Numerical modeling of interconnect
flow channel design and thermal
stress analysis of a planar anode-supported solid oxide fuel cell stack
S.-S. Wei, T.-H. Wang, J.-S. Wu
*Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan
a r t i c l e i n f o
Article history:Received 12 November 2013 Received in revised form 8 March 2014
Accepted 13 March 2014 Available online 13 April 2014 Keywords: SOFC CFD thermal stress stack interconnect
a b s t r a c t
In this paper, we propose a new design offlow channel and stack arrangement based on the numerical study considering the effect of theflow channel design on the stack performance and analyze the thermal stress of a planar anode-supported solid oxide fuel cell stack. We also attempt to simplify the cell stack design without affecting its performance and propose an easier sealing method of cell stacks through the study of the thermal stress distribution. The results indicate that the new design, created by changing the cathodeflow channel to a porous current collector, with a 6.3% increase in power density, an 8.6% increase in electrical efficiency. Both more uniform flow and current density distribution can be obtained as compared with a conventional counter-flow design. In addition, we propose a new design direction of cell stack, which could be simpler and easier to fabricate, in which material can easily un-dertake the resulting stress based on the thermal stress analysis.
Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction
A fuel cell is a device that converts chemical energy into elec-trical energy through an alternative, environmentally benign electro-chemical process. Compared to other renewable energy technologies, the non-renewable fuel cell is a relatively stable po-wer generation device. In particular, fuel cell technology is gaining attention due to its high efficiency compared to combustion en-gines and its ability to address the depletion of natural resources and global environmental concerns by zero carbon dioxide emis-sions if hydrogen is used[1].
Among the different types of fuel cells, solid oxide fuel cell (SOFC) is an all-solid-state fuel cell that has been considered as one of the promising energy technologies for residential and distrib-uted power plants due to its much higher efficiency in combination with combined heat and power (CHP), multi-fuelflexibility and potentially low production cost[2e4], even though other types of power systems have increasingly improved their efficiency over the years. Currently, there are two geometrical types of SOFCs depending on the cell structure, namely, planar and tubular. Compared to tubular cell, planar type SOFC has gained significant
interest, since it can be easily produced and sealed[5]. In addition, planar SOFCs can operate at high temperatures (700e900 C),
which is particularly attractive for CHP (combined heat and power) applications, and its overall efficiency can reach up to 90%[6e8]. However, to improve the design of the SOFCeCHP system, fuel cell stacking is considered to be one of the key factors that affect the overall efficiency, in addition to the optimization of the CHP system itself.
Understanding the details of the internal processes occurring within the SOFC experimentally is an expensive and challenging procedure. Therefore, theoretical tools, such as simulation modeling, are very important in realizing the design process of an SOFC stack system. Accordingly, this study considers the detailed mass and heat transports, together with the electro-chemical re-actions simultaneously, to obtain the distributions of power den-sity, current denden-sity, fuel/oxidizer concentrations, and thermal stress, among others, under stack operation. Based on these, it is possible to optimize the stacking of fuel cells at a low cost compared to direct experiments based on a trial-and-error approach. This makes simulation as an inevitable tool in the iter-ative design process[9,10].
In the past, numerous numerical simulation models have been developed to predict the effects of various stack geometrical and operating parameters of SOFC. Based on these results, many designs have been reported for the planar SOFC stack, with an aim to maximize the power density and fuel utilization, and to minimize
* Corresponding author. Tel.: þ886 3 573 1693; fax: þ886 3 611 0023. E-mail address:chongsin@faculty.nctu.edu.tw(J.-S. Wu).
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j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e n e r g y
http://dx.doi.org/10.1016/j.energy.2014.03.052
the non-uniform current density distribution and temperature distribution that directly contribute to the thermal stress in different SOFC components[11e19]. Thermal stress analysis is a very important method to study systematically the performance of a system operating at high temperature, e.g., gas turbine[20], laser welding[21,22], and SOFC[23e26], to name a few, because it is generally difficult to measure the detailed properties in such harsh environment. SOFC is generally operated at high temperatures, it may have stress concentration problem, which may cause the damage of the cell stack for a long-term operation. In the past, several studies have employed thefinite element method to predict the thermal stress distribution of the system which could lead to a better design of the system, which is also one of the major objec-tives of the current study.
