Thermal stress modeling of anode supported micro-tubular solid oxide fuel cell

An anode-supported micro-tubular solid oxide fuel cell (SOFC) is analyzed by a two-dimensional axisymmetric numerical model, which is validated with the experimental I-V data. The temperature distribution generated by the thermo-electrochemical model is used to calculate the thermal stress field in the tubular SOFC. The results indicate that the current transport in the anode is the same at every investigated position. The stress of the micro-tubular cell occurs mainly because of the residual stress due to the mismatch between the coefficients of thermal expansion of the materials of the membrane electrode assembly. The micro-tubular cell can operate safely, but if there is an interfacial defect or a high enough tensile stress applied at the electrolyte, a failure can arise.     

An error in solid oxide fuel cell stack modeling

This paper points out an error in the literature and analyzes its effect on electrochemical models of solid oxide fuel cell stacks. A correction is presented.     

Design for segmented-in-series solid oxide fuel cell through mathematical modeling

The segmented-in-series solid oxide fuel cell comprising fuel channel, anode, cathode and electrolyte layers has been evaluated by developing a two-dimensional model, in which the equations have been solved numerically through finite element methods. The results indicate that the voltage of each membrane electrode assembly (MEA) exhibits a parabola-like curve and is higher than the appointed voltage of unit cell (0.7 V). From fuel inlet to outlet, the voltage of each MEA deceases due to the decreasing local H₂ concentration. When both the interconnector and electrolyte gap lengths are fixed, the cell module with 5 mm long anode gives the maximal power density for the SS-SOFC. Higher power densities can be achieved through increasing the cathode thickness.     

Lattice Boltzmann modelling of the coupling between charge transport and electrochemical reactions in a solid oxide fuel cell with a patterned anode

A fundamental understanding of the electrochemical reactions and the associated transport processes in electrodes of solid oxide fuel cells (SOFCs) is critical to the development of new electrode materials. To date, however, our understanding of the electrode processes is still very limited due to the lack of well-designed experiments and carefully-validated predictive models. To facilitate studies in this area, we have developed a numerical model that has taken into consideration of the coupling between the transport of mobile charged species (e.g., ions and electrons) in conducting phases and the electrochemical reactions at the three phase boundaries of an SOFC anode. The validity of this model has been confirmed by the electrochemical performance of test cells with a patterned anode consisting of well-defined electronic and ionic conducting phases. The model is then applied to quantifying the factors that critically influence the performance of a patterned anode, resulting in three key dimensionless parameters governing the coupling of transport and reactions in the anode: the ratio of electronic-to-ionic conductivity (σ_el/σ_ion), the dimensionless exchange current density (i_ex/i₀), and the dimensionless electric potential (Fϕ₀/RT). In particular, it is found that only i_ex/i₀ and Fϕ₀/RT play a significant role under typical SOFC operating conditions: anode performance increases with the increase in i_ex/i₀ and Fϕ₀/RT. Accordingly, we have constructed a phase map to demonstrate the combined effect of i_ex/i₀ and Fϕ₀/RT, which is helpful for rational design and operation of SOFC patterned electrodes of different materials and geometries. More importantly, our present model is also applicable to the study of actual porous SOFC electrodes with known 3D microstructures.     

Fabrication of solid oxide fuel cell anode electrode by spray pyrolysis

Large triple phase boundaries (TPBs) and high gas diffusion capability are critical in enhancing the performance of a solid oxide fuel cell (SOFC). In this study, ultrasonic spray pyrolysis has been investigated to assess its capability in controlling the anode microstructure. Deposition of porous anode film of nickel and Ce_0.9Gd_0.1O_1.95 on a dense 8 mol.% yttria stabilized zirconia (YSZ) substrate was carried out. First, an ultrasonic atomization model was utilized to predict the deposited particle size. The model accurately estimated the deposited particle size based on the feed solution condition. Second, effects of various process parameters, which included the precursor solution feed rate, precursor solution concentration and deposition temperature, on the TPB formation and porosity were investigated. The deposition temperature and precursor solution concentration were the most critical parameters that influenced the morphology, porosity and particle size of the anode electrode. Ultrasonic spray pyrolysis achieved homogeneous distribution of constitutive elements within the deposited particles and demonstrated capability to control the particle size and porosity in the range of 2-17 μm and 21-52%, respectively.     

