Detailed dynamic Solid Oxide Fuel Cell modeling for electrochemical impedance spectra simulation

This paper presents a detailed flexible mathematical model for planar solid oxide fuel cells (SOFCs), which allows the simulation of steady-state performance characteristics, i.e. voltage-current density (V-j) curves, and dynamic operation behavior, with a special capability of simulating electrochemical impedance spectroscopy (EIS). The model is based on physico-chemical governing equations coupled with a detailed multi-component gas diffusion mechanism (Dusty-Gas Model (DGM)) and a multi-step heterogeneous reaction mechanism implicitly accounting for the water-gas-shift (WGS), methane reforming and Boudouard reactions. Spatial discretization can be applied for 1D (button-cell approximation) up to quasi-3D (full size anode supported cell in cross-flow configuration) geometries and is resolved with the finite difference method (FDM). The model is built and implemented on the commercially available modeling and simulations platform gPROMS™. Different fuels based on hydrogen, methane and syngas with inert diluents are run. The model is applied to demonstrate a detailed analysis of the SOFC inherent losses and their attribution to the EIS. This is achieved by means of a step-by-step analysis of the involved transient processes such as gas conversion in the main gas chambers/channels, gas diffusion through the porous electrodes together with the heterogeneous reactions on the nickel catalyst, and the double-layer current within the electrochemical reaction zone. The model is an important tool for analyzing SOFC performance fundamentals as well as for design and optimization of materials’ and operational parameters.     

A numerical study on the heat and mass transfer characteristics of metal-supported solid oxide fuel cells

The heat and mass transfer characteristics of solid oxide fuel cells (SOFCs) need to be considered when designing SOFCs because they heavily influence the performance and durability of the cells. The physical property models, the governing equations (mass, momentum, energy and species balance equations) and the electrochemical reaction models were calculated simultaneously in a 3-dimensional SOFC simulation. The current density-voltage (I-V) curves measured experimentally from a single SOFC were compared with the simulation data for code validation purposes. The error between the experimental data and the numerical results was less than 5% at operating temperatures from 700 °C to 850 °C. The current density and the mass transfer rate of an anode-supported SOFC were compared with those of a metal-supported SOFC. The metal-supported SOFC had a 17% lower average current density than the anode-supported SOFC because of the bonding layer, but it showed better thermal stability than the anode-supported SOFC because of its more uniform current density distribution. The current density, temperature and pressure drop of the metal-supported SOFC were investigated for several channel designs. A high current density was observed near the hydrogen inlet and at the intersection of the hydrogen and air channels. However, there was a low current density under the rib and at the cell edge because of an insufficient reactant diffusion flux. When the proper channel design was applied to the metal-supported SOFC, the average current density was increased by 45%.     

Property models and theoretical analysis of novel solid oxide fuel cell with triplet nano-composite electrode

Triplet nano-composite electrodes are actively examined experimentally, but there is a shortage of theoretical study. Theoretical models are helpful for understanding the experiments and provide guidance for design optimization of the novel electrode. Here new models for computing the electrode electronic and ionic conductivities, TPB length and hydraulic radius are presented. The novel properties determined by the models are used in a multi-physics numerical model that couples the intricate interdependency among electric conductions, electrochemical reaction and gas transport in SOFC. The theoretical I–V relations and hydraulic radius are in good agreement with the experiments, validatingtheproposed property models. The property models are then used to examine the influence of microstructure and material composition. The results show that: (i) Larger core-particle size and smaller nano-particle size are helpful for improving electrode properties; (ii) The required nano-particle loading is determined by the desired electronic conductivity instead of the desired TPB length.     

