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Energy 169 (2019) 338e343 Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy Three-dimensional study of stack on the performance of the proton exchange membrane fuel cell B.H. Lim a, E.H. Majlan a, *, W.R.W. Daud a, b, M.I. Rosli a, b, T. Husaini a a b Fuel Cell Institute, Universiti Kebangsaan Malaysia, 43600, UKM Bangi, Selangor Darul Ehsan, Malaysia Department of Chemical and Process Engineering, Universiti Kebangsaan Malaysia, 43600, UKM Bangi, Selangor Darul Ehsan, Malaysia a r t i c l e i n f o a b s t r a c t Article history: Received 12 September 2018 Received in revised form 30 November 2018 Accepted 4 December 2018 Available online 11 December 2018 The distribution of reactant in the proton exchange membrane fuel cell (PEMFC) is crucial because the performance of the fuel cell is determined by the lowest performance cell. The reactant is distributed from the manifold to the cells in the stack and further distributed into the ﬂow ﬁeld channels (depending on the ﬂow ﬁeld design). The three-dimensional PEMFC is comparatively studied as a dual-cell, a quadcell and a hexa-cell stack. The previously investigated modiﬁed parallel ﬂow ﬁeld is used as the anode ﬂow ﬁeld. The dual-, quad- and hexa-cell stacks are connected in series to study the effect of PEMFC performance when the number of cells increases in a PEMFC stack. Computational ﬂuid dynamics (CFD) is used to study the current density generation of a PEMFC stack. The results demonstrate that when the quantity of cells rises in a stack, the current density decreases. Six equations are formed at different cell potentials to predict the PEMFC performance as the quantity of cells increases. © 2018 Published by Elsevier Ltd. Keywords: PEMFCs stack CFD modeling Manifold 1. Introduction Fossil fuels which are the main source of energy, have put the environment in an alarming stage. Carbon emission has reached an unsustainable level and caused air pollution and greenhouse effects, which change the global climate [1,2]. The fuel cell, which has low emission and high efﬁciency, is a promising alternative solution to reduce the carbon emission [3,4]. Among all fuel cells, the proton exchange membrane fuel cell (PEMFC), which works at temperatures below 100 C, has gained more attention because it can substitute for the current internal combustion engine in automotive applications [5e7]. However, the major problem of introducing the PEMFC to mass production of automotive applications is the uncertainty of the PEMFC reliability and life span [8,9]. The PEMFC life span is affected by water and reactant management, where improper management of water and reactant will degrade the gas diffusion layer (GDL) and membrane electrode assembly (MEA) [10e12]. In a PEMFC stack, the reactant is distributed from the manifold to the cell and further into the ﬂow ﬁeld channels. The uneven reactant distribution from the manifold to the cells will reduce the performance of the PEMFC because the overall performance of a fuel cell stack is reduced by the weakest cell in the stack * Corresponding author. Tel.: þ60 389118521; fax: þ60 389118530. E-mail addresses: [email protected], [email protected] (E.H. Majlan). https://doi.org/10.1016/j.energy.2018.12.021 0360-5442/© 2018 Published by Elsevier Ltd. [13]. Adding the quantity of cells in the stack will affect the reactant distribution because a longer manifold tends to have an uneven reactant distribution to cells further from the inlet [14]. Previous literature have numerically studied the effects of the type of manifold conﬁguration on the performance of a PEMFC [14e16]. Chen et al. [15] studied the effect of the manifold dimension on the pressure distribution and reported that larger manifold widths improved the ﬂow distribution. Mustata et al. [14] investigated the Ue and Z-conﬁguration stacks and found that the Z conﬁguration had a more uniform ﬂow distribution. Wang [17] and Pandiyan et al. [18] investigated the effect of the bipolar ﬂow ﬁeld pattern on the PEMFC stack performance. Both investigation reported that the optimization of the ﬂow ﬁeld design can improve the performance of the PEMFC stack. Le & Zhou [19] numerically studied the effect of water presence on the physical and transport characteristics. They showed that the presence of water in the model affected the stack performance because the current density of a PEMFC stack is determined by the lowest current density cell. Macedo-Valencia et al. [20] numerically investigated the thermal distribution in a PEMFC stack. They observed the highest temperature near the ribs and outlet of the cathode. Multiple numerical investigations of the PEMFC stack have been conducted to consider the effects of the pattern, water and temperature on PEMFC stack performance, but few investigations have been performed on the effects of the number of cells on PEMFC performance. Thus, this paper examines the effect of the quantity of cells in a stack on B.H. Lim et al. / Energy 169 (2019) 338e343 339 PEMFC performance. The second part of this paper introduces equations to predict the performance of a PEMFC stack when the number of cells increases. 