Numerical simulation of gas-diffusion-electrodes with moving gas–liquid interface: A study on pulse-current operation and electrode flooding
Introduction
Secondary zinc air batteries might be the upcoming alternative to state-of-the-art lithium-based battery systems due to their higher theoretical energy density (Caramia and Bozzini, 2014). One key-part of zinc air batteries is the gas-diffusion-electrode. There, the transport of gaseous species, and the electrochemical reactions of gaseous and liquid species occur. Since species transport limits the electrochemical performance at high current densities, the reaction and transport processes as well as their interaction have to be investigated intensively before novel electrode structures and innovative operation strategies can be proposed.
Existing model approaches consider the gas-diffusion-electrode in zinc air batteries as zero-dimensional with sufficient supply of reactants (Deiss et al., 2002, Schröder and Krewer, 2014). Thus, these approaches are limited to describe spatial concentration distributions in the electrode and electrode-specific phenomena, such as flooding of the gas-diffusion-electrode with liquid electrolyte. Flooding can be caused by a volume expansion of anode material in zinc air batteries (Schröder et al., 2014, Arlt et al., 2014). This leads to an increased liquid level in the gas-diffusion-electrode, and shifts the gas–liquid interface with operation time. A model-based description of a gas-diffusion-electrode can help to widen the insight into the flooding mechanism and its impact on the oxygen distribution inside the electrode.
In this novel work, we set up a one-dimensional model of a gas-diffusion-electrode. The model contains partial differential equations for species concentrations, e.g. Fick's second law, and electrochemical relations. Due to the nature of the problem considered, i.e. changing liquid volume in the gas-diffusion-electrode, we aim to directly track the gas–liquid interface position during the numerical simulation. Thus, the one-dimensional model is discretized in space for this work with a moving grid finite volume method as suggested by Ferziger and Perić (2002) (chapter 12.4, p. 375–378). Primarily, this method is chosen because it can be used without violating mass conservation (Ferziger and Perić, 2002, Cao et al., 2003, Brio et al., 2010). There are multitudes of other approaches to solve the underlying partial differential equations: analytically (Crank, 1975), with various discretization methods (Eymard et al., 2000), or with volume-of-fluid methods, which require to implement momentum conservation equations and thus require additional computational effort (Hirt and Nichols, 1981).
Considering the large amount of extensive numerical studies for two-phase flows (Tryggvason et al., 2001, Muradoglu and Kayaalp, 2006, Dong et al., 2014, Balcázar et al., 2014), it is evident that moving grid methods become more and more important for a variety of engineering applications. In general there are several moving grid methods with numerous variations reported in literature. Koltakov and Fringer (2013) state that there are mainly two classes of moving grid methods: the first class of methods dynamically adds grid points during the simulation in regions where an increased resolution is necessary, and then removes grid points in regions that are not of interest. To identify cells which need modification requires high computational effort and dealing with variable sized data structures. The second class of methods leaves the number of grid points unchanged, but dynamically moves them during the simulation. Their movement is based on a certain strategy or physical phenomena in grid regions of interest. Since the number of grid points is thereby fixed, this method might be easier to implement than for methods with adding or removing grid points. Furthermore, grid points at the interface of two phases normally align with mesh elements of the exact solution of the mathematical problem, so that moving mesh methods improve simulation accuracy (Koltakov and Fringer, 2013, Huang et al., 1994).
In the following, we first will describe the mathematical model of the gas-diffusion-electrode, and then briefly explain the finite volume method with moving grid applied. Subsequently, we compare efficiencies of moving grid and standard finite volume method with fixed grid by means of specific test cases. Furthermore, we investigate parameters that influence the oxygen distribution in the gas-diffusion-electrode, and implement pulse-current operation and flooding of the electrode as test cases. This analysis will help to further understand the diverse reaction and transport processes in gas-diffusion-electrodes, which in the end helps to optimize such electrodes and operation strategies applied.
Section snippets
Gas-diffusion-electrode model
In the following, the gas-diffusion-electrode (GDE) considered in this work is described. Furthermore, it is explained where a moving gas–liquid interface is expected.
The GDE is composed of a porous gas-diffusion-layer (GDL) and an attached porous catalyst layer (CL). Both are partly filled with air and liquid electrolyte (KOH-solution), respectively. A schematic of the GDE is given in Fig. 1. At the CL, the following electrochemical reaction takes place
with r(t) being the
Application of the finite volume method with moving grid
The derivation and explanation as well as examples for the application of the moving grid finite volume method are well reported (Demirdžić and Muzaferija, 1995, Muzaferija and Perić, 1997, Ferziger and Perić, 2002). A brief introduction of the method applied is given in the following. An extended explanation of the method is given in Appendix C.
To solve the aforementioned set of equations for the GDE model, a finite volume method with moving grid is applied for the spatial discretization of
Simulation results and discussions
Simulations for the GDE model are conducted on the one hand for pulse-current operation, implying a fluctuating cell current as input value for the system, and on the other hand for constant-current operation. We aim to investigate the impact of increasing flooding with liquid electrolyte, and to estimate the calculation error for the electrolyte volume and oxygen concentration in the GDE, when compared to the standard finite volume method. The parameters applied for the simulations conducted
Conclusions
We proposed a model for a gas-diffusion-electrode and applied a moving grid finite volume method with changing discretization step-size for the analysis of pulse-currents and electrode flooding. The step-size is thereby linked to the moving interface of gas and liquid, which is linked to the polarization behavior of the electrode via the current density. This novel approach enables to analyze concentration distributions in the electrode accurately and very comfortably. In detail, we
Acknowledgement
We gratefully acknowledge Horst Müller, Christine Weinzierl and Victor Emenike for helpful discussions, and Shyamal Kumar Das for proofreading the manuscript.
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