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.     

A modeling study on the thermomechanical behavior of glass-ceramic and self-healing glass seals at elevated temperatures

Hermetic gas seals are critical components of planar Solid Oxide Fuel Cells (SOFCs). This article focuses on the comparative evaluation of a glass-ceramic seal developed by the Pacific Northwest National Laboratory (PNNL) and a self-healing glass seal developed by the University of Cincinnati. The stress and strain levels in the Positive electrode–Electrolyte–Negative electrode (PEN) seal in a single-cell stack are evaluated using a multi-physics simulation package developed at PNNL. Simulations were carried out with and without consideration of a clamping force and a stack body force, respectively. The results indicate that the overall stress and strain levels are dominated by the thermal expansion mismatches between the different cell components. Further, compared with the glass-ceramic, the self-healing glass results in a much lower steady state stress value due to its much lower stiffness at the operating temperature of the SOFC. It also exhibits much shorter relaxation times due to a high creep rate. It is also noted that the self-healing glass seal will experience continuing creep deformation at the operating temperature of a SOFC therefore resulting in possible overflow of the sealant material. Therefore, a stopper material may be required to maintain its geometric stability during operation.     

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 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.     

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.     

A coupled 3D thermofluid-thermomechanical analysis of a planar type production scale SOFC stack

This paper presents a coupled 3D thermofluid/thermomechanical analysis of a 36-layer planar type SOFC stack. Typical components such as the cell, wire mesh, frame, interconnector plate and glass-ceramic sealant have been considered, including the physical resolution of the air channels and the manifold regions. The coupled computational mechanics study accounts for the nonlinear elastoplastic behaviour of the interconnector plate, as well as the mal flow behaviour that may result in thermomechanical differences within the stack. Locations susceptible to stress within the fuel cell stack could be determined. A feasibility study considering the geometrical effect of the wire mesh structure on the thermomechanical modelling results has been introduced. The study gives an insight how full scale fuel cells can be modelled effectively with the aid to develop and design reliable and robust fuel cell stacks.     

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 and testing of glass-ceramic sealant used to join anode-supported-electrolyte to Crofer22APU in planar solid oxide fuel cells

This work describes the performance and testing of a glass-ceramic sealant used to join the ceramic electrolyte (anode-supported-electrolyte (ASE)) to the metallic interconnect (Crofer22APU) in planar SOFC stacks. The designed glass-ceramic sealant is a barium and boron free silica-based glass, which crystallizes by means of the heat-treatment after being deposited on substrates by the slurry technique.Joined ASE/glass-ceramic seal/Crofer22APU samples were tested for 500 h in H₂–3H₂O atmosphere at the fuel cell operating temperature of 800 °C.Moreover, the joined ASE/glass-ceramic seal/Crofer22APU samples were submitted to three thermal cycles each of 120 h duration, in order to evaluate the thermomechanical stability of the sealant.The microstructures and elemental distribution at Crofer22APU/glass-ceramic and ASE/glass-ceramic interfaces were investigated.SEM micrograph observations of joined samples that underwent cyclic thermal tests and exposure for 500 h in H₂–3H₂O atmosphere showed that the adhesion between the glass-ceramic and Crofer22APU at either interface was very good and no microstructural changes were detected at the interfacial boundaries.The study showed that the use of the glass-ceramic was successful in preventing strong adverse corrosion effects at the Crofer22APU/glass-ceramic sealant interface.     

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.     

A simple equation for temperature gradient in a planar SOFC stack

Our recent model of heat transport in a planar SOFC stack is extended to take into account finite hydrogen utilization. The extended model includes the heat balance equations in the interconnect and air flow, and the hydrogen mass balance equation in the anode channel. An approximate analytical expression for the gradient of stack temperature along the air channel is derived. The analytical result is in excellent agreement with the exact numerical solution. The resulting expression can be used for rapid estimate of the temperature gradient in a planar SOFC stack under real operating conditions.     

The effects of the interconnect rib contact resistance on the performance of planar solid oxide fuel cell stack and the rib design optimization

A mathematical model for the performance of the planar solid oxide fuel cell (SOFC) stack is described. The model considered the electric contact resistance between the electrode and interconnect rib, the gas transport in the electrodes, electronic and ionic conductions in the membrane-electrode assembly and the electrochemical reactions at the gas–electrode–electrolyte three phase boundaries. The model is capable of describing in detail the rib effect on the gas transport and the current distribution in the fuel cell. The contact resistance is found to be an important factor in limiting the SOFC performance. Based on the interplay of the concentration and ohmic polarizations, numerical results are provided for the optimal rib widths for different pitch sizes and different area specific contact resistance (ASR_contact). The optimal rib width is found to be linear to the pitch width for a given ASR_contact and the parameters for the linearity are given. The parameters are little affected by the hydrogen concentration and the thickness, porosity or conductivity of the cathode. The influence of the cathode thickness on the SOFC performance is also examined. Contrary to the common belief on the thin cathode (∼50 μm), thicker cathode layer (100–300 μm) is beneficial to the SOFC stack performance.     

