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Research Papers

# A Combined Finite Element-Upwind Finite Volume Method for Liquid-Feed Direct Methanol Fuel Cell Simulations

[+] Author and Article Information
Pengtao Sun1

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

Chaoyang Wang

Department of Mechanical Engineering, and Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA 16802cxw31@psu.edu

Jinchao Xu

Department of Mathematics, Pennsylvania State University, University Park, PA 16802xu@math.psu.edu

1

Corresponding author.

J. Fuel Cell Sci. Technol 7(4), 041010 (Apr 07, 2010) (14 pages) doi:10.1115/1.4000630 History: Received July 16, 2008; Revised July 30, 2009; Published April 07, 2010; Online April 07, 2010

## Abstract

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.

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## Figures

Figure 1

Schematic domain for the 3D DMFC model

Figure 2

Computational domain for the 3D model

Figure 3

Numerical mesh used for 3D simulations

Figure 4

Convergence history of our FEM-upwind FVM with new numerical techniques

Figure 5

Convergence history of the standard FEM/FVM without new numerical techniques

Figure 6

Methanol YlMeOH in the XZ-plane (left) near the inlet, (middle) near the middle of the cell length, and (right) near the outlet, in the anode

Figure 7

Oxygen YgO2 in the XZ-plane (left) near the inlet, (middle) near the middle of the cell length, and (right) near the outlet, in the cathode

Figure 8

Water YH2O in the XZ-plane (left) near the inlet, (right) near the middle of the cell length, and (bottom) near the outlet, in both the anode and the cathode

Figure 9

(Left) Methanol YlMeOH in the anode, (middle) oxygen YgO2 in the cathode, and (right) water YH2O in both the anode and cathode, in the XY-plane through the cell center

Figure 10

(Left) Temperature T in the anode and cathode, (middle) proton potential Φe in membrane electrode assemble (MEA), and (right) electron potential Φs in MEA, in the XY-plane through the cell center

Figure 11

(Left) Velocity field in the XY-plane, (middle top) blow-up velocity field in the XY-plane, (middle bottom) velocity in the XZ-plane, and (right) pressure in the XY-plane through the cell center

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