Cell-level modeling

Cell level models with varying dimensionality have been reported. To mention a few, 2D models are reported by Li et al. [88], Billigham et al. [89], and Keegan et al. [90], Burt et al. extended a ID model to simulate a cell stack using domain decomposition and parallel execution of the code [91]. Aguiar et al. have also reported ID model for direct internal reforming conditions [81,92]. 

CeU-level macroscale models consider the heat transfer, species transport, chemical reactions, and electrochemistry within the SOFC cell [27, 31, 51, 52]. In cell-level models, the detailed transport of gas in the fuel and air channels and in the porous electrodes are simulated on a macroscale. This requires a rigorous CFD simulation and commercial codes, such as FLUENT, COMSOL, and Star-CD, are used for cell-level models. Cell-level models consider the electrodes and electrolyte on a continuum scale, which means that the models do not explicitly resolve... 

Cell-level models solve the species [Eq. (26.1)], momentum [Eq. (26.5)], and energy [Eq. (26.7)] conservation equations using the effective properties of the electrodes and can include the electrochemistry using a continuum-scale (Section 26.2.4.1) or a mesoscale (Section 26.2.4.2) approach. Traditionally, cell-level models use a continuum-scale electrochemistry approach, which includes the electrochemistry as a boundary condition at the electrode-electrolyte interface [17, 51, 54] or over a specified reaction zone near the interface. The electrochemistry is modeled via the Nernst equation [Eq. (26.12)] using a prescribed current density and assumptions for the polarizations in the cell. The continuum-scale electrochemistry is then coupled to the species conservation equation [Eq. (26.1)] using Faraday s law ... 

Recently, several groups have taken cell-level macroscale models a step further to investigate the electrochemistry through the thickness of the electrodes using the mesoscale electrochemistry approach [19, 27, 31]. In these models, no assumptions are made about a reactive zone for the electrochemical reactions instead, the electrochemistry is modeled through the thickness of the electrodes based on a mesoscale electrochemistry approach (Section 26.2.4.2) in which the explicit charge-transfer reactions [27] or a modified Butler-Volmer approach [19, 31] are modeled. This extends the effects of the electrochemical reactions away from the electrolyte interface into the electrodes. In these cell-level models, the electrochemistry is coupled to the local species concentrations, pressures, and temperatures, and provides a more detailed view into the local conditions within the fuel cell and how these local conditions affect the overall SOFC performance. 

Macroscale cell-level models are able to provide a great amount of insight into the operation and performance of SOFCs. With the newer mesoscale electrochemistry models, information about the conditions within the SOFC electrodes and electrolytes can even be resolved. However, due to the continuum-scale treatment of the SOFC, these models stiU rely on effective parameters, which need to be determined through smaller scale modehng or by fitting the models to experimental data. 

In addition to cell performance, Weber and Newman [49] validated their membrane model using a simplified fuel-cell model in terms of net water flux per proton as a function of current densities, stoichiometries, and cell temperature. This net water flux is determined by a number of factors and its validation must employ cell-level models. Wang and Chen [50] provided validation of their cell-level model in terms of through-plane liquid water profiles across multiple layers, that... 

In spite of the advances made in PEFC modeling, many challenges remain. First, there is a critical need to couple, in some computationally efficient way, the pore-level or particle-level submodels with the macroscopic cell-level models in order to take into account the effects of the microstmctures of CDL/MPL and CL. Second, further efforts are also needed to model the cold start, transient, and two-phase transport at the ceU level. At present, a framework of single fuel-cell modehng has been developed, but the physics is not yet completely understood. For example, ice formation within the catalyst layer and its impact on the electrochemical reaction need further study. The two-phase transport at the CL-MPL and MPL-CDL interfaces is not clearly understood at present. Third, current... 

In this chapter the models on the cell level are summarized. Cell-level models are considered to represent the core knowledge of fuel cell development. This means, for example, that models focusing on transport on a small scale in the electrolyte or gas-diffusion layers, where macroscopic approaches do not apply. 

To provide an overview on cell-level models, in this chapter the dimensionality of the models is used as the criterion. On the cell level, zero-dimensional to fully three-dimensional approaches are known. These dimensions are illustrated in Figure 15.2 Whereas zero-dimensional models are single equations and one-dimensional approaches describe processes orthogonal to the electrolyte, simulations in two and more dimensions also include the mass, heat, and charge transport in the plane of the flow field. 

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