本研究討論水旋風分離器的幾何結構以及操作條件對其分級效率之影響。以直徑10 mm之水旋風分離器為例，使用不同種類的粉粒體，分別進行實驗與數值模擬分析。實驗結果顯示，增加操作壓降、底流與溢流流量之分流比、溫度或降低進料濃度之條件下，皆可提高其分級效率與總效率，但溫度之影響並不顯著。在所有實驗之分級效率圖中，均出現魚勾現象，有一最低分離效率出現。比較模擬與實驗之分級效率曲線，顯示二者之最大誤差值約為25%。
採用數值模擬方法，可求出水旋風分離器之速度、壓力分佈及粒子運動軌跡模擬，並了解各操作條件下之差異。模擬之結果顯示，粒徑大小及進料位置對於粒子之運動軌跡均有明顯的影響。不同的幾何結構之水旋風分離器會有不同的分離效率及分流比；增加溢流口直徑，分級效率會下降，而增加底流口直徑，則可提高分級效率。進口截面為矮胖形(寬高比為25:16)比瘦高形(寬高比為16:25)有更好的分級效率。

Effects of geometric structure of hydrocyclone and operating conditions on the classification efficiency of particles are studied and discussed. A 10 mm-diameter hydrocyclone is installed for particle classification. Four kinds of particles with different size distributions and physical properties are used in experiments and in computational fluid dynamics (CFD) analyses. Experimental results show that an increase in pressure drops, split ratio, or suspension temperature or a decrease in feed concentration leads both the partial separation efficiency and overall separation efficiency to be increase. However, the effect of suspension temperature is trivial. The Fish-hook effect in partial separation efficiency occurs in all experimental results. The maximum deviation of the partial efficiency curve between the simulation results and experimental data is about 25%.
The velocity and pressure profiles and the trajectories of particles in the hydrocyclone are simulated by computational fluid dynamics method and discussed. The simulation results show that the diameter and the feed position of particles play important roles on the particle trajectories in hydrocyclone. The flow pattern, the partial separation efficiency and the split ratio are strongly dependent on the geometric structure of hydrocyclone. Increasing the diameter of overflow pipe or decreasing the diameter of underflow pipe leads to a lower partial separation efficiency. A rectangular inlet which width exceeds height results in higher partial separation efficiency than one which height is longer.

