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.     

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.     

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.     

One-dimensional thermal model for direct methanol fuel cell stacks: Part I. Model development

A thermal energy model for the direct methanol fuel cell (DMFC) is presented, based on the differential thermal energy conservation equation. The model is used to predict the thermal behaviour of a DMFC stack comprising of many large cells in a bipolar arrangement. The model allows an assessment of the effect of operating parameters (feed and oxidant inlet temperature, flow rate and pressure, operating current density), and the system design (active area, material properties and geometry) on the temperature profile along the stack and the interactions between the various components in the cell stack. The model is designed to enable the fuel cell system designer to estimate, insulation requirements, auxiliary equipment sizing and required thermal duties and response. Furthermore, the model can be used to decide on the optimum set of operating conditions for an efficient thermal management of the whole process.     

3D transient multiphysics modelling of a complete high temperature fuel cell system using coupled CFD and FEM

Full commercialisation of the solid oxide fuel cell (SOFC) technology faces many technological challenges that prevent the incorporation of the technology into the global energy sector. The effort to increase the transient thermomechanical reliability of the interacting fuel cell components and the associated fuel cell system requires a comprehensive understanding of the complex multiphysics, occurring within the system. State of the art dynamic fuel cell system modelling comprises sub-models of the assembly, or is based on empirical nature. The present study introduces a transient, coupled 3D computational fluid dynamics/computational solid mechanics model of a complete solid oxide fuel cell system and its experimental validation. The model includes all system components; namely the fuel cell stack, afterburner, pre-reformer, air pre-heater and the auxiliary components. All components are presented in their real geometrical resolution. The capabilities of the 3D system level model are demonstrated by simulating the heating-up process and the critical system locations susceptible to thermomechanically induced stress, over time.     

Performance and water transport behaviour in Polymer Electrolyte Membrane fuel cells

Water management in fuel cells is important for avoiding the phenomenon of flooding or dehydration in the stack and for maintaining good fuel cell performance and durability. This study focuses on the evaluation of the dynamic performance and behaviour (purge cycle) of the commercial Polymer Electrolyte Membrane (PEM) fuel cell stack towards water transport (water balance) at different operating conditions. The stack was operated at different current loads (0–10 A) and operating temperature (ambient to 50 °C). The results indicated that the measured water accumulation in the stack increased with the increase in current load. The optimal current load was 4 A, with calculated efficiency of 62.8%. The optimal operating temperature was 40 °C, resulting in calculated efficiency of 52.3%. At higher temperature, the fuel cell performance decreased, and the measured water balance was not properly distributed, which could be due to the dehydration and low conductivity of the electrolyte membrane. It can be concluded that the behaviour and performance of the stack, as well as the water balance in the stack, were influenced by the operating conditions. Moreover, this study improves the understanding of fuel cell performance and behaviour based on evaluation of the water balance.     

Modeling and simulation of a PEM fuel cell stack considering temperature effects

Management of the water and heat ejected as byproducts in an operating PEM fuel cell stack are crucial factors in their optimal design and safe operations. Models currently available for a PEM fuel cell are based on either empirical or 3-D computational fluid dynamics (CFD). Both models do not fully meet the need to represent physical behavior of a stack because of either their simplicity or complexity. We propose a highly dynamic PEM fuel cell stack model, taking into account the most influential property of temperature affecting performance and dynamics. Simulations have been conducted to analyze start-up behaviors and the performance of the stack in conjunction with the cells. Our analyses demonstrate static and dynamic behaviors of a stack. Major results presented are as follows: (1) operating dependent temperature gradient across through-plane direction of the fuel cell stack, (2) endplate effects on the temperature profile during start-up process, (3) temperature profile influences on the output voltage of individual cells and the stack, (4) temperature influence on the water content in membranes of different cells, and (5) cathode inlet relative humidity influence on the temperature profile of the stack.     

Polymer electrolyte fuel cell stack thermal model to evaluate sub-freezing startup

For passenger fuel cell vehicles (FCVs), customers will expect to start the vehicle and drive almost immediately, implying a very short system warmup to full power. While hybridization strategies may fulfill this expectation, the extent of hybridization will be dictated by the time required for the fuel cell system to reach normal operating temperatures. Quick-starting fuel cell systems are impeded by two problems: (1) the freezing of residual water or water generated by starting the stack at below freezing temperatures and (2) temperature-dependent fuel cell performance, improving as the temperature reaches the normal range. Cold start models exist in the literature; however, there does not appear to be a model that fully captures the thermal characteristics of the stack during sub-freezing startup conditions. Existing models lack the following features: (1) modeling of stack internal heating methods (other than stack reactions) and their impact on the stack temperature distribution and (2) modeling of endplate thermal mass effect on end cells and its impact on the stack temperature distribution.The focus of this research is the development and use of a sub-freezing thermal model for a polymer electrolyte fuel cell stack. Specifically, the work has focused on the generation of a model in which the fuel cell is separated into layers to determine an accurate temperature distribution within the stack. Unlike a lumped model, which may use a single temperature as an indicator of the stack's thermal condition, a layered model can reveal the effect of the endplate thermal mass on the end cells, and accommodate the evaluation of internal heating methods that may mitigate this effect.     

