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General Regulation of Air Flow Distribution Characteristics within Planar Solid Oxide Fuel Cell Stacks Daifen Chen, Yu Xu, Moses O. Tade, and Zongping Shao ACS Energy Lett., Just Accepted Manuscript • DOI: 10.1021/acsenergylett.6b00548 • Publication Date (Web): 06 Jan 2017 Downloaded from http://pubs.acs.org on January 9, 2017
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ACS Energy Letters
General Regulation of Air Flow Distribution Characteristics within Planar Solid Oxide Fuel Cell Stacks Daifen Chena,b,*, Yu Xua, Moses O Tadeb, Zongping Shaob a School of Power & Energy Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China b Department of Chemical Engineering, Curtin University, WA 6845, Australia *
Corresponding author. Tel.: +86-511-887-97228; Fax: +86-511-887-97228. E-mail address:
[email protected] Abstract For solid oxide fuel cell stacks with a planar design, different structural designs were found to cause very different distribution trends of air flow rates fed to the piled cell units. Many implied optimization guidelines, which were independent of the specific structures, were achieved and verified by extensive 3D multiphysics simulations of the large-scale air flow path models. These conclusions could be very helpful for providing generality in practical structural design and parameter choice for planar SOFC stacks.
TOC graphic:
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The planar solid oxide fuel cell (SOFC) is a promising power generation device due to its many favorable properties, including fuel flexibility, clean operation, compactness, high volumetric power and density1-6. In the past decade, the performance of SOFC single units has greatly improved, and the art of the corresponding manufacturing quality has reached commercial requirements7. However, achieving high stack performance and greatly extending its entire lifetime are still two obstacles in the process of commercialization1,8. Thus, in addition to research on novel materials and single cells, it is also important to pay sufficient attention to research on engineering and theory for achieving general regulations on the stack level. Generally, achieving proper air flow distribution within a SOFC stack is one of the key tasks to ensure high performance, stable operation and enhanced lifetime of the entire stack. For a SOFC unit with an active area of approximately 100×100 mm2 and an output current density of 6000 A m-2, a large current (i.e., 60 A) will be produced with a relatively low output voltage of approximately 0.6 V. Thus, most SOFC stacks are constructed by connecting cell units in series to achieve a high output voltage. In this case, even if only one of the piled units fails to obtain enough air flow, a serious decrease in the stack performance will occur, especially when operated under high power output conditions. In addition to acting as an oxidant, air flow is also the main means of heat transport within the stack. K. P. Recknagle et al.9 found that the temperature within an SOFC unit would increase along the air flow direction for both counter- and co-flow arrangements. The quality of the air flow distribution will further determine the distributions of electrochemical reactions as well as the release and transport of the heat produced. These distributions will affect the working properties, such as ionic/electronic conductivities, thermal conductivity, diffusivity, viscosity, etc. Different air distribution means different operating conditions induced among different areas, which means the stack will suffer from a serious risk of local failure. In the past decade, various SOFC stack designs have been proposed, operated and studied
10-22
.
Many corresponding numerical models have been developed to investigate the multi-physics 2
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working process within the SOFC stacks and reach many valuable optimized parameters
5,11,23-28
.
These models are important because experimental methods are still expensive and time consuming, especially for a large-scale stack. However, it should be noted that most of the optimized results achieved are greatly dependent on the specific designs, scale size of the stack and geometric parameters. Koh J. et al. investigated the effect of different junctions on the pressure variation within the manifolds using a systematic algorithm 29. However, due to computational limitations, all of the calculated results were obtained for a large 100-cell stack using identical T-junctions and cross-sectional areas between the inlet and outlet manifolds. Thus, the study did not demonstrate a general rule referring the dependence of the air distribution quality on the stack design, scale and geometric parameter. Thus, achieving the main affecting factors and general fluid dynamics conclusions, which are independent of the particular structure design, from the typical air flow distribution phenomenon within the stack, and then verified them through 3D multiphysics modeling of the large-scale air flow path, are very important to the design and fabrication of a SOFC stack to achieve high performance.
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Fig. 1- a-b) Diagrams of two planar SOFC stack designs; c) 3D model of the 20-cell 2-in-3-out air flow path configuration with rin=rout=4 mm; d) Comparison of the distributions of the calculated normalized air flow rate fed to the 20 piled cell units between structures a and b.
