以計算流體力學模擬徑向多孔介質指形流: 流率與濕潤性的交互作用

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林怡萱(Yi-Xuan Lin) 查詢紙本館藏

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機械工程學系

論文名稱

以計算流體力學模擬徑向多孔介質指形流: 流率與濕潤性的交互作用
(Computational Fluid Dynamic Simulation of viscous fingering in radial porous media: interplay between injection and wettability)

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摘要(中)

當兩種流體存在黏度差異時，以低黏度流體驅替高黏度流體會導致流動介面不穩定，這種現象稱為指形流。根據前人研究以時變線性流率進行注入能夠有效抑制徑向Hele-Shaw cell中的黏性指形，本文進一步將其應用在具有亂數分佈的顆粒之多孔介質中，以商用軟體ANSYS Fluent進行模擬。本研究分為兩個部分：徑向Hele-Shaw cell與多孔介質，針對不同濕潤性下線性流率的抑制能力來進行探討。其中濕潤性的改變在Hele-Shaw cell中為改變上下平板壁面，多孔介質則除了上下平板更增加了顆粒的濕潤性，以探討孔隙對流動的影響。
Hele-Shaw cell結果顯示當流動為非濕潤流體驅替濕潤流體的排移流動時，線性流率可有效的抑制指形；而當濕潤流體驅替非濕潤流體的浸潤流動時，線性流率效果不彰，此結果與上下平板濕潤性造成的垂直面的介面張力方向有關，排移流動的介面張力與流動方向相反，使擾動的成長幅度較小，進而能抑制指形；而浸潤流動的介面張力與流動方向相同，增加了介面的擾動程度，較易形成指形使得線性流率失效。多孔介質中受到孔隙間毛細壓力的影響，排移流動傾向往孔隙大的地方流動，浸潤流動傾向往孔隙小的地方流動；兩者的線性流率皆因為受到孔隙影響使得線性流率抑制指形的效用十分不明顯。

摘要(英)

Displacing a more viscous fluid by another less viscous fluid leads to instabilities of the interface between two fluids due to the viscosity contrast. The phenomenon is called viscous fingering. Researchers already found out that linear time-dependent injection rate is able to suppress this phenomenon. Our work here is to take a step further, by applying the scheme in porous media. We consider the radial Hele-Shaw cell and porous media flow, and focus on how wettability may affect the instability suppress.
The results in Hele-Shaw cell show that the linear injection flow rate suppress the instabilities effectively for drainage flow, in which a non-wetting fluid displaces a wetting fluid; On the other hand, this scheme doesn’t work for imbibition flow where a wetting fluid displace a non-wetting fluid. This is because the interfacial force caused by the wettability, directs in same the direction as imbibition flow. In porous media, a linear injection rate has little impact on both kinds of flow. Drainage flow tends to flow toward larger pores while imbibition flow most likely flows toward smaller pores, which both induce the onset of instability that is hardly suppressible by the linear flow rates.

關鍵字(中)

★ 指形流
★ 多孔介質
★ 濕潤性
★ 時變流率

關鍵字(英)

★ fingering flow
★ Hele-Shaw cell
★ porous media
★ wettability
★ time-dependent injection flow rate

論文目次

中文摘要 i
Abstract ii
符號說明 iii
英文字母 iii
希臘字母 iv
上下標 iv
目錄 v
圖目錄 viii
表目錄 viii
第一章緒論 1
1.1 研究動機 1
1.2 文獻回顧 2
1.3 研究目的 4
第二章數學模型 12
2.1 問題描述 12
2.1.1 Hele-Shaw cell模型 12
2.1.2 多孔介質模型 13
2.1.3 常數流率與線性流率 13
2.2 統御方程式 15
2.2.1 質量守恆方程式 15
2.2.2 動量守恆方程式 15
2.2.3 體積分率方程式 16
2.3 VOF模型及CSF模型 16
2.3.1 VOF模型 17
2.3.2 CSF 模型 17
2.4 邊界條件 18
2.5 流體性質 19
2.6 網格測試 20
第三章 Hele-Shaw cell 26
3.1 模擬條件 26
3.2 濕潤性 27
3.3 排移流動 28
3.4 浸潤流動 29
3.5 綜合比較 30
3.5.1介面長度 30
3.5.2 壓力 32
3.5.3功率 33
第四章多孔介質 40
4.1 排移流動與浸潤流動 40
4.1.1排移流動 40
4.1.2浸潤流動 41
4.1.3綜合比較 42
4.2 毛細壓力的影響 43
4.2.1排移流動 43
4.2.2浸潤流動 44
4.2.3綜合比較 44
4.3 完全沾濕介質 45
第五章結論與未來展望 57
5.1 結論 57
5.2 未來展望 59
參考文獻 60

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指導教授

鍾志昂(Chih-Ang Chung)

審核日期

2019-1-30

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