Elsevier

Journal of Power Sources

Volume 171, Issue 2, 27 September 2007, Pages 738-746
Journal of Power Sources

Numerical investigation of transient responses of a PEM fuel cell using a two-phase non-isothermal mixed-domain model

https://doi.org/10.1016/j.jpowsour.2007.06.029Get rights and content

Abstract

In this paper, a transient two-phase non-isothermal PEM fuel cell model has been developed based on the previously established two-phase mixed-domain approach. This model is capable of solving two-phase flow and heat transfer processes simultaneously and has been applied herein for two-dimensional time-accurate simulations to fully examine the effects of liquid water transport and heat transfer phenomena on the transient responses of a PEM fuel cell undergoing a step change of cell voltage, with and without condensation/evaporation interfaces. The present numerical results show that under isothermal two-phase conditions, the presence of liquid water in the porous materials increases the current density over-shoot and under-shoot, while under the non-isothermal two-phase conditions, the heat transfer process significantly increases the transient response time. The present studies also indicate that proper consideration of the liquid droplet coverage at the GDL/GC interface results in the increased liquid saturation values inside the porous materials and consequently the drastically increased over-shoot and under-shoot of the current density. In fact, the transient characteristics of the interfacial liquid droplet coverage could exert influences on not only the magnitude but also the time of the transient response process.

Introduction

Numerical modeling and simulation of PEM fuel cells is crucial for revealing the underlying physics and facilitating cell design and optimization. Many PEM fuel cell models have been developed to achieve these goals, including the single-phase or pseudo single-phase PEM fuel cell models [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], which either do not account for liquid water transport phenomena or simplify its treatment, and the two-phase models [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], which handle the liquid water transport and the related phenomena explicitly. The majority of these models, however, consider only steady-state operation conditions of PEM fuel cells. Since a PEM fuel cell would experience start-up and shut-down processes and frequent load changes for automotive applications, a numerical model capable of investigating transient responses is thus needed.

A transient PEM fuel cell model was developed in the work of Um et al. [1], but the main studies were not focused on the transient analysis, and thus only a preliminary result concerning the cell dynamic response with a step change of cell voltage was presented. This work was further extended by Wang and Wang [27] into a transient three-dimensional single-phase isothermal PEM fuel cell model. They estimated three time constants concerning electrochemical double-layer charging/discharging, gas transport, and membrane hydration/dehydration processes, and concluded that the double-layer charging/discharging process was very fast and could thus be safely neglected in transient analyses of PEM fuel cell operations. They also conducted extensive numerical simulations with step changes of cell voltage and inlet humidity and discussed the dynamic physics of the transient phenomena. Wang and Wang [28] later studied the dynamic responses of a PEM fuel cell undergoing a step change of current based on the work of Meng and Wang [5], [29] with a proper account of the electron transport. Shimpalee et al. [30], [31] numerically simulated the transient responses of a PEM fuel cell subjected to variable load changes based on a three-dimensional single-phase isothermal PEM fuel cell model. The simulations were conducted for a PEM fuel cell with a serpentine flow-field and a 10 cm2 reactive area. They presented numerical results under excess, normal, and minimal fuel and air supplies. Recently, Wu et al. [32] developed a transient two-dimensional single-phase non-isothermal model of PEM fuel cells, and with an inclusion of the heat transfer equation, they were able to consider four transient processes, namely the electrochemical double-layer charging/discharging, species transport, membrane hydration/dehydration, and heat transfer processes. Based on their numerical results, they concluded that the heat transfer process could exert significant influences on fuel cell dynamic responses.

The transient PEM fuel cell models briefly reviewed in the early section are all based on single-phase or pseudo single-phase simplifications. Wu et al. [33] have attempted to consider the liquid water effect by defining a fixed liquid saturation of 10% in the porous materials in a PEM fuel cell based on the two-phase results provided in the review paper of Wang [34]. Natarajan and Nguyen [21] developed a transient two-dimensional two-phase model for the cathode of a PEM fuel cell, and they concluded that liquid water transport would prolong the cell response time, especially under the current-collecting land. This work only considered the cathode side under isothermal conditions. Since the inclusion of the temperature effect is crucial for correctly simulating the condensation/evaporation phenomena in two-phase flows, Shah et al. [35] recently developed a transient non-isothermal model for a PEM fuel cell. They presented numerical results in the form of potential sweeps and were able to quantitatively predict the hysteresis phenomenon often observed in PEM fuel cell experiments. However, the model is one-dimensional and thus could not be applied to fully investigate the complex multi-dimensional physics in practical PEM fuel cell operations. Song et al. [36] also developed a transient one-dimensional non-isothermal two-phase PEM fuel cell model to investigate transient liquid water transport in the cathode GDL. The phase change phenomenon and parameters affecting transient and steady-state liquid water transport were discussed.

