Lattice Boltzmann Simulation Of Fluid Flow And Heat Transfer Around A Cylinder And Tube Bundles

Lattice Boltzmann method is a newly developed numerical algorithm to simulate fluid flows and heat transfer. It is a mesoscale numerical simulation method, discreted on velocity, space, and time. It is different from the traditional method of computational fluid dynamics. Lattice Boltzmann has lots of advantages, it is very simple and it can handle complex boundary conditions. Moreover, it is of much higher parallism naturally. At present, it has been applied in various fluid dynamics areas. Lattice Boltzmann method is based on gas dynamics. In the cases of low limit of Ma, it has been proved that it is of second-order algorithms to describe incompressible viscous fluid flow and heat transfer. However, while inclusion of dealing with curved boundary conditions in certain problem, the numerical accuracy depends on the selection of difference scheme. In present study, a classical problem of fluid flow and heat transfer when the fluid passing a cylinder and tube bundles is simulated using LBGK model. The stability of algorithms and numerical precision has been discussed when the fluid flow and heat transfer at the curved boundary are simulated with the application of extrapolation scheme. The main works and conclusions would be described as follows:1) Lattice Boltzmann equations are obtained from continuous Boltzmann equation, by discreting on velocity, space and time. With Chapman-Enskog expansion, the Navier-Stokes equations are derived from the Lattice Boltzmann equation. Thus the relationships between model parameters and macro-physical parameters are established.2) A Dual-Distribution-Function model is derived from theoretical deducing. And non-equilibrium extrapolation method is used for the treatment of curved boundary. Furthermore the treatment for internal nodes in solid is proposed. Analogically, non-equilibrium extrapolation method is used to deal with the temperature boundary in the present study.3) Lattice Boltzmann simulation results of thermal flows around a cylinder indicate that flow is steady, without separation from the cylinder for Re < 10. The temperature distribution is significantly lengthened along the flow, but reduced along y direction. For the cases of 10≤Re< 50, the flow is still steady although it separated from the cylinder, it is still steady. Two stable vortexes appear at the back of the cylinder, which induces enhancing convection heat transfer. Since that, the temperature distribution appears two peak values. For the cases of Re≥50, fluid flow appears unsteady and karman vortex is showing. Heat transfer coefficient increases obviously, and temperature distribution is discontinuous.4) With increasing Re, the accuracy of computation reduces, and the critical ? c increases. Under the same Re, numerical accuracy is better with the increase of?.5) For in-line and staggered tube bundles with the same number of cylinders, fluid flow changes from steady-state to unsteady-state, and the heat transfer is enhanced with increasing Re, The greater the space between cylinders is, the easier flow state changes, and enhancement of the heat transfer is. Under the same Re, heat transfer for flow around staggered bundles is stronger than that for in-line bundles.