Journal of Mechanical Science and Technology 26 (5) (2012) 1315~1320

www.springerlink.com/content/1738-494x DOI 10.1007/s12206-012-0332-8

Prediction of flow crossover in the GDL of PEFC using serpentine flow channel†

Litan Kumar Saha1,* and Nobuyuki Oshima2 1Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh

2Graduate School of Engineering, Hokkaido University, Sapporo, 060-8628, 5, Japan

(Manuscript Received October 7, 2011; Revised February 10, 2012; Accepted March 22, 2012)

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract A serpentine flow channel is one of the most common and practical channel layouts for Polymer electrolyte fuel cells (PEFCs) since it

ensures the removal of water produced in the cell with an acceptable parasitic load. The operating parameters such as temperature, pres-sure and flow distribution in the flow channel and gas diffusion layer (GDL) has a great influence on the performance of PEFCs. It is desired to have an optimum pressure drop because a certain pressure drop helps to remove excess liquid water from the fuel cell, too much of pressure drop would increase parasitic power needed for the pumping air through the fuel cell. In order to accurately estimate the pressure drop precise calculation of mass conservation is necessary. Flow crossover in the serpentine channel and GDL of PEFC has been investigated by using a transient, non-isothermal and three-dimensional numerical model. Considerable amount of cross flow through GDL is found and its influence on the pressure variation in the channel is identified. The results obtained by numerical simula-tion are also compared with the experimental as well as theoretical solution.

Keywords: Numerical solution; Flow crossover; Serpentine channel; Gas diffusion layer; Flow rate ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction

A serpentine flow channel is one of the most common and practical channel layouts for PEFCs; it ensures the removal of water produced in the cell with an acceptable parasitic load. In a PEFC, reactant gases usually flow through the flow channel. The GDL plays an important role in distributing the reactants to the electrode catalyst. For the ordinary gas flow situation, reactants distribute towards the catalyst layer by the diffusion process. However, in the case of a large-scale cell it is thought that the differential pressure between adjoining channels in-creases and that the supplied gas flows through GDL owing to the differential pressure. In this process, reactant gases pass from one part of the channel to another by flow cross-over through the porous diffusion layer. The cross flow is a result of the pressure differences between different parts of the channel, and causes the flow rate to vary along the channel. The cross flow in turn has an important influence on the pres-sure distribution in the flow channel.

To reduce the computational effort, modeling and simula-tion studies often assume the flow distribution is symmetrical. Such simplification is reasonable for the parallel channel flow layout, but it is not acceptable for a serpentine flow channel,

because the reactants undergo a pressure drop along the chan-nel. The effect of channel-to-channel gas cross-over on the pressure drop has been investigated by Oosthuizen et al. [1]. The cross flow between channels enhances the supply of fuel and air for the chemical reaction [2], and thus improves the overall performance of a PEFC.

Nguyen [3] proposed an interdigitated channel with a closed channel, in which supplied gas was forced to flow through the GDL. Sukkee and Wang [4] examined the gas flow in this interdigitated channel with a 3D two-phase model. But, in the case of a large-scale cell with the usual channel shape, there was a possibility that such gas flow through the GDL causes a large pressure drop in the channel region. Dohle et al. [5] and Oosthuizen et al. [1] not only discussed gas flow through the GDL in a serpentine channel but also examined gas flow rate distributions experimentally and numerically. Inoue et al. [6, 7] investigated the gas flow through the gas diffusion layer considering different channel depths and measured the pres-sure drop and current density and found an optimal separator shape. The effects of flow cross-over on the GDL deformation due to compression in the fuel cell assembly process have been investigated by Shi and Wang [8] using a three-dimensional structural mechanical model.

The objective of the present work is to validate the feasibil-ity of the numerical method introduced by Saha et. al. [9] for a large-scale calculation and to quantify the flow cross-over through the GDL in a serpentine-channel setting.

*Corresponding author. Tel.: +8801715765533, Fax.: +88028615583 E-mail address: lksaha_math@yahoo.com

† This paper was presented at the AJK2011, Hamamatsu, Japan, July 2011. Recom-mended by Guest Editor Hyon Kook Myong and Associate Editor Dongshin Shin.

