The technology of the molten carbonate fuel cell (MCFC) has received much attention in the last two decades, and is now at the stage of being scaled-up for commercialization. Since the MCFC operates at a high temperature of around 650℃, the prediction of the temperature distribution is important to avoid hot spots in cells.
Hot spots of extra high temperature cause electrolytic loss by corrosion and reduce the lifetime of the fuel cells. Moreover, the variation of the temperature influences the local current density, and changes the electrical performance of the MCFC.
Therefore, many researchers have investigated the thermal and electrical performance of molten carbonated fuel cells.
In the analysis of an MCFC, the major researches focus on the temperature and current density field in a unit, a stack, or transient state. For a MCFC unit analysis, Wilemski and Wolf [6] used a numerical method to analyze a two-dimensional heat and mass transfer in a large MCFC unit with considering different cell operating conditions and design parameters. Kobayashi et al. [7] used a numerical method to
solve the steady-state temperature distribution of fuel cells with reaction areas of 900cm and 3600 2 cm . They compared experimental data with numerical results, 2 and reasonable agreement between them was reached. Lee et al. [8] calculated the temperature distribution, hydrogen conversion, and current density distribution of a unit molten carbonate fuel cell using constant voltage and constant current density methods. The results indicated that cell performance calculated by the constant voltage method fits better the experimental data than that calculated by the constant current density method.
The analysis on the thermal and electrical performance of a MCFC stack recently grows up, because a MCFC stack had applied in industry. Yoshiba et al. [9]
developed a three-dimensional numerical model to analysis the cell voltage, temperature, and current profile in molten carbonate fuel cell stacks. They compared the effects of flow patterns such as co-flow, counter-flow, and cross-flow, and found that the net output power was highest in co-flow geometry. Later, Yoshiba et al. [10]
investigated the temperature and performance of molten carbonate fuel cell stacks with co-flow configuration by applying a numerical model. Their results indicated that the increase in the partial internal resistance and an insufficiency of supplied fuel gas to the cell could induce differences in cell voltage. He and Chen [11] investigated the three-dimensional temperature distribution, the pressure, the gas concentration, and the current density of a molten carbonate fuel cell of five stacks with three manifolds, using CFD software. The results showed that the maximum temperature
locates at different positions under co-flow, counter-flow, and cross-flow configurations. The maximum temperature difference among the flow configurations is 10-20 ℃ . Recently, Ma et al. [12] developed a practical computational model for a MCFC stack. This model included three dimensional fluid flow, heat and mass transfer, gas-phase and surface chemistry, electrochemistry and structural mechanics, and this model was validated by comparing experimental data. Moreover, the materials and design of an MCFC stack are reviewed by Mugikura et al [13].
In the transient analysis of a MCFC, Lukas et al [14] developed a nonlinear mathematical model of an internal reforming MCFC stack for control system applications. This model can be used to provide realistic evaluations of the responses to varying load demands on the fuel cell stack and to define transient limitations and control requirements. Koh et al. [15] used a software package to predict the dynamic pressure and temperature distribution of gas in a co-flow molten carbonate fuel cell stack based on an assumption of uniform current density. The results indicated that the predicted axial velocity profile precisely reflects the mass change in MCFC, by showing a drop in the volumetric flow in the cathode and an increase in the anode. Later, Koh et al. [16] used computational fluid dynamics code to predict the temperature distribution of a co-flow MCFC stack considering the effects of radiation and variable gas properties. The results showed that the thermal radiation only weakly affects the calculation of the temperature field using the model,
and most of the gas properties can be treated constant, except for the specific heat capacity of the anode gas. He and Chen [17] extended their simulation to investigate the transient behavior of an MCFC stack with the cross-flow configuration; the results showed that the current density profile changes rapidly in the beginning and slowly in the following stage, and the temperature response is slow when the MCFC was under a step voltage change. Xu et al [18] developed a voltage drop and recovery analysis method to estimate the different contributions to the transient behavior of a MCFC.
