平板式直接内重整固体氧化物燃料电池的一维动态建模与仿真

This article aims to investigate the transient behavior of a planar direct internal reforming solid oxide fuel cell (DIR-SOFC) comprehensively. A one-dimensional dynamic model of a planar DIR-SOFC is first developed based on mass and energy balances, and electrochemical principles. Further, a solution strategy is presented to solve the model, and the International Energy Agency (IEA) benchmark test is used to validate the model. Then, through model-based simulations, the steady-state performance of a co-flow planar DIR-SOFC under specified initial operating conditions and its dynamic response to introduced operating parameter disturbances are studied. The dynamic responses of important SOFC variables, such as cell temperature, current density, and cell voltage are all investigated when the SOFC is subjected to the step-changes in various operating parameters including both the load current and the inlet fuel and air flow rates. The results indicate that the rapid dynamics of the current density and the cell voltage are mainly influenced by the gas composition, particularly the H2 molar fraction in anode gas channels, while their slow dynamics are both dominated by the SOLID (including the PEN and interconnects) tem-perature. As the load current increases, the SOLID temperature and the maximum SOLID temperature gradient both increase, and thereby, the cell breakdown is apt to occur because of excessive thermal stresses. Changing the inlet fuel flow rate might lead to the change in the anode gas composition and the consequent change in the current den-sity distribution and cell voltage. The inlet air flow rate has a great impact on the cell temperature distribution along the cell, and thus, is a suitable manipulated variable to control the cell temperature.     

Dynamic modeling of a finite volume of solid oxide fuel cell: The effect of transport dynamics

A dynamic model for a finite volume of cell based on physical principles is built in the form of a nonlinear state-space model to investigate dynamic behaviors of tubular solid oxide fuel cell (SOFC) and develop a control relevant model for further control studies. Dynamic effects induced by diffusions, intrinsic impedance, fluid dynamics, heat exchange and direct internal reforming/shifting (DIR) reactions are all considered. Cell temperature, ingredient mole fractions, etc. are the state variables and their dynamics are investigated. Dynamic responses of each variable when the external load changes are simulated. Simulation results show that fuel flow, inlet pressure and temperature have significant effects on the dynamic performance of SOFC. Further it is shown that, compared to other inlet flow properties, cathode side air inlet temperature has the most significant effect on SOFC solid phase temperature and performance. Compared with inlet pressures and temperatures, the effect of flow velocity is not significant. Simulation also indicates that the transient response of SOFC is controlled mainly by the dynamics of cell temperature owing to its large heat capacity.     

Modeling of a Tubular‐SOFC: The Effect of the Thermal Radiation of Fuel Components and CO Participating in the Electrochemical Process

A mathematical model based on first principles is developed to study the effect of heat and electrochemical phenomena on a tubul solid oxide fuel cell (SOFC). The model accounts fordiffusion, inherent impedance, transport (momentum, heat and mass transfer) processes, internal reforming/shifting reaction, electrochemical processes, and potential losses (activation, concentration, and ohmic losses). Thermal radiation of fuel gaseous components is considered in detail in this work in contrast to other reported work in the literature. The effect of thermal radiation on SOFC performance is shown by comparing with a model without this factor. Simulation results indicate that at higher inlet fuel flow pressures and also larger SOFC lengths the effect of thermal radiation on SOFC temperature becomes more significant. In this study, the H₂ and CO oxidation is also studied and the effect of CO oxidation on SOFC performance is reported. The results show that the model which accounts for the electrochemical reaction ofCO results in better SOFC performance than other reported models. This work also reveals that at low inlet fuel flow pressures the CO and H₂ electrochemical reactions are competitive and significantly dependent on the CO/H₂ ratio inside the triple phase boundary.     

Modelling of an indirect internal reforming solid oxide fuel cell

Creation of an autothermal system by coupling an endothermic to an exothermic reaction demands the matching of the thermal requirements of the two reactions. The application under study is a solid oxide fuel cell (SOFC) with indirect internal reforming (IIR) of methane, whereby the endothermic steam reforming reaction is thermally coupled to the exothermic oxidation reactions. A steady-state model of an IIR-SOFC has been developed to study the mismatch between the thermal load associated with the rate of steam reforming at typical SOFC temperatures and the local amount of heat available from the fuel cell reactions. Results have shown a local cooling effect, undesirable for ceramic fuel cells, close to the reformer entrance. The system behaviour towards changes in catalyst activity, fuel inlet temperature, current density, and operating pressure has been studied. Increasing the operating pressure is shown to be an effective way of reducing both the local cooling caused by the reforming reactions and the overall temperature increase across the cell. Simulations for both counter-flow and co-flow configurations have been performed and compared.     