目錄 
中文摘要 I 
英文摘要III 
目錄V 
圖表目錄 IX 
第一章 緒論1 
1.1 前言 1 
1.2 研究動機與目標 3 
第二章 文獻回顧 4 
2.1水旋風分離器之發展簡述 4 
2.1.1水旋風分離器之簡介與幾何結構 4 
2.1.2水旋風分離器之規格 7 
2.1.3水旋風分離器之優缺點 8 
2.1.4水旋風分離器選擇與應用 9 
2.2魚勾現象 (Fish-hook Effect) 11 
2.3 水旋風分離器之模型與理論16 
2.3.1滯留時間理論 (The Residence-time Theory)16 
2.3.2亂流二相流理論 (Turbulent Two Phase Flow Theory) 17 2.3.3迴歸模型 (Regression Model) 17
2.4分析水旋風分離器內部流態之方法 18 
2.4.1 分析流態模型 (Analytical Flow Model) 18 
2.4.2數值分析 (Numerical Analysis) 19 
2.4.3 流態數值模擬 (Numerical Simulation of Flow) 20 
第三章 理論 22 
3.1水旋風分離器分離原理 22 
3.2水旋風分離器之理論與模型 23 
3.2.1平衡軌道理論 (The Equilibrium Orbit Theory) 23 
3.2.2無因次群模型 (The Dimensionless Group Model) 24 
3.3固體粒子在水旋風分離器中受力分析 26 
3.3.1粒子沉降受力分析 26 
3.3.2切應力 29 
3.3.3低濃度時顆粒之自由沉降 30 
3.3.4高濃度時顆粒的干涉沉降 32
 3.3.5離心沉降與重力沉降之比較 33 
3.4水旋風離器之性能特性 34 
3.4.1影響水旋風分離器分離效率之參數 34 
3.4.1.1標準旋風分離器之基本參數 34 
3.4.1.2物性參數 35
3.4.1.3 操作參數 36 
3.5 RFLOW數值模擬 43 
3.5.1數值模擬系統 43 
3.5.2流場與粒子運動軌跡分析 44 
3.5.2.1流場運動軌跡之模擬 44 
3.5.2.2粒子運動軌跡之模擬 44 
3.5.3邊界條件 45 
3.5.4幾何結構參數45 
第四章 實驗裝置與方法 48 
4.1實驗物料 48 
4.2實驗裝置 49 
4.3實驗步驟 52 
第五章 結果與討論54 
5.1水旋風分離器基本測式與無因次群 54 
5.2壓降效應 59 
5.3濃度效應 66 
5.4分流比效應 70 
5.5溫度之效應 74 
5.6 RFLOW數值模擬結果 76 
5.6.1速度分佈 76 
5.6.2壓力分佈 80 
5.6.3粒子軌跡之模擬 83 
5.6.3.1 粒徑之影響 84 
5.6.3.2 位置之影響 86 
5.6.4 模擬溫度之效應 89 
5.6.5 改變溢流口直徑之影響 90 
5.6.6 改變底流口直徑之影響 93 
5.6.7進口截面結構之影響 95 
5.6.8 不同幾何結構之比較 100 
第六章 結論 103
符號說明 106
參考文獻 112
附錄 117
附錄A 實驗物料之種類及物性 117
附錄B .PMMA-7G、CaCO3-17與 Al2O3之實驗結果 121 
圖表目錄 
圖目錄 第一章 
Fig.1-1 Separation spectrum under different particle sizes. 2 
第二章 
Fig.2-1 Hydrocyclone flow structure. 6 
Fig.2-2 Two conventional hydrocyclone (a) Narrow-angle design ; (b) Wide-angledesign. 7 
Fig.2-3 The partition curve (Frachon and Cilliers 1999). 11 
第三章 
Fig.3-1 Diagrams to explain the equilibrium orbit theory of hydrocyclone mechanism and LZVV (Kawatra，1996). 24 
Fig.3-2 Velocity profile of three vortex types (Puprasert et al, 2004). 30 
Fig.3-3 Differential size distributions in feed, overflow and underflow. 41 
Fig.3-4 Finite volume mesh hydrocyclone geometry (DHC=10 mm). 43 
Fig.3-5 The geometric structure of the five hydrocyclones used in simulation. 46 
Fig.3-6 The geometry and coordinates of hydrocyclone used in numerical simulation (unit: m). 47 
第四章 
Fig.4-1 Size distributions of particles used in this study. 49 
Fig.4-2 Dimensions of the hydrocyclone geometry (unit: mm).50 
Fig.4-3 Schematic diagram of the experiment apparatus. 51
第五章 
Fig.5-1 Relationship between volumetric flow rate and pressure drop. 54 
Fig.5-2 Feed velocity and characteristic velocity varies with pressure drops. 55 
Fig.5-3 Relationship between Reynolds number and pressure drops. 56 
Fig.5-4 Relationship between Euler number and pressure drop. 57 
Fig.5-5 Relationship between Euler number and Reynolds number. 58 
Fig.5-6 Size distribution of Corn Starch in the overflow under different pressure drops (CF=0.34 Vol% φ=1). 59 
Fig.5-7 Size distribution of Corn Starch in the underflow under different pressure drops (CF=0.34 Vol% φ=1). 60 
Fig.5-8 Partial separation efficiency of Corn Starch under different pressure drops (CF=0.34Vol% φ=1). 62 
Fig.5-9 Partial separation efficiency of different particles. 63 
Fig.5-10 Effect of measure condition (a) with (b) without ultrasonic and agitation for size distribution of Corn Starch in the overflow and underflow. 64 
Fig.5-11 Effect of measure condition (a) with (b) without ultrasonic and agitation for partial separation efficiency under different pressure drops. 65 
Fig.5-12 Size distribution of Corn Starch in overflow and underflow under different concentrations (φ=0.62 △P=0.1MPa). 67 
Fig.5-13 Partial separation efficiency of Corn Starch in the underflow under different concentrations. 67 
Fig.5-14 Overall efficiency of Corn Starch varies with pressure drops and concentrations (φ=0.62). 69 
Fig.5-15 Partial separation efficiency of Corn Starch in the underflow varies with different φ values. 70 
Fig.5-16 V(z) profile (y=0-plane) for an uniform inlet velocity 7.55m/s at different Z position. 71 
Fig.5-17 Overall efficiency of Corn Starch varies with pressure drops and split ratio (CF=0.34Vol%). 73 
Fig.5-18 Relationships between water temperature and viscosity. 74 
Fig.5-19 Size distributions of Corn Starch in the overflow at different temperatures (CF=0.67Vol% φ=0.62). 75 
Fig.5-20 Velocity profile on (y=0-plane) for an uniform inlet velocity 7.55m/s. 77 