For theflow channel design of a proton exchange membrane
fuel cell (PEMFC), how to deal with condensed liquid water effec-tively is one of the critical issues. The liquid water, which is
pro-duced through chemical reactions, often easily plugs the flow
channels. It results in performance deterioration of the fuel cell. In general, PEMFCs with single serpentine flow channel can easily remove liquid water by supplying enough pressure difference and also recreates a relatively uniform current density distribution (e.g.,
[27,28]). In contrast, the solid oxide fuel cell is operated at high temperatures. There are only gasesflowing in the cell stack. Unlike
the PEMFCs, the flow plates of an SOFC are used to make the
temperature distribution more uniform. High-temperature
gradient may lead to either fuel cell crack or failure of the sealant. Thus, the use offlow plates with parallel channels is very common in SOFC.
Recknagle et al. [29]have shown that a counter-flow channel design results in a higher power density than co-flow and cross-flow designs. However, it has been shown that the cell stack design using counter-flow channels has certain inherent disad-vantages. These include non-uniformflow distribution and often very complex structures needed for coupling the fuel and airflow inlet and outlet. For efficient cell stack design, the uniform inlet flow is very important, which can decrease the temperature vari-ation of the cell stack structure and increase the cell power density
[30e32]. To circumvent these disadvantages, one may have to design a very complex geometrical configuration of inlet and outlet channels for fuel and oxidizer.
Thus, in this study we propose a new design of counter-flow channels in a cell stack for improving the uniformity of the ther-malefluideelectrical properties, based on extensive computational fluid dynamics (CFD) simulations, which not only retains the high power density characteristics but also maintains the simplicity of
the design. Furthermore, we have performed the simulation of the thermal stress of the stack to verify the feasibility of the design.
2. Numerical method
In the three-dimensional modeling work, commercial package,
named ANSYS-FLUENT and ANSYS[33], which was, respectively,
employed to simulate the thermalefluideelectrical field and the thermal stress distribution within a cell stack. Initially, by using the CFD model, which includes an SOFC module, we solved the conti-nuity, momentum, energy, and species continuity equations
Fig. 1. Coupling offlow solver, SOFC module, and stress solver. Table 1
Material properties used in the benchmarked case.
Porous anode (NiOþ YSZ) Thickness 1.8 mm
Density 6500 kg/m3
Specific heat 450 J/kg K Thermal conductivity 10 W/m K Electron conductivity 333,330 1/U-m Viscous resistance 1eþ 13 1/m2
Porosity 0.24
Tortuosity 3
Anode transfer coeff. 0.7 Cathode transfer coeff. 0.7 Exchange current density 200,000
Porous cathode (LSM) Thickness 0.03 mm
Density 5620 kg/m3
Specific heat 450 J/kg K Thermal conductivity 11 W/m K Electron conductivity 7937 1/U-m Viscous resistance 1eþ 13 1/m2
Porosity 0.375
Tortuosity 3
Anode transfer coeff. 0.7 Cathode transfer coeff. 0.7 Exchange current density 800
Electrolyte (YSZ) Thickness 0.02 mm
Density 5480 kg/m3
Specific heat 450 J/kg K Thermal conductivity 2 W/m K
Resistivity 0.1
Interconnect (metal) Density 8900
Specific heat 446 J/kg K Thermal conductivity 72 W/m K Electron conductivity 1.5eþ 07 1/U-m Anode contact resist. 1e07 U-m2 Cathode contact resist. 1e08 U-m2
coupled with the current continuity equations, and the electro-chemical reactions occurring within SOFC. These equations were
discretized using the finite-volume method and solved using a
pressure-based algorithm in coupling velocity and pressure
effec-tively. Following that, ANSYS, which uses the finite element
method, was employed to analyze the distribution of thermal stress on a cell stack.
