Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T21:46:25.097Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical Study of a 3D Two-Phase PEM Fuel Cell Model Via a Novel Automated Finite Element/Finite Volume Program Generator

Published online by Cambridge University Press:  20 August 2015

Pengtao Sun ,
Su Zhou ,
Qiya Hu  and
Guoping Liang
Pengtao Sun*
Affiliation:
Department of Mathematical Sciences, University of Nevada, Las Vegas, 4505 Maryland Parkway, Las Vegas, NV 89154, USA
Su Zhou*
Affiliation:
Department of Fuel Cell Power Systems, Tongji University (Jiading campus), 4800 Caoan Road, Shanghai 201804, China
Qiya Hu*
Affiliation:
Institute of Computational Mathematics and Scientific Engineering Computing, Chinese Academy of Sciences, Beijing 100080, China
Guoping Liang*
Affiliation:
Institute of Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China
*
Corresponding author.Email:pengtao.sun@unlv.edu
Email:suzhou@tongji.edu.en
Email:hqy@lsec.cc.ac.cn
Email:guopingliang@yahoo.com.ecn
Get access

Abstract

Numerical methods of a 3D multiphysics, two-phase transport model of proton exchange membrane fuel cell (PEMFC) is studied in this paper. Due to the coexistence of multiphase regions, the standard finite element/finite volume method may fail to obtain a convergent nonlinear iteration for a two-phase transport model of PEMFC [49,50]. By introducing Kirchhoff transformation technique and a combined finite element-upwind finite volume approach, we efficiently achieve a fast convergence and reasonable solutions for this multiphase, multiphysics PEMFC model. Numerical implementation is done by using a novel automated finite element/finite volume program generator (FEPG). By virtue of a high-level algorithm description language (script), component programming and human intelligence technologies, FEPG can quickly generate finite element/finite volume source code for PEMFC simulation. Thus, one can focus on the efficient algorithm research without being distracted by the tedious computer programming on finite element/finite volume methods. Numerical success confirms that FEPG is an efficient tool for both algorithm research and software development of a 3D, multiphysics PEMFC model with multicomponent and multiphase mechanism.

Keywords

65B9965K0565K1065N0865N1265N2265N3065Z05Proton exchange membrane fuel celltwo-phase transportKirchhoff transformationfinite elementfinite volumeautomated program generatoralgorithm description languagescript
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 1 , January 2012 , pp. 65 - 98
Copyright
Copyright © Global Science Press Limited 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]http://www.fegensoft.com/english/FEPG.htm.Google Scholar
[2]The dune tutorial, http://www.dune-project.org/.Google Scholar
[3]The fenics-python tutorial, http://docs.python.org/tutorial/.Google Scholar
[4]Alt, H. W. and Luckhaus, S., Quasilinear elliptic-parabolic differential equations, Math. Z., 183 (1983), 311–341.Google Scholar
[5]Arbogast, T., Wheeler, M. F. and Zhang, N., A nonlinear mixed finite element method for a degenerate parabolic equation arising in flow in porous media, SIAM J. Numer. Anal., 33 (1996), 1669–1687.CrossRefGoogle Scholar
[6]Asinari, P., Quaglia, M. C., Spakovsky, M.R. von and Kasula, B. V., Direct numerical calculation of the kinematic tortuosity of reactive mixture flow in the anode layer of solid oxide fuel cells by the lattice boltzmann method, J Power Sources, 170 (2007), 359–375.Google Scholar
[7]Barrett, R., Berry, M., Chan, T. F., Demmel, J., Donato, J. M., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C. and Vorst, H. V. der, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, Philadalphia: Society for Industrial and Applied Mathematics, 1994.Google Scholar
