Oxygen Concentration and Reaction Rate Profiles Analysis of Polymer Electrolyte Fuel Cell
Authors: Ma Yulei , Do Hoang Anh , Kageyama Miho , Kawase Motoaki 
Published: December 2024

Introduction

A one-dimensional (1D) model of polymer electrolyte fuel cells (PEFCs) is especially suitable for performance diagnostics, design optimization, and material evaluation, due to its high computational efficiency. Uniform distributions of reactants are commonly assumed in 1D models, i.e., a single representative reactant concentration inside the gas channel is required. However, this concentration is strongly dependent on the flow field. Although plenty of 1D models with sufficient accuracy as 3D models have been reported, the effects of the flow field have not been sufficiently discussed in the literature. In this work, efforts have been put into developing a generalized theory suitable for various flow fields to quantitatively analyze the in-plane reaction rate profile, so that the flow-field-sensitive representative reactant concentration can be employed to further fill the gaps in the 1D models.

Analytical model

A series of a plug flow reactor (PFR) and a continuous stirred tank reactor (CSTR) was proposed to explain the unideal flow and the macromixing behaviors inside a gas channel coupled with a gas diffusion layer (GDL), as shown in Fig. 1(a).[1] The fraction of PFR’s space time to total space time was defined as the characterization factor γ, which should be the function of flow field shape and flow rate. Furthermore, under-rib oxygen concentration and current density profiles were taken into account by introducing the dimensionless moduli.[2] Especially, the under-rib convection can be evaluated by Péclet modulus Pe, by increasing which will improve the under-rib mass transfer and the effectiveness factor f. The in-plane profile of the ohmic resistance of the membrane was assumed uniform. The oxygen reduction reaction (ORR) was regarded as a surface reaction occurring on the interface of cathode catalyst layer (CCL) and GDL. The ORR rate was assumed to be proportional to oxygen partial pressure and independent of relative humidity (RH).

Results and Discussion

The characterization factors γ of different flow fields were determined according to the residence time distribution simulated by the computational fluid dynamics (CFD) model. The ORR rate constant at each electrical potential was obtained from the measured polarization curve of a parallel gas channel (PN0) with 0.35 mm channel depth, by employing the analytical model mentioned above. Fig. 1(c) shows the polarization curves of parallel channels with staggered 1-mm-long partially narrowed structures (PSN1) and PN0 with different channel depths. Compared to the PN0, the under-rib convection improves the oxygen mass transport and the cell performance, where f increases 17 % at 0.35 V in the case of the PSN1. On the other hand, increasing the channel depth restrains the oxygen diffusion and f decreases by 18 % at 0.35 V. The analytical model results show good agreement with experiment data, which indicates that the effects of the flow field can be summarized by the parameters γ and f.
The analytical model provides the in-plane oxygen mole fraction and current density profiles. Fig. 2 shows the oxygen partial pressure distribution in a single gas channel calculated by the CFD model and analytical model. The mean oxygen partial pressure on the under-channel CCL-GDL interface calculated by the analytical model approximately equals the CFD result. By employing the ohmic resistance estimated according to the inlet conditions, although the current density is underestimated where RH is high, the integral mean of the in-plane current density offered by the analytical model has less than 5 % error compared to the CFD results, as shown in Fig. 3.
The analytical model also gives an effective way to estimate the integral mean in-plane oxygen partial pressure. Fig. 4 demonstrates the relationships among integral mean, inlet, and outlet oxygen partial pressures. When the reaction rate constant and effectiveness factor are fixed, Fig. 4 also reveals the relationships between total and local current densities. If the parameters γ and f are determined, the integral mean of the oxygen partial pressure can be obtained when the outlet oxygen partial pressure or oxygen conversion is known.

Conclusions

The analytical model quantitatively demonstrates the effects of the flow field shape and provides a quick and effective way to estimate the reaction rate profile, based on the fixed in-plane ohmic resistance assumption. This model was verified by experiment and CFD model in case of the oxygen conversion less than 0.33 and can be applied to ORR kinetics determination and rapid performance prediction.

Reference

[1] Y. Ma et al., J. Electrochem. Soc., 170, 084506 (2023).
[2] Y. Ma et al., ECS
Meet. Abstr., MA2023-02, 1867 (2023).

Figure 1