本篇研究是以直徑10 mm的水旋風分離器進行高分子溶液中懸浮粒子之分離，分別進行實驗量測與數值模擬分析，以實驗探討改變濃度之懸浮液與進料速度、壓力、分流比等操作條件對分離效率的影響，且改變不同物料之實驗結果進行比較，並使用Ansys套裝軟體，利用SIMPLE(Semi-Implicit Method for Pressure-Linked Equation)法則進行質量平衡與動量平衡等統御方程式之計算，紊流使用雷諾應力模型，並使用PRESTO!(PREssure STerring Option)進行壓力計算之疊代，分析流體之速度分布、壓降分布、以及粒子軌跡等，再藉以估算粒子的分離效率，經此研究探討最佳的操作方式。
　　在分離懸浮液時，實驗結果顯示，總分離效率會隨著操作壓力、分流比和n值的增加而增加。當懸浮液在n值從0.51增加至1，總效率最多可以增加51 %。而當分流比自0.2增加至5，總效率會增加2倍。在PVC之懸浮液n值增加，其d50值也會跟著變大，範圍從25 m降至8 m，而底流口處的粒子濃度也會跟著下降5 %。比較三種物料的總效率值之順序為：Al2O3 > PVC > Kaolin。
　　在模擬方面之結果顯示，壓降會隨著進料速度的增加而增加，也會隨著流體之黏度的增加而增加，n值從0.51至1最多增加了149 %，。在粒子軌跡部分，n值越大，使粒子迴圈數與軌跡長度增長，導致不易有粒子從由溢流管流出。Kaolin的分級效率實驗與模擬值誤差較小約13 %，反之Al2O3及PVC之模擬與實驗結果誤差約40 %，由此可知密度和粒子形狀也會影響模擬之結果，而最後由分級效率與總效率可知實驗數據與數值模擬結果可知，推斷實驗與模擬相符合。

A 10-mm hydrocyclone was used for separating particles suspended in polymer solutions. The effects of operating conditions, such as concentration of PAA solutions, inlet velocity, pressure drop and split ratio, on the separation efficiency were studied using experimental and simulated methods.  In simulation, the governing equations were coupled using the SIMPLE algorithm, and the Reynolds stress model was employed for the turbulent model in hydrocyclone. A numerical software, Ansys 14.0, was used for analyzing the distributions of fluid velocity and static pressure. The particle trajectories and separation efficiency were then simulated accordingly. Three kinds of particles, Al2O3, PVC and Kaolin, were used in experiments. The experimental results showed that the separation efficiency increased with increasing pressure drop, split ratio and fluid behavior index, n. The total separation efficiency increased 51% when n-value increased from 0.51 to 1.0, and it enhanced two-fold when the split ratio increased from 0.2 to 1.0. The index d50 increased with increasing n-value, it decreased from 25 m to 8 m as n-value increased from 0.51 to 1.0 for PVC particles. Comparing the total separation efficiency of three used particulate samples, the sequence was Al2O3 > PVC > Kaolin. The simulating results showed that the pressure drop increased 149% when n-value increased from 0.51 to 1.0. The rotation number and migration length of particles increased with increasing n-value. This causes that particles are more easily to be collected through underflow. The simulated particle separation efficiency approximately agree with available experimental data.