Fig. 1illustrates the conceptual sketch that shows the coupling
of the FLUENTflow solver and SOFC module and ANSYS stress
solver. Theflow solver provides the species and temperature dis-tributions to the SOFC module, and the SOFC module returns the species and heat fluxes at the boundaries. After obtaining the temperature distribution, we used the ANSYS workbench to port the temperature distribution results of FLUENT into the ANSYS stress solver. Subsequently, we computed the stress distribution, which includes the von Mises stress in metal and the maximum principal stress in brittle (ceramic) material. Details of the description of these can be found in the user’s manual of FLUENT
[34]and are not described here for brevity.
The fuel cell efficiency
h
, is defined as follows[35]:h
¼m
fVc
VOCV 100%;
(1)
where
m
fis the fuel utilization coefficient, defined as the ratio of thereacted fuel to supplied fuel in the anode, Vc is the operating
voltage, and Vocvis the open-circuit voltage. From this definition, it
is easy to realize that the electrical efficiency is proportional to the fuel utilization and operating voltage. Thus, the optimal operating conditions for the highest electrical efficiency of fuel cells may not be at the maximal power density since fuel utilization may not be the highest.
3. Results and discussion
To simplify the SOFC simulation model, the cell stack was
divided into interconnect, cell, and flow channel components.
Furthermore, we considered the porous electrodes as isotropic and homogeneous. Gases in the SOFC are ideal gases and heat capacities of the gaseousfluids are only functions of temperature. The fluid flow can be modeled as incompressible and laminar due to a small pressure gradient andflow channel, and flow velocities. The gas sealing is assumed to be perfect. Considering the performance, uniform distribution and convenience for fabrication, we adopted the parallel counter-flow interconnect design. Following the idea of Sembler and Kumar[36], we could estimate the performance of a cell stack by simply simulating a single cell. Thus, we simulated a single cell to improve the stack flow channel design. After the completion offlow channel design, we simulated the thermalefluid field of a single cell with different inlet and outlet port designs, within a multi-cell stack. Finally, we simulated a three-cell stack to obtain the stress distribution of each stack component at temper-atures of 700, 800, and 900C.
3.1. Effects offlow channel geometry on the single cell stack performance based on parallel counter-flow channel
Firstly, we benchmarked our simulation to that presented by Sembler and Kumar[36]using the same simulation conditions to ensure the validity of the SOFC model proposed in this study. The model assumes that theflow field at the channel inlet is uniform without considering the inlet and outlet port design.Tables 1and2
summarize the material properties and boundary conditions, respectively, employed in the simulation model discussed in this study. Here, the anode, cathode, and electrolyte are made of NiOþ YSZ, LSM, and YSZ, respectively. The H/O (molar) ratio is kept as 1.11 throughout the study, unless otherwise specified. For the benchmarking case, we have set up the grid size following Sembler
and Kumar[36]and we have performed a thorough grid
conver-gence test (w100 K, w200 K, and w400 K cells) and finally decided
Table 2
Boundary conditions used in the benchmarked case.
Anodeflow rate 4.48 107kg/s
Anodeflow inlet temperature 1123 K
Anodeflow composition (mole %) 97%H2, 3%H2O
Cathodeflow rate 2.17 105kg/s
Cathodeflow inlet temperature 1123 K
Cathodeflow composition 100% dry air
Operating pressure 1
External boundaries Adiabatic
Fig. 2. Comparison of simulated IeV and IeP curves obtained with the model proposed in this study with that of Sembler and Kumar[36].
Fig. 3. External boundary conditions of Type O and nomenclature of geometric configuration of parallel counter-flow channel.