Fig.5-21 Velocity profile on the vortex finder (z=-0.00325m) for an uniform velocity 7.55m/s. 77 
Fig.5-22 The v(r) profiles (y=0-plane) at z=-0.005 m under different pressure drops. 78 
Fig.5-23 The v(θ) profiles (y=0-plane) at z=-0.005 m under different pressure drops. 79 
Fig.5-24 The v(z) profiles (y=0-plane) at z=-0.005 m under different pressure drops. 80 
Fig.5-25 Pressure profile on (y=0-plane) for an uniform inlet velocity 12.9167m/s. 81
Fig.5-26 The pressure profiles (y=0-plane) at z=-0.005 m under different pressure drops. 82 
Fig.5-27 Schematic diagram of the particle inlet position. 83 
Fig.5-28 Simulation CaCO3-17 (d=0.26、7.7、13.2、19.9 µm) particle trajectory at position 23 under an uniform inlet velocity 7.55 (m/s). 85 
Fig.5-29 Simulation CaCO3-17 (d=0.26、7.7、13.2、19.9 µm) particle trajectory at position 23 under an uniform inlet velocity 7.55 (m/s). 85 
Fig.5-30 Simulation CaCO3-17 (d=0.26 µm) particle trajectory at different position 23、28、73、78 under an uniform inlet velocity 7.55 (m/s). 87 
Fig.5-31 Simulation CaCO3-17 (d=7.7 µm) particle trajectory at different position 23、28、73、78 under an uniform inlet velocity 7.55 (m/s). 87 
Fig.5-32 Simulation CaCO3-17 (d=13.2 µm) particle trajectory at different position 23、28、73、78 under an uniform inlet velocity 7.55 (m/s). 88 
Fig.5-33 Simulation CaCO3-17 (d=19.9 µm) particle trajectory at different position 3、28、73、78 under an uniform inlet velocity 7.55 (m/s). 88 
Fig.5-34 Compare experimental and simulation with partial efficiency at different temperatures. 89 
Fig.5-35 (a) 2 mm (b) 3 mm (c) 5 mm velocity profile at z=0.027 m (overflow) and z=-0.07 m (underflow) for uniform inlet velocity 12.916m/s for different overflow diameters. 91 
Fig.5-36 Hydrocyclone partial efficiency for different hydrocyclones overflow diameter. 92 
Fig.5-37 Hydrocyclone partial efficiency for different hydrocyclones underflow diameter. 94 
Fig.5-38 Velocity profile on (y=0-plane) for an uniform inlet velocity 12.917m/s for Case 1、2、3. 96 
Fig.5-39 Inlet structure of the hydrocyclone for (a)Case 1、Case 2 (b)Case 3. 97 
Fig.5-40 Partial separation efficiency of three different inlet types of hydrocyclone. 97 
Fig.5-41 (a)Counter plot of the inlet positions for the efficiency for CaCO3-17 at an uniform inlet velocity 12.917 m/s for Case 1. 98 
Fig.5-41 (b)Counter plot of the inlet positions for the efficiency for CaCO3-17 at an uniform inlet velocity 12.917 m/s for Case 2. 98 
Fig.5-41 (c)Counter plot of the inlet positions for the efficiency for CaCO3-17 at an uniform inlet velocity 12.917 m/s for Case 3. 99 
Fig.5-42 Velocity profile on (y=0-plane) for an uniform inlet velocity 12.917 m/s for Case 4、5. 101 
Fig.5-43 Partial separation efficiency of three different structural types of hydrocyclone. 102
附錄 
Fig.A-1 Particle size distribution of Corn starch. 117 
Fig.A-2 Particle size distribution of PMMA-7G. 118 
Fig.A-3 Particle size distribution of CaCO3-17. 119 
Fig.A-4 Particle size distribution of Al2O3. 120 
Fig.B-1 Partial separation efficiency of PMMA-7G varies with pressure drops. 121 
Fig.B-2 Partial separation efficiency of CaCO3-17 varies with pressure drops. 121 
Fig.B-3 Partial separation efficiency of Al2O3 varies with pressure drops. 122 
Fig.B-4 Partial separation efficiency of PMMA-7G varies with pressure drops and φ values. 122
 Fig.B-5 Partial separation efficiency of CaCO3-17 varies with pressure drops and φ values. 123 
Fig.B-6 Partial separation efficiency of Al2O3 varies with pressure Drops and φ values. 123 
Fig.B-7 Overall separation efficiency of PMMA-7G varies with pressure drops and φ values. 124 
Fig.B-8 Overall separation efficiency of CaCO3-17 varies with pressure drops and φ values. 124 
Fig.B-9 Overall separation efficiency of Al2O3 varies with pressure drops and φ values. 125 
表目錄 
第三章 
Table.3-1 The parameters of Geometric Structure of the Hydrocyclone. 46 
第五章 
Table.5-1 The ηhc、H of Corn Starch under different pressure drops (CF=0.34Vol% φ=1). 62
Table.5-2 Experiment results of four different kinds of particles (φ=0.62 P=0.4MPa). 63 
Table.5-3 The ηhc、H 、dh values of Corn Starch under different concentrations. 68 
Table.5-4 The dh、ηhc、H of Corn Starch under different φ values. 72 
Table.5-5 The QO、QU、φ、values for different hydrocyclones overflow diameter (VF=12.917 m/s). 92 
Table.5-6 The QO、QU、φ values for different hydrocyclones underflow diameter (VF=12.917 m/s). 94

