A review of numerical modeling of solid oxide fuel cells

The solid oxide fuel cell (SOFC) is one of the most promising fuel cells for direct conversion of chemical energy to electrical energy with the possibility of its use in co-generation systems because of the high temperature waste heat. Various mathematical models have been developed for three geometric configurations (tubular, planar, and monolithic) to solve transport equations coupled with electrochemical processes to describe the reaction kinetics including internal reforming chemistry in SOFCs. In recent years, considerable progress has been made in modeling to improve the design and performance of this type of fuel cells. The numbers of the contributions on this important type of fuels have been increasing rapidly. The objective of this paper is to summarize the present status of the SOFC modeling efforts so that unresolved problems can be identified by the researchers.     

A hierarchical modeling approach to the simulation and control of planar solid oxide fuel cells

The main aim of the paper is to propose hierarchical modeling as a suitable methodology to perform control-oriented analysis of planar solid oxide fuel cells (P-SOFC).     

A quasi-two-dimensional electrochemistry modeling tool for planar solid oxide fuel cell stacks

A quasi-two-dimensional numerical model is presented for the efficient computation of the steady-state current density, species concentration, and temperature distributions in planar solid oxide fuel cell stacks. The model reduction techniques, engineering approximations, and numerical procedures used to simulate the stack physics while maintaining adequate computational speed are discussed. The results of the model for benchmark cases with and without on-cell methane reformation are presented with comparisons to results from other research described in the literature. Simulations results for a multi-cell stack have also been demonstrated to show capability of the model on simulating cell to cell variation. The capabilities, performance, and scalability of the model for the study of large multi-cell stacks are then demonstrated.     

Silver (Ag) as anode and cathode current collectors in high temperature planar solid oxide fuel cells

Planar electrolyte supported solid oxide fuel cells were operated at 900 °C with humidified H₂ for 200 h using silver mesh and paste for cathode current collection. Continuous potentiostatic tests at 0.7 V appeared to induce migration of Ag towards electrode-electrolyte interphase, while continuous OCV tests caused no mass transport. Similar SOFCs fueled by coal syngas at 850 °C using Ag for both anode and cathode current collection indicated little, if any, Ag migration; providing the possibility of employing Ag for 100 h laboratory scale tests using coal-derived syngas. Use of high temperature steam, carbon dioxide and carbon monoxide did not result in the formation of silver carbonates.     

Development of methanol‐fueled low‐temperature solid oxide fuel cells

Low‐temperature solid oxide fuel cell (SOFC, 300–600°C) technology fueled by methanol possessing significant importance and application in polygenerations has been developed. Thermodynamic analysis of methanol gas‐phase compositions and carbon formation indicates that direct operation on methanol between 450 and 600°C may result in significant carbon deposition. A water steam/methanol ratio of 1/1 can completely suppress carbon formation in the same time enrich H₂ production composition. Fuel cells were fabricated using ceria–carbonate composite electrolytes and examined at 450–600°C. The maximum power density of 603 and 431 mW cm^?2 was achieved at 600 and 500°C, respectively, using water steam/methanol with the ratio of 1/1 and ambient air as fuel and oxidant. These results provide great potential for development of the direct methanol low–temperature SOFC for polygenerations. Copyright © 2010 John Wiley & Sons, Ltd.     

High performance metal-supported solid oxide fuel cells fabricated by thermal spray

Metal-supported solid oxide fuel cells (SOFCs) have been fabricated and characterized in this work. The cells consist of porous NiO-SDC as anode, thin SDC as electrolyte, and SSCo as cathode on porous stainless steel substrate. The anode and electrolyte layers were consecutively deposited onto porous metal substrate by thermal spray, using standard industrial thermal spray equipment, operated in an open-air atmosphere. The cathode materials were applied to the as-sprayed half-cells by screen-printing and heat-treated at 800 °C for 2 h. The cell components and performance were examined by scanning electron microscopy (SEM), X-ray diffraction, leakage test, ac impedance and electrochemical polarization at temperatures between 500 and 700 °C. The half-inch button cells exhibit a maximum power density in excess of 0.50 W cm⁻² at 600 °C and 0.92 W cm⁻² at 700 °C operated with humidified hydrogen fuel, respectively. The half-inch button cell was run at 0.5 A cm⁻² at 603 °C for 100 h. The cell voltage decreased from 0.701 to 0.698 V, giving a cell degradation rate of 4.3% kh⁻¹. Impedance analysis indicated that the cell degradation included 4.5% contribution from ohmic loss and 1.4% contribution from electrode polarization. The 5 cm × 5 cm cells were also fabricated under the same conditions and showed a maximum power density of 0.26 W cm⁻² at 600 °C and 0.56 W cm⁻² at 700 °C with dry hydrogen as fuel, respectively. The impedance analysis showed that the ohmic resistance of the cells was the major polarization loss for all the cells, while both ohmic and electrode polarizations were significantly increased when the operating temperature decreased from 700 to 500 °C. This work demonstrated the feasibility for the fabrication of metal-supported SOFCs with relatively high performance using industrially available deposition techniques. Further optimization of the metal support, electrode materials and microstructure, and deposition process is ongoing.     