Numerical thermomechanical modelling of solid oxide fuel cells

Over the last decade, many computational models have been presented to describe the complex thermomechanical behaviour of solid oxide fuel cells. The present study elucidates a detailed literature review of the proposed numerical models, ranging from a single channel or unit layer, up to coupled 3D high-end system models. Thermomechanical modelling foundations, including material properties and thermomechanical stress sources in SOFCs are emphasized. Employed material models for SOFC components are highlighted. Thermomechanical modelling issues such as geometrical idealisation, initial and boundary conditions for the highly coupled fluid and solid mechanics problem, as well as numerical solutions have been discussed. Thermomechanical stress–strain formulation of the common fuel cell components is highlighted. Finally, an overview of the numerically solved thermomechanical modelling studies in solid oxide fuel cells is given. Case studies are used throughout this review to exemplify and shed light on several modelling aspects.     

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.     

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.     

Study of geometric stability and structural integrity of self-healing glass seal system used in solid oxide fuel cells

A self-healing glass seal has the potential to restore its mechanical properties upon being reheated to the solid oxide fuel cell (SOFC) stack operating temperature. Such a self-healing feature is desirable for achieving high seal reliability during thermal cycling. Self-healing glass is also characterized by its low mechanical stiffness and high creep rate at SOFC operating temperatures. Therefore, the geometric stability and structural integrity of the glass seal system are critical to its successful application in SOFCs. This paper describes studies of the geometric stability and structural integrity of the self-healing glass seal system and the influence of various interfacial conditions during the operating and cooling-down processes using finite element analyses. For this purpose, the test cell used in the leakage tests for compliant glass seals, conducted at Pacific Northwest National Laboratory (PNNL), was taken as the initial modeling geometry. The effect of the ceramic stopper on the geometric stability of the self-healing glass sealants was studied first. Two interfacial conditions of the ceramic stopper and glass seals, i.e., bonded (strong) or unbonded (weak), were considered. Then the influences of interfacial strengths at various interfaces, i.e., stopper/glass, stopper/PEN, as well as stopper/IC plate, on the geometric stability and reliability of glass during the operating and cooling processes were examined.     

Dynamic response and long-term stability of a small direct methanol fuel cell stack

This study examines the operating characteristics and durability of a small direct methanol fuel cell (DMFC) stack (volume: 39.6 cm³). To investigate the operating characteristics in a real multi-user operating mode, various load cycles (such as gradual acceleration and deceleration), two operating modes (current mode or voltage mode) and four interrupted operating methods (load on-off, load-methanol on-off, load-air on-off, and load-methanol-air on-off) are used. The durability of the DMFC stack is examined at a constant voltage of 2.4 V (0.4 V per cell) by using the load-methanol-air on-off mode for more than 2000 h. In these tests, the DMFC stack exhibits a rapid, stable and dynamic response regardless of the load cycle and operating mode, though the stack performance and response behaviour vary with the interrupted operating modes. Among the operating modes, the air-interruption modes exhibit better stability and higher performance. Moreover, the load-methanol-air on-off mode provides the stack with good durability and a high performance in a long-term test of 2045 h.     

Flow rate and humidification effects on a PEM fuel cell performance and operation

A new algorithm is presented to integrate component balances along polymer electrolyte membrane fuel cell (PEMFC) channels to obtain three-dimensional results from a detailed two-dimensional finite element model. The analysis studies the cell performance at various hydrogen flow rates, air flow rates and humidification levels. This analysis shows that hydrogen and air flow rates and their relative humidity are critical to current density, membrane dry-out, and electrode flooding. Uniform current densities along the channels are known to be critical for thermal management and fuel cell life. This approach, of integrating a detailed two-dimensional across-the-channel model, is a promising method for fuel cell design due to its low computational cost compared to three-dimensional computational fluid dynamics models, its applicability to a wide range of fuel cell designs, and its ease of extending to fuel cell stack models.     

