Effect of inlet flow maldistribution in the stacking direction on the performance of a solid oxide fuel cell stack

This study examines the performance of a ten-cell solid oxide fuel cell (SOFC) stack with a non-uniform flow rate in the stacking direction. The author develops a two-dimensional numerical method to solve the electrochemical, mass and energy equations one stack at a time. The energy equations couple the heat exchange between the interconnector and both the cell and the flowing gas of adjacent cells. Moreover, this paper considers two boundary conditions, adiabatic and constant temperature, on the top and bottom faces of the SOFC. The results show that the non-uniform inlet flow rate of the fuel dominates the current density distribution; it causes the cell voltage to vary by over 13% for both boundary conditions. In addition, the constant temperature condition in this study can produce 3% more power than with the adiabatic condition. On the other hand, the air dominates the temperature field of a SOFC, and the non-uniform inlet flow rate of the air produces a variation of 3% in the average cell temperature of the cells when the boundary condition is adiabatic. This non-uniform effect on the electrical performance of each stack is apparently larger than in the transverse direction, which has been examined in our previous research.     

Effect of air flow rate distribution and flowing direction on the thermal stress of a solid oxide fuel cell stack with cross-flow configuration

This study investigates the effect of non-uniform distribution of the air inlet flow rate and change of air flowing direction on the thermal stress of a solid oxide fuel cell stack with cross-flow configuration. This study considers three patterns of air inlet flow rate in the transverse direction of each stack, and five patterns of air inlet flow rate in the stacking direction. The software package for simulation is reliable through an accuracy comparison, and it analyzes the current density, temperature, and thermal stress distribution of a SOFC stack with 20 layers. The results show that the progressively increasing profile of the air inlet flow rate along the x direction drops the cell thermal stress of a SOFC unit. Moreover, the non-uniform profile of air inlet flow rate in the stacking direction affects the position of the region with high thermal stress of the SOFC stack, and changing flow direction of the air obviously drops down the thermal stress without affecting the power generation of the SOFC stack.     

Design and analysis of SOFC stack with different types of external manifolds

In this study, a four-cell stack of anode-supported planar solid oxide fuel cells (SOFCs) was designed and simulated to investigate the flow/heat transport phenomena and the performance of the SOFC stack. This SOFC stack was designed based on the external manifold types with one side open toward the cathode inlet and components such as base station, manifold, end plate, press jig, and housing. To investigate the performance of the SOFC stack, a step-by-step heat and flow analysis was conducted. First, the separator, functioning as a current collector and a gas channel, was designed to have repeated convex shapes. As the boundary of the flow passage was periodic in both streamwise and transverse directions, only a small part of the flow channel was simulated. In the case of simple homogeneous porous media, the computational results for flow resistance could be expressed by following Darcy's Law. Subsequently, these calculation results from the separator flow analysis were used in the housing and stack analysis. Second, the flow of the cathode region in the housing of SOFC stack was analyzed to verify the flow uniformity in the cathode channel of the separators. Finally, a stack analysis was executed using the electrochemical reaction model to investigate the performance and transport phenomena of the stack. Owing to the uniformity in flow and temperature, each SOFC cell exhibited similar contours of reactant gases, temperature, and current density. In the case of two different fuel utilizations with different flow rates, the low fuel utilization performed slightly better than the high fuel utilization.     

基于容阻建模技术的SOFC电堆数值模拟

借助MATLAB软件，通过建模对固体氧化物燃料电池堆的运行进行仿真。为了计算的方便，模型采用了容阻建模技术。采用由质量守恒、能量守恒、动量守恒和电化学过程组成的模型，对SOFC电堆通道中的气体组成、温度分布、电压分布和电流密度分布进行了计算分析。这些分析结果可对电堆的设计提供参考。     

Three‐dimensional nonisothermal modeling of solid oxide fuel cell coupling electrochemical kinetics and species transport

A three‐dimensional (3D) nonisothermal model is developed and applied for anode‐supported planar solid oxide fuel cell (SOFC). The mass and momentum, species, ion, electric, and heat transport equations are solved simultaneously by implementing the electrochemical kinetics and electrochemical reaction as volumetric source terms. The interconnect land limits the O₂ transport under the land and lowers the local current density under the land. The effects of interconnect land width and cathode substrate thickness on SOFC cell performance are quantified in this study. Cathode stoichiometry is found to have a large effect on the SOFC cell temperature distribution. Under low‐cathode stoichiometry, significant temperature gradients are seen in the SOFC cell. Higher‐cathode stoichiometry is beneficial for lower temperature and more uniform current density distribution in SOFC cell. Co‐flow and counter‐flow arrangements are investigated and discussed with the model. Counter‐flow arrangement is found to induce a high temperature and high current density region near the H₂ inlet. On the other hand, co‐flow arrangement leads high temperature and high current density to occur relatively downstream, a slightly lower maximum temperature on cell and considerably more uniform current density distribution. A 67.2‐cm² SOFC cell is simulated considering the side cooling effect. The side cooling effectively lowers the cell temperature, at the same time, causes temperature, current density, and fuel utilization nonuniformity in the across multichannel direction. Because of the strong coupling of the in‐plane current density distribution and temperature distribution, limiting the locally high temperature and temperature gradient is critical for achieving a more uniform current density distribution in anode‐supported planar SOFC.     

