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.     

Mini CHP based on the electrochemical generator and impeded fluidized bed reactor for methane steam reforming

The paper presents a configuration of mini CHP with the methane reformer and planar solid oxide fuel cell (SOFC) stacks. This mini CHP may produce electricity and superheated steam as well as preheat air and methane for the reformer along with cathode air used in the SOFC stack as an oxidant. Moreover, the mathematical model for this power plant has been created. The thermochemical reactor with impeded fluidized bed for autothermal steam reforming of methane (reformer) considered as the basis for the synthesis gas (syngas) production to fuel SOFC stacks has been studied experimentally as well. A fraction of conversion products has been oxidized by the air fed to the upper region of the impeded fluidized bed in order to carry out the endothermic methane steam reforming in a 1:3 ratio as well as to preheat products of these reactions. Studies have shown that syngas containing 55% of hydrogen could be produced by this reactor. Basic dimensions of the reactor as well as flow rates of air, water and methane for the conversion of methane have been adjusted through mathematical modelling.The paper provides heat balances for the reformer, SOFC stack and waste heat boiler (WHB) intended for generating superheated water steam along with preheating air and methane for the reformer as well as the preheated cathode air. The balances have formed the basis for calculating the following values: the useful product fraction in the reformer; fraction of hydrogen oxidized at SOFC anode; gross electric efficiency; anode temperature; exothermic effect of syngas hydrogen oxidation by air oxygen; excess entropy along with the Gibbs free energy change at standard conditions; electromotive force (EMF) of the fuel cell; specific flow rate of the equivalent fuel for producing electric and heat energy. Calculations have shown that the temperature of hydrogen oxidation products at SOFC anode is 850 °C; gross electric efficiency is 61.0%; EMF of one fuel cell is 0.985 V; fraction of hydrogen oxidized at SOFC anode is 64.6%; specific flow rate of the equivalent fuel for producing electric energy is 0.16 kg of eq.f./(kW·h) while that for heat generation amounts to 44.7 kg of eq.f./(GJ). All specific parameters are in agreement with the results of other studies.     

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 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.     

Evaluation of hydrogen and methane-fuelled solid oxide fuel cell systems for residential applications: System design alternative and parameter study

Design-point and part-load characteristics of a solid oxide fuel cell (SOFC) system, fuelled by methane and hydrogen, are investigated for its prospective use in the residential application. As a part of this activity, a detailed SOFC cell model is developed, evaluated and extended to a stack model. Models of all the required balance of plant components are also developed and are integrated to build a system model. Using this model, two system base cases for methane and hydrogen fuels are introduced. Cogeneration relevant performance figures are investigated for different system configurations and cell parameters i.e. fuel utilization, fuel flow rate, operation voltage and extent of internal fuel reforming. The results show high combined heat and power efficiencies for both cases, with higher thermal-to-electric ratio and lower electric efficiency for the hydrogen-fuelled cases. Performance improvements with radiation air pre-heaters and anode gas recycling are presented and the respective application limits discussed.     

Numerical evaluation of a parallel fuel feeding SOFC–PEFC system using seal-less planar SOFC stack

We propose a system that combines a seal-less planar solid oxide fuel cell (SOFC) stack and polymer electrolyte fuel cell (PEFC) stack. In the proposed system, fuel for the SOFC (SOFC fuel) and fuel for the PEFC (PEFC fuel) are fed to each stack in parallel. The steam reformer for the PEFC fuel surrounds the seal-less planar SOFC stack. Combustion exhaust heat from the SOFC stack is used for reforming the PEFC fuel. We show that the electrical efficiency in the SOFC–PEFC system is 5% higher than that in a simple SOFC system using only a seal-less planar SOFC stack when the SOFC operation temperature is higher than 973 K.     

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.     

Thermal management oriented steady state analysis and optimization of a kW scale solid oxide fuel cell stand-alone system for maximum system efficiency

This research attempts to ensure system safety while to maximize system efficiency by addressing steady state analysis and optimization for solid oxide fuel cell (SOFC) systems. Firstly, a thermal management oriented kW scale SOFC stand-alone system (primarily comprising a planar SOFC stack, a burner, and two heat exchangers) is developed, in which a special consideration for stack spatial temperature management is conducted by introducing an air bypass manifold around heat exchangers. The dynamic model of the system is performed using transient energy, species, and mass conservation equations. Secondly, based on the system model, the effects of operating parameters including fuel utilization (FU), air excess ratio (AE), bypass ratio (BR), and stack voltage (SV) on the system steady-state performances (e.g. system efficiency, stack inlet, stack outlet, and burner temperatures) are revealed. Particularly, an optimal relationship between the system efficiency and the operating parameters is proposed; the maximum system efficiency can certainly be obtained at the inlet outlet temperature critical point of the BR-AE or FU-AE planes for all SV operating points. Finally, according to the optimal relationship, a traverse optimization process is designed, and the maximum system efficiency and safe operating parameters at any efficient SV operating point are calculated. The results provide an optimal reference trajectory for control design, where the system is safe and efficiency optimization. Moreover, the results reveal two important system characteristics: (1) the burner operates within safe temperature zone as long as the temperature of the upstream stack is well controlled; (2) the control design for the system is a nonlinear optimal control with switching structure, which is a challenging control issue.     