[8]Brezzi, F. and Pitkaranta, J., On the stabilization of finite element approximations of stokes problem, Efficient solutions of elliptic systems, Notes on Numerical Fluid Mechanics, Viewig 10 (1984), 11–19.Google Scholar
[9]Carslaw, H. S. and Jaeger, J. C., Conduction of Heat in Solids, 2nd ed, Oxford University Press, Oxford, UK, 1959.Google Scholar
[10]Chen, Z., Formulations and numerical methodsof the black oil modelinporous media, SIAM J. Numer. Anal., 38 (2000), 489–514.CrossRefGoogle Scholar
[11]Van, M. A. Doormaal and Pharoah, J. G., Determination of permeability in fibrous porous media using the lattice boltzmann method with application to pem fuel cells, Int. J. Numer. Meth. Fluids, 59 (2009), 75–89.Google Scholar
[12]Elman, H. and Silvester, D., Fast nonsymmetric iterations and preconditioning for navier-stokes equations, SIAM J. Sci. Comput., 17 (1996), 33–46.Google Scholar
[13]Eyres, N. R., Hartree, D. R., Ingham, J., Jackson, R., Sarjant, R. J. and Wagstaff, S. M., The calculation of variable heat flow in solids, Philos. Trans. R. Soc. Lond., A240 (1946), 1–57.Google Scholar
[14]Feistauer, M., Felcman, J., Lukáčová-Medvid’Ovaá, M. and Warnecke, G., Error estimates for a combined finite volume-finite element method for nonlinear convection-diffusion problems, SIAM J. Numer. Anal., 36 (1999), 1528–1548.Google Scholar
[15]Gottesfeld, S., Polymer Electrolyte Fuel Cells, Volume 5 of Advances in Electrochemical Science and Engineering, John Wiley & Sons, New York, 1997.CrossRefGoogle Scholar
[16]Hughes, T. J. R., Franca, L. P. and Balestra, M., 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. Meth. Appl. Mech. Eng., 59 (1986), 85–99.CrossRefGoogle Scholar
[17]Ji, S., Park, Y., Sudicky, E. A. and Sykes, J. F., A generalized transformation approach for simulating steady-state variably-saturated subsurface flow, Adv. Water Res., 31 (2008), 313–323.CrossRefGoogle Scholar
[18]Kačur, J. and Keer, R. V., Numerical approximation of a flow and transport system in unsaturated-saturated porous media, Chem. Eng. Sci., 58 (2003), 4805–4813.Google Scholar
[19]Kay, D., Loghin, D. and Wathen, A., A preconditioner for the steady-state navier-stokes equations, SIAM J. Sci. Comput., 24 (2002), 237–256.CrossRefGoogle Scholar
[20]Klawonn, A. and Starke, G., Block triangular preconditioners for nonsymmetric saddle point problems: field-of-values analysis, Numer. Math., 81 (1999), 577–594.Google Scholar
[21]Liang, G. P., Finite Element Language, Science Press, Beijing, China, 2008.Google Scholar
[22]Liu, F. Q., Lu, G. Q. and Wang, C. Y., Low crossover of methanol and water through thin membranes in direct methanol fuel cells, J. Electrochem. Soc., 153 (2006), A543–553.Google Scholar
[23]Liu, F. Q. and Wang, C. Y., Optimization of cathode catalyst layer for direct methanol fuel cells: part II-computational modeling and design, Electrochim. Acta, 52 (2006), 1409–1416.CrossRefGoogle Scholar
[24]Liu, F. Q. and Wang, C. Y., Mixed potential in a direct methanol fuel cell-modeling and experiments, J. Electrochem. Soc., 154 (2007), B514–B522.Google Scholar
[25]Liu, W. and Wang, C. Y., Modeling water transport in liquid feed direct methanol fuel cells, J. Power Sources, 164 (2007), 189–195.Google Scholar
[26]Liu, W. and Wang, C. Y., Three-dimensional simulations of liquid feed direct methanol fuel cells, J. Electrochem. Soc., 154 (2007), B352–B361.Google Scholar
[27]Loghin, D. and Wathen, A. J., Analysis of preconditioners for saddle-point problems, SIAM J. Sci. Comput., 25 (2004), 2029–2049.CrossRefGoogle Scholar
