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.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Spiegel, C. S. , 2007, Designing & Building Fuel Cells, McGraw-Hill, New York.
Ren, X. , Davey, J. , Zelenay, P. , and Gottesfeld, S. , 2000, “ Direct Methanol Fuel Cells For Portable Power Applications,” 198th Meeting of the Electrochemical Society, Phoenix, AZ, Oct. 22–27.
Kulikovsky, A. , 2000, “ Two-Dimensional Numerical Modelling of a Direct Methanol Fuel Cell,” J. Appl. Electrochem., 30(9), pp. 1005–1014. [CrossRef]
Fan, J. , Hu, G. , Yao, J. , and Cen, K. , 2002, “ A Two-Dimensional Mathematical Model of Liquid-Feed Direct Methanol Fuel Cells,” Energy Fuels, 16(6), pp. 1591–1598. [CrossRef]
Birgersson, E. , Nordlund, J. , Ekström, H. , Vynnycky, M. , and Lindbergh, G. , 2003, “ Reduced Two-Dimensional One-Phase Model for Analysis of the Anode of a DMFC,” J. Electrochem. Soc., 150(10), pp. A1368–A1376. [CrossRef]
Birgersson, E. , Nordlund, J. , Vynnycky, M. , Picard, C. , and Lindbergh, G. , 2004, “ Reduced Two-Phase Model for Analysis of the Anode of a DMFC,” J. Electrochem. Soc., 151(12), pp. A2157–A2172. [CrossRef]
Garcia, B. L. , Sethuraman, V. A. , Weidner, J. W. , and White, R. E. , 2004, “ Mathematical Model of a Direct Methanol Fuel Cell,” ASME J. Fuel Cell Sci. Technol., 1(1), pp. 43–48. [CrossRef]
Scott, K. , and Argyropoulos, P. , 2004, “ A One Dimensional Model of a Methanol Fuel Cell Anode,” J. Power Sources, 137(2), pp. 228–238. [CrossRef]
Danilov, V. A. , Lim, J. , Moon, I. , and Chang, H. , 2006, “ Three-Dimensional, Two-Phase, CFD Model for the Design of a Direct Methanol Fuel Cell,” J. Power Sources, 162(2), pp. 992–1002. [CrossRef]
Rousseau, S. , Coutanceau, C. , Lamy, C. , and Leger, J. , 2006, “ Direct Ethanol Fuel Cell (DEFC): Electrical Performance and Reaction Products Distribution Under Operating Conditions With Different Platinum-Based Anodes,” J. Power Sources, 158(1), pp. 18–24. [CrossRef]
Liu, W. , and Wang, C.-Y. , 2007, “ Three-Dimensional Simulations of Liquid Feed Direct Methanol Fuel Cells,” J. Electrochem. Soc., 154(3), pp. B352–B361. [CrossRef]
Miao, Z. , He, Y.-L. , Li, X.-L. , and Zou, J.-Q. , 2008, “ A Two-Dimensional Two-Phase Mass Transport Model for Direct Methanol Fuel Cells Adopting a Modified Agglomerate Approach,” J. Power Sources, 185(2), pp. 1233–1246. [CrossRef]
Oliveira, V. , Falcao, D. , Rangel, C. , and Pinto, A. , 2008, “ Heat and Mass Transfer Effects in a Direct Methanol Fuel Cell: A 1D Model,” Int. J. Hydrogen Energy, 33(14), pp. 3818–3828. [CrossRef]
Ee, S. L. , and Birgersson, E. , 2009, “ Two-Dimensional Approximate Analytical Solutions for the Anode of a Direct Methanol Fuel Cell,” J. Electrochem. Soc., 156(11), pp. B1329–B1338. [CrossRef]
Ee, S. L. , and Birgersson, E. , 2011, “ Two-Dimensional Approximate Analytical Solutions for the Direct Liquid Fuel Cell,” J. Electrochem. Soc., 158(10), pp. B1224–B1234. [CrossRef]
Rosenthal, N. S. , Vilekar, S. A. , and Datta, R. , 2012, “ A Comprehensive Yet Comprehensible Analytical Model for the Direct Methanol Fuel Cell,” J. Power Sources, 206, pp. 129–143. [CrossRef]
Chiu, Y.-J. , and Sun, J.-L. , 2013, “ An Analytical Overpotential Model of a Direct Liquid Feed Fuel Cell,” IEEE 10th International Conference on Power Electronics and Drive Systems (PEDS), Kitakyushu, Japan, Apr. 22–25, pp. 924–929.
