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.     

Performance comparison of cocurrent and countercurrent flow solid oxide fuel cells

Solid oxide fuel cell (SOFC) is a complicated system with heat and mass transfer as well as electrochemical reactions. The flowing configuration of fuel and oxidants in the fuel cell will greatly affect the performance of the fuel cell stack. Based on the developed mathematical model of direct internal reforming SOFC, this paper established a distributed parameters simulation model for cocurrent and countercurrent types of SOFC based on the volume-resistance characteristic modeling method. The steady-state distribution characteristics and dynamic performances were compared and were analyzed for cocurrent and countercurrent types of SOFCs. The results indicate that the cocurrent configuration of SOFC is more suitable with regard to performance and safety.     

Numerical study of a flat-tube high power density solid oxide fuel cell: Part I. Heat/mass transfer and fluid flow

The flat-tube high power density (HPD) solid oxide fuel cell (SOFC) is a new design developed by Siemens Westinghouse, based on their formerly developed tubular type SOFC. It has increased power density, but still maintains the beneficial feature of secure sealing of a tubular SOFC. In this paper, a three-dimensional numerical model to simulate the steady state heat/mass transfer and fluid flow of a flat-tube HPD-SOFC is developed. In the numerical computation, governing equations for continuity, momentum, mass, and energy conservation are solved simultaneously. The highly coupled temperature, concentration and flow fields of the air stream and the fuel stream inside and outside the different chambers of a flat-tube HPD-SOFC are investigated. The variation of the temperature, concentration and flow fields with the current output is studied. The heat/mass transfer and fluid flow modeling and results will be used to simulate the overall performance of a flat-tube HPD-SOFC, and to help optimize the design and operation of a SOFC stack in practical applications.     

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.     

A three-dimensional model for transient performance of a solid oxide fuel cell

This paper presents an analysis of transient behavior of an anode-supported solid oxide fuel cell (SOFC) using a model, which has recently been built for steady state operation. The model is three dimensional (3D), which takes into account heat and mass transport, chemical and electrochemical reactions taking place simultaneously in the cell. The electrochemical processes are assumed to take place in a layer of finite thickness at electrode–electrolyte interfaces. A repeating unit of a planar anode-supported SOFC with co-flow configuration is investigated. Step changes of working voltage and fuel composition are applied to the cell. Results for the dynamic profiles of the temperature, the current density and the activation overpotential distributions in the cell are presented and discussed.     

Thermo-electrochemical modeling of ammonia-fueled solid oxide fuel cells considering ammonia thermal decomposition in the anode

Ammonia (NH₃) is a promising hydrogen carrier and a possible fuel for use in Solid Oxide Fuel Cells (SOFCs). In this study, a 2D thermo-electrochemical model is developed to investigate the heat/mass transfer, chemical (ammonia thermal decomposition) and electrochemical reactions in a planar SOFC running on ammonia. The model integrates three sub-models: (1) an electrochemical model relating the current density-voltage characteristics; (2) a chemical model calculating the rate of ammonia thermal decomposition reaction; (3) a 2D computational fluid dynamics (CFD) model that simulates the heat and mass transfer phenomena. Simulations are conducted to study the complicated physical-chemical processes in NH₃-fueled SOFCs. It is found that increasing the inlet temperature of NH₃-fueled SOFC is favorable for a higher electric output, but the temperature gradient in the SOFC is considerably higher, particularly near the inlet of the SOFC. The effects of operating potential and inlet gas velocity on NH₃-fueled SOFC performance are investigated. It is found that an increase in inlet gas velocity from 1 m s⁻¹ to 10 m s⁻¹ slightly decreases the SOFC performance and does not affect the temperature field significantly. For comparison, decreasing the gas velocity to 0.2 m s⁻¹ is more effective to reduce the temperature gradient in SOFC.     

