本研究探討水旋風分離器以串聯連接方式及操作條件對其分級效率之影響。採用直徑10 mm之水旋風分離器來分離玉米澱粉(Corn starch)及PMMA粒子，分別進行實驗量測與數值模擬分析。實驗結果顯示，無論增加第一個或第二個水旋風分離器之壓降、增加第一個或第二個水旋風分離器之分流比，皆可提高其分級效率與總效率，且可使最後溢流口之粒子濃度降低，達到固液分離的目的。以串聯方式連接水旋風分離器分離Corn Starch為例，在本研究之操作範圍內，最佳的操作條件為：第一個水旋風分離器之壓降為0.4 MPa、分流比為3.3，第二個水旋風分離器之分流比為1.57；在此條件下，溢流口之粒子濃度可以比使用單一水旋風分離器還要降低13%。
本研究並以FLUENT軟體模擬水旋風分離器內之流體速度與壓力分佈。由模擬之結果可以獲得平衡軌道理論的零速包絡面，可以證實在分離器中心空氣柱的存在，並可了解在vortex finder附近的粒子抄近路現象。兩相流的模擬結果亦顯示，增加水旋風分離器之分流比可以提高分級效率，而且有明顯的魚鉤現象出現，這和實驗結果有相同的趨勢；但是模擬的分級效率比實驗結果低了大約2倍，因此尚有進一步的改善空間。

Effects of operating conditions on the particle separation efficiency of multiple hydrocyclones are studied and discussed. Two 10 mm-diameter hydrocyclones installed in series are used in experiments and in computational fluid dynamics (CFD) analyses. Experimental results show that an increase in pressure drop or split ratio, whatever in the first or the second hydrocyclone, leads the partial separation efficiency to be increase and the concentration of the final overflow to be decrease. The optimum operating condition for the separation of corn starch suspension can be selected as: the split ratios are set as 3.3 and 1.57 in the first and the second hydrocyclone, respectively, and the pressure drop is set as 0.4 MPa in the first hydrocyclone. The particle concentration in the final overflow is 13% lower than that in the use of single hydrocyclone. The fluid velocity and pressure profiles in the hydrocyclone are simulated by computational fluid dynamics method. The locus of zero velocity in the equilibrium orbit theory, the air core in the center of hydrocyclone and the short-cut phenomenon near the vortex finder can also be simulated using FLUENT software. Although the tendency and the occurrence of fish-hook effect in partial separation efficiency curve agree with experimental data, simulation results are still two-fold lower than experimental data. It is necessary to improve the simulation method to obtain accurate data in the near future.