© KSME & Springer 2012

1316 L. K. Saha and N. Oshima / Journal of Mechanical Science and Technology 26 (5) (2012) 1315~1320

2. Numerical procedure

2.1 Governing equation

The flow field in the separator channel and GDL can be ob-tained by solving the conservation equations of mass and mo-mentum. A single set of governing equations valid for the sub regions (1) gas channel and (2) porous GDL is used. Therefore interfacial conditions of the internal boundaries between gas channel and GDL need not to be specified. Considering the assumptions the governing equations can be written as:

Mass conservation:

( ) ( ) 0 .t

ερερ

∂+ ∇ ⋅ =

∂u (1)

Momentum conservation:

( ) ( ) 2( ) .p gt K

ερ μερ ε εμ ερ ε∂+ ∇ ⋅ = −∇ + ∇ ⋅ ∇ + −

∂u uu u u

(2)

where u is the velocity vector, μ the viscosity, ρ the density, ε the porosity of the GDL and K is the permeability of the GDL. Porosity, ε is defined by the ratio of the volume occupied by the pore to the total volume of the porous media where as permeability, K is defined by the square of the effective vol-ume to surface area ratio of the porous matrix as in Mazumder and Cole [10]. The last term of Eq. (2) represents the Darcy’s drag force in the porous media. In the gas channel, ε →1 and K→∞, so Eq. (2) becomes the original Navier-Stokes equation.

2.2 Boundary conditions

A constant velocity was used at the inlet of the channel. All wall boundary conditions were considered as no-slip. A con-stant pressure condition was assumed at the outlet of the flow channel.

2.3 Computational domain

The computational domain used for the present numerical simulation considers an entire cell consisting of five parallel serpentine flow channels grooved into a bipolar plate and a GDL placed under the channel and the bipolar plate. For the purpose of direct comparison with experimental results, the computational domain was designed on the basis of the experi-mental observation by Tabe et al. [11]. Schematic figures of the PEFC used in the experiment and its apparatus are shown in Fig. 1. The layout of the five parallel serpentine channels used in the numerical simulation and the grid arrangement for representa-tive sections are given in Fig. 2. Dimensions of the computa-tional domain are listed in Table 1. A large-scale domain is considered here to identify and quantify the performance of the numerical scheme. The computational domain was divided into more than 10 million (10788000) control volumes. The vertex number used for this grid was 11966526.

2.4 Solution algorithm

The conservation equation of mass and momentum, to-gether with the boundary condition are discretized by finite volume method and solved by the software ForntFlow/PEFC which is a general purpose numerical simulator. The numeri-cal simulator adopted in our study is developed by the labora-tory of computational fluid dynamics, Hokkaido University, Japan and collaborates with New Energy and Industrial Tech-nology Development Organization (NEDO). The simulator also includes electrical field, porous media, electrochemical kinetics and water transport phenomena. Flow behavior inside the porous media will be treated as a key technology for this flow simulator. The solution begins by setting the initial val-ues of the physical variables. Then the conservation equations of mass and momentum are solved for the velocities u, v, w and pressure p. Euler implicit scheme has been used for time integration. The first order upwind scheme has been applied to discretize the convection terms in the governing equations.

Table 1. Dimensions of the computational domain.

Each serpentine channel length, l (m) 0.526

Channel width, b (m) 0.002

Channel height, a (m) 0.0005

Land width (m) 0.0002

GDL thickness (m) 0.0003

Number of channels 5

Number of U turns 4

Fig. 1. Structure of the PEFC and the experimental apparatus for pres-sure measurements (Tabe et al. [11]).

L. K. Saha and N. Oshima / Journal of Mechanical Science and Technology 26 (5) (2012) 1315~1320 1317

The fractional step algorithm is used to update the pressure and velocity fields from the solutions of pressure Poisson equation. Implicit treatment of the Darcy drag term well de-scribed in Ref. [9] is considered to verify the performance of the three dimensional numerical simulator. The solutions are considered to be convergent if the variables of Eqs. (1) and (2) have the absolute error less than 10-8 and the relative maxi-mum errors less than 10-6.

The present full-scale simulation was carried out using the supercomputing resources of Hokkaido University (Hitachi SR1100/K1); namely, 40 high-performance nodes and 5 TB of main memory. Each of these nodes consists of 16 CPUs. For the present purpose 64 CPUs were assigned to run the simulation consisting 11966526 nodes, and 2.5-hour execution of these CPUs could simulate the physical time of 1 ms.

3. Results and discussion

The numerical scheme described above and the physical and operational parameters listed in Table 2 were used to ob-tain the numerical results represented in the following section.

