Lattice Boltzmann Simulation Of Gaseous Micro-flows And Heat Transfer

In the last several decades, one of the important tendencies of the development for nature science and engineering technology is forward to the minisize and micromation, its theory study has been made great progress, and applied in various fields. Micro-Electro-Mechanical System (MEMS) is one of the most important fields in micrscale applications, among all of the MEMS's design and applications, the fluid flow and heat mass transfer become very evident and important, which lead to the larger need of the theory analyse and experimental technology for the micro-flow and heat transfer.Though much progress has been achieved with lots of experiment research, some certain difficulties and limitations are still in existence, such as the restriction of experimental condition and equipments, the uncertainty results from the same measurement, and so on. Meanwhile, in the field of theory study and numerical stimulation, the full Boltzmann equation has been universally recognized as an efficient method. But due to the existence of the non-linear collision term, it becomes very difficult to be solved directly. Direct Simulation Monte-Carlo (DSMC) is one of the most popular numerical approach. However, the disadvantage of DSMC is obvious: the enormous computation cost and the numerical statistical noises. A novel mesoscopical numerical scheme——Lattice Boltzmann Method (LBM), which was originated from the last 90s, could be considered as a certain difference solution of the Boltzmann equation. 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. In this work, we complete the numerical study by the LBM, which could overcome some limitations of the conventional numerical approaches and reveal more properties and characters of micro-flows and heat transfer.Initially, we should discuss the thermal lattice Boltzmann model and"He"thermal lattice model which includes viscous heat dissipation and compression work. And then, some simplications and modification have been made specially aiming at the viscous heating effects. The novel thermal LBM model directly roots from the incompressible Temperature equations including viscous heating effect and fully takes advantage of the numerical characteristic of the nonequilibrium distribution function moments in lattice Boltzmann model to obtain the value of strain rate tensor conveniently, and avoids the difficulty of solving velocity derivative term. The simulation results show that this viscous thermal LBM model stimulates the non-linear temperature distribution due to the viscous heating effects, and keeps the numerical stability and precision even under higher parameters ( higher Ec and Pr numbers), and the precision has been improved by magnitude.For the study on micro-flow in slip region ( 10 ?3≤Kn≤0.1), we discuss from the two key points of micro-flows simulation by LBM——the introduction of Knudsen number and the treatment of velocity slip boundary conditions are discussed in detail. For the former, we intakes Kn into the model after the rigorous derivation according to the relations of viscous coefficient which concludes from relevant definition of the kinetic theory; on the treatment of slip boundary conditions, unlike the existing schemes, we gives both first-order and second-order implicit differential scheme aiming at the Mexwell slip model. Then we carry out some numerical tests on certain typical micro-flows, focus on the velocity distribution, velocity slip and non-linear effect of pressure which corresponds to the analysis and discussion to the rarefaction and incompressible effects in micro-flows.Till now, numerical simulation research on the thermal micro-flow is still very exiguous, and the empirical constants have to be used in the models. We use the above thermal LBM model including viscous heating effects. And for the treatment of boundary conditions, we take the new scheme for the temperature jump boundary. Compared our simulation results with the analytical solution, the temperature profiles and the temperature jump are both in good agreement. Moreover, we take a series of simulations of micro Couette flows with various Ec numbers, and find that: For different Kn numbers, there is a critical Ec number around 3.0, which cause the temperature jump at upper wall is zero. With the systematic numerical tests on various Pr and Ec numbers, we find that temperature jump is linearly proportional to the Ec number approximately; and is decreased rapidly with the increasing of Pr number while becomes constant (0.15 approximately) gradually.It is a great disputation and large challenge for LBM simulation of micro-flow in transitional regime. In order to simulate the transitional micro-flow, a certain velocity correction function is needed to picture the non-linear effect in the Knudsen layer. The form of corrected function and determination of the adjustable parameter are discussed. Moreover, we use a high-order slip substitute treatment of the boundary condition which only includes the first-order derivation term, which can avoid the difficulty of solving high-order velocity derivation term directly. The simulation results have showed that this corrected and improved model and high-order boundary coditions treatment are suitable for the simulation of transional region micro-flows. The velocity profile and non-linear pressure distribution are both in consistent with the DSMC results, and compared with the former LBM simulaitons, both the suitable range of Kn number and the numerical precision have been improved greatly.In this thesis, we take the lattice Boltzmann method, a novel computational stimulation method, to do the numerical research on the gaseous micro-flows and heat transfer systematicly and detailedly, from the slip region to transition regime. Steady foundations have been settled and effective approaches are also supplied for the further work on the simulation of micro-flows and heat transfer.