Numerical Simulation Of The Flow Over Three Cylinders By Lattice Boltzmann Method

Lattice Boltzmann model (LBM) has a ability to simulate the complex fluids flow and has developed into a new tool for modeling complicated physical phenomena. The model is regarded as a particle perspective in which the entire conceptual framework is composed of collisions, streaming, and particle-particle/particle-surface interactions. It is different from the traditional Computational Fluid Dynamics (CFD) methods for he Lattice Boltzmann Method, which is based on macroscopic continuum equations and is the basis of microscopic model or mesoscopic kinetics equations. LBM is based on mass and momentum conservations and is a commendable mesoscopic simulation method, where the Continuity and the Navier-Stokes equations can be satisfied. As against the traditional CFD methods in contrast with LBM, which has some unique advantages, such as good parallelism, easy implementation of boundary conditions and simple codes, and is suitable for investigating the problems of flow around the circular cylinders.A full 2-D numerical simulation of flow around three circular cylinders in a cross flow using the multiple relaxation time lattice Boltzmann method (MRT-LBM) has been carried out in this paper. Among these three circular cylinders, one of the three cylinders on which a forced in-line vibrating is used to do this research and attempt to found out the effects of the moving cylinder and the other two rigid cylinders on the wake characteristics and vortex formation. Basing on LBM and D2Q9 model, this paper select the incompressible fluid with the Reynolds number Re=100. Two of the cylinders are rigid and the other one is an in-line vibrated cylinder lying downstream, in addition, forced vibrating amplitude and frequency are A/D= 0.5 and fv=0.4 (where A is the forced amplitude, D is the cylinder diameter and fv stands for the vibrating frequency, respectively). As a benchmark problem to discuss the problem of lift coefficient r.m.s for these cylinders with spacing ratios T/D (T is the center-to-center spacing between the two upstream cylinders)between other rigid side-by-side cylinders. The calculated results not only indicate that the spacing ratios T/D have influence on the wake patterns and the formation of vortex shedding, but also analyze the lift coefficient r.m.s for the three cylinders with the spacing ratios S/D (where S is the center-to-center spacing between the center of upstream two side-by- side cylinders and downstream cylinder).