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研究生:李明哲
研究生(外文):Ming-Che Li
論文名稱:非均勻結構膠羽群在流場中的拖曳係數
論文名稱(外文):Drag coefficient of a dispersion of non-homogenously structured flocs in a flow field
指導教授:徐治平徐治平引用關係
指導教授(外文):Jyh-Ping Hsu
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:化學工程學研究所
學門:工程學門
學類:化學工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:53
中文關鍵詞:非均勻結構膠羽濃度分布細胞模型兩層模型拖曳係數
外文關鍵詞:two-layer modeldrag coefficientcell modelConcentrated floc dispersionnonuniform structure
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本文以數值模擬方式探討膠羽結構及其濃度效應對其在流場中所受的拖曳力之影響。由於膠羽實際的組成結構相當複雜,為簡化問題,我們假設整個膠羽粒子為一具有不同穿透係數的雙層多孔性物質。實際的情形下,膠羽粒子在流體中運動時雷諾數往往高達數十以上,Stokes law將不再適用。本文使用的主控方程式包括描述流體在多孔體外運動的Navier-Stokes方程式及描述多孔體內運動的Darcy-Brinkman model,並以數值方法求解該組高度非線性的主控方程式。在探討膠羽濃度的方面,採用廣為接受的free surface cell model來模擬群體效應。吾人探討下列參數對膠羽拖曳力的影響,包括:膠羽群孔隙度ε、流體雷諾數Re及膠羽外內層之穿透度比k1/k2。藉由改變膠羽內、外層結構的穿透度,我們發現膠羽群在自由沉降時,在相同的雷諾數及平均穿透度下,結構愈不均勻的膠羽所受的拖曳力愈大,且在雷諾數較高時,由其拖曳係數對雷諾數之作圖觀察,偏離Stokes-law-like correlation的偏差值也愈大。藉由改變群體間的孔隙度,我們發現當膠羽彼此分佈愈鬆散(濃度低),系統所造成的拖曳力愈小,由流線圖扭曲的程度觀察,對流現象愈趨明顯,偏離Stokes-law-like correlation的偏差值也愈大。
The influences of the structure of floc and its concentration on the hydrodynamic drag acting on it are investigated theoretically. Due to the fact that floc formation involves various nonlinear, random processes, its structure is of complicated nature. Here, a two-layer model is adopted to simulate the behavior of a floc where various possible floc structures are simulated by varying the permeability of each layer, and a cell model is used to model the behavior of a concentrated floc dispersion. Experimental evidence reveals that the Reynolds number associated with the sedimentation of floc can be on the order of ten, that is, the Stokes law is inapplicable. In this study, a Navier-Stokes equation governing the flow field outside a floc and a Darcy-Brinkman model describing the motion of fluid inside it are solved numerically based on a finite scheme. The influence of the key parameters of the problem under consideration, including the swarm voidage ε, the Reynolds number Re, and the permeability ratio k1/k2, k1 and k2 being respectively the permeability of the outer layer and the inner layer of a floc, on the drag acting on a floc are discussed. The results of numerical simulation reveal that the more heterogeneous the structure of floc, the greater the drag is. Also, the more heterogeneous the structure of a floc the more serious the deviation of the variation of drag against Re curve from a Stokes-law-like relation. The drag on a floc decreases with the decrease in its concentration, and, due to the convective flow of fluid, the distortion of streamlines between flocs becomes more serious, and the deviation of the variation of drag against Re curve from a Stokes-law like relation is more significant.
中文摘要 Ⅰ
英文摘要 Ⅱ
目錄 Ⅲ
圖目錄 Ⅳ
表目錄 Ⅶ
第一章 緒論 1
第二章 文獻回顧 3
2.1 Darcy-Brinkman model 3
2.2 Two-layers model 4
2.3 Free surface cell model 5
第三章 理論分析 7
3.1系統分析 7
3.1.1 液相中的流場 7
3.1.2 膠羽內的流場 9
3.1.3 邊界條件 10
3.2 拖曳力分析 11
第四章 結果討論 13
附錄一 計算流體力學軟體FIDAP7.6簡介 17
附錄二 有限元素法簡介 22
符號說明 28
參考文獻 34
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