Filtration in gas micro flows is an important problem complicated by possible slip flow for the filter media and the particles. Slip complicates Navier-Stokes solutions for the flow field. The direct simulation Monte Carlo method and its derivatives can be applied, but they are very complex. The Lattice Boltzmann Method (LBM) appears to offer some advantages for these slip and transitional flows. To evaluate the method, it was used to compute micro channel and micro orifice flows for a range of Knudsen numbers (Kn). The micro orifice simulates an array of micro filter fibers. The Lattice Bhatnagar-Gross-Krook (LBGK) single relaxation time approximation was used with the relaxation parameter accounting for density variations. The effects of different techniques for satisfying slip and no-slip boundary conditions were investigated. Both no-slip bounce-back and slip bounce-back boundary conditions were used. For the slip bounce-back boundary condition, the reflection factor and the accommodation coefficient were applied to improve accuracy. The micro channel computations were performed for conditions matching well-documented compressible slip-flow Navier-Stokes results in the literature. The channel had a length to height ratio of 100 and an inlet to outlet pressure ratio of 2.15. Knudsen numbers of 0.00194, 0.0194, and 0.194 were examined. The bounce-back boundary condition was applied at the top and bottom walls. A reflection factor of 0.85 provided the best agreement with the results in the literature for a Kn = 0.0194. The computed velocity profiles and the nonlinear streamwise pressure profile display excellent agreement with the Navier-Stokes results in the literature at this Knudsen number. At Kn = 0.00194, pure bounce back and bounce back with reflection factor both yield very good results. At Kn = 0.194, the bounce back with reflection factor results exhibit significant deviations from the literature. The accommodation coefficient scheme does not show good results for these micro flows. The reflection factor boundary condition also was applied for the micro orifice flows. The two-dimensional orifice computations were conducted with a 0.6 ratio of the open orifice area to the total area to match results in the literature. The micro orifice LBM results are in good agreement with the literature for Reynolds numbers between 4.8 and 12.5. In summary, the Lattice Boltzmann Method appears promising for micro filter computations, but improvements are needed for larger Knudsen numbers and more sophisticated relaxation time models may be needed for increased compressibility effects at higher Reynolds numbers.
Intermediate Lattice Boltzmann-BGK method and its application to micro-flows
