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.     

Numerical analysis of coupled transport and reaction phenomena in an anode-supported flat-tube solid oxide fuel cell

Heat and mass transfer with electrochemical reaction in an anode-supported flat-tube solid oxide fuel cell (FT-SOFC) is studied by means of three-dimensional numerical simulation. The distributions of the reaction fields in the anode-supported FT-SOFC are found to be similar to those in the planar SOFC with co-flow arrangement. However, in comparison with the latter, the concentration and activation overpotentials of the former can be reduced by additional reactant diffusion through the porous rib of the fuel channel. Parametric survey reveals that, for a fixed activation overpotential model, the output voltage can be improved by increasing the pore size of anode, while the cross-sectional geometry has smaller effect on the cell performance. Based on the results of three-dimensional simulation, we also develop a simplified numerical model of anode-supported FT-SOFC, which takes into account the concentration gradients in the thick anode of complex cross-sectional geometry. The simplified model can sufficiently predict the output voltage as well as the distributions of temperature and current density with very low computational cost. Thus, it can be used as a powerful tool for surveying wide range of anode-supported FT-SOFC design parameters.     

Computational analysis of thermo-fluid and electrochemical characteristics of MOLB-type SOFC stacks

A 3D simulation tool for solid oxide fuel cells (SOFCs) was described to simulate the mass, momentum and energy conversions in the mono-block layers built (MOLB)-type SOFC system. Considering the co-flow and counter-flow cell designs, the temperature distributions, variations of reaction species and current densities of the single-unit cell were calculated under the different working conditions. The simulation results show that the co-flow case has more uniform temperature and current density distributions. Similar to the planar SOFC, in co-flow case, increasing fuel delivery rate or hydrogen mass fraction in the fuel, average temperatures of PEN (positive/electrolyte/negative) and current densities rise, but the average temperatures of PEN decrease with increasing the delivery rate of air. In particular, MOLB-type SOFC has some advantages such as: higher hydrogen utilizations, lower temperature difference and higher current density. However the current density distributions are less uniform in MOLB-type SOFC, which is a disadvantage in this type SOFC.     

Numerical analysis of a planar anode-supported SOFC with composite electrodes

This paper investigates a planar anode-supported solid oxide fuel cell (SOFC) with mixed-conducting electrodes. Direct internal methane reforming in the high-temperature cell is included. The numerical model used is three-dimensional, a single computational domain comprising the fuel and air channels and the electrodes–electrolyte assembly. The oxygen ion transport through the electrolyte is mimicked with an algorithm for Fickian diffusion built into the commercial computational package Star-CD. The equations describing transport, chemical and electrochemical processes for mass, momentum, species and energy are solved using Star-CD with in-house developed subroutines. Results for temperature, chemical species and current density distribution for co- and counter-flow configurations are shown and discussed. For co-flow, a sub-cooling effect manifests itself in the methane-rich region near the fuel entrance, while for counter-flow a super-heating effect manifests itself somewhat further downstream, where all the methane is consumed. Effects of varying air inlet conditions are also investigated.     

A simple equation for temperature gradient in a planar SOFC stack

Our recent model of heat transport in a planar SOFC stack is extended to take into account finite hydrogen utilization. The extended model includes the heat balance equations in the interconnect and air flow, and the hydrogen mass balance equation in the anode channel. An approximate analytical expression for the gradient of stack temperature along the air channel is derived. The analytical result is in excellent agreement with the exact numerical solution. The resulting expression can be used for rapid estimate of the temperature gradient in a planar SOFC stack under real operating conditions.     

Numerical modelling and experimental validation of a planar type pre-reformer in SOFC technology

A computational model of the Jülich type pre-reformer and its experimental validation used in solid oxide fuel cells (SOFCs) is introduced. A continuum modelling approach has been attended and its feasibility verified. The fluid flow, heat transfer and chemical reacting species transport within the pre-reformer are numerically solved using 3D computational fluid dynamics (CFD) based on the finite volume method. The model considers the typical sub-components of the pre-reformer including the solid frame, air channels, catalyst and the wire mesh structures. Experimental measurements are used to supply appropriate boundary conditions for the simulations. The predicted results of the simulations are experimentally validated using thermocouples and gas chromatography. The results show good agreement, implying that the proposed model is an invaluable tool that can be used to reduce costly experiments in the design and process optimisation of the pre-reformer.     

