Thermal stress analysis of the planar SOFC bonded compliant seal design

A new materials joining approach known as the bonded compliant seal (BCS) has recently been developed for hermetically sealing the cell and window frame components in planar solid oxide fuel cell stacks. At the heart of the BCS is a thin deformable metal foil that is designed to decouple the effects of differential thermal expansion between the two components and thereby mitigate the generation of potentially destructive thermal stresses in the stack. While preliminary viability of the BCS design has been demonstrated in small-scale rotationally symmetric test specimens, issues concerning the scale-up of this seal to a size and shape that is prototypic of full-size stacks are addressed here. Finite element analysis was undertaken to investigate the magnitudes of thermally induced stress, strain, and part deflection in the cell, seal, and window frame components under uniform heating and cooling conditions. From the point of stress mitigation, particularly in the brittle ceramic cell, the initial BCS design appears to function quite well by accommodating the mismatch thermal strains as elastic and plastic strain within the sealing foil. However, the model predicts that some bowing will take place within the cell. While the amount of bowing is likely manageable through proper design of the adjacent interconnects, it is believed that a substantial portion of the predicted bow can be eliminated via minor adjustments to the various seal parameters.     

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.     

Numerical simulation and analysis of thermal stress distributions for a planar solid oxide fuel cell stack with external manifold structure

A three-dimensional numerical model based on the finite element method (FEM) is constructed to calculate the thermal stress distribution in a planar solid oxide fuel cell (SOFC) stack with external manifold structure. The stack is composed of 5 units which include cell, metallic interconnect, seal and anode/cathode current collectors. The temperature profile is described according to measured temperature points in the stack. It can be clearly seen that the maximum stress concentration area appears at the corner of the components when the stack is heated from room temperature (RT) to 780 °C. The effects of stack components on maximum stress concentration have been investigated under the operation temperature, as well as the thermal stress simulation results. It is obvious that the coefficient of thermal expansion (CTE) mismatch between the interconnect and the seal plays an important role in determining the thermal stress distribution in the stack. However, different compressive loads have almost no effect on stress distribution, and the influence of glass-based seal depends on the elastic modulus. The simulation results can be applied for optimizing the structural design of the stack and minimizing the high stress concentration in components.     

A 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.     

Design and numerical analysis of a planar anode-supported SOFC stack

In the present study, numerical simulations are conducted to examine the flow characteristics and attributes of electrochemical reactions in the stack through three-dimensional analysis using finite volume approach prior to the fabrication of the SOFC stack. The stack flow uniformity index is employed to investigate the flow uniformity whereas in the case of electrochemical modeling, different mathematical models are adopted to predict the characteristics of activation and ohmic overpotentials that occur during electrochemical reactions in the cell. The normalized mass flow rate is found almost same in each cell with flow uniformity index of 0.999. The calculated voltage and power curves under different average current densities are compared with experimental results for the model validation. The changes in the voltage and power of the SOFC stack, current density, temperature, over potential and reactants distributions in relation to varying amounts of reactants flow are also examined. The current density distribution in each cell is observed to vary along the anode flow direction. The temperature difference in each cell is almost same along the flow direction of reactants, and the irreversible resistance showed an opposite trend with a temperature distribution in each cell.     

Development of a 700 W anode-supported micro-tubular SOFC stack for APU applications

A 700 W anode-supported micro-tubular solid-oxide fuel cell (SOFC) stack for use as an auxiliary power unit (APU) for an automobile is fabricated and characterized in this study. For this purpose, a single cell was initially designed via optimization of the current collecting method, the brazing method and the length of the tubular cell. Following this, a high-power single cell was fabricated that showed a cell performance of at 0.7 V and using H₂ (fuel utilization=45%) and air as fuel and oxidant gas, respectively. Additionally, a fuel manifold was designed by adopting a simulation method to supply fuel gas uniformly into a single unit cell. Finally, a 700 W anode-supported micro-tubular SOFC stack was constructed by stacking bundles of the single cells in a series of electrical connections using H₂ (fuel utilization=49%) and air as fuel and oxidant gas, respectively. The SOFC stack showed a high power density of ; moreover, due to the good thermo-mechanical properties of the micro-tubular SOFC stack, the start-up time could be reduced by 2 h, which corresponds to 6/min.     

