the geometric parameters. A multi-regression model representing the correlation between the sealant failure probability and the geometric parameters is established for rapid estimation of creep strength and optimization design of geometric dimensions. The sealant failure probability is decreased from 0.994 to 0.015 by the optimization of SOFC geometrical size. And the error between results predicted by the FEM and results predicted by the multi-regression model is less than 10%. Therefore, the multi-regression model is proven to be an excellent tool for creep failure prediction and structural design optimization, reducing research costs and time, and improving design efficiency.     

3D transient thermomechanical behaviour of a full scale SOFC short stack

Hermetic sealing of planar solid oxide fuel cell components is a critical issue. The long term operation and structural reliability of the fuel cell stacks depend strongly on the thermomechanically induced stress–strain behaviour of the fuel cell stack. These are especially affected through the thermal transients, which the fuel cell stack is subjected to, over time. Hence, the thermomechanical characterisation of the fuel cell stack during thermal cycling is indispensable. The current paper elucidates a fully three dimensional thermomechanical analysis of a planar type SOFC short stack over a whole thermal cycle. A coupled computational fluid dynamics and computational structural mechanics analysis has been performed. Typical stack components i.e., cell component, wire-mesh, metal frame, interconnector plates and sealant materials have been considered. The model represents the physical resolution of the air channels and the manifold regions. The non-linear elasto-plastic behaviour of the metal components as a function of temperature is considered. The study gives an insight about the transient thermal behaviour of a full scale fuel cell stack and its thermomechanical response, determining the mechanisms that trigger the thermomechanically induced stress during the heating-up, operation and shut-down stages.     

Numerical evaluation of a parallel fuel feeding SOFC–PEFC system using seal-less planar SOFC stack

We propose a system that combines a seal-less planar solid oxide fuel cell (SOFC) stack and polymer electrolyte fuel cell (PEFC) stack. In the proposed system, fuel for the SOFC (SOFC fuel) and fuel for the PEFC (PEFC fuel) are fed to each stack in parallel. The steam reformer for the PEFC fuel surrounds the seal-less planar SOFC stack. Combustion exhaust heat from the SOFC stack is used for reforming the PEFC fuel. We show that the electrical efficiency in the SOFC–PEFC system is 5% higher than that in a simple SOFC system using only a seal-less planar SOFC stack when the SOFC operation temperature is higher than 973 K.     

Effect of operating temperature on creep and damage in the bonded compliant seal of planar solid oxide fuel cell

This paper studies the effect of operating temperature on creep and damage in bonded compliant seal of solid oxide fuel cell by finite element method. A strain based creep damage model is used, and its feasibility to predict the creep damage behavior of the materials is verified firstly by the experimental data. The results show that the failure locates at the foil and the location varies with the temperature increasing. When the temperature is lower than 600 °C, there is nearly no crack occurs. When the temperature is 600 °C, the creep crack belongs to internal crack and the length is about 2.5 mm. While the temperature is 650 °C or higher, the crack locates at the foil surface and the length is larger than 25 mm at an operation time of 50,000 h. Compared to the size of the whole structure, an internal crack of 2.5 mm is small and the gas leakage will not happen. Therefore, it can satisfy the requirement of safe operation for more than 40,000 h. Thus, it recommends that the operating temperature should not be higher than 600 °C on the condition of insuring the power performance and operation cost of the SOFC.     

3D thermomechanical behaviour of solid oxide fuel cells operating in different environments

Hermetic sealing and long-term structural reliability of fuel cell stacks depend strongly on the thermomechanically induced stress–strain behaviour. These are especially affected by the environment; the fuel cell is operating in. Most of the research and development studies, as well as laboratory studies are conducted within electrically heated furnaces rather than operating in an insulated system environment. The thermomechanical comparison of them is not fully understood, yet. The present study utilises a previously developed full scale three dimensional planar type 6-cell SOFC short stack model to shed light on the thermomechanical response of high temperature fuel cells operating in system and furnace environments. The physically resolved coupled computational fluid dynamics and computational structural mechanics model has been improved, accounting for the rate dependent creep strain, as well as including the furnace domain and thermal radiation to fully describe the thermal and deformation behaviour of the stack. The non-linear elastoplastic behaviour of the metal components as a function of temperature is considered. The results are validated using creep strain data from the literature and in-house post-mortem images. The study gives an insight about the critical regions prone to failure due to creep strain operating in different environments and the long-term fuel cell behaviour. Moreover, the critical locations appear to be prone to high creep strain after 1000 h operation time.     

