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Research Papers

Mechanistic Three-Dimensional Analytical Solutions for a Direct Liquid Fuel Cell Stack

[+] Author and Article Information
Chun Yu Ling

Department of Chemical and
Biomolecular Engineering,
National University of Singapore,
Singapore 117576, Singapore

Ming Han, Yunzhong Chen

Clean Energy Research Center,
Temasek Polytechnic,
Singapore 529757, Singapore

Erik Birgersson

Department of Chemical and
Biomolecular Engineering,
National University of Singapore,
Singapore 117576, Singapore
e-mail: chebke@nus.edu.sg

1Corresponding author.

Manuscript received June 6, 2014; final manuscript received October 18, 2015; published online December 4, 2015. Assoc. Editor: Rak-Hyun Song.

J. Fuel Cell Sci. Technol 12(6), 061003 (Dec 04, 2015) (11 pages) Paper No: FC-14-1074; doi: 10.1115/1.4031958 History: Received June 06, 2014; Revised October 18, 2015

An optimal or near to optimal design and operation of a direct liquid fuel cell (DLFC) stack requires an understanding of the relevant physical phenomena across length scales in the stack. In particular, perturbations between cells can arise due to external manifold design as well as variations in material and design parameters between cells. In this work, we seek to derive closed-form analytical expressions that capture the global stack performance, as well as individual cell behavior such as cell potential, current density, and methanol distribution. This approach allows for the simulation of large stacks with near to negligible computational overhead. Finally, the solutions are demonstrated for a stack subjected to perturbations in the anode inlet velocity of each cell.

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Figures

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Fig. 1

Schematic of procedure used to obtain closed-form analytical solutions for a DMFC stack. (a) The stack comprising of n cells is first decoupled; (b) each cell, cell j, is considered individually. (c) Symmetry is used to reduce the computational domain to a representative volume cell; (d) the anode of the representative volume cell is decoupled from the membrane and cathode based on high stoichiometry of the latter. (e) Spatial smoothing is used to reduce the remaining computational domain to two dimensions while retaining salient features from the third dimension; (f) leading-order asymptotics is employed to simplify the set of PDEs, and the approximate analytical solutions for cell j is found. The solutions for each individual cell can then be recoupled to yield the closed-form analytical solution for a stack.

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Fig. 2

Schematic of a single cell depicting the various functional layers and their dimensions for the (a) 3D model and (b) spatially smoothed model

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Fig. 3

Polarization curves for decoupled cells with anode inlet velocity 2.19 × 10−3 (cell 1, ), 4.38 × 10−3 (cell 2, ), and 7.3 × 10−3 (cells 3–10, ) m s−1 as well as overall ten cell stack . Individual cell potentials along a prespecified stack current can be summed to obtain the stack potential ; this process can be repeated multiple times using different currents to yield the stack polarization curve.

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Fig. 6

Local current densities of a ten cell stack operating at Vstack = 3.5 V for cell 1 , cell 2 , and cells 3–10 . Cells 3–10 are operated with the highest anode inlet velocity; hence, they have the most uniform streamwise local current density profile.

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Fig. 5

Individual cell potentials for a perturbed ten cell stack operating at Vstack = 3.5 V . Due to the difference in inlet velocities, each cell is operating at a different potential in order to sustain an equal current density within each cell. Cells 1, 2, 3–10 and the normalized stack potential are 0.320, 0.347, 0.354, and 0.350 V, respectively.

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Fig. 7

Parasitic current densities of a ten cell stack operating at Vstack = 3.5 V for cell 1 , cell 2 , and cells 3–10 . Cells 3–10 are operated with the highest anode inlet velocity; therefore, they experience the highest parasitic current due to high methanol crossover via diffusion.

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Fig. 8

Methanol mass fraction within the anode flow channel and diffusion layer of cells 1, 2, and 3–10 of the perturbed stack. The analytical stack solution is able to resolve the boundary layer formed near the catalyst surface in each cell.

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Fig. 4

Polarization curves for the best performing single cell , worst performing single cell , ten cell stack , and limiting stack current

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