Modeling of transport, chemical and electrochemical phenomena in a cathode-supported SOFC

This paper investigates the performance of a planar cathode-supported solid oxide fuel cell (SOFC) with composite electrodes using a detailed numerical model. The methane reforming reaction is included in the model and takes place mostly in the porous, thin anode at the high operating temperature of 800-1000^°C. A single computational domain comprises the fuel and air channels and the electrodes-electrolyte assembly eliminating the need for internal boundary conditions. The equations governing transport and chemical and electrochemical processes for mass, momentum, chemical and charged species and energy are solved using Star-CD augmented by subroutines written in-house. The operating cell voltage is determined by the potential difference between the cathode and the anode, whose potentials are fixed. Results of temperature, chemical species, current density and electric potential distribution for a co-flow configuration are shown and discussed. It is found that the sub-cooling effect observed in anode-supported cells is almost ameliorated, making the cathode-supported cell favorable from the viewpoint of material stability.     

Numerical Investigation into Thermofluidic and Electrochemical Characteristics of Tubular‐type SOFC

Three‐dimensional simulations based on a multi‐physics model are performed to examine the thermofluidic and electrochemical characteristics of a tubular, anode‐supported solid oxide fuel cell (SOFC). The simulations focus on the local transport characteristics of the cathode and anode gases and the distribution of the temperature field within the fuel cell. In addition, the electrochemical properties of the SOFC are systematically examined for a representative range of inlet gas temperatures and pressures. The validity of the numerical model is confirmed by comparing the results obtained for the correlation between the power density and the current density with the experimental results presented in the literature. Overall, the present results show that the performance of the tubular SOFC is significantly improved under pressurised conditions and a higher operating temperature.     

Experimental Study of Internal Reforming on Large‐area Anode Supported Solid Oxide Fuel Cells

The effect of endothermic internal steam reformation of methane and exothermic fuel cell reaction on the temperature of a planar‐type anode‐supported solid oxide fuel cell was experimentally investigated as a function of current density and fuel utilization. We fabricated a large‐area (22 × 33 cm²) cell and compared temperature profiles along the cell using 30 thermocouples inserted through the cathode end plate at 750 °C under various conditions (Uf ∼50% at 0.4 A cm⁻²; Uf ∼70% at 0.4 A cm⁻²; Uf ∼50% at 0.2 A cm⁻²) with hydrogen fuel and methane‐steam internal reforming. The endothermic effect due to internal reforming mainly occurs at the gas inlet region, so this process is not very effective to cool down the hot spot created by the exothermic fuel cell reaction. This eventually results in a larger temperature difference on the cell. The most moderate condition with regards to thermal gradient on the cell corresponds to high fuel utilization (Uf ∼70%) and low current density (∼0.2 A cm⁻²). The electrochemical performance was also measured, and it was found that the current–voltage characteristics are comparable for the cell operated under hydrogen fuel and internal steam reforming of methane because of lower polarization resistance with high partial pressure of water vapor.     

Modeling of Direct H2S Fueled Solid Oxide Fuel Cells with Reforming Chemical Kinetics

A direct H₂S fueled SOFC model is developed based on Ni‐YSZ/YSZ/YSZ‐LSM button cell test stand. The model considers the detailed reforming chemical processes of H₂S and multi‐physics transport processes in the fuel cell and fuel supply tubes. The model is validated using experimental data. Extensive simulations are performed to study the complicated interactions between multi‐physics transport processes and chemical/electrochemical reactions. The results elucidate the fundamental mechanisms of direct H₂S fueled SOFCs. It is found that suitably increasing the H₂O content in the supplied H₂S fuel can improve SOFC electrochemical performance; high operating temperature may facilitate the reforming of H₂S and improve the electrochemical performance. The sulfur poisoning effect may be mitigated by increasing the H₂O content in the fuel, increasing the operating temperature, decreasing the flow rate, and/or making the cell work at low voltage (or high current) conditions.     

