去除奈米微粒的低壓旋風分離器

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(1)國立交通大學. 環境工程研究所. 博士論文. 去除奈米微粒的低壓旋風分離器. A low pressure cyclonic separator for nanoparticle removal. 研究生：. 陳聖傑. 指導教授：. 蔡春進. 中華民國九十五年十二月.

(2) 去除奈米微粒的低壓旋風分離器 A low pressure cyclonic separator for nanoparticle removal. 研究生：陳聖傑. Student: Sheng-Chieh Chen. 指導教授：蔡春進. Adviser: Chuen-Jinn Tsai 國立交通大學環境工程研究所博士論文. A Dissertation. Submitted to Institute of Environmental Engineering. College of Engineering. National Chiao Tung University. in Partial Fulfillment of the Requirements. for the Degree of. Doctor of Philosophy. in Environmental Engineering. December 2006. Hsinchu, Taiwan, Republic of China. 中華民國九十五年十二月.

(3) 去除奈米微粒的低壓旋風分離器研究生：陳聖傑. 指導教授：蔡春進博士國立交通大學環境工程研究所. 摘要本研究設計並測試一個低壓旋風分離器來去除奈米微粒，此設備包含一個臨界流孔板和連接於其下游的一個軸向旋風器，臨界流孔板用於降低旋風器的壓力，使微粒滑動校正係數提高、阻力降低，進而提升旋風器對奈米微粒的收集效率。由於微粒通過流孔板時可能會損失在其中，所以本研究探討微粒流經流孔板時的損失情形，並研究減少損失的方法。本研究探討的流孔板為 O’Keefe 公司的 E-9 流孔板(O’Keefe Control Co.)，其孔徑為 0.231 mm，上下游各接有入口管(內徑 10.4 mm,長度 90 mm)和出口管(內徑 6.2 mm,長度 60 mm)，臨界流量為 0.455 slpm。當上游壓力為 760 Torr，下游為 260 Torr 時，奈米微粒(氣動直徑小於 100 奈米)於流孔板內的擴散損失很小，粒徑 15 奈米時僅為 3.4%，慣性衝擊損失也接近於零。當下游壓力降低至 5.4 Torr 時，奈米微粒擴散損失仍很小，但慣性衝擊損失會高達 50%，主要發生在流孔板下游管壁上，解決方法為加大下游管徑，如將下游管徑從 6.2 mm 增加至 25 mm，則奈米微粒慣性衝擊損失會降為零。本研究的軸向旋風器有一個旋轉三圈的導翼片，其內徑為 15 mm，中心軸半徑為 10 mm。實驗時的旋風器進口壓力為 4.3~7 Torr, 流量為 0.351~0.566 slpm，測試微粒為固體氯化鈉和液體油酸微粒，直徑 12~100 奈米。結果顯示當流量固定，旋風器的效率會隨進口壓力降低而增加，如流量為 0.455slpm 時，當旋風器進口壓力從 6.0 Torr 降為 5.4 Torr，旋風器對油酸和氯化鈉微粒的截取氣動直徑分別會從 49.8 和 47.1 奈米減少為 23.1 和 21.2 奈米。此外本研究發現氯化鈉和油酸微粒有相近的收集效率，所以固體微粒在此旋風器內的彈跳問題幾乎不存在。 I.

(4) 以三維數值模擬方法計算旋風器的流場，發現在導翼片內的切線速度分布近似拋物面，根據這個發現，本研究推導出旋風器的收集效率的理論值，其結果與實驗數據符合，最大誤差在 15%以內。本研究也推出一個可預測不同旋風器壓力及操作流量下旋風器截取氣動直徑的半經驗公式，此公式可準確預測截取氣動直徑，誤差在 9%以 * 內，根據此半經驗公式，我們算得半經驗的截取史托克數平方根 St 50 為 0.241 的常數. 值。上述的理論收集效率僅考慮導翼片中微粒受離心力之去除作用，未考慮到導翼片下游腔體中的微粒去除，且沒有考慮到細微粒的擴散作用，因此誤差較大。為進一步準確計算旋風器的微粒收集效率，本研究先以三維數值模擬求得旋風器內全部的流場，再運用布朗尼動力模擬方法進行微粒收集效率的計算，同時考慮微粒受離心力及擴散作用的影響。結果顯示在不同操作條件下，旋風器的收集效率和截取粒徑都和實驗數據相當接近，最大誤差在 3.5%以內。此外發現微粒的擴散損失主要發生於導翼片之後的微粒收集腔體中，因為氣流出了導翼片之後速度大幅降低，微粒因而有較長的停留時間由於擴散作用而被收集。本研究的低壓旋風分離器可有效去除奈米微粒，推導出的旋風器截取氣動直徑半經驗公式和布朗尼動力模擬的結果，可設計低壓旋風分離器用於篩選某粒徑以下的奈米粉體、去除高科技製程反應腔真空排氣中的有毒微粒、及作為奈米微粒的採樣之用。. II.

(5) A low pressure cyclonic separator for nanoparticle removel Student: Sheng-Chieh Chen. Adviser: Dr. Chuen-Jinn Tsai. Institute of Environmental Engineering National Chiao Tung University. ABSTRACT In this study, a low pressure cyclonic separator for nanoparticle removal was designed and tested. The device included a critical orifice and an axial flow cyclone connected downstream of the orifice. The orifice was used to reduce the pressure of the cyclone. At reduced pressure, particle slip correction factor is increased and particle drag force decreased by a significant amount resulting in an increasing collection efficiency of nanoparticles. Particle loss may occur as particles pass through the orifice. Therefore, this study investigated particle loss in the orifice and the method to reduce the loss at first. The investigated orifice was the O’Keefe E-9 (O’Keefe Control Co.) orifice whose inner diameter was 0.231 mm and critical flow rate was 0.455 slpm. At the upstream and downstream of the orifice, there is an inlet tube (inner diameter=10.4 mm, length=90 mm) and outlet tube (inner diameter=6.2 mm, length=60 mm), respectively. As the upstream pressure (Pou) and downstream pressure (Pod) of the orifice was 760 Torr and 260 Torr, respectively, nanoparticle (smaller than 100 nm in aerodynamic diameter) diffusion loss in the orifice was found to be very low and impaction loss was nearly zero. Diffusion deposition loss was only 3.5% for 15 nm particles. When Pod was reduced to 5.4 Torr, nanoparticle diffusion loss was still low however inertial impaction loss was increased to 50%, which mainly occurs at the tube wall downstream of the orifice. Increasing the inner diameter of the outlet tube was found to reduce particle loss due to inertial impaction. For example, increasing inner diameter from 6.2. III.

(6) mm to 25 mm, particle loss was reduced to zero. The axial flow cyclone tested in the present study has one vane which makes three complete turns. The inner radius of the cyclone was 15 mm and the radius of the spindle was 10 mm. In the experiment, the operated pressures at cyclone inlet (Pin or Pod) and the flow rates were ranged from 4.3 to 7 Torr and 0.351 to 0.566 slpm, respectively. Liquid OA (oleic acid) and solid NaCl particles in size between 12 and 100 nm were used to examine the collection efficiency of the cyclone. Results showed that at a fixed flow rate, particle collection efficiency of the cyclone was increased with decreasing Pin. For example, when the flow rate was fixed at 0.455 slpm, the cutoff aerodynamic diameters of OA and NaCl were reduced from 49.8 and 47.1 to 23.1 and 21.2 nm, respectively as Pin was reduced from 6 to 5.4 Torr. In addition, it was found the collection efficiencies of NaCl and OA particles were close to each other in the size range from 25 to 180 nm in aerodynamic diameter. This is to say the effect of solid particle bounce on collection efficiency does not exist in the cyclone. Using 3-D numerical simulation to calculate the flow field of the axial flow cyclone, it was found the tangential flow velocity distribution in the vane section was paraboloid. Based on this finding, theoretical equation for particle collection efficiency of the cyclone was derived and showed good agreement with the experimental data with the maximum error of 15%. A semi-empirical equation for predicting the cutoff aerodynamic diameter at different inlet pressures and flow rates was also obtained. The semi-empirical equation is able to predict the cutoff aerodynamic diameter accurately within 9 % of error. From the empirical * cutoff aerodynamic diameter, a semi-empirical square root of the cutoff Stokes number, St 50 ,. was calculated and found to be a constant value of 0.241. The above theoretical collection efficiency only considered particle centrifugal force in the vane section, without considering particle removal in the chamber downstream of the vane. Also the diffusional effect of fine particles was not included. These all led to errors in. IV.

