Thermal management of a PEMFC stack by 3D nodal modeling

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Abstract

This paper describes a 3D thermal modeling by a nodes network model for two PEMFC of 150 and 500 W (respectively, 3 and 20 cells). Modeling are realized for each case for one cell before to be integrated on all the stack. Absolute temperatures of H2, air and water channels are used as Dirichlet conditions. Temperatures of external surfaces are obtained thanks to an infrared thermographic camera. Final external heat fluxes are deduced from the integrated model.

Introduction

Operating conditions of a fuel cell widely depend on the thermal management. It is used to control the cooling system, to maintain a good hygrometry level in the fuel cell and to optimize the global efficiency of the system. Some studies concerning the solid structures have been made by considering isothermal cells. Then, the computations of the temperatures are obtained in the fluids of the ducts [1]. Other studies are made where the distribution of temperatures is computed on the working plates [2], but the gradients of temperature through the layers (MEA) are not taken into account, then the heat transfer can only be estimated along the channels. These studies are realized with two kinds of boundary conditions: free convection or with a water circulation on the external faces (forced convection). 3D thermal computations are done considering the imposed temperatures of the working plates as Dirichlet boundary conditions [3], [4]. The main object of this work is to study the influence of temperature on physical parameters as for example, the hygrometry rate of the membrane. The cooling system is not taken into account. All these works focused on different parts of one cell. This latter is not considered as an entire unit. Different ways where the cell evacuates the produced heat power are studied to establish a thermal management. So the thermal flux paths must be known and particularly the part of the heat which must be removed by the cooling system or transferred by conduction–convection across the faces of the stack. It is necessary to know the ability of the heat fluxes to cross through the cells and to quantify the part concentrated in the bipolar plates and dissipated on the external surfaces. This study uses a 3D thermal nodes network to compute the temperatures and the flux distribution in the cell. Various boundary conditions are applied, cyclic or imposed flux to study the thermal operating mode between two adjoining cells or the heat transfer along the length of the stack. The distribution of temperatures is obtained for different current densities for two stacks respectively of 150 W (3 cells) and 500 W (20 cells). The surface temperature is supposed as constant and defined by the cooling system whose temperature is controlled at the output and the heat transfer through the faces is also constant. The heat flux extracted by the cooling system is therefore greatly depending on the current density. Comparisons with experiments are presented.

Section snippets

Thermal modeling by 3D nodal network

The modeling of the solid structure of one cell (14 cm × 14 cm × 0.3 cm) is carried out with a nodal network consisted of 172 nodes (temperatures of the wall are measured and used as boundary condition) or 236 nodes (temperatures of the wall are computed) of volume and surface. The nodes represent heat and mass transfer between fluid and solid interfaces [5]. Fig. 1 shows a typical node with its thermal conductances, each of them can represent radiation, convection, conduction and/or mass transfer

Model implementation

Fig. 3 describes the developed model. The modeled water channels are represented as channels 1–3. These nodal “conductances” characterize heat transfer by convection between the fluid and the surrounding solid surfaces so that the mass transfer exists along the duct. Conductance 4 is the Dirichlet condition imposed at the input of the cooling channel at the entrance of the stack. The input temperature of the water is represented with the conductance 12.

Its value is calculated and compared to

Boundary conditions

Three configurations of modeling have been considered for the studied cell. Differences come from different applications of boundary conditions. First, applied boundary conditions have to represent the heat fluxes (B.C. First kind) between different associated cells. The other applied boundary conditions on the external surfaces are first kind boundary conditions of Dirichlet (absolute temperature) [7]. The knowledge (or not) of these lasts is at the origin of a two different configurations.

Equations

To define the conductances and the thermal resistances, it is necessary to know all internal power sources. In that way, chemical energy released by consummation of hydrogen is given by Eq. (3):Pchemical=ΔHH2OgI2F

Eq. (4) gives the electric energy supplied to the load:Pelectrical=UI

Finally, internal thermal power source is equal to the difference between (3) and (4) is shown by Eq. (5):Pthermal=PchemicalPelectrical

Thermal conductivities used for the modeling are given in Table 2.

Different

Results

Solved equations are given thanks to expression (2a), (2b), (2c). Expressions of Eqs. (2a), (2b), (2c) are obtained with precedent dimensionless numbers.

Three loaded experimental tests (0.3, 0.4 and 0.5 A cm−2) are presented with their corresponding modeling for the output temperature regulated at 50 °C. Other experimental phases with no load are realized for 40, 50 and 60 °C as output water temperatures. The reason of the constant temperature of the water for the tests with load is to

Discussion

Heat transfers in the stack change with the operating conditions. When the stack operates without load (3 cells stack), the feeding system is used to reach the operating temperature. For a water output temperature regulated at 40 °C, the heat flux between two cells is negligible. Indeed, the difference of temperatures between the wall and the external air is about 15 °C. The different cells also operate under adiabatic conditions (configuration 2). As the temperature of the water increases the

Conclusion

To realize the thermal modeling of a PEMFC, it is necessary to predict internal temperatures reached for different functioning configurations. Finally, the global efficiency of the cell with its feed system can be estimated. To validate the model developed for one cell (instead of 3 or 20), it has been necessary to obtain the convergence of computed and simulated temperatures at the output of the cooling water. The approach is particularly complicated in reason of the relative absence of

References (12)

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