Thermal stress analysis of a planar SOFC stack

Typical operating temperature for a solid oxide fuel cell (SOFC) ranges from 700°C to 800°C. A large temperature gradient and thermal stress are induced by internal losses and electro-chemical reactions, resulting in significant structural damage and performance degradation of a SOFC stack, which has become a hindrance to its applications. In this study, a three-dimensional multi-physics CFD model is developed and employed to study the temperature and thermal stress distribution of a planar SOFC stack, then effects of the structure design parameters are investigated, including the flow channel arrangement (i.e., co- and cross-flow) and thickness of the electrolyte layer. The stack modeled is composed of three-unit cells, metallic interconnect layers, sealing components, and anode/cathode current collectors. The simulation results show that the temperature difference in the co-flow case is smaller and the thermal stress is lower than those predicted in the cross-flow. The overall performance of the stack improves as the thickness of the electrolyte layer decreases, but the temperature and its gradient inside the stack become higher. In addition, a large temperature gradient is observed inside the thin electrolyte layer, which leads to a significant increase of the thermal stress. The findings and the research methods in this study can be applied to design and optimize the stack structures by considering the temperature and the thermal stress distribution.

Typical operating temperature for solid oxide fuel cells (SOFC) is between 700~800°C. A large temperature gradient and thermal stress caused by internal losses and electrochemical reactions may cause SOFC stack performance degradation and even structural damage, which has become a hindrance to its applications.In this study, a three-dimensional multiphysics CFD (computational fluid dynamics) model is developed and applied for a planar SOFC stack to study the temperature and thermal stress distribution, as well as effects of structure and design parameters, including the flow channel arrangement (e.g., co- and count-flow) and thickness of the electrolyte layer. The stack is composed of three-unit cells, metallic interconnect layers, sealing and anode/cathode current collectors.The simulation results reveal that the temperature difference in the counter-flow mode is smaller and the thermal stress is lower than those in the co-flow mode. The overall performance of the stack is better when the electrolyte layer thickness becomes smaller, but the stack temperature and the temperature gradient become higher. In addition, a large temperature gradient due to the thin electrolyte layer leads to a significant increase of the thermal stress in the electrolyte. The findings and research method from this study can be applied to optimize the design of the stack structures, by consideration of the maximum thermal stress and its distribution.AcknowledgementsThis work is supported by the National Key Research and Development Project of China (2018YFB1502204), the Ningbo major special projects of the Plan “Science and Technology Innovation 2025” (2018B10048).

Due to mismatching of thermophysical properties between involved materials, a non-uniform distribution of generated thermal stress may result in a deformation and warpage in the cell sintering steps for SOFC (solid oxide fuel cell). A three-dimensional CFD (computational fluid dynamics) model is developed to study the displacement and thermal stress distribution within the SOFC sintered functional layers. It is found that the thermal stress is concentrated on the interface between the anode and the electrolyte layers; the warpage is larger during the co-sintering of anode and electrolyte layers (i.e., half-cell sintering). A parameter study is also conducted for the thickness variation of the anode, as well as for the four corners being chamfered. Considering effects of microscopic structure evolution on the cell shrinkage, a correlated method is developed to evaluate the thermal expansion coefficients varied with the sintering temperature. It is found that the difference becomes bigger in the correlated thermal expansion coefficients between the YSZ and anode layers, which leads to even larger displacement predictions. The findings and predicted results may be applied for optimization of the material designs and the sintering parameters for SOFC.

A fuel cell is an electro-chemical device capable of converting chemical energy into electricity. High operating temperature of solid oxide fuel cell (SOFC), between 700°C and 1000°C, causes thermal stress. Thermal stress causes gas leakage, structure instability and cease operation of the SOFC before its life time. The purpose of the current paper is to present a method that predicts the thermal stress distribution in an anisotropic porous cathode of planar SOFC. The coupled governing non-linear differential equations, heat transfer, fluid flow, mass transfer, mass continuity, and momentum are solved numerically. An in-house computer code based on computational fluid dynamics (CFD), computational structural mechanics and finite-element method (FEM) is developed and utilized. The code determines the temperature and stress distribution from the energy, Darcy, Navier–Stokes thermo-fluid model. The code uses the generated data inside the porous cathode in order to obtain the thermal stress distribution. The numerical results used to determine the areas of high values of stresses were higher than the yield strength of materials. The results show that the highest thermal stress occurs at the upper corners of the cathode electrode and the maximum temperature at the middle of the electrolyte-cathode boundary, where the maximum pressure concentrated at the upper and lower section of the middle part of cathode electrode.