(7) theoretical collection efficiency. In order to improve the accuracy of particle collection efficiency, 3-D numerical simulation was conducted to obtain the total flow field first. Then Brownian Dynamic (BD) simulation was applied to calculate particle collection efficiency considering both particle centrifugal and diffusional effects. The simulated results of both particle collection efficiency and cutoff aerodynamic diameter are in good agreement with the experimental data with the maximum derivation of less than 3.5% at different operating conditions. The increase in the diffusional deposition was found to occur mainly in the chamber after the vane section when the gas expands and slows down. Therefore, particles have longer residence time to be collected in the chamber by diffusion. The low pressure cyclonic separator developed in this study can remove nanoparticles efficiently. The derived semi-empirical equation of cutoff aerodynamic diameter and the results of BD simulation can facilitate the design of the low pressure cyclonic separator to classify nanopowders below a certain diameter, to remove toxic nanoparticles from the vacuum exhaust of process chambers commonly used in high-tech industries, and can be used for nanoparticle sampling.. V.

(8) TABLE OF CONTENTS. ABSTRACT (Chinese) ............................................................................................................ I. ABSTRACT (English).......................................................................................................... III. ACKNOWLEDGEMENTS ................................................................................................. VI. TABLE OF CONTENTS ....................................................................................................VII. LIST OF TABLES ................................................................................................................ IX. LIST OF FIGURES ................................................................................................................ X. LIST OF SYMBOLS ...........................................................................................................XII. CHAPTER 1 INTRODUCTION............................................................................................1. 1.1 Motivation ..................................................................................................................1. 1.2 Objective.....................................................................................................................2. 1.3 Content of this thesis .................................................................................................4. CHAPTER 2 LITERATURE REVIEW................................................................................7. 2.1 Particle loss in a critical orifice ................................................................................7. 2.2 Particle collection efficiency of cyclones................................................................13. CHAPTER 3 METHODS .....................................................................................................18. 3.1 Experimental method ..............................................................................................18. 3.1.1 Particle loss of the critical orifice assembly..................................................18. 3.1.2 Particle collection efficiency of the axial flow cyclone ................................23. 3.2 Theoretical method for particle collection efficiency of the axial flow cyclone .27. 3.3 Numerical method ...................................................................................................29. 3.3.1 Flow field of the critical orifice assembly.....................................................29. 3.3.2 Particle loss in the critical orifice assembly..................................................29. 3.3.3 Particle collection efficiency of the axial flow cyclone ................................36. 3.3.4 Brownian Dynamic simulation of particle collection efficiency..................38. CHAPTER4 RESULTS AND DISCUSSION......................................................................44. 4.1 Particle loss in the critical orifice assembly...........................................................44. 4.1.1 Diffusion loss .................................................................................................44. 4.1.2 Inertial impaction loss on the front surface of the orifice ...........................45. 4.1.3 Inertial impaction loss in the downstream tube of the orifice......................49. VII.

(9) 4.1.4 Particle loss at different parts of the orifice..................................................50. 4.2 Particle collection efficiency of the axial flow cyclone..........................................56. 4.2.1 Comparison of liquid and solid particles ......................................................56. 4.2.2 Solid particle loading effect...........................................................................56. 4.2.3 Collection efficiency of OA particles at different operating conditions.......60. 4.3 Numerical results for flow field and particle collection efficiency. of the cyclone ...........................................................................................................62. 4.3.1 Simulated flow and pressure fields ...............................................................62. 4.3.2 Semi-empirical equation of cutoff aerodynamic diameter ...........................69. 4.4 Results of Brownian Dynamic simulation for particle collection efficiency.......75. 4.4.1 Comparison of simulated collection efficiency with present. experimental data............................................................................................75. 4.4.2 Comparison of simulated collection efficiency with the results of Hus et al. (2005)..............................................................................................80. CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS .......................................83. 5.1 Conclusions...............................................................................................................83. 5.2 Recommendations....................................................................................................85. REFERENCES ......................................................................................................................87. VITA .......................................................................................................................................92. PUBLICATION LIST ...........................................................................................................93. VIII.

(10) LIST OF TABLES. Table 4.1 Comparison of SQRT(St’) and particle loss in the TAO for different outlet tube diameters, Pod=260 Torr.................................................................................52. Table 4.2 Comparison of SQRT(St’) and particle loss in the TAO for different outlet. tube diameters, Pod=5.4 Torr..................................................................................55. Table 4.3 Cutoff aerodynamic diameter at different operating conditions,. liquid oleic acid (OA) particles..............................................................................72. Table 4.4 Cutoff aerodynamic diameter for different operating conditions. ....................77. IX.

(11) LIST OF FIGURES. Figure 1.1 Schematic diagram of a local scrubber in semiconductor industry...................5. Figure 1.2 Schematic diagram of the low pressure cyclonic separator ...............................6. Figure 2.1 Schematic diagrams of the orifice assembly. (a) Locations of particle loss, (b). 2-D view of the computational domain. ..............................................................12. Figure 3.1 Experimental setup for measuring loss of small particle (<1 μm). ..................20. Figure 3.2 Experimental setup for measuring loss of lager particle (2-15 μm).................22. Figure 3.3 Experimental setup for testing collection efficiency of the cyclone. ................24. Figure 3.4 Schematic diagrams of the spindle and vane design .........................................26. Figure 3.5 Schematic diagram of a tetrahedral cell. ...........................................................33. Figure 3.6 Critical particle radial positions and collection regions at the entry plane of. the inlet tube. (OP: orifice plate; TAO: tube after orifice) ...............................35. Figure 4.1 Comparison of simulated diffusional deposition efficiencies with. experimental data. ................................................................................................47. Figure 4.2 Particle deposition efficiency on the front surface of the orifice......................48. Figure 4.3 Particle deposition efficiency on the tube after the orifice. ..............................51. Figure 4.4 Particle deposition efficiency on different parts of the orifice assembly. ........54. Figure 4.5 Particle collection efficiency versus aerodynamic diameter for solid. NaCl and liquid OA particles at different inlet pressures.................................58. Figure 4.6 Particle loading effect on collection efficiency, solid NaCl particles................59. Figure 4.7 Particle collection efficiency versus aerodynamic diameter for. OA particles at different inlet pressures and flow rates....................................61. Figure 4.8 Maximum tangential velocity and pressure distribution in the vane,. numerical results...................................................................................................63. Figure 4.9 Tangential velocity profile at the cutting plane of the vane section,. the end of (a) 2 turns (2-D), (b) 3 turns (2-D) and (c) 3 turns (3-D).................64. Figure 4.10 Critical curves at the entry plane of the first segment for. particle collection................................................................................................67. Figure 4.11 Comparison of numerical collection efficiencis and experimental data........68. Figure 4.12 Collection efficiencies versus. St / St50 for OA particles at different inlet X.

(12) pressures and flow rates.....................................................................................73. Figure 4.13 Comparison of numerical collection efficiencies and present experimental. data, (a) Pin=6.0 Torr; (b) Pin=7.0 Torr..............................................................78. Figure 4.14 Comparison of numerical collection efficiencies and present experimental. data, Pin=4.3, 5.4, 6.8 torr. ..................................................................................79. Figure 4.15 Comparison of the present numerical collection efficiencies with the. experimental data and the theory by Hsu et al. (2005) ...................................82. XI.

(13) LIST OF SYMBOLS English Symbols A. a parameter. Ac. collection area. Ai. inlet area of the orifice assembly. Ao. orifice area. B. pitch of vane. C. mass concentration of nanoparticles. Cc. Cunningham slip correction factor. CD. drag coefficient. Cd. particle concentration of the orifice downstream. Cu. particle concentration of the orifice upstream. Di. inlet tube diameter of the orifice assembly. Do. orifice diameter. Dout. inner diameter of the outlet tube of the cyclone. Dp. particle diameter. Dpa. aerodynamic diameter. Dpa50. cutoff aerodynamic diameter. Dpa,cent. centrifugal cutoff aerodynamic diameter. Dpa,diff. diffusional cutoff aerodynamic diameter. dr. differential radial migration distance of particle. Ds. diffusivity of the species. Dt. tube inner diameter after the orifice. F. a variable. F(B). random force resulting from the particle bombardment by gas molecules. F(D). drag force on the particle. F(ext). external force. g. gravitational acceleration. XII.

