Three-dimensional multiphase simulation and multi-objective optimization of PEM fuel cells degradation under automotive cyclic loads

https://doi.org/10.1016/j.enconman.2021.113837Get rights and content

Highlights

  • New combination of 3D-CFD simulation and degradation model for PEMFC is developed.

  • A new set of single/multi-objective optimization is planned through four scenarios.

  • The degradation rate is minimized as well as the initial performance is maximized.

  • Temperature is the most effective parameter on aging rate and initial performance.

  • The optimization results show an improvement of 36% in the final power density.

Abstract

One of the remaining bottlenecks of PEM fuel cell vehicle commercialization as a probable alternative to conventional vehicles is the performance degradation during dynamic loads. Herein, an innovative coupling is presented between a three-dimensional, multiphase computational fluid dynamic simulation with eight conservation equations and a novel degradation model to predict the performance loss of PEM fuel cell under vehicular load cycling. Moreover, a multi-objective optimization problem with four different scenarios is also planned for the first time as the other novelty, to minimize the cell power density loss as well as maximize the initial cell power density, in order to find the optimum value of some operating and structural parameters. The model predicts the power density degradation rate of about 0.001627 kW cycle−1 (equivalent to 4.067 kW m−2 loss after 2500 cycles) which is in good agreement with experimental data. The results reveal that the operating temperature is the most influential parameter with rank 1 for the cost functions. The optimization results also show a considerable enhancement of about 36.9% in the final power density after load cycling compared to the base case conditions by fine-tuning five operating and structural parameters.

Introduction

Fuel cell vehicles have been favored dramatically during recent years. According to the last 4 th energy wave report, the capacity of the installed fuel cell in the transport system has been grown from 390 MW in 2016 to 760 MW in 2017, approximately 100% growth [1]. This issue reveals that fuel cells are considered as one of the probable alternatives for internal combustion engines in the future. Although, at least two major bottlenecks, the durability, and the cost, remain to touch the target point of commercialized fuel cell systems for transport operation [2], [3]. The lifetime of polymer exchange membrane fuel cells (PEMFCs) is not as long as it needs for vehicular conditions [4]. Because on one hand, a fuel cell in automotive use is exposed to a wide range of temperature and humidity changes, [5] and on the other hand dynamic and transient loadings [6], [7] (including startup-shutting down cycling, [8] idle operation, potential cycling, [9] and high current (low voltage) operation [10]) are applied to the fuel cell during the driving. Under these conditions, the degradation of fuel cell components is exacerbated. Potential cycling is one of the most prevalent and significant conditions with a high degradation rate, [11] which causes structural and morphological changes in catalyst layers, especially in the cathode catalyst layer [12], [13]. The effects of voltage cycling, which have been known so far include Pt particle detachment, [14] Pt particle growth via Ostwald ripening, [15], [16] Pt dissolution into ionomer phases, forming Pt band at the interface of membrane and cathode catalyst layer (CCL), [17] and coalescence of fine particles [18]. These effects lead to a considerable reduction in electrochemical surface area (ECSA) [19]. The voltage cycling and its effects on the PEM fuel cell performance are widely being investigated in recent researches. Here some experimental and theoretical studies have been addressed.

Garcia-Sanchez et al. investigated the relationship between power density loss and local cell current density to evaluate the local degradation under three different potential cycling [20]. They showed that the regions with high current densities cause to form a Pt band near to membrane/CCL interface and increases the irreversible losses [20]. Kneer et al. designed a set of experiments to study the correlation between the ECSA loss, the structural changes in CCL, and voltage cycling [21]. They also investigated the effect of cycle duration and the dwell time for square wave and the scan rate for the triangular wave on the ECSA reduction [22]. Kneer et al. also found that the dwell time in the upper potential limit (UPL) is the main stressor so that the longer the dwell time at high potential, the higher the degradation rate. Similar results are also reported by Harzer et al. [23] for 30,000 cycles of the square and triangular cycling between 0.6 and 1 V [23]. Kneer et al. finally presented a semi-empirical model to evaluate the ECSA loss during potential cycling [24]. They tuned the empirical-based model presented in our work, [25] for their experimental data. The results showed that an increase in temperature, relative humidity, or UPL leads to reinforcing the ECSA loss, however, the lower potential limit (LPL) does not have a considerable effect in this case [24]. The same results have been reported for the influence of operating parameters (relative humidity and LPL) on ECSA loss by Takei et al. [26].

Koltsiva et al. presented an analytical model to compute the ECSA loss due to the growth (Ostwald ripening), migration, coalescence, and dissolution of Pt nanoparticles for both commercialized and synthesized catalyst layers [27]. They could evaluate the time-variation of Pt particle size distribution and the ECSA. The outputs of their model may be used as inputs of the performance predictor model to estimate the performance of fuel cells under potential cycling. Li et al. [28] did this job by presenting a framework for performance degradation prediction of a PEMFC during startup-shutdown cycles. They used a cathode catalyst performance predictor which has already been presented in our earlier work [29] and coupled it with a degradation model. Recently, Jahnke et al. developed a 2D PEMFC performance model coupled with a complete degradation model to study the effects of cathode catalyst layer degradation through modeling the aging phenomena of Pt particles such as oxidation, dissolution, Ostwald ripening, and band formation near the membrane [30]. They compared the steady-state and load cycling conditions and concluded that degradation is much higher under the second condition.

