Dimensionless Moduli Governing Under-Rib Transport Phenomenon in Polymer Electrolyte Fuel Cell
Authors: Ma Yulei , Kageyama Miho , Gyoten Hisaaki , Kawase Motoaki 
Published: February 2024

Introduction

The performance of polymer electrolyte fuel cell (PEFC) can be considerably improved by promoting the under-rib convection or cross flow between adjacent gas channels, e.g., applying the serpentine and staggered partially narrowed flow fields[1]. Although a lot of efforts have been devoted to analyze the under-rib transport phenomenon, an analytical model which quantitively demonstrates the dominant factors of the under-rib processes has not been established. In this study, a theoretical analysis of the relations between oxygen reduction reaction (ORR) and mass transfer capacity is carried out. The dimensionless moduli which combine physical properties, flow field dimensions and operating conditions are derived, which provides a theory for optimization of flow field and operating condition design for PEFC.

Theoretical Analysis

The water is assumed to only exist in vapor phase in a steady-state isothermal cell. The gas diffusion layer (GDL) is considered as uniform porous medium, in which Darcy’s law is applicable. The even velocity and oxygen mass fraction profiles in through-plane direction inside GDL is considered. The ORR was experimentally proven as a first order reaction of oxygen partial pressure according to our previous study,[2] and is regarded as a surface reaction, so that the oxygen consumption rate can be expressed as Eq. (1). The ORR rate constant, which is the function of the cathode overpotential or electromotive force, is assumed to be fixed across the rib.
The theoretical model was derived from one-dimensioned mass balance of oxygen, which exhibits that the under-rib process is dominated by 3 dimensionless moduli, Péclet number Pe, Thiele number φ and the ratio of oxygen mass fractions θ at two sides of the under-rib GDL, which were defined by Eqs. (2)–(4). Péclet number represents the ratio of oxygen convection rate to oxygen diffusion rate, which is determined by the pressure difference between adjacent channels. Thiele number represents the ratio of oxygen diffusion resistance to reaction resistance. The average oxygen mass fraction can thus be calculated from Eq. (5).

Results and Discussion

The theoretical model was compared with the computational fluid dynamics (CFD) simulation in the computational domain shown in Fig. 1, where the GDL was placed between two parallel gas channels, instead of being laid under the gas channel, and the active area was only located under the rib. In the CFD simulation, the velocity and pressure distributions were calculated by solving Navier-Stokes equations, and the component distribution dependencies on density, diffusivity and viscosity were also considered. Fig. 2 shows the under-rib average current density at different geometries and operating conditions. The dimensionless moduli calculated from the inlet conditions offer an accurate current density prediction, which demonstrates these moduli dominate the under-rib transport phenomenon.
The typical operating condition gives φ = 1.5 and Pe = 4, where the model provides the average current density with high confidence. The model provides lower oxygen mass fraction than the CFD results especially in case of θ = 1, which exists in the staggered partially narrowed flow field. The reason can be attributed to the interface between gas channel and GDL, where the low velocity cannot eliminate the mass transport resistance, so that the model overestimated the oxygen mass fraction at rib boundaries, as shown in Fig. 3.
The effects of dimensionless moduli on the current density are exhibited in Fig. 4. In case of θ = 1, when Pe is lower than 5, the under-rib convection cannot obviously boost the under-rib oxygen concentration, which was also reported in our previous study[1]. On the other hand, in case of θ< 1 and Pe > 0, although little increase on Pe remarkably improves the under-rib mass transfer which explains the good performance of serpentine flow field, the benefits from the under-rib convection reduces when Pe is high. Additionally, since oxygen cannot be supplied sufficiently from the gas channel, higher φ gives lower under-rib oxygen concentration.

Conclusions

The theoretical model for describing the under-rib transport phenomenon was established and verified by CFD calculation, which was found to be dominated by 3 dimensionless moduli. The model demonstrates that the Péclet number is required to be large enough in partially narrowed flow fields to maximize the profits from the under-rib convection.

Acknowledgment

This work was supported by the FC-Platform Program: Development of design-for-purpose numerical simulators for attaining long life and high performance project (FY 2020–FY 2023) conducted by the New Energy and Industrial Technology Development Organization (NEDO), Japan.

Reference

[1] Y. Ma et al., ECS Trans., 109 (9), 171–197 (2022).
[2] M. Kawase et al., ECS Trans., 75(14), 147–156 (2016).

Figure 1