Numerical study of thermoelectric characteristics of a planar solid oxide fuel cell with direct internal reforming of methane

A three-dimensional mathematical thermo-fluid model coupling the electrochemical kinetics with fluid dynamics was developed to simulate the heat and mass transfer in planar anode-supported solid oxide fuel cell (SOFC). The internal reforming reactions and electrochemical reactions of carbon monoxide and hydrogen in the porous anode layer were analyzed. The temperature, species mole fraction, current density, overpotential loss and other performance parameters of the single cell unit were obtained by a commercial CFD code (Fluent) and external sub-routine. Results show that the current density produced by electrochemical reactions of carbon monoxide cannot be ignored, the cathode overpotential loss is the biggest one among the three overpotential losses, and that the proper decrease of the operating voltage leads to the increase of the current density, PEN structure temperature, fuel utilization factor, fuel efficiency and power output of the SOFC.     

Design and numerical analysis of a planar anode-supported SOFC stack

In the present study, numerical simulations are conducted to examine the flow characteristics and attributes of electrochemical reactions in the stack through three-dimensional analysis using finite volume approach prior to the fabrication of the SOFC stack. The stack flow uniformity index is employed to investigate the flow uniformity whereas in the case of electrochemical modeling, different mathematical models are adopted to predict the characteristics of activation and ohmic overpotentials that occur during electrochemical reactions in the cell. The normalized mass flow rate is found almost same in each cell with flow uniformity index of 0.999. The calculated voltage and power curves under different average current densities are compared with experimental results for the model validation. The changes in the voltage and power of the SOFC stack, current density, temperature, over potential and reactants distributions in relation to varying amounts of reactants flow are also examined. The current density distribution in each cell is observed to vary along the anode flow direction. The temperature difference in each cell is almost same along the flow direction of reactants, and the irreversible resistance showed an opposite trend with a temperature distribution in each cell.     

Two-dimensional numerical study of temperature field in an anode supported planar SOFC: Effect of the chemical reaction

In the present work the effect of the chemical reaction on the temperature field in an anode supported planar SOFC is numerically studied by the aid of a two-dimensional mathematical model. For the model development the mass transport phenomena, the energy conservation, the species flow governed by Darcy’s law and the electrochemistry are coupled. The finite difference method is used to solve numerically the system of the equations.The temperature field within each component of the SOFC (interconnection, cathode, anode and electrolyte) is calculated via the mathematical model which is implemented in FORTRAN language. The model results demonstrate the effect of different expressions of the chemical heat source, expressed in terms of enthalpy and entropy, on the temperature field and the location of the higher temperatures that occur within the SOFC during its operation.     

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.     

A CFD-based model of a planar SOFC for anode flow field design

This study presents a 3D CFD model of a planar SOFC with internal reforming for anode flow field design. The developed model reflects the influence of various factors on fuel cell performance including flow field design and kinetics of chemical and electrochemical reactions. The case study illustrates applications of the CFD model for planar SOFC with different anode flow field designs. Simulation results indicate the importance of the anode flow field design for planar SOFCs. The model is useful for optimization of fuel cell design and operating conditions.     

Numerical investigation of the chemical and electrochemical characteristics of planar solid oxide fuel cell with direct internal reforming

A fully three-dimensional mathematical model of a planar solid oxide fuel cell (SOFC) with complete direct internal steam reforming was constructed to investigate the chemical and electrochemical characteristics of the porous-electrode-supported (PES)-SOFC developed by the Central Research Institute of Electric Power Industry of Japan. The effective kinetic models developed over the Ni/YSZ anode takes into account the heat transfer and species diffusion limitations in this porous anode. The models were used to simulate the methane steam reforming processes at the co- and counter-flow patterns. The results show that the flow patterns of gas and air have certain effects on cell performance. The cell at the counter-flow has a higher output voltage and output power density at the same operating conditions. At the counter-flow, however, a high hotspot temperature is observed in the anode with a non-fixed position, even when the air inlet flow rate is increased. This is disadvantageous to the cell. Both cell voltage and power density decrease with increased air flow rate.     

