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TECHNICAL PAPERS

# Development of a Three-Dimensional Molten Carbonate Fuel Cell Model and Application to Hybrid Cycle Simulations

[+] Author and Article Information
P. Iora

Dipartimento di Ingegneria Meccanica, Università degli Studi di Brescia, Brescia, Italypaolo.iora@unibs.it

S. Campanari

Dipartimento di Energetica, Politecnico di Milano, Milano, Italystefano.campanari@polimi.it

This is a common assumption, given the laminar flow conditions in the reactant channels, where the Nusselt number can be considered independent on the Reynolds number.

Crossover is far less important in SOFCs due to the solid nature of the electrolyte.

According to [9] a complete combustion of the cross-over streams is assumed in the model.

As the available data refers to the whole stack, the input data for the single cell are obtained assuming the same behavior for each cell within the stack.

As matter of fact, the time requested for the resolution of a ten plane stack is $∼10h$ on a PC with a $2.8GHz$ processor and $512Mb$ RAM.

As far as the number of channels is concerned, a sensitivity analysis has shown that the effects of a variation in the $H∕W$ ratio, discussed in Sec. 3, remain very limited also for the 3D stack. Therefore, it makes sense to use the same approximation for the 3D model.

In future works, a more accurate analysis will be carried out based on a detailed cycle layout.

The minimum $CO2$ percentage at cathode inlet is indicated close to 4% by the manufacturers (4-5,18).

J. Fuel Cell Sci. Technol 4(4), 501-510 (Apr 14, 2006) (10 pages) doi:10.1115/1.2756850 History: Received November 21, 2005; Revised April 14, 2006

## Abstract

In this paper, a three-dimensional finite volume model of a molten carbonate fuel cell (MCFC) is presented. The model applies a detailed electrochemical and thermal analysis to a planar MCFC stack of given geometry and assigned input flows conditions, material properties and assigned external heat losses, calculating global energy balances and reactant utilization, as well as internal temperature and chemical composition profiles, pressure profiles, polarization losses, and current density and voltage distribution over the stack. The model is calibrated on the available data for an experimented MCFC stack manufactured by Ansaldo Fuel Cells. The comparison of 2D versus 3D simulations is first discussed, showing the importance of the 3D model for an accurate analysis of real stack operation under significant heat loss conditions, but also showing the mutual influence of heat transfer between adjoining cells and evidencing the variable electrical performances between different cells of the same stack. As a counterpart, application of the 2D model, which takes advantage by much shorter calculation time while keeping a reasonable accuracy in the overall energy balances, is anyway indicated for complex cycle analysis and cycle optimization, where a complete 3D stack analysis may be limited to selected cases. Then, the model is applied to the off-design analysis of hybrid cycles based on a recuperated gas turbine arrangement where variable pressure ratios and fuel supply conditions are assumed for the fuel cell. The effects of the operating pressure and of the adoption of different fuel compositions are considered, with a cycle layout that may include natural gas reforming or is directly fed by a syngas provided by an external source, simulating different fuel feedstocks (e.g., coal gasification). Complete results are presented, in terms of fuel cell and overall cycle performances.

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## Figures

Figure 1

Two-dimensional MCFC stack, with evidenced an elementary finite-volume and its internal subdivision

Figure 2

Simulation results for the rectangular planar MCFC (from left: temperature, current density, and anodic/cathodic pressure gradient)

Figure 3

Iteration algorithm of the 3D stack model (I: current; V: cell potential; n: number of cells in the stack; ε: residual error) (11)

Figure 4

(a) Voltage distribution along a stack of ten planar MCFCs as a function of the heat losses expressed as a fraction of the thermal power of the fuel at the stack inlet, (b) mean temperature distribution for the cell PEN structure along a stack of ten planar MCFCs as a function of the heat losses expressed as a fraction of the thermal power of the fuel at the stack inlet, and (c) average unit-cell voltage as function of the number of planar cells in case of perfectly insulated stacks

Figure 5

Hybrid plant layout

Figure 6

Comparison between the overall plant efficiency as a function of the pressure ratio, calculated with the detailed finite volume stack model (DSM) and the lumped volume stack model (LVSM)

Figure 7

Current distribution for SR (left) and coal syngas (right)

Figure 8

Temperature distribution for SR (left) and coal syngas (right)

Figure 9

Nernst potential distribution for SR (left) and coal syngas (right)

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