(14) GLi. a random number. GVi. a random number. H. a dimensionless variable. H1. modified Stokes number. J. mass flux. K. an empirical factor. kB. Boltzmann’s constant. Kn. Knudsen number. L. effective body length. Lmin. minimum length of the cells adjacent to the particle’s present cell. M. equation of Chandrasekhar’s first lemma. m. particle mass. ms. mass fraction of the species. N. number of vanes. n. number of vane turns. nT. total number of turns of the vane. nζ. total number of turns of a particle in the cyclone. P760. 760 Torr. Pcyc. average pressure of cyclone inlet and outlet. Pen. overall particle penetration of the axial flow cyclone. Pin. inlet pressure of the cyclone. Pn. pressure at nth turn of the vane. Pod. downstream pressure of the orifice. Pou. upstream pressure of the orifice. Pout. outlet pressure of the cyclone. Q. gas volumetric flow rate. Q0. standard gas volumetric flow rate. R. contraction ratio. Re. Reynolds number. Rep. particle Reynolds number XIII.

(15) rmax. inner radius of the cyclone. rmin. radius of the vane spindle. ro. inlet tube radius of the orifice assembly. rOP. critical particle radial position of collection region OP. rTAO. critical particle radial position of collection region TAO. s. species. St. Stokes number. St'. modified Stokes number relative to Uo and Dt. St50. Stokes number correspondinf to 50% deposition (or collection) efficiency. * St50. semi-empirical cutoff Stokes number. Stb. Stokes number of the axial flow cyclone. Sto. Stokes number based on Ui and Do. T. absolute temperature. tv. transit time of a particle in the vane section. U. flow velocity. Ua. mean axial gas velocity in the body section of the cyclone. Ui. average velocity at the inlet tube of the orifice. Umax. maximum flow velocity of the cells adjacent to particle’s present cell. Uo. average flow velocity at the orifice. V. particle velocity. Va. mean gas velocity in the vane section of the cyclone. Vr. particle radial velocity. Vol. effective volume in the vane section. Vt ,nth ( r , z ). tangential velocity of the entry plane of the nth segment at position (r,z). Va. average axial velocity. Vt. average tangential gas velocity in the vane section. XIV.

(16) Vt ,1. average tangential gas velocity at the entry plane of the 1st segment of the vane section. Vt ,nth. average tangential gas velocity at the entry plane of the nth segment of the vane section. Vt ′,1. average tangential gas velocity at the first segment of the collection area. w. vane thickness. x, y, z. Cartesian coordinate. Greek symbols. Δr. total particle radial migration distance. ΔLi. particle linear displacement. Δt. time step of each iteration. ΔVi. change of particle velocity. <ΔLi>. expected values of particle displacement in the i-th direction. <ΔVi>. expected values of particle velocity change in the i-th direction. Γ. a factor, defined as Va/Ua. α, β, γ. fractions of the difference vectors P1P 4 , P1P 2 and P1P3 , respectively. ηDpa. collection efficiency of Dpa particle. ηo. particle deposition efficiency in the orifice assembly. ηOP. deposition efficiency of particles at OP. ηTAO. deposition efficiency of particles at TAO. ϕ(M). probability distribution of M. ϕ i(ΔVi, ΔLi). bivariate normal density probability distribution function. λ. mean free path of the air molecules. λ0. mean free path of the air molecules at standard condition. μ. air dynamic viscosity. θ. contraction half-angle. ρ. air density XV.

(17) ρc. a coefficient of correlation. ρp. particle density. ρp0. unit density. σLi. standard deviations of displacement. σVi. standard deviations of particle velocity change. τ. particle relaxation time. τ nth. average relaxation time of particle. ψ(ξ). any function of time, varying much slower than the fluctuating Brownian force. XVI.

(18) CHAPTER 1. INTRODUCTION. 1.1 Motivation Many toxic gas pollutants (SiH4, TEOS, SiH2Cl2, SiCl4, etc.) (McMahon, 1989) as well as fine particles (SiO2 and metallic particles, such as As oxide) are emitted from the reaction chambers of semiconductor and photo-electronic industries. Residual gases are usually treated by local scrubbers located behind a vacuum pump with high efficiency (Blachman and Lippmann, 1974), as shown in Fig. 1.1. However, local scrubbers are not efficient for fine particle removal (Librizzi and Manna, 1983). Particles can deposit on the tube wall after the reaction chamber or in between the vacuum pump and local scrubber. Once particles accumulate to a significant amount, they can clog up the tube resulting in process intervention or explosion hazard. Furthermore, fine particles emitted from the local scrubber are not treated efficiently by the central scrubber either. Between the reaction chamber and the vacuum pump, pressure is very low, typically less than several Torr. It is desirable to have a particle control device which works at this condition. Otherwise particles have to be removed at ambient pressure by a baghouse or an electrostatic precipitator, which is costly and occupies too much space to use in the high-tech industry. If the pressure is reduced below several Torr, particle drag force will be reduced by a significant amount and then it is possible to use a cyclone to remove fine particles by centrifugal force. An axial flow cyclone is such a good candidate. Additional advantage is that the axial flow cyclone can be installed in line with the flow direction. To determine size distribution of nanoparticle in ambient air, inertial impactors such as the low pressure cascade impactor developed by Vanderpool et al. (1990) and the nanoMOUDI by commercialized MSP Co. are normally used. However, previous studies (Tsai and 1.

(19) Cheng, 1995; Tsai and Lin, 2000; Biswas and Flagan, 1988) showed that solid particles can bounce easily from the impaction substrate. In contrast, solid particle bounce in a cyclone is less a problem. Therefore it is desirable to develop a low pressure axial flow cyclone for nanoparticle sampling. The objective of this study is to design and test an axial flow cyclone operated at reduced pressure. In case nanoparticles to be removed or sampled are suspended in ambient condition, a pressure reducing device has to be installed in front of the cyclone. In this study, a critical orifice was used to reduce the pressure of the cyclone. The schematic diagram of the low pressure cyclonic separator for removing nanoparticles is shown in Fig. 1.2, in which particles are suspended at ambient condition. After passing through the orifice, the pressure of the aerosol flow is reduced to several Torr. Nanoparticles then can be removed by the downstream axial flow cyclone. 1.2 Objective In order to reduce the pressure in the cyclone, commercial critical orifices (O’Keefe Controls Co., type E-8, E-9 and E-10) were installed at the upstream of the cyclone. Because the diameter of the orifice is very small, particle loss may occur in the orifice and eventually clog it up. Therefore, particle loss in the orifice must be reduced. Orifices are widely used to control flow rate, or use as a pressure reducing device for high purity gas sampling (Lee et al., 1993), or used in a particle focusing apparatus (Liu et al., 1995; Lee et al., 2003; Das and Phares, 2004). In these applications, it is desirable to have particle loss in the orifice as minimum as possible. Previous works on axial flow cyclones include the experimental studies of Liu and Rubow (1984), Weiss et al. (1987) and Vaughan (1988), and the theoretical study of Maynard (2000). In these studies, axial flow cyclones were tested in ambient conditions. Until now, no researchers have ever investigated the collection efficiency of an axial flow cyclone in 2.

(20) reduced pressure conditions. In the previous study of Tsai et al. (2004), a theoretical equation was derived to predict the cutoff aerodynamic diameter of an axial flow cyclone. They found the theoretical cutoff diameter had to be adjusted by the flow Reynolds number to fit the experimental data. The reason why there is such as a discrepancy has yet to be found. Brownian Dynamic (BD) simulation was successfully applied to calculate the single fiber efficiency in which both inertial impaction and Brownian diffusion were taken into account (Ramarao et al., 1994). If BD simulation can be used to calculate the particle collection efficiency of the axial flow cyclone, both centrifugal force and Brownian diffusion can be taken into account. It is expected to be more accurate than the theoretical equation of Tsai et al. (2004) in which the Brownian diffusion effect on collection efficiency was not considered. The objectives of this study are summarized below: 1.. To use both numerical and experimental methods to study particle deposition efficiency at different parts of the orifice assembly and find out a best geometry of the orifice assembly to reduce particle loss.. 2.. To test and compare the collection efficiency of the axial flow cyclone for both liquid (OA) and solid (NaCl) nanoparticles and to examine the solid particle loading effect on collection efficiency.. 3.. To calculate the flow and pressure fields and the particle efficiency of the cyclone using a 3-D numerical method and BD simulation.. 4.. To compare experimental collection efficiencies with theoretical results obtained using simulated flow and pressure fields and numerical results by BD simulation.. 5.. To develop a semi-empirical equation to predict the cutoff aerodynamic diameter of the axial flow cyclone.. 3.

