Lattice-boltzmann Simulation On Fluid Dynamics And Mixing In Micro Channels

As a newly developed numerical method in the computational fluid dynamics area and beyond, the lattice-Boltzmann method has gained numerous significant achievements during the past two decades. Distinguishing from the traditional method based on the discretization of macroscopic equations, the lattice-Boltzmann method is a mesoscopic method derived from the Boltzmann equation and has attracted more and more attention from the academia recently due to the elegant features of the method such as the simplicity in implementation and the potential for effective parallelization.In this thesis, the fundamental theory of the lattice-Boltzmann method is explained and both 2D and 3D simulation codes are established with the single-relaxation-time lattice-Boltzmann method incorporating a multiphase model. Typical cases such as Poiseuille flow, entry length effect in laminar flow, flow past a cylinder, phase separation from a metastable state, diffusion from plane instantaneous source in an unbounded domain, etc. are studied to validate the codes as well as to show the great capability of the lattice-Boltzmann method in describing a wide range of problems in fluid dynamics and beyond.An estimation of the relation between the variations of the computational cost and the Reynolds number is derived. It is shown that under certain reasonable conditions, the increase rate of the number of necessary lattice nodes equals to that of the Reynolds number to the power of dimension; the increase rate of computational cost equals to that of the Reynolds number to the power of dimension through increasing characteristic length of the system; and the increase rate of computation cost equals to that of the Reynolds number to the power of dimension plus two through increasing characteristic velocity of the system. Thus, the computational cost of lattice-Boltzmann method increases rapidly with the increase of Reynolds number, which limits the capability of solving the fluid dynamics at a relatively high Reynolds number.In order to increase the capability of our in-house codes applying to the cases at a comparatively high Reynolds number, parallelization is achieved with the OpenMP technique and a simple method of optimizing data storage of the Tecplot? IJK ordered data format is brought forward. The performance test of the parallel code shows nearly ideal performance: an approximately linear speed-up with an average efficiency of 98.79%. The optimization in data storage saves 25.00%-42.86% in storage space and processing time.A special phenomenon in the T-shaped micro-channel, i.e. fluctuation of the mixing interface, is studied, and the 2D simulation result is compared with the 3D one while analyzing the occurrence of the phenomenon. The 2D simulation cannot give good result probably owing to the lack of inclusion of the dynamics in the third dimension. As a comparison, the 3D simulation result shows that there exists non-symmetric flow structure in the direction perpendicular to the measuring plane and velocity field in the colliding plane which locates in the fluid colliding area and is perpendicular to the measuring plane and parallel to the collision direction plays an important role in the occurrence of the phenomenon.Simulation results of lower and higher Reynolds numbers show different potential flow regime respectively: stratified flow and engulfment flow. The velocity field in the upstream colliding plane has a close relationship to the downstream potential flow regime: different velocity field corresponds to different potential flow regime. By adding a disturbing structure, the velocity field similar to the case at higher Reynolds number is achieved and potential flow regime changes to that at higher Reynolds number, which shows the significant effect of the velocity field in the colliding plane in the occurrence of the phenomenon.