Two-dimensional temperature distribution estimation for a cross-flow planar solid oxide fuel cell stack

The uniform temperature distribution of a cross-flow planar solid oxide fuel cell (SOFC) stack plays an essential role in stack thermal safety and electrical property. However, because of the strict requirements in stack sealing struture, it is hard to acquire the temperature inside the stack using thermal detection devices within an acceptable cost. Therefore, accurately estimating the two-dimensional (2-D) temperature distribution of the cross-flow stack is crucial for its thermal management. In this paper, Firstly, a 2-D mechanism model of a cross-flow planar SOFC stack is established. The stack is divided into 5*5 nodes along the gas flow directions, which can reflect the stack states with moderate computational burden. Then, experimental test data is utilized to modify and validate the stack model, guaranteeing the model accuracy as well as the reliability of model-based state estimator design. Finally, easily-measured stack inputs and outputs are selected, and a temperature distribution estimator combined with unscented kalman filter (UFK) approach is developed to achieve accurate and fast temperature distribution estimation of a cross-flow SOFC stack. Simulation results demonstrate that the UKF-based temperature distribution estimator can precisely and quickly achieve the temperature distribution estimation of the cross-flow stack under both static state and dynamic state changes and is applicable to cross-flow stacks with different size or cell number as well, the maximum estimated absolute error is less than 0.15 K with an absolute error rate of 0.015%, which indicates the developed estimator has good estimation performances.     

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.     

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.     

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.     

Comparison of heat and mass transfer between planar and MOLB-type SOFCs

A numerical simulation tool for calculating the planar and mono-block layer built (MOLB) type solid oxide fuel cells (SOFC) is described. The tool combines the commercial computational fluid dynamics simulation code with an electrochemical calculation subroutine. Its function is to simulate the heat and mass transfer and to predict the temperature distribution and mass fraction of gaseous species in the SOFC system. The three-dimensional geometry model of SOFC was designed to simulate a co-flow case and counter-flow case. The finite volume method was employed to calculate the conservation equations of mass, momentum and energy. Moreover, the influences of working conditions on the performances of planar and MOLB-type SOFCs were also discussed and compared, such as the delivery rate of gas and the components of fuel gas. Simulation results show that the MOLB-type SOFC has higher fuel utilization than the planar SOFC. For the co-flow case, average temperatures of PEN (positive electrode–electrolyte–negative electrode) in both types of SOFCs rise with the increase in delivery rate and mass fraction of hydrogen. In particular, the temperature of planar SOFC is more sensitive to the working conditions. In order to decrease the average temperatures in SOFC, it is effective to increase the delivery rate of air.     

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.     

Time dependent failure probability estimation of the solid oxide fuel cell by a creep-damage related Weibull distribution model

In present paper, a new model is proposed and embedded into the finite element software ABAQUS to estimate the time dependent failure probability of the solid oxide fuel cell stack. The results show that sealant is the potential failure region of the solid oxide fuel cell stack, while the failure probability of the anode, electrolyte and cathode are very small within the operation time of 50,000 h. The creep and damage distribution of the components reflect that the proposed model can reasonably predict the time dependent failure probability of the solid oxide fuel cell stack. Increasing either the characteristic strain, Weibull modulus or decreasing the operating temperature can decrease the failure probability of the SOFC stack. For the sealant, to ensure the high temperature integrity of the SOFC stack, the characteristic strain should be larger than 0.01 or Weibull modulus should be higher than 8.0 under the operating temperature of 600 °C.     

Three‐dimensional nonisothermal modeling of solid oxide fuel cell coupling electrochemical kinetics and species transport

A three‐dimensional (3D) nonisothermal model is developed and applied for anode‐supported planar solid oxide fuel cell (SOFC). The mass and momentum, species, ion, electric, and heat transport equations are solved simultaneously by implementing the electrochemical kinetics and electrochemical reaction as volumetric source terms. The interconnect land limits the O₂ transport under the land and lowers the local current density under the land. The effects of interconnect land width and cathode substrate thickness on SOFC cell performance are quantified in this study. Cathode stoichiometry is found to have a large effect on the SOFC cell temperature distribution. Under low‐cathode stoichiometry, significant temperature gradients are seen in the SOFC cell. Higher‐cathode stoichiometry is beneficial for lower temperature and more uniform current density distribution in SOFC cell. Co‐flow and counter‐flow arrangements are investigated and discussed with the model. Counter‐flow arrangement is found to induce a high temperature and high current density region near the H₂ inlet. On the other hand, co‐flow arrangement leads high temperature and high current density to occur relatively downstream, a slightly lower maximum temperature on cell and considerably more uniform current density distribution. A 67.2‐cm² SOFC cell is simulated considering the side cooling effect. The side cooling effectively lowers the cell temperature, at the same time, causes temperature, current density, and fuel utilization nonuniformity in the across multichannel direction. Because of the strong coupling of the in‐plane current density distribution and temperature distribution, limiting the locally high temperature and temperature gradient is critical for achieving a more uniform current density distribution in anode‐supported planar SOFC.     

Effect of frame material on the creep of solid oxide fuel cell

During long term operation at high temperature, creep is inevitable and can cause damages and cracks, which should be decreased to ensure the stack integrity. A strain based creep damage model is used to predict the creep damage behavior of a planar solid oxide fuel cell (SOFC). It demonstrates the maximum creep damage locates at the corner of glass-ceramic (GC) facing the frame after 50 000 h creep. The effect of frame material on the creep is studied. By increasing the creep parameter B of frame, the creep and damage in the cell and GC are decreased. This indicates the frame with a larger creep parameter can alleviate the interaction between components and decrease the deformation of the system. It recommends to use frame materials which have creep parameters larger than 1.3752 × 10⁻¹⁵ MPa^-nh⁻¹ besides CTEs closed to the cell to compensate and mitigate the creep and damage of SOFC system.