Ling, C. Y. , Ee, S. L. , and Birgersson, E. , 2013, “ Three-Dimensional Approximate Analytical Solutions for Direct Liquid Fuel Cells,” Electrochim. Acta, 109, pp. 305–315. [CrossRef]
Yin, K.-M. , Lin, H.-L. , and Yu, T.-L. , 2009, “ An Algebraic Model of Liquid Feed Direct Methanol Fuel Cell With Co-Current Channel Flow,” J. Chem. Eng. Jpn., 42(5), pp. 358–367. [CrossRef]
Cai, W. , Li, S. , Li, C. , Liang, L. , Xing, W. , and Liu, C. , 2013, “ A Model Based Thermal Management of DMFC Stack Considering Double-Phase Flow in the Anode,” Chem. Eng. Sci., 93, pp. 110–123. [CrossRef]
Kulikovsky, A. , 2006, “ Model of a Direct Methanol Fuel Cell Stack,” J. Electrochem. Soc., 153(9), pp. A1672–A1677. [CrossRef]
Mclntyre, J. , Kulikovsky, A. , Muller, M. , and Stolten, D. , 2013, “ Large-Scale DMFC Stack Model: The Effect of a Condensation Front on Stack Performance,” Int. J. Hydrogen Energy, 38(8), pp. 3373–3379. [CrossRef]
Mclntyre, J. , Kulikovsky, A. , Müller, M. , and Stolten, D. , 2012, “ Large-Scale DMFC Stack Model: Feed Disturbances and Their Impact on Stack Performance,” Fuel Cells, 12(6), pp. 1032–1041. [CrossRef]
Sharma, A. , Birgersson, E. , and Khor, S. , 2014, “ Computationally-Efficient Hybrid Strategy for Mechanistic Modeling of Fuel Cell Stacks,” J. Power Sources, 247, pp. 481–488. [CrossRef]
Sharma, A. , Birgersson, E. , Vynnycky, M. , and Ly, H. , 2013b, “ On the Interchangeability of Potentiostatic and Galvanostatic Boundary Conditions for Fuel Cells,” Electrochem. Acta, 109, pp. 617–622. [CrossRef]
Sharma, A. , Birgersson, E. , and Vynnycky, M. , 2013, “ An Aggregate Measure for the Local Current Density Coupling in Fuel Cell Stacks,” J. Electrochem. Soc., 160(11), pp. F1237–F1240. [CrossRef]
Maplesoft, 2013, “ Maple Soft 16,” Maplesoft, Waterloo, ON Canada, http://www.maplesoft.com
Mathworks, 2013, “ Matlab and Simulink,” Mathworks Inc., Natick, MA, http://www.mathworks.com
Placca, L. , Kouta, R. , Blachot, J.-F. , and Charon, W. , 2009, “ Effects of Temperature Uncertainty on the Performance of a Degrading PEM Fuel Cell Model,” J. Power Sources, 194(1), pp. 313–327. [CrossRef]
Mawardi, A. , and Pitchumani, R. , 2006, “ Effects of Parameter Uncertainty on the Performance Variability of Proton Exchange Membrane (PEM) Fuel Cells,” J. Power Sources, 160(1), pp. 232–245. [CrossRef]
Kulikovsky, A. A. , 2010, Analytical Modelling of Fuel Cells, Elsevier, Oxford, UK.
Casalegno, A. , Grassini, P. , and Marchesi, R. , 2007, “ Experimental Analysis of Methanol Cross-Over in a Direct Methanol Fuel Cell,” Appl. Therm. Eng., 27(4), pp. 748–754. [CrossRef]
He, Z. , Birgersson, E. , and Li, H. , 2014, “ Reduced Non-Isothermal Model for the Planar Solid Oxide Fuel Cell and Stack,” Energy, 70, pp. 478–492. [CrossRef]


Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
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.

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In