Arterburn, R. A. “The sizing and Selection of Hydrocyclone”,http://www.krebs.com/literature.php/industrial_wastewater/

Bloor, M. I. G. and D. B. Ingham, “Turbulent spin in a cyclone”, Trans. Inst. Chem. Eng., 53, 1, 1-46 (1975).
Bradley, D., “The Hydrocyclone”, Perga mmon Press, London, (1965).

Coelho, M. A. Z. and R. A. Medronho, “A Model for Performance Prediction of Hydrocyclones”, Chem. Eng. J. 84, 7-14 (2001).

Chu, L. Y., W. M. Chen and X. Z. Lee, “Effect of structural modification on hydrocyclone performance” Separation and Purification Technology Vol. 21, Issue: 1-2, November 1, 71 – 86 (2000).

Cullivan, J. C., R. A. Williams, T. Dyakowski, C. R. Cross “New understanding of a hydrocyclone flow field and separation mechanism from computational fluid dynamics”, Trans. IchemE, 81, Part A (2003).

Dai, G. Q., W. M. Chen, J. M. Li and L. Y. Chu,“Experimental Study of Solid-Liquid Two Flow In a Hydrocyclone”, Chem. Eng. J., 74, 211-216 (1999).

Dwari, R. K., M. N. Biswas and B. C. Meikap, “Performance
Characteristics for Particles of Sand Fcc and Fly ash in a Novel Hydrocyclone”, Chem. Eng. Sci., 59, 671-684 (2004).

Dyakowski, T. and R. A. Williams, “Modelling Turbulent Flow within a Small-Diameter Hydrocyclone”, Chem. Eng. Sci., 48, 1143-1152 (1993).

Dyakowski, T. and R. A. Williams, “Prediction of High Solids Concentration Regions Within a Hydrocyclone”, Powder Technology, 87, 1, 43-47 (1996).

Flintoff, B. C., L. R. Plitt and A. A. Turak, “Cylone Modelling A Review of Present Technologies”, CIM Bulletin 80(905), 39-50 (1987).

Frachon, M. and Cilliers, J. J, “A general model for hydrocyclone partition curves” Chem. Eng. Sci., 73, 1, April, 53-59 (1999).

Flintoff, B. C., L. R. Plitt and A. A.Turak, , “Cylone Modelling A Review of Present Technologies”, CIM Bulletin 80 (905), 39-50 (1987).

Grady, S. A., G. D. Wesson, M. Abdullab and E. E. Kalu, ”Prediction of 10- mm Hydrocyclone Separation Efficiency Using Computational Fluid Dynamics”, Researcharticle, 41-46 (2003).

He, P., M. Salcudean and I. S. Gartshore, “A Numerical Simulation of Hydrocyclones”, Trans. Inst. Chem. Eng., 77, 429-441 (1999).

Hottand-Batt, A. B., ”A Bulk Model for Separation in Hydrocyclones”, Trans. Inst Min. Metall. (Sect. C: Min. Process Extr. Metall.), 91 (1982).

Kawatra, S. K., A. K. Bakshi, and M. T. Rusesky, “Effect of Viscosity on The Cut (d50) Size of Hydrocyclone Classifiers”, Min. Eng., 9, 881-891 (1996).

Kelsall, D. F., “A Study of The Motion of Solid Particles in A Hydraulic Cyclone”, Trans. Inst. Chem. Eng., 30, 87-108 (1952).

