臺灣博碩士論文加值系統

本研究以計算流力、影像拍攝法、壓降和透過量之實驗量測法，進行薄膜模組間隔網（spacer）內輸送機制之微觀流力解析。過去文獻對膜組間隔網進行理論與實驗分析時，皆以平板系統流來進行理論分析，而真實螺捲式膜組（spiral-wound module）內的渠道是具有彎曲度的，因此理論預測結果常與實驗值具有相當程度的差異。
本文內容針對不同薄膜模組渠道之彎曲度、膜組間隔網之類型、膜組間隔網纖維直徑之大小排列、薄膜透過率和掃流速度探討對內置間隔網膜組渠道之壓降、剪應力和粒子沉積之影響。結果顯示當膜組渠道彎曲度增加時，內外膜層剪應力和透過量之差異值將隨之增加，進而造成螺捲式膜組內外膜層不同之剪應力與透過量；而這種現象將會導致螺捲式膜組渠道內外膜層產生不同的堵塞特性，進而對整個膜組的分離效能造成影響，因此，本研究透過理論與實驗分析，提出調整纖維直徑大小的方法來改善：內外層剪應力分佈不均、透過量和粒子沉積率（deposition ratios）不同，並獲得最適化之設計參數。
此外，就二維簡化系統的階梯型膜組間隔網渠道而言，流體通過壁面上的膜組間隔網纖維時，會在纖維前後形成迴流區；但是在不同位置下所產生的迴流區，卻有不同的效應：纖維後方之迴流區是會把粒子帶走，但是纖維前方的迴流區卻會把粒子帶入膜面沉積。
另外，從三維系統的鑽石型膜組間隔網渠道研究發現：粗直徑的膜組間隔網纖維可增加其對面膜面區域之剪應力和透過量，卻造成纖維與膜面之間的渠道縮小，導致粒子在通過纖維與膜面時，受到垂直膜面之拖曳力增加，而沉積於膜面上；而從剪應力分佈結果是無法完全說明粒子之沉積行為，還需藉由流場分佈才可以解釋其粒子之沉積機制。
最後，基於以上多相流之計算流力研究及實驗技術，本研究建立了一基礎的膜組間隔網渠道之研究平台，並提供了有助於了解其他薄膜模組設計之方法。

Effect of spacer design on fluid flow and separation efficiency in a spacer-filled channel was conducted using computational fluid dynamic (CFD) and experimental techniques. The spacer serves both as mechanical stabilizer for channel geometry and turbulence promoters for reducing polarization phenomena near the membrane surface. Previously, several factors affect the pressure drop and mass transfer in a spacer-filled spiral-wound module have been studied based upon flat channel module. However, the curvature of the spacer varies along the spiral flow path. No any effort has been placed on the effects of curvature of the spacer in the spiral-wound modules on the pressure drop, shear stress and filtrate rate through the curved module.
Purposes of this study were emphasized on the effects of curvature of the spacer-filled channel, filament arrangement, feed velocity and membrane resistance in the spiral-wound modules on the pressure drop, shear stress and particles deposition through the modules by CFD, experimental equipment and direct observation through the membrane. Results showed that increase of the curvature of the spacer-filled channel will result in increases the shear stress ratio and variations in inner and outer filtrate. On the other hand, the spacer-filled curved channel in a spiral wound module causes unequal shear stress at inner and outer membrane surfaces. Such unequal shear stress at the inner and outer surfaces would be expected to have an adverse impact on the membrane module performance because of different fouling characteristics for adjacent membrane leaves. Results showed that decreasing of the diameter of outer filament and increasing of the diameter of inner filament can improve this adverse impact.
Furthermore, particle deposition in spacer-filled membrane modules is investigated using a computational fluid dynamic (CFD) technique. The flow field and particle transport in the channels with permeable membrane surfaces are calculated using the commercial available CFD software FLUENT®. A scheme similar to the Eulerian–Lagrangian numerical method is adopted for the two-phase flow simulation. Particle transport in spacer-filled channel is analyzed by considering fluid drag, body force, lift force and interaction forces exerted on the colloids. Feed velocity, permeation flux, and spacer arrangement effects on particle deposition are discussed comprehensively. Based on conclusive preliminary study results, multi-phase flow simulation can provide microscopic understanding of the fouling mechanism in the spacer-filled channel and prove to be a powerful tool to aid in membrane module design.
Finally, a platform was constructed based on multi-phase CFD approach and experimental techniques for fundamental study of membrane module design.