Mathematical modeling of ammonia-fed solid oxide fuel cells with different electrolytes

An electrochemical model was developed to study the ammonia (NH₃)-fed solid oxide fuel cells with proton-conducting electrolyte (SOFC-H) and oxygen ion-conducting electrolyte (SOFC-O). Different from previous thermodynamic analysis, the present study reveals that the actual performance of the NH₃-fed SOFC-H is considerably lower than the SOFC-O, mainly due to higher ohmic overpotential of the SOFC-H electrolyte. More analyses have been performed to study the separate overpotentials of the NH₃-fed SOFC-H and SOFC-O. Compared with the NH₃-fed SOFC-H, the SOFC-O has higher anode concentration overpotential and lower cathode concentration overpotential. The effects of temperature and electrode porosity on concentration overpotentials have also been studied in order to identify possible methods for improvement of SOFC performance. This study reveals that the use of different electrolytes not only causes different ion conduction characteristics at the electrolyte, but also significantly influences the concentration overpotentials at the electrodes. The model developed in this article can be extended to 2D and 3D models for further design optimization.     

Study on GDC-KZnAl composite electrolytes for low-temperature solid oxide fuel cells

Development of low-temperature solid oxide fuel cells (LTSOFC) is now becoming a mainstream research direction worldwide. The advancement in the effective electrolyte materials has been one of the major challenges for LTSOFC development. To further improve the performance of electrolyte, composite approaches are considered as common strategies. The enhancement on ionic conductivity or sintering behavior ceria-based electrolyte can either be done by adding a carbonate phase to facilitate the utilization of the ionic-conducting interfaces, or by addition of alumina as insulator to reduce the electronic conduction of ceria. Thus the present report aims to design a composite electrolyte materials by combining the above two composite approaches, in order to enhance the ionic conductivity and to improve the long-term stability simultaneously. Here we report the preparation and investigation of GDC-KAlZn materials with composition of Gd doped ceria, K₂CO₃, ZnO and Al₂O₃. The structure and morphology of the samples were characterized by XRD, SEM, etc. The ionic conductivity of GDC-KAlZn sample was determined by impedance spectroscopy. The composite samples with various weight ratio of GDC and KAlZn were used as electrolyte material to fabricate and evaluate fuel cells as well as investigate the composition dependent properties. The good ionic conductivity and notable fuel cell performance of 480 mW cm⁻² at 550 °C has demonstrated that GDC-KAlZn composite electrolyte can be regarded as a potential electrolyte material for LTSOFCs.     

Self-rising synthesis of Ni-SDC cermets as anodes for solid oxide fuel cells

Ni-SDC cermets have been obtained using a self-rising approach by two different ways, one-step direct synthesis (OS) and ball milling the separately prepared NiO and SDC powders (BM). The results showed that self-rising approach was an efficient way for the synthesis of porous materials composed of evenly distributed uniform size nanocrystals. The as-synthesized powders have been applied as anodes for solid oxide fuel cells, whose electrochemical properties have been systematically studied. Cells with anodes from the BM method showed better performance compared with those of the OS method, achieving a maximum power density of 400 mW cm⁻² at 600 °C.     

Layered perovskite GdBaCoFeO5+x as cathode for intermediate-temperature solid oxide fuel cells

A layered perovskite oxide, GdBaCoFeO_5+x (GBCF), was investigated as a novel cathode for intermediate-temperature solid oxide fuel cells (IT-SOFCs). A laboratory-sized Sm_0.2Ce_0.8O_1.9 (SDC)-based tri-layer cell of NiO–SDC/SDC/GBCF was tested under intermediate-temperature conditions of 550–650 °C with humidified H₂ (∼3% H₂O) as a fuel and the static ambient air as oxidant. A maximal power density of 746 mW cm⁻² was achieved at 650 °C. The interfacial polarization resistance was as low as 0.42, 0.18 and 0.11 Ω cm² at 550, 600 and 650 °C, respectively. The experimental results indicate that the layered perovskite GBCF is a promising cathode candidate for IT-SOFCs.     