The modeling of a standalone solid-oxide fuel cell auxiliary power unit

In this research, a Simulink model of a standalone vehicular solid-oxide fuel cell (SOFC) auxiliary power unit (APU) is developed. The SOFC APU model consists of three major components: a controller model; a power electronics system model; and an SOFC plant model, including an SOFC stack module, two heat exchanger modules, and a combustor module. This paper discusses the development of the nonlinear dynamic models for the SOFC stacks, the heat exchangers and the combustors. When coupling with a controller model and a power electronic circuit model, the developed SOFC plant model is able to model the thermal dynamics and the electrochemical dynamics inside the SOFC APU components, as well as the transient responses to the electric loading changes. It has been shown that having such a model for the SOFC APU will help design engineers to adjust design parameters to optimize the performance. The modeling results of the SOFC APU heat-up stage and the output voltage response to a sudden load change are presented in this paper. The fuel flow regulation based on fuel utilization is also briefly discussed.     

Electrolytic effect in solid oxide fuel cells running on steam/methane mixture

A two-dimensional model is developed to study the performance of a planar solid oxide fuel cell (SOFC) running on steam/methane mixture. The model considers the heat/mass transfer, electrochemical reactions, direct internal reforming of methane (CH₄), and water gas shift reaction in an SOFC. It is found that at an operating potential of 0.8 V, the upstream and downstream of SOFC work in electrolysis and fuel cell modes, respectively. At the open-circuit voltage, the electricity generated by the downstream part of SOFC is completely consumed by the upstream through electrolysis, which is contrary to our common understanding that electrochemical reactions cease under the open-circuit conditions. In order to inhibit the electrolytic effect, the SOFC can be operated at a lower potential or use partially pre-reformed CH₄ as the fuel. Increasing the inlet gas velocity from 0.5 m s⁻¹ to 5.0 m s⁻¹ does not reduce the electrolytic effect but decreases the SOFC performance.     

Response of a planar solid oxide fuel cell to step load and inlet flow temperature changes

To explore the dynamic characteristics of the SOFC systems and to develop relevant control strategies, a previously developed steady state SOFC model is converted to a dynamic model. The model includes mass, momentum, thermal and electrochemical analysis, as well as the kinetic model of hydrocarbon reactions. Applying two control strategies i.e., cell constant fuel flow rate and constant fuel utilization during the transient time, the model is implemented to analyse the dynamic behaviour of a planar direct internal reforming (DIR) SOFC cell under several step-load changes. Transient response, resulting from an inlet temperature variation, is also investigated. The results show that the relaxation time is strongly related to the thermal behaviour of the cell and the applied control strategy. However, it is almost independent of the load variation magnitude.     

Performance analysis of a SOFC button cell using a CFD model

In this study, a 2-D numerical model is investigated to predict and evaluate the performance of an anode-supported SOFC button cell. The flow field is calculated using 2D Navier–Stokes equations. Heat and mass transfer equations are solved to calculate species and temperature distribution in the cell body and in fuel and air channels. The electrical and electrochemical processes are simulated coupled with the heat and mass transfer model. A discretized network circuit is adopted to the cell geometry for considering the ohmic losses and joule heating of the current that passes through the cell body. The model predicts the cell output voltage, the local EMF and the state variables pressure, temperature and species concentrations. The local electrical parameters are calculated based on the local pressure, temperature and concentration of the species. The numerical results are compared with the experimental data and good agreement is observed. The simulation is carried out for different input fuel flow rates and humidification. The results show how the input fuel mass flow rate and humidification level affects the button cell SOFC performance. In addition, influences of the anode thickness on cell performance through the ohmic over potential are investigated.     

Mechanistic modelling of a cathode-supported tubular solid oxide fuel cell

A two-dimensional mechanistic model of a tubular solid oxide fuel cell (SOFC) considering momentum, energy, mass and charge transport is developed. The model geometry of a single cell comprises an air-preheating tube, air channel, fuel channel, anode, cathode and electrolyte layers. The heat radiation between cell and air-preheating tube is also incorporated into the model. This allows the model to predict heat transfer between the cell and air-preheating tube accurately. The model is validated and shows good agreement with literature data. It is anticipated that this model can be used to help develop efficient fuel cell designs and set operating variables under practical conditions. The transport phenomena inside the cell, including gas flow behaviour, temperature, overpotential, current density and species concentration, are analysed and discussed in detail. Fuel and air velocities are found to vary along flow passages depending on the local temperature and species concentrations. This model demonstrates the importance of incorporating heat radiation into a tubular SOFC model. Furthermore, the model shows that the overall cell performance is limited by O₂ diffusion through the thick porous cathode and points to the development of new cathode materials and designs being important avenues to enhance cell performance.     

