Lattice Boltzmann Computations of Micro Channel Gas Flows Using Different Boundary Conditions

Lattice Boltzmann method simulations were performed for isothermal gas flows through a micro channel at Knudsen (Kn) numbers of 0.00194, 0.0194, and 0.194 and Reynolds numbers between 2 and 12. The goal of the work was to compare the performance of the no-slip bounce back, the accommodation coefficient, and the reflection factor boundary condition schemes, particularly for slip flows. For the micro channel flows considered, the reflection factor boundary condition provided results which matched best with the literature, while the no-slip bounce-back and accommodation coefficient boundary conditions showed greater deviations. For Kn = 0.0194, a reflection factor of 0.85 yielded velocity profiles in very good agreement with the unified flow analytical results with deviations of approximately 0.3\% in the maximum velocity and 2.3\% in the slip velocity. For Kn = 0.00194, the no-slip bounce- back and 0.85 reflection factor yield good velocity profiles although there are deviations from the analytical solution near the wall. However, in the transitional flow regime at Kn = 0.194, none of the approaches yielded acceptable results.