Table 3
Power density with various geometric configurations of the flow channels at 0.6 V. Type Configurations (mm) Power density
(mW/cm2) Electrical efficiency ha hc wa wc ca cc A 1 1 1 1 1 1 752.2 49.2% B 0.5 1 1 1 1 1 758.5 (0.83%) 49.6% C 1 0.5 1 1 1 1 754.9 (0.36%) 49.6% D 1 1 2 1 1 1 755.5 (0.44%) 49.3% E 1 1 1 2 1 1 753.1 (0.12%) 49.7% F 1 1 1.4 1.4 0.6 0.6 767.4 (2%) 50.7%
to use about 200 K cells for the results presented next because the results of 200 K cell are almost the same as those of 400 K cells.
Fig. 2shows that the simulated IeV and IeP curves are in excellent agreement with those obtained by Sembler and Kumar[36]. The results clearly validate the current SOFC model.
Secondly, we performed a parametric study of theflow channel configuration for optimizing power generation.Fig. 3illustrates the
geometrical configuration of the planar parallel counter-flow
design. Important parameters include the widths of anode and cathodeflow channels (wa, wc), the height of anode cathodeflow
channel (ha, hc) and the width of current collector (interconnect)
contact with the cell (ca, cc). In the configurations considered in this
study, the cell dimension isfixed as 50 mm 50 mm with different combinations of ca, cc, wa, wc, ha, and hc. Furthermore, to make the
simulation results more close to our experiment currently in progress, we changed the anode thickness to 1 mm and the cathode thickness to 0.1 mm. In addition, the external boundaries were set as adiabatic at the top of the stack and radiation walls at the sides of the stack at 1123 K, as shown in Fig. 3. Other parameters and conditions are the same as those listed inTables 1 and 2. Note that the electrolyte between the anode and cathode is intentionally enlarged in the sketch for a clear view.
Table 3summarizes the power density and electrical efficiency at 0.6 V with various geometrical configurations of the flow chan-nels (Types AeF). It shows that the electrical efficiency of Type A is 49.2%. In addition, the results indicate that the changes in power density and electrical efficiency due to variation of flow channel sizes were relatively small. However, the current density distribu-tion became more uniform when the contact area between the cell and the current collector of cathode becomes smaller (Fig. 4a, b). Because of the anode-supported structure, the cathode is compar-atively thin (20e100
m
m). As the rib width of the current collector at the cathode side become smaller, the channel width forflowingair becomes larger. This results in that it becomes easier for the air (especially oxygen) to diffuse into the cathode region which is located near the rib. In addition, if the rib width is larger, the diffusion of the oxygen into the cathode region near the rib will cause a large drop of the oxygen concentration because of electro-chemical reactions. Therefore, the contact area of the cathode current collector with the cathode has a remarkable effect on ox-ygen distribution and of course overall cell performance. However, it is not easy to fabricate very thin straight-rib interconnects and there may also be a problem related to structural strength under high-temperature environment. Ideally, the current collector at the cathode side of the anode-support solid oxide fuel cell should have a uniform contact with the cathode, but with a minimal contact area. This observation leads us to replace the straight-rib typeflow channel design with the porous current collector at the position between the cathode and the interconnect. The porous media current collector design is relatively easy to fabricate using electric porous cermet or metal mesh, as shown inFig. 5. In addition, we would expect the cell has a better stress distribution since the contact is more uniformly distributed.
For this reason, we changed the cathode current collector of the parallelflow channel to a porous media with a height of 1 mm and a porosity of 0.6 in the simulation, which we denote as Type G.Fig. 6
compares the simulated IeV and IeP curves of Type A and Type G. Results indicated that the maximal power density, fuel utilization,
Fig. 4. Comparison of the current density distributions of (a) Type A, (b) Type F.
and electrical efficiency with a porous media cathode current col-lector increase 6.9%, 8.6%, and 8.6%, respectively, as compared to that of Type A.Fig. 7shows some typical distribution of the prop-erties with a porous media cathode current collector when the voltage is 0.8 V. In practice, either a corrugated interconnect, which can be easily fabricated[24], or metal mesh[15]can be used as the equivalent porous media at the cathode interconnect, to reduce the contact area between cathode and the interconnect.
