Three-dimensional rarefied gas flows in constricted microchannels with different aspect ratios: asymmetry bifurcations and secondary flows

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 (Kno) 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 (Rec) of asymmetric bifurcation with experimental ones measured by others. The results are discussed in the way to explore effects of AR and Kno on the bifurcation limits Rec of symmetric and asymmetric streamwise flows and effects of AR on the cross-sectional secondary flow patterns, which are lacking in the literature. Specifically, Rec for asymmetry bifurcation is found to first decrease linearly with increasing AR and then level off at 112 for AR > 3, whereas Rec decreases approximately linearly with increasing Kno. Moreover, Rec can be correlated with AR and Kno 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.