[28]Lu, Z. and Zhang, D., Analytical solutions to steady state unsaturated flow in layered, randomly heterogeneous soils via kirchhoff transformation, Adv. Water Res., 27 (2004), 775–784.Google Scholar
[29]Martinez, M. J. and McTigue, D. F., A boundary integral method for steady flow in unsatu-rated porous media, Int. J. Numer. Anal. Meth. Geomech., 16 (1992), 581–601.Google Scholar
[30]McWhorster, D. B. and Sunada, D. K., Exact integral solutions for two-phase flow, Water Resour. Res., 26 (1990), 399–413.Google Scholar
[31]Ozisik, M. N., Boundary Value Problems of Heat Conduction, Dover, New York, 2002.Google Scholar
[32]Pasaogullari, U., Mukherjee, P., Wang, C. Y. and Chen, K., Anisotropic heat and water transport in a pefc cathode gas diffusion layer, J. Electrochem. Soc., 154 (2007), B823–B834.Google Scholar
[33]Pasaogullari, U. and Wang, C. Y., Liquid water transport in gas diffusion layer of polymer electrolyte fuel cells, J. Electrochem. Soc., 151 (2004), A399–A406.Google Scholar
[34]Pasaogullari, U. and Wang, C. Y., Two-phase modeling and flooding prediction of polymer electrolyte fuel cells, J. Electrochem. Soc., 152 (2005), A380–A390.Google Scholar
[35]Perng, S. and Wu, H., Effects of internal flow modification on the cell performance enhancement of a pem fuel cell, J. Power Sources, 175 (2008), 806–816.Google Scholar
[36]Perng, S., Wu, H., Jue, T. and Cheng, K., Numerical predictions of a pem fuel cell performance enhancement by a rectangular cylinder installed transversely in the flow channel, Appl. Energy, 86 (2009), 1541–1554.Google Scholar
[37]Pop, I. S., Radu, F. and Knabner, P., Mixed finite elements for the richards’ equation: linearization procedure, J. Comput. Appl. Math., 168 (2004), 365–373.CrossRefGoogle Scholar
[38]Pourhashemi, S. A., Hao, O. J. and Chawla, R. C., An experimental and theoretical study of the nonlinear heat conduction in dry porous media, Int. J. Energy Res., 23 (1999), 389–401.Google Scholar
[39]Prater, K. B., Polymer electrolyte fuel cells: a review of recent developments, J. Power Sources, 51 (1994), 129–144.Google Scholar
[40]Radu, F. A., Pop, I. S. and Attinger, S., Analysis of an euler implicit-mixed finite element scheme for reactive solute transport in porous media, Numer. Methods Part. Differ. Eq., 26 (2010), 320–344.Google Scholar
[41]Rodrigues, J. F. and Urbano, J. M., On a darcy-stefan problem arising in freezing and thawing of saturated porous media, Cont. Mech. Thermodyn., 11 (1999), 181–191.Google Scholar
[42]Rose, M., Numerical methods for flows through porous media I, Math. Comput., 40 (1983), 435–467.Google Scholar
[43]Ross, P. J. and Bristow, K. L., Simulating water movement in layered and gradational soils using the kirchhoff transform, Soil Sci. Soc. Am. J., 54 (1990), 1519–1524.Google Scholar
[44]Schweizer, B., Regularization of outflow problems in unsaturated porous media with dry regions, J. Differential Equations, 237 (2007), 278–306.CrossRefGoogle Scholar
[45]Silvester, D., Elman, H., Kay, D. and Wathen, A., Efficient preconditioning of the linearized navier-stokes equations for incompressible flow, J. Comput. Appl. Math., 128 (2001), 261– 279.Google Scholar
[46]Sui, P. C. and Djilali, N., Analysis of coupled electron and mass transport in the gas diffusion layer of a pem fuel cell, J. Power Sources, 161 (2006), 294–300.Google Scholar
[47]Sun, P. T., Wang, C. Y. and Xu, J. C., A combined finite element-upwind finite volume method for liquid-feed direct methanol fuel cell simulations, J. Fuel Cell Sci. Technol., 7 (2010).Google Scholar
[48]Sun, P. T. and Wang, Y., A new formulation and an efficient numerical technique for a non-isothermal, anisotropic, two-phase transport model of pemfc, in Proceeding of Eighth International Fuel Cell Science, Engineering and Technology Conference, Brooklyn, New York, June 14-16, 2010, ASME.Google Scholar
