(181w) Porous Media Flow Simulation Via Lattice Boltzmann Method with Representative Elementary Volume Method

Chung, P. S., Carnegie Mellon University
Jhon, M. S., Carnegie Mellon University

Nanotechnology applications such as micro fuel cells (FCs) are alternative power generation sources which have gained tremendous attention recently due to their high efficiency, negligible greenhouse emissions, and simplicity and modularity in design. Among the various FC systems, direct methanol fuel cell (DMFC) is seen as a strong candidate for power supply in portable electronic devices. This can be attributed to the advantages DMFCs possess over the hydrogen PEMFCs, due to ease in liquid fuel delivery and storage, lack of humidification requirements, and reduced design complexity, overcoming the need of any ancillary equipment. In spite of these compelling advantages, there are many technological concerns in this technology. A solution of methanol and water (typically 0.5~2M[1]) is fed to the DMFC anode, which is internally reformed by the catalyst. However, there is significantly low electro-activity of methanol oxidation at the anode, and efficiency reduction due to resistance to fuel (methanol) transport by the CO2 bubbles produced in the electrochemical reaction. Moreover, significant fraction of fuel methanol is transported through the PEM from the anode to the cathode (termed as fuel crossover) which leads to fuel loss, and reduction in cell potential due to the undesirable methanol oxidation reaction at the cathode. The resistance to methanol transport by CO2 can be rectified by improved fuel distribution and gas removal mechanisms. This requires the prediction of muti-phase, multi-component fuel transport in the gas diffusion layer (GDL), and a detailed understanding of various physical phenomena such as: (i) the interfacial phenomena of liquid and gas on solid surface, (ii) the phenomena of gas desorption, nucleation and growth of bubbles at the interface of GDL and catalyst layer, and (iii) bubble transport in the porous media.

In this paper, we develop a methodology of calculating the fluid flow in the porous media using lattice Boltzmann method (LBM) [2, 3]. The advantages of clear physical pictures, an inherently transient nature, multiscale simulation capabilities, geometric flexibility, and fully parallel algorithms, make LBM to be an attractive candidate for multi-scale, multi-phase simulation tool in DMFC. We first developed standard LBM with Bhatnagar-Gross-Krook (BGK) model, which is applicable to complex porous geometry. Later, we developed a representative elementary volume (REV) method, which appears to be a more suitable method for studying multi-phase flow problems in porous media, as compared to other computational fluid dynamics codes.

The REV method along with lattice Boltzmann kinetic equation (modified by the Brickman-Forchheimer-extended Darcy equations) [4] is solved, and the results are compared with standard LBM calculations.

To illustrate the essence of our simulation, REV was used to examine 2-D flow in the porous media descriptive for GDL. In our simulation, the porosity (f) is set to be 0.1, Reynolds number (Re) ranges from 10-2 to 102, and Darcy number (Da) ranges from 10-6 to 102. The lattice used is a 80×80 square mesh, and the relaxation time is set to be 0.8. Periodic boundary conditions are applied at the entrance and the exit. The velocity field is initialized to zero at each lattice node with a constant density, r=1.0, and the distribution function is set to be at equilibrium initially. We calculated the velocity profiles for different values of Re and Da. It was found that, the streamwise velocity component vx is uniform along the channel as the flow reaches the steady state, and other velocity component vy is on the order of 1012 over the entire flow field, which gives excellent agreement with the numerical results obtained by Guo and Zhao[5] confirming the validity of our REV method. Upon the successful formulation of REV/LBM descriptive for the single phase porous media flow, we will generalize our methodology to multi-phase flow by incorporating the surface tension of CO2 bubble and the pore shape.


  1. M.M. Mench, C.Y. Wang, and S. Thynell, Int. J. Transport Phenomena, 3, 1 (2001).
  2. W.T. Kim, S.S. Ghai, Y. Zhou, I. Staroselsky, H.D. Chen, and M.S. Jhon, IEEE Trans. Magn., 41, 3016 (2005).
  3. W.T. Kim, M.S. Jhon, Y. Zhou, I. Staroselsky, and H.D. Chen, J. Appl. Phys., 97, 10P304 (2005).
  4. P. Nithiarasu, K.N. Seetharamu, and T. Sundararajan, Int. J. Heat Mass Transfer, 40, 3955 (1997).
  5. Z. Guo and T.S. Zhao, Phys. Rev. E, 66, 036304 (2002).