Basic properties of a liquid tin anode solid oxide fuel cell

An unconventional high temperature fuel cell system, the liquid tin anode solid oxide fuel cell (LTA-SOFC), is discussed. A thermodynamic analysis of a solid oxide fuel cell with a liquid metal anode is developed. Pertinent thermochemical and thermophysical properties of liquid tin in particular are detailed. An experimental setup for analysis of LTA-SOFC anode kinetics is described, and data for a planar cell under hydrogen indicated an effective oxygen diffusion coefficient of 5.3 × 10⁻⁵ cm² s⁻¹ at 800 °C and 8.9 × 10⁻⁵ cm² s⁻¹ at 900 °C. This value is similar to previously reported literature values for liquid tin. The oxygen conductivity through the tin, calculated from measured diffusion coefficients and theoretical oxygen solubility limits, is found to be on the same order of that of yttria-stabilized zirconia (YSZ), a traditional SOFC electrolyte material. As such, the ohmic loss due to oxygen transport through the tin layer must be considered in practical system cell design since the tin layer will usually be at least as thick as the electrolyte.     

Investigation of the electrochemical active thickness of solid oxide fuel cell anode

Determination of the electrochemical active thickness (EAT) is of paramount importance for optimizing the solid oxide fuel cell (SOFC) electrode. However, very different EAT values are reported in the previous literatures. This paper aims to systematically study the EAT of SOFC anode numerically. An SOFC model coupling electrochemical reactions with transport of gas, electron and ion is developed. The microstructure features of the electrode are modeled based on the percolation theory and coordinate number theory. Parametric analysis is performed to examine the effects of various operating conditions and microstructures on EAT. Results indicate that EAT increases with decreasing exchange current density (or decreasing TPB length) and increasing effective ionic conductivity. In addition to the numerical simulations, theoretical analysis is conducted including various losses in the electrode, which clearly shows that the EAT highly depends on the ratio of concentration related activation loss R_act,con to ohmic loss R_ohmic. The theoretical analysis explains very well the different EATs reported in the literature and is different from the common understanding that the EAT is controlled mainly by the ionic conductivity of electrode.     

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.     

Pore-scale investigation of mass transport and electrochemistry in a solid oxide fuel cell anode

The development and validation of a model for the study of pore-scale transport phenomena and electrochemistry in a Solid Oxide Fuel Cell (SOFC) anode are presented in this work. This model couples mass transport processes with a detailed reaction mechanism, which is used to model the electrochemical oxidation kinetics. Detailed electrochemical oxidation reaction kinetics, which is known to occur in the vicinity of the three-phase boundary (TPB) interfaces, is discretely considered in this work. The TPB regions connect percolating regions of electronic and ionic conducting phases of the anode, nickel (Ni) and yttria-stabilized zirconia (YSZ), respectively; with porous regions supporting mass transport of the fuel and product. A two-dimensional (2D), multi-species lattice Boltzmann method (LBM) is used to describe the diffusion process in complex pore structures that are representative of the SOFC anode. This diffusion model is discretely coupled to a kinetic electrochemical oxidation mechanism using localized flux boundary conditions. The details of the oxidation kinetics are prescribed as a function of applied activation overpotential and the localized hydrogen and water mole fractions. This development effort is aimed at understanding the effects of the anode microstructure within TPB regions. This work describes the methods used so that future studies can consider the details of SOFC anode microstructure.     

Single solid oxide fuel cell modeling and optimization

In this paper a dynamic model of a single solid oxide fuel cell (SOFC) is developed using a volume element methodology. It consists of a set of algebraic and ordinary differential equations derived from physical laws (e.g., the first law of thermodynamics, Fick's law, and Fourier's law), which allow for the prediction of the temperature and pressure spatial distribution inside the single SOFC, as functions of geometric and operating parameters. The thermodynamic model is coupled with an electrochemical model that is capable of determining the voltage, current, and power output. Based on the simulation results, the internal configuration (structure of the positive electrode-electrolyte-negative electrode assembly) and the operating conditions (air stoichiometric ratio and fuel utilization factor), as well as their impact on the performance of the single SOFC are discussed. Optimal geometric and operating parameters are obtained so that electrical power of the single SOFC at the nominal operating point is maximized. The method used is general and the fundamental optimization results are sharp, showing up to a 357% single SOFC performance variation within the studied parameters’ range, therefore these findings show the potential to use the model as a tool for future SOFC design, simulation and optimization.     