YSZ films fabricated by a spin smoothing technique and its application in solid oxide fuel cell

A dense single-layer YSZ film has been successfully fabricated by a spin smoothing method. Followed by a simplified slurry coating, an additional spin smoothing process was conducted to obtain a thinner and smoother film. By employment of high-viscosity slurry including high YSZ content, the film has a suitable thickness by a single coating cycle. With Sm_0.2Ce_0.8O_1.9 (SDC)-impregnated La_0.7Sr_0.3MnO₃ (LSM) cathode and porous NiO–YSZ anode, single solid oxide fuel cell (SOFC) based on an 8-μm-thick YSZ film was obtained. Open-circuit voltage (OCV) of the cell was 1.04 V at 800 °C, and maximum power densities were 676, 965 and 1420 mW cm⁻² at 700, 750 and 800 °C, respectively, using H₂ at a flow rate of 40 mL min⁻¹ as fuel and ambient air as oxidant. The power density could be increased to 1648 mW cm⁻² at 800 °C when the flow rate of H₂ was enhanced to 200 mL min⁻¹.     

Air plasma spray processing and electrochemical characterization of Cu-SDC coatings for use in solid oxide fuel cell anodes

Air plasma spraying has been used to produce porous composite anodes based on Ce_0.8Sm_0.2O_1.9 (SDC) and Cu for use in solid oxide fuel cells (SOFCs). Preliminarily, a range of plasma conditions has been examined for the production of composite coatings from pre-mixed SDC and CuO powders. Plasma gas compositions were varied to obtain a range of plasma temperatures. After reduction in H₂, coatings were characterized for composition and microstructure using EDX and SEM. As a result of these tests, symmetrical sintered electrolyte-supported anode-anode cells were fabricated by air plasma spraying of the anodes, followed by in situ reduction of the CuO to Cu. Full cells deposited on SS430 porous substrates were then produced in one integrated process. Fine CuO and SDC powders have been used to produce homogeneously mixed anode coatings with higher surface area microstructures, resulting in area-specific polarization resistances of 4.8 Ω cm² in impedance tests in hydrogen at 712 °C.     

Three-dimensional thermo-fluid and electrochemical modeling of anode-supported planar solid oxide fuel cell

This paper presents a three-dimensional model of an anode-supported planar solid oxide fuel cell with corrugated bipolar plates serving as gas channels and current collector above the active area of the cell. Conservation equations of mass, momentum, energy and species are solved incorporating the electrochemical reactions. Heat transfer due to conduction, convection and radiation is included. An empirical equation for cell resistance with measured values for different parameters is used for the calculations. Distribution of temperature and gas concentrations in the PEN (positive electrode/electrolyte/negative electrode) structure and gas channels are investigated. Variation of current density over the cell is studied. Furthermore, the effect of radiation on the temperature distribution is studied and discussed. Modeling results show that the relatively uniform current density is achieved at given conditions for the proposed design and the inclusion of thermal radiation is required for accurate prediction of temperature field in the single cell unit.     

Alkaline metal doped strontium cobalt ferrite perovskites as cathodes for intermediate-temperature solid oxide fuel cells

Perovskite oxides Sr_0.9K_0.1Fe_xCo_1-xO_3-δ (SKFCx, x = 0.1, 0.3, 0.5, 0.7, 0.9 and 1.0) are investigated as potential cathode materials for intermediate-temperature solid oxide fuel cells (IT-SOFCs) on Sm_0.2Ce_0.8O_1.9 (SDC) electrolyte. The cubic phase of the SKFCx oxides is demonstrated by x-ray diffraction. The SKFCx cathode shows good compatibility with the SDC electrolyte up to 900 °C. Among the investigated compositions, SKFC0.1 displays the highest electrical conductivity of 443–146 S·cm^?1 from 350 °C to 800 °C in flow air. The area specific resistances (ASRs) of the SKFCx (x = 0.1, 0.3, 0.5, 0.7, 0.9 and 1.0) cathodes are 0.047, 0.058, 0.066, 0.101, 0.155 and 0.175 Ω cm² at 650 °C in air on an SDC electrolyte. Among the five tested cathodes, SKFC0.1 exhibits the lowest area specific resistances between 550 °C and 750 °C, when tested on its symmetric cell configuration of cathode|SDC|cathode. The thermally stabilized cubic perovskite structure of the SKFC0.1 powder is demonstrated by high-temperature XRD. The average linear thermal expansion coefficient α_L of SKFC0.1 is 18.9$\times$10^?6 K^?1. A peak power density of 1643 mW·cm^?2 is achieved on SKFC0.1|SDC|Ni-SDC anode supported fuel cell at 650 °C. These features, and excellent electrocatalytic activity and good stability, indicate the potential of alkaline metal doped strontium cobalt ferrite perovskites are promising cathode materials for IT-SOFCs.     

