不可互溶流體層推斥之數值模擬

Abstract

摘要

此項研究我們使用了 FORTRAN 工具以擴散界面的方法模擬了非混流體的 非定常流體動力過程。此項方法已經應用於物理現象與流體流動中界面變形的界 面區研究。採用此項方法意在探索兩種粘性不同的流體在多孔介質中彌散效果之 間粘性指狀物的形式。 我們發現驅替液的粘性會影響粘性指進的效果，其次便是不同參數的影響。 通過對研究的大量分析，我們採用四個相關參數來輔助模擬過程。例如，Péclet 參數(Pe)，Capillary 參數(Ca)，Atwood 參數(A)，以及 Cahn 參數(Cahn)。在研究中， Pe 固定為 1*105 來保證在我們數值編碼內的穩定的粘性指狀物。此外，由於此項 研究指向不可互溶流體的流體流動，因此 Capillary 參數和 Atwood 參數將作為主 要的控制參數。 通過在多孔介質中流體流動中不混溶層的數值模擬，此項研究展示了粘性指 進的機構（指進的寬長）。今後我們還將繼續關注多孔介質中多層次不可互溶的 位移過程。

Abstract The research used software FORTRAN to simulate the pattern of unsteady fluid dynamics for immiscible fluids by diffuse-interface methods. These methods have been applied in the interfacial region of physical phenomena and fluid flows implicating interface deformation. The purpose by using the method is to get the pattern of viscous fingering between two fluids with different viscosities and effect of finite dispersion in porous media. We investigate the influence of viscous fingering due to the differences between the viscosities of the displacing fluid and followed by effect of different parameters. A quantitative analysis of the contribution of fingering to this research we conducted as a function of four relevant parameters to simulate the problem, i.e., the Péclet number Pe, the Capillary number Ca, the Atwood number A, and the Cahn number Cahn. In this study, we used the high Peclet number were 1*105 to get stable condition of viscous fingering in our numerical code. Furthermore, since this study is immiscible the fingering fluid flows, so that Capillary number and Atwood number being the main control parameters of the fluid flows. Finally, the results obviously presented the immiscible viscous fingering structures by numerical simulation of fluid flow in porous medium for qualitative results and quantitative results. Influences of Capillary number parameters are given not much effect for the fingering pattern of the layer in porous media. On the other hand, the Atwood number parameter gave much effects of the immiscible pattern of fingering.