Extended application of lattice Boltzmann method to rarefied gas flow in micro-channels

• A lattice Boltzmann model for micro-channel gas flow with Knudsen number up to 10 is proposed.
• Knudsen layer effect on rarefied gas flow with Knudsen number up to 30 is investigated.
• A constant non-dimensional flow rate and linear pressure distribution along the micro-channel are observed for the free molecular flow.

Simulation of rarefied gas flow in micro-channels is of great interest owing to its diverse applications in many engineering fields. In this study, a multiple-relaxation-time lattice Boltzmann (MRT-LB) model with a general second-order slip boundary condition is presented to investigate the behaviour of gas flow with a wide range of Knudsen number in micro-channels. With the aid of a Bosanquet-type effective viscosity, the effective relaxation time is correlated with local Knudsen number (Kn  ) to account for the varying degree of rarefaction effect. Unlike previous studies, the derived accommodation coefficient rr for the combined bounce-back/diffusive reflection (CBBDR) boundary condition is dependent on the local Kn, which allows more flexibility to simulate the slip velocity along the channel walls. When compared with results of other methods, such as linearised Boltzmann equation, experimental data, direct simulation Monte Carlo (DSMC) and Information Preservation DSMC (IP-DSMC), it is found that the LB model is capable of capturing the flow behaviour, including the velocity profile, flow rate, pressure distribution and Knudsen minimum of rarefied gas with Kn up to 10. The effect of Knudsen layer (KL) on the velocity of gas flow with a wide range of Kn   is also discussed. It is found that KL effect is negligible in the continuum flow and yy-independent in the free molecular flow, while in the intermediate range, especially in transition flow, KL effect is significant and particular efforts should be made to capture this effect.