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.     

Performance analysis for the part-load operation of a solid oxide fuel cell–micro gas turbine hybrid system

In this paper, the performance evaluation of a solid oxide fuel cell (SOFC)–micro gas turbine (MGT) hybrid power generation system under the part-load operation was studied numerically. The present analysis code includes distributed parameters model of the cell stack module. The conversions of chemical species for electrochemical process and fuel reformation process are considered. Besides the temperature distributions of the working fluids and each solid part of cell module by accounting heat generation and heat transfers, are taken into calculation. Including all of them, comprehensive energy balance in the cell stack module is calculated. The variable MGT rotational speed operation scheme is adopted for the part-load operation. It will be made evident that the power generation efficiency of the hybrid system decreases together with the power output. The major reason for the performance degradation is the operating temperature reduction in the SOFC module, which is caused by decreasing the fuel supply and the heat generation in the cells. This reduction is also connected to the air flow rate supplement. The variable MGT rotational speed control requires flexible air flow regulations to maintain the SOFC operating temperature. It will lead to high efficient operation of the hybrid system.     

Prediction of the performance of a solid oxide fuel cell fuelled with biosyngas: Influence of different steam-reforming reaction kinetic parameters

SOFCs are often designed to operate with specific fuels, quite often natural gas. CFD modeling is often used to arrive at efficient and safe SOFC designs. Therefore, when an SOFC is fed with different fuels, i.e., biosyngas, CFD can be used as a tool to predict whether the cell and stack will be safe and operate efficiently, and thus can give suggestions for the operation strategies for SOFCs. For that reason, a combined mass and heat transport model of an SOFC (single channel) has been developed for an anode-supported SOFC fed with biosyngas with special attention to the reaction kinetics of the direct internal reforming (DIR) reaction together with the water–gas shift reaction. An SOFC design jointly developed by ECN and Delft University of Technology is employed for the calculations. This work aims to predict the influence of different reforming reaction kinetic parameters on the cell performance by using an anode-supported intermediate temperature DIR planar solid oxide fuel single channel model, under co-flow operation. The DIR reaction of methane, the water–gas shift reaction and the electrochemical oxidation of hydrogen are being considered. As different reaction kinetic models are available in literature and employing them in CFD calculations will yield different results, a comparative analysis is carried out. Several cases were studied with a variety of DIR and water gas shift reaction kinetic parameters available from literature. For the different cases considered, the modeling results show differences in the current density distribution and temperature profile in the channel and in gas concentration profile along the channel. These differences are presented and discussed in detail. Predictions of the behaviors of internal reforming reaction in the reaction zone, and the possibilities of unwanted side reactions such as carbon deposition and Ni oxidation are given with constructive suggestions for future lab experiments.     

Model-based development of low-level control strategies for transient operation of solid oxide fuel cell systems

The exploitation of an SOFC-system model to define and test control and energy management strategies is presented. Such a work is motivated by the increasing interest paid to SOFC technology by industries and governments due to its highly appealing potentialities in terms of energy savings, fuel flexibility, cogeneration, low-pollution and low-noise operation.The core part of the model is the SOFC stack, surrounded by a number of auxiliary devices, i.e. air compressor, regulating pressure valves, heat exchangers, pre-reformer and post-burner. Due to the slow thermal dynamics of SOFCs, a set of three lumped-capacity models describes the dynamic response of fuel cell and heat exchangers to any operation change.The dynamic model was used to develop low-level control strategies aimed at guaranteeing targeted performance while keeping stack temperature derivative within safe limits to reduce stack degradation due to thermal stresses. Control strategies for both cold-start and warmed-up operations were implemented by combining feedforward and feedback approaches. Particularly, the main cold-start control action relies on the precise regulation of methane flow towards anode and post-burner via by-pass valves; this strategy is combined with a cathode air-flow adjustment to have a tight control of both stack temperature gradient and warm-up time. Results are presented to show the potentialities of the proposed model-based approach to: (i) serve as a support to control strategies development and (ii) solve the trade-off between fast SOFC cold-start and avoidance of thermal-stress caused damages.     