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…………………………………… 4
      2.1.2水旋風分離器之結構…………………………………… 5
      2.1.3水旋風分離器之規格…………………………………… 6
      2.1.4水旋風分離器之程序設計……………………………… 9
      2.1.5水旋風分離器之優缺點…………………………………10
      2.1.6 水旋風分離器之選擇與應用………………………… 11
  2.2 收集效率之魚勾現象(Fish-hook Effect)………………… 13
  2.3 水旋風分離器之模型與理論………………..……………… 18
2.3.1滯留時間理論 (The Residence-time Theory)………………19
2.3.2亂流二相流理論 (Turbulent Two Phase Flow Theory)……20
2.3.3迴歸模型 (Regression Model)……………………………… 21
  2.4分析水旋風分離器內部流態之方法……………………………22
2.4.1 分析流態模型 (Analytical Flow Model)………………… 22
2.4.2 數值分析 (Numerical Analysis)……………………………23
2.4.3 流態數值模擬 (Numerical Simulation of Flow)…………24
第三章 理論……………………………………………………………27
  3.1水旋風分離器分離原理…………………………………………27
  3.2水旋風分離器之理論與模型……………………………………28
3.2.1平衡軌道理論 (The Equilibrium Orbit Theory)………… 28
3.2.2無因次群模型 (The Dimensionless Group Model)…………29
  3.3固體粒子在水旋風分離器中受力分析…………………………31
3.3.1粒子沉降受力分析………………………………………………31
3.3.2切應力……………………………………………………………34
3.3.3低濃度時顆粒之自由沉降………………………………………35
3.3.4高濃度時顆粒的干涉沉降………………………………………37
3.3.5離心沉降與重力沉降之比較……………………………………38
  3.4水旋風離器之性能特性…………………………………………39
3.4.1影響水旋風分離器分離效率之參數……………………………39
3.4.1.1標準旋風分離器之基本參數…………………………………39
3.4.1.2物性參數………………………………………………………40
3.4.1.3操作參數………………………………………………………41
  3.5FLUENT數值模擬…………………………………………………48
3.5.1模擬軟體與基本假設……………………………………………48
3.5.2幾何結構與網格建立……………………………………………48
3.5.3主導方程式………………………………………………………50
3.5.4多相流方程式……………………………………………………50
3.5.5邊界條件…………………………………………………………53
3.5.6參數設定…………………………………………………………54
3.5.7收斂情形…………………………………………………………54
3.5.8數值方法…………………………………………………………55
第四章 實驗裝置與方法………………………………………………57
    4.1實驗物料………………………………………………………57
    4.2實驗裝置………………………………………………………59
    4.3實驗步驟………………………………………………………62
第五章 結果與討論……………………………………………………64
5.1壓降效應……………………………………………………………64
5.2加入不同物料效應…………………………………………………71
5.3進料濃度效應………………………………………………………73
5.4分流比效應…………………………………………………………74
5.5FLUENT數值模擬結果………………………………………………86
5.5.1速度分佈…………………………………………………………86
5.5.2壓力分佈…………………………………………………………88
5.5.3不同位置之速度分佈……………………………………………89
5.5.4純水模擬與實驗比較……………………………………………92
5.5.5固體粒子與水混合之FLUENT模擬………………………………94
5.5.6分級效率之模擬與實驗比較……………………………………96
第六章 結論…………………………………………………………99
   符號說明……………………………………………………102     
   參考文獻……………………………………………………108
   附錄…………………………………………………………115
   附錄A 實驗物料之種類及物性……………………………115 
   附錄B 實驗操作之表………………………………………117