In this paper, a foundation of a semi-transient simulation is prepared to couple a new degradation model that forecasts the morphological changes of CCL during a given potential cycling protocol, with a complete 3D-CFD model that computes the PEM fuel cell performance. The degradation model captures the structural changes within the CCL including ECSA loss, Pt particle growth through Ostwald ripening, and Pt dissolution in ionomer during potential cycling. These parameters could be used as inputs for the CFD model to forecast the performance loss. The CFD model predicts the fuel cell performance through solving mass, momentum, energy, species transport, electric and protonic charge, liquid water saturation level, and dissolved water content in ionomer conservation equations. Linking the new degradation model which forecasts the structural changes of CCL with a complete 3D-CFD simulation that computes the PEMFC performance is the major innovation of the present investigation to predict the performance loss of PEM fuel cell under vehicular load cycling. Finally, based on the foundation of the simulation part, a multi-objective optimization with four different scenarios is designed for the first time to find the optimum value of effective operating and structural parameters in order to minimize the degradation rate during potential cycling as well as maximizing the initial performance. In fact, this kind of optimization problem has been designed for the first time and it is the second novelty of the current study. The results may be very helpful for fuel cell vehicle manufacturers to investigate the degradation of PEM fuel cells during the vehicular conditions and find the optimum value of structural and operating parameters to design the stacks according to them.

The rest of this article is organized as follows: Sections 2 explains the 3D-CFD and degradation models. Then, the boundary conditions are determined in Section 3. The assumed optimization problem is expressed in Section 4. The model input parameters and the solution procedure are explained in 5 Results and discussion, 6 Validation, respectively. The results are reported in Section 7. Finally, the concluding remarks will be presented at the end of the article.

Section snippets

Model descriptions

In the present study, a three-dimensional (3D) simulation is propounded to predict the reduction in performance of a polymer exchange membrane fuel cell (PEMFC) regarding the degradation process that takes place due to the potential cycling as one of the most significant applied loads in automotive uses. Then an optimization problem is designed and solved to minimize the performance reduction during its lifetime and also maximize the practical performance of the fuel cell. Therefore, at first,

Boundary conditions

To complete the model, boundary conditions must be specified. The model is based on a single domain approach where all the governing equations are solved throughout the entire domain, without imposing the boundary conditions at the interfaces between different zones. So, the boundary conditions are needed at the outer surfaces of the domain. These boundary conditions which demonstrate the operating conditions of the PEMFC are expressed as follows:

Optimization problem

Based on the result of our earlier work and also some other references [24], [25], [28], the power density degradation rate (PDR) of PEM fuel cell under cyclic load could be controlled and decreased by adjusting some of the operating and structural parameters in specific values. Nevertheless, fine-tuning of these parameters cause to reduce the current density and power density of a pristine fuel cell. Thus, the optimum value of these parameters must be computed so that the PDR is minimized as

Results and discussion

At first, the predicted polarization curves of the model for the pristine and degraded fuel cell are compared and validated against the experimental results in the literature. The validation case is presented in Section 7.1. On the other hand, a set of grid independency study is performed to show that the results are independent of the grid size. In this way, the grid convergence index (GCI) is computed and presented in Section 7.2. The main results of this paper are divided into two sections:

Validation

The polarization curves of degraded PEMFC are computed after 2500, 4000, and 5500 cycles and compared with the experimental results have been published in Ref,. [48] the results are indicated in Fig. 6. For validation purposes to be the same situations, the anode and cathode inlets are fed with pure hydrogen and air with flow rates of 0.38 dm3 min−1 and 0.91 dm3 min−1, respectively [48]. The load cycling protocol for validation purposes is also set to a square wave with Vmin=0.87V, Vmin=1.2V,

Grid convergence index

The grid independency of the present model is investigated using three different mesh sizes from coarse to fine. Therefore, the three different mesh sizes, Δ, with the constant ratio (r = Δ coarsemedium = Δ mediumfine) are used and reported in Table 10. The full description of the grid convergence index (GCI) calculation is presented in the literature [54]. However, a brief explanation is expressed about GCI calculation in the following:

A representative grid size, Δ, is defined as:Δ=i=1

Concluding remarks

A novel method of coupling between a performance predictor model of PEM fuel cell and a degradation model of catalyst layer under cyclic load has been presented in the current study. In fact, the major innovation is to develop a complete 3D-CFD model in the Ansys Fluent® software package which is equipped with a performance loss predictor model that forecasts the aging process of the fuel cell during load cycling by computing ECSA degradation, growth of Pt particles, and consequently the

Future plan

To improve the present model and develop the research, two main duties will be planned in the future works by the authors. The first one is to develop a degradation model of the anode catalyst layer during the dynamic loads to add to the simulation part of the present study which may cause some improvements. The second one is modeling the flooding in the gas channels at high current densities in order to investigate the interactions between the fine-tuning of the relative humidity of the

CRediT authorship contribution statement

M. Moein-Jahromi: Conceptualization, Investigation, Visualization, Software, Validation. M.J. Kermani: Supervision, Conceptualization, Methodology, Data curation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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