The pressure distributions in the serpentine channel and GDL at 5 axial positions (0, 30, 60, 90, and 108 mm from the inlet) are depicted in Fig. 3. From this figure we observe that pressure in the flow channel decreases along the downstream. It is also observed that GDL has a larger pressure gradient than that of the channel region, so that the pressure contour occurs only in the GDL region of Fig. 3. The highest pressure gradient can be observed when there is a significant pressure differential between two adjacent channels. As the pressure drop is proportional to the distance, the maximum value can be found when the distance traveled by the fluid between those adjacent channels reaches a maximum.

A constant velocity was used at the inlet of the channel. All wall boundary conditions were considered as no-slip. A con-stant pressure condition was assumed at the outlet of the flow channel.

Velocity profiles at the mid-plane of the channels and the enlargement of representative areas are shown in Fig. 4. It is shown that, as expected, the velocity becomes laminar fully developed in the downstream direction with the maximum velocity at the center of the channel. As the flow approaches the turning region, the symmetric velocity profile becomes asymmetric with the highest velocity closer to the inner wall, and it remains asymmetric until the flow leaves the turning region. A recirculation zone can be seen around the corner of the U-turn. This zone contributes to higher friction, leading to the higher pressure drop around the channel bends. So, the bend factor given in the circuit model of Tabe et al. [11] is not

Fig. 2. Bipolar plate with the serpentine flow channel layout (upper) and grid arrangements of the numerical domain (lower).

Table 2. Physical properties and operational parameters for serpentine channel.

Porosity, ε 0.7

Permeability, K (m2) 1.76×10-11

Density, ρ (kg/m3) 1.2

Viscosity, μ (kg/m s) 1.83×10-5

Operational temperature, T (K) 333

Operational pressure, P (Pa) 101325

Flow rate, Q (m3/s) 3.39×10-6

Gas composition O2:21%, N2:79%

Fig. 3. Pressure distribution in the flow channel and gas diffusion layer at several axial positions (y = 0, 30, 60, 90 and 108 mm from inlet).

1318 L. K. Saha and N. Oshima / Journal of Mechanical Science and Technology 26 (5) (2012) 1315~1320

needed in the present simulation, which can be captured from the flow field automatically. Further downstream from the turning region, the velocity profile becomes fully developed again and remains so until the flow approaches the next bend region.

Fig. 5 shows the distribution of pressure drops in the chan-nel with and without the GDL. The simulation result is pre-sented together with the experimental results as well as the

circuit model of Tabe et al. [11]. Here, the abscissa is the equivalent position along the channel inlet including the influ-ence of bends. In the numerical solution, information about the bending factor is not needed separately. It is well captured in the flow simulation. So, for the purpose of comparison, numerical results were multiplied by a constant factor, which is the ratio of the actual length of the channel to the equivalent position length. In numerical simulation, the interface between the GDL and the gas channel is treated as wall to consider the without GDL case. The pressure drop decreased along the channel for both cases (with and without GDL). The amount of pressure drop in the case of the GDL was lower than that of the case without it. Flow cross-over through the GDL plays an important role in decreasing the pressure drop. Our numerical results had a very good agreement with the experimental as well as circuit model results of Tabe et al. [11], which vali-dates our numerical result. The validation of our numerical code in small scale has been validated by Saha et. al. [12]. Here we validated it for large scale also.

Fig. 6 shows the pressure and velocity profile in the gas channel and GDL (x-z plane) in the y = 30 mm plane from x = 17 mm to x = 23 mm as indicated by the rectangular box in Fig. 4. In the channel region we see that a significant decrease of axial velocity occurs when the gas approaches the GDL due to the solid matrix drag caused by the GDL permeability. The substantial pressure difference between these two channels causes a high pressure gradient in the GDL region, and a sig-nificant amount of flow crosses through the GDL in such a high pressure gradient region.

The stream line in the flow channel and GDL where most of the flow passes through the channel area is depicted in Fig. 7. As in the previous analysis, we see that the stream line passes through the GDL, from one flow channel to the next, when there is a large pressure difference resulting in a high pressure

Fig. 4. Velocity profile in the mid-plane of the gas flow channel (upper), turning region (lower left) and middle of the channel (lower right).

0

0.5

1

1.5

2

2.5

0 0.1 0.2 0.3 0.4 0.5 0.6

Equivalent position along channel from inlet [m]

Experiment(with GDL)

Experiment(without GDL)

Circuit model (without GDL)

Circuit model (with GDL)

CFD (with GDL)

CFD(without GDL)

Fig. 5. Pressure drop along the serpentine channel with and without the GDL.

Fig. 6. Distribution of pressure and velocity in the gas channel and GDL on the x-z plane at y = 30 mm with x = 17 mm to x = 23 mm.