中文摘要	I
英文摘要	III
目錄	V
圖目錄	VIII
表目錄	XV
第一章 緒論 1
1.1 前言	1
1.2 研究動機與目標 4
第二章 文獻回顧 5
2.1 水旋風分離器之概述 5
2.1.1 水旋風分離器之簡介 5
2.1.2 水旋風分離器之幾何結構 5
2.1.3 水旋風分離器之規格 7
2.1.4 水旋風分離器之優缺點 8
2.1.5 水旋風分離器之選擇與應用 8
2.1.6 水旋風分離器之程序設計 10
2.1.7 水旋風分離器之幾何結構設計 11
2.2 水旋風分離器之特殊現象	14
2.2.1 魚勾現象 14
2.2.2 底流效應與離心效應 16
2.2.3 短路流現象	18
2.2.4 空氣柱 19
2.3 水旋風分離器之理論 20
2.3.1 平衡軌道理論（The Equilibrium Orbit Theory）	20
2.3.2 滯留時間理論（The Residence-Time Theory）22
2.3.3 無因次群模型（Dimensionless model）22
2.4 水旋風分離器之原理 24
2.5 固體顆粒在水旋風分離器中之受力分析 25
2.5.1 顆粒沉降受力分析 25
2.5.2 切應力 28
2.5.3 低濃度時顆粒之自由沉降 29
2.5.4 高濃度時顆粒之自由沉降 30
2.5.5 離心沉降與重力沉降之比較 31
2.6 水旋風分離器之參數 32
2.6.1 結構參數 32
2.6.2 物性參數 33
2.6.3 操作參數	34
2.7 黏度對水旋風分離器之相關研究 39
第三章 數值與模擬	41
3.1 CFD之水旋風分離器模擬	41
3.2 統御方程式 44
3.3 邊界條件 45
3.4 參數設定 46
第四章 實驗裝置與方法 47
4.1 實驗物料 47
4.2 實驗裝置 54
4.3 實驗步驟 56
4.4 實驗儀器 58
第五章 結果與討論	59
5.1 PAA溶液黏彈性質的測量與計算 59
5.2 水旋風分離器之實驗結果	69
5.2.1 壓降之效應	73
5.2.2 黏度之效應	85
5.2.3 分流比之效應 97
5.3 FLUENT數值模擬結果 104
5.3.1 壓降與壓力分佈 104
5.3.2 速度分佈 106
5.3.3 表面黏度 120
5.3.4 粒子軌跡之影響 125
5.3.5 分離效率之影響 128
第六章 結論 132
符號說明	134
參考文獻	137

圖目錄
第一章
Fig.1-1 Separation spectrum under different particle sizes.	3
第二章
Fig.2-1 Hydrocyclone with main flow pattern.	6
Fig.2-2 （a）Long cone cyclone（b）Long cylinder steep cone cyclone.	7
Fig.2-3 A typical curve of partial separation efficiency.（Hwang, 2008）	14
Fig.2-4 The construction of a selectivity curve.（Hwang, 2008）	17
Fig.2-5 The actual selectivity curve by summing underflow and centrifugal effects.（Hwang, 2008）	18
Fig.2-6 The axial velocity and LZVV orbit in hydrocyclone. （Holdich, 2002）	21
Fig.2-7 Equilibrium orbit at the LZVV with liquid drag and centrifugal forces balanced.（Holdich, 2002）	21
Fig.2-8 Spiral flow profiles inside a micro hydrocyclone.（Sen, 2012）	25
Fig.2-9 Velocity profile of three vortex types.（Puprasert等人, 2004）	29
Fig.2-10 Differential size distributions in feed, overflow and underflow.（Trawinski, 1977）	37
Fig.2-11 Relationships between water temperature and viscosity. （Yoshida, 2004）	39
第三章
Fig.3-1 The procedural steps of numerical simulation.	41
Fig.3-2 Finite volume mesh hydrocyclone geometry.	43
Fig.4-1 Al2O3 particle size distribution.	48
Fig.4-2 The microscope of Al2O3 suspension (a) before (b) after experiment at 1800X.	48
Fig.4-3 PVC particle size distribution.	49
Fig.4-4 The microscope of PVC suspension at (a) 900X (b) 1800X.	50
Fig.4-5 Kaolin particle size distribution.	51
Fig.4-6 The microscope of Kaolin suspension at (a) 900X (b) 1800X.	52
Fig.4-7 Dimensions of the hydrocyclone geometry.(unit: mm)	54
Fig.4-8 Schematic diagram of the experiment apparatus.	55
第五章
Fig.5-1 The n of value under various solutions at 273K.	61
Fig.5-2 A plot of shear stress vs. shear rate of distilled water at 273K.	62
Fig.5-3 Viscosity versus shear rate of the distilled water at 273K.	63
Fig.5-4 A plot of shear stress vs. shear rate of the PAA aqueous solutions.	64
Fig.5-5 Viscosity of the PAA aqueous solutions at 273K.	65
Fig.5-6 Viscosity of the 2000ppm PAA aqueous solutions in different mass of particles.	66
Fig.5-7 A plot of shear stress vs. shear rate of the 500ppm PAA aqueous solution at different temperatures.	67
Fig.5-8 Viscosity of the 500ppm PAA aqueous solutions at different temperatures.	68
Fig.5-9 Inlet velocity in hydrocyclone varies with pressure drops at n=1.	69
Fig.5-10 Relationship between Reynolds number and pressure drops n=1.	70
Fig.5-11 Relationship between Euler number and pressure drops n=1.	71
Fig.5-12 The residence time in different pressure drops n=1.	72
Fig.5-13 The particle size distribution of Al2O3 under different pressure drops.	74
Fig.5-14 Partial separation efficiency of Al2O3 under 0.4 MPa.	76
Fig.5-15 The particle size distribution of Kaolin under different inlet velocities.	77
Fig.5-16 Partial separation efficiency of Kaolin under different inlet velocities.	78
Fig.5-17 Cut-size of materials under various pressure drops. (ϕ=0.8)	79
Fig.5-18 Partial separation efficiency of PVC under different pressure drops.	81
Fig.5-19 The total separation efficiency of materials at different inlet velocity in split 0.8.	83
Fig.5-20 The particle size distribution of Al2O3 under different concentrations.	86
Fig.5-21 Partial separation efficiency of Al2O3 under different concentrations.	87
Fig.5-22 The total separation efficiency of materials at different concentrations in split 0.8.	88
Fig.5-23 Partial separation efficiency of Kaolin under different concentrations and pressure drops.	89
Fig.5-24 The total separation efficiency of materials at different concentrations in split 0.8.	90