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.     

Three-dimensional multi-physics modelling and structural optimization of SOFC large-scale stack and stack tower

Multi-physics modelling of the Solid Oxide Fuel Cell (SOFC) stack requires significant computational resources. Design optimization of large-scale stacks and stack towers has always been a challenge in recent years. This study establishes a three-dimensional multi-physics model based on a two-step coupling using the BP neural network. The comparison between the novel model and the traditional fully coupled model in both accuracy and computing resource requirements are explored. The novel method has high effectiveness for modelling the large-scale stacks. Based on this, planar SOFC 50-cell stacks and 150-cell stack towers are simulated. The results show that, the flow uniformity of fuel distribution of the stack towers can decrease more than 30% comparing with the 50-cell stack, which leads to significant deterioration of the voltage and temperature distribution. The parameters of manifold and buffer area and channel height of the stack tower is optimized to achieve better uniformity of flow and voltage distribution and lower temperature gradient simultaneously.     

Two-dimensional dynamic simulation of a direct internal reforming solid oxide fuel cell

This study presents a two-dimensional mathematical model of a direct internal reforming solid oxide fuel cell (DIR-SOFC) stack which is based on the reforming reaction kinetics, electrochemical model and principles of mass and heat transfer. To stimulate the model and investigate the steady and dynamic performances of the DIR-SOFC stack, we employ a computational approach and several cases are used including standard conditions, and step changes in fuel flow rate, air flow rate and stack voltage. The temperature distribution, current density distribution, gas species molar fraction distributions and dynamic simulation for a cross-flow DIR-SOFC are presented and discussed. The results show that the dynamic responses are different at each point in the stack. The temperature gradients as well as the current density gradients are large in the stack, which should be considered when designing a stack. Further, a moderate increase in the fuel flow rate improves the performances of the stack. A decrease in the air flow rate can raise the stack temperature and increase fuel and oxygen utilizations. An increased output voltage reduces the current density and gas utilizations, resulting in a decrease in the temperature.     

The influence of flow direction variation on the performance of a single cell for an anode-substrate flat-panel solid oxide fuel cell

This study was performed for a computational investigation of a single cell for an anode-substrate flat-panel solid oxide fuel cell (SOFC) to scrutinize the performance related to thermodynamic potential and overpotentials according to three other flow configurations: parallel flow, countercurrent flow, and perpendicular flow. To understand the performance differences based on the typical three flow configurations, the contour plots of temperature, species, and current density were simulated, and the trends and the portions of the diverse overpotentials were analyzed. The calculated results demonstrated that the parallel flow configuration had a tendency to deliver the highest performance and the lowest overpotentials of the three configurations because the temperature and H₂ concentration in the parallel flow configuration were changed countercurrently along the anode flow direction. These overpotentials were complemented by interacting with the more uniform current density and the total impedance induced by the opposite directional change for the temperature and H₂ concentration.In designing the anode-substrate flat-panel SOFC, the uniformity of flow rate in each channel, which affects significantly to both performance and lifetime of the cell, has been checked. From this numerical analysis result, the design performance of single cell was satisfactorily verified by obtaining negligible flow deviation in each channel of the designed separator deviation, which was less than 3% of the average velocity.     

3D CFD model of a multi-cell high-temperature electrolysis stack

A three-dimensional (3D) computational fluid dynamics (CFDs) electrochemical model has been created to model high-temperature electrolysis stack performance and steam electrolysis in the Idaho National Laboratory (INL) Integrated Lab Scale (ILS) experiment. The model is made of 60 planar cells stacked on top of each other operated as solid oxide electrolysis cells (SOECs). Details of the model geometry are specific to a stack that was fabricated by Ceramatec, Inc. [References herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the U.S. Government, any agency thereof, or any company affiliated with the Idaho National Laboratory]. and tested at INL. Inlet and outlet plenum flow and distribution are considered. Mass, momentum, energy, and species conservation and transport are provided via the core features of the commercial CFD code FLUENT. [References herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the U.S. Government, any agency thereof, or any company affiliated with the Idaho National Laboratory]. A solid oxide fuel cell (SOFC) model adds the electrochemical reactions and loss mechanisms and computation of the electric field throughout the cell. The FLUENT SOFC user-defined subroutine was modified for this work to allow for operation in the SOEC mode. Model results provide detailed profiles of temperature, Nernst potential, operating potential, activation over potential, anode-side gas composition, cathode-side gas composition, current density, and hydrogen production over a range of stack operating conditions. Variations in flow distribution and species concentration are discussed. End effects of flow and per-cell voltage are also considered.     

