Numerical multi-physical optimization of operating condition and current collecting setup for large-area solid oxide fuel cells

Abstract

Due to the depletion of traditional fossil fuels and the aggravation of related environmental problems, hydrogen energy is gaining more attention all over the world. Solid oxide fuel cell (SOFC) is a promising power generation technology operating on hydrogen with a high efficiency. To further boost the power output of a single cell and thus a single stack, increasing the cell area is an effective route. However, it was recently found that further increasing the effective area of an SOFC single cell with a flat-tubular structure and symmetric double-sided cathodes would result in a lower areal performance. In this work, a multi-physical model is built to study the effect of the effective area on the cell performance. The distribution of different physical fields is systematically analyzed. Optimization of the cell performance is also pursued by systematically tuning the cell operating condition and the current collection setup. An improvement of 42% is revealed by modifying the inlet gas flow rates and by enhancing the current collection. In the future, optimization of cell geometry will be performed to improve the homogeneity of different physical fields and thus to improve the stability of the cell.

Graphical abstract

Keywords

solid oxide fuel cell (SOFC) / large effective area / flow rate / discharge performance / current collection

1 Introduction

The global reliance on fossil fuels has led to the rapid depletion of natural resources and the aggravation of environmental issues [1–6]. To tackle the problem, hydrogen energy has emerged as a prominent and environmentally friendly alternative, gaining more attention worldwide due to its carbon-free nature [7–11]. Solid oxide fuel cell (SOFC) is a power generation device that directly converts the chemical energy in hydrogen into electric energy, offering the advantages of high efficiency, low emission, and reduced noise levels [12–16]. SOFC is suitable for many applications such as transportation, stationary power generation, portable devices, and grid configurations [17–20].

The structure of an SOFC can be mainly divided into two categories, planar type and tubular type. The planar SOFC offers great advantages, including a simple manufacturing process and low cost. In addition, it has a short current transport path, resulting in a high discharge performance. However, it suffers from complicated sealing structures and poor thermal cycle resistance, which can impact the overall lifespan [21]. The tubular SOFC, whose sealing and the assembly of a stack is much easier, boasts a higher mechanical strength. However, its power density is low due to the long current collection path, and its manufacturing requires special equipment [22,23]. In recent years, a novel type of double-sided cathode structure SOFC (DSC-SOFC), combining the advantages of both planar and tubular SOFCs, was proposed [24]. Based on a series of experimental tests on both cell level and stack level, the novel structure has exhibited a strong anti-destructive load and anti-oxidation cycle capabilities [21]. The stability of the cell is largely improved while also achieving a high power density, demonstrating promising commercial application prospects.

To improve the performance of an SOFC stack, one of the key factors is the optimization of the structure and the operation condition of both a single cell and a stack. While the optimization via experimental approached can be tedious, time-consuming, and costly, employing multi-physical modeling can provide insights into the effect of the cell/stack structure and the operation condition on the overall electrochemical performance [25–36]. For instance, Li et al. [25], Khazaee & Rava [26], and Shen et al. [27] respectively investigated the effect of the cross-sectional shape of the flow channel on the cell performance and the distribution of temperature. The results demonstrated that SOFCs with rectangular channel cross-sections performed better. Regarding the interconnect, Jiang et al. [36] and Saied et al. [30] have investigated the effects of gas channel configurations, including serpentine type, straight parallel type, etc., on the electrochemical performance of SOFCs. They also investigated the distribution of different physical fields to elucidate the dependence of the performance on the gas channels. Kong et al. [35] developed a novel interconnector structure design to enhance the current collection and thus the electrochemical performance.

At present, it is desired to increase the effective area of a single cell of SOFC stack in order to increase the power output of a single stack, further simplifying the fabrication procedure and driving down the cost [37,38]. However, the increase in the effective area will significantly hamper the gas transport and lengthen the current collection path within the stack [36]. This phenomenon in turn results in a more uneven distribution of gas, temperature, and current, leading to stress concentration and compromising the electrochemical performance and long-term stability. Two cells with different effective areas have been fabricated (denoted as SOFC_S and SOFC_L, respectively), 3505.5 and 26400 mm², with images shown in Fig.1(a). However, the cell performance is largely reduced by comparing the discharging curves (Fig.1(b)). Therefore, the impacts of the cell area need to be fully investigated and the cell structure and operation condition have yet to be optimized.