Comparison of two IT DIR-SOFC models: Impact of variable thermodynamic, physical, and flow properties. Steady-state and dynamic analysis

This paper compares two dynamic, one-dimensional models of a planar anode-supported intermediate temperature (IT) direct internal reforming (DIR) solid oxide fuel cell (SOFC): one where the flow properties (pressure, gas stream densities, heat capacities, thermal conductivities, and viscosity) and gas velocities are taken as constant throughout the system, based on inlet conditions, and one where this assumption is removed to focus on the effect of considering the variation of local flow properties on the prediction of the fuel cell performance. The refined model consists of mass, energy, and momentum balances, and of an electrochemical model that relates the fuel and air gas compositions and temperatures to voltage, current density, and other relevant fuel cell variables. Simulations for steady-state and dynamic conditions have been carried out and the results obtained from the two models compared. For a co-flow SOFC operating on a 10% pre-reformed methane fuel mixture, with 75% fuel utilisation, inlet fuel and air temperatures of 1023 K, average current density of , and an air ratio of 8.5, the results show that, although the error incurred in the prediction of the flow properties in the first model is significant, there is good agreement between both models in terms of the overall cell performance: the maximum difference in the local temperature values is about 7 K and the cell efficiency differs by less than 1%. However, the discrepancies between the two models increase, especially in the fuel channel, when higher current density values are assigned to the cell.     

Limiting Factors for a Planar Solid Oxide Fuel Cell Under Different Flow and Temperature Conditions

The work investigates the performance of an anode supported solid oxide fuel cell under relevant conditions at different flow and temperature settings with the aim to identify performance limiting factors through impedance spectroscopy. Impedance spectroscopy is used to deconvolute impedance spectra of an in‐operating SOFC and identify limiting overpotentials. Those measurements are made under a wide range of flow and temperature conditions. In particular, oxidant flow rate is varied yielding fuel cell operation with 20, 40, 60, 80% oxidant utilization; fuel is instead changed in terms of flow and composition: fuel utilization factors in the range of 20–80% are investigated as well as the dilution with nitrogen. The operating temperature is varied in the range between 650 and 800 °C with steps of 50 °C. Results show that charge and mass transport can lead to a performance limitation according to the selected operating range for the investigated cell design. For the investigated anode‐supported design, a major improvement of performance could arise by reducing ohmic resistances (i.e. employing a thin electrolyte) and by an improvement of the anode geometry aiming at enhancing mass transport. In particular, at low temperature and high fuel utilization, fuel oxidation seems to be a relevant performance limiting factor.     

Alternative concept for SOFC with direct internal reforming operation: Benefits from inserting catalyst rod

Mathematical models of direct internal reforming solid oxide fuel cell (DIR‐SOFC) fueled by methane are developed using COMSOL® software. The benefits of inserting Ni‐catalyst rod in the middle of tubular‐SOFC are simulated and compared to conventional DIR‐SOFC. It reveals that DIR‐SOFC with inserted catalyst provides smoother temperature gradient along the system and gains higher power density and electrochemical efficiency with less carbon deposition. Sensitivity analyses are performed. By increasing inlet fuel flow rate, the temperature gradient and power density improve, but less electrical efficiency with higher carbon deposition is predicted. The feed with low inlet steam/carbon ratio enhances good system performances but also results in high potential for carbon formation; this gains great benefit of DIR‐SOFC with inserted catalyst because the rate of carbon deposition is remarkably low. Compared between counter‐ and co‐flow patterns, the latter provides smoother temperature distribution with higher efficiency; thus, it is the better option for practical applications. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Modeling Flow Distribution for Internally Manifolded Direct Methanol Fuel Cell Stacks

A model is presented for the liquid feed direct methanol fuel cell, which describes the hydraulic behavior of an internally manifolded cell stack. The model is based on the homogeneous two‐phase flow theory and mass conservation equation. The model predicts the pressure drop behavior of an individual fuel cell, and is used to calculate flow distribution through fuel cell stack internal manifolds. The flow distribution of the two‐phase fluids in the anode and the cathode chambers is predicted as a function of cell operating parameters. An iterative numerical scheme is used to solve the differential equations for longitudinal momentum and continuity.     