Three dimensional stress analysis of solid oxide fuel cell anode micro structure

One of the most common problems in solid oxide fuel cells (SOFCs) is the delamination and thus the degradation of electrode/electrolyte interface which occurs in the consequences of the stresses generated within the different layers of the cell. Nowadays, the modeling of this problem under certain conditions is one of the main issues for the researchers. The structural and thermo-physical properties of the cell materials (i.e. porosity, density, Young's modulus etc.) are usually assumed to be homogenous in the mathematical modeling of solid oxide fuel cells at macro-scale. However, during the real operation, the stresses created in the multiphase porous layers might be very different than those at macro-scale. Therefore, micro-level modeling is required for an accurate estimation of the real stresses and the performance of SOFCs. This study presents a microstructural characterization and a finite element analysis of the delamination and the degradation of porous solid oxide fuel cell anode and electrode/electrolyte interface under various operating temperatures, compressing forces and material compositions by using the synthetically generated microstructures. A multi physics computational package (COMSOL) is employed to calculate the Von Misses stresses in the anode microstructures. The maximum thermal stress in the electrode/electrolyte interface and three phase boundaries is found to exceed the yield strength at 900 °C while 800 °C is estimated as a critical temperature for the delamination and micro cracks due to thermal stress generated. The thermal stress decreases in the grain boundaries with increasing content of one of the phases (either Ni or YSZ) and the porosity of the electrode. A clamping load higher than 5 kg cm⁻² is also found to exceed the shear stress limit.     

Influence of fuel flow rate on the performance of micro tubular solid oxide fuel cell

Through mathematical analysis, the performance of micro tubular solid oxide fuel cell (SOFC) is evaluated successfully, which is in good agreement with the experimental data under different fuel flow. The results show that under the condition of high fuel utilization, a part of current path passing through the anode can increase by 16% compared with that under the condition of low fuel utilization, which can reduce the output performance of the cell. In the process of increasing fuel flow, the current gradually increases and reaches the platform value. When the length of cathode is long and the inner diameter of anode is small, the loss can be effectively reduced by changing the thickness of anode tube.     

Pressurized solid oxide fuel cells: Experimental studies and modeling

The hybrid power plant project at DLR aims at investigating the fundamentals and requirements of a combined fuel cell and gas turbine power plant. A specific aim is to demonstrate stable operation of a plant in the 50 kW class. Prerequisite for the power plant realization is the detailed characterization of each subsystem and their interactions. The pressurized solid oxide fuel cell (SOFC) is an essential part of one main subsystem. A combined theoretical and experimental approach allows a thorough insight into nonlinear behavior. This paper focuses on the influence of pressurization on SOFC performance in the range from 1.4 to 3 bar. Conclusions are based on experimental V(i)-characteristics as well as on overpotentials derived from elementary kinetic models. Experiments are performed on planar, anode-supported 5-cell short stacks. The performance increases from 284 mW cm⁻² at 1.4 bar to 307 mW cm⁻² at 2 bar and 323 mW cm⁻² at 3 bar (at 0.9 V; anode: H₂/N₂ 1/1; cathode: air; temperature: 800 °C). The benefit of a temperature rise increases at elevated pressures. Moreover, the effect of gas variation is enhanced at higher pressures. The main conclusion is that pressurization improves the performance. Due to different effects interfering, operation of pressurized SOFC requires further detailed analysis.     

On modeling multi-component diffusion inside the porous anode of solid oxide fuel cells using Fick's model

Stefan-Maxwell model (SMM) and simple Fick's model (FM) type of relations both including Knudsen diffusion for the calculation of species mole fraction distribution inside the porous anode of a solid oxide fuel cell (SOFC) were compared and it was found that at low current densities the models agree well but as current increases the differences also increase. Based on the findings an empirical correction is proposed for the effective diffusivity used in Fick's model. The corrected diffusivity coefficient gave better agreement with the Stefan-Maxwell model and even at higher current densities the error is less than 5%. This correction was implemented via a three-dimensional, in-house SOFC simulation code (DREAMSOFC) which uses Fick's model type relations for diffusion flux calculations. The code also takes into account methane steam reforming (MSR) and water gas shift (WGS) reactions and the electrochemical oxidation of both H₂ and CO. As an application, a SOFC button cell which is being tested at West Virginia University was simulated. The results with and without the proposed correction for effective diffusivity are compared.     

Thermal imaging of solid oxide fuel cell anode processes

A Si-charge-coupled device (CCD), camera-based, near-infrared imaging system is demonstrated on Ni/yttria-stabilized zirconia (YSZ) fragments and the anodes of working solid oxide fuel cells (SOFCs). NiO reduction to Ni by H₂ and carbon deposition lead to the fragment cooling by 5 ± 2 °C and 16 ± 1 °C, respectively. When air is flowed over the fragments, the temperature rises 24 ± 1 °C as carbon and Ni are oxidized. In an operational SOFC, the decrease in temperature with carbon deposition is only 4.0 ± 0.1 °C as the process is moderated by the presence of oxides and water. Electrochemical oxidation of carbon deposits results in a ΔT of +2.2 ± 0.2 °C, demonstrating that electrochemical oxidation is less vigorous than atmospheric oxidation. While the high temperatures of SOFCs are challenging in many respects, they facilitate thermal imaging because their emission overlaps the spectral response of inexpensive Si-CCD cameras. Using Si-CCD cameras has advantages in terms of cost, resolution, and convenience compared to mid-infrared thermal cameras. High spatial (0.1 mm) and temperature (0.1 °C) resolutions are achieved in this system. This approach provides a convenient and effective analytical technique for investigating the effects of anode chemistry in operating SOFCs.     

