In this paper, a three-dimensional, two-phase transport model of liquid-feed direct methanol fuel cell (DMFC), which is based on the multiphase mixture formulation and encompasses all components in a DMFC using a single computational domain, is specifically studied and simulated by a combined finite element-upwind finite volume discretization along with Newton’s method, where flow, species, charge-transport, and energy equations are simultaneously addressed. Numerical simulations in three dimensions are carried out to explore and design efficient and robust numerical algorithms for the sake of fast and convergent nonlinear iteration. A series of efficient numerical algorithms and discretizations is specifically designed and analyzed to assist in achieving this goal. Our numerical simulations demonstrate that the convergent and correct physical solutions can be attained within 100 more steps, against the oscillating and long-running nonlinear iterations (up to 5000 steps) performed by standard finite element/volume method without new numerical techniques.
Issue Section:
Research Papers
1.
Gottesfeld
, S.
, and Zawodzinski
, T. A.
, 1997, “Polymer Electrolyte Fuel Cells
,” Advances in Electrochemical Science and Engineering
, Vol. 5
, R. C.
Alkire
, H.
Gerischer
, D. M.
Kolb
, and C. W.
Tobias
, eds., Willey-VCH
, Weinheim, Germany
, pp. 195
–301
.2.
Gottesfeld
, S.
, and Wilson
, M. S.
, 2000, “Polymer Electrolyte Fuel Cells as Potential Power Sources for Portable Electronic Device
,” Energy Storage Systems for Electronics Devices
, T.
Osaka
and M.
Datta
, eds., Gordon & Breach Science Publishers
, Singapore
, pp. 486
–517
.3.
Lamy
, C.
, Leger
, J. -M.
, and Srinivasan
, S.
, 2001, “Direct Methanol Fuel Cells: From a 20th Century Electrochemist’s Dream to a 21st Century Emerging Technology
,” Modern Aspects of Electrochemistry
, J.
OM Bockris
, B. E.
Conway
, and R. E.
White
, eds., Kluwer Academic/Plenum
, New York
, pp. 53
–118
.4.
Wang
, Z. H.
, and Wang
, C. Y.
, 2001, Direct Methanol Fuel Cells
, Vol. 2001-4
, S. R.
Narayanan
, S.
Gottesfeld
, and T.
Zawodz
, eds., Electrochemical Society
, Pennington, NJ
.5.
Wang
, Z. H.
, and Wang
, C. Y.
, 2003, “Mathematical Modeling of Liquid-Feed Direct Methanol Fuel Cells
,” J. Electrochem. Soc.
0013-4651, 150
, pp. A508
–A519
.6.
Liu
, W.
, and Wang
, C. Y.
, 2007, “Three-Dimensional Simulations of Liquid Feed Direct Methanol Fuel Cells
,” J. Electrochem. Soc.
0013-4651, 154
, pp. B352
–B361
.7.
Sun
, P. T.
, Xue
, G.
, Wang
, C. Y.
, and Xu
, J. C.
, 2009, “Fast Numerical Simulation of Two-Phase Transport Model in the Cathode of Polymer Electrolyte Fuel Cell
,” Comm. Comp. Phys.
1815-2406, 6
, pp. 49
–71
.8.
Sun
, P. T.
, Xue
, G.
, Wang
, C. Y.
, and Xu
, J. C.
, 2009, “A Domain Decomposition Method for Two-Phase Transport Model in the Cathode of a Polymer Electrolyte Fuel Cell
,” J. Comput. Phys.
0021-9991, 228
, pp. 6016
–6036
.9.
Sun
, P. T.
, Xue
, G.
, Wang
, C. Y.
, and Xu
, J. C.
, 2009, “New Numerical Techniques for a Three-Dimensional Liquid-Feed Direct Methanol Fuel Cell Model
,” SIAM J. Appl. Math.
0036-1399, 70
, pp. 600
–620
.10.
Wang
, C. Y.
, and Cheng
, P.
