다공성 매체에서의 유체 흐름에 대한 전산모사

Abstract

When the metal alloy solidifies, the segregation can occur due to the fluid flow between the dendrites in the mushy zone. The fluid flow in the mushy zone is regarded as the flow in the porous material by the Darcy's law which is applied to the Navier-Stokes equation since there are very few passages that can allow the fluid flow to occur. To verify the Darcy's law, which is used to calculate the permeability of fluid in the mushy zone, the permeability was calculated by simulating the phenomenon of the fluid flow passing through the artificially-constructed porous media without any assumption for the porous material. The solidification process of metal alloy was expressed by the change of solid fraction, and the solid fraction was controlled by varying size and interdistance of two-dimensional solid particles of various shapes forming the artificially-constructed porous media. The fluid flow in the porous media was assumed to be incompressible and laminar flow, and calculated by the continuity equation and the Navier-Stokes equation. As a result, the permeability calculated by the artificially-constructed porous media varied depending on the shape of solid particles assumed dendrites and control method of the solid fraction. To evaluate the reliability for the permeability calculated by the artificially-constructed porous media, it was compared with the theoretical permeability calculated by the Kozeny-Carman model. Summarizing the constants in the Kozeny-Carman model and expressing them as constant C, the constant C is usually defined as 150 or 180. However, in this study, the values of constant C for each solid fraction were different and determined by the dendritic shapes and configurations through the simulation of various conditions. After obtaining the constant C and the average constant C for each solid fraction, respectively, the permeability of the artificially-constructed porous media was compared with the theoretical permeability obtained by applying the average constant C to the Kozeny-Carman model. In the case of using the average constant C, the theoretical permeability of Kozeny-Carman model was calculated incorrectly. However, in the case of using the constant C according to the shapes, configurations, and each solid fraction, almost accurate results can be obtained.