Simulation of thermal stresses in anode-supported solid oxide fuel cell stacks. Part II: Loss of gas-tightness, electrical contact and thermal buckling

Structural stability issues in planar solid oxide fuel cells arise from the mismatch between the coefficients of thermal expansion of the components. The stress state at operating temperature is the superposition of several contributions, which differ depending on the component. First, the cells accumulate residual stresses due to the sintering phase during the manufacturing process. Further, the load applied during assembly of the stack to ensure electric contact and flatten the cells prevents a completely stress-free expansion of each component during the heat-up. Finally, thermal gradients cause additional stresses in operation.The temperature profile generated by a thermo-electrochemical model implemented in an equation-oriented process modelling tool (gPROMS) was imported into finite-element software (ABAQUS) to calculate the distribution of stress and contact pressure on all components of a standard solid oxide fuel cell repeat unit.The different layers of the cell in exception of the cathode, i.e. anode, electrolyte and compensating layer were considered in the analysis to account for the cell curvature. Both steady-state and dynamic simulations were performed, with an emphasis on the cycling of the electrical load. The study includes two different types of cell, operation under both thermal partial oxidation and internal steam-methane reforming and two different initial thicknesses of the air and fuel compressive sealing gaskets.The results generated by the models are presented in two papers: Part I focuses on cell cracking. In the present paper, Part II, the occurrences of loss of gas-tightness in the compressive gaskets and/or electrical contact in the gas diffusion layer were identified. In addition, the dependence on temperature of both coefficients of thermal expansion and Young's modulus of the metallic interconnect (MIC) were implemented in the finite-element model to compute the plastic deformation, while the possibilities of thermal buckling were analysed in a dedicated and separate model.The value of the minimum stable thickness of the MIC is large, even though significantly affected by the operating conditions. This phenomenon prevents any unconsidered decrease of the thickness to reduce the thermal inertia of the stack. Thermal gradients and the shape of the temperature profile during operation induce significant decreases of the contact pressure on the gaskets near the fuel manifold, at the inlet or outlet, depending on the flow configuration. On the contrary, the electrical contact was ensured independently of the operating point and history, even though plastic strain developed in the gas diffusion layer.     

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.     

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.     

Measurement of the temperature distribution in a large solid oxide fuel cell short stack

During the operation of solid oxide fuel cells (SOFCs), nonhomogeneous electrochemical reactions in both electrodes and boundary conditions may lead to a temperature gradient in the cell which may result in the development of thermal stresses causing the failure of the cell. Thus, in this study, effects of operating parameters (current density, flow configuration and cell size) on the temperature gradient of planar SOFCs are experimentally investigated. Two short stacks are fabricated using a small (16 cm² active area) and a large size (81 cm² active area) scandia alumina stabilized zirconia (ScAlSZ) based electrolyte supported cells fabricated via tape casting and screen printing routes and an experimental set up is devised to measure both the performance and the temperature distribution in short stacks. The temperature distribution is found to be uniform in the small short stack; however, a significant temperature gradient is measured in the large short stack. Temperature measurements in the large short stack show that the temperature close to inlet section is relatively higher than those of other locations for all cases due to the high concentrated fuel resulted in higher electrochemical reactions hence the generated heat. The operation current is found to significantly affect the temperature distribution in the anode gas channel. SEM analyses show the presence of small deformations on the anode surface of the large cell near to the inlet after high current operations.     

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.     

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.     

Thermal start-up behaviour and thermal management of SOFC's

Solid oxide fuel cells (SOFCs) have many attractive features for widespread applications. The high operating temperature provides a valuable heat source and in contrast to low temperature fuel cells they not only tolerate substances such as CO but can even use them as fuel. Thus, reforming of hydrocarbon fuels for SOFCs can be done without additional gas purification. As both stack and hydrocarbon reformer unit have to be operated at high temperatures (700–1000 °C), thermal management plays an important role in the successful operation of SOFC systems. As the SOFC system contains ceramic components, both large thermal gradients in the system and thermal expansion coefficient (TEC) mismatch must be avoided.Matching TECs is done by selecting the suitable materials. Avoiding high temperature gradients is done by selecting the right system design and control strategies. In order to achieve both, we have built a finite element simulation for a complete SOFC systems which allows to study system parameters both during steady operation and during transients. Examples of the thermal start-up behaviour for several system configurations are given for selected components as well as internal temperatures of the SOFC-stack during start-up. The simulation model includes also the option to simulate the effects of internal methane reformation in the SOFC stack.As the minimum operation temperature is high, cooling down of the system has to be avoided if instant operation is desired. This can be achieved either passively by selecting suitable thermal insulation materials and/or actively by adopting a strategy for maintaining the temperature.     

