Coupled continuum and condensation–evaporation pore network model of the cathode in polymer-electrolyte fuel cell

Highlights

• A coupled continuum and condensation pore network model of the cathode in PEMFC is presented.

• Location of liquid water condensation is in good agreement with already published experiments.

• Current density distribution at rib-channel scale is discussed for coupled and non-coupled model.

Abstract

A model of the cathode side of a Proton Exchange Membrane Fuel Cell coupling the transfers in the GDL with the phenomena taking place in the cathode catalyst layer and the protonic transport in the membrane is presented. This model combines the efficiency of pore network models to simulate the liquid water formation in the fibrous substrate of the gas diffusion layer (GDL) and the simplicity of a continuum approach in the micro-porous layer (MPL). The model allows simulating the liquid pattern inside the cathode GDL taking into account condensation and evaporation phenomena under the assumption that the water produced by the electro-chemical reactions enters the MPL in vapor form from the catalyst layer. Results show the importance of the coupling between the transfers within the various layers, especially when liquid water forms as the result of condensation in the region of the GDL fibrous substrate located below the rib.

Introduction

Proton Exchange Membrane Fuel Cell (PEMFC) is considered as a key alternative to thermal engines for transport application, allowing no use of oil fuels and no emission of greenhouse gases. Numerous studies have been conducted in the last thirty years to increase its performance and durability, and reduce its cost, which are the three main bottlenecks to be solved to ensure the mass market development of this solution. Water management remains up-to-date a major limiting factor to performance and durability of PEMFC, see for instance Ref. [1]. Inside the Membrane Electrode Assembly (MEA) a trade-off is to be found between drying and flooding. Drying occurs when the membrane and/or the ionomer in the active layers do not contain enough water to ensure good proton conductivity, whereas flooding occurs when too much liquid water is present inside the MEA and reduces the gas access to the catalytic sites. In addition to increasing the performance, a controlled water management also allows increasing the durability of PEMFC as some degradation mechanisms are linked to the presence of liquid water and/or to the level of water vapor partial pressure inside the catalyst layer, see for instance Ref. [2].

Water management is closely linked to the operating conditions of the PEMFC (temperature, pressure and hydration of the gases, steady-state or transient…) but also to the properties of the layers used in the MEA, gas diffusion layer, catalyst layer and membrane. The multiple and conflicting functions of these layers (electrical and thermal conduction, gas diffusion and liquid water removal) and their coupling, see for instance Ref. [3], make however complex their optimization by semi-empirical trial and error test procedures. The development of more descriptive and predictive numerical simulation tools is necessary to better understand water management inside the MEA and its link to the properties of the layers. This is mandatory to progress towards “design” tools.

Important developments have been carried out in this domain for several years, such as the modeling of the MEA with more and more sophisticated representations of the various layers, see for instance Ref. [4], or the progressive consideration of the coupling between electrical, fluidic and thermal transports [5]. In these models, see also Ref. [6], the two-phase transport is based on the classical continuum approach to porous media. These models have allowed making progress in the understanding of the transfers within the PEMFC. However, the relevance of this approach has been questioned, i.e. Ref. [7], because of the capillary regime prevailing in the gas diffusion layers (GDL) and the obvious lack of length scale separation (only a few pores over the thickness of the fibrous substrate of the GDL). The latter is generally a two-layer system resulting from the assembly of a fibrous substrate, referred to as the diffusion medium (DM), and a micro-porous layer (MPL).

As an alternative, Pore Network Model (PNM) has been applied to PEMFC. PNM is well adapted to model the capillary regime, especially in thin layers such as the DM of the GDL, e.g. Ref. [8], as well as the more complex cases where the wettability is mixed (mixed refers here to situations where hydrophilic pores and hydrophobic pores coexist in the DM), e.g. Refs. [9], [10]. For this reason, the use of PNM has up-to-date mainly focused on the DM even if some developments have also been conducted for the Cathode Catalyst Layer (CCL), e.g. Ref. [11]. To our knowledge, PNM has not been applied to the micro-porous layer (MPL) of the GDL, at least as a tool of simulation directly at the scale of the pore network of a MPL. However, results obtained from PNM simulations are exploited for example in Ref. [12] to study the optimal thickness of the MPL. For this reason, PNM is used in the present work to model the liquid water formation in the DM.

Regarding the simulation of two-phase flows in the DM with PNM, one can distinguish the simulations performed in conjunction with ex-situ experiments from the more challenging simulations aiming at predicting the liquid water distributions within the GDL in an operating fuel cell. Regarding the former, recent works have confirmed that a standard invasion percolation algorithm is well adapted to describe the ex-situ situation where typically liquid water is injected from one side in a dry GDL [13], [14], at least when the medium is hydrophobic.

The situation regarding the in-situ case is much less clear. In a majority of works, see references in [15], a scenario similar to the ex-situ case is considered. Namely, liquid water enters the GDL in liquid phase from the CCL. This situation of liquid water injection is referred to as the injection scenario.