Generally, the manufacturing technology of fuel cell units is considered to satisfy the current commercialization requirements. However, achieving a high-performance and durable stack design is still an obstacle in its commercialization. The solid oxide fuel cell (SOFC) stack is considered to have performance characteristics that are distinct from the proton exchange membrane fuel cell (PEMFC) stacks. Within the SOFC stack, vapor is produced on the anode side instead of the cathode side and high flow resistance within the fuel flow path is recommended. In this paper, a 3D multiphysics model for a one-cell SOFC stack with the interdigitated channels for fuel flow path and conventional paralleled line-type rib channels for air flow path is firstly developed to predict the multiphysics distribution details. The model consists of all the stack components and couples well the momentum, species, and energy conservation and the quasi-electrochemical equations. Through the developed model, we can get the working details within those SOFC stacks with the above interdigitated flow channel features, such as the fuel and air flow feeding qualities over the electrode surface, hydrogen and oxygen concentration distributions within the porous electrodes, temperature gradient distribution characteristics, and so on. The simulated result shows that the multiphysics field distribution characteristics within the SOFC and PEMFC stacks with interdigitated flow channels feature could be very different. The SOFC stack using the paralleled line-type rib channels for air flow path and adopting the interdigitated flow channels for the fuel flow path can be expected to have good collaborative performances in the multiphysics field. This design would have good potential application after being experimentally confirmed.

This paper reports the results from the European project PROSOFC (funded by FCH-JU, FP7). Within the project an innovative methodology for a production and reliability oriented SOFC cell and stack design is developed. In particular the PROSOFC project aims at improving the robustness, manufacturability, efficiency and cost of SOLIDpowers state-of-the-art SOFC stacks so as to reach market entry requirements. The key issues are the mechanical robustness of solid oxide fuel cells (SOFCs), and the delicate interplay between cell properties, stack design, and operating conditions of the SOFC stack. The novelty of the project lies in combining state of the art methodologies for cost-optimal reliability-based design (COPRD) with actual production optimization. To achieve the COPRD beyond state of the art multi-physical modeling concepts were developed and validated for significantly improved understanding of the production and operation of SOFC stacks. The most critical failure modes for stack operation were identified in order to align the experimental investigations to generate suitable data for modelling these failures. The multi-physics model allows a probabilistic approach to consider statistical variations in production, material and operating parameters for the optimization phase. The project provides a methodology for 3D description of spatial distribution of material properties based on a random field models. The key for the whole methodology are validating experiments, homogenized models on multiple levels of the SOFC system (cell, interconnect, sealings) and introduction of extensive test programs specified by the COPRD methodology. The probabilistic models were related to the experimentally obtained properties of base materials to establish a statistical relationship between the material properties and the most relevant load effects in view of potential damage/failure based on multi-physics simulation can be established. Software algorithms for meta models that allow the detection of relationships between input parameters (materials, loading, etc.) and output parameters and to perform a sensitivity analysis were developed and implemented. The capabilities of the methodology for COPRD being developed is illustrated on two practical cases. A procedure based on meta models has been developed to estimate elastic, primary and secondary creep model parameters from 4-point bending tests. The goal is to (i) account for the effects of the friction between the sample and the rollers, anticlastic curvature, contact point shift and large deflection, which can affect the accuracy of the measurements, and (ii) measure properties which cannot be obtained using closed-form analytical solutions. This could be achieved by model-based parameter estimation with a 3-D continuum finite-element (FE) model, at the cost of very high running time. The proposed approach is computationally much more efficient. It starts with a sensitivity analysis to generate distributed meta models of the displacement at the inner rollers during loading-unloading cycles and creep measurements simulated by the 3-D FE model. The optimization problem for parameter estimation is then solved using the meta models. The accuracy of the approach was tested using a set of numerical experiments and comparison with results from 3-D imaging and computational homogenization. The experiments on Ni-YSZ samples were then analyzed. For the stochastic investigation of the thermo-electrochemical behavior of the stack a multi-physics stack model implemented in gPROMS and Fluent was linked and controlled automatically by optiSlang to perform a sensitivity analysis. The outcome is (i) the identification of the most relevant production and operating parameters which can have a significant impact on the stack lifetime and (ii) meta models of the efficiency and of the 3-D temperature distribution generated in the view of optimization. The tests show for instance that the accuracy of the 3-D meta model of the temperature distribution is sufficient to identify the minimum of variations in the spatial distribution of the temperature during cycling between full and part load by using sets of operating conditions for optimization.

