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Research Papers

# Lattice Boltzmann Modeling of Three-Dimensional, Multicomponent Mass Diffusion in a Solid Oxide Fuel Cell Anode

[+] Author and Article Information
Abhijit S. Joshi, Kyle N. Grew, John R. Izzo, Aldo A. Peracchio

Department of Mechanical Engineering, University of Connecticut, 191 Auditorium Road, Storrs, CT 06269-3139

Wilson K. S. Chiu1

Department of Mechanical Engineering, University of Connecticut, 191 Auditorium Road, Storrs, CT 06269-3139wchiu@engr.uconn.edu

1

Corresponding author.

J. Fuel Cell Sci. Technol 7(1), 011006 (Oct 06, 2009) (8 pages) doi:10.1115/1.3117251 History: Received July 13, 2007; Revised July 20, 2008; Published October 06, 2009

## Abstract

The lattice Boltzmann method (LBM) was used to study the three-dimensional (3D) mass diffusion of three species ($H2$, $H2O$, and $N2$) in the pore phase of a porous solid oxide fuel cell (SOFC) anode. The method used is an extension of a two-dimensional (2D) LBM model (2007, “Lattice Boltzmann Method for Continuum, Multi-Component Mass Diffusion in Complex 2D Geometries  ,” J. Phys. D, 40, pp. 2961–2971) to study mass transport in SOFC anodes (2007, “Lattice Boltzmann Modeling of 2D Gas Transport in a Solid Oxide Fuel Cell Anode  ,” J. Power Sources, 164, pp. 631–638). The 3D porous anode geometry is initially modeled using a set of randomly packed and overlapping solid spheres. Results using this simple geometry model are then compared with results for an actual SOFC anode geometry obtained using X-ray computed tomography (XCT) at sub-50 nm resolution. The effective diffusivity $Deff$ of the porous anode is a parameter, which is widely used in system-level models. However, empirical relationships often used to calculate this value may not be accurate for the porous geometry that is actually used. Solution of the 3D Laplace equation provides a more reliable and accurate means to estimate the effective diffusivity for a given anode geometry. The effective diffusivity is calculated for different geometries and for a range of porosity values, both for the 3D sphere packing model and for the real geometry obtained by XCT. The LBM model is then used to predict species mole fractions within the spherical packing model geometry and the XCT geometry. The mole fraction variation is subsequently used to calculate the concentration polarization. These predictions compare well with previously obtained 2D results and with results reported in the literature. The 3D mass transport model developed in this work can be eventually coupled with other transport models and be used to optimize the anode microstructure geometry.

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## Figures

Figure 3

3D SOFC anode geometry reconstructed using XCT; the bright region represents pores and the dark region is the solid phase

Figure 4

Solution domain and boundary conditions used for numerical solution of Laplace’s equation through the pore phase in a porous medium (solid phase not shown)

Figure 5

(a) Domain decomposition used for parallel implementation and (b) typical speed up plot for the LBM simulation

Figure 6

Comparison of the porosity-tortuosity factors Ψ for sphere packing structures and a real SOFC structure obtained using XCT

Figure 7

Comparison between the LBM and Stefan–Maxwell prediction for mole fraction variation along the axis of a cylindrical pore

Figure 8

Mole fraction variation in the spherical packing model for J∗=0.041 and porosity=30%: (a) 3D mole fraction variation in the pore phase and (b) in-plane variation of H2 mole fraction

Figure 10

Concentration polarization calculated using different models

Figure 9

Mole fraction variation in the actual SOFC geometry for J∗=0.013 and porosity=30%. The gas channel is at x∗=0 where mole fractions of H2, H2O, and N2 are 0.47, 0.03, and 0.5, respectively, and the TPB is at x∗=1 where H2+O2−=H2O+2e−: (a) 3D percent variation in H2 mole fraction (0.47 at x∗=0 and minimum value of 0.085 at x∗=1) and H2O mole fraction (0.03 at x∗=0 and maximum value of 0.55 at x∗=1) in the pore phase, where percent variation for H2=(H2[x,y,z]−H2_min)×100/(H2_max−H2_min), with a similar definition for H2O and (b) in-plane variation in H2 mole fraction.

Figure 2

Slice by slice conversion of the 3D geometry into a 3D binary array suitable for performing calculations using the lattice Boltzmann method

Figure 1

Schematic representation of 3D mass transport through a porous SOFC anode

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