In this work, based on a three-dimensional electro-chemical-thermal multi physical numerical model developed previously [36,39], the effect of effective cell area on the electrochemical performance of the latest flat-tubular SOFC with symmetric cathodes is investigated. The distribution of gas composition and flow rate, current density, and temperature are analyzed to gain insights into the key affecting parameters. Based on the numerical model, the gas flowrate and the current collection setup are systematically tuned and optimized for the large-area SOFC single cell.

2 Model

2.1 Geometric model

According to the cell size produced and tested in the laboratory (Fig.1), the corresponding geometric models of SOFC_S and SOFC_L are established, as shown in Fig.2, and the corresponding geometric parameters are listed in Tab.1. The width of the flow channel remains the same while the effective area is enlarged. Given the symmetric design with double-sided cathodes, a symmetric treatment was employed in the calculation, as shown in Fig.3(a). The SOFC single cell consists of a Ni–3 mol% yttria-stabilized zirconia (YSZ) anode support layer embedded with fuel gas channels, a Ni–8 mol.% YSZ anode functional layer, a YSZ electrolyte layer, an La_0.6Sr_0.4Co_0.2Fe_0.8O_3–δ (LSCF) perovskite cathode layer, and metallic alloy ribs on the interconnect. The gas flow direction in the gas channels is illustrated in Fig.3(b).

2.2 Multi-physical model development

The electro-chemical-thermal multi-physical numerical model established previously includes the coupling of governing equations of electrochemical reaction, gas flow, chemical diffusion, and heat transfer processes. The model has been described in detail and the related parameters are given [36,39], thus only a brief description is presented here.

The overall performance of an SOFC is characterized by the characteristic current–voltage curve. In practical operation, various losses are brought by the electrochemical reactions at the electrode-electrolyte interface, the oxygen-ion transport in the electrolyte, and the gas transport in the porous electrodes, i.e., activation polarization, ohmic polarization, and concentration polarization [40,41]. The cell operating voltage can be obtained by subtracting the overpotential induced by the losses from the Nernst voltage of a fuel cell [41,42]. A modified Navier–Stokes equation incorporating Darcy’s term is used to model the momentum transfer of the gases in the flow channels and the porous electrodes [40,43]. The diffusion of species is expressed by Fick’s law combined with Knudsen’s diffusion [44]. During the operation, three heat sources are considered, Joule heat from the electrolyte, activation heat due to the electrochemical reaction, and entropy heat due to the irreversible loss of the reaction. The energy conservation law in the heat transfer model is applied.

2.3 Boundary conditions

The initial boundary temperature of 1023 K is set in the model according to the experimental condition, which is the same as the temperature at the gas inlet. The thermal boundary condition is thermal convection. The current collection is set on the gas inlet and outlet metal tubes, and insulation condition is adopted for other boundaries. In the gas flow field, the gas inlet adopts laminar flow. The default flow rate of hydrogen is 0.6 L/min (equal to 0.5 m/s) and the default flow rate of air is 5 L/min (equal to 8 m/s). The pressure at the outlet is fixed at 1.013 × 10⁵ Pa. The anode is fed with a mixed fuel composed of steam (3 mol.%) and hydrogen (97 mol.%). Meanwhile, the cathode is fed with a mixture composed of oxygen (21 mol.%) and nitrogen (79 mol.%).

2.4 Model validation

Commercial software, COMSOL Multiphysics 5.4, is used to obtain numerical solutions. To verify the established numerical model, the modeled characteristic current–voltage curve is compared with the experimental results. The simulation data of the SOFC_S cell are used in the validation. When 153368, 240533, and 395325 units are used, the simulated average electrolyte current density is 972.46, 971.64, and 972.13 A/m², respectively, indicating that the result is independent of the number of units. To save computational time, 153368 units are selected to perform the calculation. As shown in Fig.4, the simulation result is in good agreement with the experimental data at three different operation temperatures. Therefore, the effectiveness of the multi-physical field model is validated.

3 Results and discussion

3.1 Effect of effective area

With identical boundary conditions, the gas flow rate, concentration of different species, and the electrolyte current density of the two cells with different sizes were extracted from the modeling results and compared, to gain insights into the lower performance of the SOFC_L. To facilitate a direct comparison between the results of the two cells, the same color legend is adopted in each figure.

