An error in solid oxide fuel cell stack modeling

This paper points out an error in the literature and analyzes its effect on electrochemical models of solid oxide fuel cell stacks. A correction is presented.     

A simple equation for temperature gradient in a planar SOFC stack

Our recent model of heat transport in a planar SOFC stack is extended to take into account finite hydrogen utilization. The extended model includes the heat balance equations in the interconnect and air flow, and the hydrogen mass balance equation in the anode channel. An approximate analytical expression for the gradient of stack temperature along the air channel is derived. The analytical result is in excellent agreement with the exact numerical solution. The resulting expression can be used for rapid estimate of the temperature gradient in a planar SOFC stack under real operating conditions.     

Numerical simulation of flow distribution for external manifold design in solid oxide fuel cell stack

In this study, a three dimensional model is constructed to investigate the flow distributions and the pressure variations for a 40-cell solid oxide fuel cell (SOFC) stack. Computational fluid dynamics (CFD) is used to optimize the design parameters of external manifold in the stack. The model consists of equations for the network with chamber structure of manifold. Simulation results indicate that the flow uniformity strongly depends on geometric shapes of manifold, including the joined position between tube and manifold, the dimension of manifold and the number of tubes. The ratio of flow velocity which describes the uniformity of flow distribution can be decreased by optimizing the geometrical structure of manifolds. In addition, it is found that the flow distribution can be intensively influenced by the gas resistance of the stack, which is closely related to the configuration of interconnect channels. The results summarize the importance of structure design of external manifold for stack performance. The numerical results are in good agreement with the experimental measurement in a 40-cell stack.     

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.     

Measurement of the temperature distribution in a large solid oxide fuel cell short stack

During the operation of solid oxide fuel cells (SOFCs), nonhomogeneous electrochemical reactions in both electrodes and boundary conditions may lead to a temperature gradient in the cell which may result in the development of thermal stresses causing the failure of the cell. Thus, in this study, effects of operating parameters (current density, flow configuration and cell size) on the temperature gradient of planar SOFCs are experimentally investigated. Two short stacks are fabricated using a small (16 cm² active area) and a large size (81 cm² active area) scandia alumina stabilized zirconia (ScAlSZ) based electrolyte supported cells fabricated via tape casting and screen printing routes and an experimental set up is devised to measure both the performance and the temperature distribution in short stacks. The temperature distribution is found to be uniform in the small short stack; however, a significant temperature gradient is measured in the large short stack. Temperature measurements in the large short stack show that the temperature close to inlet section is relatively higher than those of other locations for all cases due to the high concentrated fuel resulted in higher electrochemical reactions hence the generated heat. The operation current is found to significantly affect the temperature distribution in the anode gas channel. SEM analyses show the presence of small deformations on the anode surface of the large cell near to the inlet after high current operations.     

High-fidelity stack and system modeling for tubular solid oxide fuel cell system design and thermal management

Effective thermal integration of system components is critical to the performance of small-scale (<10 kW) solid oxide fuel cell systems. This paper presents a steady-state design and simulation tool for a highly-integrated tubular SOFC system. The SOFC is modeled using a high fidelity, one-dimensional tube model coupled to a three-dimensional computational fluid dynamics (CFD) model. Recuperative heat exchange between SOFC tail-gas and inlet cathode air and reformer air/fuel preheat processes are captured within the CFD model. Quasi one-dimensional thermal resistance models of the tail-gas combustor (TGC) and catalytic partial oxidation (CPOx) complete the balance of plant (BoP) and SOFC coupling. The simulation tool is demonstrated on a prototype 66-tube SOFC system with 650 W of nominal gross power. Stack cooling predominately occurs at the external surface of the tubes where radiation accounts for 66-92% of heat transfer. A strong relationship develops between the power output of a tube and its view factor to the relatively cold cylinder wall surrounding the bundle. The bundle geometry yields seven view factor groupings which correspond to seven power groupings with tube powers ranging from 7.6-10.8 W. Furthermore, the low effectiveness of the co-flow recuperator contributes to lower tube powers at the bundle outer periphery.     

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.     

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.     