(21) 1.3 Content of this thesis In chapter 2, previous studies on particle loss in a critical orifice are reviewed. Then the experimental and theoretical works on the collection efficiency of tangential or axial flow cyclones in the literature are also reviewed. In chapter 3, experimental methods for determining particle loss in the critical orifice and particle collection efficiency of the axial cyclone are first described. Then a theoretical method for calculating the particle collection efficiency of the cyclone is introduced. After the theoretical method, numerical methods for calculating the flow field and the particle loss of the orifice are presented. Next is the numerical method for calculating the flow field and the collection efficiency of the cyclone. Finally, BD simulation is introduced which calculates nanoparticle collection efficiency considering both centrifugal force and Brownian diffusion simultaneously. In chapter 4, particle loss at different parts of the orifice and the comparison of present experimental data and numerical results are shown. Then the experimental data for particle collection efficiency of the axial cyclone are presented. The experimental data and the numerical results of particle collection efficiency are compared. At last, the results of BD simulation for particle collection efficiency are compared with the present data and the results of Hus et al. (2005). In chapter 5, conclusions of this thesis are summarized and recommendations are suggested.. 4.

(22) cleanroom reaction chamber. metal etcher special gases Cl2--30sccm BCl3--50sccm CF4--40sccm PN2--30sccm RC floor. perforated floor location of an appropriate device to remove particles particle deposition. vacuum pump. central scrubber. local scrubber. Figure 1.1 Schematic diagram of a local scrubber in semiconductor industry.. 5.

(23) 1atm aerosol flow. critical orifice. reduced pressure. axial flow cyclone. pressure. reducing device. vacuum pump. nanoparticle. removal. Figure 1.2 Schematic diagram of the low pressure cyclonic separator. 6.

(24) CHAPTER 2. LITERATURE REVIEW. 2.1 Particle loss in a critical orifice Orifices are widely used to control flow rate. In this study, commercial critical orifices (O’Keefe Controls Co., type E-8, E-9 and E-10) were installed at the upstream of the cyclone to reduce pressure in the cyclone. Because the diameter of the orifice is very small, particle loss may occur in the orifice and eventually clog it up. Therefore, particle loss in the orifice must be reduced. The critical orifice was used as a pressure reducing device for high purity gas sampling by Lee et al. (1993). In this case it is important to avoid particle loss in the orifice so that particle concentration in the pipe flow can be measured accurately. Lee et al. (1993) reviewed particle deposition mechanisms in orifice-type pressure reducers including inertial impaction at the front side and the back side of the orifice, and on the chamber (or tube) wall downstream of the orifice. They also illustrated that the loss of nanoparticles (<100 nm) can also occur due to diffusional mechanism. The schematic diagram of the critical orifice assembly and the deposition regions of particles are shown in Fig. 2.1. The deposition loss due to particle inertial impaction on the front surface of the orifice was studied by Ye and Pui (1990) for an abruption contraction with a contraction half-angle, θ of 90o. Assuming the air flow is laminar and fully developed, they obtained an empirical equation of the deposition efficiency, ηo, as. η o = 1 − exp(1.721 − 8.557 F + 2.227 F 2 ). (2.1). where the variable F and the contraction ratio R are defined as 7.

(25) F = St o /( R) 0.31. (2.2). R = Di / Do. (2.3). In above equations, Do is the orifice diameter, Di is the inner diameter of the inlet tube and Sto is the Stokes number which is defined as. St o =. ρ p D 2pU i Cc 9 μDo. (2.4). where Ui (m/s) is the average velocity at the inlet tube, Dp (m) is the particle diameter, ρp (kg/m3) is the particle density, Cc is the Cunningham slip correction factor and μ is the air dynamic viscosity. In their study, the contraction ratio R was in the range of 2-10 and the Reynolds number was in the range of 100-200, which was based on the inlet tube diameter (Di) and the average velocity at the inlet tube (Ui). Chen and Pui (1995) extended the work of Ye and Pui (1990) further to consider the effect of different θ (15o to 90o) on the inertial particle deposition efficiency. The Reynolds number was fixed at 1000 while the R was varied from 2.0 to 5.0. The results of the deposition efficiency for θ>75° were found to be the same as those in Ye and Pui (1990). For θ<60o, the following empirical equation for the deposition efficiency on the front side of the orifice was obtained:. η = [0.882 + 0.0272H 0.5 − 8.272H 0.5 exp(−3.627H 0.5 )]2. 8. (2.5).

(26) where the dimensionless variable H is defined as. H = St. St50. (2.6). ,. St50 is the Stokes number corresponding to 50% deposition efficiency, which is related to the R and θ as. St50 = 0.235R 0.61 (sin θ ) −1.119. (2.7). Muyshondt et al. (1996) proposed that the deposition efficiency for a given contraction angle is related to the modified Stokes number as. η=. 1 ⎤ 1 + ⎡ H1 ⎢⎣ a exp(bθ )⎥⎦. (2.8). c. where H1 is the modified Stokes number, Sto (1-Ao/Ai), Ao is the orifice area and Ai is the inlet area. Constants in Eq. (2.8) were obtained from the least-square fitting of the data as a = 3.14, b = -0.0185, c = -1.24. Eq. (2.8) is only valid up to the limiting value of η=1-(Ao/Ai) as the Stokes number becomes very large and the particles travel in a straight line. Sato et al. (2002) investigated the particle deposition at low pressure experimentally and numerically. In their experiment, the pressure at downstream of the orifice ranged from 0.2 to 0.28 Torr, the contraction ratios R were fixed at 2, 3 and 5, and the Reynolds number based on Di and Ui was 3. In the numerical simulation, R was also varied among 2, 3 and 5 while the flow Re was controlled at 0.1, 0.3, 3, 10 and 30. After comparing their own experimental and numerical results, the authors found the deposition efficiency could be correlated as 9.

(27) η = exp(−0.5376 / H − 0.1824 / H 7.019 ). (2.9). In addition to the impaction loss on the front surface of the orifice, Pui et al. (1988) also found that particles could also deposit on the tube wall after the orifice. The deposition efficiency was related to another modified Stokes number, SQRT(St') defined as. SQRT (St ′) =. StoU o (Do / Dt )0.58 Ui. (2.10). where Uo and Dt are the average flow velocity at the orifice and the tube diameter after the orifice. The authors plotted their experimental deposition efficiency versus SQRT(St') and found the data almost fell in a unique curve. From the curve, significant particle loss was found to occur as SQRT(St')>0.5. Therefore, to design an expansion chamber to replace the downstream tube and keep SQRT(St')<0.1 is necessary to reduce particle loss. Orifices are also used in a particle focusing apparatus, called aerodynamic lenses, to form nanoparticle beams (Liu et al., 1995; Lee et al., 2003; Das and Phares, 2004). Narrow particle beams with small divergence angles are desirable in many applications in order to achieve high transport efficiencies of particles from a sampling regime to a detector and high resolution of particle size measurements. Based on the study of Liu et al. (1995), the TSI developed the aerodynamic lens which can effectively transmit particles in the size ranges 30 to 300 nm or 100 to 3000 nm. In this device, a precision bore tube holds five thin plate orifices (aerodynamic lenses) which were mounted in sequence with spacers in between (TSI Model 3801-030 Manual). The series of apertures (orifices) can move particles closer to the center axis after passing each individual aperture if their aerodynamic sizes are less than a critical value.. 10.

(28) Another study on particle focusing was conducted theoretically at atmospheric pressure by Lee et al. (2003) and verified by the particle beam size measured by laser light scattering. The results showed that a strongly focused particle beam was obtainable with a single orifice at atmospheric pressure when the orifice Reynolds number was in the range of 300 ≤ Re ≤ 700, which was based on Do and Uo. In the application of orifices for aerodynamic lenses, it is also desirable to have particle loss in the orifices as minimum as possible.. 11.

(29) (a). (b) inlet : (0, 0, 151.5). unit: mm particle loss at:. Di=10.4 90. :IT, inlet tube. Do=0.231. :OP, orifice plate. :OB, orifice back. :TAO, tube after orifice. 1.5 Dt=6.2. 60. z. x. :(0, 0, 0) outlet. Figure 2.1 Schematic diagrams of the orifice assembly. (a) Locations of particle loss, (b) 2-D view of the computational domain.. 12.

