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Modeling of Cross-Flow Stack: Sensitivity to Thermal Properties of the Materials
Abstract
LENI activities in SOFC are focused on development of a new planar stack concept based on anode supported cells in collaboration with the company HTceramix SA. Modeling of repeat element, stack and systems is starting in parallel. This work presents a model of a SOFC stack in cross flow configuration. Concentrations, temperature and current density fields are computed, with a focus on sensitivity study for thermal parameters, while operating parameters are kept constant for the different cases. The main parameter considered was the thickness of the metallic interconnect and the related thermal conductivity. Stack height and cell size effects are presented as well. Importance of the temperature field on the design point and degradation behavior is briefly discussed.
... Different flow designs considered are shown inFig. 7. The stack and repeat element model, implemented in gPROMS, is based on a 2D flow field description and volume averaging for the solid energy equations272829 where radiative boundary conditions are applied on the faces of the stack (border of the cells and the first and last repeat element). Degradation is temperature activated as the diffusion of oxygen at the interconnect interface increases with temperature. ...
... s significantly with the number of cells from 8.7% for a 5 cells stack to 11.5% for a 30 cells stack. For the border cells, the degradation rate is almost constant with the number of cells. This is explained by the strong heat loss at the stack extremes that prevents the temperature level to rise significantly with the number of cells (see in refs. [27,29]). This non-homogeneous degradation rate could lead to modify the cell potential profile along the height of the stack; initially, owing to the temperature distribution, the cells in the middle are performing better than the cells on the border but degradation leads to a quasi homogeneous profile for 10,000 h. ...
Reliability of SOFC stacks is a complex and key issue. This paper presents a simulation study including some degradation processes, namely, interconnect degradation and the anode reoxidation potential. Quantification for these phenomena has been included in a repeat element model to simulate stack degradation and study the influence of design and operating parameters on the degradation. Interconnect degradation is based on Wagner’s law for oxide scale growth, parameters applying to metallic interconnects used in planar SOFCs are used. Anode re-oxidation is modeled by thermodynamic equilibrium which allows identification of the operating conditions where the anode is likely to be re-oxidized. Simulations have been carried out for a large number of cases at different current density, fuel utilization and temperature, for 2 different stack designs (base-case and modified design). Using an appropriate criterion to express degradation, all these cases point to a clear trade-off between interconnect degradation and local temperature. The base case design is likely to be exposed to anode reoxidation.
Electrical output behaviour obtained on solid oxide fuel cell stacks, based on planar anode supported cells (50 or 100 cm2 active area) and metallic interconnects, is reported. Stacks (1–12 cells) have been operated with cathode air and anode hydrogen flows between 750 and 800 °C operating temperature. At first polarisation, an activation phase (increase in power density) is typically observed, ascribed to the cathode but not clarified. Activation may extend over days or weeks. The materials are fairly resistant to thermal cycling. A 1-cell stack cycled five times in 4 days at heating/cooling rates of 100–300 K h−1, showed no accelerated degradation. In a 5-cell stack, open circuit voltage (OCV) of all cells remained constant after three full cycles (800–25 °C). Power output is little affected by air flow but markedly influenced by small fuel flow variation. Fuel utilisation reached 88% in one 5-cell stack test. Performance homogeneity between cells lay at ±4–8% for three different 5- or 6-cell stacks, but was poor for a 12-cell stack with respect to the border cells. Degradation of a 1-cell stack operated for 5500 h showed clear dependence on operating conditions (cell voltage, fuel conversion), believed to be related to anode reoxidation (Ni). A 6-cell stack (50 cm2 cells) delivering 100 Wel at 790 °C (1 kWel L−1 or 0.34 W cm−2) went through a fuel supply interruption and a thermal cycle, with one out of the six cells slightly underperforming after these events. This cell was eventually responsible (hot spot) for stack failure.
A model for planar solid oxide fuel cell repeat elements and stacks has been developed. Distribution of concentrations, reaction rates and temperatures (both gases and solids) are computed as well as overall performance results. Specific experiments provide inputs to the model by a parameter estimation method. The modeling approach developed allows to compare several configurations. As the number of design parameters is large (from cell size, component thicknesses to gas flow configuration), the model is designed to change easily these parameters so as to explore as many cases as possible. This is particularly true for the flow configuration (inlet position, outlets) for which several options are considered. This model assists in choosing a configuration and allows to perform sensitivity studies in an efficient way (without having to produce a new mesh such as for CFD tools) or to be combined with an optimization tool. A first validation with experimental results, performed on a particular stack design, is presented. Issues of model accuracy and sensitivity to uncertain inputs are discussed.