Silver wire seal design for planar solid oxide fuel cell stack

A method for sealing solid oxide fuel cells with silver wire gaskets was developed and tested. The 1.6 mm diameter gaskets were fitted into machined channels, 1.5 mm deep in the interconnect plates. The channels were machined into 430 stainless steel plate along the edge of both surfaces and around alternate gas inlets. The interconnect plates were 6.35 mm thick, 152.4 mm long and 76.2 mm wide. A one-cell-stack was assembled for pressure testing with a stainless steel sheet in place of the ceramic membrane. The gas connections were brazed to the stack with a nickel–chromium brazing alloy. The apparatus was bolted together and tested for gas leakage at 137.8 kPa between room temperature and 500 °C. At room temperature, the measured leak rate was 5.14 kPa min⁻¹. With the stack heated to 500 °C, the leak rate decreased to 75.8 Pa min⁻¹.     

Processing of high-performance anode-supported planar solid oxide fuel cell

Anode-supported planar single cells of dimensions 5 cm × 5 cm × 1.5 mm and 10 cm × 10 cm × 1.5 mm have been successfully fabricated using inexpensive and simple processing techniques. The process involves room temperature lamination of several porous layers of tapecast NiO–YSZ together with a dense layer of YSZ electrolyte followed by cofiring. The half-cell fabrication is optimized while the electrolyte thickness is lowered down from 40 to 10 μm. The fabricated single cells with screen printed La(Sr)MnO₃ (LSM)–YSZ as cathode active layer and LSM as current collector layer shows very high electrochemical performance although no separate active layer is used on the anode side of the fabricated cells. The single cells are tested with hydrogen on the anode and oxygen on the cathode sides. The current density and power density of a typical coupon cell of diameter 16 mm is found to be ≈1.7 A/cm² and ≈1.2 W/cm², respectively, at a cell voltage of 0.7 V measured at 800 °C. Area specific resistance (ASR) value, evaluated from the current–voltage plot, is as low as 0.205 Ω cm² at 800 °C. The performances of these cells are found to be almost size independent having excellent repeatability.     

Redox stable Ni-YSZ anode support in solid oxide fuel cell stack configuration

State-of-the-art nickel-based SOFC anode-supported cells are highly sensitive to reoxidation of the metal phase at the temperature of utilization. This work presents results on redox stable nickel-YSZ (yttria-stabilized zirconia) anode-supported cells, for both smaller and larger scale cells. A 55 cm² cell was mounted in a SOFC stack repeat element and tested over 40 full redox cycles. Performances and electrochemical impedance results of the repeat element are compared to the smaller sized cells of similar anode support structure.     

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.     

Integrated thermal management strategy and materials for solid oxide fuel cells

The application of positive temperature coefficient (PTC) thermistors to thermal management of solid oxide fuel cells (SOFCs) is considered. A strategy is proposed for eliminating hotspots and reducing temperature gradients in SOFCs via inclusion of a material that exhibits a dramatic change in resistance near the desired maximum cell temperature. Three PTC thermistor materials with transition temperatures near the maximum desirable SOFC operating temperature are identified and screened for compatibility with common SOFC materials. All are found to be unsuitable because of reaction with the SOFC materials or unacceptably small PTC effect.     

Development of 1 kW class solid oxide fuel cell stack using anode-supported planar cells

We have developed a 1 kW class solid oxide fuel cell (SOFC) stack composed of 50 anode-supported planar 120-mm-diameter SOFCs. Intermediate plates, which exhibited negligible deformation under operating conditions, were placed in the stack to cancel out the cumulative error related to the position and angle of the stack parts. The stack provided an electrical conversion efficiency of 54% (based on the lower heating value (LHV) of the methane used as a fuel) and an output of 1120 W when the fuel utilization, current density, and operating temperature were 67%, 0.28 A cm⁻², and 1073 K, respectively. The stack operated stably for almost 700 h.     

Modeling of thermal stresses and lifetime prediction of planar solid oxide fuel cell under thermal cycling conditions

A typical operating temperature of a solid oxide fuel cell (SOFC) is above 600 °C, which leads to severe thermal stresses caused by the difference in material mechanical properties during thermal cycling. Interfacial shear stress and peeling stress are the two types of thermal stresses that can cause the mechanical failure of the SOFC. Two commonly used SOFC configurations (electrolyte-supported and anode-supported) were considered for this study. The paper developed a mathematical model to estimate the thermal stresses and to predict the lifetime of the cell (Ni/8YSZ-YSZ-LSM). Due to the mismatch of the material mechanical properties of the cell layers, a crack nucleation induced by thermal stresses can be predicted by the crack damage growth rate and the initial damage distribution in the interfacial layer for each thermal cycle. It was found that the interfacial shear stress and peeling stress were more concentrated near the electrode free edge areas. The number of cycles needed for failure decreased with the increase in the porosity of electrode. The number of cycle for failure decreased with increase in electrolyte thickness for both anode- and electrolyte-supported SOFC. The model provides insight into the distribution of interfacial shear stress and peeling stress and can also predict damage evolution in a localized damage area in different SOFC configurations.     