A CFD study of hygro–thermal stresses distribution in PEM fuel cell during regular cell operation

A three-dimensional, multi-phase, non-isothermal computational fluid dynamics model of a proton exchange membrane fuel cell has been developed and used to investigate the displacement, deformation, and stresses inside the whole cell, which developed during the cell operation due to the changes of temperature and relative humidity. The behaviour of the fuel cell during operation has been studied and investigated under real cell operating conditions. A unique feature of the present model is to incorporate the effect of hygro and thermal stresses into actual three-dimensional fuel cell model for a complete cell with both the membrane-electrode-assembly and the gas distribution flow channels. The results show that the non-uniform distribution of stresses, caused by the temperature gradient in the cell, induces localized bending stresses, which can contribute to delaminating between the membrane and the gas diffusion layers. The non-uniform distribution of stresses can also contribute to delaminating between the gas diffusion layers and the channels, especially in the cathode side. These stresses may explain the occurrence of cracks and pinholes in the fuel cells components under steady-state loading during regular cell operation, especially in the high loading conditions.     

An integrated modeling approach for temperature driven water transport in a polymer electrolyte fuel cell stack after shutdown

The concept of using controlled temperature gradients to non-parasitically remove excess water from porous media during PEFC stack shutdown has been numerically investigated. An integrated modeling approach focusing both at stack and single cell level is presented. The stack thermal model is developed to obtain detailed temperature distribution across the PEFC stack. The two-phase unit fuel cell model is developed to investigate the detailed water and thermal transport in the PEFC components after shutdown, which for the first time includes thermo-osmotic flow in the membrane. The model accounts for capillary and phase-change induced flow in the porous media, and thermo-osmotic and diffusive flow in the polymer membrane. The single cell model is used to estimate the local water distribution with land or channel boundary condition, and the experimentally validated stack thermal model provided the transient temperature boundary conditions. Two different stack designs are compared to quantify the residual water in the stack. Model results indicate that a favorable temperature gradient can be formed in the stack to enhance the water drainage rate, esp. at anode end cell locations, where freeze/thaw damage has been observed to occur.     

A spatially resolved physical model for transient system analysis of high temperature fuel cells

This work builds upon previous high temperature fuel cell (HT-FC) modeling studies, capturing both steady state performance and transient behavior of HT-FC stacks by merging simplified dimensional aspects of a planar fuel cell stack with first principles physical modeling. Dynamic simulations are developed that spatially resolve fluctuations in temperature, pressure and concentration distributions during transient operation. A significant portion of the heat transfer occurs prior to and after the air passes over the electrochemically active portions of the cell, justifying additional heat transfer pathways from the stack to the air in order to accurately characterize the thermal transients and temperature distributions in the HT-FC stack. The highly configurable MatLab-Simulink® model developed can simulate both solid oxide and molten carbonate fuel cells utilizing either direct or indirect internal reforming. The perturbation response characteristics of the dynamic model to load, fuel flow, air flow and composition perturbations are discussed, and control strategies are introduced that minimize temperature fluctuations. Analysis indicates air flow and inlet temperature controls are sufficient to control average temperature and average internal temperature gradients. Internal heat transfer dynamics substantially change the spatial temperature distribution and local temperature gradients during typical operating conditions and perturbations.     

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.     

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.     

Investigation of solid oxide fuel cell sealing behavior under stack relevant conditions at Forschungszentrum Jülich

Hermetic sealing is a key requirement for the operation of solid oxide fuel cell (SOFC) stacks in a system environment. The sealant material has to withstand stresses due to mechanical loading, mismatch in thermal expansion coefficient and thermal gradients that arise during operation. Based on leakage tests performed at Forschungszentrum Jülich it was obvious that stacks, having been operated successfully in a furnace, are not necessarily usable in a system, e.g. because of deviating pressure differences and temperature gradients. Thorough investigations including stack and stack dummy tests, and finite element modeling (FEM) were performed to get a comprehensive understanding of the various parameters, influencing the leak tightness of the sealing material. It was found that even small temperature differences especially in the area of gas and air manifolds can create excessively high tensile stresses. Based on initial FEM analyses, a better understanding of the problem has been obtained and a tool was developed that can assist in the design of more robust stacks. These investigations and modeling activities will be continued with a main focus on thermal cycling, which is the next step in the list of requirements.     