Fig.5-25 Partial separation efficiency of PVC under different concentrations.	91
Fig.5-26 Cut-size of materials under various concentrations. (ϕ=0.8)	92
Fig.5-27 The particle concentrations in the outlet of hydrocyclone under various PAA concentrations.	93
Fig.5-28 The total separation efficiency of materials at various PAA concentrations in split 0.8.	95
Fig.5-29 The centrifugal force and drag force at various PAA concentrations with materials.	96
Fig.5-30 Partial separation efficiency of Al2O3 under different split ratios.	98
Fig.5-31 The total separation efficiency of Al2O3 with different split ratios.	99
Fig.5-32 The particle size distribution of Kaolin under split ratios.	100
Fig.5-33 Partial separation efficiency of PVC under different split ratios.	101
Fig.5-34 The particle concentrations in the outlet of hydrocyclone under various split ratios.	102
Fig.5-35 The total separation efficiency of materials at various PAA concentrations in split 0.8.	103
Fig.5-36 Contours of static pressure profile at the cross-section of x=0 m under pressure of 0.1 MPa for different n values.	105
Fig.5-37 The contours of velocity magnitude profiles at the cross-section of x=0 m under inlet velocity of 6.7 m/s. for different n values.	107
Fig.5-38 The contours of velocity vector at the cross-section of x=0 m under inlet velocity of 6.7 m/s. for different n values.	108
Fig.5-39 The contours of Tangential velocity profiles at the cross-section of x=0 m under inlet velocity of 6.7 m/s. for different n values.	110
Fig.5-40 Tangential velocity profiles at the cross-section of z=0.086 m under inlet velocity of 6.7 m/s. for different n values	111
Fig.5-41 Tangential velocity profiles at the cross-section of z=0.078 m under inlet velocity of 6.7 m/s. for different n values.	112
Fig.5-42 Tangential velocity profiles at the cross-section of z=0.077 m under inlet velocity of 6.7 m/s. for different n values.	113
Fig.5-43 The contours of Aaxial velocity velocity profiles at the cross-section of x=0 m under inlet velocity of 6.7 m/s. for different n values.	116
Fig.5-44 Axial velocity profiles at the cross-section of z=0.086 m under inlet velocity of 6.7 m/s. for different n values.	117
Fig.5-45 Axial velocity profiles at the cross-section of z=0.078 m under inlet velocity of 6.7 m/s. for different n values.	118
Fig.5-46 Axial velocity profiles at the cross-section of z=0.077 m under inlet velocity of 6.7 m/s. for different n values.	119
Fig.5-47 Counter plot of the positions for the shear rate at the cross-section of x=0 m under inlet velocity of 6.7 m/s. for various n values.	120
Fig.5-48 Counter plot of the positions for the shear rate at the cross-section of x=0 m under various velocities for n=0.51.	121
Fig.5-49 Counter plot of the effective viscosity at the cross-section of x=0 m under inlet velocity of 6.7 m/s for various n values.	122
Fig.5-50 Counter plot of the effective viscosity at the cross-section of x=0 under various velocities for n=0.51.	123
Fig.5-51 Counter plot of the effective viscosity at the cross-section of x=0 under different splits and inlet velocity of 6.7 m/s for n=0.51.	124
Fig. 5-52 Typical particle trajectories of underflow under inlet velocity of 6.7 m/s. for various n values.	126
Fig. 5-53 Typical particle trajectories of underflow under inlet velocity of 6.7 m/s. for various n values.	127
Fig. 5-54 Typical particle trajectories of overflow under inlet velocity of 6.7 m/s. for various n values.	127
Fig.5-55 Comparison of partial separation efficiency with hydrocyclone under different n values under a fixed inlet velocity of 13 m/s in split 0.8.	129
Fig.5-56 Comparison of total separation efficiency different n values under a fixed inlet velocity of 13 m/s in split 0.8.	130
Fig.5-57 Comparison of partial separation efficiency with hydrocyclone under different materials under a fixed inlet velocity of 13 m/s in split 0.8	131

表目錄
第三章
Table.3-1 The simulation standards in the Gambit 2.4.	42
Table.3-2 Simulation setting.	46
第五章
Table 5-1 Flow behavior index for various concentrations of PAA aqueous solutions at 273K.	60
Table5-2 The centrifugal force of three kinds of particles in different inlet velocities.	83
Table5-3 Experiment results of three kinds of particles.	84
Table.5-4 The pressure drops through the hydrocyclone under various inlet velocities and n values.	104

Bicalho, I.C., Mognon, J.L., Shimoyama, J., Ataíde, C.H., Duarte, C.R., “Effects of operating variables on the yeast separation process in a hydrocyclone”, Separation Science and Technology, 48, 915-922 (2013). 