(30) 2.2 Particle collection efficiency of cyclones. Cyclones are normally used to remove particles larger than 5-10 μm in aerodynamic diameter. To reduce the cutoff diameter, the cyclone diameter must be reduced or the flow rate must be increased. For example, Zhu and Lee (1999) tested a small tangential cyclone (cyclone diameter, D=3.05 cm) and found the cutoff size to be 0.3 μm when it was operated at 110 slpm. For axial flow cyclones, Liu and Rubow (1984), Weiss et al. (1987) and Vaughan (1988) studied the axial flow cyclone operating at ambient condition. For example, Liu and Rubow (1984) developed an axial flow cascade cyclone at a design flow rate of 30 L/min for sampling high concentration of particles. The cutoff aerodynamic diameter of the five stages are 12.2, 7.9, 3.6, 2.05 and 1.05 μm. Total particle loss in the system, including the loss in the body, vane insert and exit tube of the collection cup, was shown to be significant. It ranged from 15 % for particles of 1 μm in diameter to 33.3 % for particles of 8 μm in diameter. Therefore, using this cascade cyclone to measure particle size distributions requires complete recovery of all particles lost in the cyclone. Different materials of particles may result in different collection efficiencies. For impactors, it is well-known that the collection of liquid particles is better than that of solid particles due to solid particles bounce or reentainment from the impactor substrates (Tsai and Cheng, 1995; Tsai and Lin, 2000; Biswas and Flagan, 1988). Zhu and Lee (1999) also studied the collection efficiencies differences of solid and liquid particles of a tangential flow cyclone for. Liquid dioctyl-phthalate (DOP) and solid polystyrene latex (PSL) particles in the size range of 1.0 and 3.6 μm were found to have similar collection efficiencies even at a high flow rate of 80 slpm. However, the effect of solid particle bounce on the collection efficiency of the axial flow cyclone operating in low pressure conditions remains to be investigated. The effect of deposited solid particles on the cyclone wall of the tangential flow cyclone has been investigated in Blachman and Lippmann (1974) and Tsai et al. (1999). The particle collection efficiency was found to increase with increasing particle mass deposited in the 13.

(31) cyclone (Blachman and Lippmann, 1974). Such increase is mainly due to the accumulation of dust on the cyclone wall opposite to the inlet that gradually reduces the effective diameter of the cyclone. But when the amount of deposited particles is heavy enough, the aggregated particles will be detached and then the collection efficiency will reduce again (Blachman and Lippmann, 1974). Blachman and Lippmann (1974) did not study the effect of different amounts of deposited particle mass on the collection efficiency. The solid particle loading effect on the collection efficiency for a 10 mm nylon cyclone and a new 18 mm aluminum cyclone was studied by Tsai et al. (1999). They found the cutoff aerodynamic diameter of both cyclones decreased with increasing deposited particle mass. But the 18 mm cyclone appeared to have less deposited particle mass effect on the collection efficiency due to its larger inner diameter. The cyclones tested in Blachman and Lippmann (1974) and Tsai et al. (1999) were tangential flow cyclones. There have been no studies on the solid particle loading effect on the collection efficiency for axial flow cyclones and it is expected that the axial flow cyclones will be less affected by the loaded particles on the cutoff diameter than impactors since the particle deposit in the cyclones is more diffuse. Maynard (2000) is the first to study the particle penetration of the axial flow cyclone in ambient condition theoretically. He derived the particle penetration of the axial flow cyclone based on the assumption that particle collection mainly occurs in the vane and body sections only. The overall particle penetration, Pen, is combined from the penetrations derived separately for the vane and body sections as. Pen = (1 −16π 2 Stb L*)1/ 2 +. (. ). 1/ 2 4 π 2 n 2 Γ 2 Stb2 2 n ΓStb *2 − *2 1 + 4π 2 rmin + 4π 2 1−16π 2 Stb L * *2 *2 *2 rmax − rmin rmax − rmin. (2.11). where n is the number of vane turns, rmax is the inner radius of the cyclone (m), rmin is the radius of the vane spindle (m) and L is the effective body length (refer to Fig. 1 in Maynard,. 14.

(32) 2000) (m). The relative dimensions of these three variables, denoted by the variables with asterisk, is the actual dimension divided by the pitch of vanes, B (m). Stokes number Stb is defined in the body section as Stb= τ Ua/B, in which τ is the particle relaxation time (sec). The factor Γ= Va/Ua, in which Va is the mean gas velocity in the vane section and Ua is the mean axial gas velocity in the body section. If there are N vanes and each has a finite thickness w (m), then Γ in Eq. (2.11) is calculated as. Γ=. * *2 rmax 1 + 4π 2 rmax. (2.12). * * 2(1 − Nw*)(rmax − rmin ). The form of Eq. (2.12) does not allow one to obtain a simple analytical form for St50 (Stokes number with 50 % penetration), it must be calculated by numerical iteration. It is expected to have an analytical equation to calculate the cutoff diameter and predict the particle collection efficiency. Tsai et al. (2004) derived an theoretical equation for predicting the cyclone cutoff aerodynamic diameter based on the air volumetric flow rate, the geometry of the cyclone, the properties of carrying gas and the pressure of the cyclone. The cutoff aerodynamic diameter Dpa50 for the cyclone with one vane making 3 turns was derived as. D pa50. (. 0.106μ (B − w) r 2 max − r 2 min = ρ p0 λ0 r 2 min Q0 nζ. ). 2. ⎛ Pcyc ⎞ ⎟⎟ × ⎜⎜ ⎝ P760 ⎠. 2. (2.13). In the above equation, ρp0 is unit density (1000 kg/m3), λ0 is mean free path of air molecules at standard condition (m), Q0 is standard volumetric flow rate (m3/sec), Pcyc is the average pressure of cyclone inlet and outlet (Torr), P760 is 760 Torr. The nζ is the total number of turns of a particle in the cyclone, assuming that the vortex makes n turns in the vane and 15.

(33) additional n(ζ-1) turns downstream the vane. ζ was chosen to be 1.5 to give the best fit to the experimental data. The equation agrees well with the published experimental data on cutoff diameter (Weiss et al., 1987; Liu and Rubow, 1984; Vaughan, 1988) in ambient conditions. But at low pressure conditions (several Torr), the equation predicts the cutoff diameter much smaller than the experimental data. Hsu et al. (2005) studied the particle collection efficiency theoretically and experimentally using the same axial flow cyclone designed in Tsai et al. (2004). They derived the equation to predict the particle collection efficiency in which both centrifugal and diffusional forces were taken into account. Plug flow assumption was made for the tangential flow in the vane section. The collection efficiency derived by Hsu et al. (2005) is. η = 1 − exp[−(. D pa 50,diff D pa. +. D pa 2 D pa 50,cent 2. )],. (2.14). where the centrifugal cutoff aerodynamic diameter Dpa50,cent is. D pa 50 =. 2 2 − rmin 9 μ (rmax ) 2 (B − Nw) 2 ln 2 , 2 N 2 BCc 8π nζQ0 rmin. (2.15). and the diffusional cutoff aerodynamic diameter Dpa50,diff is. D pa50,diff =. 4nζ k BTCc . 3Q0 μ ln 2. (2.16). In Eq. (2.15), kB is the Boltzmann’s constant and T is absolute temperature (K). For the flow rate of 0.455 slpm and the pressure in the cyclone of several Torr, Eq. (2.14) predicts. 16.

(34) centrifugal force is the predominant mechanism for particle removal when particles are larger than 40 nm in aerodynamic diameter. For particles smaller than 40 nm in diameter, diffusional deposition is the main mechanism. Below 40 nm, the collection efficiency of nanoparticles increases with decreasing particle size. Experimental data presented by Hsu et al. (2005) show similar trends, but substantial disagreement exists between theoretical results and experimental data. The flow field in the cyclone is complicated. Several researchers (Boysan et al., 1983; Hoekstra et al, 1999; Schmidt and Thiele, 2002; Harwood and Slack, 2002; Schmidt et al., 2003; Xiang and Lee, 2004) have studied the flow fields numerically for tangential flow cyclones and examined the influence of different geometries and operating conditions on the collection efficiency. Recently, Gimbun et al. (2005) used the CFD approach to simulate the particle collection efficiency of a tangential flow cyclone. In the study, in order to calculate the trajectories of particle in the flow, the discrete phase model (DPM) was used to track individual particles through the continuum fluid. The DPM model is a embedded code of the CFD program. In the model, the collection efficiency was obtained by releasing a specified number of monodisperse particles at the inlet of the cyclone and by monitoring the number escaping through the outlet. Results obtained by the authors match very well with the experimental data that were obtained by Xiang et al. (2001). However, there have been no numerical studies on the flow field and particle collection efficiency calculations with considering the both impaction and diffusion depositions of an axial flow cyclone, in particular at low pressure conditions.. 17.

