Short CommunicationUnsteady three-dimensional numerical study of mass transfer in PEM fuel cell with spiral flow field
Introduction
The flow channel configuration is one of the important factors that influence the performance of a PEMFC. The optimization of the channel geometrical parameters such as, the length, the width and the depth of the channel as well as the shape of its cross section, can improve the performance of the fuel cell [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]. The same result can be obtained by increasing the contact area between the flow field channel and the gas diffusion layer [12]. Several research works were realized to study the influence of the geometrical parameters on the PEMFC performance. It is confirmed that the presence of a chicane in the flow channel, can push reactants to seep into the diffusion and catalyst layers, which enhances the electrochemical reaction rate in this region and results in an increase in the local current density. Downstream the chicane, the reactants consumption is relatively low because of the flow deflection phenomenon that brings the reactants outside the GDL [9], [13], [14], [15], [16]. Reducing the channels outlet section can partially block the gasses flow and force them to break into the porous layer [17]. At steady state, the use of a narrow channel with wider ribs can improve cell performance [4], [11] while for the transient case, a wider channel and narrower ribs improve performance [4], [13]. The use of a serpentine channel design which contains an inlet in each branch can improve current density and water production because of the reactants distribution uniformity enhancement [5]. Yuh Ming Ferng et al. [18] compared the serpentine channel with parallel one and found that the former gives a higher performance. They also found that for parallel configuration, the channel depth affects the performance of the cell, while it has no influence in the case of serpentine channel configuration. For a serpentine channel design, high flow velocity and GDL permeability enhance the infiltration rate of reactants into the GDL, which represents an advantage comparing to the parallel channels configuration. For serpentine channel, the flow becomes turbulent even at relatively low Reynolds numbers which represents a singularity in downstream bends regions [19]. A narrower serpentine channel with longer straight channel segments enhances the convective transfer process. This design increases the pressure gradient between the adjacent branches of the channel, which improves the transfer process in the GDL [9]. Comparing to the parallel channel configuration, an interdigitated channel configuration creates a transversal flow in the GDL that improves the convective heat transfer and the evacuation of water from the area under ribs [20], [21]. However, an important pressure gradient is necessary to create the transversal flow in the GDL [21], [22]. A parallel channel configuration produces higher power under low current densities because of the low production of water. However, an interdigitated flow field can be advantageous at high current density because of the performance gain from the transversal flow [21]. Both configurations are sensible to channel-rib width ratio [23]. The comparison between serpentine channels configuration and interdigitated ones allows as concluding that; more the humidification of reactants is important, more the performance of the cell with interdigitated channels design is better [24]. Chang-Whan Lee et al. [25] have investigated the effect of the flow direction on a single cell performance. They found that counter-flow resulted in a more uniform distribution of the current density, which enhances the cell performance. Jang et al. [17] studied numerically and experimentally the performance of a PEM fuel cell with spiral channel geometry, and compared it to that of a cell with serpentine channels. They found that the former shape can decrease the pressure drop and increase heat and mass transfer which improve the fuel cell performance. Juarez-Robles et al. [26] developed a three-dimensional, single-phase, non-isothermal model of PEM fuel cell with concentric spiral flow channels, in order to study the influence of the number of channels on the performance of the cell. They found that the four-channel model produces the best performance with, relatively, low pressure drop, uniform reactants distribution, and current density. The higher power is obtained using this configuration. The eight-channel model generates the worst performance. Rangel-Hernandez et al. [27] built a numerical model of a PEM fuel cell with a spiral channel, to study the irreversibility origins. To make the study easier, they also introduced a dimensionless parameter, which is the ratio of the entropy generation due to mass transfer to the total entropy generation. They found that concentration losses are the main cause of the irreversibility in a fuel cell.
The aim of this work is to investigate how the modification of geometrical parameters, namely, the channel-rib width ratio, the flow direction and the number of turns of the channel can improve the performance of PEM fuel cell with spiral flow field.
Section snippets
Physical model
The fuel cell geometry is shown in Fig. 1. It consists of a membrane, an anode and a cathode superposed as three thin disks, two catalyst layers between membrane and electrodes, and two spiral flow channels on both sides of the sandwich. To investigate the effect of the channel-rib width ratio, three ratios are considered in this study: b = 1, b = 2 and b = 3.
To study the effect of the number of turns of the spiral channel on reactants distribution, we realized a comparison between three
Model assumptions
A complete fuel cell is an extremely complex system involving fluid dynamics, mass transport phenomena, and electrochemical reactions feature. In order to solve a complete three-dimensional model problem, we need to make the following sensible simplifying assumptions:
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Flows in channels are supposed laminar, incompressible and unsteady;
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Water in the channels and in gas diffusion layers is considered as vapor;
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Water is produced in vapor state;
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The diffusion layer is homogeneous and isotropic;
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The
Governing equations
To investigate the fuel cell performance, we have to study many coupled phenomena in different parts of the cell such as reactants flow, species transfer, reactants consumption and water production, as well as the electric power generation.
To study the different phenomena, a three-dimensional unsteady model including the conservation equations of momentum and species is employed, using cylindrical coordinates.
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Continuity equation
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Momentum equations
Fully
Initial and boundary conditions
Initial conditions
It is assumed that the stack is initially empty (there is no reactant) while the initial concentrations of the different species are null. The speed is initialized by a null value as:
The boundary conditions are applied to all external borders of the computational domain.
Inlet conditions
At the channel inlet, Pressure, velocity, and Species concentrations are imposed (Dirichlet condition).
Output conditions
At the flow channels outlet, we assume that the
Numerical method
A FORTRAN program had been developed to construct the geometry and to generate the mesh of the computation domain, and to solve the algebraic equations systems obtained from the discretization of the problem governing equations, using the finite volume method with the power law scheme for space and fully implicit scheme for the time. The essential steps of the program are shown in Fig. 2. The module responsible on the generation of geometry and mesh is presented in Fig. 3. In order to check the
Results and discussion
We have obtained profiles of velocity and concentrations of oxygen and hydrogen in the different parts of the fuel cell, as well as the polarization curve. The velocity fields along the spiral path are shown in Fig. 5. We can easily notice that the highest velocity is reached in the center of the channel along which the velocity laminar profile is maintained. In the gas diffusion layer, the velocity is moderated which means that the convective forces are negligible. Hence, the diffusive mass
Conclusions
We have realized this work in order to investigate how to improve the performance, of a planar PEM fuel cell with spiral flow field, by changing the channel configuration parameters and the flow direction. The governing equations of the problem were solved by the finite volume method. A FORTRAN program was developed to resolve the discretized equations. The results show that:
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The configuration with wider channel has better reactants distribution than the configuration with narrower channels.
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The
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