Fig. 1a-b shows two typical planar SOFC stack designs with counter- or co-flow arrangements from the Jülich (FZJ) research center
30,31
. The corresponding components and air flow distribution
process in Fig. 1c are described. The air flow distribution characteristics within the stack can be modeled by 3D stack models coupling the momentum, mass, heat and quasi electrochemical conversation equations within the large-scale air flow path. The normalized air flow rate distributions and single-cell mc, j level and their corresponding distribution quality evaluation on the stack mL,i
indexes ( L and
c ) are illustrated (see Supporting Information for details).
fed to the 20 Fig. 1d shows the distributions of the calculated normalized air flow rate mL,i rather than the physical piled cell units on the stack level. The normalized variable mL,i
variable mL,i is used to provide generality in comparing the performances among SOFC stacks with distribution different designs, scales and working conditions. It is interesting to find that the mL,i
referencing the structure in Fig. 1a follows the opposite trend compared with that of the structure in does not change monotonically with increasing cell number i. Fig. 1b. Furthermore, mL,i
Generally, this irregular result may be attributed to either an improper modeling process or to important factors that determine the air flow distribution. The validation of these results is firstly verified by i) checking the mesh qualities around the corners and important connections between different shapes and ii) testing the mesh dependence of the simulated results (see Supporting Information). Then, a careful fluid dynamics analysis should be performed to analyze its rationality. Generally, the ‘static pressure drop’ throughout (or within) each cell unit pi piin piout is an important factor indicating the flow rate fed to that layer26. To further clarify the air flow distribution characteristics in Fig. 1d, the static pressure p distribution within the entire 20-cell air flow path, referenced to 0 Pa at 4
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the outlet manifold exits, is shown in Fig. 2a. The blue arrows indicate the flow directions. It should be noted that unlike in the outlet manifold zone, p increases along the air flow direction in the inlet manifold zone. For further investigation, the fluid momentum balances within the manifolds are discussed.
Fig. 2- a) The corresponding p distribution; b) diagram of a typical U-type manifold configuration to analyze the air flow characteristics; c) p fluctuations along three different axes within the inlet/outlet manifolds.
Fluid momentum balance analyzing: for a specific control system ‘cs’ within a steady flow, its net flow momentum in a specified direction should equal the sum of both mass and surface forces
u u dA F n
m
Fpn ,
(1)
cs
The y-direction momentum balance of the control system ‘cs’ in the outlet manifold zone (blue color zone in Fig. 2b) is out miout uiout mout Fyout piout Aout pout j uj j Aout (j>i),
(2)
where miout and uiout are the mass air flow rate and average velocity, respectively, within the outlet manifold at the i-th cell unit position. The left side of Eq. (2) is the net momentum outflow of the control system in the y direction. Fyout is the drag resistance due to the frictional drag of the straight pipe and local head loss from T-junctions, which is opposite to the flow direction. piout Aout and
p out j Aout are the pressure forces over the bottom and top surfaces of the control system, respectively. Aout is the overall cross-sectional area of the outlet manifolds. Then, the pressure drop along the flow direction from the j-th to i-th layer position is 5
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p
out j
p
out i
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out out (miout uiout mout j u j ) Fy
Aout
(j>i),
(3)
Obviously, miout will increase from the j-th to i-th layer position because the air flow is gradually out discharged from each cell layer to the outlet manifolds. Thus, (miout uiout mout j u j ) 0 . Therefore, p out within the outlet manifold should always decrease along the air flow direction (j i) p out 0 j pi out due to the superimposed contributions of Fyout and (miout uiout mout j uj ) .
