B201 格子ボルツマン法による複雑流路内の移動現象解析(LBMによる流体解析)

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The lattice Boltzmann method (LBM) for a binary miscible fluid mixture proposed by Inamuro et al. [submitted to J. Comput. Phys. (2001)] is developed and applied to problems of transport phenomena in complex geometries such as porous media. In their method the equilibrium distribution function for the concentration of diffusing species has an additional term with a parameter, which is determined so that the numerical stability can be maintained at high Peclet numbers. As an example of transport phenomena in complex geometries, we consider the problems of flow and mass transfer in a three-dimensional porous structure which consists of many identical spherical bodies in the rectangular domain. In this study, it is assumed that the fluid flows through the structure and the diffusing species is diffused from the bodies. A periodic boundary condition with pressure difference is used at the inlet and outlet. A slip wall condition is applied to the other sides of the domain. Also, boundary conditions of the particle distribution functions for the concentration are presented in this paper. We first carry out the calculations of a mass transfer problem under the condition that the diffusing species is diffused from only one body in the structure. The Schmidt number is fixed at Sc=1. The Reynolds number Re, which is defined by using the time-averaged superficial velocity and the equivalent diameter of the bodies, ranges from 2.09 to 209. Flow characteristics and concentration profiles of the diffusing species at a pore scale are obtained at different Reynolds numbers. At low Reynolds number of Re=2.09, the fluid flow avoids the bodies and goes through open spaces, and the concentration of the diffusing species spreads in every direction mainly by the effect of diffusion. At moderate Reynolds number of Re=33.0, on the other hand, the flow speed becomes a little larger and the diffusing species is diffused together with fluid flow. At high Reynolds number of Re=209 the flow separations occur and several vortices appear behind the bodies. Also, the concentration profiles are highly affected by the flow convection and become completely different from those at low Reynolds numbers. We next perform the calculations of the same mass transfer problem on another condition that the diffusing species is diffused from all the bodies in the structure. The Schmidt number is kept at Sc=0.6 in this case. The Sherwood numbers are calculated and compared with experimental data by Petrovic and Thodos. The calculated values are in good agreement with the experimental data at low and high Reynolds numbers. From these results, it is found that the present method is useful for the investigation of transport phenomena in complex geometries.
一般社団法人日本機械学会の論文
2001-11-14

B201 格子ボルツマン法による複雑流路内の移動現象解析(LBMによる流体解析)

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