Three-dimensional computational fluid dynamics modeling of anode-supported planar SOFC

Modeling plays a very important role in the development of fuel cells and fuel cell systems. The aim of this work is to investigate the electrochemical processes of a Solid Oxide Fuel Cell (SOFC) and to evaluate the performance of the proposed SOFC design. For this aim a three-dimensional Computational Fluid Dynamics (CFD) model has been developed for an anode-supported planar SOFC with corrugated bipolar plates serving as gas channels and current collector. The conservation of mass, momentum, energy and species is solved by using the commercial CFD code FLUENT in the developed model. The add-on FLUENT SOFC module is implemented for modeling the electrochemical reactions, loss mechanisms and related electric parameters throughout the cell. The distributions of temperature, flow velocity, pressure and gaseous (fuel and air) concentrations through the cell structure and gas channels is investigated. The relevant fuel cell variables such as the potential and current distribution over the cell and fuel utilization are calculated and studied. The modeling results indicate that, for the proposed SOFC design, reasonably uniform distributions of current density over the active cell area can be achieved. The geometry of the cathode gas channel has a substantial effect on the oxygen distribution and thus the overall cell performance. Methods for arriving at improved cell designs are discussed.     

Three-dimensional multi-physics modelling and structural optimization of SOFC large-scale stack and stack tower

Multi-physics modelling of the Solid Oxide Fuel Cell (SOFC) stack requires significant computational resources. Design optimization of large-scale stacks and stack towers has always been a challenge in recent years. This study establishes a three-dimensional multi-physics model based on a two-step coupling using the BP neural network. The comparison between the novel model and the traditional fully coupled model in both accuracy and computing resource requirements are explored. The novel method has high effectiveness for modelling the large-scale stacks. Based on this, planar SOFC 50-cell stacks and 150-cell stack towers are simulated. The results show that, the flow uniformity of fuel distribution of the stack towers can decrease more than 30% comparing with the 50-cell stack, which leads to significant deterioration of the voltage and temperature distribution. The parameters of manifold and buffer area and channel height of the stack tower is optimized to achieve better uniformity of flow and voltage distribution and lower temperature gradient simultaneously.     

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.     

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.     

Durability test and degradation behavior of a 2.5 kW SOFC stack with internal reforming of LNG

Forschungszentrum Jülich has demonstrated SOFC stacks and systems ranging from 50 W to 20 kW. Previous studies have shown the reproducible stable long-term performance of the F10-design short stacks developed in Forschungszentrum Jülich. Within this work, a 2.5 kW F20-stack consisting of eighteen cells was assembled, and tested at a furnace temperature of 700 °C mainly with the simulated reformate gas, which corresponds to 10% pre-reforming of liquefied natural gas (LNG). The current density and fuel utilization were mostly kept at 0.5 A cm⁻² and 70%, respectively. The purpose was to investigate the behavior of the stack in the kW-range for at least 5000 h with internal reforming of LNG or methane at a fuel utilization of at least 60%. A voltage degradation rate of around 0.3%/1000 h was obtained during the operation with pre-reformed LNG. The stack performance under normal working conditions and an unplanned redox cycle, as well as the results from post mortem analysis are discussed.     

Air-breathing miniature planar stack using the flexible printed circuit board as a current collector

To maximize power density, the volume of a fuel cell stack should be reduced by miniaturizing the stack components. In this study, thin flexible printed circuit board was utilized as a current collector in order to reduce an air-breathing monopolar stack's volume. Also, the effects of varying the geometry and opening ratios of the ports to the cathode on stack performance were evaluated in order to determine the optimal cathode structure. Use of the thin current collector and cathode port optimization resulted in an output of 3.5 W from an 18 cm³ stack (power density of 350 mW/cm²). The effects of orientation under passive air-breathing operation were determined to be nearly negligible. All data was measured at ambient pressure and temperature, baseline conditions for mobile fuel cell intended for use in consumer electronics.     

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.     

Numerical analysis of a planar anode-supported SOFC with composite electrodes

This paper investigates a planar anode-supported solid oxide fuel cell (SOFC) with mixed-conducting electrodes. Direct internal methane reforming in the high-temperature cell is included. The numerical model used is three-dimensional, a single computational domain comprising the fuel and air channels and the electrodes–electrolyte assembly. The oxygen ion transport through the electrolyte is mimicked with an algorithm for Fickian diffusion built into the commercial computational package Star-CD. The equations describing transport, chemical and electrochemical processes for mass, momentum, species and energy are solved using Star-CD with in-house developed subroutines. Results for temperature, chemical species and current density distribution for co- and counter-flow configurations are shown and discussed. For co-flow, a sub-cooling effect manifests itself in the methane-rich region near the fuel entrance, while for counter-flow a super-heating effect manifests itself somewhat further downstream, where all the methane is consumed. Effects of varying air inlet conditions are also investigated.     