[49]Sun, P. T., Xue, G., Wang, C. Y. and Xu, J. C., A domain decomposition method for two-phase transport model in the cathode of a polymer electrolyte fuel cell, J. Comput. Phys., 228 (2009), 6016–6036.Google Scholar
[50]Sun, P. T., Xue, G., Wang, C. Y. and Xu, J. C., Fast numerical simulation of two-phase transport model in the cathode of a polymer electrolyte fuel cell, Commun. Comput. Phys., 6 (2009), 49–71.Google Scholar
[51]Sun, P. T., Xue, G., Wang, C. Y. and Xu, J. C., New numerical techniques for a liquid feed 3d full direct methanol fuel cell model, SIAM Appl. Math., 70 (2009), 600–620.Google Scholar
[52]Tartakovsky, D. M., Prediction of steady-state flow of real gases in randomly heterogeneous porous media, Physica D, 133 (1999), 463–468.Google Scholar
[53]Tartakovsky, D. M., Guadagnini, A. and Riva, M., Stochastic averaging of nonlinear flows in heterogeneous porous media, J. Fluid Mech., 492 (2003), 47–62.Google Scholar
[54]Tartakovsky, D. M., Neuman, S. P. and Lu, Z., Conditional stochastic averaging of steady state unsaturated flow by means of kirchhoff transformation, Water Resour. Res., 35 (1999), 731–745.Google Scholar
[55]Tezduyar, T. E., Stabilized finite element formulations for incompressible flow computations, Adv. Appl. Mech., 28 (1992), 1–44.Google Scholar
[56]Tirnovan, R., Giurgea, S., Miraoui, A. and Cirrincione, M., Proton exchange membrane fuel cell modelling based on a mixed moving least squares technique, Int. J. Hydrogen Energy, 33 (2008), 6232–6238.CrossRefGoogle Scholar
[57]Tirnovan, R., Giurgea, S., Miraoui, A. and Cirrincione, M., Surrogate model for proton exchange membrane fuel cell (pemfc), J. Power Sources, 175 (2008), 773–778.Google Scholar
[58]Vadasz, P., Analytical solution to nonlinear thermal diffusion: Kirchhoff versus cole-hopf transformations, J. Heat Trans., 132 (2010), 121302–1–121302-6.Google Scholar
[59]Wan, S., Wu, B. and Chen, N., Application of program generation technology in solving heat and flow problems, J. Therm. Sci., 16 (2007), 170–175.Google Scholar
[60]Wang, C. Y., Fundamental models for fuel cell engineering, Chem. Rev., 104 (2004), 4727–4766.CrossRefGoogle ScholarPubMed
[61]Wang, C. Y. and Cheng, P., Multiphase flow and heat transfer in porous media, Adv. Heat Trans., 30 (1997), 93–196.Google Scholar
[62]Wang, Y., Modeling of two-phase transport in the diffusion media of polymer electrolyte fuel cells, J. Power Sources, 185 (2008), 261–271.Google Scholar
[63]Wang, Y. and Wang, C. Y., A nonisothermal two-phase model for polymer electrolyte fuel cells, J. Electrochem. Soc., 153 (2006), A1193–A1200.Google Scholar
[64]Wang, Y., Wang, C. Y. and Chen, K. S., Elucidating differences between carbon paper and carbon cloth in polymer electrolyte fuel cells, Electr. Acta, 52 (2007), 3965–3975.Google Scholar
[65]Wang, Z. H., Wang, C. Y. and Chen, K. S., Two-phase flow and transport in the air cathode of proton exchange membrane fuel cells, J. Power Sources, 94 (2001), 40–50.Google Scholar
[66]Wu, B., Qian, H. and Wan, S., Promotion of frontier science research by aid of automatic program generation technology, in Computational Methods in Engineering & Science, Proceedings of “Enhancement and Promotion of Computational Methods in Engineering and Science X”, Sanya, China, Aug 21-23, 2006, Tsinghua University Press & Springer-Verlag.Google Scholar
[67]Zhua, X., Sui, P. C. and Djilali, N., Dynamic behaviour of liquid water emerging from a gdl pore into a pemfc gas flow channel, J. Power Sources, 172 (2007), 287–295.Google Scholar