Effect of methane slippage on an indirect internal reforming solid oxide fuel cell

Creation of an autothermal system by coupling an endothermic to an exothermic reaction demands matching the thermal requirements of the two reactions. The application studied here is the operation of a solid oxide fuel cell (SOFC) with both direct (DIR) and indirect (IIR) internal reforming of methane. Such internal reforming within a high-temperature fuel cell module can lead to an overall autothermal operation which simplifies the system design and increases efficiency. However, such coupling is not easy to achieve because of the mismatch between the thermal load associated with the rate of steam reforming at typical SOFC temperatures and the local amount of heat available from the fuel cell reactions. Previous results have shown that the use of typical metal-based (e.g. Ni) IIR catalysts leads to full methane consumption but undesirable local cooling at the reformer entrance and the use of less active IIR catalysts (e.g. non-metals or diffusion limited nickel) leads to methane being carried-over into the SOFC anode (methane slippage). In order to evaluate performance in the latter case, a combined DIR and IIR SOFC steady-state model has been developed. Simulation results have shown that, lowering the IIR catalyst activity to prevent local cooling effects at the reformer entrance is not adequate, as the fast kinetics of the direct reforming reaction then lead to full methane conversion and steep temperature gradients in the first 10% of the fuel channel length. It is shown that the simultaneous reduction of the anode DIR reaction rate improves performance considerably. The system behaviour towards changes in current density, operating pressure, and flow configuration (counter-flow vs. co-flow) has been studied. Reduction of both DIR and IIR catalyst activity combined with a counter-flow operation leads to the best performance. System performance with an IIR oxide-based catalyst is also evaluated.     

空气自呼吸式直接甲醇燃料电池传输特性数值研究

针对空气自呼吸式直接甲醇燃料电池（DMFC）建立了二维两相非等温的传质模型,通过自编程序模拟了电池内的传热、传质和电化学反应过程。并基于此模型研究了主要的操作参数,包括甲醇进口温度、环境中空气的温度、甲醇进口浓度,及对电池性能的影响。研究表明甲醇溶液的进口温度和环境温度上升都会使电池的性能得到提高,其中甲醇溶液的进口温度对电池性能的影响更大;当甲醇进口浓度提高后,在大电流密度下电池的性能得到了显著的提高。     

Computational Studies for the Evaluation of Fuel Flexibility in Solid Oxide Fuel Cells: A Case with Biosyngas

The fuel flexibility of solid oxide fuel cells (SOFCs) is one of the advantages of this technology, and biosyngas produced from biomass is emerging as a new fuel. The fuelling of SOFCs with different fuels is always challenging because of the associated risks. Mathematical modeling tools are useful for predicting the operational safety constraints and designs of SOFCs that are suitable for different fuels. Using a single channel model that incorporates direct internal reforming (DIR), this work investigates the fuel flexibility of an anode‐supported intermediate temperature planar solid oxide fuel under co‐flow operation. The DIR reaction of methane, the water‐gas shift reaction (WGS) and the electrochemical reaction of hydrogen are the three reactions taken into account in this simulation work. Detailed comparisons of the gas concentrations, the current density distributions and the temperature change profiles are presented and discussed. These simulation results provide the initial data for performance analyses and safety predictions, which will be helpful for our future experimental investigations. The thermodynamic predictions of both nickel oxidation and carbon deposition are employed to check the operational safety of SOFCs fuelled with biosyngas.     

Analysis of a proton-conducting SOFC with direct internal reforming

This paper presents a performance analysis of a planar SOFC (solid oxide fuel cell) with proton-conducting electrolyte (SOFC-H⁺). The SOFC-H⁺ is fueled by methane and operated under direct internal reforming and isothermal conditions. A one-dimensional steady-state model coupled with a detailed electrochemical model is employed to investigate the distribution of gas composition within fuel and air channels and all the electrochemical-related variables. The current–voltage characteristics of SOFC-H⁺ are analyzed and the result shows that the operation of SOFC-H⁺ at 0.7 V gives a good compromise on power density and fuel utilization. However, high CO content at fuel channel is observed at this condition and this may hinder the SOFC-H⁺ performance by reducing catalyst activity. The effect of key cell operating parameters, i.e., steam to carbon ratio, temperature, pressure, and water content in oxidant, on the performance of SOFC-H⁺ and the content of CO is also presented in this study.     