Performance simulation for an anode-supported SOFC using Star-CD code

Experimental activities and computational fluid dynamics (CFD) simulation are presented in this paper for investigating the performance of an anode-supported solid oxide fuel cell (SOFC). The goal of this work is to assess a commercial CFD code, Star-CD with es-sofc module, to simulate the current–voltage (I–V) characteristics with respect to the experimental data. Compiled with the geometry of cell test housing, a 3D numerical model and test conditions were established to analyze the anode-supported cell (ASC) performance including current density and temperature distributions, fuel concentration, and fuel utilization. After adjusting parameters in the electrochemical model, the simulation results showed good agreements with the experimental data. The results also revealed that the power density increased while the fuel utilization decreased as the fuel flow rate increased.     

Three-dimensional computational fluid dynamics modeling of anode-supported planar SOFC

Modeling plays a very important role in the development of fuel cells and fuel cell systems. The aim of this work is to investigate the electrochemical processes of a Solid Oxide Fuel Cell (SOFC) and to evaluate the performance of the proposed SOFC design. For this aim a three-dimensional Computational Fluid Dynamics (CFD) model has been developed for an anode-supported planar SOFC with corrugated bipolar plates serving as gas channels and current collector. The conservation of mass, momentum, energy and species is solved by using the commercial CFD code FLUENT in the developed model. The add-on FLUENT SOFC module is implemented for modeling the electrochemical reactions, loss mechanisms and related electric parameters throughout the cell. The distributions of temperature, flow velocity, pressure and gaseous (fuel and air) concentrations through the cell structure and gas channels is investigated. The relevant fuel cell variables such as the potential and current distribution over the cell and fuel utilization are calculated and studied. The modeling results indicate that, for the proposed SOFC design, reasonably uniform distributions of current density over the active cell area can be achieved. The geometry of the cathode gas channel has a substantial effect on the oxygen distribution and thus the overall cell performance. Methods for arriving at improved cell designs are discussed.     

An analytical model for solid oxide fuel cells with bi-layer electrolyte

A theoretical model for a solid oxide fuel cell (SOFC) with a bi-layer electrolyte is developed and analytical solutions of various important relationships, such as I–V relationship, distribution of oxygen partial pressure in the bi-layer electrolyte, leakage current density etc. are obtained. Based on the assumptions of constant ionic conductivity and reversible electrodes, the model takes into considerations of transports of both ions and electrons in the electrolyte. The modeling results are compared with both experimental data and results from other models in the literature and very good agreements are obtained.     

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.     

Modeling of a planar solid oxide fuel cell based on proton‐conducting electrolyte

A 2D computational fluid dynamics (CFD) model is developed to study the performance of an advanced planar solid oxide fuel cell based on proton conducting electrolyte (SOFC‐H). The governing equations are solved with the finite volume method (FVM). Simulations are conducted to understand the transport phenomena and electrochemical reaction involved in SOFC‐H operation as well as the effects of operating/structural parameters on SOFC‐H performance. In an SOFC based on oxygen ion conducting electrolyte (SOFC‐O), mass is transferred from the cathode side to the anode side. While in an SOFC‐H, mass is transferred from the anode to the cathode, which causes different velocity fields of the fuel and oxidant gas channels and influences the distributions of temperature and gas composition in the cell. It is also found that increasing the inlet gas velocity leads to an increase in the local current density and a slight decrease in the SOFC‐H temperature due to stronger cooling effect of the gas species at a higher velocity. Another finding is that the electrode structure does not significantly affect the heat and mass transfer in an SOFC‐H at typical operating voltages. Copyright © 2009 John Wiley & Sons, Ltd.     

Computational analysis of species transport and electrochemical characteristics of a MOLB-type SOFC

A multi-physics model coupling electrochemical kinetics with fluid dynamics has been developed to simulate the transport phenomena in mono-block-layer built (MOLB) solid oxide fuel cells (SOFC). A typical MOLB module is composed of trapezoidal flow channels, corrugated positive electrode-electrolyte-negative electrode (PEN) plates, and planar inter-connecters. The control volume-based finite difference method is employed for calculation, which is based on the conservation of mass, momentum, energy, species, and electric charge. In the porous electrodes, the flow momentum is governed by a Darcy model with constant porosity and permeability. The diffusion of reactants follows the Bruggman model. The chemistry within the plates is described via surface reactions with a fixed surface-to-volume ratio, tortuosity and average pore size. Species transports as well as the local variations of electrochemical characteristics, such as overpotential and current density distributions in the electrodes of an MOLB SOFC, are discussed in detail.     