Thermal stress analysis of a planar SOFC stack

The aim of this study is, by using finite element analysis (FEA), to characterize the thermal stress distribution in a planar solid oxide fuel cell (SOFC) stack during various stages. The temperature profiles generated by an integrated thermo-electrochemical model were applied to calculate the thermal stress distributions in a multiple-cell SOFC stack by using a three-dimensional (3D) FEA model. The constructed 3D FEA model consists of the complete components used in a practical SOFC stack, including positive electrode–electrolyte–negative electrode (PEN) assembly, interconnect, nickel mesh, and gas-tight glass-ceramic seals. Incorporation of the glass-ceramic sealant, which was never considered in previous studies, into the 3D FEA model would produce more realistic results in thermal stress analysis and enhance the reliability of predicting potential failure locations in an SOFC stack. The effects of stack support condition, viscous behavior of the glass-ceramic sealant, temperature gradient, and thermal expansion mismatch between components were characterized. Modeling results indicated that a change in the support condition at the bottom frame of the SOFC stack would not cause significant changes in thermal stress distribution. Thermal stress distribution did not differ significantly in each unit cell of the multiple-cell stack due to a comparable in-plane temperature profile. By considering the viscous characteristics of the glass-ceramic sealant at temperatures above the glass-transition temperature, relaxation of thermal stresses in the PEN was predicted. The thermal expansion behavior of the metallic interconnect/frame had a greater influence on the thermal stress distribution in the PEN than did that of the glass-ceramic sealant due to the domination of interconnect/frame in the volume of a planar SOFC assembly.     

Total polarization effect on the location of maximum temperature value in planar SOFC

The aim of the present study is the evaluation and the location of the maximum temperature values within the solid and porous components of a planar SOFC under the effect of total polarization: Ohmic, activation, concentration and the chemical reaction.The temperature field in SOFC components (interconnection, cathode, anode and electrolyte) is obtained by developing a mathematical model in FORTRAN language.The mathematical model predictions show the effect of the overpotentials on the thermal gradient and its locations in an SOFC with two geometries: i) anode or ii) electrolyte supported. The results are also discussed, following the SOFC low or high operating temperatures.     

Effect of anode thickness and Cu content on consolidation and performance of planar copper-based anode-supported SOFC

Planar, Cu-containing Gadolinia-doped ceria anode-supported solid oxide fuel cells to be used at intermediate temperature (500–750 °C) were produced in the present work. The Intermediate temperature solid oxide fuel cells were fabricated using Li₂O as sintering aid for Gadolinia-doped ceria, varying the anode-to-electrolyte thickness ratio (r) from 2 to 10 and the CuO content in the anode from 45 vol% to 55 vol%. Co-sintering of the thermo-pressed green cells was carried out at 900 °C for 3 h. The electrolyte densification was favoured by increasing the r value, this being accounted for the enhanced compressive stresses induced by the supporting anode on the electrolyte upon sintering. Larger CuO content positively influences the overall cell performance, due to the improved electronic conductivity of the anode. Nevertheless, CuO concentration cannot exceed 50 vol% because of the tensile stresses (and corresponding flaws) generated in the electrolyte for larger amount. IT-SOFC containing 50 vol% CuO was characterized by an Open Circuit Voltage ≈0.82 V and a maximum power density of 200 mW cm^?2 at 700 °C.     