Solid oxide fuel cell (SOFC) stacks were operating with metallic interconnects that separate each cells. Metallic interconnects play an important role in gas flow system and heat transfer mechanism, because its geometry makes gas flow channel and it has a high thermal conductivity. Many researcher design the flow channel for optimizing the cell performance like a ratio of height and width, channel to channel distance, or new type channels. For high conversion efficiency, most solid oxide fuel cell in power generation application operate at high fuel utilization and low current condition. However, high fuel utilization condition makes a large gradient of chemical potential by fuel depletion and it induces a low cell performance and a large chemical stress in flow direction. This phenomena can be observed at high performance cell or high operating temperature condition, because almost fuel is consumed at upstream of fuel channel by high electrochemical reaction kinetics and most cell area has a low chemical potential environment. Therefore, even distribution of electrochemical reaction rate is important. In this study we reduce the gradient of chemical potential by using diffuser-shape fuel channel, and optimize the diffuser-shape by design study. In chemical species conservation law, higher flow velocity at upstream makes higher convective flux in flow direction compared to diffusive flux in cell-thickness direction, and it can reduce the electrochemical reaction rate at reacting electrode. Optimized diffuser-shape fuel flow channel from this study may enhance the performance and the durability of solid oxide fuel cell stacks.

Parametric exergy analysis of a tubular Solid Oxide Fuel Cell (SOFC) stack through finite-volume model

In this paper the operation and performance of a high temperature solid oxide fuel cell (SOFC) stack on biomass syn-gas from a demonstration biomass gasification combined heat and power (CHP) plant is investigated. The objective of this work is to develop a computer simulation model of a biomass-SOFC CHP system, flexible enough for use in industry, capable of predicting system performance under various operating conditions and using diverse fuels. The biomass gasifier is of the dual fluidised bed (DFB) type with steam as the gasifying agent and is operated at atmospheric pressure. The tubular SOFC configuration, developed by Siemens Power Generation Inc (SPGI), is selected. It is considered to be the most advanced design and is approaching commercialisation. The SOFC stack model, developed using the chemical process flowsheet simulator Aspen Plus, is of equilibrium type and is based on Gibbs free energy minimisation. The SOFC model performs heat and mass balances and considers the ohmic, activation and concentration losses for the voltage calculation. Data available in the literature on the SPGI SOFC operating on natural gas is used to validate the model. The system model predicts thermodynamic condition and composition of all internal flow streams, the heat generated by the SOFC stack, voltage (V), current (I) and efficiency. Operating parameters are varied over a wide range, parameters such as fuel utilisation factor (Uf), current density (j) and steam to carbon ratio (STCR) have significant influence. The results indicate that there must be a trade-off between voltage, efficiency and power with respect to j and the SOFC stack should be operated at low STCR and high Uf, within certain limits. SOFC stack operation on biomass syn-gas is compared to operation on natural gas and as expected there is a drop in performance, which is attributed to increased input fuel and air flow due to the lower quality of the fuel gas. The optimum realistic operating conditions with regard to SOFC stack performance are identified. High electrical efficiencies are predicted making these systems very attractive for CHP applications.

Recent developments in control and integration of solid oxide fuel cells: From stack to system

The Solid oxide fuel cell (SOFC) is an electrochemical energy-conversion device which offers tremendous promise for delivering high electrical efficiency and significant environmental benefits in terms of fuel flexibility, as well as clean and efficient electric power generation. However, the state-of-the-art SOFC cell currently involves expensive and time-consuming multi-step manufacturing processes including tape casting, screen printing, shaping, lamination, sintering, etc. In addition, SOFC stacks are usually assembled with pre-fabricated cells, metal interconnects, and glass-ceramic sealing. These indispensable components add extra layers of complexity to the stack structure’s fabrication and maintenance, significantly increasing the size and weight of the final product. These intrinsic limitations on the current planar stack cannot be easily removed by traditional manufacturing processes. However, as additive manufacturing (AM) technologies start to mature and show increasing market penetration, it lends itself admirably to breaking the limits on high-power-density SOFC stack manufacturing. Storagenergy’s SOFC project is developing an all-ceramic AM-SOFC by a high-speed AM process of multiple materials. The developed technology allows the fabrication of robust and compact AM-SOFC stacks with unique features such as monolithic architecture with embedded novel micro flow channels and thinner elements (anode, cathode, electrolyte, and interconnect) by only three production steps (3D printing, sintering, and catalyst infiltration) without the need for subsequent assembly of individual layers and indispensable components. This simplification of the fabrication process is expected to reduce the cost of the SOFC and increase SOFC design flexibility and manufacturing reliability.

