Lbm and Md Simulations of a Flow in a Nano-porous Medium

To evaluate a lattice Boltzmann method (LBM) for the three dimensional continuum to non-continuum transitional flow regimes, the results are compared with those of the molecular dynamics (MD) simulations by the Leonard-Jones potential. The flow field considered is in a modeled nanoporous medium whose porosity is 0.88 and consists of square cylinder rods. The equations used in the LBM are modified lattice Boltzmann equations introducing Knudsen number dependency. In the MD simulations, novel boundary treatments are applied. The results of a nano-porous flow at a Knudsen number Kn=0.24 show reasonable agreement in both the simulation methods and confirm the reliability of the LBM. The difference in the predicted values of the permeability, however, implies that the wall boundary condition of the LBM requires further improvement. INTRODUCTION Flows in micro porous media have been focused on by many researchers [1,2] due to the recent rapid development of the fuel cell technology. Since the catalytic layers and the electrolyte membranes of the fuel cells are usually made of micro-nano porous materials, the flows there are usually distinguished by large Knudsen numbers: Kn= / 0.01 H λ > , where λ is the molecular mean free path of the fluid and H is the characteristic length of the flow domain. Accordingly, when one considers fluid flows in sub-micro flow geometries, it is necessary to understand the flows at the molecular level. The continuum Navier-Stokes equations are, however, no longer applicable for such high Knudsen number flows. The processes in these kinds of flows are described by the Boltzmann equation (BE) of the gas kinetic theory [3,4]. The numerical solution of the BE, either directly [5] or via the direct simulation Monte Carlo (DSMC) method [6], is very time expensive. This means that it is virtually impossible to perform such simulations for flows in complex large scale geometries even by the modern computer environment. Thus, there are strong needs for accurate models which allow engineering flow simulations in microscale geometries at lower computational costs. Recently, alternative strategies to simulate flows in the continuum to the slip and transitional regimes have been thus proposed. Nie et al. [7] introduced Knudsen number dependency into the relaxation parameter of the lattice Boltzmann equation (LBE) and simulated micro-channel flows at 0.01<Kn<0.4 using a slip velocity condition [8] on the channel walls. Shen et al. [9] validated this strategy comparing the results of DSMC simulations of microchannel flows. The authors’ group [10] also devised an alternative strategy to simulate such flows in the continuum to the slip and transitional regimes by a lattice Boltzmann method (LBM) where a diffuse scattering wall boundary condition and an effective relaxation time associated with the Knudsen number are employed with the D2Q21 velocity model. Its results were validated with the results of the DSMC in Couette-Poiseuille flows [11]. Hence, the present study attempts to validate further the LBM for the transitional flow regime in simulating a three dimensional flow in a nano-porous medium. A nano-mesh consisting of crossed square cylinder arrays, is considered in this study as the flow field geometry. Since accurate experimental measurements are very difficult to obtain reliable flow field data in nanoscale flows, the aforementioned direct numerical simulations of the BE may be replaceable for them. Another option for simulating nanoscale flows is, however, the molecular dynamics (MD) simulation method [12] which is based on simpler Newtonian mechanics and is getting popular [13]. Although the present topic does not include phase changes, the MD simulation is promising on treating phase changes and/or multiphase nanomicro flow phenomena which are important issues in the fuel cell technology. In fact, there is no special treatment is required for the MD simulation to distinguish the phase difference [14,15]. Therefore, to assess the LBM for the transitional flow