Ceria coated Ni as anodes for direct utilization of methane in low-temperature solid oxide fuel cells

A new type of anode, a Ni framework coated with Sm-doped ceria (SDC), was developed for direct utilization of methane fuel in low-temperature solid oxide fuel cells (SOFCs) with thin-film SDC electrolytes. The coated SDC was prepared with an ion impregnating method and the electrolyte films were fabricated with a co-pressing and co-firing technique. The impregnating process produced an ideal anode microstructure where nickel particles were effectively connected and uniformly covered with nanosized SDC. This anode microstructure was believed to enlarge the triple-phase boundaries and therefore enhance the anode performance. The cell performance was much higher than that of a conventional fuel cell with a Ni-SDC composite anode. In addition, the performance increased with impregnated SDC loading up to a maximum at 20 mg cm⁻², indicating that the coated SDC is the contributing factor for the enhanced fuel cell performance. Power density as high as 571 and 353 mW cm⁻² were obtained at 600 °C when humidified hydrogen and methane were used as fuels, respectively. The stability of the cell also increased with the SDC loading. No significant degradation was observed for anodes coated with 20 and 25 mg cm⁻² SDC. This verifies that the coated SDC electrodes are very effective in suppressing catalytic carbon formation by blocking methane from approaching the Ni, which is catalytically active towards methane pyrolysis. The high performance of this anode shows high promise in the developing field of direct hydrocarbon SOFCs.     

Entropy generation analysis in a monolithic-type solid oxide fuel cell (SOFC)

The aim of the paper is to investigate possible improvements in the geometry design of a monolithic solid oxide fuel cells (SOFCs) through analysis of the entropy generation terms. The different contributions to the local rate of entropy generation are calculated using a computational fluid dynamic (CFD) model of the fuel cell, accounting for energy transfer, fluid dynamics, current transfer, chemical reactions and electrochemistry. The fuel cell geometry is then modified to reduce the main sources of irreversibility and increase its efficiency.     

Model-oriented cast ceramic tape seals for planar solid oxide fuel cells

A straight capillary model is developed to estimate the mass leak rate of the cast ceramic tape seals for planar solid oxide fuel cells (SOFCs), which is further rectified with consideration of microstructure complexity including the tortuosity, cross-section variation and cross-link of leak paths. The size distribution of the leak path, effective porosity and the microstructure complexity are the main factors that influence the leak rate of the cast tape seals. According to the model, Al₂O₃ powders are selected for preparation of the seals by tape casting, and the leak rate is evaluated under various compressive stresses and gauge pressures. The results indicate that Al₂O₃ powder with D₅₀ value about 2 μm and specific surface area near 5 m² g⁻¹ can be used for the cast tape seals; and the obtained leak rate can satisfy the allowable leak limit.     

Transient modeling of anode-supported solid oxide fuel cells

An isothermal 2-D transient model is developed for an anode-supported solid oxide fuel cell. The model takes into account the transient effects of both charge migration and species transport in PEN assembly. Due to the lack of transient experimental data, the transient model, under steady state operating conditions, is validated using experimental results from open literature. Numerical results show that the cell can obtain very quick transient current response when subjected to a step voltage change, followed by a slow current transient period due to species diffusion effects within porous electrodes. It is also found that the transient response of the cell current is sensitive to oxygen concentration change at cathode/channel interface, whereas the current response is slow when step change of hydrogen concentration is applied at anode/channel interface. The cell transient performance can be improved by increasing porosity or decreasing tortuosity of electrodes.     

Effect of a shielded slot on a planar solid oxide fuel cell

A shielded slot was designed for use in a typical current collector/gas distributor fuel cell and was formed from a series of arches with heights suitable for providing sufficient quantities of fuel gases and reaction areas. The shielded slot was substituted in place of the interconnect and offered several advantages in terms of mechanical support and electrical contact. A three-dimensional (3-D) electrochemical reaction model and a microelectrode model of the planar solid oxide fuel cells (SOFC) were used to predict the performances of the shielded slots in planar SOFCs. Prior to analyzing the complex arrangement of the shielded slot, a variety of interconnect arrangements were simulated to understand the relationship between the gas supply and the electrical contact arrangements. The reactivity properties were examined and the most effective arrangement of shielded slots was identified in an effort to design an optimal shielded slot.