致謝 …………………………………………………………………………….I

中文摘要 ……………………………………………………………………….….III

英文摘要 ………………………………………………………………..…..…..…..V

目錄 …………………………………………………………………………VII

圖索引 ……………………………………………………………………….…...X
表索引 …………………………………………………………………………XVI



第一章 緒論…………………………………………………………………..….…………….1

第二章 文獻回顧……………………………………………………………………..……….3
2-1 薄膜模組…………………………...…………………………………..….…….3
2-1-1 片狀膜之模組……………………………...…………………....4
2-1-2 管狀膜之模組………………………………………………….……...10
2-1-3 薄膜模組之選擇………………………………………….…………...17
2-2 螺捲式薄膜模組之研究回顧………………………………………….…….20
2-2-1 膜組進料式間隔網之影響…………….……………….……....…….21
2-2-2 螺捲式薄膜模組之效能分析………………………...……………26
2-2-3 螺捲式薄膜模組串接方式之效能分析……....…………………….28

第三章 理論分析與實驗方法……………………………..……………………….………31
3-1 數值計算……………………………..………………………………..….…....31
3-1-1 網格製作前處理………………………………………...…………….31
3-1-2 CFD計算核心模組……………………………………...……..…...33
3-2 主控方程式…..………………………………..………………….………..…..38
3-3 實驗方法……………...……………………..………………………….….…..42
3-3-1 實驗材料…………………………...………………………………..…42
3-3-2 實驗設備……………………………….……..………….………….…44
3-3-3 實驗裝置與步驟……………...………….……..……….………….…45
3-3-3-1 量測間隔網渠道壓降之裝置與步驟…...…….…………45
3-3-3-2 比較內外膜層透過量之裝置與步驟…………...…………47
3-3-3-3 觀察粒子沉積之裝置與步驟…………………....…….…47

第四章 階梯型膜組間隔網渠道彎曲度對流態之影響…………………………………51
4-1 模擬系統………………………………………………………...…….…….…51
4-2 結果與討論…………………………………………………...……….……….56
4-2-1 不同膜組間隔網渠道彎曲度對速度分佈之影響…………..…….56
4-2-2 不同膜組間隔網渠道彎曲度對壓降和剪應力之影響………….60
4-2-3 不同膜組間隔網纖維直徑大小之影響…………….………………68
4-3 結論…………………………………………………………………….….……72

第五章 階梯型膜組間隔網渠道內粒子沉積之微觀解析……………………………73
5-1 模擬系統…………………………………………………………...……..……73
5-2 結果與討論………………………………………………………….…...…….76
5-2-1 粒子在膜組間隔網渠道內之運動軌跡….…………………………76
5-2-2 進料速度和透過速率對粒子沉積之影響………………....…….78
5-2-3 不同膜組間隔網類型對粒子沉積之影響………………....………79
5-2-4 不同膜組間隔網渠道彎曲度對粒子沉積之影響…………...……88
5-3 結論……………………………………………………………..……...….……96

第六章 流體流過鑽石型膜組間隔網渠道之流力解析…………………….....……..…97
6-1 模擬系統………………………………………………………….…...…….…97
6-1-1 完整膜組間隔網………………………………………….…..…….…97
6-1-2 週期性邊界條件………………………………………….…..…….…98
6-2 結果與討論………………………………………………………….…....……99
6-2-1 不同週期性邊界類型之探討..………............................………....…99
6-2-2 膜組間隔網渠道端效應之影響…………...………...……………104
6-2-3 計算流力結果與實驗值之比較..…………..….……....………...105
6-3 結論……………………………………………………………………....……111