Charge,mass and heat transfer interactions in solid oxide fuel cells operated with different fuel gases—A sensitivity analysis

The interaction between charge, heat and mass transfer occurring in SOFCs is investigated applying a finite-volume-based SOFC model. The strong interactions are the consequence of the high degree of integration of different processes (chemical/electrochemical reactions, diffusion, heat and mass transfer) within SOFCs. The understanding of these interactions is a key for the future development and application of SOFCs. The investigation was conducted by means of a sensitivity analysis for two different fuel gases, where one gas features a considerable amount of methane inducing steam reforming reactions as additional disturbance factor in the energy and mass balance system of SOFCs. In order to isolate the impact of the varied model parameters and the according changes in the interactions of charge, mass and heat transfer from side effects, the sensitivity analysis was conducted at constant fuel utilization. It was found that the impact of different fuel gases on the operational conditions of SOFCs dominates geometrical and material-induced phenomena. The power output was most affected by the fuel, followed by the values for the activation polarization activation energy that reflects the employed electrode catalysts activity.     

An analytical model of view factors for radiation heat transfer in planar and tubular solid oxide fuel cells

Radiant heat transfer plays an important role in the distribution of cell temperature and current density in solid oxide fuel cells (SOFC). The objective of this paper is to introduce a mathematical model of view factors for radiation heat exchange in an in-house longitudinally distributed SOFC model. A differential view factor model is first developed for planar and tubular SOFC configurations, but is found invalid when the infinitesimal element size is comparable to the characteristic size. Then, a finite-difference view factor model is developed to solve the problem of discontinuities in the differential view factor model. Starting from a classical problem of convective and radiant heat transfer for a transparent gas flow in a gray-wall tube, a fast and accurate computation is available for the finite-difference view factor model without extra mathematical derivations of the governing equations. Compared to the simple modeling which only takes into account the surface-to-surface radiation exchange between two directly opposed elements, the detailed radiation model based on analytical view factors predicts more uniform distribution of cell temperature and current density in the overall SOFC modeling.     

Multi-physics modeling of a symmetric flat-tube solid oxide fuel cell with internal methane steam reforming

Methane is regarded as one of the ideal fuels for solid oxide fuel cells (SOFCs) due to its huge reserves and transportation properties. In this study, a 3D numerical model coupling with chemical reaction, electrochemical reaction, mass transfer, charge transfer, and heat transfer is developed to understand the heat and mass transfer processes of methane steam direct internal reforming based on double-sided cathodes (DSC) SOFC. After the model verification, the parametric simulations are performed to study the effects of operating voltage, inlet temperature, and steam to carbon (S/C) ratio on the performance of a DSC. It is found that the non-uniform distribution of flow rate among channels results in the non-uniform distribution of each physical field. Increasing the inlet temperature significantly enhances the performance of DSC, however, when the temperature is above 1073 K, the concentration loss and the temperature gradient of DSC increase, which is not conducive to the long-term operation of the DSC. In addition, we revealed the effect of the S/C ratios on the heat and mass transfer process. This study provides an insight into the heat and mass transfer process of SOFC with a mixture of steam and methane and operating conditions for enhancing the performance.     

