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.     

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.     

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.     

进口温度不均匀对涡轮叶片热应力的影响

针对航空涡轮叶片的温度场预测问题,采用CFD(computational fluid dynamics)软件和有限元计算理论与方法,以对流冷却叶片的温度场与热应力求解为例,分别计算了涡轮进口温度均匀和不均匀时叶片的温度场和热应力,分析了涡轮进口温度不均匀对叶片热应力的影响,其中叶片温度场的求解采用气热耦合的方法即直接应用CFD软件计算叶片温度场,再依据温度场进行了有限元热应力分析.结果表明,进口温度不均匀时比进口温度均匀时叶片的热应力增大10%左右.     

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.     

Thermal analysis and management of proton exchange membrane fuel cell stacks for automotive vehicle

The thermal management of a proton exchange membrane fuel cell (PEMFC) is crucial for fuel cell vehicles. This paper presents a new simulation model for the water-cooled PEMFC stacks for automotive vehicles and cooling systems. The cooling system model considers both the cooling of the stack and cooling of the compressed air through the intercooler. Theoretical analysis was carried out to calculate the heat dissipation requirements for the cooling system. The case study results show that more than 99.0% of heat dissipation requirement is for thermal management of the PEMFC stack; more than 98.5% of cooling water will be distributed to the stack cooling loop. It is also demonstrated that controlling cooling water flow rate and stack inlet cooling water temperature could effectively satisfy thermal management constraints. These thermal management constraints are differences in stack inlet and outlet cooling water temperature, stack temperature, fan power consumption, and pump power consumption.     

Numerical modeling of manifold design and flow uniformity analysis of an external manifold solid oxide fuel cell stack

Computational fluid dynamics (CFD) technique and experimental measurement are combined to investigate the effects of several geometric parameters on flow uniformity and pressure distribution in an external manifold solid oxide fuel cell (SOFC) stack. The model of numerical simulation is composed of channels, tubes and manifolds based on a realistic 20-cell stack. Analysis results show that gas resistance in the channel can improve the flow uniformity. However, channel resistance only has a limited effect under high mass flow rate. With the increase of inlet tube diameter, the flow uniformity improves gradually but this has little impact on pressure drop. On contrary, the larger diameter of outlet tube reduces the pressure drop effectively with minor improvement on flow uniformity. The dimensions of the flared inlet tube and the round perforated sheet in the manifold are designed to optimize both flow uniformity and pressure drop. Practical experimental stack is established and the velocity in the outlet of the channel is measured. The trends of the experimental measurements are corresponding well with the numerical results. The investigation emphasizes the importance of geometric parameters to gas flow and provides optimized strategies for external manifold SOFC stack.     

Effect of inlet flow maldistribution on the thermal and electrical performance of a molten carbonate fuel cell unit

This study investigates the temperature and current density distributions in a molten carbonate fuel cell unit when the inlet flows of the anode gas and the cathode gas are mal-distributed in eight patterns. The two-dimensional simultaneous partial differential equations of mass, energy and electrochemistry are solved numerically. The results indicate that the maldistribution of anode and cathode gases dominates the current density field and the cell temperature field, respectively. Moreover, the non-uniform inlet flow slightly affects the mean temperature and mean current density, but worsens the distribution of temperature and current density for most maldistribution patterns. According to the results, the variations of the cell temperature in Pattern G and the current density in Pattern D are 12% and 37% greater than those in the uniform pattern when the deviation of the non-uniform profile is 0.25. Consequently, the effect of non-uniform inlet flow on the temperature and current density distribution on the cell plane is evident, and cannot be neglected.     

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.     

Numerical simulation and analysis of thermal stress distributions for a planar solid oxide fuel cell stack with external manifold structure

A three-dimensional numerical model based on the finite element method (FEM) is constructed to calculate the thermal stress distribution in a planar solid oxide fuel cell (SOFC) stack with external manifold structure. The stack is composed of 5 units which include cell, metallic interconnect, seal and anode/cathode current collectors. The temperature profile is described according to measured temperature points in the stack. It can be clearly seen that the maximum stress concentration area appears at the corner of the components when the stack is heated from room temperature (RT) to 780 °C. The effects of stack components on maximum stress concentration have been investigated under the operation temperature, as well as the thermal stress simulation results. It is obvious that the coefficient of thermal expansion (CTE) mismatch between the interconnect and the seal plays an important role in determining the thermal stress distribution in the stack. However, different compressive loads have almost no effect on stress distribution, and the influence of glass-based seal depends on the elastic modulus. The simulation results can be applied for optimizing the structural design of the stack and minimizing the high stress concentration in components.     