第七章 鑽石型膜組渠道彎曲度對流態之影響………………….………….…...…......113
7-1 模擬系統………………………………………………………….…...……...113
7-2 結果與討論…………………………………………………………...…....…118
7-2-1 不同膜組間隔網渠道彎曲度之影響…………………………...…118
7-2-2 不同膜組間隔網纖維直徑大小之影響…………………………123
7-3 結論……………………………………………………………………....……136

第八章 結論..…………………………………………………..….………………...……137
第九章 未來展望………..………………………………………….………………...……139

符號說明 ……………………………………………….……………….…..141
參考文獻 ……………………………………………………………….…..143
自述 ………………………………………………….…………….…..149


圖索引
圖目錄 頁次
第二章


Fig. 2-1 Different methods for inducting flow instabilities (Belfort et al., 1994)…………..…5

Fig. 2-2 Schematic representation of the plate-and-frame module
(Zeman and Zydney, 1996)………………………………………………..………….7

Fig. 2-3 Plate and frame module construction (Rautenbach and Albrecht, 1989)………….....7

Fig. 2-4 Schematic representation of the spiral wound membrane module………………..….8

Fig. 2-5 Schematic representation of the rotating cylinder module
(Zeman and Zydney, 1996)…………………………………………………..……….9

Fig. 2-6 Schematic representation of the pleated membrane cartridge
(Zeman and Zydney, 1996). ………………………………………………………...10



Fig. 2-7 Schematic drawing of tubular module..……………………………………………..12

Fig. 2-8 Cross section of a monolithic ceramic module..…………………………………….12

Fig. 2-9 Schematic drawing of a capillary module/hollow fiber module..…………………...14

Fig. 2-10 Special hollow fiber construction……………………….…………………………..16

Fig. 2-11 Schematic drawing of a transversal flow module with fibers arranged………..……17

Fig. 2-12 A single flat leaf of the spiral wound module showing the flow direction
across the leaf……………...………………………………………………….…….20

Fig. 2-13 Schematics of the configurations of mesh-type spacers…………………………….21

Fig. 2-14 The spacer with a zigzag pattern………………………………………………...….23

Fig. 2-15 Transverse filament configurations used in the channel to obstruct the flow…...….24

Fig. 2-16 The difference between critical flux (Jcrit) and limiting flux (Jlim) under a regime

of controlled flux operation…………………………………………………………27


Fig. 2-17 The main categories of straight through membrane plant design…………………...29


第三章

Fig. 3-1 Volume element shapes………………………………………………………..……32

Fig. 3-2 Feed spacers. …………………………………………………………………..……43

Fig. 3-3 Geometric characterization of spacers………………………………………………43

Fig. 3-4 Schematic diagram of the flow system……………………………………………...45

Fig. 3-5 Construction diagram of a flat plate channel………………………………………..46

Fig. 3-6 Schematic diagram of the filtration system…………………………………………48

Fig. 3-7 Construction diagram of a curve plate channel……………………………………..49

Fig. 3-8 Schematic diagram of the filtration system for observing particles deposition….…50


第四章

Fig. 4-1 Cross section of a spiral wound membrane module. ……………………….……....51

Fig. 4-2 Definitions of Ro, Ri and θr………………………………………………………….52

Fig. 4-3 Es value for various dimensionless radiuses with different height
channels under laminar flow………………………………………………………...53

Fig. 4-4 (a) The simulation system, (b) transverse filament configurations used in the
(c) the filament located at the outer and inner wall : o-cavity type and i-cavity
type (d) grids generation for attached ……..……………………………..…………54
.