2. Modeling and simulation A three-dimensional model of the dual, quad and hexa cells with a single inlet/outlet for the cathode and a dual inlet/outlet for the anode is shown in Fig. 1. The three-dimensional PEMFC stack model includes the manifold of the anode and cathode, and each cell has a MEA as well as GDL and bipolar plates. The cells are connected in series; the conventional parallel ﬂow ﬁeld is used in the cathode, on the anode a modiﬁed parallel ﬂow ﬁeld from previous studies is used [21] (Fig. 2). Hydrogen and air are used as the reactant. Hydrogen is supplied to each cell from two manifolds in the X-directions, and air is supplied through a single manifold in the negative Z-direction. The parameters of the model are tabulated in Table 1. Simulation was conducted using ANSYS where Design Modular was used to create geometry and Meshing was used to create mesh that will be used to solve the governing equations in Fluent. The governing equation was solved with the commercial software ANSYS, Fluent R15.0 was used to solve the governing equations. An additional add-on PEMFC module, which was developed by ANSYS, was used to solve the ﬂuid-based equation for the PEMFC. The parameter inputs for the PEMFC add-on module were set as suggested by the ANSYS manual [22]. In a previous study, a grid independence test was performed for the ﬂow ﬁeld dimension. Thus, in this study, only the MEA and GDL grid independence test were performed. The result shows that approximately 1.2 million elements were generated for each cell. The boundary conditions to solve the governing equations are as follows: Inlet condition: minlet ¼ min Outlet condition: Poutlet ¼ Pout Boundary condition: no-slip boundary condition was imposed for all channel walls Two phases were considered in the model, where the liquid and gaseous phases co-existed in the model. The governing equation to solve the model is as follows: The momentum conservation equation is given by V$ðεrmuÞ ¼ εVp þ εmeff Vu þ Su (1) where p denotes pressure, and m denotes viscosity. Su in the above equation results from the presence of porous media, where k is the permeability of the porous media. . Su ¼ meff ε2 U k (2) Continuity equation, where the mass conservation in the channels and GDL is given by: VðεruÞ ¼ Sm (3) where ε denotes porosity of the porous electrode, r denotes gas mixture density, and u denotes ﬂuid velocity vector. Sm indicates the consumption and production of species during the electrochemical reaction in the PEMFC; it is zero in majority parts of the model other than the anode and cathode catalyst layers. Sm denotes the usage of reactant in anode and cathode as well as the generation of water in the cathode: Fig. 1. Three-dimensional model: (a) dual cell; (b) quad cell; (c) hexa cell. Sm ¼ X Sk (4) k Here, Sk is the source term of the kth species induced by the electrochemical reaction in the active catalyst layers. 340 B.H. Lim et al. / Energy 169 (2019) 338e343 Fig. 2. Flow ﬁeld: (a) anode; (b) cathode. Table 1 Parameters for the simulation. Parameters Value Active area (cm2) Channel/rib width (mm) Channel depth (mm) Manifold width (mm) GDL depth (mm) Catalyst layer depth (mm) Membrane depth (mm) Operating temperature (K) Operating pressure (atm) Anode & cathode stoichiometry 1.69 1.0 0.8 2 0.5 0.005 0.06 353 1.0 2 SH2 ¼ 1 (11) 4FCO2 jc SH2 O ¼ 1 2FCH2 O jc (12) Finally, the electrochemical reaction in the fuel cell simulation is solved by the following two potential equations: (5) where leff is the effective thermal conductivity, Cp denotes isobaric heat, and Sh denotes energy source term Sh ¼ hreaction hja;c þ I 2 Rohm þ hphase (6) hphase ¼ rw h (7) rw ¼ cr max ð1 xÞ pwv psat R T MwH2 o :½sr1 g (8) where I denotes local current density, hreaction denotes water heat formation, hphase is the rate of enthalpy change due to the formation of water, ja and jc are the exchange current densities in the anode and cathode, h is the over potential, rw denotes condensation rate and x denotes liquid water. The chemical reaction in the fuel cell, where hydrogen, oxygen and water have a convective ﬂow and a diffusion ﬂow, is govern by Fick's law equation V$ðεruYi Þ ¼ V$ rDi:eff VYi þ Si (10) 2FCH2 ja SO2 ¼ The energy equation is V$ leff VT ¼ V$ εrCp uT þ Sh 1 (9) where Yi denotes mass fraction for species i and Di:eff denotes effective diffusion coefﬁcient for species i. Si denotes the source term of oxygen consumption and water generation in the catalyst layer and the species phase change in the liquid computation domain. The subscript i denotes the sources terms in the fuel cell given by the following: V$ðss V∅s Þ þ js ¼ 0 (13) V$ðsm V∅m Þ þ jm ¼ 0 (14) where the ﬁrst equation shows the potential equation of the electron transfer through a solid conductive material, such as the gas diffusion layer and the current collectors. The second potential equation describes the protonic transport through the membrane. ∅ is the electric potential, s denotes the electrical conductivity and s and m represents solid and membrane phases. The Butler-Volmer equation shown below is used to solve the transfer current in the catalyst layer given by ja and jc , which are the exchange current densities. . ja ¼ za jref ½A ½A a ref . jc ¼ zc jref ½C ½C c ref !ga !gc aa F ha= e RT ac F ha= RT e a F h a Fh e c c=RT e a c=RT (15) (16) where z is the surface-active area, g is the concentration dependence, a denotes transfer coefﬁcient, F denotes Faraday constant and R denotes universal gas constant. The term h denotes the overpotential or activation losses, which is computed as follows, where VOC is the open circuit voltage. ha ¼ ∅s ∅m (17) hc ¼ ∅s ∅m VOC (18) B.H. Lim et al. / Energy 169 (2019) 338e343 341 Fig. 3. Comparison of the numerical and experimental data. 3. Results and discussion The numerical investigation of PEMFC using Fluent has been commonly demonstrated in many studies. Macedo-Valencia et