Highly efficient and durable anode-supported SOFC stack with internal manifold structure

We have developed a solid oxide fuel cell (SOFC) stack with an internal manifold structure. The stack, which is composed of 25 anode-supported 100-mm-diameter SOFCs, provided an electrical conversion efficiency of 56% (based on the lower heating value of methane, which was used as a fuel) and an output of 350 W when the fuel utilization, current density, and operating temperature were 75%, 0.3 A cm⁻², and 1073 K, respectively. The electrical efficiency and the output were maintained for 1100 h. The cell voltage fluctuation was ±2% for 25 cells. The relationship between average cell voltage and current density in the 25-cell stack was as almost the same as that in the 1- and 10-cell stacks, which suggests that our stack provides almost the same cell performance regardless the number of the cells.     

Three dimensional CFD modeling and experimental validation of an electrolyte supported solid oxide fuel cell fed with methane-free biogas

In the present study a comprehensive numerical model of a planar cross-flow electrolyte-supported solid oxide fuel cell (SOFC) is reported. This model is solved in a 3D environment using COMSOL Multiphysics software. To verify the simulation results, an experimental set-up of a six-cell stack was built. Cell temperature and current–voltage measurements are used for validation of the simulation results. Good agreement between the simulation results and the experimental measurements is achieved. Temperature validation in addition to the popular current/voltage validation ensures that the model performs well in predicting local processes like chemical reactions. In this study methane-free biogas (CO₂ + H₂) is fed to the SOFC, and the performance of the system is investigated and explained. It is concluded that the methane-free biogas reduces the cooling air flow due to endothermic reverse water gas shift reaction and gives better current density distribution over the cell compared to hydrogen.     

Numerical analysis of output characteristics of tubular SOFC with internal reformer

In the solid oxide fuel cell (SOFC) system, the internal reforming of raw fuel will act as an efficient cooling system. To realize this cooling system, a special design of the internal reformer is required to avoid the inhomogeneous temperature distribution caused by the strong endothermic reforming reaction at the entrance of the internal reformer. For this purpose, a tubular internal reformer with adjusted catalyst density can be inserted into the tubular SOFC stack. By arranging this, the raw fuel flows along the axis of the internal reformer to be moderately reformed and returns at the end of the internal reformer as a sufficiently reformed fuel.In this paper, the output characteristics of this configuration are simulated using mathematical models, in which one-dimensional temperature and molar distributions are computed along the flow direction. By properly mounting the catalyst density in the internal reformer, the temperature distribution of the cell stack becomes moderate, and the power generation efficiency and the exhaust gas temperature are higher. Effects of other operating conditions such as fuel recirculation, fuel inlet temperature, air recirculation and air inlet temperature are also examined under the condition where the maximum temperature of the stack is kept at 1300 K by adjusting the air flow rate. Under this condition, these operating conditions exert a considerable effect on the exhaust temperature but have a slight effect on the efficiency.     

Numerical simulation of intermediate-temperature direct-internal-reforming planar solid oxide fuel cell

A numerical model for an anode-supported intermediate-temperature direct-internal-reforming planar solid oxide fuel cell (SOFC) was developed. In this model, the volume-averaging method is applied to the flow passages in the SOFC by assuming that a porous material is inserted in the passages as a current collector. This treatment reduces the computational time and cost by avoiding a full three-dimensional simulation while maintaining the ability to solve the flow and pressure fields in the streamwise and spanwise directions. In this model, quasi-three-dimensional multicomponent gas flow fields, the temperature field, and the electric potential/current fields were simultaneously solved. The steam-reforming reaction using methane, the water-gas shift reaction, and the electrochemical reactions of hydrogen and carbon monoxide were taken into account. It was found that the endothermic steam-reforming reaction led to a reduction in the local temperature near the inlet and limited the electrochemical reaction rates therein. Computational results indicated that the local temperature and current density distributions can be controlled by tuning the pre-reforming rate. It was also found that a small amount of heat loss from the sidewall can cause significant nonuniformity in the flow and thermal fields in the spanwise direction.     

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.     

