Abstract
Results are presented of three-dimensional (3D) lattice Boltzmann method (LBM) simulation on pressure-driven rarefied gas flows through microchannels with a sudden contraction–expansion of 3:1:3. The main parameters examined are channel aspect ratio (AR) and Knudsen number (Kn<inf>o</inf>) of 1–7 and 0.001–0.1, respectively. To cover the slip flow regime, a Bosanquet-type effective viscosity and a modified second-order slip boundary condition are used to account for the rarefaction effect on gas viscosity. The in-house 3D LBM code is verified by comparing the computed centerline streamwise pressure distribution and critical Reynolds number (Re<inf>c</inf>) of asymmetric bifurcation with experimental ones measured by others. The results are discussed in the way to explore effects of AR and Kn<inf>o</inf> on the bifurcation limits Re<inf>c</inf> of symmetric and asymmetric streamwise flows and effects of AR on the cross-sectional secondary flow patterns, which are lacking in the literature. Specifically, Re<inf>c</inf> for asymmetry bifurcation is found to first decrease linearly with increasing AR and then level off at 112 for AR > 3, whereas Re<inf>c</inf> decreases approximately linearly with increasing Kn<inf>o</inf>. Moreover, Re<inf>c</inf> can be correlated with AR and Kn<inf>o</inf> in a simple expression. The observed cross-sectional two- or four-pair counter-rotating vortices in the present rarefied laminar microchannel flows are new in terms of its absence in Newtonian laminar flows through straight micro- and macrochannels. Its driving force is the anisotropic secondary normal stresses over the cross-section as a result of the nonlinearity of the axial pressure gradient and, in turn, compressibility effect.