(35) CHAPTER 3. METHODS. 3.1 Experimental method. 3.1.1 Particle loss of the critical orifice assembly The experimental set-up for measuring loss of small particle (<1 μm) in the orifice assembly is shown in Fig. 3.1. Polydisoerse NaCl particles were generated using a constant output automizer (TSI Model 3076) and then passed through silica gel diffusion dryer. The evaporation-condensation method using a tube furnace was employed to generate ultrafine aerosol particles. The tube furnace (Lindberg/Blue, model HTF55342C) was operated at 880 ℃ and the residence time of aerosol particles in the furnace was 1.2 seconds. Subsequently. aerosols were cooled by mixing with filtered ambient air in the mixing chamber. An impactor was used to cut particles larger than 500 nm before particles were passed through the NDMA (TSI Model 3085), which was used to classify monodisperse NaCl particles of size 15-177 nm in aerodynamic diameter. The long DMA (TSI Model 3071) was used to obtain monodisperse NaCl particles of size 132-856 nm in aerodynamic diameter when the impactor was not used. Then, the aerosol flow was divided into two streams, one was introduced into the orifice system and the other into the scanning mobility particle sizer SMPS (TSI model 3934). A critical orifice (E-9 O' Keefe Controls Co.) with the orifice diameter Do=0.0231 cm and inlet diameter Di=1.04 cm was used in the experiment (Fig. 2.1). The lengths of the inlet and outlet tubes (Dt=0.62 cm) are 9 and 6 cm, respectively. The flow rate of the experiment was fixed at 0.455 slpm which corresponded to Re= 61.4. When the flow rate was 0.455 slpm, the corresponding downstream pressure, Pod, was 260 Torr while the upstream pressure, Pou, was fixed at 760 Torr. The flow rate of 0.455 slpm is the critical condition. For real time measurement of total particle loss, an aerosol electrometer (AE, TSI Model 18.

(36) 3068) was used to measure the electrical current of singly charged particles. For comparison purpose, flow rate 0.242 slpm which corresponded to Re= 32.6 was also tested. The corresponding downstream pressure, Pod, was 602 Torr while the upstream pressure, Pou, was also fixed at 760 Torr. Monodisperse particles were allowed to pass through the orifice line or the by pass line alternately to measure the downstream (Cd) and upstream (Cu) aerosol concentrations. The loss was calculated as. loss % = (1−. Cd ). Cu. (3.1). For measuring particle loss at each part of the orifice assembly, the EA was substituted by an after filter. After introducing monodisperse NaCl particles into the orifice assembly for about 10 minutes, the assembly was disassembled and the deposited NaCl particles were wiped by using cotton swabs. The cotton swabs were then dissolved in DI water and the solutions were analyzed by an ion chromatography (Model DX-120, Dionex Corp.). The deposition efficiency at IT, OP, OB and TAO (Fig. 2.1) can be calculated as. (%) at part i =. amount of Cl − at part "i" total amount of Cl −. (3.2). where “i” denotes the IT, OP, OB or TAO (referring to Fig. 2.1) and the total amount of Cl was the summation of Cl－ at IT, OP, OB, TAO and AF (after filter).. 19.

(37) furnace. compressed air sheath air. TSI 3076 atomizer. dryer. diluter excess aerosol. mixing chamber. △P. impactor. excess air monodisperse aerosol TSI 3085 or 3071 sheath air. pressure gauge. orifice by-pass line TSI 3068 vacuum pump aerosol electrometer. computer. TSI 3022 CPC. TSI 3071 EC. Figure 3.1 Experimental setup for measuring loss of small particle (<1 μm).. 20.

(38) For measuring the deposition loss of lager particles (>1μm), monodisperse fluorescein OA (oleic acid) particles of size 2-12 μm in aerodynamic diameter were generated by a VOMAG (TSI Model 3450). The experimental setup is shown in Fig. 3.2. The generated particle was introduced into the mixing chamber and the test chamber, in which the orifice assembly was located. The orifice assembly was oriented vertically upward in the test chamber with the inlet tube at the top. The air velocity in the test chamber was nearly zero. The electrostatic neutralizer (Kr-85) was used with the TSI VOMAG to neutralize particles and the APS (TSI Model 3321) was used to monitor the size and uniformity of the particles. A pressure gauge (Varian Model CT-100) was used to monitor the pressure at the upstream and downstream of the orifice. After introducing monodisperse fluorescein OA particles into the orifice assembly for about 30 minutes, fluorescein OA particle loss in each part of the orifice assembly was determined in the similar way as the NaCl particles, except that the cotton swabs were dissolved in xylene after wiping fluorescein OA particles and the solution were analyzed by a fluorometer (Turner Designs Model 10-AU-005). The deposition efficiency at IT, OP, OB and TAO was also calculated by the same way as in Eq. (3.2).. 21.

(39) mixing chamber. electrostatic neutralizer. test chamber inlet pressure gauge orifice. TSI 3450. VOMAG. after filter vacuum pump. TSI 3321 APS. Figure 3.2 Experimental setup for measuring loss of lager particle (2-15 μm).. 22.

(40) 3.1.2 Particle collection efficiency of the axial flow cyclone The experimental system for collection efficiency test of the axial flow cyclone is shown in Fig. 3.3. Monodisperse OA (ρp= 894 kg/m3) and NaCl (ρp= 2200 kg/m3) particles in diameter between 12 and 100 nm were generated also by the atomization and electrostatic classification technique. Polydisperse particles were first generated by atomizing (Atomizer, TSI Model 3076) 0.05 or 0.1% (v/v) OA and NaCl solution. Then the aerosol flow was dried by a silica gel drier. The dried aerosol stream was passed through a furnace (Lindberg/Blue Model CC58114C-1) and mixed with clean air to produce sufficiently small particles (< 100 nm) after the furnace. The temperature of the furnace was fixed at 350 and 880 ℃ for OA and NaCl particles, respectively. Fine polydisperse particles were generated by mixing the vapor with dry compressed air. Monodisperse, singly charged particles were generated by classifying the polydisperse particles by a nano-DMA (TSI Model 3085). The SMPS (Condensation Particle Counter, TSI Model 3022 and Electrostatic Classifier, TSI Model 3071) was used to monitor the concentrations of particles in the monodisperse particle stream from the nano-DMA. The concentrations were used to correct for the multiple charge effect on the collection efficiency. An aerosol electrometer (TSI Model 3068) was used to measure the electric current of the upstream and downstream aerosol concentrations of the cyclone. A homemade Faraday cage with a larger inlet and outlet than the TSI Model 3068 electrometer was used to reduce the pressure drop through it. A critical orifice (O’Keefe Controls Co., E-8, 0.351 slpm or E-9, 0.455 slpm or E-10, 0.566 slpm) was installed at the cyclone inlet to achieve the low-pressure condition. A powerful vacuum pump (DUO 65, Pfeifeer, Germany, nominal pumping speed: 70 m3/hr) was used to achieve the desired low pressure conditions. The inlet pressures at the cyclone inlet in this study are 4.3, 6.0 5.4, 6.8 and 7 Torr.. 23.

(41) Figure 3.3 Experimental setup for testing collection efficiency of the cyclone.. 24.

(42) The bypass line was used to determine the particle concentration at the cyclone inlet which can be controlled by an on-off valve (valve 1) as shown in Fig. 3.3. When valve 1 is open and valve 2 is closed, the aerosol flow will pass through the bypass line and the inlet aerosol concentration can be measured. On the other hand, when valve 1 is closed and valve 2 is open, the aerosol flow will pass through the cyclone and the particle concentration at the cyclone outlet can be obtained. By adjusting the angle valve (valve 3) at the downstream of the Faraday cage, the pressure at the cyclone inlet can be controlled. The loading effect test was conducted by introducing polydisperse particles continuously into the cyclone of vane over a period of time. The particle collection efficiency was tested after loading polydisperse particles (total number conc.: 8.26x106～1.29x107 #/cm3, NMD: 69.5～82 nm, σg: 1.53～1.58) for 1-h (loaded mass: 0.33 mg), 3-h (1.24 mg), and 5-h (1.73 mg), respectively. Schematic diagram of the vane design which has one vane and makes 3 complete turns was shown in the right-hand side of Fig. 3.4. The radius of the spindle and the inner radius of the cyclone are 10 and 15 mm, respectively. The width and the height of the vane section are 5 and 4 mm, respectively. The left-hand side of Fig. 3.4 shows the detailed geometries of the spindle and vane.. 25.

(43) aerosol inlet. 30. inlet 5. vane section. 15. 20 115 chamber after the vane 27 1. outlet tube. aerosol outlet. Figure 3.4 Schematic diagrams of the spindle and vane design. (the r-z coordinate and the dimension of the vane section are also indicated.). 26.

