Research Paper

An Effective Combined Finite Element-Upwind Finite Volume Method for a Transient Multiphysics Two-Phase Transport Model of a Proton Exchange Membrane Fuel Cell

[+] Author and Article Information
Pengtao Sun

Department of Mathematical Sciences,
University of Nevada,
Las Vegas 4505 Maryland Parkway,
Las Vegas, NV 89154
e-mail: pengtao.sun@unlv.edu

Su Zhou

College of Automotive Studies/New Energy Automotive Engineering Center,
Tongji University,
4800 Caoan Road,
Shanghai 201804, China
e-mail: suzhou@tongji.edu.cn

Qiya Hu

Institute of Computational Mathematics and Scientific Engineering Computing,
Chinese Academy of Sciences,
Beijing 100080, China
e-mail: hqy@lsec.cc.ac.cn

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF FUEL CELL SCIENCE AND TECHNOLOGY. Manuscript received August 26, 2012; final manuscript received January 13, 2013; published online May 14, 2013. Editor: Nigel M. Sammes.

J. Fuel Cell Sci. Technol 10(3), 031004 (May 14, 2013) (11 pages) Paper No: FC-12-1079; doi: 10.1115/1.4023837 History: Received August 26, 2012; Revised January 13, 2013

In this paper, an effective combined finite element-upwind finite volume method is studied for a three-dimensional transient multiphysics transport model of a proton exchange membrane fuel cell (PEMFC), in which Navier–Stokes–Darcy coupling flow, species transports, heat transfer, electrochemical processes, and charge transports are fully considered. Multiphase mixture (M2) formulation is employed to define the involved two-phase model. Kirchhoff transformation is introduced to overcome the discontinuous and degenerate water diffusivity that is induced by the M2 model. By means of an adaptive time-stepping fourth-order multistep backward differencing formula (BDF), we design an effective temporal integration scheme to deal with the stiff phenomena arising from different time scales. In addition, all the governing equations are discretized by a combined finite element-upwind finite volume method to conquer the dominant convection effect in gas channels, while the diffusion and reaction effects are still dealt with by finite element method. Numerical simulations demonstrate that the presented techniques are effective to obtain a fast and convergent nonlinear iteration within a maximum 36 steps at each time step; in contrast to the oscillatory and nonconvergent iteration conducted by commercial CFD solvers and standard finite element/finite volume methods.

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Fig. 1

Water diffusivity DH2O(CH2O) (left) and DmH2O,eff(CH2O) (right) at 80 °C

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Fig. 2

Computational domain and mesh of a single-channel PEFC

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Fig. 3

Convergence history of our numerical method (left) versus that of standard FEM/FVM (right) at the 449th time step (13.79 s), where the iteration error tolerance is 10-6

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Fig. 4

Hydrogen concentration CH2 at 1 s (left), 3 s (middle), and 9 s (right)

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Fig. 5

Oxygen concentration CO2 at 1 s (left), 3 s (middle), and 9 s (right)

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Fig. 6

Liquid saturation s at 1 s (left), 3 s (middle), and 9 s (right)

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Fig. 7

Liquid saturation in GDLs at the anode (top part) and the cathode (bottom part) along flow direction at 9 s (top), 59 s (middle), and 100 s (bottom)




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