Polarization characteristics and fuel utilization in anode-supported solid oxide fuel cell using three-dimensional simulation

A three-dimensional numerical simulation for anode-supported tubular solid oxide fuel cell (SOFC), which is characterized by good electrical conductivity, has been carried out. Performance results by simulation are in good agreement with those by experiments, reported in [7]. Effect of various process conditions such as operating temperature, inlet velocity of fuel, and flow direction of inlet gases on the cell performance and fuel utilization has been further scrutinized. Polarization curve rises with increasing temperature of preheated gases and chamber, resulting from the incremented activity of catalysts within electrode. An effective way to reduce the temperature variation in the single cell with increasing current density has been sought, considering the temperature-dependent thermal expansion of materials. It has also been found that the fuel utilization is enhanced by increasing the cell length and operating temperature and lowering the inlet velocity of fuel.     

Development of a novel test system for in situ catalytic, electrocatalytic and electrochemical studies of internal fuel reforming in solid oxide fuel cells

A test system based around a thin‐walled extruded solid electrolyte tubular reactor has been developed, which enables the fuel reforming catalysis and surface chemistry occurring within solid oxide fuel cells and the electrochemical performance of the fuel cell to be studied under genuine operating conditions. It permits simultaneous monitoring of the catalytic chemistry and the cell performance, allowing direct correlation between the fuel cell performance and the reforming characteristics of the anode, as well as enabling the influence of drawing current on the catalysis and surface reaction pathways to be studied. Temperature‐programmed reaction measurements can be carried out on anodes in an actual SOFC, and have been used to investigate the reduction characteristics of different anode formulations, methane activation and methane steam reforming, and to evaluate the nature and level of carbon deposition on the anode during reforming. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modelling and Performance Evaluation of Solid Oxide Fuel Cell for Building Integrated Co‐ and Polygeneration

Models of fuel cell based combined heat and power systems, used in building energy performance simulation codes, are often based on simple black or grey box models. To model a specific device, input data from experiments are often required for calibration. This paper presents an approach for the theoretical derivation of such data. A generic solid oxide fuel cell (SOFC) system model is described that is specifically developed for the evaluation of building integrated co‐ or polygeneration. First, a detailed computational cell model is developed for a planar SOFC and validated with available numerical and experimental data for intermediate and high temperature SOFCs with internal reforming (IT‐DIR and HT‐DIR). Results of sensitivity analyses on fuel utilisation and air excess ratio are given. Second, the cell model is extended to the stack model, considering stack pressure losses and the radiative heat transfer effect from the stack to the air flow. Third, two system designs based on the IT‐DIR and HT‐DIR SOFCs are modelled. Electric and CHP efficiencies are given for the two systems, as well as performance characteristics, to be used in simulations of building integrated co‐ and polygeneration systems.     

Effect of Creep of Ferritic Interconnect on Long‐Term Performance of Solid Oxide Fuel Cell Stacks

High‐temperature ferritic alloys are potential candidates as interconnect (IC) materials and spacers due to their low cost and coefficient of thermal expansion (CTE) compatibility with other components for most of the solid oxide fuel cells (SOFCs). However, creep deformation becomes relevant for a material when the operating temperature exceeds or even is less than half of its melting temperature (in degrees of Kelvin). The operating temperatures for most of the SOFCs under development are around 1,073 K. With around 1,800 K of the melting temperature for most stainless steel (SS), possible creep deformation of ferritic IC under the typical cell operating temperature should not be neglected. In this paper, the effects of IC creep behaviour on stack geometry change and the stress redistribution of different cell components are predicted and summarised. The goal of the study is to investigate the performance of the fuel cell stack by obtaining the changes in fuel‐ and air‐channel geometry due to creep of the ferritic SS IC, therefore indicating possible changes in SOFC performance under long‐term operations. The ferritic IC creep model was incorporated into software SOFC‐MP and Mentat‐FC, and finite element analyses (FEAs) were performed to quantify the deformed configuration of the SOFC stack under the long‐term steady‐state operating temperature. It was found that the creep behaviour of the ferritic SS IC contributes to narrowing of both the fuel‐ and the air‐flow channels. In addition, stress re‐distribution of the cell components suggests the need for a compliant sealing material that also relaxes at operating temperature.