3.1.1 Effect of the number of air flow channels

Before investigating the effect of the effective cell area on the cell performance, the effect of the number of flow channels is studied. For the fuel channel, as the thickness of the anode remains similar (Tab.1), if the number of the fuel channels remains the same, the shape of the channels will change accordingly. Thus, the number of the fuel channels is determined to increase proportionally with the width of the cell. For the number of the air flow channels, the performance of SOFC_L with 26 channels (Fig.5(a)) and with 65 channels are compared. The average current density of SOFC_L with 26 air flow channels is shown in Fig.5(b), which is deduced to be 767 A/cm². In contrast, that of SOFC_L with 65 flow channels is 856 A/cm². Therefore, to increase the number of the cathode flow channels proportionally leads to a higher electrochemical performance. As a result, the number of the flow channels for both the anode side and the cathode side are set to increase proportionally with increasing effective area in this study.

3.1.2 Stress evaluation of cells with different effective areas

The mechanical stability of the cell is evaluated by the stress level during operation. Fig.6 shows the stress distribution of the cells with different effective areas. For SOFC_S and SOFC_L respectively, the maximum 1st principal stresses are 7.49 and 7.16 MPa in the anode functional layer, 12.86 and 13.65 MPa in the electrolyte layer, and 5.67 and 1.26 MPa in the cathode layer. Overall, the stresses are similar for the two cells with different areas. As a result, the enlarged cell area does not pose any negative effect on the mechanical stability of the cell.

3.1.3 Flow rate distribution in flow channel

Fig.7 shows the flow rate distribution in the anode channel of SOFC_S (Fig.7(a)) and SOFC_L (Fig.7(b)) at a working voltage of 0.9 V. It is observed that the flow rate steadily increases along the direction of gas flow in the anode flow channels. Upon investigating a single channel, it is found that the faster flow rate at the outlet results from the electrochemical conversion of hydrogen to steam. However, the steam possesses a higher molecular weight compared to hydrogen and the flow rate should be lower at the outlet due to the higher average density of the gas. The detailed mechanism needs further investigation. In addition, it is worth mentioning that the flow rate in the flow channel is smaller at the edge of the flow channel as shown in the inset of Fig.7(b). In the flow channel, the gas on the wall of the flow channel loses mechanical energy due to friction. In addition, the gas near the wall of the pipe tends to diffuse into the porous electrode, resulting in a higher flow in the middle of the pipe compared to its edges. When the flow rate distributions of the two sizes of anode gas are compared, the flow rate of the anode channel outlet of SOFC_L is found to be larger than that of SOFC_S.

Fig.8 shows the flow rate distribution of the air in the cathode flow channel of SOFC_S and SOFC_L at a working voltage of 0.9 V. Based on this cathode flow channel structure, a lower flow rate appears in the middle area with vertical flow channels, for both the two cells. A comparison of the results of the two cells indicates that due to a higher length-width ratio of the flow channels in the middle area, the flow rate of SOFC_L is lower than that of SOFC_S. The lower flow rate, which leads to a slower supply of oxygen to the reacting sites, could be a contributing factor to the decreased performance of SOFC_L. Therefore, while increasing the size of the cell, it is necessary to optimize the design of the flow channel structure, in order to have a better flow rate distribution in the flow channel.

3.1.4 Gas composition and distribution

Fig.9 shows the hydrogen mole fraction distribution in the functional layer of the anodes of SOFC_S (Fig.9(a)) and SOFC_L (Fig.9(b)) at a working voltage of 0.9 V. For both cells, the hydrogen concentration reaches the minimum at the gas outlet due to the dilution effect by the steam generation during electrochemical reactions. A comparison of the two cells suggests that the overall hydrogen concentration is much lower for SOFC_L than for SOFC_S. This outcome aligns with expectations, as the total input of hydrogen is the same for the two cells while the total area increases by approximately 6-fold. The fast consumption of the hydron in SOFC_L generates more steam which lowers the hydrogen concentration. In addition, the SOFC_L exhibits a more uniform distribution of the hydrogen concentration, possibly ascribed to the larger convective diffusion rate in the porous medium of SOFC_L due to the increased flow rate.

