Numerical simulations of microflow by lattice Boltzmann method with different lattice models and wall functions

Abstract

Microchannel flows study has been focused due to MEMS applications recently. In this thesis, we employ kinetic Lattice Boltzmann method(LBM) to simulate microchannel flows. In our simulation, considering a long microchannel with pressure boundary conditions at both inlet and outlet, using three different models, D2Q9, D2Q13, and D2Q21 to simulate Poiseuille flow, respectively. In order to predict the accurate slip velocity at the wall and pressure distribution along streamwise direction, it is essential to apply modification to these models. There are two key points, one is correction of wall function, the other is boundary condition. Firstly, we use three different wall functions to test, which are Lockerby’s wall function(LWF), Stop’s wall function(SWF), and Guo’s wall function(GWF). LWF,SWF,and GWF not only lower the slip velocity but also predict a nonlinear behavior in nearwall region. Here, wall function is applied to the modification of relaxation time. Secondly, boundary condition is discussed. The traditional boundary conditions were implemented for walls, such as bounceback scheme, but it can not generate enough slip velocity on walls. However, kinetic boundary condition like diffuse scattering boundary conditions(DSBC) [18], may over predict the slip velocity on wall. For capturing the slip velocity correctly, we introduce β-weighted diffusive-bounceback boundary condition, which combines the bounceback and diffuse-scattering boundary condition. β is a function of Knudsen number and it ’s obtained by fitting the linearized Boltzmann solutions at wall. In addition, we utilize two different schemes to calculate the unknown distribution function at inlet and outlet after streaming step. All present results are compared with Direct Simulation Monte Carlo (DSMC).