Study on microchannel flows with a sudden contraction–expansion at a wide range of Knudsen number using lattice Boltzmann method

Abstract

Numerical simulations have been performed on the pressure-driven rarefied flow through channels with a sudden contraction–expansion of 2:1:2 using isothermal two and three-dimensional lattice Boltzmann method (LBM). In the LBM, a Bosanquet-type effective viscosity and a modified second-order slip boundary condition are used to account for the rarefaction effect on gas viscosity to cover the slip and transition flow regimes, that is, a wider range of Knudsen number. Firstly, the in-house LBM code is verified by comparing the computed pressure distribution and flow pattern with experimental ones measured by others. The verified code is then used to study the effects of the outlet Knudsen number Kn o , driving pressure ratio P i /P o , and Reynolds number Re, respectively, varied in the ranges of 0.001–1.0, 1.15–5.0, and 0.02–120, on the pressure distributions and flow patterns as well as to document the differences between continuum and rarefied flows. Results are discussed in terms of the distributions of local pressure, Knudsen number, centerline velocity, and Mach number. The variations of flow patterns and vortex length with Kn o and Re are also documented. Moreover, a critical Knudsen number is identified to be Kn oc = 0.1 below and above which the behaviors of nonlinear pressure profile and velocity distribution and the variations of vortex length with Re upstream and downstream of constriction are different from those of continuum flows.