Analogously, the y-direction momentum balance of the control system within inlet manifolds (the red region in Fig. 2b) is
minj uinj miin uiin Fyin piin Ain pinj Ain (j>i),
(4)
Then, the static pressure change along the flow direction is obtained as, piin pinj
(minj u inj miin uiin ) Fyin Ain
(j>i),
(5)
The drag resistance Fyout is opposite to the flow direction and contributes to the decrease in p. As air flow is fed into each piled cell by the dividing T-junctions, miin minj and uiin u inj (j>i). They contribute to the gradual decrease in the momentum of air flow minj u inj miin uiin 0 along the flow direction ( i j ), which will contribute to the increase of p along the air flow direction. As Fyout 0 and minj u inj miin uiin 0 contribute opposite effects to the p distribution, the comparison of magnitudes among uiin , Fyin and minj u inj miin uiin ultimately determine the p distribution within the inlet manifolds. Therefore, the calculated result in Fig. 1d is reasonable. To further illustrate the effects of the T-junctions, the simulated p distributions along three different axes of manifolds are displayed in Fig. 2c: a) axis near pipe wall; b) center axis; and c) axis near T-junctions. Obviously, great fluctuations are found along the c) axes near the T-junctions. These results further support the fact that while the air flows with relatively large densities and 6
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velocities are addressed, the dividing and collecting T-junctions will greatly affect the variations of air flow momentum and further determine the p distribution within the manifolds. The main affecting factors and implied conclusions: As it is generally agreed that the air flow distribution characteristics within the SOFC stack greatly depend on the configuration and geometric parameters, it will be very helpful to determine achieve the key affecting factors, general regulation and optimizing operation approaches by fluid dynamics. As the above fluid dynamics analyses referring to the characteristics in Fig. 1d are performed without pointing to any particular structure, similar characteristics are applicable to other types of air flow path designs. We can further conclude the following: i) As static pressures within the air inlet and outlet manifolds have opposite distributions along the air flow direction, planar SOFC stacks with U-type rather than Z-type manifold configurations promise a more uniform air flow distribution among the piled cells, allowing pi throughout each cell layer to be more uniform (shown in Fig. 2c). Fig. 3a displays the diagram of a typical Z-type manifold configuration. Fig. 3b shows the corresponding p distribution within both inlet and outlet manifolds obtained by 3D simulation of the air flow path. The largest ‘pressure drop’ pi is obtained at the top unit layer. This result means that only a small part of the air flow is fed to the cells closest to the inlet manifold entrances. This distribution in Fig. 3c. Compared with the deduction is further supported by the corresponding mL,i
distribution within the U-type air flow path in Fig. 1d, the air flow distribution quality on the stack level within the Z-type air flow path is greatly decreased (the stack uniformity index L decreases occurred in cell 20, and most of the SOFC units near the from 0.857 to 0.306). The maximum mL,i
inlet manifold entrances could only receive a small amount of air flow. These results support the above conclusion.
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Fig. 3- a) Diagram of a Z-type manifold configuration; b) p distribution within both inlet and outlet manifolds for a
distribution. 2-in-3-out Z-type 20-cell structure; c) the corresponding mL,i
ii) Taking j = i+1 as an example, we can determine from Eqs. (3) and (5) that a smaller pressure out change (i.e., piin1 piin or piout 1 pi ) within the U-type manifold occurs in the cells that are farther
away from the inlet manifold entrances because of relative lower flow rate and velocity. This phenomenon means a smaller momentum difference and drag resistance. This conclusion is supported by the calculated result in Fig. 2c, in which the pressure drop within the inlet/outlet manifold decreases with increasing cell number i. iii) The ‘pressure drop’ difference between the i-th and j-th layers pi - p j is expressed by subtracting Eq. (3) from Eq. (5) Fyin Fyout ( piin piout ) ( pinj p out ) j A Aout in
(miin uiin minj u inj ) Ain 1 (j>i), Ain Aout
(6)
out in in in in where (miout uiout mout j u j ) / (mi ui m j u j ) represents the effects of the O2 consumption and
rising temperature. For the air flow within the SOFC stack, the mole fraction of O2 within the supplied air mixture is only 21%, and the utilization of air flow within the stack is only approximately 30%. Taking a 0.6 A cm-2 operating current density and a 0.6 V voltage as an example, the simulated result shows there is a temperature increase of approximately 200 K. Thus, can be distribution is reached. will greatly evaluated to be approximately 1.03, while ideal uniform mL,i
distribution quality. Compared with the effect of excess air flow supply, the depend on the mL,i 8
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effect of O2 consumption and rising temperature on the conclusions of fluid dynamics analysis would be quite small (Supporting Information). Generally, as the air flow rate fed to each piled cell is driven by the ‘pressure drop’ pi piin piout within it, a smaller ‘pressure drop’ difference pi p j among the piled cells distribution quality. Thus, the optimization process is focused on achieving the means a better mL,i
minimal pi p j by adjusting the configuration and geometric parameters. The first item enclosed in parentheses on the right side of Eq. (6) is attributed to the drag friction, and its value is positive in any situation. The optimization relies on the second item. Firstly, for U-type air flow paths with Ain Aout, the second item on the right side of Eq. (6) is positive and contributes to an increasing effect on the ‘pressure drop’ difference pi p j 0 (j>i). will monotonically increase with increasing cell number i in any situation. Thus, mL,i
Secondly, for U-type configurations with AinAout), and c) 2-in-3-out rin=rout=4 mm (Ain