Three-dimensional computational analysis of gas and heat transport phenomena in ducts relevant for anode-supported solid oxide fuel cells

Various transport phenomena occurring in an anode duct of medium temperature solid oxide fuel cell (SOFC) have been simulated and analyzed by a fully three-dimensional calculation method. The considered composite duct consists of a thick porous layer, the gas flow duct and solid current interconnector. Unique fuel cell boundary and interfacial conditions, such as the combined thermal boundary conditions on solid walls, mass transfer associated with the electrochemical reaction and gas permeation across the interface, were applied in the analysis. Based on three characteristic ratios proposed in this study, gas flow and heat transfer were investigated and presented in terms of friction factors and Nusselt numbers. It was revealed that, among various parameters, the duct configuration and properties of the porous anode layer have significant effects on both gas flow and heat transfer of anode-supported SOFC ducts. The results from this study can be applied in fuel cell overall modeling methods, such as those considering unit/stack level modeling.     

Critical issues in heat transfer for fuel cell systems

The current state of the art in fuel cell system development will be reviewed with an emphasis of the critical issues on heat transfer.

The heat transfer issues for both PEM based systems and SOFC based fuel cell systems will be addressed.

For systems that are based on hydrocarbon fuels a reforming step is needed and critical heat transfer issues are also present in this fuel processing part of the system where the primary feedstock is converted to reformate. Also, in both the PEM and SOFC fuel cell itself, heat transfer is a critical issue. It will be shown what are the implications of the fuel cell heat transfer to the total system architecture for the various fuel cell applications (stationary power, transport).

The heat transfer issues in fuel cell system development will be clarified with several examples.     

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%.     

Novel solid oxide fuel cell system controller for rapid load following

A novel SOFC system control strategy has been developed for rapid load following. The strategy was motivated from the performance of a baseline control strategy developed from control concepts in the literature. The basis for the fuel cell system control concepts are explained by a simplified order of magnitude time scale analysis. The control concepts are then investigated in a detailed quasi-two-dimensional integrated dynamic system model that resolves the physics of heat transfer, chemical kinetics, mass convection and electrochemistry within the system.     

Thermal Modeling and Management of Solid Oxide Fuel Cells Operating with Internally Reformed Methane

A detailed three-dimensional mechanistic model of a large-scale solid oxide fuel cell (SOFC) unit running on partially pre-reformed methane is developed. The model considers the coupling effects of chemical and electrochemical reactions, mass transport, momentum and heat transfer in the SOFC unit. After model validation, parametric simulations are conducted to investigate how the methane pre-reforming ratio affects the transport and electrochemistry of the SOFC unit. It is found that the methane steam reforming reaction has a “smoothing effect”, which can achieve more uniform distributions of gas compositions, current density and temperature among the cell plane. In the case of 1500 W/m² power density output, adding 20% methane absorbs 50% of internal heat production inside the cell, reduces the maximum temperature difference inside the cell from 70 K to 22 K and reduces the cathode air supply by 75%, compared to the condition of completely pre-reforming of methane. Under specific operating conditions, the pre-reforming ratio of methane has an optimal range for obtaining a good temperature distribution and good cell performance.     

Comparison of heat and mass transfer between planar and MOLB-type SOFCs

A numerical simulation tool for calculating the planar and mono-block layer built (MOLB) type solid oxide fuel cells (SOFC) is described. The tool combines the commercial computational fluid dynamics simulation code with an electrochemical calculation subroutine. Its function is to simulate the heat and mass transfer and to predict the temperature distribution and mass fraction of gaseous species in the SOFC system. The three-dimensional geometry model of SOFC was designed to simulate a co-flow case and counter-flow case. The finite volume method was employed to calculate the conservation equations of mass, momentum and energy. Moreover, the influences of working conditions on the performances of planar and MOLB-type SOFCs were also discussed and compared, such as the delivery rate of gas and the components of fuel gas. Simulation results show that the MOLB-type SOFC has higher fuel utilization than the planar SOFC. For the co-flow case, average temperatures of PEN (positive electrode–electrolyte–negative electrode) in both types of SOFCs rise with the increase in delivery rate and mass fraction of hydrogen. In particular, the temperature of planar SOFC is more sensitive to the working conditions. In order to decrease the average temperatures in SOFC, it is effective to increase the delivery rate of air.