Performance analysis of a solid oxide fuel cell with reformed natural gas fuel

In the present study a two‐dimensional model of a tubular solid oxide fuel cell operating in a stack is presented. The model analyzes electrochemistry, momentum, heat and mass transfers inside the cell. Internal steam reforming of the reformed natural gas is considered for hydrogen production and Gibbs energy minimization method is used to calculate the fuel equilibrium species concentrations. The conservation equations for energy, mass, momentum and voltage are solved simultaneously using appropriate numerical techniques. The heat radiation between the preheater and cathode surface is incorporated into the model and local heat transfer coefficients are determined throughout the anode and cathode channels. The developed model has been compared with the experimental and numerical data available in literature. The model is used to study the effect of various operating parameters such as excess air, operating pressure and air inlet temperature and the results are discussed in detail. The results show that a more uniform temperature distribution can be achieved along the cell at higher air‐flow rates and operating pressures and the cell output voltage is enhanced. It is expected that the proposed model can be used as a design tool for SOFC stack in practical applications. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Solid oxide fuel cell operating on liquid organic hydrogen carrier-based hydrogen – making full use of heat integration potentials

Our contribution demonstrates the technological potential of coupling Liquid Organic Hydrogen Carrier (LOHC)-based hydrogen storage and hydrogen-based Solid Oxide Fuel Cell (SOFC) operation. As SOFC operation creates waste heat at a temperature level of more than 600 °C, clever heat transfer from the SOFC operation to the LOHC dehydrogenation process is possible and results in an overall efficiency of 45% (electric output of SOFC vs. lower heating value of LOHC-bound hydrogen). Moreover, we demonstrate that LOHC vapour does not harm the operational stability of a typical 150 W SOFC short stack. By operating the stack with LOHC-saturated hydrogen, operation times of more than 10 years have been simulated without noticeable degradation of SOFC performance.     

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.     

Simulation analysis of a system combining solid oxide and polymer electrolyte fuel cells

We evaluated the performance of system combining a solid oxide fuel cell (SOFC) stack and a polymer electrolyte fuel cell (PEFC) stack by a numerical simulation. We assume that tubular-type SOFCs are used in the SOFC stack. The electrical efficiency of the SOFC–PEFC system increases with increasing oxygen utilization rate in the SOFC stack. This is because the amount of exhaust heat of the SOFC stack used to raise the temperature of air supplied to it decreases as its oxygen utilization rate increases and because that used effectively as the reaction heat of the steam reforming reaction of methane in the stack reformer increases. The electrical efficiency of the SOFC–PEFC system at 190 kW ac is 59% (LHV), which is equal to that of the SOFC-gas turbine combined system at 1014 kW ac.     

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.     

4×4阵列管式固体氧化物燃料电池（SOFC）堆温度场和流场初步分析

通过对实验中管式SOFC堆的数学建模仿真方法，研究实验中的百瓦级4×4管式电池堆内部的流体流动、传热和组分浓度等特性，分析电池参数对电池内部气体流速、温度和浓度分压分布。计算结果和实验测试发现：流场和压力场基本均匀，温度场变化在±34．7K，而阵列电池管开路电压测试值在1．0～1．15vg间，基本满足电堆工作要求。     

Mass transport limitation in inlet periphery of fuel cells: Studied on a planar Solid Oxide Fuel Cell

It was recently clarified on a microtubular Solid Oxide Fuel Cell (SOFC) that the range of mass transport limitation might commence from the inlet periphery (inlet opening and inlet pipe), i.e., the concentration gradient of reactants may extend inward the inlet periphery. For demonstrating that this phenomenon occurs regardless of the form and type of the fuel cell operating at high reactant utilization rate, herein we investigate the mass transport in the anode side of a one-cell stack of a planar SOFC. The investigation leans upon experimental and numerical data analyzed from both conventional (non spatial) and spatial perspectives. The experimental data were spatially obtained in the lateral direction by applying the segmentation method. Regarding analyses let us to confirm that mass transport limitation occurs in the inlet periphery of the planar stack. Besides, the critical ratio of the consumed/supplied mass fluxes of hydrogen is valid for assessing whether the concentration gradient of hydrogen extends inward the inlet periphery. Furthermore, the virtual inlet opening is useful for accurately calculating the mass transport within the active field of the stack via hypothetically preventing the mass transport limitation in the inlet periphery. These findings are expected to help researchers and engineers for accurately designing and characterizing fuel cell systems at varying scales from cells to stacks.