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.     

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.     

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.     

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.     

Control of a solid oxide fuel cell stack based on unmodeled dynamic compensations

To guarantee solid oxide fuel cell (SOFC) safe operation, plenty control strategies have been developed to control stack temperature and voltage within a reasonable range. However, these control approaches ignore unmodeled dynamics of the SOFC system, which may lead to unsatisfactory control results, sometimes even make the system unstable. To overcome this challenge, a unique control strategy which considers unmodeled dynamic compensations of the SOFC system is proposed in this paper. A model of the SOFC system is firstly built, which includes a known linear model and an unmodeled nonlinear dynamic estimation. A nonlinear controller based on the unmodeled dynamic compensation is then developed to force the SOFC to track desired stack temperature and voltage. To evaluate the control performance, the proposed control method is compared with a traditional sliding mode controller. The simulation results show if the unmodeled dynamics have a small effect on the SOFC, both the sliding mode controller and the proposed controller can achieve a precise tracking. If the unmodeled dynamics have a great impact on the SOFC, the temperature and voltage can be well controlled with the proposed control strategy. However, in the sliding mode controller, the temperature and voltage trajectories deviate largely from the reference values.     

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.     

Thermal management oriented steady state analysis and optimization of a kW scale solid oxide fuel cell stand-alone system for maximum system efficiency

This research attempts to ensure system safety while to maximize system efficiency by addressing steady state analysis and optimization for solid oxide fuel cell (SOFC) systems. Firstly, a thermal management oriented kW scale SOFC stand-alone system (primarily comprising a planar SOFC stack, a burner, and two heat exchangers) is developed, in which a special consideration for stack spatial temperature management is conducted by introducing an air bypass manifold around heat exchangers. The dynamic model of the system is performed using transient energy, species, and mass conservation equations. Secondly, based on the system model, the effects of operating parameters including fuel utilization (FU), air excess ratio (AE), bypass ratio (BR), and stack voltage (SV) on the system steady-state performances (e.g. system efficiency, stack inlet, stack outlet, and burner temperatures) are revealed. Particularly, an optimal relationship between the system efficiency and the operating parameters is proposed; the maximum system efficiency can certainly be obtained at the inlet outlet temperature critical point of the BR-AE or FU-AE planes for all SV operating points. Finally, according to the optimal relationship, a traverse optimization process is designed, and the maximum system efficiency and safe operating parameters at any efficient SV operating point are calculated. The results provide an optimal reference trajectory for control design, where the system is safe and efficiency optimization. Moreover, the results reveal two important system characteristics: (1) the burner operates within safe temperature zone as long as the temperature of the upstream stack is well controlled; (2) the control design for the system is a nonlinear optimal control with switching structure, which is a challenging control issue.     

Three dimensional CFD modeling and experimental validation of an electrolyte supported solid oxide fuel cell fed with methane-free biogas

In the present study a comprehensive numerical model of a planar cross-flow electrolyte-supported solid oxide fuel cell (SOFC) is reported. This model is solved in a 3D environment using COMSOL Multiphysics software. To verify the simulation results, an experimental set-up of a six-cell stack was built. Cell temperature and current–voltage measurements are used for validation of the simulation results. Good agreement between the simulation results and the experimental measurements is achieved. Temperature validation in addition to the popular current/voltage validation ensures that the model performs well in predicting local processes like chemical reactions. In this study methane-free biogas (CO₂ + H₂) is fed to the SOFC, and the performance of the system is investigated and explained. It is concluded that the methane-free biogas reduces the cooling air flow due to endothermic reverse water gas shift reaction and gives better current density distribution over the cell compared to hydrogen.     

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.     

3D multiphysics modeling aided APU development for vehicle applications: A thermo-structural investigation

Solid oxide fuel cells (SOFC) are suitable for on-board electricity generation as Auxiliary Power Unit (APU) to support the electric power supply in heavy-duty vehicles. In order to satisfy the requirements of a lightweight fuel cell stack for mobile applications, thin-walled components must be used for the stack structure. This necessity is associated with material, process and design difficulties that must be solved in order to achieve a successful utilization. In this work a novel lightweight SOFC stack design with metal-supported cell was studied both numerically and experimentally. The metallic components are made from the Intermediate Temperature Metal (ITM), a high performance, high chromium ferritic stainless steels alloy. The multiphysics modeling approach (fluid dynamics, heat transfer, structural mechanics) was utilized in this work to predict the temperature distribution and the thermo-structural behavior of the new developed design. Geometric details of the fuel cell stack components as well as appropriate nonlinear, temperature and time-dependent constitutive models were developed to describe the material behavior. Experimental data were used to determine the material model parameters and validated the simulation results. The three-dimensional stress and deformation distributions in the individual stack components were evaluated and their maximum values for elements at risk were identified. Thus, the developed model enables the investigation of sustainability and serviceability of the structural elements to ensure a reliable operation of the stack. The developed computational model can be used as a design tool for parametric studies and optimization analysis to investigate the effects of process boundary conditions, material properties as well as geometrical design parameters and their variation on the induced thermal stresses.     