Feedback control of solid oxide fuel cell spatial temperature variation

A high performance feedback controller has been developed to minimize SOFC spatial temperature variation following significant load perturbations. For thermal management, spatial temperature variation along SOFC cannot be avoided. However, results indicate that feedback control can be used to manipulate the fuel cell air flow and inlet fuel cell air temperature to maintain a nearly constant SOFC electrode electrolyte assembly temperature profile. For example temperature variations of less than 5 K are obtained for load perturbations of ±25% from nominal. These results are obtained using a centralized control strategy to regulate a distributed temperature profile and manage actuator interactions. The controller is based on H-infinity synthesis using a physical based dynamic model of a single co-flow SOFC repeat cell. The model of the fuel cell spatial temperature response needed for control synthesis was linearized and reduced from nonlinear model of the fuel cell assembly. A single 11 state feedback linear system tested in the full nonlinear model was found to be effective and stable over a wide fuel cell operating envelope (0.82-0.6 V). Overall, simulation of the advanced controller resulted in small and smooth monotonic temperature response to rapid and large load perturbations. This indicates that future SOFC systems can be designed and controlled to have superb load following characteristic with less than previously expected thermal stresses.     

Air and H2 feed systems optimization for open-cathode proton exchange membrane fuel cells

In this study, air and H₂ feed systems optimization for open-cathode proton exchange membrane fuel cells (PEMFCs) has been evaluated. For air feed system, a spoiler was introduced. The air velocity distribution, polarization curve, single-cell voltage distribution, and temperature distribution of the 11-cell open-cathode fuel cell stack with blowing, blowing-spoiler, and drawing air feed system were assessed. On this basis, the influences of the distance between the fan and stack with different air feed systems were investigated. The results show that the application of the spoiler could solve the problem of low air velocity in the middle of the stack and increase stack performance by 7.3%. And drawing air feed system could enhance the heat dissipation capacity of the stack and the uniformity of temperature distribution, resulting in the 7.9% stack performance increase. Optimization of the distance between the fan and stack enhances the full development of turbulence and the rate of heat transfer. In addition, the effects of four different H₂ feed systems and the flow direction between air and hydrogen on the fuel cell performance were also investigated. It is beneficial for open-cathode PEMFC to be operated with the location of the H₂ inlet and outlet staggered in two different endplates for better stack performance and single-cell voltage uniformity. Evidence also shows that the higher performance also could be obtained when the flow direction of air and hydrogen is vertical with lower ohmic resistance, charge and mass transfer resistance. The study contributes to the design of the open-cathode fuel cell stack to get better performance and reliability.     

Liquid water transport in parallel serpentine channels with manifolds on cathode side of a PEM fuel cell stack

Water management in a proton exchange membrane (PEM) fuel cell stack has been a challenging issue on the road to commercialization. This paper presents a numerical investigation of air–water flow in parallel serpentine channels on cathode side of a PEM fuel cell stack by use of the commercial Computational Fluid Dynamics (CFD) software package FLUENT. Different air–water flow behaviours inside the serpentine flow channels with inlet and outlet manifolds were discussed. The results showed that there were significant variations of water distribution and pressure drop in different cells at different times. The “collecting-and-separating effect” due to the serpentine shape of the gas flow channels, the pressure drop change due to the water distribution inside the inlet and outlet manifolds were observed. Several gas flow problems of this type of parallel serpentine channels were identified and useful suggestions were given through investigating the flow patterns inside the channels and manifolds.     

Two-dimensional temperature distribution estimation for a cross-flow planar solid oxide fuel cell stack

The uniform temperature distribution of a cross-flow planar solid oxide fuel cell (SOFC) stack plays an essential role in stack thermal safety and electrical property. However, because of the strict requirements in stack sealing struture, it is hard to acquire the temperature inside the stack using thermal detection devices within an acceptable cost. Therefore, accurately estimating the two-dimensional (2-D) temperature distribution of the cross-flow stack is crucial for its thermal management. In this paper, Firstly, a 2-D mechanism model of a cross-flow planar SOFC stack is established. The stack is divided into 5*5 nodes along the gas flow directions, which can reflect the stack states with moderate computational burden. Then, experimental test data is utilized to modify and validate the stack model, guaranteeing the model accuracy as well as the reliability of model-based state estimator design. Finally, easily-measured stack inputs and outputs are selected, and a temperature distribution estimator combined with unscented kalman filter (UFK) approach is developed to achieve accurate and fast temperature distribution estimation of a cross-flow SOFC stack. Simulation results demonstrate that the UKF-based temperature distribution estimator can precisely and quickly achieve the temperature distribution estimation of the cross-flow stack under both static state and dynamic state changes and is applicable to cross-flow stacks with different size or cell number as well, the maximum estimated absolute error is less than 0.15 K with an absolute error rate of 0.015%, which indicates the developed estimator has good estimation performances.     