, 1997, “Multiphase Flow and Heat Transfer in Porous Media
,” Adv. Heat Transfer
0065-2717, 30
, pp. 93
–196
.11.
Feistauer
, M.
, and Felcman
, J.
, 1997, “On the Convergence of a Combined Finite Volume-Finite Element for Nonlinear Convection-Diffusion Problems
,” Numer. Methods Partial Differ. Equ.
0749-159X, 13
, pp. 163
–190
.12.
Feistauer
, M.
, Slavik
, J.
, and Stupka
, P.
, 1999, “On the Convergence of a Combined Finite Volume-Finite Element Methods for Nonlinear Convection-Diffusion Problems. Explicit Schemes
,” Numer. Methods Partial Differ. Equ.
0749-159X, 15
, pp. 215
–235
.13.
Feistauer
, M.
, Felcman
, J.
, and Lukáčová-Medvid’ová
, M.
, 1995, “Combined Finite Element-Finite Volume Solution of Compressible Flow
,” J. Comput. Appl. Math.
0377-0427, 63
, pp. 179
–199
.14.
Tezduyar
, T. E.
, 1992, “Stabilized Finite Element Formulations for Incompressible Flow Computations
,” Adv. Appl. Mech.
0065-2156, 28
, pp. 1
–44
.15.
Brezzi
, F.
, and Pitkäranta
, J.
, 1984, “On the Stabilization of Finite Element Approximations of the Stokes Equations
,” Efficient Solution of Elliptic System
, W.
Hackbusch
, ed., Notes on Numerical Fluid Mechanics
, Vol. 10
, Vieweg & Sohn
, Braunschweig
, pp. 11
–19
.16.
Hughes
, T. J. R.
, Franca
, L. P.
, and Balestra
, M.
, 1986, “A New Finite Element Formulation for Computational Fluid Dynamics: V. Circumventing the Babuska-Brezzi Condition: A Stable Petrov-Galerkin Formulation of the Stokes Problem Accommodating Equal-Order Interpolations
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 59
, pp. 85
–99
.17.
Greenbaum
, A.
, 1997, “Iterative Methods for Solving Linear Systems
,”Frontiers in Applied Mathematics
, SIAM
, Philadelphia, PA
.18.
Saad
, Y.
, and Schlutz
, M. H.
, 1986, “GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput.
0196-5204, 7
, pp. 856
–869
.19.
Barrett
, R.
, Berry
, M.
, Chan
, T. F.
, Demmel
, J.
, Donato
, J. M.
, Dongarra
, J.
, Eijkhout
, V.
, Pozo
, R.
, Romine
, C.
, and der Vorst
, H. V.
, 1994, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods
, Society for Industrial and Applied Mathematics
, Philadelphia, PA
.20.
Elman
, H.
, and Silvester
, D.
, 1996, “Fast Nonsymmetric Iterations and Preconditioning for Navier-Stokes Equations
,” SIAM J. Sci. Comput. (USA)
1064-8275, 17
, pp. 33
–46
.21.
Klawonn
, A.
, and Starke
, G.
, 1999, “Block Triangular Preconditioners for Nonsymmetric Saddle Point. Problems: Field-of-Values Analysis
,” Numer. Math.
0029-599X, 81
, pp. 577
–594
.22.
Loghin
, D.
, and Wathen
, A. J.
, 2004, “Analysis of Preconditioners for Saddle-Point Problems
,” SIAM J. Sci. Comput. (USA)
1064-8275, 25
, pp. 2029
–2049
.23.
Kay
, D.
, Loghin
, D.
, and Wathen
, A.
, 2002, “A Preconditioner for the Steady-State Navier-Stokes Equations
,” SIAM J. Sci. Comput. (USA)
1064-8275, 24
, pp. 237
–256
.24.
Silvester
, D.
, Elman
, H.
, Kay
, D.
, and Wathen
, A.
, 2001, “Efficient Preconditioning of the Linearized Navier-Stokes Equations for Incompressible Flow
,” J. Comput. Appl. Math.
0377-0427, 128
, pp. 261
–279
.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.
