不可互溶液滴於旋轉非均質多孔性介質數值模擬

Rotationally-induced fingering instability in a two-dimensional heterogeneous porous medium

林涏鄉(Ting-Shiang Lin)

指導教授 ： 陳慶耀

國立交通大學/工學院/機械工程系所/碩士(2016年)

摘要

本篇論文主要是透過使用界面擴散法，並將此法應用於多孔性介質之中，我們更搭配高精準度之數值方法針對不可互溶之流場進行流場分析及觀察其模擬結果。我們將流場假設在可旋轉之多孔性非均質介質之中，觀察其流場中兩流體介面因黏性的不一所產生的界面不穩定現象的變化。再者，我們透過高精準度的數值方法能夠成功地模擬出在相關實驗中，介面不穩定現象所導致之黏性指狀物的物理特徵。主要透過不同的無因次參數所代表的物理意義，如兩流體黏滯度比值、離心力/表面張力比值、科氏力及表面張力等，代表施加於流場的作用力，觀察其不同的作用力在多孔性介質的黏性指狀化現象的影響，藉此比較其與均質性介質下的黏性指狀化現象的差異。透過多孔性介質的控制參數，如變異數及相關長度，來比較其不同多孔性介質下的液滴變形結果。

關鍵字

指狀物 ； 指狀化現象 ； 非均質性 ； 不可互溶 ； 多孔性介質

並列摘要

In this study, we successfully use high-order numerical scheme and diffuse-interface method based on Darcy-Cahn-Hilliard model to simulate immiscible flow in various porous media with ranges of possible values for the viscosity contrast and by including inertial effects due to the Coriolis force. The role played by these two physical contribution on the development of interface singularities is illustrated and discussed. On the other hand, with the presence of heterogeneity, active secondary phenomena such as finger competition, and tip-splitting are triggered. Prominences of fingering instability are evaluated by the channeling and interfacial lengths.

並列關鍵字

viscous fingering ； immiscible ； heterogeneous ； porous medium

參考文獻

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