Bicalho, I.C., Mognon, J.L., Shimoyama, J., Ataíde, C.H., Duarte, C.R., “Separation of yeast from alcoholic fermentation in small hydrocyclones”, Separation and Purification Technology, 87, 62-70 (2012). 
Bo, Z.W., Yi, M., You-hai, J., “Simulation and experiment of flow field in axial-flow hydrocyclone”, Chemical Engineering Research Design, 89, 603-610 (2011). 
Chu, L., Chen, W., Lee, X., “Enhancement of hydrocyclone performance by controlling the inside turbulence structure”, Chemical Engineering Science, 57, 207-212 (2002).
Cilliers, J.J., Harrison, S.T.L., “The application of mini-hydrocyclones in the concentration of yeast suspensions”, Chemical Engineering Journal, 65, 21-26 (1997).
Frachon, M. and J. J. Cilliers, “A Generall Model for Hydrocyclone Partition Curves”, Chemical Engineering Journal, 73, 53-59 (1999).
Gao, S.L., D.Z. Wei, W.G. Liu, L.Q. Ma, T. Lu and R.Y. Zhang “CFD numerical simulation of flow velocity characteristics of hydrocyclone” Transactions of Nonferrous Metals Society of China, 21, 2783-2789 (2011).
Ghadirian, M., Hayes, R.E., Mmbaga, J., Afacan, A., Xu, Z., “On the simulation of hydrocyclones using CFD”, The Canadian Journal of Chemical Engineering, 91, 950-958 (2013). 
Golyk, V., S. Huber , M.G. Farghaly , G. Prolss , E. Endres , T. Neesse , M.A. Hararah   “Higher kaolin recovery with a water-injection cyclone”, Minerals Engineering, 24, 98–101 (2011).
Hwang, K.J., Hsueh, W.S., Nagase, Y., “Mechanism of particle separation in small hydrocyclone”, Drying Technology, 26, 1002-1010 (2008). 
Hwang, K.J., Lyu, S., Nagase, Y., “Particle separation efficiency in two 10-mm hydrocyclones in series”, Journal of the Taiwan Institute of Chemical Engineers, 40, 313-319 (2009). 
Hwang, K.J., Y.W. Hwang , H. Yoshida and K. Shigemori “Improvement of particle separation efficiency by installing conical top-plate in hydrocyclone”, Powder Technology, 232, 41–48 (2012).
Hwang, K.J., Y.W. Hwang and H. Yoshida, “Design of novel hydrocyclone for improving fine particle separation using computational fluid dynamics”, Chemical Engineering Science, 85, 62–68 (2013).
Habibian, M., Pazouki, M., Ghanaie, H., Abbaspour-Sani, K., “Application of hydrocyclone for removal of yeasts from alcohol fermentations broth”, Chemical Engineering Journal, 138, 30-34 (2008). 
Kashiwaya, K., T. Noumachi, N. Hiroyoshi, M. Ito and M. Tsunekawa, “Effect of particle shape on hydrocyclone classification”, Powder Technology, 226, 147–156 (2012).
Kumar, S., T. W. Piorg. and D. Ramkrishna, “A New Method for Estimating Hindered Creaming/Settling velocity of Particles in Polydisperse Systems”, Chemical Engineering Science, 55, 1893-1904 (2000).
