Computer methods for performance prediction in fuel cells

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Abstract

Several transport models for fuel cells have been developed. The models are compared and tested for single fuel cells and multi-cell stacks of planar solid-oxide fuel cells, the three main approaches considered are (a) a detailed numerical model (DNM) of flow, heat and mass transfer and electrochemistry, (b) a flow-based methodology based on a distributed resistance analogy (DRA), and (c) a presumed-flow methodology (PFM). The results from each of the above approaches are compared in detail, and merits and drawbacks discussed. It is shown that, under certain circumstances, the simpler approaches have the potential to supplant or complement the direct numerical method in the analysis of fuel cells.

Introduction

High power generation and heat recovery efficiency with low pollution rate make fuel cells [1] potential useful energy conversion systems. Initial modelling efforts have been focused on planar solid oxide fuel cells (SOFCs). Experimental data are scarce and for this reason substantial effort is being devoted to developing numerical analysis tools capable of performing calculations on transport and electrochemical phenomena within the passages of fuel cells.

Since the first SOFC computations, Vayenas and Hegedus [2], the detail of the mathematical modeling has increased. Numerical simulations have been conducted at the electrode, cell, and stack levels. Modelling at the electrode level aims at building better electrodes through study of microscopic processes, while modelling at the stack level aims at optimizing the design, by considering alternatives and determining operational strategies. Chemical reactions (shift reactions and internal reforming), electrical potential distribution, and porous-media flow are all issues to be addressed.

Fiard and Herbin [3], Ferguson [4], Herbin et al. [5], and Bernier et al. [6] developed a detailed three-dimensional (3D) SOFC model with governing equations for mass, heat and electrical current for both solid and gas-channel flows. Numerical schemes for the boundary condition at the interfaces between the electrolyte and electrodes are given. The 3D model was applied to planar stack simulations. Karoliussen and Nisanciouglu [7], Achenbach [8], Bessette and Wepfer [9], and Bernier et al. [6] took into account the reforming and shift reactions in their respective models. In addition, Ahmed et al. [10], Sira and Ostenstad [11], Achenbach [8], Bessette and Wepfer [9], Costamagna and Honegger [12], Chan et al. [13], Dong et al. [14] and Beale et al. [15], [16] applied their models to heat and mass transfer in SOFCs.

The complexity of the SOFC problem requires the use of large fast computers to tessellate the geometry into a large number of mesh points, and solve the coupled partial differential equations describing the transport phenomena. The theoretical framework for stack modeling based on simplified numerical methods, so that numerical simulation become tractable on personal computers, was introduced by various authors, Achenbach [8], Bernier et al. [6], Beale et al. [15]. Both single cells and stacks of fuel cells are considered in the present work. Fig. 1 is a schematic of a stack considered in this study.

Section snippets

Detailed numerical model (DNM)

For single cells and small stacks it is possible to discretize the entire domain and solve the governing equations directly. This is referred to below as a detailed numerical model (DNM). The equations to be considered are the usual transport equations, namely∂(ρrφ)∂t+divuφ)=divΓgradφ+Swhere φ takes the value 1 (continuity), u (momentum), yi (mass fraction) and h (enthalpy), and Γ and S are exchange coefficients and source terms, respectively. Reynolds numbers for both fuel and air are

Results

All three classes of code were employed in the study of both single fuel cells and stacks of cells under a variety of operating conditions. The dimensions of the reference geometry are nominally 0.1m×0.1 m. Boundary conditions and property values are similar to those given in reference [16]. Detailed comparisons of the models were undertaken for a single cell of known geometry with constant mass source (i.e. current density) and heat source, and also under the more realistic situation where

Discussion

Inspection of Fig. 3 reveals that for the ‘idealized case’ of uniform heating and mass transfer by the electrolyte; the temperature is lowest at the location corresponding to the (bottom–left) air-fuel inlets, and highest at the corresponding outlets (top–right). The bi-linear temperature distribution associated with cross-flow is due to the overall energy balance being dominated by the convection and heat-source terms. Thus, even if the fluid flow and chemical reaction rates are completely

Conclusions

Calculations were performed on single and 10-cell stacks of SOFC fuel cells using three distinct approaches referred to as the PFM, DRA and DNM. Both constant heat and current density, and variable local current density, corresponding to known average values of ī, were considered under adiabatic and isothermal wall conditions. For single cells, all of these methods can be reliably used to perform calculations in planar SOFCs with the DNM being the most accurate since it does not require

Future work

A semi-empirical resistance model, which combines the Ohmic and overpotential terms was used in this paper, owing to the sparse experimental data available for the particular design under consideration. This has now been supplanted with a Butler–Volmer equation for anodic and cathodic over-potential in most of the codes, and the latter will be adopted from now on. To further improve the correlation between the PFM, DRA, and DNMs, additional effort is required when prescribing mass transfer

Acknowledgements

Financial support for this work was provided by the Fuel Cells Program of the National Research Council. Ron Jerome provides technical support for our research group. We would also like to thank Global Thermoelectric Inc., for their technical and financial support in the early stages of this research program.

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Present address: Global Thermoelectric Inc., 4908—52nd Street, S.E. Calgary, Alta., Canada T2B 3R2.

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