The porosity, composition, and temperature dependence of thermal properties in porous Ni/yttria-stabilized zirconia (YSZ) cermets has been investigated at high temperatures by the laser flash diffusivity method. At a temperature range of 1073 to 1273 K, there is no temperature dependence of thermal diffusivity of the cermets. Observable, however, is a slight increase in both of specific heat and thermal conductivity with an increase in temperature. Although the specific heat is governed by the law of mixing in composition, it is independent of the porosity. Pores in the cermet act as heat barriers to prevent heat transfer, in which thermal conductivity is regarded as zero. The relationship between thermal conductivity and porosity can be expressed by the resultant conductivity calculated on the basis of the modified effective medium theory. In this calculation, a porous Ni/YSZ cermet is regarded as a simple cubic resistance network composed of two kinds of unit resistors corresponding to the solid and pore phases. Moreover, the composition dependence of the thermal conductivity of a dense Ni/YSZ cermet could be expressed using the resultant conductivity of the resistance network of unit resisters corresponding to Ni and YSZ. On the basis of these results, the following equation expressing the thermal conductivity of porous Ni/YSZ cermets λC/Wm−1 K−1, has been derived as a function of Ni-volume fraction for total solids VNi, and porosity P, for 1273 K(Remark: Graphics omitted.)where KA⁄Wm−1K−1=0.16−55.62VNi+195.7VNi2, KB⁄(Wm−1K−1)2=95.23+1432.3VNi+1257VNi2. The validity is confirmed.
This paper identifies a number of key issues regarding the development of general modelling languages for combined lumped and distributed parameter processes, and proposes one such language. The latter has been implemented in the gPROMS process modelling system and permits the mathematical modelling of arbitrarily complex unit operations that are distributed over rectangular domains in terms of mixed systems of integral, partial differential, and algebraic equations (IPDAEs). Following language translation, validation and analysis, the method of lines is employed automatically to convert the IPDAEs to sets of ordinary differential-algebraic equations (DAEs). The latter are then solved simultaneously with the DAEs that model the behaviour of the lumped parameter units in the process. Three examples are presented to illustrate the capability of the proposed modelling system to deal with a wide variety of complex processes described in terms of IPDAEs.
Modeling activities at PNNL support design and development of modular SOFC systems. The SOFC stack modeling capability at PNNL has developed to a level at which planar stack designs can be compared and optimized for startup performance. Thermal-fluids and stress modeling is being performed to predict the transient temperature distribution and to determine the thermal stresses based on the temperature distribution. Current efforts also include the development of a model for calculating current density, cell voltage, and heat production in SOFC stacks with hydrogen or other fuels. The model includes the heat generation from both Joule heating and chemical reactions. It also accounts for species production and destruction via mass balance. The model is being linked to the finite element code MARC to allow for the evaluation of temperatures and stresses during steady state operations.
The mathematical simulation of a planar solid oxide fuel cell (SOFC) is presented. The model accounts for three-dimensional and time-dependent effects. Internal methane-steam reforming and recycling of the anode gas are also considered. The effects of different flow manifolding, i.e., cross-, co-, or counter-flow are discussed. After a short description of the mathematical procedure, computational results are presented. In particular the distribution of the gases, of the current density and the solid structure temperature across the cell are shown. Furthermore the effects of different flow manifolding, of radiation from the outer stack surface to the surroundings and of anode gas recycling on the operating conditions of the stack are considered. The response of the cell voltage to a load change is also discussed.
A three-dimensional mathematical model for a planar SOFC was constructed. The concentrations of the chemical species, the temperature distribution, the potential distribution, and the current density were calculated using a single-unit model with double channels of co-flow or counter-flow pattern. The finite volume method was employed for the calculation, which is based on the fundamental conservation laws of mass, energy, and electrical charge. The internal or external steam-reforming, the water-shift reaction, and the diffusion of gases in the porous electrodes were taken into the model. The effects of the cell size, the operating voltage and the thermal conductivity of the cell components on the calculated results were investigated. From the simulated temperature distributions in the electrolyte and the inter-connector, the stress distributions were calculated using the finite element method. The results demonstrated that the steam reforming would generate internal stresses of several tens MPa in an electrolyte.