Fig. 4-5 Schematic diagrams of the cured channels with zigzag spacer for
various dimensionless radiuses……………………………………………………...55


Fig. 4-6 The velocity distribution between filament and wall for
the zigzag spacer (uf = 0.2 m/s). ………...………………………………………….58

Fig. 4-7 The effect of spacer-filled channel curvature on the velocity distribution
between filament and wall for the zigzag spacer (uf = 0.2 m/s)…………………….59



Fig. 4-8 The effect of spacer-filled channel curvature on the velocity distribution
between filament and wall for the cavity spacer (uf = 0.2 m/s)…………………..…61

Fig. 4-9 The effect of spacer-filled channel curvature on the velocity distribution
between filament and wall for the submerged spacer (uf = 0.2 m/s) …...……..……62

Fig. 4-10 Es value for various dimensionless radiuses with spacer-filled
channels and empty channels………………………………………………………..64

Fig. 4-11 The effect of spacer-filled channel curvature on the shear stress distribution
in the zigzag type spacer-filled module. ………………………………………....…65

Fig. 4-12 The effect of spacer-filled channel curvature on the shear stress distribution
between filament and wall for various types of spacer (uf = 0.2 m/s). ………......…68


Fig. 4-13 The effect of spacer-filled channel curvature on the velocity distribution between
filament and wall for the original and the modified spacer(uf = 0.2 m/s).….…........71


第五章

Fig. 5-1 Schematic diagrams of transverse filament types and the empty channel……..……74

Fig. 5-2 Grids generation for attached filament………………………………………..…….75

Fig. 5-3 The trajectory of particles for channels with various spacer configurations
(Rm = 1.0 × 1012 1/m, uf = 0.1 m/s, q = 4.7×10-4 m/s)……………………….…..….76

Fig. 5-4 Deposition ratios at the different positions of the top and bottom membrane
in the empty channel (Rm = 1.0 × 1012 1/m, uf = 0.1 m/s, q = 4.7 × 10-4 m/s)………78


Fig. 5-5 Deposition ratios at the different positions of the top and bottom membrane in
the submerged channel (Rm = 1.0 × 1012 1/m, uf = 0.1 m/s, q = 4.7 × 10-4 m/s)….....79

Fig. 5-6 Deposition ratios at the different positions of the top and bottom membrane
in the submerged configuration spacer-filled channel (Rm = 1.0 × 1012 1/m,
uf = 0.23 m/s, q = 4.7 × 10-4 m/s)………………………………………………...….80

Fig. 5-7 Deposition ratios at the different positions of the top and bottom membrane
in the submerged configuration spacer-filled channel (Rm = 1.0 × 1012 1/m,
uf = 0.23 m/s, q = 9.4 × 10-5 m/s)……………………………………………..……..81

Fig. 5-8 Deposition ratios at the different positions of the top and bottom membrane
in the cavity configuration spacer-filled channel (Rm = 1.0 × 1012 1/m,
uf = 0.1 m/s, q = 4.7 × 10-4 m/s)……………………...…………………..………….82

Fig. 5-9 Deposition ratios at the different positions of the top and bottom membrane
in the cavity configuration spacer-filled channel (Rm = 1.0 × 1012 1/m,
uf = 0.23 m/s, q = 4.7 × 10-4 m/s)……………………………………..…….....…….83

Fig. 5-10 The velocity vector near the filament in the cavity configuration

spacer-filled channel……………………………………………………………..….84

Fig. 5-11 Deposition ratios at the different positions of the top and bottom membrane
in the zigzag configuration spacer-filled channel (Rm = 1.0 × 1012 1/m,
uf = 0.1 m/s, q = 4.7 × 10-4 m/s)…………………………………………..…...…….85

Fig. 5-12 Deposition ratios at the different positions of the top and bottom membrane
in the zigzag configuration spacer-filled channel (Rm = 1.0 × 1012 1/m,
uf = 0.23 m/s, q = 4.7 × 10-4 m/s)………………..…………………………..…….86

Fig. 5-13 The velocity vector near the filament in the zigzag configuration
spacer-filled channel…………………………………………………………..…….87
Fig. 5-14 Deposition ratios at the different positions of the inner and outer membrane
in the empty and curved channel (Rm = 1.0 × 1012 1/m,
uf = 0.23 m/s, q = 4.7 × 10-4 m/s). ……………………………………….....……….88