Performance of a glass-ceramic sealant in a SOFC short stack

The development of sealants for solid oxide fuel cells (SOFCs) is a significant challenge as they must meet very restrictive requirements; they must withstand the severe environment of the SOFC (i.e., be resistant to oxidative and reducing gas environments) and be thermo-chemically and thermo-mechanically compatible with the materials to which they are in contact with. This work discusses the design and the operation of two SOFC short stacks (based on planar anode-supported cells) along with the performance of a glass ceramic sealant inside the stack.     

Effect of anode thickness and Cu content on consolidation and performance of planar copper-based anode-supported SOFC

Planar, Cu-containing Gadolinia-doped ceria anode-supported solid oxide fuel cells to be used at intermediate temperature (500–750 °C) were produced in the present work. The Intermediate temperature solid oxide fuel cells were fabricated using Li₂O as sintering aid for Gadolinia-doped ceria, varying the anode-to-electrolyte thickness ratio (r) from 2 to 10 and the CuO content in the anode from 45 vol% to 55 vol%. Co-sintering of the thermo-pressed green cells was carried out at 900 °C for 3 h. The electrolyte densification was favoured by increasing the r value, this being accounted for the enhanced compressive stresses induced by the supporting anode on the electrolyte upon sintering. Larger CuO content positively influences the overall cell performance, due to the improved electronic conductivity of the anode. Nevertheless, CuO concentration cannot exceed 50 vol% because of the tensile stresses (and corresponding flaws) generated in the electrolyte for larger amount. IT-SOFC containing 50 vol% CuO was characterized by an Open Circuit Voltage ≈0.82 V and a maximum power density of 200 mW cm^?2 at 700 °C.     

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.     

Computational model to predict thermal dynamics of planar solid oxide fuel cell stack during start-up process

Solid oxide fuel cell (SOFC) systems have been recognized as the most advanced power generation system with the highest thermal efficiency with a compatibility with wide variety of hydrocarbon fuels, synthetic gas from coal, hydrogen, etc. However, SOFC requires high temperature operation to achieve high ion conductivity of ceramic electrolyte, and thus SOFC should be heated up first before fuel is supplied into the stack. This paper presents computational model for thermal dynamics of planar SOFC stack during start-up process. SOFC stack should be heated up as quickly as possible from ambient temperature to above 700 °C, while minimizing net energy consumption and thermal gradient during the heat up process. Both cathode and anode channels divided by current-collecting ribs were modeled as one-dimensional flow channels with multiple control volumes and all the solid structures were discretized into finite volumes. Two methods for stack-heating were investigated; one is with hot air through cathode channels and the other with electric heating inside a furnace. For the simulation of stack-heating with hot air, transient continuity, flow momentum, and energy equation were applied for discretized control volumes along the flow channels, and energy equations were applied to all the solid structures with appropriate heat transfer model with surrounding solid structures and/or gas channels. All transient governing equations were solved using a time-marching technique to simulate temporal evolution of temperatures of membrane-electrode-assembly (MEA), ribs, interconnects, flow channels, and solid housing structure located inside the insulating chamber. For electrical heating, uniform heat flux was applied to the stack surface with appropriate numerical control algorithm to maintain the surface temperature to certain prescribed value. The developed computational model provides very effective simulation tool to optimize stack-heating process minimizing net heating energy and thermal gradient within the stack.     

On flow uniformity in various interconnects and its influence to cell performance of planar SOFC

This paper investigates flow uniformity in various interconnects and its influence to cell performance of a planar SOFC. A transparent hydraulic platform was used to measure flow uniformity in different rib-channel modules of interconnects. Several 3D numerical models implemented by CFD-RC packages were established to first simulate these hydraulic experiments and then used to evaluate the cell performance of a single-cell stack using different designs of interconnects with different flow uniformity over a wide range of a hydraulic Reynolds number (Re) based on a hydraulic diameter of rib-channels. Numerical flow data are found in good agreement with experimental results. It is proposed that a new design, using simple small guide vanes equally spaced around the feed header of the double-inlet/single-outlet module, can effectively improve the degree of flow uniformity in interconnects resulting in 11% increase of the peak power density (PPD) which can be further increased when applying a Ni-mesh on anode. Numerical analyses demonstrate a strong influence of Re on cell performance, of which appropriate ranges of Re in both anode and cathode sides are identified for achieving a reasonably good PPD while remaining an economic fuel utilization rate and having less temperature variations in the single-cell stack.