Fuel utilization and fuel sensitivity of solid oxide fuel cells

Fuel utilization and fuel sensitivity are two important process variables widely used in operation of SOFC cells, stacks, and generators. To illustrate the technical values, the definitions of these two variables as well as practical examples are particularly given in this paper. It is explicitly shown that the oxygen-leakage has a substantial effect on the actual fuel utilization, fuel sensitivity and V-I characteristics. An underestimation of the leakage flux could potentially results in overly consuming fuel and oxidizing Ni-based anode. A fuel sensitivity model is also proposed to help extract the leakage flux information from a fuel sensitivity curve. Finally, the “bending-over” phenomenon observed in the low-current range of a V-I curve measured at constant fuel-utilization is quantitatively coupled with leakage flux.     

Nano-grain SnO2 electrodes for high conversion efficiency SnO2-DSSC

The nano-grain ZnO/SnO₂ composite electrode was prepared by adding 5 w% of the 200-250 nm ZnO particles to the 5 nm SnO₂ colloid in the presence of hydroxypropylcellulose (M.W.=80,000). The nano-grain SnO₂ electrode was obtained by removing the ZnO particles from the composite electrode using acetic acid. The FE-SEM micrographs revealed that both electrodes consisted of interconnected nano-grains that were ca. 800 nm in size, and the large pores between the grains furnished the wide electrolyte diffusion channels within the electrodes. The photovoltaic properties of the nano-grain electrodes were investigated by measuring the I-V behaviors, the IPCE spectra and the ac-impedance spectra. The nano-grain electrodes exhibited remarkably improved conversion efficiencies of 3.96% for the composite and 2.98% for the SnO₂ electrode compared to the value of 1.66% for the usual nano-particle SnO₂ electrode. The improvement conversion efficiencies were mainly attributed to the formation of nano-grains, which facilitated the electron diffusion within the grains. The improved electrolyte diffusion as well as the light-scattering effects enhanced the photovoltaic performance of the SnO₂ electrode.     

Combined micro-scale and macro-scale modeling of the composite electrode of a solid oxide fuel cell

The design of a cathode inter-layer is important to the high performance of a solid oxide fuel cell (SOFC). In this paper, the processes of electrochemical reactions, electronic and ionic conductions and gas transports in an SOFC are discussed in detail. An analysis shows that the current conduction and electrochemical processes can be replicated by an equivalent circuit model. A corresponding macro-scale model using the Butler-Volmer equation for electrochemical reactions, Ohm's law for current conduction and the Dusty-gas model for gas transport is described. A percolation theory based micro-model is used to obtain the effective electrode properties in the macro-model from the microstructure parameters of the porous electrode. Experimental I-V relations can be accurately accounted for by the proposed theory. The macro- and micro-models are then combined to systematically examine the effects of various parameters on the performance of a composite cathode inter-layer. The examined parameters include the thickness, effective electronic and ionic conductivities, exchange current density, operating temperature, output current density, electrode- and electrolyte-particle radii, composition and porosity of the cathode inter-layer. The comprehensive study shows conclusively that a cathode inter-layer thickness in a range of 10-20 μm is optimal for all practical material choices and microstructure designs.     