Fig. 5-15 Deposition ratios at the different positions of the inner and outer membrane
in the submerged configuration spacer-filled flat and curved channel
(Rm = 1.0 × 1012 1/m, uf = 0.23 m/s, q = 4.7 × 10-4 m/s)………………………..…..89

Fig. 5-16 Deposition ratios at the different positions of the inner and outer membrane
in the zigzag configuration spacer-filled flat and curved channel
(Rm = 1.0 × 1012 1/m, uf = 0.23 m/s, q = 4.7 × 10-4 m/s)……………………….…...90

Fig. 5-17 Deposition ratios at the different positions of the inner and outer membrane
in the i-cavity configuration spacer-filled flat and curved channel
(Rm = 1.0 × 1012 1/m, uf = 0.23 m/s, q = 4.7 × 10-4 m/s)………………………...….91

Fig. 5-18 The velocity contours near the filament in the i-cavity configuration
spacer-filled flat and curved channel (Rm = 1.0 × 1012 1/m,
uf = 0.23 m/s, q = 4.7 × 10-4 m/s)…………………………………………………....92

Fig. 5-19 Deposition ratios at the different positions of the inner and outer membrane
in the o-cavity configuration spacer-filled flat and curved channel
(Rm = 1.0 × 1012 1/m, uf = 0.23 m/s, q = 4.7 × 10-4 m/s)……………………..….….93

Fig. 5-20 The velocity contours near the filament in the o-cavity configuration
spacer-filled flat and curved channel (Rm = 1.0 × 1012 1/m,
uf = 0.23 m/s, q = 4.7 × 10-4 m/s)……………………………………………..……..95


第六章

Fig. 6-1 A schematic diagram of cell number in the spacer-filled channel…………………..98

Fig. 6-2 A schematic diagram of the simulation system for the full-scale spacers…………..99

Fig. 6-3 A schematic diagram of periodic boundary conditions…………………………..100

Fig. 6-4 The effect of different periodic boundary conditions on the velocity profile at
point A between bottom and top wall (lb = lt = 3 mm,θ= 90º, db = dt = 0.5 mm；
db = 0.4 mm, dt = 0.6 mm)…………………………………………………………101

Fig. 6-5 The effect of different periodic boundary conditions on the shear stress
distributions at the bottom and top walls at an average velocity ca. 0.13 m/s
(lb = lt = 3 mm, θ= 90º, db = dt = 0.5 mm)……………………………………..…..103




Fig. 6-6 The effect of different periodic boundary conditions on the shear stress
distributions at the bottom and top walls at an average velocity ca. 0.13 m/s
(lb = lt = 3 mm,θ= 90º, db = 0.4 mm, dt = 0.6 mm)……………………………….103

Fig. 6-7 The effect of spacer length on pressure drop (J = 8, lb = lt = 2.55 mm,
θ= 90º,db = dt = 0.5 mm)………………………………………………….………..106


Fig. 6-8 Effects of spacer length and width on pressure drop (lb = lt = 2.55 mm,
θ= 90º, db = dt = 0.5 m).……...…………………………………………...………106

Fig. 6-9 Comparisons between the simulation results and experimental data………….…107

Fig. 6-10 The friction factor dependence on the Reynolds number
(db = dt = 0.5 mm, lb = lt = 3 mm)……………………………………………….…110

Fig. 6-11 The friction factor dependence on the Reynolds number
(db = dt = 1 mm, lb = lt = 2.5 mm)………………………………………….………110



第七章

Fig. 7-1 Unit cell for periodic boundary conditions………………………………………...115

Fig. 7-2 Schematic diagrams of the cured channels with diamond spacer for various
dimensionless radiuses…………….……………………………………………….115

Fig. 7-3 Spacers-filled annulus tube for periodic boundary conditions

(di = do = 0.5 mm, lf = 3 mm, Rr = 0.15)……………………………………….…..119


Fig. 7-4 The effect of different periodic boundary conditions on the velocity profile at
point A between inner and outer wall (di = do = 0.5 mm, lf = 3 mm, Rr = 0.15)…..119