Influence of hydrogen fuel cell temperature safety on bus driving characteristics and stack heating mode

Hydrogen fuel cells have developed rapidly in bus because of their cleanliness. The driving parameters of hydrogen fuel cell bus and the internal temperature distribution of hydrogen fuel stack are investigated in this study. The 1-D model of hydrogen fuel cell bus and the 2-D model of hydrogen fuel cell stack are established based on AMESim. In the cooling process, for the existing typical thermal management system, the influence of ambient temperature on the fuel cell bus driving parameters is analyzed by the 1-D model. In the heating process, the internal temperature distribution of the stack is analyzed under three heating modes by the 2-D model. As the ambient temperature increases, to ensure the safe operating temperature of the fuel cells, the bus top speed should be reduced, and the acceleration time should be extended. When the stack needs to be heated, the gas-liquid heating mode can supply a more uniform temperature distribution inside the stack.     

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

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

A mathematical model of a tubular solid oxide fuel cell with specified combustion zone

A numerical model has been developed to simulate the effect of combustion zone geometry on the steady state and transient performance of a tubular solid oxide fuel cell (SOFC). The model consists of an electrochemical submodel and a thermal submodel. In the electrochemical model, a network circuit of a tubular SOFC was adopted to model the dynamics of Nernst potential, ohmic polarization, activation polarization, and concentration polarization. The thermal submodel simulated heat transfers by conduction, convention, and radiation between the cell and the air feed tube. The developed model was applied to simulate the performance of a tubular solid oxide fuel cell at various operating parameters, including distributions of circuits, temperature, and gas concentrations inside the fuel cell. The simulations predicted that increasing the length of the combustion zone would lead to an increase of the overall cell tube temperature and a shorter response time for transient performance. Enlarging the combustion zone, however, makes only a negligible contribution to electricity output properties, such as output voltage and power. These numerical results show that the developed model can reasonably simulate the performance properties of a tubular SOFC and is applicable to cell stack design.     

Response of a planar solid oxide fuel cell to step load and inlet flow temperature changes

To explore the dynamic characteristics of the SOFC systems and to develop relevant control strategies, a previously developed steady state SOFC model is converted to a dynamic model. The model includes mass, momentum, thermal and electrochemical analysis, as well as the kinetic model of hydrocarbon reactions. Applying two control strategies i.e., cell constant fuel flow rate and constant fuel utilization during the transient time, the model is implemented to analyse the dynamic behaviour of a planar direct internal reforming (DIR) SOFC cell under several step-load changes. Transient response, resulting from an inlet temperature variation, is also investigated. The results show that the relaxation time is strongly related to the thermal behaviour of the cell and the applied control strategy. However, it is almost independent of the load variation magnitude.     

Estimation of heat generation rate in solid oxide fuel cell module from single cell performance and module performance based on impedance analysis

Heat generation rate in SOFC module was estimated under various thermal self-sustained conditions. SOFC module and system was designed to evaluate power generation property and temperature of module. Single cell was also evaluated the performance and electrode overpotential by impedance analysis under the similar condition to module power generation state. We estimated the heat generation rate with enthalpy calculation based on the actual module performance, and also with entropy calculation based on the impedance analysis of single cell. It was found that the heat generation rate calculated by enthalpy is approximately corresponded with that calculated by entropy. There still contains small error between heat generation rate calculated by enthalpy and that calculated by entropy. It was considered that these errors are originated from distribution in stack temperature and reforming gas temperature in the module. According to impedance analysis, it was found that the ohmic resistance is varied under operating condition and related with the current distribution which is calculated with the current path length in the cell. It was suggested that power generation state of module is affected by the current path length in the cell (in another word, distribution of power density) and distribution of overpotential; these phenomena is dominated by gas composition and thermal self-sustainable temperature.     

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 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.     

Machine learning based soft sensor and long-term calibration scheme: A solid oxide fuel cell system case

To quickly and accurately obtain the multi-dimensional state in a sealing reactor is critical for the safety and high performance of industrial system. In this work, a generic machine learning based multi-dimensional soft sensor and a long-term calibration scheme is proposed by using the case of steam reforming solid oxide fuel cell (SR-SOFC) system. Firstly, based on a validated SR-SOFC system model, the temporal-spatial temperature distribution (TSTD) characteristics are analyzed and a TSTD characteristic model is constructed by Multivariable Linear Regression. Then, the central node temperature of the stack is estimated by applying the Least Square Support Vector Machine and the SR-SOFC stack temperature distribution is accurately obtained by explaining the TSTD characteristics model with the central node temperature. In addition, the temperature distribution is calibrated by Stochastic Gradient Descent algorithm to eliminate the estimation error resulting from stack degradation in a long term. The simulation results show that the proposed method can obtain the SR-SOFC stack temperature distribution in time and effectively, the average error is less than 1 K. The proposed estimation strategy can be easily expanded to other scenarios with similar operation conditions.     

Cold start dynamics and temperature sliding observer design of an automotive SOFC APU

This paper presents a dynamic model for studying the cold start dynamics and observer design of an auxiliary power unit (APU) for automotive applications. The APU is embedded with a solid oxide fuel cell (SOFC) stack which is a quiet and pollutant-free electric generator; however, it suffers from slow start problem from ambient conditions. The SOFC APU system equips with an after-burner to accelerate the start-up transient in this research. The combustion chamber burns the residual fuel (and air) left from the SOFC to raise the exhaust temperature to preheat the SOFC stack through an energy recovery unit. Since thermal effect is the dominant factor that influences the SOFC transient and steady performance, a nonlinear real-time sliding observer for stack temperature was implemented into the system dynamics to monitor the temperature variation for future controller design. The simulation results show that a 100 W APU system in this research takes about 2 min (in theory) for start-up without considering the thermal limitation of the cell fracture.