Liu, M., Mao, Y., Wang, J., Sun, X., Xu, C., “Effect of swirl on hydrodynamics and separation performance of a spray granulation tower with array nozzles”, Powder Technology, 227, 61-66 (2012).
Marthinussen, S.A., Y.F. Chang, B. Balakin, A.C. Hoffmann, “Removal of particles from highly viscous liquids with hydrocyclones”, Chemical Engineering Science, 108, 169-175 (2014).
Mori, M., S. Bernardo, A.P. Peres and R.P. Dionı´sio, “3-D computational fluid dynamics for gas and gas-particle flows in a cyclone with different inlet section angles”, Powder Technology, 162, 190–200 (2006).
Nenu, T.R.K., Yoshida, H., “Comparison of separation performance between single and two inlets hydrocyclones”, Advanced Powder Technology, 20, 195-202 (2009).
Pinto, A.A., Bicalho, I.C., Mognon, J.L., Duarte, C.R., Ataíde, C.H., “Separation of saccharomyces cerevisiae from alcoholic fermentation broth by two commercial hydrocyclones”, Separation and Purification Technology, 120, 69-77(2013).
Sripriya, R., N. Suresh, S. Chandra and D. Bhattacharjee, “The effect of diameter and height of the inserted rod in a dense medium cyclone to suppress air core”, Minerals Engineering, 42, 1–8 (2013)
Trawinski, H.F., ‘‘Solid/Liquid Separation Equipment Scale UP’’, Ed. D. B. Purchas, Uplands Press, England, 241-286 (1997).
Wang, L., Wang, J., “Experimental study of the drag reduction and separation efficiency for a new hydrocyclone with a reducing pressure drop stick”, Separation and Purification Technology, 98, 7-15 (2012).
Yoshida, H., T. Takashinab, K. Fukuia, T. Iwanagaa, “Effect of inlet shape and slurry temperature on the classification performance of hydro-cyclones”, Powder Technology, 140, 1–9 (2004).
Yoshida, H., Fukui, K., Pratarn, W., Tanthapanichakoon, W., “Particle separation performance by use of electrical hydro-cyclone”, Separation and Purification Technology, 50, 330-335 (2006).
Yang, J., Sun, G., Gao, C., “Effect of the inlet dimensions on the maximum-efficiency cyclone height”, Separation and Purification Technology, 105, 15-23(2013).
Yang, L., J.L. Tian, Z. Yang, Y. Li, C.H. Fu, Y.H. Zhu, X.L. Pang, “Numerical analysis of non-Newtonian rheology effect on hydrocyclone flow field”, Petroleum, 1-7 (2015).
Yang, Q., Li, Z., Lv, W., Wang, H., “On the laboratory and field studies of removing fine particles suspended in wastewater using mini-hydrocyclone”, Separation and Purification Technology, 110, 93-100 (2013).
Yang, Q., Wang, H., Liu, Y., Li, Z., “Solid/liquid separation performance of hydrocyclones with different cone combinations”, Separation and Purification Technology, 74, 271-279 (2010).
Yu, A.B. and B. Wang, “Numerical study of particle–fluid flow in hydrocyclones with different body dimensions”, Minerals Engineering, 19, 1022–1033 (2006)
Yu, A.B. and B. Wang, “Numerical study of the gas–liquid–solid flow in hydrocyclones with different configuration of vortex finder”, Chemical Engineering Journal, 135, 33–42 (2008).
Yu, A.B., K.W. Chu, B. Wang and A. Vince, “Particle scale modelling of the multiphase flow in a dense medium cyclone: Effect of vortex finder outlet pressure”, Minerals Engineering, 31, 46–58, (2012).
Zhao, L., M. Jiang and B. Xu, B. Zhu “Development of a new type high-efficient inner-cone hydrocyclone”, Chemical Engineering Research and Design, 90, 2129–2134 (2012).
劉仁桓，“旋流過濾器分離機理研究“，中國:中國石油大學，化工工程機械研究所，(2011)。
呂信毅，“改進複合型水旋風分離器之分離效率“，碩士學位論文，化學工程與材料工學學系研究所，(2006)。
呂維明 編著，“固液過濾技術“，高立圖書館，台北，(2004)。
朱宏武，馮進，薛敦松，”液-液分離旋流器結構選型計算”，石油礦場機械，第32卷，第五期， 30-34(2003)。
孫玉波，”淺談水力旋流器的工作原理和影響參數”，礦業快報，總第403期，1月第1期(2003)。