Dynamic fuel cell stack model for real-time simulation based on system identification

The authors have been developing an empirical mathematical model to predict the dynamic behaviour of a polymer electrolyte membrane fuel cell (PEMFC) stack. Today there is a great number of models, describing steady-state behaviour of fuel cells by estimating the equilibrium voltage for a certain set of operating parameters, but models capable of predicting the transient process between two steady-state points are rare. However, in automotive applications round about 80% of operating situations are dynamic. To improve the reliability of fuel cell systems by model-based control for real-time simulation dynamic fuel cell stack model is needed. Physical motivated models, described by differential equations, usually are complex and need a lot of computing time. To meet the real-time capability the focus is set on empirical models. Fuel cells are highly nonlinear systems, so often used auto-regressive (AR), output-error (OE) or Box-Jenkins (BJ) models do not accomplish satisfying accuracy. Best results are achieved by splitting the behaviour into a nonlinear static and a linear dynamic subsystem, a so-called Uryson-Model. For system identification and model validation load steps with different amplitudes are applied to the fuel cell stack at various operation points and the voltage response is recorded. The presented model is implemented in MATLAB environment and has a computing time of less than 1 ms per step on a standard desktop computer with a 2.8 MHz CPU and 504 MB RAM. Lab tests are carried out at DaimlerChrysler R&D Centre with DaimlerChrysler PEMFC hardware and a good agreement is found between model simulations and lab tests.     

Proton exchange membrane fuel cell multi-physical dynamics and stack spatial non-homogeneity analyses

This paper presents a multi-physical dynamic fuel cell stack model. This model covers three major physical domains: electrical, fluidic and thermal. The dynamic model in each domain is presented. The fuel cell stack model is obtained by stacking method from a generalized single cell model, thus the spatial effect through the stack can be modelled and observed. The stack model is validated temporally and spatially against a Ballard NEXA 1.2 kW 47 cells fuel cell stack. Then, the dynamic behaviour in each physical domain is analysed. It can be approximated by a first order system, thus the expressions of time constants in different domain are obtained. Finally, the fuel cell stack spatial non-homogeneity is analysed. From the results, a fuel cell stack model reduction method is proposed in order to reduce the computation time during simulations. The reduced fuel cell stack model is validated against the full model.     

Performance optimization of polymer electrolyte membrane fuel cells using the Nelder-Mead algorithm

The direct-search simplex method for function optimization has been adapted to performance optimization of polymer electrolyte membrane fuel cells (PEMFCs). The established method is strongly application oriented and uses only experimentally determined data for optimization. It is not restricted to discrete parameters optimums and does not require the use of third-party software or computational resources. Hence, it is easy to implement in fuel cell testing stations. The optimization consists of finding, for a given fuel cell load, an optimum set of values of the 7 fuel cell operating parameters: the fuel cell temperature, the reactants' stoichiometric ratios, the reactants' inlet relative humidity, and the reactants' outlet pressures, resulting in the highest fuel cell performance. The performance is measured using a scalar function of the operating parameters and the load and can be defined according to needs.Two PEMFC performance functions: the fuel cell voltage and the system-related fuel cell efficiency were optimized using the procedure for practically sized PEMFC stacks of two designs. With respect to the nominal operating conditions defined as optimal for each stack design by its manufacturer, the gains from the optimization procedure were up to over 12% and up to over 7% for the stack voltage and efficiency, respectively. The validation of the procedure involved 5 stack specimens and four laboratories and consistent results were obtained.     

Modelling of polymer electrolyte membrane fuel cell stacks based on a hydraulic network approach

Polymer electrolyte membrane (PEM) fuel cells convert the chemical energy of hydrogen and oxygen directly into electrical energy. Waste heat and water are the reaction by‐products, making PEM fuel cells a promising zero‐emission power source for transportation and stationary co‐generation applications. In this study, a mathematical model of a PEM fuel cell stack is formulated. The distributions of the pressure and mass flow rate for the fuel and oxidant streams in the stack are determined with a hydraulic network analysis. Using these distributions as operating conditions, the performance of each cell in the stack is determined with a mathematical, single cell model that has been developed previously. The stack model has been applied to PEM fuel cell stacks with two common stack configurations: the U and Z stack design. The former is designed such that the reactant streams enter and exit the stack on the same end, while the latter has reactant streams entering and exiting on opposite ends. The stack analysed consists of 50 individual active cells with fully humidified H₂ or reformate as fuel and humidified O₂ or air as the oxidant. It is found that the average voltage of the cells in the stack is lower than the voltage of the cell operating individually, and this difference in the cell performance is significantly larger for reformate/air reactants when compared to the H₂/O₂ reactants. It is observed that the performance degradation for cells operating within a stack results from the unequal distribution of reactant mass flow among the cells in the stack. It is shown that strategies for performance improvement rely on obtaining a uniform reactant distribution within the stack, and include increasing stack manifold size, decreasing the number of gas flow channels per bipolar plate, and judicially varying the resistance to mass flow in the gas flow channels from cell to cell. Copyright © 2004 John Wiley & Sons, Ltd.