This study presents a comparative evaluation of Molten Carbonate Fuel Cell (MCFC) and Solid Oxide Fuel cell (SOFC) stacks coupled with a micro gas turbine (MGT). For the analysis, it is assumed that the fuel supply to the stacks is constant in all the analyzed conditions. The components of the system have been sized using the first law of thermodynamics to meet the thermal conditions required to maintain fuel cell stack operation, while an exergetic analysis has been implemented in order to assess the components in terms of irreversibilities. Furthermore, an economic analysis to estimate the Levelized Cost of Electricity (LCOE) has been carried out to indicate the most feasible option between the two analyzed systems. The capacity of the fuel cell stacks is 500kWdc operating at 350 kPa and 600 °C/650 °C. The results indicate that MCFC stacks are more efficient than SOFC stacks, but are considerably more expensive. Nevertheless, the SOFC/MGT system has a global efficiency higher than that of the MCFC/MGT; also its Total Capital Investment (TCI) is 2.5–3.5 times lower, thus making the SOFC/MGT coupling more attractive. The only product considered coming out from the systems to determine the LCOE is electricity. The LCOE for the SOFC/MGT system is 0.339–0.402$/kWh and for the MCFC/MGT is 0.875–0.897$/kWh, which for both configurations is still higher than the current electricity prices. One aspect that increases the investment and consequently the LCOE is the high cost of the stacks and their replacements which is around 19 % and 10 % of the total Purchased Equipment Cost (PEC) for MCFC and SOFC stacks, respectively.

Feasibility study on saturated water cooled solid oxide fuel cell stack

The paper presents the scheme of mini CHP with methane reformer and planar solid oxide fuel cells (SOFC) stack. The mini CHP produces electricity, superheated steam, hot air and methane for the reformer and it also preheats cathode air used in the SOFC stack as an oxidant. Moreover, the scheme’s mathematical model is constructed. The thermochemical reactor with impeded fluidized bed for autothermal steam reforming of methane (reformer) studied experimentally is the key element in producing synthesis gas – fuel for the SOFC stack. The research indicates that synthesis gas containing 55% of hydrogen can be derived using the reactor. Through mathematical modeling, the entire reactor’s principal dimensions as well as flow rates of air, water and methane were adjusted to the methane reforming for the mini CHP studied. The paper includes the heat balances of the reformer, SOFC stack and waste heat boiler that produces the superheated steam, hot air and methane for the reformer as well as preheated cathode air. These balances were instrumental for calculating the useful product fraction in the reformer, fraction of hydrogen oxidized in the SOFC anode channel, electric gross efficiency, anode temperature, exothermic effect of synthesis gas hydrogen oxidation by air oxygen, excess entropy and Gibbs free energy change at standard conditions, SOFC electromotive force (EMF), specific flow rate of standard fuel for heat, and power generation. The simulation study has shown that the hydrogen oxidation products temperature in the SOFC anode channel is 850ºС, electric gross efficiency 61.0%, single fuel cell EMF 0.985 V, fraction of hydrogen oxidized in the SOFC anode channel 64.6%, specific flow rate of standard fuel for power generation 0.16 kg/(kW·h), for heat generation 44.7 kg/GJ. All the specific parameters are in good agreement with other publications results.

Ztek`s Planar Solid Oxide Fuel Cell (SOFC) system has exceptional potential for utility electric power generation because of: simplicity of components construction, capability for low cost manufacturing, efficient recovery of very high quality by-product heat (up to 1000{degrees}C), and system integration simplicity. Utility applications of the Solid Oxide Fuel Cell are varied and include distributed generation units (sub-MW to 30MW capacity), repowering existing power plants (i.e. 30MW to 100MW), and multi-megawatt central power plants. A TVA/EPRI collaboration program involved functional testing of the advanced solid oxide fuel cell stacks and design scale-up for distributed power generation applications. The emphasis is on the engineering design of the utility modules which will be the building blocks for up to megawatt scale power plants. The program has two distinctive subprograms: Verification test on a 1 kW stack and 25kW module for utility demonstration. A 1 kW Planar SOFC stack was successfully operated for 15,000 hours as of December, 1995. Ztek began work on a 25kW SOFC Power System for TVA, which plans to install the 25kW SOFC at a host site for demonstration in 1997. The 25kW module is Ztek`s intended building block for the commercial use of the Planar SOFC. Systems of up to megawatt capacity can be obtained by packaging the modules in 2-dimensional or 3-dimensional arrays.