Transient phenomenological modeling of photoelectrochemical cells for water splitting - Application to undoped hematite electrodes

A phenomenological model is proposed for a better understanding of the basic mechanisms of photoelectrochemical (PEC) cells. The main assumptions of the one-dimensional transient phenomenological model are: i) bulk recombination of the conduction band electrons with holes in the valence band; ii) the mobile charge transport takes place via diffusion, which arises from the concentration profiles, and migration, caused by a macroscopic electric field; iii) negligible effects of microscopic electric fields in the cell and screening effects, as well as negligible Helmholtz and diffuse layers. For modeling purposes, the photoanode was assumed to be a homogeneous nanocrystalline hematite structure, with thickness L, porosity ?_p and tortuosity τ. The TCO/semiconductor interface was modeled as an ideal ohmic contact, while the electrolyte/platinized TCO interface was described by a Butler-Volmer approach. An alkaline electrolyte solution was used, allowing the transport of the ionic species from the counter-electrode to the photoanode. The continuity and transport governing equations are defined for the mobile species involved: electrons in the conduction band of the semiconductor, holes in the valence band and hydroxyl ions in the electrolyte. Simulated I-V characteristics were computed and the corresponding results compared with the experimental values. The simulated results were in straight agreement with the experimental data.     

Effect of characteristic lengths of electron,ion, and gas diffusion on electrode performance and electrochemical reaction area in a solid oxide fuel cell

A precise evaluation of the active reaction zone in the electrodes is important to design an effective solid oxide fuel cell (SOFC). A scale analysis and one‐dimensional numerical simulations are conducted to obtain a better understanding of the electrochemical reaction zone in a SOFC anode. In the scale analysis, the characteristic lengths of the electron, oxide ion, and gas transports are evaluated from their conservation equations. Relative comparisons of the characteristic lengths show that the transport phenomena in the SOFC anode are primarily governed by the oxide‐ion conduction under standard operating conditions. The gas diffusion may affect the extent and the location of the active reaction zone at high temperature and/or low reaction gas concentration conditions. The one‐dimensional numerical simulations for an anode provided detailed information such as the electric potential of electron‐ and ion‐conducting phases, the gas concentration, and local charge‐transfer current distributions. It is found that the electrochemical reaction actively occurs in the vicinity of the anode–electrolyte interface. The effective thickness increases as the characteristic length of the ion conduction is increased resulting in better power generation performance. The effective thickness is also increased when the gas‐diffusion length is short. The cell performance is, however, lowered in this case because the low gas diffusivity yields the increase of the ohmic loss of ion conduction as well as the concentration overpotential. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20373     

Modeling and simulation of solid oxide fuel cell based on the volume–resistance characteristic modeling technique

Solid oxide fuel cell (SOFC) is a complicated system with heat and mass transfer as well as electrochemical reactions. The real-time dynamic simulation of SOFC is still a challenge up to now. This paper develops a one-dimensional mathematical model for direct internal reforming solid oxide fuel cell (DIR-SOFC). The volume–resistance (V–R) characteristic modeling technique is introduced into the modeling of the SOFC system. Based on the V–R modeling technique and the modular modeling idea, ordinary differential equations meeting the quick simulation are obtained from partial differential equations. This model takes into account the variation of local gas properties. It can not only reflect the distributed parameter characteristics of SOFC, but also meet the requirement of the real-time dynamic simulation. The results indicate that the V–R characteristic modeling technique is valuable and viable in the SOFC system, and the model can be used in the quick dynamic and real-time simulation.     

Electrical modeling of CIGS thin-film solar cells working in natural conditions

In the paper, results of electrical modeling of Cu(In_xGa_1−x)Se₂ (CIGS) thin-film photovoltaic (PV) modules are presented. Whether the equivalent double diode model—DEM (Double diode Equivalent Model) is appropriate to model CIGS PV modules was investigated. Modeling was based on large amount of data (including current-voltage (I-V) curves) collected during long-term outdoor monitoring of PV systems. The process of applying baseline physical parameters to two of five DEM parameters: diffusion I_S1 and recombination I_S2 related components of dark diode saturation current was carried out. Modeled I_S1 and I_S2 values were used to replace previously approximated DEM parameters and then to predict measured I-V curves in order to determine electrical parameters of the PV modules. The parameters are used to predict energy yield in natural operating conditions. Results of modeling are presented and compared with measured data.     