Kumar, S., T. W. Pirog and D. Ramkrishna, “A New Method for Estimating Hindered Creaming/Settling Velocity of Particles in Polydisperse Systems”, Chem. Eng. Sci., 55, 1893-1904 (2000).

Majumder, A. K., O. Yerriswamy and J. P. Barnwal, “The “Fish-Hook” Phenomenon in Centrifugal Separation of Fine Particles”, Min. Eng., 6, 1005-1007 (2003).

Lynch, A. J. and T. C. Rao, Ind. J. Technol., 6, 106-114 (1968).

Nageswararao, K., “A Critical Analysis of The Fish Hook Effect in Hydrocyclone Classifiers”, Chem. Eng. J., 80, 251-265 (2000).

Nageswararao, K., D.M. Wiseman and T. J. Napier-Munn, “Two
Empirical Hydrocyclone Models Revisited”, Min. Eng. 17, 671-681 (2004).

Nowakowski, A. F., J. C. Cullivan, R. A. Williams and T. Dyakowski.,“Application of CFD to modelling of the flow in hydrocyclones.Is this a realizable option or still a research challenge?”, Min. Eng. 17, 661–669 (2004).

Olson, T.J. and R. Van O mmen, “Optimizing hydrocyclone design using advanced CFD model” Min. Eng. 17, 713-720 (2004).

Pasquier, S. and J. J. Cilliers, “Sub-Micron Particle Dewatering Using Hydrocyclones”, Chem. Eng. J., 80, 283-288 (2000).

Plitt, L. R., “A Mathematical Model of The Hydrocyclone Classifier”, CIM Bull., December, 114-122 (1976).

Plitt, L. R., “The Analysis of Solid-Solid Separations in Classifiers”, CIM Bull., 708, 64 (1971).

Puprasert, C., G. Hebrard, L. Lopez and Y. Aurelle, “Potential of Using Hydrocyclone and Hydrocyclone Equipped with Grit Pot as A Pre-Treatment in Run-Off Water Treatment”, Chemical Engineering and Processing, 43, 67-83 (2004).

Rietema, K., “Performance and Design of Hydrocyclone, Parts I to IV”, Chem. Eng. Sci., 15, 293-325 (1961).
Richardson, P. H. and W. N. Zaki, Chem. Eng. Sci., 3, 65 (1954).

Svarovsky, L., “Hydrocyclone”, Holt, Rinehart and Winston Ltd, London (1984).

Svarovsky, L., “Solid-Liquid Separation”, 3rd ed., (1990).

Schuetz, S., G. Mayer, M. Bierdel and M. Piesche, “Investigations on The Flow And Separation Behavious of Hydrocyclones Using Computational Fluid Dynamics”, Int. J. Miner. Process., 73, 229-237 (2004).

Tang, L., F. Wen, Y. Yang, C. T. Crowe, J. N. Chung and T. R. Troutt, “Self-Organizing Particle Dispersion Mechanism in A Plane Wake”, Physics of Fluids A4 10, 2244-2251 (1992).

Trawinski, H. F., “Solid/Liquid Separation Equipment Scale Up”, Ed. D. B .Purchas, Uplands Press, England, 241~286 (1977).

Uhlherr, P. H. T., “Hindered Settling in Non-Newtonian Fluids”, an Appraisal. CHER75, 1,Dept. of Chem. Eng., Monash University, Australia (1975).

Vallebuona, G., A. Casali, G. Ferrara, O. Leal and P.Bevilacqua, “Technical Note Modelling For Small Diameter Hydrocyclones”, Min. Eng., 8, 321-327 (1995).

Yoshioka, N. and Y. Hotta, “Liquid Cyclone As A Hydraulic Classifier”, Chem. Eng. Jap., 19(12), 623 (1955).

Yang, G. A. B. and W. D. Wakley, “Oil-Water Separation Using Hydrocyclones: An Experimental Search for Optimum Dimensions”, Oil Gas, 11(1), 37-50 (1994).

Yang, Y., C. T. Crowe, J. N. Chung and T. R. Troutt, “Experiments On Particle Dispersion in A Plane Wake”, International Journal of Multiphase Flow, 26, 1583-1607 (2000).

Yoshida Hideto, Taniguchi Satoru and Fukui Kunihiro, “Effect of Apex Cone on Particle Classification Performance of Cyclone Separator”, J. Chin. Inst. Chem. Eng., 35, 1, 41-46 (2004).

孫玉波，“淺淡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)。

呂維明、呂文芳 編，“過濾技術”，高立圖書有限公司 (1994)。

呂維明 編，“過濾技術”，高立圖書有限公司 (2004)。