Their results showed that the model predictions were in reasonable agreement with the experiment data, and it is an efficient tool to analyze the transient characteristics of a MCFC. Heidebrecht and Sundmacher [19] used a general notation in dimensionless form to analyze the transient state of a single counter-flow MCFC with considering the concentration, temperature, and potential field of the gas and the solid phases. This general notation of calculation can easily be extended to describe cross-flow 2D unit and 3D stacks. Lee et al. [20] used a numerical method to analyze the beginning of the operation of a MCFC unit, and investigated the effects of the molar flow rates of gases and the utilization of fuel gas. Their results showed that the time required to approach a steady-state decreases with an increase in the inlet gas-flow rates or the hydrogen utilization.
The electrodes and electrolyte phenomena are important to the overall performance in a MCFC unit or stack, so there are many literatures investigating the analysis on the anode, cathode, and electrolyte. Vallet and Braunstein [21] modified
steady-state equations for composition gradients in battery analogs with binary mixtures of molten salts as electrolytes to apply to a MCFC, and used a numerical method to solve the diffusion-migration equation to predict the development with time of the concentration gradient. Wilemski [22] used individual porous electrode models for calculating the local cell overpotential and current density in a MCFC, and their results had compared with experiment data. Kunz et al [23] developed a cathode model of a MCFC, which was a function of cathode electrolyte content including the effective agglomerate diameter, porosity, tortuosity, and number based on knowledge of the electrode’s pore spectrum. Lee et al. [24] presented the experimental characterization of a MCFC unit with transient response analysis methods such as electrochemical impedance spectroscopy and current interrupt method. They found that the cathode over-potential was controlled by mixed diffusion of oxygen and carbon dioxide. Prins-Jansen et al [25, 26] considered the cathode was constructed by an easiest-to-handle shape of semi-infinite slabs, and used the agglomerate model for porous electrodes in MCFC. Using analytical mathematical tools, this model can give the optimal electrode thickness and agglomerate size based on general problem properties and analytic solutions for special cases. Fehribach et al [27] derived an electrochemical-potential model for the peroxide mechanism describing the electrochemistry of a MCFC cathode. This model made clear the connection to the underlying reaction stoichiometry, and requiring the fewest equations consistent with that stoichiometry. Their results
showed that the mean current density associated with a small portion of electrode may be increased by as much as a factor of five, and on this scale the current density is most sensitive to the electrolyte diffusivity. Bergman et al [4] investigated two cathode materials to elucidate the impact of the cathode material on the formed corrosion layer by polarization measurements and electrochemical impedance spectroscopy. The results indicated that the contact resistance between the cathode and the current collector contributed with a large value to the total cathode polarization. Morita et al [28] estimated the potential of Li/Na carbonate as the MCFC electrolyte by investigating the dependence of the cell performance on the operating conditions and the behavior during long-term performance in several bench-scale cell operations. Arato et al. [29] investigated the limitation on the performance of molten carbonate fuel cells due to gas diffusion phenomena in the porous electrodes when high reactant utilization factors were used. The expression of voltage decay depends on concentration polarization due to hydrogen and carbon dioxide, while oxygen diffusion effects have been considered to be negligible.
Furthermore, the limiting diffusion conditions must also be correctly evaluated for the local temperature and pressure drops. For over-potential from the anode gas to the cathode gas, Bosio et al. [30] presented a model and experimental investigation of electrochemical reactors in the molten carbonate fuel cell. Additionally, they used their formula for total cell resistance, tested with experimental data, to analyze the temperature distribution and current density distribution for a single cell and stacks,
using FORTRAN program. Their numerical results agree with the experimental results, and showed that the thermodynamics fails to predict the open circuit voltage because of the effects of gas crossover phenomena at the cell level. Although thermodynamic equilibrium should be established under open circuit conditions in principle, short circuit electrical currents circulate within the cell, and the consequent voltage loss is responsible for irreversibility.
For a power plant, there are also many researches analyze its overall efficient by using a simple or rapid calculation for a MCFC. Mangold and Sheng [31] applied a reduced nonlinear model to solve a planar molten carbonate fuel cell with cross-flow.