(44) 3.2 Theoretical method for particle collection efficiency of the axial flow cyclone. In this study, a theoretical equation for calculating particle collection efficiency of the cyclone was derived. According to the equation and the numerical results of flow field, the numerical results of particle collection efficiency and an empirical equation for predicting the cutoff aerodynamic diameter of the cyclone were obtained. As a particle enters the cyclone, it experiences the centrifugal force and migrates toward the wall. The Stokes law was adopted to calculate the particle drag force since the Rep (particle Reynolds number) was much smaller than 0.1 of the cyclone. The particle radial velocity and hence the collection efficiency is calculated theoretically based on the gas volumetric flow rate, properties of the cyclone, carrying gas and particles. The transit time of a particle in the vane section, tv, is given by the ratio of the effective volume in the vane section (Vol) to the gas volumetric flow rate (Q). The effective volume in the vane, Vol, is. 2 2 Vol = π (rmax − rmin )n (P − Nw). (3.3). Therefore the particle (or gas) transit time in the vane section, tv, is. tv =. 2 2 π (rmax − rmin )n (P − Nw). (3.4). Q. The average tangential gas velocity in the vane section, Vt , can be calculated as. Vt =. 2 π rmin nN 2 rmin QN 2 = 2 2 tv (rmax − rmin )(P − Nw). (3.5). 27.

(45) Due to centrifugal force Vt 2τ/r, the particle will move in the radial direction. Neglecting the transient state of particle motion, the steady state particle radial velocity, Vr, is. Vr =. 2 4τ rmin Q2 N 2 dr τ Vt 2 = = 2 2 dt r r(rmax − rmin ) 2 (P − Nw) 2. (3.6). where τ is the particle relaxation time, which is written as. 2 ρ p0 D pa C c (D pa ) τ= 18μ. (3.7). where Cc(Dpa) is the slip correction factor of Dpa particle. Based on Eq. (3.6), the differential radial migration distance of particle, dr, can be calculated as. dr = Vr dt =. τVt 2 rdθ r. Vt. = τVt dθ. (3.8). Integrating Eq. (3.8), the total particle radial migration distance Δr can be calculated. Then the collection efficiency, η, of the particle can be calculated as. η=. Δr . rmax − rmin. (3.9). 28.

(46) 3.3 Numerical method. 3.3.1 Flow field of the critical orifice assembly In order to obtain the flow field in the orifice, a 3-D numerical simulation was conducted in the present study. The governing equations are Navier-Stokes and the continuity equations. Since the gas velocity inside the orifice in this study is supersonic, steady-state and compressible laminar flow (Re<<2000) was assumed in the simulations. The Navier-Stokes and the continuity equations were solved by using the STAR-CD 3.22 code (CD-adapco Japan Co., LTD) which is based on the finite volume discretization method. The pressure-velocity linkage was solved by the PISO algorithm (Issa, 1986) and the UD (upwind differencing) and CD (central differencing) schemes were used for the space discretization methods of the flow velocity and density, respectively. Hexahedral cells which allow for finer grids near the wall were generated by an automatic mesh generation tool, Pro-Modeler 2003 (CD-adapco Japan Co., LTD). The total numbers of cells used were 500,000 and 1,000,000. The average cell length was around 0.25 or 0.2 mm and the smallest length of 0.005 mm was assigned near the wall. The convergence criterion of the flow field calculation was set to be 0.1 % for the summation of the residuals. The total number of iterations was about 500 and the time required to reach convergence was about 3000 minutes. Non-slip condition was applied on the walls and the constant mass flow rate (0.455 slpm) was set on the inlet boundary assuming uniform velocity profile. On the outlet boundary, a fixed pressure was assigned based on the experimental data. 3.3.2 Particle loss in the critical orifice assembly The flow field of the orifice was calculated first. For calculating diffusional loss of nanoparticles (<100 nm), the concentration field of nanoparticles was calculated based on the following convection-diffusion equation: 29.

(47) ∂ρ ∂x j. ⎛ ⎞ ⎜ u j ms − Ds ∂ms ⎟ = 0 ⎜ ∂x j ⎟⎠ ⎝. (3.10). where subscript s denotes the species, ms and Ds are the mass fraction (kg/kg) and the diffusivity (m2/s) of the species, respectively. After the concentration field was obtained, particle loss (kg/s) due to diffusion was then calculated at the surfaces of different parts of the orifice assembly as. J y = −Ds. ∂C ∂y. ,. (3.11). y =0. total loss = ∫∫ J y d x d z .. (3.12). In the above equations, Jy, Ds and C are mass flux in y direction (kg/s m2), diffusivity of nanoparticles (m2/s) and mass concentration of nanoparticles (kg/m3), respectively. Once the total loss of the nanoparticles was obtained, deposition efficiency was then calculated as a ratio of the total loss to the incoming mass flow rate of nanoparticles. For calculating inertial impaction loss of large particles, particle trajectories were calculated after the flow field was obtained. In order to track the particle location in the computational domain, the computational cells had to be tetrahedral instead of hexahedral used in the calculation of diffusion loss of nanoparticles. The equation of particle motion was solved numerically by using the fourth order Runge-Kutta integration to obtain the particle trajectories. In the Cartesian coordinate, the particle equations of motion in x, y and z directions are:. 30.

(48) m m. m. dVx C = C D Re P c (U x −Vx ) dt 24τ dVy dt. = CD Re P. (3.13). Cc (U y − Vy ) 24τ. (3.14). dVz C. = CD Re P c (U z − Vz ) − mg . dt 24τ. (3.15). In the above equations, subscript x, y and z denote the velocity in x, y and z directions, respectively; V and U are the velocities of the particle and flow (m/s); Rep and CD are the particle Reynolds number and the empirical drag coefficient; m is particle mass (kg); g is the gravitational acceleration (m/s2). CD was expressed by Rader and Marple (1985) as a function of Rep:. ⎧ ⎪ ⎪ ⎪ CD = ⎨ ⎪ ⎪ ⎪ ⎩. 24 , for Re P ≤ 1. Re P. 24 (1 + 0.0916 Re P ), for 1 < Re P ≤ 5 Re P 24 23 (1 + 0.158Re P ), for 5 < Re P ≤ 1000 Re P. (3.16). where Rep is defined as. Re p =. ρ (U −V )D p μ. (3.17). where ρ is the density of air (kg/m3). In this study, a dilute suspension of particles in a perfect gas was assumed. Particle-particle interactions were neglected and the presence of particles was assumed not to affect the gas flow. Particles were released at the inlet tube entrance and the trajectories of the particles were. 31.

(49) calculated by integrating Eqs. (3.13)-(3.15). In the calculation, the method of Schafer and Breuer (2002) was used to determine which tetrahedral cell a particle was located. If the vertices of a regular tetrahedral are designated by P1, P2, P3 and P4 as shown in Fig. 3.5, the difference vectors P1P 2 , P1P3 and P1P 4 are linearly independent and form a threedimensional space for the cell. Any particle position P* (x*, y*, z*) in space can be written as. ⎧ α ( x4 − x1 ) + β ( x2 − x1 ) + γ ( x3 − x1 ) = x * −x1 ⎪ ⎨ α ( y4 − y1 ) + β ( y2 − y1 ) + γ ( y3 − y1 ) = y * − y1 . ⎪ α ( z − z ) + β ( z − z ) + γ (z − z ) = z * −z 4 1 2 1 3 1 1 ⎩. (3.18). where α, β and γ are fractions of the difference vectors P1P 4 , P1P 2 and P1P3 , respectively and can be calculated analytically. If point P* is located inside a tetrahedral cell (such as point P5 shown in Fig. 3.5), α, β and γ should meet the following criteria (Schafer and Breuer, 2002):. ⎧ ⎪⎪ ⎨ ⎪ ⎪⎩. α ≥0 β ≥0 . γ ≥0 α + β +γ ≤1. (3.19). If one or more of these conditions are violated, the particle is not in the cell. Then the computer program proceeds to the adjacent cells until the cell containing the particle is found. The adjacent cells are the cells which have more than one joint vertices with the particle’s original cell. The list of the adjacent cells will be updated when the particle moves to another cell. The program will stop when the particle touches the wall or leaves the computational domain.. 32.

(50) P1 (x1, y1, z1). P* (x* ,y* ,z*) P5 (x, y, z). P4 (x4, y4, z4). P2 (x2, y2, z2). P3 (x3, y3, z3). Figure 3.5 Schematic diagram of a tetrahedral cell.. 33.