We think the uniformflow can have greatest temperature dis-tribution and power efficiency. In general, we need the design in
the front of cellflow channel to build uniform inlet flow; because of our design is counter-flow channel, the inlet flow and outlet flow tube at the same side. This design we will continue to discuss in the following.
3.2. Stack design
For cell stack design, especially on the fuelflow side, a uniform inletflow is very important.Fig. 8shows the proposed design of a
Fig. 7. Typical distribution of properties with porous media cathode current collector (Type G) with 0.8 V: (a) fuel mole fraction, (b) O2mole fraction, (c) current density, and (d) temperature.
multi-cell stack. It is a hexagonal cell stack consisting of planar anode-supported SOFCs of area 50 50 mm2, with a single-inlet
and a double-outlet design for both the anode and cathode, based on a Type G arrangement (Fig. 5). The air and fuelflow in opposite directions (counter flow). If we include more stacks, it looks like a honeycomb structure (Fig. 9). Eachflow pipe is shared by three stacks. This design has the potential to reduce the problem of using a large-scale cell and multi-stack system, termed as Type H.
Since we are interested in developing an SOFC system running at intermediate temperature, we have changed the inlet temper-ature radiation wall to 973 K and heat transfer coefficient to 0.5.
Fig. 10 shows the typical simulated distribution of single planar SOFC properties in a Type H stack with an H/O ratio of 1.11 and a voltage of 0.65 V. We can see that, with the simple design of a single inlet and two outlets, inflow distribution is fairly uniform, similar to that in Type G, even though H2 concentrations are
slightly higher at the sides than those in the middle. To further
improve this situation, we can simply change the inlet flow
diffusion channel to be more“constricted” to make the inlet flow more uniform (Fig. 11), which is clearly demonstrated inFig. 12. This is much simpler than addingflow deflectors at the diffusion side by xHuang et al.[30].
Fig. 10. Distribution of properties with H/O ratio¼ 1.11 and 0.65 V (a) O2mole fraction, (b) H2mole fraction, (c) current density distribution, and (d) temperature distribution.
Fig. 11. Sketch of hexagonal cell stack new design, termed as Type H new.
Fig. 12. Distribution of massflow rate of anode flow side with Type H and Type H new.
Table 4
Mechanical properties of metal material used in the simulations[37,38]. Properties Interconnect (structure steel) Steel wire mesh
Density (kg/m3) 7850 3680
CTE (Reference T) 1.2 105/C (22C) 1.2 105/C (22C)
Young’s modulus (GPa) 200 140
Poisson’s ratio 0.3 0.3
Bulk modulus (GPa) 166.6 116.6
Shear modulus (GPa) 76.9 53.8
3.3. Stress distribution of 3-cell stack
Sealing material is a very important factor in the current cell stack practice. It prevents leakage of gas and decreases cell damage caused by the cell stack in the course of thermal expansion[37]. Due to the design of the cell stack, which requires a cell support to maintain the airtightness between the air and fuelflow channel, the use of the sealing process becomes very cumbersome. There-fore, we consider direct use of sealing materials for the support frame to reduce the complexity of the cell stack. The material used is ceramics or others. In this case, we use the Grancrete[38]which has a better strength (maximum strength is about 41 Mpa) and
higher resistance to high temperature related cracking. In addition, it can be easily molded into various shapes, which eventually re-duces the cell stack manufacturing cost.
With this aim in mind, we analyzed the stress distribution of a three-cell stack of Type H using ANSYS software.Tables 4 and5
summarize the mechanical properties of “metal” and “brittle”
materials, respectively[39e46]. In general, the cell stack damage is usually located in brittle materials. By analyzing the stress distri-bution and maximum principal stress, it is possible to understand whether the current design can withstand the operating conditions we are interested in. Similarly, we have performed a thorough grid convergence test and we have decided to employw1.6 million el-ements for the CFD simulation and about 0.3 million elel-ements for the stress simulation in the 3-cell stack design for all the results presented next.
