Computational Particle Mechanics

, Volume 4, Issue 3, pp 285–295 | Cite as

On the application of the PFEM to droplet dynamics modeling in fuel cells

  • Pavel B. Ryzhakov
  • Alex Jarauta
  • Marc Secanell
  • Jordi Pons-Prats


The Particle Finite Element Method (PFEM) is used to develop a model to study two-phase flow in fuel cell gas channels. First, the PFEM is used to develop the model of free and sessile droplets. The droplet model is then coupled to an Eulerian, fixed-grid, model for the airflow. The resulting coupled PFEM-Eulerian algorithm is used to study droplet oscillations in an air flow and droplet growth in a low-temperature fuel cell gas channel. Numerical results show good agreement with predicted frequencies of oscillation, contact angle, and deformation of injected droplets in gas channels. The PFEM-based approach provides a novel strategy to study droplet dynamics in fuel cells.


PFEM Embedded model Fuel cells Droplet dynamics Sessile droplet 


Compliance with ethical standards


This work was supported under the auspices of the FPDI-2013-18471 and BES-2011-047702 grants of the Spanish Ministerio de Economia y Competitividad as well as partially funded by the COMETAD project of the National RTD Plan (ref. MAT2014-60435-C2-1-R) of the mentioned ministry.

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Akhtar N, Kerkhof PJAM (2011) Dynamic behavior of liquid water transport in a tapered channel of a proton exchange membrane fuel cell cathode. Int J Hydrog Energy 36(4):3076–3086CrossRefGoogle Scholar
  2. 2.
    Bird R, Stewart W, Lightfoot E (2002) Transport phenomena, 2nd edn. Wiley, HobokenGoogle Scholar
  3. 3.
    Bouwhuis W, Winkels KG, Peters IR, Brunet P, van der Meer D, Snoeijer JH (2013) Oscillating and star-shaped drops levitated by an airflow. Phys Rev E 88:023017CrossRefGoogle Scholar
  4. 4.
    Brennen CE (2005) Fundamentals of multiphase flow, 1st edn. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  5. 5.
    Carton J, Lawlor V, Olabi A, Hochenauer C, Zauner G (2012) Water droplet accumulation and motion in PEM (Proton Exchange Membrane) fuel cell mini-channels. Energy 39:63–73CrossRefGoogle Scholar
  6. 6.
    Chen K, Hickner M, Noble D (2005) Simplified models for predicting the onset of liquid water droplet instability at the gas diffusion layer/gas flow channel interface. Int J Energy Res 29(12):1113–1132CrossRefGoogle Scholar
  7. 7.
    Cho SC, Wang Y, Chen K (2012) Droplet dynamics in a polymer electrolyte fuel cell gas flow channel: forces, deformation, and detachment. I: theoretical and numerical analyses. J Power Sources 206:119–128CrossRefGoogle Scholar
  8. 8.
    Choi J, Son G (2009) Numerical study of droplet dynamics in a PEMFC gas channel with multiple pores. J Mech Sci Technol 23(7):1765–1772CrossRefGoogle Scholar
  9. 9.
    Chorin AJ (1967) A numerical method for solving incompressible viscous problems. J Comput Phys 2:12–26CrossRefzbMATHGoogle Scholar
  10. 10.
    Codina R (2001) A stabilized finite element method for generalized stationary incompressible flows. Comput Methods Appl Mech Eng 190 (20–21):2681–2706. doi: 10.1016/S0045-7825(00)00260-7
  11. 11.
    Codina R (2001) Pressure stability in fractional step finite element method for incompressible flows. J Comput Phys 170:112–140MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Crowe CT (2006) Multiphase flow handbook, 1st edn. Taylor & Francis, AbingdonzbMATHGoogle Scholar
  13. 13.
    Feng Y, Idelsohn S, Nigro N, Gimenez J, Rossi R, Marti J (2013) A fast and accurate method to solve the incompressible Navier–Stokes equations. Eng Comput 30(2):197–222CrossRefGoogle Scholar
  14. 14.
    Ferreira RB, Falcão DS, Oliveira VB, Pinto AMFR (2015) Numerical simulations of two-phase flow in proton exchange membrane fuel cells using the volume of fluid method - A review. J Power Sources 277:329–342CrossRefGoogle Scholar
  15. 15.
    Gerstenberger A, Wall W (2008) An extended finite element/Lagrange multiplier based approach for fluid-structure interaction. Comput Methods Appl Mech Eng 197:1699–1714MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Gerstenberger A, Wall W (2010) An embedded Dirichlet formulation for 3D continua. Int J Numer Methods Eng 82(5):537–563MathSciNetzbMATHGoogle Scholar
  17. 17.
    Gopala V, van Wachem G (2008) Volume of fluid methods for immiscible-fluid and free-surface flows. Chem Eng J 141:204–221CrossRefGoogle Scholar
  18. 18.
