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系統識別號 U0002-1707200614374200
中文論文名稱 三維模擬兩同軸與平行多孔球在水中沉降之受力分析
英文論文名稱 Three Dimensional Simulations of Hydrodynamic Drag Forces on Two Porous Spheres Settling Parallel or In-Line
校院名稱 淡江大學
系所名稱(中) 化學工程與材料工程學系碩士班
系所名稱(英) Department of Chemical and Materials Engineering
學年度 94
學期 2
出版年 95
研究生中文姓名 林勉宏
研究生英文姓名 Mien-Hung Lin
學號 693361379
學位類別 碩士
語文別 中文
口試日期 2006-06-19
論文頁數 79頁
口試委員 指導教授-吳容銘
委員-李篤中
委員-陳錫仁
委員-吳容銘
委員-蔡榮進
委員-郭修伯
中文關鍵字 三維  模擬  透過率  同軸  平行  拖曳力 
英文關鍵字 three dimension  simulation  permeability  in-line  parallel  drag force 
學科別分類
中文摘要 本論文為兩同軸或平行多孔球在牛頓流體中穩定移動的流體拖曳力的數值估計,雷諾數範圍從0.1到40。對於兩同軸多孔球,在緩流範圍中,兩球體的拖曳力幾乎一樣。在較高的雷諾數,第一顆球的拖曳力會高於後面的球,因為第一顆球對於第二個球有遮蔽的影響。當直徑b<2(b=df/2k^0.5,df跟k分別為球的直徑跟透過率),兩球體可視為非球體限制。增加兩球的b值,第二個球的拖曳力會增加,因為球內部的透過率較低;同時由於第一個球產生的強烈的遮蔽效應造成第二個球所受的拖曳力會降低,此兩種效應相互影響,導致第二個球的受力很難判斷,而當b值最小時,上述的影響會最小;平行沉降中兩球的受力幾乎相同,孔隙度(e)的影響遠大於兩多孔球間的影響,緻密多孔球的沉降速度比疏鬆多孔球的沉降速度快
英文摘要 This paper numerically evaluates the hydrodynamic drag force exerted on two highly porous spheres moving steadily parallel or in-line through a quiescent Newtonian fluid over a Reynolds number ranging from 0.1 to 40. At creeping flow limit, the drag forces exerted on both spheres were approximately identical. At higher Reynolds numbers the drag force on the leading sphere (sphere #1) was higher than the following sphere (sphere #2), revealing the shading effects produced by sphere #1 on sphere #2. At dimensionless diameter b<2 (b=df/2k^0.5, df and k are sphere diameter and interior permeability, respectively), the spheres can be regarded as “no-spheres” limit. At increasing b for both spheres, the drag force on sphere #2 was increased because of the more difficult advective flow through its interior, and at the same time the drag was reduced owing to the stronger wake flow produced by the denser sphere #1. The competition between these two effects leads to complicated dependence of drag force on sphere #2 on b value. These effects were minimal when b became low. In parallel settling, the forces of the two spheres force are nearly the same. The influence of porosity is larger than that of distances between the two porous spheres. The settling velocity of dense porous sphere is faster than highly porous sphere.
論文目次 目錄
中文摘要..................................................i
英文摘要.................................................ii
誌謝....................................................iii
目錄.....................................................iv
圖目錄...................................................vi
表目錄....................................................x
第一章 前言.............................................1
第二章 文獻回顧.........................................3
2.1 膠羽所受拖曳力.......................................3
2.2 膠羽的孔隙度.........................................9
2.3 膠羽的透過率....................................11
第三章 統御方程式與數值解析.............................13
3.1 兩同軸球體於無限流場中穩定運動......................13
3.2 兩平行球體於無限流場中穩定運動......................19
3.3 網格大小與受力分析..................................24
第四章 結果與討論.......................................25
4.1 同軸球體於無限流場中穩定運動........................25
4.1.1 流體之流場........................................25
4.1.2 拖曳力............................................32
4.1.3 兩球之交互作用力..................................38
4.1.4 兩球非均勻的影響..................................46
4.1.5 沉降之結果........................................50
4.2 平行球體於無限流場中穩定運動........................53
4.2.1 流體之流場........................................53
4.2.2 拖曳力............................................58
4.2.3 兩球之交互作用力..................................63
4.2.4 平行沉降之結果....................................66
第五章 結論與建議.......................................70
符號說明.................................................72
參考文獻.................................................75