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 lumped parameter model of the polymer electrolyte fuel cell

A model of a polymer electrolyte fuel cell (PEFC) is developed that captures dynamic behaviour for control purposes. The model is mathematically simple, but accounts for the essential phenomena that define PEFC performance. In particular, performance depends principally on humidity, temperature and gas pressure in the fuel cell system. To simulate accurately PEFC operation, the effects of water transport, hydration in the membrane, temperature, and mass transport in the fuel cells system are simultaneously coupled in the model. The PEFC model address three physically distinctive fuel cell components, namely, the anode channel, the cathode channel, and the membrane electrode assembly (MEA). The laws of mass and energy conservation are applied to describe each physical component as a control volume. In addition, the MEA model includes a steady-state electrochemical model, which consists of membrane hydration and the stack voltage models.     

Advanced measurement techniques to characterize thermo-mechanical aspects of solid oxide fuel cells

Advanced characterization methods have been used to analyze the thermo-mechanical behaviour of solid oxide fuel cells in a model stack. The primarily experimental work included contacting studies, sealing of a model stack, thermal and re-oxidation cycling. Also an attempt was made to correlate cell fracture in the stack with pore sizes determined from computer tomography. The contacting studies were carried out using pressure sensitive foils. The load to achieve full contact on anode and cathode side of the cell was assessed and applied in the subsequent model stack test. The stack experiment permitted a detailed analysis of stack compaction during sealing. During steady state operation thermal and re-oxidation cycling the changes in open cell voltage and acoustic emissions were monitored. Significant softening of the sealant material was observed at low temperatures. Heating in the thermal cycling loop of the stack appeared to be less critical than the cooling. Re-oxidation cycling led to significant damage if a critical re-oxidation time was exceeded. Microstructural studies permitted further insight into the re-oxidation mechanism. Finally, the maximum defect size in the cell was determined by computer tomography. A limit of maximum anode stress was estimated and the result correlated this with the failure strength observed during the model stack testing.     

One-dimensional thermal model for direct methanol fuel cell stacks: Part II. Model based parametric analysis and predicted temperature profiles

Using the one-dimensional thermal model for the direct methanol fuel cell (DMFC) (presented in Part 1), based on the differential thermal energy conservation equation, which describes the thermal behaviour of a DMFC stack comprised of up to 25 large (272 cm²) cells, temperature profiles are predicted along the stack length. The model is used to assess the effect of operating parameters (temperature gradient, current density, flow rate and pressure) on the temperature profile along the stack. In addition, it enables investigation of the stack thermal management and the effect of altering a number of systematic parameters such as the number of cells in the stack, the active and exposed area and the interactions between the physical properties of the various components. The model aids the fuel cell system designer to gain an insight in the stack structure and select materials and geometric configurations that are optimal from a thermal management point of view.     

Analysis of the water and thermal management in proton exchange membrane fuel cell systems

Water and thermal management is essential to the performance of proton exchange membrane (PEM) fuel cell system. The key components in water and thermal management system, namely the fuel cell stack, radiator, condenser and membrane humidifier are all modeled analytically in this paper. Combined with a steady-state, one-dimensional, isothermal fuel cell model, a simple channel-groove pressure drop model is included in the stack analysis. Two compact heat exchangers, radiator and condenser are sized and rated to maintain the heat and material balance. The influence of non-condensable gas is also considered in the calculation of the condenser. Based on the proposed methodology, the effects of two important operating parameters, namely the air stoichiometric ratio and the cathode outlet pressure, and three kinds of anode humidification, namely recycling humidification, membrane humidification and recycling combining membrane humidification are analyzed. The methodology in this article is helpful to the design of water and thermal management system in fuel cell systems.     

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.     

Thermal modeling and temperature control of a PEM fuel cell system for forklift applications

Temperature changes in PEM fuel cell stacks are considerably higher during load variations and have a negative impact as they generate thermal stresses and stack degradation. Cell hydration is also of vital importance in fuel cells and it is strongly dependent on operating temperature. A combination of high temperature and reduced humidity increases the degradation rate. Stack thermal management and control are, thus, crucial issues in PEM fuel cell systems especially in automotive applications such as forklifts.