Analysis of chemical,electrochemical reactions and thermo-fluid flow in methane-feed internal reforming SOFCs: Part I – Modeling and effect of gas concentrations

Direct internal reforming solid oxide fuel cells (DIR SOFCs) have complicated distributions of temperature and species concentrations due to various chemical and electrochemical reactions. The details of these properties are studied by a 3-D numerical simulation in this work. The simulation modeling used governing equations (mass, momentum, energy and species balance equations) generally suitable to porous medium with porosity variable of zero (solid), 0.3 (porous medium) and 1.0 (fluid). Chemical kinetics equations for the internal reforming and shift reactions based on the Langmuir–Hinshelwood model were incorporated. Hydrogen and carbon monoxide oxidations were considered both participating in electrochemical reactions. The experimentally measured current density–potential curves were compared with the simulation data to validate the code, which revealed that the simulation model was able to predict the dilution effect of nitrogen and the mass transfer under high current densities. It is found that the temperature dramatically declined near the fuel inlet with strong endothermic reactions, but it increased along the fluid flow with electrochemically exothermic reactions. A low steam-to-carbon ratio (SCR) led to high steam reforming and water gas shift reaction rates, which generated a greater amount of hydrogen. Therefore, current density increased with low SCR. The average current density due to carbon monoxide electrochemical oxidation varies from 205.3 A/m² under an SCR of 2.0 to 47.6 A/m² under an SCR of 4.0. The average current density due to hydrogen electrochemical oxidation was 5535.4 A/m² under an SCR of 2.0, which was 27 times higher than that of carbon monoxide. The total current density ranged from 5740.8 A/m² under an SCR of 2.0 to 2268.9 A/m² under an SCR of 4.0.     

Numerical study on micro-reformer performance and local transport phenomena of the plate methanol steam micro-reformer

The objective of this work is to investigate the transport phenomena and performance of a plate steam methanol micro-reformer. Micro channels of various height and width ratios are numerically analyzed to understand their effects on the reactant gas transport characteristics and micro-reformer performance. In addition, influences of Reynolds number and geometric size of micro channel on methanol conversion of micro-reformer and gas transport phenomena are also explored. The predicted results demonstrated that better performance is noted for a micro channel reformer with lower aspect-ratio micro channel. This is due to the larger the chemical reaction surface area for a lower aspect-ratio channel reformer. It is also found that the methanol conversion decreases with increasing Reynolds number Re. The results also indicate that the smaller micro channel size experiences a better methanol conversion. This is due to the fact that a smaller micro channel has a much more uniform temperature distribution, which in turn, fuel utilization efficiency is improved for a smaller micro channel reformer.     

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.     

A dimensionless analysis of heat and mass transport in an adsorber with thin fins; uniform pressure approach

A numerical study on heat and mass transfer in an annular adsorbent bed assisted with radial fins for an isobaric adsorption process is performed. A uniform pressure approach is employed to determine the changes of temperature and adsorbate concentration profiles in the adsorbent bed. The governing equations which are heat transfer equation for the adsorbent bed, mass balance equation for the adsorbent particle, and conduction heat transfer equation for the thin fin are non-dimensionalized in order to reduce number of governing parameters. The number of governing parameters is reduced to four as Kutateladze number, thermal diffusivity ratio, dimensionless fin coefficient and dimensionless parameter of Γ which compares mass diffusion in the adsorbent particle to heat transfer through the adsorbent bed. Temperature and adsorbate concentration contours are plotted for different values of defined dimensionless parameters to discuss heat and mass transfer rate in the bed. The average dimensionless temperature and average adsorbate concentration throughout the adsorption process are also presented to compare heat and mass transfer rate of different cases. The values of dimensionless fin coefficient, Γ number and thermal diffusivity ratio are changed from 0.01 to 100, 1 to 10^− 5 and 0.01 to 100, respectively; while the values of Kutateladze number are 1 and 100. The obtained results revealed that heat transfer rate in an adsorbent bed can be enhanced by the fin when the values of thermal diffusivity ratio and fin coefficient are low (i.e., α^? = 0.01, Λ = 0.01). Furthermore, the use of fin in an adsorbent bed with low values of Γ number (i.e. Γ = 10^− 5) does not increase heat transfer rate, significantly.