Fig.10 shows the distribution of oxygen mole fractions in the cathodes of SOFC_S (Fig.10(a)) and SOFC_L (Fig.10(b)) at a working voltage of 0.9 V. Similar to the hydrogen side, the overall oxygen concentration is lower for the SOFC_L, but the oxygen concentration distribution is much more uniform. Further, it appears that the oxygen deficiency is less severe than the hydrogen deficiency shown in Fig.9.

3.1.5 Current density distribution in electrolyte

Fig.11 shows the current density distribution of SOFC_S (Fig.11(a)) and SOFC_L (Fig.11(b)) electrolyte layers at an operating voltage of 0.9 V. It can be observed that the current density distribution bears a similar pattern to the distribution of hydrogen concentration, and that the overall current density is lower in the center of the cell. Especially for SOFC_L, a large area of low current density can be observed in the center area, probably a result of the deficiency in the supply of hydrogen. A conclusion can be drawn from the above analysis that ensuring the adequate supply of reactant gases to the active reaction sites is a pivotal factor in attaining a high performance. The flow rate of the SOFC_L necessitates careful tuning, which will be presented in the next section.

3.2 Effect of inlet gas flow rate

Increased SOFC effective area requires the optimization of the gas inlet flow rates to maximize the advantage of the large cell area. Here, the discharge capabilities of SOFC_L was simulated under various cathode and anode inlet gas flow rate conditions.

3.2.1 Influence of anode inlet gas flow rate

To model the discharge performance of SOFC_L at varied flow rates, ten sets of anode inlet gas flow rates from 0.5 to 5 m/s (with an interval of 0.5 m/s, 1 m/s equaling 3.36 L/min) were created. The inlet air flow rate is kept at 8 m/s. The dependence of the average current density in the electrolyte layer of the cell at a voltage of 0.9 V on the anode gas flow rate is shown in Fig.12. The electrolyte current density first increases as the flow rate increases to 1008 A/m² as the flow rate reaches 3.5 m/s. Then, it decreases slightly and stabilizes at around 990 A/m².

The anode channel flow rate distribution at an anode inlet gas flow rate of 1, 3.5, and 5 m/s is demonstrated in Fig.13. It is observed from Fig.13 that with the increase of the inlet flow rate, the flow rate in the anode flow channel increases. Correspondingly, the distribution of hydrogen mole fraction in the functional anode at different inlet fuel gas flow rates is shown in Fig.14. The hydrogen concentration on the functional anode increases obviously as the flow rate increases from 1 to 3.5 m/s. However, no further improvement on the hydrogen concentration can be observed when the flow rate increases to 5 m/s, aligning with the dependence of the current density on the inlet fuel gas flow rate. Therefore, it can be concluded that the poor performance at inlet fuel gas flow rates (< 3.5 m/s) is due to the deficiency of the supply of hydrogen to the active reaction sites. When operating at higher flow rates, the performance drop could be ascribed to the resulting lower average temperature, as discussed in the subsequent section. Furthermore, it should be noted that although the effective area increases more than 6 times, the optimum inlet gas flow rate is only 3.5 times that of the SOFC_S, indicating a nonlinear relationship between the effective size area and the flow rate.

Fig.15 shows the temperature distribution of the electrolyte layer under different flow rates. The general electrolyte temperature distribution can be used to estimate the internal distribution of the SOFC. The average temperature of the electrolyte layer shows constantly decreases, being 1033.6, 1033.2, and 1032.4 K when the anode inlet gas flow rate is 1, 3.5, and 5 m/s, respectively. The temperature at the anode gas entrance gradually declines as the flow rate increases, and the high temperature distribution is concentrated at the gas outlet, as shown in Fig.15. This phenomenon could be attributed to the higher convective heat dissipation with a higher gas flow rate. As the flow rate escalates, more heat is removed from the cell, potentially leading to lower temperatures. Consequently, the slow electrochemical reaction kinetics at lower temperatures could contribute to the observed lower performance at higher inlet fuel gas flow rates (> 3.5 m/s).

