本研究使用計算流體力學(CFD)的方法來討論迴轉盤結構對速度和剪應力分佈的影響，其中結構的改變包含了迴轉盤葉片的種類與數目。研究選用的模組為內置迴轉盤的單一圓柱形濾室，並且將濾膜固定在靠近濾室底部的多孔性支撐材。本研究利用Fluent計算流體力學軟體來模擬三個維度之模組內部流場，其數值方法為網格有限體積法與紊流中的RNG k-epsilon模式進行連續及動量守恆方程式求解，並且選用不同迴轉盤結構與改變操作條件進行分析探討。迴轉盤的操作轉速設定至3000 rpm並且選用進料流速範圍從1.18 m/s到3.18 m/s。在不同操作條件下之速度、壓力和剪應力的模擬結果與先前文獻和實驗數據相比較。
由結果可以得知，迴轉盤的轉速是主導過濾通量的最重要因素，在無葉片迴轉盤系統轉速每增加1000 rpm，提升幅度約20至30 %。最適化的葉片設計可以有效地提升濾膜表面的剪切力，達到更高的過濾通量與更低的薄膜結垢，以加裝雙凹凸狀之迴轉盤效果最佳。另外，在固定的系統轉速下，迴轉盤上的葉片越多會造成濾膜表面上的剪應力更高，每多增加一個葉片會使得剪切力提升約30 Pa。然而，增加葉片的數目亦會導致越大的耗能，造成越高的操作成本；隨著葉片數目的增加會使功率急遽地的提升，但濾速的上升卻是趨緩的情況，四個葉片功率3290 J/s。

Rotating-disk filtration modules have been increasingly used for solid-liquid separation in industrial processes in recent years. The high shear stress generated by rotating disk is believed to effectively reduce the cake formation and concentration polarization on the membrane surface, as a result, to enhance the filtration flux. To evaluate the shear stress and the velocity distributions are therefore the essential steps not only to grasp the filtration performance but also to design high-efficiency modules. In this study, the effects of rotating disk structure, including the blade type and number, on the velocity and shear stress distributions are discussed using computational fluid dynamics (CFD). The module consists of a testing rotating disk installing inside a cylindrical chamber. A circular membrane is fixed on a porous support near the chamber bottom. The 3-dimensional flow fields in the module with different rotating disks under various operating conditions are simulated using the Fluent CFD software. The equations of continuity and momentum balances are solved numerically using a finite volume scheme with the Renormalization-Group k-epsilon model. The disk rotating speeds are set up to 3000 rpm, and the inlet suspension velocity ranges from 1.18 to 3.18 m/s. The simulated results of velocity, pressure and shear stress profiles under various conditions are compared with those in previous study and experimental data. It can be concluded that the disk rotating speed is the most important factor in determining the filtration flux. The optimum disk design for higher permeate fluxes and less membrane fouling can be achieved by increasing the shear stress on the membrane surface. A disk with more blades could generate higher shear stress on the membrane surface under a given rotation speed. However, more power should be supplied to drive the rotating shaft and disk.

目錄
中文摘要-I
英文摘要-II
目錄-IV
圖目錄-VI
表目錄-VIII
第1章 序論-1
1-1 前言-1
1-2 研究動機與研究目的-5
第2章 文獻回顧-6
2-1 迴轉盤微過濾系統-6
2-2 計算流體力學於迴轉盤裝置上之應用-10
第3章 理論-11
3-1 阻力串聯模式-11
3-2 濾餅平均過濾比阻與孔隙度-12
3-3 濾餅平均過濾比阻、孔隙度與固體壓縮壓力之關係-13
3-4 粒子在膜面附著之力平衡模式-14
3-5 濾速與濾餅高度之估計-16
3-6 迴轉盤系統之動量平衡方程式-19
3-7 迴轉盤之力矩與功率消耗-22
第4章 數值模擬與計算-24
4-1 數值模擬-24
4-1-1 基本假設-24
4-1-2 統御方程式-24
4-2 模擬程序步驟-27
4-3 前處理-29
4-4 計算求解-35
4-5 後處理-38
第5章 結果與討論-39
5-1 無葉片迴轉盤系統之流態-39
5-2 操作條件對無葉片迴轉盤系統之影響-50
5-3 無葉片迴轉盤系統之過濾性能-53
5-4 迴轉盤系統之流態-58
5-5 迴轉盤系統之過濾性能-67
5-5-1 局部過濾性能-67
5-5-2 平均過濾性能-71
5-5-3 平均濾速提升率-75
5-5-4 功率消耗-77
第6章 結論-82
符號說明-84
參考文獻-86

