격자볼츠만 방법을 이용한 다공성 매체에서의 대류 열전달과 투과성의 전산모사에 관한 연구

Abstract

Recently the lattice Boltzmann method has been developed as a computational fluid dynamics method. The lattice Boltzmann method is a powerful approach to hydrodynamics, with applications ranging from large Reynolds number flows to flows at a micrometer scale, porous media and multiphase flows. In most lattice Boltzmann method so far, only mass and momentum conservation is implemented. However it is important and sometimes critical to have the capability of simulating temperature distribution and permeability in porous media. This study performed a series of simulations of two dimensional convective heat transfer in a channel, cavity and natural convection using the hybrid lattice Boltzmann-finite difference method which neglects viscous thermal dissipation. The algorithm is simple, but the requirement on computational resources is twice of that for a nonthermal lattice Boltzmann method code. In hybrid lattice Boltzmann-finite difference method, the velocities are given by the lattice Boltzmann method and then they are used to compute the energy equation. This latter is discretized by the finite difference method to obtain the temperature field. Also, The simulations of various flows as a function of porosity in fibrous media are conducted using the single relaxation time ? lattice Boltzmann method. The porosity media are reconstructed by regular placement of particles. We have used the lattice Boltzmann method to calculate the flow and permeability in complex 3D porous media. First, we considered the flow in a realistic three dimensional particle sample. Second, we calculate the single phase permeability and detailed flow field for a 3D micromodel. Predictions of the permeability for media of four different porosities are in good agreement with the value of Gebart. We found that we can predict permeability value in porous media using the lattice Boltzmann method. Namely, permeability values strongly depend on the porosity of the sample and the permeability as a function of pressure drop fell within the same order of magnitude.