    Guermond J, Minev P, Shen J (2006) An overview of projection methods for incompressible flows. Comput Methods Appl Mech Eng 195:6011–6045MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Idelsohn SR, Oñate E, Pin FD (2004) The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves. Int J Numer Methods Eng 61(7):964–989MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Israelachvili J (2011) Intermolecular and surface forces, 3rd edn. Elsevier, WalthamGoogle Scholar
  21. 21.
    Jarauta A, Ryzhakov PB, Secanell M, Waghmare PR, Pons-Prats J (2015) Numerical study of droplet dynamics in a Proton Exchange Fuel Cell gas channel using an embedded formulation. J Power Sources (submitted)Google Scholar
  22. 22.
    Jarauta A, Secanell M, Pons-Prats J, Ryzhakov PB, Idelsohn SR, Oñate E (2015) A semi-analytical model for droplet dynamics on the GDL surface of a PEFC electrode. Int J Hydrog Energy 40:5375–5383CrossRefGoogle Scholar
  23. 23.
    Kamran K, Rossi R, Onate E, Idelsohn S (2013) A compressible Lagrangian framework for the simulation of the underwater implosion of large air bubbles. Comput Methods Appl Mech Eng 255:210–225MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Kandlikar S, Lu Z, Domigan W, White A, Benedict M (2009) Measurement of flow maldistribution in parallel channels and its application to ex-situ and in-situ experiments in pemfc water management studies. Int J Heat Mass Transf 52(7):1741–1752CrossRefGoogle Scholar
  25. 25.
    Küttler U, Wall W (2009) Vector extrapolation for strong coupling fluid-structure interaction solvers. J Appl Mech 76(2):021–205CrossRefGoogle Scholar
  26. 26.
    Lamb H (1916) Hydrodynamics, 4th edn. Cambridge University Press, Cambridge.
  27. 27.
    Marti J, Ryzhakov P, Idelsohn S, Oñate E (2012) Combined Eulerian-PFEM approach for analysis of polymers in fire situations. Int J Numer Methods Eng 92:782–801MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Mier-Torrecilla, M (2010) Numerical simulation of multi-fluid flows with the Particle Finite Element Method. Ph.D. thesis, Universitat Politécnica de CatalunyaGoogle Scholar
  29. 29.
    Oñate E, Idelsohn S, del Pin F, Aubry R (2004) The particle finite element method: an overview. Int J Comput Methods 1:267–307CrossRefzbMATHGoogle Scholar
  30. 30.
    Ryzhakov P, Oñate E, Rossi R, Idelsohn S (2010) Lagrangian FE methods for coupled problems in fluid mechanics. CIMNE. ISBN: 978-84-96736-97-9Google Scholar
  31. 31.
    Ryzhakov PB, Jarauta A (2015) An embedded approach for immiscible multi-fluid problems. Int J Numer Methods Fluids. doi: 10.1002/fld.4190
  32. 32.
    Sussman M, Ohta M (2009) A stable and efficient method for treating surface tension in incompressible two-phase flow. SIAM J Sci Comput 31:2447–2471MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Temam R (1969) Sur l’approximation de la solution des equations de Navier-Stokes par la methode des pase fractionaires. Arch Ration Mech Anal 32:135–153MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Theodorakakos A, Ous T, Gavaises M, Nouri J, Nikolopoulos N, Yanagihara H (2006) Dynamics of water droplets detached from porous surfaces of relevance to PEM fuel cells. J Colloid Interface Sci 300:673–687CrossRefGoogle Scholar
  35. 35.
    Weber AZ, Borup RL, Darling RM, Das PK, Dursch TJ, Gu W, Harvey D, Kusoglu A, Litster S, Mench MM, Mukundan R, Owejan JP, Pharoah JG, Secanell M, Zenyuk IV (2014) A critical review of modeling transport phenomena in Polymer-Electrolyte fuel cells. J Electrochem Soc 161(12):F1254–F1299CrossRefGoogle Scholar
  36. 36.
    Wörner M (2012) Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications. Microfluid Nanofluid 12:841–886CrossRefGoogle Scholar
  37. 37.
    Wu T, Djilali N (2012) Experimental investigation of water droplet emergence in a model polymer electrolyte membrane fuel cell microchannel. J Power Sources 208:248–256CrossRefGoogle Scholar
  38. 38.
    Zhu X, Sui P, Djilali N (2008) Three-dimensional numerical simulations of water droplet dynamics in a PEMFC gas channel. J Power Sources 181:101–115CrossRefGoogle Scholar

Copyright information

© OWZ 2016

Authors and Affiliations

  • Pavel B. Ryzhakov
    • 1
    • 2
  • Alex Jarauta
    • 2
  • Marc Secanell
    • 3
  • Jordi Pons-Prats
    • 2
  1. 1.Centre Internacional de Métodes Numérics en Enginyeria (CIMNE), Gran Capitán s/nBarcelonaSpain
  2. 2.CIMNEBarcelonaSpain
  3. 3.Energy Systems Design Lab (ESDLab)University of AlbertaEdmontonCanada

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