圖目錄
Fig. 1 1 Schematics of dead-end filtration and cross-flow filtration.-3
Fig. 1 2 Application range of various membrane processes.-4
Fig. 3 1 The resistance of microfiltration.-11
Fig. 3 2 The overall filtration equation model.-16
Fig. 3 3 The force balance model.-17
Fig. 3 4 Schematic of rotating-disk dynamic microfilter system for cylindrical coordinates.-19
Fig. 4 1 The procedural steps of numerical simulation.-28
Fig. 4 2 The geometry of rotating-disk dynamic filtration.-29
Fig. 4 3 The side view of rotating-disk dynamic filtration without blade (A1 Type).-32
Fig. 4 4 The side view of rotating-disk dynamic filtration (a)A2 Type (b)B1 Type (c)C Type (d)D Type.-32
Fig. 4 5 The side view of rotating-disk dynamic filtration (a)B1Type (b)B2 Type (c)B3 Type and the top view of rotating-disk dynamic filtration (d)B1 Type (e)B2 Type (f)B3 Type.-33
Fig. 4 6 The simulation of specify continuum types in the Gambit 2.4.-34
Fig. 4 7 The mash of rotating-disk dynamic filtration.-34
Fig. 4 8 The simulation of specify boundary types in the Gambit 2.4.-35
Fig. 4 9 The procedural steps of numerical soluation.-37
Fig. 5 1 The compare of theory and simulation velocity magnitude at r=20 mm.-40
Fig. 5 2 The compare of theory and simulation velocity magnitude at z=2 mm.-40
Fig. 5 3 (a)-(d) The contours of velocity magnitude and (e)-(f) the velocity vectors by velocity magnitude of A1 type.-41
Fig. 5 4 The velocity distribution of membrane surface.-45
Fig. 5 5 The velocity magnitude of membrane surface under rotation speed 150-500rpm.-46
Fig. 5 7 (a) The contours of wall shear stress and (b) the velocity vectors by wall shear stress of A1 type.-48
Fig. 5 9 The relationship of mean shear stress between filtration pressure and inlet velocity under rotation speed 150-500rpm.-50
Fig. 5 10 The relationship of mean shear stress between filtration pressure and inlet velocity under rotation speed 1000-3000rpm.-51
Fig. 5 11 The relationship of mean shear stress and rotation speed.-52
Fig. 5 12 The experiment and theoretical cake thickness in rotating-disk dynamic microfiltration with different mean shear stress under rotation speed 150-1000rpm.-54
Fig. 5 13 The experiment cake thickness in rotating-disk dynamic microfiltration with different mean shear stress under rotation speed 1000-3000rpm.-55
Fig. 5 14 The pseudo steady state filtration rates and cake weight in rotating-disk dynamic microfiltration with different mean shear stress under rotation speed 150-500rpm.-56
Fig. 5 15 The pseudo steady state filtration rates and cake weight in rotating-disk dynamic microfiltration with different mean shear stress under rotation speed 1000-3000rpm.-57
Fig. 5 16 The contours of velocity magnitude of A1 type.-58
Fig. 5 17 The contours of velocity magnitude of A2, B1, C and D type.-60
Fig. 5 18 The contours of velocity magnitude of B1, B2 and B3 type.-62
Fig. 5 19 The contours of wall shear stress of A1 type.-63
Fig. 5 20 The contours of wall shear stress of A2, B1, C and D type.-64
Fig. 5 21 The contours of wall shear stress of B1, B2 and B3 type.-65
Fig. 5 22 The particle trajectories with the side view (a)B1Type (b)B3 Type and the top view (c)B1Type (d)B3 Type.-66
Fig. 5 23 The local shear stress on membrane surface.-67
Fig. 5 24 The local pseudo steady state filtration rates on membrane surface.-69
Fig. 5 25 The local cake thickness on membrane surface.-70
Fig. 5 26 The mean shear stress with different rotation speed and types of rotating-disk dynamic microfiltration.-71
Fig. 5 27 The mean pseudo steady state filtration rates with different rotation speed and types of rotating-disk dynamic microfiltration.-73
Fig. 5 28 The mean cake weight with different rotation speed and types of rotating-disk dynamic microfiltration.-74
Fig. 5 29 The compare of flux increase with different rotation speed and types of rotating-disk dynamic microfiltration.-75
Fig. 5 30 The power of rotating-disk dynamic microfiltration with different rotation speed.-78
Fig. 5 31 The power of rotating-disk dynamic microfiltration with different types.-80
Fig. 5 32 The relationship of Power number and Reynolds number.-81

表目錄
Table 3 1 The average specific filtration resistance and permeability.-13
Table 4 1 The compare of rotating-disk dynamic filtration by the distance between disk and membrane.-30
Table 4 2 The compare of rotating-disk dynamic filtration by the geometry of blades.-30
Table 4 3 The compare of rotating-disk dynamic filtration by the number of blades.-31
Table 5 1 The power of rotating-disk dynamic microfiltration with different rotation speed.-77
Table 5 2 The power of rotating-disk dynamic microfiltration with different types.-79

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