3.2.2 Influence of inlet air flow rate

The electrochemical performance of the large-area cell is simulated at various air flow rates ranging from 4 to 17 m/s (1 m/s equaling 4.11 L/min), with an interval of 1 m/s and the inlet fuel gas flow rate being kept as 3.5 m/s. The electrolyte current density of the SOFC is displayed in Fig.16 at a variety of flow rates. A comparable pattern of initial increase followed by a subsequent decline can again be observed in the effect of air flow rate on the current density, but the effect is less significant. The current density increases from 970 to 1008 A/m² when the air flow rate increases from 4 to 17 m/s. This is in agreement with the above observations from Fig.8 that the oxygen deficiency is less significant for SOFC_L in terms of practical stack operation.

The cathode channel flow rate distribution is shown in Fig.17 for inlet air flow rates of 1, 10, and 17 m/s. It can be found that with the increase of the flow rate from 1 to 10 m/s, the flow rate in the cathode channel increases. However, with the further increase of the inlet air flow rate, only the flow rate in the horizontal main channel increases, while that in the vertical channels remains constant. The oxygen molar fraction distribution in the cathode channels is shown in Fig.18, which reveals that as the inlet air flow rate increases, the average molar fraction of oxygen increases and the oxygen distribution in the cathode becomes more uniform.

Fig.19 demonstrates the temperature distribution of the electrolyte layer at different inlet air flow rates. Again, a larger inlet flow rate results in a lower average temperature. The average temperatures are 1034.6, 1032.8, and 1031.1 K for the cells operating with inlet air flow rates of 1, 10, and 17 m/s, respectively. As discussed above, this could be due to the faster convective heat dissipation and could be one of the reasons for the lower performance at a higher inlet air flow rate (> 10 m/s).

3.2.3 Electrolyte current density at optimized flow rates

As illustrated above, the optimization of the inlet flow rate makes the gas concentration in the gas channels of SOFC_L increase and the distribution more uniform. The resulting optimized electrolyte current density distribution is shown in Fig.20. In comparison with the unoptimized case shown in Fig.11(b), the overall average current density demonstrates a significant enhancement, validating the critical role of flow rate optimization. However, the distribution pattern of the current density remains consistent, with the middle part of the cell exhibiting a lower current density than the inlet and outlet. The main reason for this is that with increased cell area, the electrons need to transport a longer path and thus the overall resistance is increased due to the poor current collection. The optimization of the current collection is then performed and the result is shown in the next section.

3.3 Effect of current collection design

To boost the current collection efficiency, Ni wire is placed into the supporting anode. The SOFC with 45 Ni wires added to the anode supporting layer for current collection, as illustrated in Fig.21, is then simulated at the ideal flow rate configuration according to Fig.12 and Fig.16 (anode: 3.5 m/s, cathode: 10 m/s).

The distribution of the current density in the electrolyte, of the temperature, and of the electron transfer path of the SOFC with additional Ni wire current collector is shown in Fig.22. The same color legend as that in Fig.20 is utilized here. After the addition of Ni wire, it is obviously observed that the current density is improved, which reaches 1213 A/m, 20% higher compared to the case without current collector (1008 A/m) and 42% higher compared to the case without current collector and with default inlet gas flow rates (856 A/m). Fig.22(b) gives the streamline vector diagram, representing the path of electron transfer, of the anode functional layer (dashed lines indicating the additional Ni wire, while arrows indicating the electron transfer). It can be seen from Fig.22(b) that the electron transfer takes place mainly on the Ni wires, and that at the inlet and outlet of the support anode, a large number of electrons are transferred through the Ni wire, indicating the enhanced current collection efficiency by the Ni wire addition. It should be noted that at the middle part of the cell, the current density is still lower than the part at the edge. Further optimization on the geometry of the cell is required.

4 Conclusions

Expanding the effective area of a single cell to boost the power output is essential in advancing the commercial viability of the SOFC technology. However, it was demonstrated experimentally that merely enlarging the cell area of a flat-tubular SOFC cell would results in a lower performance, particularly concerning average current density. In this work, a macro-scale electro-chemical-thermal multi-field coupling model is built to simulate the discharging performance of the cell. The impact of increasing the effective area is examined. Subsequently, in order to optimize the cell performance, the effect of the inlet gas flow rate and the current collection setup is systematically investigated. Compared with the initial case at 0.9 V, the current density is improved by 42% by optimizing the gas flow rates and adding additional current collectors. Additionally, the optimized SOFC also demonstrates an improved stability. Nonetheless, the cell geometry requires further optimization to improve the uniformity of the current density and the temperature distribution, which will be addressed in the future research endeavors.

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