However, a completely different option is considered in Ref. [15] where it is assumed that water enters the GDL in vapor form. According to the scenario considered in Ref. [15], liquid water can form in the DM as a result of the condensation of the water vapor in the colder zones of the DM (essentially in the region of the DM below the ribs). This situation of liquid water condensation is referred to as the condensation scenario. An important feature of the model in Ref. [15] is therefore to take into account the temperature variations within the GDL. The liquid distribution is significantly different between the two options. As discussed in Ref. [15], the condensation scenario is in good agreement with several experimental results presented in Refs. [16], [17], noting that these experiments are performed at temperatures close to the standard operating temperature of PEMFC (∼80 °C). As in the experiments [16], the simulations show that the GDL is completely dry at sufficiently low current density and/or relative humidity in the channel. As in the experiments [16], a strong rib–channel separation effect is observed when liquid water is present, i.e. the liquid water accumulates in the region below the rib and no water is observed bellow the channels. As in the experiments [17], the saturation along the DM thickness increases from CCL to rib/channel area, whereas this saturation typically decreases according to the simulations based on the liquid injection scenario, e. g. Ref. [18]. The impact of average current density and channel relative humidity on saturation profiles are also consistent with the experimental results reported in Ref. [17]. Despite all these elements showing several points of good agreement between the experiments and the simulations, we do not claim that the PNM presented in Ref. [15], is adapted to describe all the situations encountered in PEMFC as regards the liquid water formation and displacement in the GDL. For instance, it could be not sufficient when the operating temperature is significantly colder than 80 °C or when the relative humidity in the channel is close to 100%. Further work is needed to test or improve the model for those conditions. Nevertheless, based on the overall good agreement between the condensation–evaporation PNM [15], [19] and several experimental observations as mentioned above, the model presented in what follows adopts the same option as in Ref. [15] as regards the computation of the liquid water formation.

It can be noted that the consideration of condensation phenomenon in a discrete approach as a key aspect of liquid water in the DM is not restricted to the works presented in Refs. [15], [19]. A condensation algorithm is also presented in Refs. [20], [21] and the conclusion is that condensation has a significant influence of the liquid distribution. However, the model is different from the one proposed in Ref. [15]. This is actually not a PNM but a somewhat different discrete approach. In contrast with the model presented in Ref. [15], only simulations in 2D discrete structures are presented in Refs. [20], [21], and liquid injection is considered together with condensation. Thus, the fact that the GDL can be completely dry is not pointed out. The condensation algorithm is completely different and relies on a coupling with a continuum model to compute the source–sink terms in the GDL associated with condensation and evaporation phenomena. By contrast, all the phenomena are directly computed at the pore network scale in the DM (which is referred to as the fibrous substrate (FS) in Refs. [20], [21]), in our model. We can also mention the recent numerical work presented in Ref. [22] on the impact of the MPL. This work is based on a two-dimensional dynamic pore network taking into account the condensation evaporation phenomena. There is, however, no coupling with the electrochemical phenomena in the CCL.

Compared to the model presented in Ref. [15], the objective of the present article is to improve the modeling of the cathode by essentially coupling the PNM presented in Ref. [15] with the phenomena occurring in the adjacent layers, namely the MPL, CCL and the membrane and in particular with the electrochemical reactions taking place in the CCL.

In Ref. [15], only the DM is considered and important data such as the current density and heat flux distributions at the DM inlet are not computed but are imposed as input data. By introducing the coupling, these data will be outputs of the computations. Another important objective is to evaluate the impact of the coupling on the results obtained using the simpler approach proposed in Ref. [15]. As we shall see the coupling is performed by coupling the PNM describing the transport phenomena and the water formation in the DM, with continuum models for the MPL, and with the phenomena taking place in the CCL.

Developing mixed approaches coupling PNM and continuum models is not a novelty in the context of PEMFC. The previously mentioned work presented in Ref. [21] is an example. More recently, on can refer to the works presented in Ref. [23], where three different coupling methods are discussed. The pore network is however only 2D and again it is assumed that water enters in liquid form into the GDL. As a result the liquid distribution in the DM depicted in this paper (see Fig. 10 in Ref. [23]) has nothing to do with the liquid distributions presented in Ref. [15]. This also holds for the liquid water distributions computed by the same group in Ref. [24]. Interestingly, the temperature in Ref. [24] is quite low (25 °C), much below the standard operating temperature (∼80 °C) considered in Ref. [15]. A coupled continuum-PN models is also presented in Ref. [25]. This model couples a three-dimensional PNM in the GDL to continuous models in the other layers for anode and cathode sides. However, this model is limited to isothermal situations and the injection scenario in the DM (no MPL is modeled) for which the injection points at the interface GDL/CCL are inputs of the models. The condensation phenomenon is completely ignored.

The paper is organized as follows. The fuel cell cathode sub-domain of interest is described in Section “Cathode unit cell”. The physical models used in the different layers are presented in Section “Transport phenomena in GDL and associated boundary conditions (dry condition)”. The pore network approach for computing the various transport phenomena in the DM is presented in Section “Pore network approach of transport in DM”. Section “Continuum approach of transport in MPL” describes the continuum model used for the MPL. The CCL and membrane discrete representations are presented in Section “Catalyst Layer and membrane”. The coupling procedure is described in Section “Coupling GDL with CCL and membrane”. Results are presented and discussed in Section “Results and discussion”. Finally conclusions are discussed in Section “Conclusions”.