Numerical investigations for a solid oxide electrolyte cell stack

The performance of a solid oxide electrolyzer cell (SOEC) is highly related to the stack structure and operating conditions. This work presents numerical investigations on a 10-cell SOEC stack under different operating mass flow rates. The distribution characteristics of the flow field, pressure field and temperature field with different mass flow rates are compared. The cell performances of SOEC at different layers in the stack are investigated and discussed. The simulation results show that the performances of SOECs in the stack are differentiated by mass flow rate and species mass fraction of fuel channels at different heights. Under the small mass flow rate condition, the Nernst voltages and operating voltages of cells at the lower positions are slightly higher than that of cells at upper positions. Under the large mass flow rate condition, the Nernst voltages and operating voltages of the cells in the middle stack is slightly higher than that of the upper and lower cells.     

Control of a solid oxide fuel cell stack based on unmodeled dynamic compensations

To guarantee solid oxide fuel cell (SOFC) safe operation, plenty control strategies have been developed to control stack temperature and voltage within a reasonable range. However, these control approaches ignore unmodeled dynamics of the SOFC system, which may lead to unsatisfactory control results, sometimes even make the system unstable. To overcome this challenge, a unique control strategy which considers unmodeled dynamic compensations of the SOFC system is proposed in this paper. A model of the SOFC system is firstly built, which includes a known linear model and an unmodeled nonlinear dynamic estimation. A nonlinear controller based on the unmodeled dynamic compensation is then developed to force the SOFC to track desired stack temperature and voltage. To evaluate the control performance, the proposed control method is compared with a traditional sliding mode controller. The simulation results show if the unmodeled dynamics have a small effect on the SOFC, both the sliding mode controller and the proposed controller can achieve a precise tracking. If the unmodeled dynamics have a great impact on the SOFC, the temperature and voltage can be well controlled with the proposed control strategy. However, in the sliding mode controller, the temperature and voltage trajectories deviate largely from the reference values.     

Engineered anode structure for enhanced electrochemical performance of anode-supported planar solid oxide fuel cell

A novel approach of fabricating SOFC anode comprising graded compositions in constituent phases having layer wise microstructural variation is reported. Such anode encompasses conventional NiO–YSZ (40 vol% Ni) with higher porosity at the fuel inlet side and Ni–YSZ electroless cermet (28–32 vol% Ni) with less porosity toward the electrolyte. Microstructures and thicknesses of the bilayer anodes (BLA) are varied sequentially from 50 to 250 μm for better thermal compatibility and cell performance. Significant augmentation in performance (3.5 A cm⁻² at 800 °C, 0.7 V) is obtained with engineered trilayer anode (TLA) having conventional anode support in conjunction with layers of electroless cermet each of 50 μm having 28 and 32 vol% Ni. Engineered TLA accounts for substantial reduction both in cell polarization (ohmic ASR: 78 mΩ cm² versus 2835 mΩ cm²; cell impedance: 0.35 Ω cm² versus 0.9 Ω cm²) and degradation rate (76 μV h⁻¹ versus 219 μV h⁻¹) compared to cells fabricated with conventional cermet.     

Effects of operations and structural parameters on the one-cell stack performance of planar solid oxide fuel cell

A three-dimensional mathematical model coupling the electrochemical kinetics with fluid dynamics is developed to simulate the heat and mass transfer in the one-cell stack of planar solid oxide fuel cells (SOFCs). Based on flow uniformity analysis, the distributions of temperature, current density, overpotential loss and other performance parameters in various operating parameters are obtained using a commercial CFD code (Fluent) coupled with the external subroutines programmed by VC++. Numerical flow data are observed in good agreement with experimental results reported in the literature. Results show that the one-cell stack in counter flow case has the advantages in better uniform current density and temperature distributions of PEN (Positive/Electrolyte/Negative) structure in the width direction, higher power output, fuel utilization factor and fuel efficiency than that in co-flow case. For counter flow case, better thermoelectric characteristics are observed in the temperature gradient, power output, fuel utilization factor and fuel efficiency with the decrease in the fuel inlet flow rate or the anode porosity. Increasing the air inlet flow rate and decreasing the fuel inlet temperature will reduce the temperature gradient; power output, fuel utilization factor and fuel efficiency are enhanced with the increase of the air inlet temperature and the decrease of the anode pore size and thickness.