Performance improvement of proton exchange membrane fuel cell by using annular shaped geometry

A complete three-dimensional and single phase CFD model for a different geometry of proton exchange membrane (PEM) fuel cell is used to investigate the effect of using different connections between bipolar plate and gas diffusion layer on the performances, current density and gas concentration. The proposed model is a full cell model, which includes all the parts of the PEM fuel cell, flow channels, gas diffusion electrodes, catalyst layers and the membrane. Coupled transport and electrochemical kinetics equations are solved in a single domain; therefore no interfacial boundary condition is required at the internal boundaries between cell components.This computational fluid dynamics code is used as the direct problem solver, which is used to simulate the three-dimensional mass, momentum and species transport phenomena as well as the electron- and proton-transfer process taking place in a PEMFC that cannot be investigated experimentally. The results show that the predicted polarization curves by using this model are in good agreement with the experimental results. Also the results show that by increasing the number of connection between GDL and bipolar plate the performance of the fuel cell enhances.     

A novel parameter extraction method for the one-diode solar cell model

With the increase in the capacity of photovoltaic generation systems, studies are being actively conducted to improve system efficiency. To develop precise solar cell simulators or design a high-performance photovoltaic generation system, it is important to accurately understand the physical properties of solar cells. However, solar cell models have a non-linear form with numerous parameters. To obtain accurate parameter values, assumptions that differ from real operating conditions must be made to avoid computational complexity. In this paper, a new method for extracting parameter values is proposed. The proposed method deduces the characteristic curve of an ideal solar cell without resistance using the I-V characteristic curve measured and reported by solar cell manufacturers and calculates the difference between the deduced and actual measured curves. In addition, the precision of the proposed method is demonstrated by calculating the correlation between the I-V characteristic curve based on modeling parameters and the I-V curve actually measured employing the least-squares method.     

Performance prediction of proton exchange membrane fuel cells using a three-dimensional model

In this study a steady-state three-dimensional computational fluid dynamics (CFD) model of a proton exchange membrane fuel cell is developed and presented for a single cell. A complete set of conservation equations of mass, momentum, species, energy transport, and charge is considered with proper account of electrochemical kinetics based on Butler–Volmer equation. The catalyst layer structure is considered to be agglomerate. This model enables us to investigate the flow field, current distribution, and cell voltage over the fuel cell which includes the anode and cathode collector plates, gas channels, catalyst layers, gas diffusion layers, and the membrane. The numerical solution is based on a finite-volume method in a single solution domain. In this investigation a CFD code was used as the core solver for the transport equations, while mathematical models for the main physical and electrochemical phenomena were devised into the solver using user-developed subroutines. Three-dimensional results of the flow structure, species concentrations and current distribution are presented for bipolar plates with square cross section of straight flow channels. A polarization curve is obtained for the fuel cell under consideration. A comparison between the polarization curves obtained from the current study and the corresponding available experimental data is presented and a reasonable agreement is obtained. Such CFD model can be used as a tool in the development and optimization of PEM fuel cells.     

Thermal stress and thermo-electrochemical analysis of a planar anode-supported solid oxide fuel cell: Effects of anode porosity

A 3D integrated numerical model is constructed to evaluate the thermal-fluid behavior and thermal stress characteristics of a planar anode-supported solid oxide fuel cell (SOFC). Effects of anode porosity on performance, temperature gradient and thermal stress are investigated. Using commercial Star-CD software with the es-sofc module, simulations are performed to obtain the current-voltage (I-V) characteristics of a fuel cell as a function of the anode porosity and the temperature distribution within the fuel cell under various operating conditions. The temperature field is then imported into the MARC finite element analysis (FEA) program to analyze thermal stresses induced within the cell. The numerical results are found to be in good agreement with the experimental data. It is shown that the maximum principal stress within the positive electrode-electrolyte-negative electrode (PEN) increases at a higher current and a higher temperature gradient. It is recommended that the temperature gradient should be limited to less than 10.6 °C mm⁻¹ to maintain the structural integrity of the PEN.