al. [20] reported their model development and validated their simulation results with experimental data. Thus, a model validation is performed with their reported results, where their parameters, such as the dimensions, membrane electrode assembly (MEA) properties, operating conditions and geometric characteristics, were used. The comparison results of the simulation with the Macedo-Valencia et al. [20] data are shown in Fig. 3. The simulation results show that there are differences with their experimental data. However, Macedo-Valencia et al. produced a similar result for the simulation data and reported that the difference in the experimental and numerical data results from different component properties for the experiment and numerical analyses. The author simulation data are more consistent with the experimental data, where the calculated current densities are less different from the experimental data than the simulation data of Macedo-Valencia et al. [20]. This result occurs because the multiphase condition was used in the current simulation, which reduced the discrepancy of water vapor existence in the model and the experimental condition, which caused the larger difference in current densities. The main aim of this investigation is to obtain the performance of the PEMFC stack for different quantities of cells. The single-cell model was considered in this study, it is to understand the effect of stacking the PEMFC on its performance. The simulation was performed, and the polarization curves of the single-, dual-, quad- Fig. 4. Polarization curve of the single, dual-, quad- and hexa-cell PEMFC models. 342 B.H. Lim et al. / Energy 169 (2019) 338e343 Fig. 5. Change in current density as the quantity of cells changes in a PEMFC stack. and hexa-cell PEMFC stacks are shown in Fig. 4. The cell potential is the average potential of the number of cells considered in the simulation. All the simulations were performed under the identical operating condition for this study. Fig. 4 clearly shows that the single-cell PEMFC model performs better than the dual-, quad- and hexa-cell PEMFC stack models. When the number of cells increases Table 2 Equations of the relationship between the current density and the number of cells. Cell Potential, V (V) Equation 0.4 I ¼ 0:679 þ 1:7988e1:6926n 0.5 I ¼ 0:615 þ 2:1275e2:0445n 0.6 I ¼ 0:530 þ 1:4601e1:9377n 0.7 I ¼ 0:440 þ 0:9550e1:723n 0.8 I ¼ 0:339 þ 0:5576e1:4496n 0.9 I ¼ 0:226 þ 0:2013e0:6592n from 1 to 2, Fig. 4 shows that at the cell potential of 0.6 V, there is a 23.4% current density reduction because of the addition of manifold in the PEMFC simulation model. The addition of a manifold into the model decreases the performance of the PEMFC because the variation of ﬂow resistance for each cell affects the reactant distribution. The captured current density was determined by the lowest cell performance. Thus, the current density is higher for the singlecell PEMFC model. Further comparison of the dual-, quad- and hexa-cell PEMFC stack current densities shows that the current density decreases when the number of cells increases. However, the current density almost did not deteriorate as the quantity of cells increases from quad-to hexa-cell. Thus, the increase in the quantity of cells in a stack stabilizes the PEMFC stack performance. Fig. 4 shows that the performance decreases with the increase in quantity of cells in a PEMFC stack. To predict the performance of a larger PEMFC stack, the correlation amid the current density and the quantity of cells is plotted and shown in Fig. 5. It was shown Fig. 6. Prediction of the current density for different numbers of cells at 0.6 V. B.H. Lim et al. / Energy 169 (2019) 338e343 that as the number of cell increases, the reduction rate of the current density in a stack is reduced. Thus, Table 2 shows the equations of the relationship of different cell potentials between the current density and the number of cells in Fig. 5. The equations in Table 2 can be used to predict the current density generation with the increase in number of cells in a stack. From Table 2, the prediction of the current density generation for different numbers of cells can be calculated. Therefore, the current density of a 40-cell PEMFC stack at a cell potential of 0.6 V was predicted in this study. The equation at 0.6 V from Table 2 was used to predict the current density of the 40-cell PEMFC stack. Fig. 6 shows the predicted current density at 0.6 V from a single cell to 40 cells. The predicted current density for 40 cells is 5.3 A/cm2. There was almost no change in current density from 20 cells to 40 cells because the PEMFC stack performance had reached stability. The equations in Table 2 to predict the polarization curve of a PEMFC stack are limited to only the author design because changes in the ﬂow ﬁeld design, manifold design and stacking method will affect the performance of the PEMFC. 4. Conclusion In this study, a numerical simulation was performed on threedimensional dual-, quad- and hexa-cell PEMFC stacks. The results show that as the quantity of cells rises, the performance of the PEMFC decreases. The largest difference in calculated current density is between the single- and dual-cell models at 0.6 V the current density difference was 23.4%. When the number of cells increases from 2 to 6, the difference in calculated current density is reduced dramatically. This research was carried out to predict the performance of a PEMFC stack as the number of cells in stack increases. 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