The Simulation To Micro-scale Gas Flows Based On Lattice Boltzmann Method

Micro-flow has opened up a new research field of Fluid Dynamics, which greatly promotes the theory development of the Fluid Dynamics. At the same time, Micro-Electro-Mechanical-System (MEMS) is a new technology area of miniaturization.Developing the research of the micro-flow that is of important significance to these fields.The deviation of rarefied gas from the equilibrium state of continuum is characterized by Knudsen number, Kn=?/L, which is defined as the ratio of mean free path to system's Characteristic length. Flow can be divided into continuous region (Kn?0.001), sliping region (0.001< Kn÷0.1), transition region (0.1< Kn?10) and free molecular area (0.1< Kn?10). When the flow falls into the transition flow regime, there are rare molecule collisions in the flow. The Navier-Stokes equations, which is based on linear constitutive relation between the stress and strain, fails to describe the gas flow in this regime. On the other hand, the direct simulation Monte Carlo(DSMC) method,which is molecule based,converges slowly and requires lots of computational time, especially for the low velocity flow. In this thesis, we takea novel mesoscopical numerical scheme-Lattice Boltzmann Method (LBM), to do the numerical research on the gaseous micro-flows. Therefore, it has the strongly theorical foundation and physical background. Another advantage of LBM is the convenient treatment of the boundary conditions and easy coding.Taking the standard LBM model in slip region, it needs to take the Kn into the stack time of the calculation model and the first order slip boundary format. Then we carry out this model on certain typical micro-flows, focus on the non-linear pressure distribution,velocity distribution and velocity slip which corresponds to the analysis and discussion to the rarefaction and incompressible effects in micro-flows; For the transitional micro-flow a certain velocity correction function is needed to picture the non-linear effect in the Knudsen layer and taking the second-order slip boundary condition. The velocity profile and non-linear pressure distribution are both in consistent with the DSMC results.In this thesis, we take the lattice Boltzmann method, to do the numerical research on the gaseous micro-flows detailedly, from the slip region to transition regime. Some foundations have been settled and effective approaches are also supplied for the further work on the simulation of micro-flows.