Fig. 7-5 The effect of different Rr values on the velocity between inner and
outer wall (di = do = 0.5 mm, lf = 3 mm, u�V = 0.16 m/s)…………………………..120


Fig. 7-6 The distributions of the inner and outer wall (di = do = 0.5 mm, lf = 3 mm)………122

Fig. 7-7 Effects of the PMMA concentration and the average velocity on flux
(di = do = 0.5 mm, lf = 2.5 mm, Rr = 0.1, TMP = 0.3 bar)…………………………123


Fig. 7-8 The effect of diameter ratios on the average velocity (lf = 3 mm, Rr = 0)…………124

Fig. 7-9 Distributions of the shear stress at the top and bottom wall
(�嵐 / ls = 60000 N/m3, Rr = 0)….……………..………………………….…….…..125


Fig. 7-10 The effect of diameter ratios on the velocity vectors
(�嵐 / ls = 60000 N/m3, Rr = 0)………...………………………………………..…..126

Fig. 7-11 Distributions of the shear stress at the inner and outer wall
(�嵐 / ls = 15000 N/m3, Rr = 0.15)……..…………………………………….……...130
Fig. 7-12 Distributions of the shear stress at the inner and outer wall
(�嵐 / ls = 15000 N/m3, Rr = 0.15)……..…………………………………….……...132

Fig. 7-13 The effect of different filament arrangement on flux (TMP = 0.3 bar)……………133

Fig. 7-14 Particles deposition patterns (ua = 0.43 m/s, TMP = 0.3 bar)：
(a) di / do = 0.4 / 0.6 mm, lf = 2.5 mm, Rr = 0.1,

(b) di / do = 0.6 / 0.4 mm, lf = 2.5 mm, Rr = 0.1………………………………..…..134

Fig. 7-15 The effect of diameter ratios on the velocity vectors (ua = 0.43 m/s, Rr = 0.09).….135








表索引
表目錄 頁次
第二章

Table 2-1 Approximate dimensions of tubular membranes (Mulder, 1997)…………...………11

Table 2-2 Qualitative comparison of various membrane configurations (Mulder, 1997)…...…19

Table 2-3 Suitable module types(Rautenbach and Albrecht, 1989)……………………………19


第三章

Table 3-1 Simulation processes of the computational fluid……………………………………31

Table 3-2 Comparisons among the discretization method………..……...………………….…34

Table 3-3 Comparisons among the turbulence models……………………………...…………36


Table 3-4 Comparisons between the Eulerian and Lagrangian approach……………………...37


第四章

Table 4-1 Geometric parameters of the channels with various spacer arrangements………….55

Table 4-2 The pressure drop and averaged wall shear stress for various dimensionless
radiuses with different spacer-filled channels (uf = 0.2 m/s)……………………..…63
….

Table 4-3 The pressure drop, averaged wall shear stress and shear stress ratio for various
dimensionless radiuses with improved spacer-filled channels (uf = 0.2 m/s)….…....70



第五章

Table 5-1 Geometric parameters of the channels with various spacer arrangements…...…......75

Table 5-2 The effect of various spacer configurations on the deposition ratio of particles
and the pressure drop in the spacer-filled channels under different feed velocities

of uf =0.1 m/s and 0.24 m/s (Rm = 1.0 × 1012 1/m, q = 4.7 × 10-4 m/s)…………..….87


Table 5-3 The effect of various spacer configurations on the deposition ratio of particles
and the difference from the deposition ratio of particles on the inner and
outer membrane in the spacer-filled flat and curved channel under the feed
velocity of uf = 0.23 m/s (Rm = 1.0 × 1012 1/m, q = 4.7 × 10-4 m/s)……………..….95




第六章

Table 6-1 The area of three types of PBCs………...……………………………..…..………102


第七章

Table 7-1 Geometric parameters of various Rr value…………………………………………113

Table 7-2 The effect of various Rr value on the velocity and hydraulic diameter……………117

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