In order to fully investigate the dynamic responses of a PEM fuel cell under practical operation conditions and further enhance fundamental understandings of the intricate interactions of thermal and water managements during the cell transient operations, a transient two-phase non-isothermal PEM fuel cell model is developed in the present paper based on a previously established two-phase mixed-domain approach [26]. The model is capable of solving two-phase flow and heat transfer processes simultaneously with a proper consideration of the effect of liquid droplet coverage at the gas diffusion layer (GDL) and the gas channel (GC) interface. The model will be applied herein for two-dimensional time-accurate simulations in a cross-section perpendicular to the flow direction so that the effects of liquid water transport and heat transfer phenomena on the transient responses of a PEM fuel cell, with and without condensation/evaporation interfaces, could be fully examined and clearly presented.

Section snippets

Theoretical formulation

The complete conservation equations in their transient forms are developed in this paper based on a previously established steady-state multi-dimensional two-phase mixed-domain PEM fuel cell model [26]. First, the transient conservation equations of mass, momentum, species concentrations in the gaseous phase are presented.

  • Mass conservation:[ε(1s)ρ]t+(ρu)=0

  • Momentum conservation:1ε(1s)(ρu)t+1ε2(1s)2(ρuu)=p+τ+Su

  • Species conservation:[εeff(1s)ci]t+(uci)=(Dieffci)+Si

In Eq.

Result and discussion

The present transient two-phase non-isothermal PEM fuel cell model has been implemented into a commercial CFD package, Fluent, through its user coding capabilities and applied herein for two-dimensional numerical simulations, as shown in Fig. 1. The geometric parameters of the fuel cell are listed in Table 3.

Hydrogen and water vapor is fed into the anode while air and water vapor into the cathode. The fuel cell is operated at 2 atm on both the anode and cathode sides. The cell stoichiometry

Conclusion

In this paper, a transient two-phase non-isothermal PEM fuel cell model has been developed based on the previously established two-phase mixed-domain approach. This model is capable of solving two-phase flow and heat transfer processes simultaneously with a proper consideration of the effect of liquid droplet coverage at the gas diffusion layer and the gas channel interface. The model has been applied for two-dimensional time-accurate simulations in a cross-section perpendicular to the flow

Acknowledgements

This work is partially supported by The Ministry of Personnel of PR China and The Department of Personnel of Zhejiang Province (J20070016).

References (37)

  • S. Dutta et al.

    Int. J. Heat Mass Transfer

    (2001)
  • N.P. Siegel et al.

    J. Power Sources

    (2003)
  • H. Meng et al.

    Chem. Eng. Sci.

    (2004)
  • H. Ju et al.

    Int. J. Heat Mass Transfer

    (2005)
  • T. Berning et al.

    J. Power Sources

    (2002)
  • B.R. Sivertsen et al.

    J. Power Sources

    (2005)
  • H. Meng

    J. Power Sources

    (2006)
  • H. Meng

    J. Power Sources

    (2007)
  • Z.H. Wang et al.

    J. Power Sources

    (2001)
  • L. You et al.

    Int. J. Heat Mass Transfer

    (2002)
  • W.Q. Tao et al.

    J. Power Sources

    (2006)
  • H. Meng

    J. Power Sources

    (2007)
  • Y. Wang et al.

    Electrochim. Acta

    (2005)
  • Y. Wang et al.

    Electrochim. Acta

    (2006)
  • S. Shimpalee et al.

    J. Power Sources

    (2006)
  • S. Shimpalee et al.

    J. Power Sources

    (2006)
  • H. Wu et al.

    J. Power Sources

    (2007)
  • H. Wu et al.

    Int. J. Hydrogen Energy

    (2007)
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