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.     

Model based evaluation of the electrochemical reaction sites in solid oxide fuel cell electrodes

The electrode microstructure plays an important role in determining the performance of the Solid Oxide Fuel Cells (SOFCs). The conventional SOFC electrodes are based on two kinds of particles, one electron conducting and another ion conducting. Over the years, electrodes with alternative microstructures have been proposed for performance enhancement based on the developments in materials and fabrication techniques. Analytical models for the microstructure offer the scope of quick evaluation of the effect of various microstructural parameters on important microstructural properties like the triple phase boundary densities. However, validation of these models in the light of the experimental data is seldom reported. In this work, the microstructural data derived from image-based reconstruction of the electrodes is used to calibrate and validate an analytical model for the conventional SOFC electrode microstructure revealing insights into the model's applicability. This model forms the basis for the models of other modified microstructures studied in this work. Designing of improved SOFC microstructures require an understanding of the effect of controllable parameters on the reaction sites. Model based evaluation of the electrochemical reaction sites in five different SOFC microstructures is performed in this work. The results and insights will enable the selection of microstructural parameters for tailoring the electrode microstructure to achieve improved performance.     

Thermo-economic modeling of a solid oxide fuel cell/gas turbine power plant with semi-direct coupling and anode recycling

Power generation using gas turbine (GT) power plants operating on the Brayton cycle suffers from low efficiencies, resulting in poor fuel to power conversion. A solid oxide fuel cell (SOFC) is proposed for integration into a 10 MW gas turbine power plant, operating at 30% efficiency in order to improve system efficiencies and economics. The SOFC system is semi-directly coupled to the gas turbine power plant, with careful attention paid to minimize the disruption to the GT operation. A thermo-economic model is developed for the hybrid power plant, and predicts an optimized power output of 21.6 MW at 49.2% efficiency. The model also predicts a breakeven per-unit energy cost of USD 4.70 ¢/kWh for the hybrid system based on futuristic mass generation SOFC costs. Results show that SOFCs can be semi-directly integrated into existing GT power systems to improve their thermodynamic and economic performance.     

Solid oxide fuel cell bi-layer anode with gadolinia-doped ceria for utilization of solid carbon fuel

Pyrolytic carbon was used as fuel in a solid oxide fuel cell (SOFC) with a yttria-stabilized zirconia (YSZ) electrolyte and a bi-layer anode composed of nickel oxide gadolinia-doped ceria (NiO-GDC) and NiO-YSZ. The common problems of bulk shrinkage and emergent porosity in the YSZ layer adjacent to the GDC/YSZ interface were avoided by using an interlayer of porous NiO-YSZ as a buffer anode layer between the electrolyte and the NiO-GDC primary anode. Cells were fabricated from commercially available component powders so that unconventional production methods suggested in the literature were avoided, that is, the necessity of glycine-nitrate combustion synthesis, specialty multicomponent oxide powders, sputtering, or chemical vapor deposition. The easily-fabricated cell was successfully utilized with hydrogen and propane fuels as well as carbon deposited on the anode during the cyclic operation with the propane. A cell of similar construction could be used in the exhaust stream of a diesel engine to capture and utilize soot for secondary power generation and decreased particulate pollution without the need for filter regeneration.     

An experimental study of ammonia decomposition rates over cheap metal catalysts for solid oxide fuel cell anode

Solid oxide fuel cell (SOFC) is an electrochemical device for power generation with high efficiency and low emission. Ammonia is a low-cost and carbon-free hydrogen carrier that can be directly used as a fuel for SOFC. To further improve the performance and stability of SOFC fueled by ammonia (NH₃–SOFC), the design of NH₃–SOFC anode for efficient and stable utilization of NH₃ is critical. In this paper, the decomposition rates of NH₃ over four kinds of cheap metal catalysts (nickel, iron, copper and 304 stainless steel) were tested based on metal flakes with known fixed dimensions, and the empirical correlations of the decomposition rate over different catalysts were derived. These correlations are independent of catalyst structure parameters and only related to the catalyst material and the decomposition temperature, which are important basis for realizing the oriented design of NH₃–SOFC anode.