Figs.13and14shows the maximal principal stress distribution for the anode and the cathode at 970 K, respectively, which uses different types of cell support materials. The results show that the use of Grancrete cell support can effectively reduce the maximum prin-cipal stress of the cell, which the failure is defined by the maximum principal stress exceeds the ultimate tensile strength of the brittle materials. Note the maximum material strength of the
anode-supported cell (NiO-YSZ-LSM) is about 187 Mpa (RT)w 112 Mpa
(800C)[47]. Instead, the cathode could be damaged, should the
Table 5
Mechanical properties of brittle material[39e44]. Properties Niþ YSZ (40:60) porosity 40% LSM porosity 30% Grancrete Density (kg/m3) 6500 5620 2000 CTE (Reference T) 1.25 105/C (700C) 1.05 105/C (700C) 1 106/C (20C) Young’s modulus (GPa) 50 47.5 4.14 Poisson’s ratio 0.387 0.3 0.2
Bulk modulus (GPa) 73.75 39.6 2.3
Shear modulus (GPa) 18 18.3 1.725
Fig. 13. Distribution of maximum principal stress of anode at 2.4 V, 970 K (a) max: 77.4 Mpa using steel cell support and (b) max: 57.1 Mpa using Grancrete cell support. Maximum principal stress of cathode: 112 Mpa (800C).
Fig. 14. Distribution of maximum principal stress of cathode at 2.4 V, 970 K (a) max: 172 Mpa using steel cell support and (b) max: 79.4 Mpa using Grancrete cell support. Maximum principal stress of cathode: 112 Mpa (800C).
steel support be used (Fig. 14a). Therefore, it is better to use other sealing materials or sealing designs in the steel cell support.
Fig. 15shows the distribution of von Mises stress of steel cell support and maximum principal stress of Grancrete cell support at 970 K, respectively. It can be seen that stainless steel cell support and Grancrete cell support can both withstand the thermal stress under the specified operation of the cell. InFig. 15a, the simulated maximum von Mises stress is 342 Mpa, which is slightly lower than the yield strength of stainless steel 430 (363 Mpa). However, the cathode is already damaged under this operating condition, as shown inFig. 14a. In addition, the stress is more concentrated near the air inletflow diffusion side of the cell support, which is mainly caused by the large temperature gradient and large thermal expansion coefficient of the stainless steel at this location. In
Fig. 15b, the simulated maximal principal stress is 21.7 MPa that is much smaller than the maximal principal stress of the Grancrete material (41 MPa). The stress is also concentrated near the inlet flow diffusion side of the cell support due to the large temperature gradient, but it is far below the material strength because of very low thermal expansion coefficient.
Fig. 16shows the maximum principal stress of anode-supported cell cathode and Grancrete cell support at the operating tempera-tures from 700C to 900C by using Grancrete cell support. We can see even if the operating temperature is raised up to 900C, the current stack design using Grancrete cell support is still very safe
considering the maximal principal stress is still well below the material strength.
4. Conclusion
In the current study, effects of the geometry offlow channels of interconnect, inlet and outlet port designs, and stress distribution of the design, have been numerically investigated for a counter-flow planar anode-supported SOFC (50 50 mm2) stack. The
ma-jorfindings are summarized as follows:
1. Use of a porous media current collector at the cathode side in-creases the maximal power density, fuel utilization, and elec-trical efficiency by 6.9%, 8.6%, and 8.6%, respectively. Uniformity of theflow across the channels can be greatly improved by a constricted inletflow port design as proposed in the current study.
2. The stack design proposed in this study has the potential in producing more uniformflow and current density distribution. 3. Lower stress distribution using cheaper materials, e.g., Gran-crete for the cell support, could be achieved based on the ther-mal stress analysis.
Corresponding experiments on validating the simulations are currently in progress and will be reported in the very near future. Acknowledgments
Thefinancial support provided by the National Science Council of Taiwan through Grants no. NSC-99-3113-P-009-005,
NSC-101-3113-P-009-002 and NSC-102-3113-P-009-001 is highly
appreciated. References
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