A study of solid oxide fuel cell stack failure by inducing abnormal behavior in a single cell test

It is well known that cell imbalance can lead to failure of batteries. Prior theoretical modeling has shown that similar failure can occur in solid oxide fuel cell (SOFC) stacks due to cell imbalance. Central to failure model for SOFC stacks is the abnormal operation of a cell with cell voltage becoming negative. For investigation of SOFC stack failure by simulating abnormal behavior in a single cell test, thin yttria-stabilized zirconia (YSZ) electrolyte, anode-supported cells were tested at 800 °C with hydrogen as fuel and air as oxidant with and without an applied DC bias. When under a DC bias with cell operating under a negative voltage, rapid degradation occurred characterized by increased cell resistance. Visual and microscopic examination revealed that delamination occurred along the electrolyte/anode interface. The present results show that anode-supported SOFC stacks with YSZ electrolyte are prone to catastrophic failure due to internal pressure buildup, provided cell imbalance occurs. The present results also suggest that the greater the number of cells in an SOFC stack, the greater is the propensity to catastrophic failure.     

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.     

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.     

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.     

Theoretical modeling of air electrode operating in SOFC mode and SOEC mode: The effects of microstructure and thickness

A theoretical model of solid oxide cells coupled with heterogeneous elementary reactions, electrochemical reactions, electrode microstructure and mass and charge transport is developed and validated. The effects of microstructure, thickness and temperature of air electrode on the cell performance in both solid oxide electrolysis cell (SOEC) and solid oxide fuel cell (SOFC) are individually discussed. The simulation results indicate that the growth in the thickness of air electrode reduces the effect of particle diameter while dramatically enlarges the effect of porosity. The microstructure and thickness of air electrode and temperature have significantly different impacts on solid oxide cells operating in SOEC mode and SOFC mode. The results indicate that the optimizing strategy of air electrode for SOEC and SOFC should be different especially for a thicker air electrode. The proposed model can be a useful tool for bridging the electrode geometry and microstructure design and optimization.     

Monolithic flat tubular types of solid oxide fuel cells with integrated electrode and gas channels

A new monolithic solid oxide fuel cell (SOFC) design stacked with flatten tubes of unit cells without using metallic interconnector plate is introduced and evaluated in this study. The anode support is manufactured in a flat tubular shape with fuel channel inside and air gas channel on the cathode surface. This design allows all-ceramic stack to provide flow channels and electrical connection between unit cells without needing metal plates. This structure not only greatly reduces the production cost of SOFC stack, but also fundamentally avoids chromium poisoning originated from a metal plate, thereby improving stack stability. The fuel channel was created in the extrusion process by using the outlet shape of mold. The air channel was created by grinding the surface of pre-sintered support. The anode functional layer and electrolyte were dip-coated on the support. The cathode layer and ceramic interconnector were then spray coated. The maximum power density and total resistance of unit cell with an active area of 30 cm² at 800 °C were 498 mW/cm² and 0.67 Ωcm², respectively. A 5-cell stack was assembled with ceramic components only without metal plates. Its maximum power output at 750 °C was 46 W with degradation rate of 0.69%/kh during severe operation condition for more than 1000 h, proving that such all-ceramic stack is a strong candidate as novel SOFC stack design.     

Experimental characterization of glass-ceramic seal properties and their constitutive implementation in solid oxide fuel cell stack models

This paper discusses experimental determination of solid oxide fuel cell (SOFC) glass-ceramic seal material properties and seal/interconnect interfacial properties to support development and optimization of SOFC designs through modeling. Material property experiments such as dynamic resonance, dilatometry, flexure, creep, tensile, and shear tests were performed on PNNL's glass-ceramic sealant material, designated as G18, to obtain property data essential to constitutive and numerical model development. Characterization methods for the physical, mechanical, and interfacial properties of the sealing material, results, and their application to the constitutive implementation in SOFC stack modeling are described.     

Electrochemical performance assessment of low-temperature solid oxide fuel cell with YSZ-based and SDC-based electrolytes

In this work, solid oxide fuel cells (SOFCs) based on different electrolytes, i.e., the yttria-stabilized zirconia (YSZ) and the samaria-doped ceria (SDC), were investigated to study their performances at low-temperature operation. The predicted performance of both SOFCs was validated with the experimental results. The verified models were implemented to study the impact of operating conditions, i.e., cell temperature, pressure, thicknesses of cathode, anode, and electrolyte, on their performances. The decrease in the operating temperature from intermediate range (800–900 °C) to low range (550–650 °C) has a considerable effect on the performance of the YSZ-based SOFC as conventional type, which dropped from 0.67–1.40 W/cm² to 0.027–0.13 W/cm². Under the low operating temperature range, the performance of SDC-based SOFC was superior to that of the YSZ-based SOFC, due to the lower ohmic loss. Nevertheless, the SDC-based SOFC has higher concentration overpotentials than the YSZ-based SOFC. The concentration overpotentials of the SDC-based SOFC can be reduced by the thinner anode and cathode thicknesses. In addition, the SDC-based SOFC at low operating temperature with the pressurized operation could significantly improve its power density, about 20% at 2 bar, which was close to that of YSZ-based SOFC at intermediate temperature of 800 °C.     

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.