圖目錄
圖3.1 同軸球體於無限流場穩定運動之示意圖.............14
圖3.2(a) 同軸球體於無限流場穩定運動之網格圖.............16
圖3.2(b) 同軸球體附近之網格(放大)圖.....................17
圖3.3 平行球體於無限流場穩定運動之示意圖.............20
圖3.4(a) 平行球體於無限流場穩定運動之網格圖.............21
圖3.4(b) 平行球體附近之網格(放大)圖.....................22
圖4.1(a) 同軸球體於無限流場穩定運動之流場圖
(S/df=3, Re=0.1, b=2)..........................27
圖4.1(b) 同軸球體於無限流場穩定運動之流場圖
(S/df=3, Re=40, b=2)...........................27
圖4.1(c) 同軸球體於無限流場穩定運動之流場圖
(S/df=3, Re=0.1, b=50).........................28
圖4.1(d) 同軸球體於無限流場穩定運動之流場圖
(S/df=3, Re=40, b=50)..........................28
圖4.2(a) 同軸球體於無限流場穩定運動之流場圖
(S/df=9, Re=0.1, b=2)..........................29
圖4.2(b) 同軸球體於無限流場穩定運動之流場圖
(S/df=9, Re=40, b= 2)..........................29
圖4.2(c) 同軸球體於無限流場穩定運動之流場圖
(S/df=9, Re=0.1, b=50).........................30
圖4.2(d) 同軸球體於無限流場穩定運動之流場圖
(S/df=9, Re=40, b=50)..........................30
圖4.3(a) 同軸實心球與多孔球(b=5)在Re=0.1之受力..........33
圖4.3(b) 同軸實心球與多孔球(b=5)在Re=40之受力...........34
圖4.4(a) 修正因子與透過率在雷諾數為1之不同條件關係圖....36
圖4.4(b) 修正因子與透過率在雷諾數為40之不同條件關係圖...37
圖4.5(a) 雷諾數為1時不同透過率(b1=2, b2=50)的受力情形...39
圖4.5(b) 雷諾數為40時不同透過率(b1=2, b2=50)的受力情形..40
圖4.6(a) 雷諾數為1時不同透過率(b1=50, b2=2)的受力情形...41
圖4.6(b) 雷諾數為40時不同透過率(b1=50, b2=2)的受力情形..42
圖4.7(a) 兩不同孔隙度之同軸球體穩定運動之流場圖
(S/df=3, Re=0.1, b1=50, b2=2)..................44
圖4.7(b) 兩不同孔隙度之同軸球體穩定運動之流場圖
(S/df=3, Re=40, b1=50, b2=2)...................44
圖4.7(c) 兩不同孔隙度之同軸球體穩定運動之流場圖
(S/df=3, Re=0.1, b1=2, b2=50)..................45
圖4.7(d) 兩不同孔隙度之同軸球體穩定運動之流場圖
(S/df=3, Re=40, b1=2, b2=50)...................45
圖4.8(a) 雷諾數為1時非均勻多孔球的受力情形..............48
圖4.8(b) 雷諾數為40時非均勻多孔球的受力情形.............49
圖4.9 三種系統之同軸沈降結果(S/df=3).................52
圖4.10(a) 兩平行球於無限流場穩定運動之流場圖
(S/df=2, Re=0.1, b=2)..........................54
圖4.10(b) 兩平行球於無限流場穩定運動之流場圖
(S/df=2, Re=40, b=2)...........................54
圖4.10(c) 兩平行球於無限流場穩定運動之流場圖
(S/df=2, Re=0.1, b=50).........................55
圖4.10(d) 兩平行球於無限流場穩定運動之流場圖
(S/df=2, Re=40, b=50)..........................55
圖4.11(a) 兩平行球於無限流場穩定運動之流場圖
(S/df=4, Re=0.1, b=2)..........................56
圖4.11(b) 兩平行球於無限流場穩定運動之流場圖
(S/df=4, Re=40, b=2)...........................56
圖4.11(c) 兩平行球於無限流場穩定運動之流場圖
(S/df=4, Re=0.1, b=50).........................57
圖4.11(d) 兩平行球於無限流場穩定運動之流場圖
(S/df=4, Re=40, b=50)..........................57
圖4.12(a) 平行多孔球不同(b)在Re=0.1的受力................59
圖4.12(b) 平行多孔球不同(b)在Re=40的受力.................60
圖4.13(a) 兩平行多孔球在雷諾數為1之不同條件關係圖........61
圖4.13(b) 兩平行多孔球在雷諾數為40之不同條件關係圖.......62
圖4.14(a) 雷諾數為1時不同透過率(b1=2, b2=50)的受力情形...64
圖4.14(b) 雷諾數為40時不同透過率(b1=2, b2=50)的受力情形..65
圖4.15(a) 兩平行多孔球在不同孔隙度(e)之沉降結果
(密度為1020kg/m^3).............................67
圖4.15(b) 兩平行多孔球在不同孔隙度(e)之沉降結果
(密度為1050kg/m^3).............................68
圖4.15(c) 不同密度與不同孔隙度(e)之平行沉降比較圖........69

表目錄
表4.1 圖形符號命名與球之性質.........................47

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