Characterization of a novel, highly integrated tubular solid oxide fuel cell system using high-fidelity simulation tools

A novel, highly integrated tubular SOFC system intended for small-scale power is characterized through a series of sensitivity analyses and parametric studies using a previously developed high-fidelity simulation tool. The high-fidelity tubular SOFC system modeling tool is utilized to simulate system-wide performance and capture the thermofluidic coupling between system components. Stack performance prediction is based on 66 anode-supported tubular cells individually evaluated with a 1-D electrochemical cell model coupled to a 3-D computational fluid dynamics model of the cell surroundings. Radiation is the dominate stack cooling mechanism accounting for 66-92% of total heat loss at the outer surface of all cells at baseline conditions. An average temperature difference of nearly 125 °C provides a large driving force for radiation heat transfer from the stack to the cylindrical enclosure surrounding the tube bundle. Consequently, cell power and voltage disparities within the stack are largely a function of the radiation view factor from an individual tube to the surrounding stack can wall. The cells which are connected in electrical series, vary in power from 7.6 to 10.8 W (with a standard deviation, σ = 1.2 W) and cell voltage varies from 0.52 to 0.73 V (with σ = 81 mV) at the simulation baseline conditions. It is observed that high cell voltage and power outputs directly correspond to tubular cells with the smallest radiation view factor to the enclosure wall, and vice versa for tubes exhibiting low performance. Results also reveal effective control variables and operating strategies along with an improved understanding of the effect that design modifications have on system performance. By decreasing the air flowrate into the system by 10%, the stack can wall temperature increases by about 6% which increases the minimum cell voltage to 0.62 V and reduces deviations in cell power and voltage by 31%. A low baseline fuel utilization is increased by decreasing the fuel flowrate and by increasing the stack current demand. Simulation results reveal fuel flow as a poor control variable because excessive tail-gas combustor temperatures limit fuel flow to below 110% of the baseline flowrate. Additionally, system efficiency becomes inversely proportional to fuel utilization over the practical fuel flow range. Stack current is found to be an effective control variable in this type of system because system efficiency becomes directly proportional to fuel utilization. Further, the integrated system acts to dampen temperature spikes when fuel utilization is altered by varying current demand. Radiation remains the dominate heat transfer mechanism within the stack even if stack surfaces are polished lowering emissivities to 0.2. Furthermore, the sensitivity studies point to an optimal system insulation thickness that balances the overall system volume and total conductive heat loss.     

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.     

Mass transfer and cell performance of a unitized regenerative fuel cell with nonuniform depth channel in oxygen‐side flow field

In this study, the cell performance of nonuniform depth and conventional straight channel in a unitized regenerative fuel cell (URFC) is compared. Various shapes of oxygen‐side channel cases are also proposed. Several parameters, such as the distribution of reactants and products and current density and powers in fuel cell (FC) and electrolytic cell (EC) modes, are investigated. A steady‐state model of two‐dimensional, two‐phase, nonisothermal, and coupled electrochemical reaction is developed. Five oxygen‐side channel shapes are also designed, in which the depth along the flow direction is narrowed. Result shows that narrowing the average channel depth can promote and guide the reactant transfer to the catalyst layer and avoid the blocking of the production. Thus, in comparison with the conventional channel, the cell performances of nonuniform depth and shallow straight channel cases are improved in both modes. In addition, with the decrease of average channel depth, the temperature uniformity gets better, which is also conductive to the improvement of cell performance. Furthermore, in FC mode at low voltage and EC mode, the cell net power basically increases with the decrease of the average channel depth ratio. And when the average channel depth is the same, the net power of straight channel is always lower than nonuniform depth case. This study introduces the round‐trip energy efficiency as an evaluation indicator of URFC. This efficiency can be increased by improving the cell performance of both modes, especially at high current density.     

Performance analysis and temperature gradient of solid oxide fuel cell stacks operated with bio-oil sorption-enhanced steam reforming

A high temperature gradient within a solid oxide fuel cell (SOFC) stack is considered a major challenge in SOFC operations. This study investigates the effects of the key parameters on SOFC system efficiency and temperature gradient within a SOFC stack. A 40-cell SOFC stack integrated with a bio-oil sorption-enhanced steam reformer is simulated using MATLAB and DETCHEM. When the air-to-fuel ratio and steam-to-fuel ratio increase, the stack average temperature and temperature gradient decrease. However, a decrease in the stack temperature steadily reduces the system efficiency owing to the tradeoff between the stack performance and thermal balance between heat recovered and consumed by the system. With an increase in the bio-oil flow rate, the system efficiency decreases because of the lower resident time for the electrochemical reaction. This is not, however, beneficial to the maximum temperature gradient. To minimize the temperature gradient of the SOFC stack, a decrease in the bio-oil flow rate is the most effective way. The maximum temperature gradient can be reduced to 14.6 K cm⁻¹ with the stack and system efficiency of 76.58 and 65.18%, respectively, when the SOFC system is operated at an air-to-fuel ratio of 8, steam-to-fuel ratio of 6, and bio-oil flow rate of 0.0041 mol s⁻¹.     

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.