Fig. 7. Stream lines in the gas channel and GDL on the x-z plane at y = 30 mm with x = 15 mm to x = 25 mm.

Pres

sure

dro

p

L. K. Saha and N. Oshima / Journal of Mechanical Science and Technology 26 (5) (2012) 1315~1320 1319

gradient in the GDL. The relationship between the local cross-flow velocities

through the GDL (ugdl) for different pressure differences is shown in Fig. 8(a). The positions of the calculated cross-flow velocity are shown in blue in Fig. 8(b). The pressure points measured for the corresponding surfaces are indicated by green points. From Fig. 8(a) we observe that ugdl is linearly proportional to the pressure difference, which is related to the channel length.

Here, the maximum Reynolds number corresponding to the maximum cross-flow velocity is about 9. The situation con-sidered in the one-dimensional case was the worst condition as the GDL was placed in between the channel. In the case of sufficient cross flow, the situation is similar to the one-dimensional case. The algorithm developed in Saha et. al. [9] has been verified by considering a difficult situation, so the algorithm is also efficient for the present case.

The ratio of the volume flow rate for the flow cross-over through the GDL to the total inlet flow rate (Qin) for five dif-ferent channels is given in Fig. 9. The flow rate for the cross leakage flow is quantified as the volume flux through the GDL (QGDL) for each channel length, under the land area and in between the two channels. The surface over which the flux was calculated is shown in Fig. 8(b) (red surfaces). The ratio of the flow cross-over increases and reaches its maximum level for the GDL surface placed between the consecutive channels before and after the U-turn because the pressure dif-ference between these consecutive channels is very high. The flow rate through this GDL surface (before and after the U-

turn) was QGDL = 2.01×10-6. This is comparable to the inlet flow rate of channel Qin = 3.39×10-6. The serpentine channels before and after the U-turn can be considered as similar to the case of a single serpentine channel. According to the simula-tion, approximately 60% of the total inlet flow crosses through the GDL between these two channels when the permeability parameter of the GDL, K = 1.76×10-11 was used.

The ratio of the flow cross-over obtained in the present simulation was compared to the results obtained by Park and Li [13]; they also presented the flow cross-over ratio for dif-ferent permeability values. The ratio for the same permeability as in the present case was approximately 50%, which is lower than the result obtained in our present simulation. The model used by Park and Li [13] had a single serpentine channel in-stead of multiple serpentine channels. Presumably, flow cross-over from other channels contributed to the higher value of flow cross-over in the present case.

4. Conclusions

In the present study the three-dimensional numerical scheme was used in a full-scale calculation to observe the cross flow through the gas diffusion layer between two adja-cent channels of PEFCs with a five-serpentine-flow-channel layout. The distribution of pressure drops from the channel inlet to outlet of the serpentine channel with and without the GDL by numerical simulation was compared with the experi-mental findings as well as circuit model of Tabe et al. [11], and an excellent agreement found, validating the accuracy of our numerical scheme. The local cross-flow velocity (uGDL) is linearly proportional to the differential pressure between the two adjacent channels. A significant amount of flow cross-over through the GDL surface, before and after the U-turn was found, at a rate almost 60% of the channel inlet flow rate. The Reynolds number for the uGDL indicates that the transport of the reactants towards the reaction site is driven not only by diffusion but also by convection; this convection flow can help to remove liquid water from the electrode, which can improve the performance of the PEFC.

(a)

(b) Fig. 8. (a) Local cross-flow velocity (uGDL) for various values of pres-sure difference; (b) The position of the points and surfaces.

Fig. 9. Distribution of pressure and velocity in the gas channel and GDL on the x-z plane at y = 30 mm with x = 17 mm to x = 23 mm.

QG

DL/

Qin

[%]

1320 L. K. Saha and N. Oshima / Journal of Mechanical Science and Technology 26 (5) (2012) 1315~1320

Acknowledgment

Financial support of this research by the New Energy and Industrial Technology Development Organization (NEDO), Japan is greatly acknowledged.

Nomenclature------------------------------------------------------------------------

ε : Porosity of porous media μ : Viscosity, kgm-1 s-1 ρ : Density, kgm-3 K : Permeability, m2 p : Pressure, Pa Q : Volume Flow rate, m3s-1 u : Flow velocity in the flow channel, ms-1

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L. K. Saha received his Ph.D (2010) from Hokkaido University. He is work-ing as a Lecturer in the Department of Mathematics, University of Dhaka, Bangladesh. His current interests in-clude gas flow and water transport in polymer electrolyte fuel cell, computa-tional fluid dynamics and magnetohy-

drodynamics.