可互溶流體質量傳遞與流場分析之數值模擬 蔡宗儒、溫志湧，陳慶耀
E-mail: [email protected]
摘 要
本文研究數值模擬流經一非均勻隨機分佈孔隙率之多孔性界質之流場分析及其壓力損失，並對其控制參數如平均孔隙率之 大小、孔隙率分佈特性之相關長度及平方差、多孔性界質之慣性效應， 對流場之影響做一系統式之分析。結果顯示，多孔 性界質之平均孔隙率之大小對有效進入多孔性界質內之流量有顯著之影響。而孔隙率分佈之特性則對有效流量產生不同之 效應，特徵相關長度之差 異並未對有效流量有顯著影響，相對的，分佈平方差則影響較為顯著。至於慣性效應之影響，則 於工業實用範圍內之數值進行模擬，其影響有效流量之效果亦不顯著。 在毛細管中可互溶流體的置換情況上，預先濕潤之 薄層存在對注入毛細管的推斥置換流體之指狀物前緣速度的影響，可利用軸對稱之stokes模擬方式分析。在預先濕潤之薄 層的設定上，其黏滯度與注入毛細管的推斥置換流體相同，但卻較毛細管內固有的流體黏滯度低。注入毛細管的推斥置換 流體之指狀物以半穩態形式持續推斥管內固有的流體，且其前緣速度在相同體積的Poiseuille flow中心線速度之下。此現象 與先前無預先濕潤之薄層存在時相較下，可發現預先濕潤之薄層所產生之潤滑影響。且是在注入之推斥置換流體推斥如同 固體之管內固有流體時最明顯。
關鍵詞 : 數值模擬,非均勻多孔性材質，相關長度，有效流量，預先濕潤之薄層 目錄
簽名頁 授權書 iii 中文摘要 v 英文摘要 vi 誌謝 viii 目錄 ix 圖目錄 xi 符號說明 xiv 第一章 問題描述 1 1.1 研究背景 1 1.2 研究 目的 5 第二章 物理問題與統御方程式 7 2.1 可互溶流體於毛細管 7 2.2可互溶流體於多孔性材質 11 第三章 結果與討論 15 3.1 可互溶流體於毛細管內之流場 15 3.1.1 模擬機制與參考範例 15 3.1.2 黏滯度比控制參數R之影響 19 3.1.3 預先濕潤之薄 層控制參數δ之影響 22 3.2 可互溶流體於非均勻多孔性材質之流場 24 3.2.1 模擬機制與參考範例 24 3.2.2 滲透性比控制參 數k之影響 25 3.2.3 均方差控制參數s之影響 28 3.2.4 相關長度控制參數l之影響 30 3.2.5 慣性力控制參數Ref之影響 31 第四章 結論 32 參考文獻 34 附錄一 無因次化動量方程式 83
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