Calculation of friction coefficient and analysis of fluid flow in a stepped micro-channel for wide range of Knudsen number using Lattice Boltzmann (MRT) method

• A stepped micro-channel has been studied at wide range of Knudsen number.
• Friction coefficient has been calculated for micro scale flow.
• A new correlation is suggested for calculation of friction coefficient.
• Lattice Boltzmann (MRT) method has been applied in the modeling.
• A modified second order slip boundary condition has been used in the modeling.

Micro scale gas flows have attracted significant research interest in the last two decades. In this research, the fluid flow of gases in a stepped micro-channel has been conducted. Wide range of Knudsen number has been implemented using the Lattice Boltzmann (MRT) method in this study. A modified second-order slip boundary condition and a Bosanquet-type effective viscosity are used to consider the velocity slip at the boundaries and to cover the slip and transition regimes of flow to obtain an accurate simulation of rarefied gases. The flow specifications such as pressure loss, velocity profile, stream lines and friction coefficient at different conditions have been presented. The results show, good agreement with available experimental data. The calculation shows, that the friction coefficient decreases with increasing the Knudsen number and stepping the micro-channel has an inverse effect on the friction coefficient value. Furthermore, a new correlation is suggested for calculation of the friction coefficient in the stepped micro-channel flows as below; CfRe=3.113+2.9151+2Kn+0.641exp(3.2031+2Kn).