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(Trawinski，1977)………………….………...8
Fig.2-3 Different inlet sites of hydrocyclone. (Yalcin，2003)……………9
Fig.2-4 The partition curve (Frachon and Cilliers 1999)………………..13
Fig.2-5 Diagrams to explain the equilibrium orbit theory of hydrocyclone        mechanism and LZVV (Kawatra等人，1996)…………………19
Fig.2-6 Meshed hydrocyclone geometry (Narasimha等人，2005)…….26
第三章
Fig.3-1 Diagrams to explain the equilibrium orbit theory of hydrocyclone mechanism and LZVV (Kawatra，1996)……………………….29
Fig.3-2 Velocity profile of three vortex types (Puprasert et al, 2004)…..35
Fig.3-3 Differential size distributions in feed, overflow and underflow..46
Fig.3-4 Gambit structure of the hydrocyclone………………………….49
Fig.3-5 The meshing structure of the hydrocyclone…………………….50
第四章
Fig.4-1 Size distributions of Corn Starch used in this study……………58
Fig.4-1 Size distributions of PMMA-7G used in this study………….....58
Fig.4-3 Dimensions of the hydrocyclone geometry(unit: mm)………....60
Fig.4-4 Schematic diagram of the experiment apparatus……………….61
第五章
Fig.5-1 Feed velocity in HC1 and HC2 varies with pressure drops…….65
Fig.5-2 Size distribution of PMMA7g in the HC1 underflow under different pressure drops (CF=0.34Vol% Φ1=1 Φ2=1)…………….66
Fig.5-3 Size distribution of PMMA7g in the HC2 underflow under different pressure drops (CF=0.34Vol% Φ1=1 Φ2=1)…………….67
Fig.5-4 HC1 partial separation efficiency of PMMA7g under different pressure drops (CF=0.34Vol% Φ1=1 Φ2=1)………………………69
Fig.5-5 HC2 partial separation efficiency of PMMA7g under different pressure drops (CF=0.34Vol% Φ1=1 Φ2=1)……………………..69
Fig.5-6 Relationship between energy loss and total pressure drop……..70
Fig.5-7 Size distribution of Corn Starch and PMMA7g in HC1 and HC2 underflow………………………………………………………..71
Fig.5-8 The concentrtion of Corn Starch and PMMA7g in the overflow of HC2……………………………………………………………...71
Fig.5-9 Size distribution of Corn Starch in HC1 and HC2 underflow under different concentrations…………………………………..73
Fig.5-10 Feed velocity of Corn Starch in HC1 and HC2 varies with different Φ1 values……………………………………………...75
Fig.5-11 Size distribution of Corn Starch in the underflow of HC1 under different Φ1 values (CF=0.34wt% Φ2=1)………………………...77
Fig.5-12 Size distribution of Corn Starch in the underflow of HC2 under different Φ1 values (CF=0.34wt% Φ2=1)………………………...77
Fig.5-13 Energy loss of Corn Starch in HC1 and HC2 varies with different Φ1 values ………………………...78
Fig.5-14 The overall efficiency E(-) varies with different Φ1 values……79
Fig.5-15 Size distribution of Corn Starch in the HC1 underflow under different Φ2 values (CF=0.34wt% Φ1=1)………………………..81
Fig.5-16 Size distribution of Corn Starch in the HC2 underflow under different Φ2 values (CF=0.34wt% Φ1=1)………………………..81
Fig.5-17 Partial separation efficiency of Corn Starch in the HC1 underflow varies with different Φ2 values………………………..82
Fig.5-18 Partial separation efficiency of Corn Starch in the HC2 underflow varies with different Φ2 values………………………..83
Fig.5-19 Overall efficiency of Corn Starch in HC1 and HC2 varies with different Φ2 values………………………..85
Fig.5-20 Concentration of Corn Starch in HC2 overflow varies with different Φ1 and Φ2 
values………………………..85
Fig.5-21 Velocity profile on (y=0-plane) for an uniform inlet velocity
10m/s Po=0(Mpa)Pu=0(MPa)…………………………………87
Fig.5-22 Velocity profile near vortex finder for an uniform inlet velocity 
10m/s Po=0(Mpa)Pu=0(MPa)…………………………………87
Fig.5-23 Pressure profile on (y=0-plane) for an uniform inlet velocity
10m/s Po=0(Mpa)Pu=0(MPa)…………………………………88
Fig.5-24 The different sites in the geometry hydrocyclone.(mm)………89
Fig.5-25 Velocity profile varis different sites in the hydrocyclone for an uniform inlet velocity 10m/s Po=0(Mpa)Pu=0(MPa)…………90
Fig.5-26 Velocity profile on the overflow(z=24mm)…………………...91
Fig.5-27 Velocity profile on the underflow(z=-74mm)…………………91
Fig.5-28 Compare experimental data and simulated data with the flow split at different feed velocity………………………………….93
Fig.5-29 Compare experimental data and simulated data with the flow split at different underflow pressure…………………………...93
Fig.5-30 Solid velocity profile on (y=0-plane) for Pf=0.4(MPa) Po=0(Mpa)Pu=0(MPa)………………………………………...95
Fig.5-31Solid velocity profile near vortex finder for Pf=0.4(MPa) Po=0(Mpa)Pu=0(MPa)………………………………………...95
Fig.5-32 Partial separation efficiency of Corn Starch(0.34wt% ρs=1480kg/m3) in the underflow for △P1=0.4MPa Po=0MPa Pu=0MPa……………………………………………………….97
Fig.5-33 Partial separation efficiency of simulation with solid particles in the underflow…………………………………..………………98
Fig.5-34 Partial separation efficiency of simulation with solid particles in the underflow varies different Φ value…………………………98
附錄
Fig.A-1 Particle size distribution of Corn starch……………………....115
Fig.A-2 Particle size distribution of PMMA-7G………………………116


表目錄
第五章
Tab5-1 The pressure in HC1 and HC2 under the same PF pressure…....64
Tab5-2 Pressure and velocity in HC1 and HC2 varies with different  Φ1 values…………………………………………….………… 74
Tab5-3 Boundary conditions and physical properties in simulation particles………………………………………………….…..…97
附錄
Tab B-1 Operating range of flow split in multiple hydrocyclones……117

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