Since the reduced model was of the lower order than the original model, it markedly reduced the computational time. Therefore, this model was suitable for application in predicting the behavior of a control system in a power plant. He [32] presented a simulation model for investigating the dynamic performance of MCFC power-generation systems. This simulation model consists of nine types of component models, which are fuel cell, external reformer, steam generator, water separator, rotation equipment, heat exchanger, DC/AC invertor, pipeline and control valve. Later, He [33] extended his analysis to a MCFC power generation system including twelve types of component models. De Simon et al [34] simulated a global MCFC power plant in steady state. This simulation can conduct a sensitivity analysis with the preliminary input specification, and find the process parameters whose change improves the global efficiency. Yoshiba et al [35] calculated the
materials and heat balance of integrated coal gasification and MCFC combined system with considering the electricity generating performance of the practical cell.
The results showed that the net thermal efficiency of the anode gas recycling system has a peak for carbon dioxide partial pressure where the net thermal efficiency of the anode heat exchange system increases as the carbon dioxide partial pressure of the cathode gas decreases. Recently, Baranak et al [36] developed a MCFC model for a unit analysis with considering several performance model equations separately for anode and cathode, and then they applied this model into a process simulation software to simulate a power system.
In a MCFC, there are simultaneous reactions in anode side, which are chemical reaction in anode, reforming reaction, and water-gas shift reaction. Most MCFC use internal reformer because of its simplicity in structure. Park et al [37] investigated the effects of the reformer in an internal-reforming MCFC on the temperature distributions, conversion of methane, and compositions of gases by a numerical method. Their results indicated that the methane-reforming reaction and the water-gas shift reaction occur simultaneously and the conversion of methane to hydrogen reached 99%, and the endothermic-reforming reaction contributes to a uniform temperature distribution. Seo et al [38] analyzed the performance and operation results of an external-reformer that supplied synthesis gases to a 100kW class MCFC. In order to maintain the outlet temperature of the reforming reactor over 580°C, it is necessary to heat the reformed gases at the convection zone of
combustion gases. Kim et al [39] discussed the effects of water-gas shift reaction on the temperature distribution, voltage distribution, conversion, and performance in a MCFC unit. Their results indicated that the voltage calculated without the shift reaction would be higher than the real value, and the effect of the shift reaction on the voltage distribution and cell performance is quite small.
Bosio et al [40] reported the development of molten carbonate fuel cell technology at Ansaldo Ricerche, from small-scale single cell up to stacks of several KW capacities, for industrial applications. Although the report showed that MCFC technology had been successfully tested on stacks in the kW power class, the control of the start-up phase, electrolyte migration through the manifolds and gas feed distribution have not yet been to be solved. Notably, the gas feed distribution in [40]
identified the variation of mole flow rate in different stacks. Hence, the stack nearest the anode gas inlet duct has largest flow rate and the farthest one has the lowest. The cross-sectional geometry of a fuel cell is similar to that of a heat exchanger, whose inlet distributor is responsible for a non-uniform flow distribution in the frontal area.
Therefore, the maldistribution of the inlet flow rate on the frontal area is realistic and it must affect the performance of fuel cells. In the research of a heat exchanger, Chiou [41] first investigated the thermal performance deterioration in a cross-flow heat exchanger due to the flow non-uniformity. Later, Yuan [42, 43] analyzed the thermal performance and exergy of a three-fluid cross-flow heat exchanger with considering a non-uniform inlet flow. The results showed that most non-uniform
will drop the performance of a heat exchanger, but some of the non-uniform profiles in a three-fluid cross-flow heat exchanger may promote the performance.
Hirata and Hori [44] adopted a numerical method to examine the relationships among the gas flow uniformities in the planar direction, the gas flow uniformity in the stacking direction, and the cell performance in a co-flow MCFC. Their results showed that the gas flow uniformity in the stacking direction is about two to ten times that in the planar direction. Later, Hirata et al [45] investigated the relationship between the gas channel height, the gas flow characteristics, and the gas diffusion characteristics in a plate heat-exchanger type MCFC stack. They used numerical method to evaluate the effect of the gas channel height on the uniformity and pressure loss of the gas flow. Recently, Okada et al [46] presented an investigation of the gas distribution in a large-scale stack with internal reforming MCFC stack. They proposed a large-scale stack divided into four blocks from the point of view of the gas flow scheme in order to achieve more uniform supply gas to each cell. The results showed that the flow variation among the four blocks is less than 1.5%, and it can improve the prospects for a MCFC stack.