Computational model to predict thermal dynamics of planar solid oxide fuel cell stack during start-up process

Solid oxide fuel cell (SOFC) systems have been recognized as the most advanced power generation system with the highest thermal efficiency with a compatibility with wide variety of hydrocarbon fuels, synthetic gas from coal, hydrogen, etc. However, SOFC requires high temperature operation to achieve high ion conductivity of ceramic electrolyte, and thus SOFC should be heated up first before fuel is supplied into the stack. This paper presents computational model for thermal dynamics of planar SOFC stack during start-up process. SOFC stack should be heated up as quickly as possible from ambient temperature to above 700 °C, while minimizing net energy consumption and thermal gradient during the heat up process. Both cathode and anode channels divided by current-collecting ribs were modeled as one-dimensional flow channels with multiple control volumes and all the solid structures were discretized into finite volumes. Two methods for stack-heating were investigated; one is with hot air through cathode channels and the other with electric heating inside a furnace. For the simulation of stack-heating with hot air, transient continuity, flow momentum, and energy equation were applied for discretized control volumes along the flow channels, and energy equations were applied to all the solid structures with appropriate heat transfer model with surrounding solid structures and/or gas channels. All transient governing equations were solved using a time-marching technique to simulate temporal evolution of temperatures of membrane-electrode-assembly (MEA), ribs, interconnects, flow channels, and solid housing structure located inside the insulating chamber. For electrical heating, uniform heat flux was applied to the stack surface with appropriate numerical control algorithm to maintain the surface temperature to certain prescribed value. The developed computational model provides very effective simulation tool to optimize stack-heating process minimizing net heating energy and thermal gradient within the stack.     

Numerical characterization of a microscale solid-oxide fuel cell

In this study, a single unit of planar micro-solid-oxide fuel cell (μSOFC) is investigated numerically to evaluate the influences of flow channel design, oxygen composition, and thermal operating conditions on cell performance. Four flow channel designs are examined under the co-flow configuration: serpentine, double serpentine, rod bundle, and oblique rib. For all designs, the contacts areas of interconnect to electrodes are kept consistent to maintain the ohmic losses at the same level. To characterize the mass transport effects, there are three different compositions, 100% O₂, 50% O₂/50% N₂ and air, fed to the cathode inlet. Different thermal conditions, adiabatic and isothermal, are applied to the outer boundary of the μSOFC and the results are compared. The outcomes suggest that both thermal conditions and oxidant composition show remarkable influences on μSOFC performance. Under adiabatic conditions, the rise of cell temperature causes a decrease in reversible voltage, deteriorating the overall cell competence. When oxygen is diluted with nitrogen, local gas diffusion becomes dominant to the cathode reaction. Bulk flow, on the other hand, plays a minor role in cell performance since there is little deviation in the polarization curves for all flow channel designs, even at high current densities. For comparison, the flow visualization technique is employed to observe the transport phenomena in various flow channel designs. The flow patterns are found to resemble the concentration distribution, providing a useful tool to design μSOFCs.     

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.     

Flow sharing and turbulence phenomena in proton exchange membrane fuel cell stack headers

The distribution of the gas flow in a PEMFC stack is of paramount importance to the stack's performance and lifetime. Uneven flow distribution influences the flow rate through each cell, which in turn causes uneven distribution of the current flow of the entire cell stack and ultimately reduces the performance of the fuel cell stack. In this work, different simulation methods are compared, and large eddy simulations are selected to investigate the flow characteristics in a model stack and study the effects of operating conditions on flow sharing. The simulation results indicate different flow patterns in the inlet header and outlet header; the former features a turbulent entrance region that progressively transits to a laminar region, whereas the latter exhibits a complex flow with jets mixing downstream. Moreover, the flow patterns and distributions for different inlet/outlet configurations, i.e., U-type and Z-type, are investigated. The distribution of the flow through the unit cells for both configurations is different. The Z-type arrangement offers a more uniform flow distribution and has a smaller number of fluctuations than the U-type. The effects of different inlet flow velocity and jet inflow pattern are also studied. The findings from this work can provide guidelines to improve header design.     

Experimental study on spatiotemporal distribution and variation characteristics of temperature in an open cathode proton exchange membrane fuel cell stack

This paper experimentally explores the spatiotemporal distribution and variation characteristics of temperature in an open cathode proton exchange membrane fuel cell stack based on thermal imager and thermocouples inserted in the cathode flow channels. The temperature distribution and evolution during the dynamic process are analyzed in detail. Besides, the effects of air flow rate and load current on the thermal characteristics of the stack are also investigated. The results show that during the start-up, the hot spot first sprouts in the central area and then spreads rapidly to the surrounding area. During the shutdown, the central and lower regions are first cooled, followed by the hydrogen inlet region, and finally the endplates. The temperature during the load stepwise increase is inconsistent with that during the load stepwise decrease, showing a temperature drift phenomenon. Moreover, there is a time lag in the response of temperature and voltage to changes in current.     

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.