(51) In the calculation of particle trajectory, time step, Δt, for each iteration was calculated based on the cell size and particle velocity as. Δt =. 0.1Lmin U max. (3.20). where Lmin and Umax are the minimum length and maximum flow velocity, respectively, of the cells adjacent to the particle’s present cell. The critical particle trajectory method was used to obtain the impaction deposition efficiency of the particle at different parts of the orifice. In the simulation, particles were found to deposit only in the collection regions OP (the front surface of the orifice plate) and TAO (the tube after the orifice), no particles deposited in OB (the back side of the orifice). The critical particle radial positions and collection regions of particles at OP and TAO are shown in Fig. 3.6. If a particle starts at a radial position greater than rOP and smaller than r0 at the entry plane, it will deposit at the collection region OP which is the annular area from rOP to r0 shown in the figure. If the particle starts at a radial position smaller than rOP and greater than rTAO, it will deposit at the collection region TAO which is the annular area from rTAO to rOP shown in the figure. Otherwise, the particle will not deposit in the orifice. The deposition efficiencies of the particle at OP, ηOP, and TAO, ηTAO , were respectively calculated as. η OP =. 2. 2. 2 2 r0 − rOP rOP − rTAO and η . = TAO r02 r02. (3.21). After obtaining ηOP and ηTAO, the penetration of the particle was then calculated as 1-ηOP-ηTAO.. 34.

(52) Figure 3.6 Critical particle radial positions and collection regions at the entry plane of the inlet tube. (OP: orifice plate; TAO: tube after orifice). 35.

(53) 3.3.3 Particle collection efficiency of the axial flow cyclone In order to obtain accurate flow and pressure fields of the axial flow cyclone, 3-D numerical simulation was conducted. The computational domain is shown in Fig. 3.4. Since the maximum Knudsen number in the cyclone corresponding to outlet pressure, Pout, of 1.46 Torr (inlet pressure Pin=4.31 Torr) is around 0.01 in the present study, the flow was considered as a continuum. The maximum Knudsen number, Kn,max is defined as. K n ,max =. 2λ , Dout. (3.22). where Dout is the inner diameter of the outlet tube of the cyclone (m); λ is the mean free path of the air molecules (m). The methods for calculating the flow field were the same as section 3.3.1 expect the computational cell types and the pressure-velocity linkage algorithm were different. The type chosen was the hybrid cells which contained both hexahedral and tetrahedral types. The hybrid cells allow for finer grids close to the wall and match the vane geometry. The pressure-velocity linkage here was solved by the SIMPLE algorithm (semi implicit method for pressure linked equation) (Pantankar, 1980). The paraboloid flow was assumed to calculate the particle migration distance. Since the flow in the cyclone was found to spin for slightly greater than 2 turns starting slightly ahead of the end of the first turn and ending slightly beyond the end of the third turn, only the particle migration distance during 2 turns was calculated. To simplify the calculation, the total radial migration distance of a particle, Δr, was calculated based on Eq. (3.8) as the sum of the migration distance from ten segments of the vane section, each segment corresponded to 1/4 turn of the vane. The first segment or the first 1/4 turn was added before the end of the first turn while another 1/4 turn was added after the end of the third turn. The second and third turn each constituted four segments in the calculation. All together there were 10 segments. As will 36.

(54) be shown later, the tangential flow develops very fast and becomes nearly fully developed near the end of the first turn of the vane. The fully developed profile is paraboloid which can be written as. Vt ,nth (r, z ) = 2(V t ,nth. ⎡ ⎛ 2 z ⎞ 2 ⎤ ⎡ ⎛ 2 r ⎞ 2 ⎤. − 1) ⎢1 − ⎜ ⎟ ⎥ ⎢1 − ⎜ ⎟ ⎥ + 2 , ⎢⎣ ⎝ 4 ⎠ ⎥⎦ ⎢⎣ ⎝ 5 ⎠ ⎥⎦. (3.23). where the coordinates r and z are illustrated in Fig. 3.4 shown later. Vt ,n (r , z ) and Vt ,n are th. th. the tangential velocity of the entry plane of the nth segment at position (r, z) and the average tangential velocity of the nth segment, respectively. The constant 2 m/s at the right-hand side of Eq. (3.23) represents the tangential velocity near the wall, which is obtained from the numerical simulation shown later. If the total migration distance of a particle of aerodynamic diameter, Dpa, and the initial radial position is greater than 5 mm (or rmax-rmin, the width of the vane section) then the particle hits the wall and is collected. Assuming different initial radial positions of a particle at the entry plane of the first segment, the critical curve which delineates the collection and non-collection regions of the particle can be found. As the collection area is obtained, then the collection efficiency of Dpa particles can be calculated by the following equation as. η D pa =. Ac × Vt′ ,1 , 5 × 4 × Vt ,1. (3.24). where Ac is the collection area (mm2); Vt ′,1 is the average tangential velocity of the collection area (m/s); 5 mm and 4 mm are the width and gap of the vane section, respectively (mm); Vt ,1 is the average tangential velocity at the entry plane of the 1st segment of the vane section. 37.

(55) Since the pressure drop of the cyclone occurs mainly in the vane section, Vt ,nth is calculated based on the pressure at the nth section following the ideal gas law and mass conservation principle. For comparison purpose, if the tangential flow field is assumed to be plug flow, the total radial migration distance Δr can be calculated as (referring to Eq. (3.8)). Δr =. 10. π. ∑ 2τ th. n =1. nth. Vt ,n th ,. (3.25). where Vt ,nth is the average tangential velocity (m/s), τ th is the average relaxation time of n the particle. Both Vt ,nth and τ th depend on the average pressure at the nth segment. n 3.3.4 Brownian Dynamic simulation of particle collection efficiency For simulating the cyclone collection efficiency, the Lagrangian method was used for calculating particle trajectories. For each particle diameters, particle trajectories of 10,000 particles uniformly distributed in the inlet were calculated. When a particle touched the wall of the cyclone it was assumed to have been collected by the cyclone. Neither bounce-back nor re-suspension of previously deposited particles was taken into account. The collection efficiency was calculated as the number of particles deposited in the cyclone divided by the number of particles entering the cyclone, or 10,000. This number was chosen to obtain reliable results in a reasonable computational time. For small particles, the stochastic momentum exchange with bombarding gas molecules becomes significant. BD simulation was used to include the influence of diffusional motion on particle deposition. The equation of the particle motion can be written as the following Langevin equation (Kanaoka et al., 1983):. 38.

(56) m. dV = F ( D ) + F ( ext ) + F ( B ) , dt. (3.26). where m is the particle mass, V is the particle velocity, F(D) is the drag force on the particle, F(ext) denotes the external force and F(B) is the rapidly fluctuating, random force resulting from the particle bombardment by gas molecules. Thus F(B) can be defined as. F ( B ) = mA(t).. (3.27). where A(t) is the random acceleration of the particle (m/s2). In this study, no other external force but the gravitational force was considered. But the gravity was found to be negligible as compared to the drag force. The drag force is given by. F ( D) =. 3πμD p Cc. (U − V ),. (3.28). The BD simulation was established by Chandrasekhar (1943) for Stokesian particles in a stationary fluid (U=0) and force free field (F(ext)=0). The Chandrasekhar's first lemma was:. t. M = ∫ ψ (ξ )F ( B) (ξ ) / mdξ .. (3.29). 0. The function ψ(ξ) was defined to be. ψ (ξ ) = τ (1−[exp(. ξ −t )], τ. (3.30). Then the probability distribution of M is given by. 39.

(57) t. ϕ (M ) =. exp[− | M |2 / 4q ∫ ψ 2 (ξ )dξ ] 0. ⎡ ⎤ 2 ⎢4πq ∫ψ (ξ )dξ ⎥ 0 ⎣ ⎦ t. 3/ 2. (3.31). ,. where q is defined as. q=. k BT . τm. (3.32). From Eq. (3.31), expected values of particle displacement in the i-th direction <ΔLi> and its velocity change <ΔVi> during time interval Δ t can be found as. < Δ L i >= V iτ [1 − exp( − Δ t / τ )],. (3.33). < ΔVi >= Vi [1 − exp( −Δt / τ )].. (3.34). The standard deviations of displacement σLi and particle velocity change σVi has been derived to be. σ V = (1 − exp(−2Δt / τ ))k BT / m,. (3.35). σ L = (2Δt / τ − 3 + 4 exp( −Δt / τ ) − exp( −2Δt / τ )k BT /(m / τ 2 ).. (3.36). i. i. In this study, extension of BD in the case of moving fluid with external forces derived by Podgórski (2002) was used. Integration of Langevin equation for a time interval small enough that the host fluid velocity U and external forces F(ext) may be assumed constant over (t,t+Δt), 40.