Numerical simulation and optimization of fluid flow in cyclone vortex finder

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Chemical Engineering and Processing 47 (2008) 128–137

Numerical simulation and optimization of fluid flow in cyclone vortex finder Arman Raoufi, Mehrzad Shams ∗ , Meisam Farzaneh, Reza Ebrahimi Department of Mechanical Engineering, K.N. Toosi University of Technology, No.15, Pardis Square, Mola Sadra St., Vanak Square, Tehran, Iran Received 16 May 2007; received in revised form 5 August 2007; accepted 8 August 2007 Available online 19 August 2007

Abstract In this study, a computational fluid dynamics is used to predict and evaluate the effects of vortex finder shape and diameter on cyclones performance and flow field. The Eulerian–Lagrangian computational procedure is used to predict particles tracking in the cyclone. The flow field is calculated using 3D Reynolds-averaged Naveir–Stokes equations. The Reynolds stress transport model (RSTM) is used to simulate the Reynolds stresses. The Newton’s second law is used to study the particles trajectory with modeling the drag and gravity forces acting on the particles. The velocity fluctuations are simulated using the discrete random walk (DRW). Four different cylinder-shaped and six cone-shaped vortex finders are simulated for various flow rates of 30, 50 and 70 l/min. The cylinder-shaped vortex finders have different diameters, i.e. 15, 11 and 7 mm, and the cone-shaped vortex finders have different cone lengths, i.e. 10, 25 and 45 mm, with 7 and 15 mm diameters at both ends of the cone. The particles size range is 0.5–3 ␮m. The details of the flow field are studied in the cyclones and the effects of the different vortex finders are observed. The numerical results are compared with the experimental data and good agreement is observed. © 2007 Elsevier B.V. All rights reserved. Keywords: Cyclone; Shape and dimension of vortex finder; CFD; Collection efficiency

1. Introduction Many industrial processes, such as mineral processing, petroleum refining, chemical engineering, food processing and environmental cleaning, involve the separation of particles from an air stream. Several technologies, including fabric filters, electrostatic precipitators, air classifiers and cyclone separators can be used for gas–solid separation. Because of fabric filters and electrostatic precipitators incur high initial and operating costs; they are not suitable for many industrial applications, although they have a high efficiency for fine particle separation. Cyclone separators are widely used in the field of air pollution control and gas–solid separation for aerosol sampling and industrial applications. Due to relative simplicity to fabricate, low cost to operate, and well adaptability to extremely harsh conditions, cyclone separators have become one of the most important particle removal devices which are preferably utilized in both engineering and process operation.

∗

Corresponding author. Tel.: +98 912 359 6236; fax: +98 21 88877273. E-mail address: [email protected] (M. Shams).

0255-2701/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2007.08.004

The cyclone works by inducing spiral rotation in the primary phase (liquid or gas) and using this rotation to induce radial acceleration on a particulate suspension. In conventional cylindrical cyclone devices, there are two outlets, both on the axis of symmetry. The underflow outlet is situated at the apex of the cone at the base of the cyclone, and the overflow outlet is an inner tube (or so-called vortex finder) that descends from the top. The density of the suspended particulate phase is normally greater than that of the primary phase. Due to the imposed swirl, large particles migrate rapidly to the outer wall and then spiral down to the underflow. Smaller particles migrate more slowly, so are captured in an upward spiral near the center of the cyclone, and leave through the top. Since cyclones have been used extensively in various industries, a considerable number of experimental and theoretical investigations have been performed on cyclone separators to the present. Among these, Stairmand [1] presented one of the most popular design guides which suggested that the cylinder height and exit tube length be, respectively, 1.5 and 0.5 times of the cyclone body diameter for the design of a high efficiency cyclone. Based on the static particle approach, equations for particle collection were developed by Barth [2]. Muschelk-

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nautz improved Barth’s theory by considering the effects of the particle load, the wall roughness, the secondary flow, and the change in particle size distribution within the body on the collection efficiency and the pressure loss. This theory may be the most practical method for modeling cyclone separators at the present time [2]. This approach involves determining the particle diameter for which the centrifugal force on the particle is exactly balanced by the inward drag force. Other cyclone models allow for the calculation of the grade efficiency curve for any specific geometrical layout of a cyclone (see, e.g. Leith and Licht [3] and the three-region model of Dietz [4]). Also in these models, analytical expressions are used to describe the main gas flow field characteristics, such as the size of the vortex core and the distribution of the tangential velocity component. Bryant et al. [5] observed if the vortex touched the cone wall, particle re-entrainment occurred. Leith and Dirgo [6], Bhatia and Cheremisinoff [7] discussed the effects of the cone opening size. Rongbiao et al. [8] were suggested that flow rate strongly influenced the efficiency and the reduction in cone size results in higher collection efficiency without significantly increasing the pressure drop. Bohnet [9], Kim and Lee [10], Michael and Martin [11], investigated the effects of the pressure drop and grade efficiency at high temperature and high pressure. The complexity of the gas–solid flow pattern in cyclones has long been a matter of many experimental and theoretical works. At present, laser Doppler anemometry (LDA) and hot-wire anemometry are frequently employed to study experimentally the flow structure in the cyclones. As for the theoretical work, computational fluid dynamics (CFD) codes have proven to be a useful tool for simulating cyclonic gas flows [12]. Recently, research efforts by computational fluid dynamics are frequently carried out for the resolution of flow field and dust particle behavior with different degree of numerical and modeling accuracy in order to assist in the time consuming experimental works. In conjunction with the complex flow structure, numerical simulation is momentarily not able to completely substitute experiments but can reduce, to a certain degree, experimental costs for design and optimization. CFD has a great potential to predict the flow field characteristics and particle trajectories inside the cyclone as well as the pressure drop (Griffiths and Boysan [13]). The complicated swirling turbulent flow in a cyclone places great demands on the numerical techniques and the turbulence models employed in the CFD codes. It has been shown in the previous work on the prediction of the cyclone performance under a different operating temperature and inlet velocity (Gimbun et al. [14,15]). Very little information is available on the effects of the vortex finder size and shape, if other cyclone dimensions are fixed. The vortex finder size is an especially important dimension, which significantly affects the cyclone performance as its size plays a critical role in defining the flow field inside the cyclone, including the pattern of the outer and inner spiral flows. Saltzman and Hochstrasser [16] studied the design and performance of miniature cyclones for respirable aerosol sampling, each with a different combination of three cyclone cone lengths

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and three vortex finder diameters. Iozia and Leith [17] optimized the cyclone design parameters, including the vortex finder diameter, to improve the cyclone performance using their optimization program. Kim and Lee [18] described how the ratio of the diameters of cyclone body and the vortex finder affected the collection efficiency and pressure drop of cyclones, and proposed an energy-effective cyclone design. Moore and Mcfarland [19] also tested cyclones, with six different vortex finders, and concluded that the variation in the vortex finder diameter under the constraint of a constant cyclone Reynolds number produced a change in the aerodynamic particle cutoff diameter. Zhu and Lee [20] have conducted detailed experiments on cyclones of different height and found that like other important dimensions such as body diameter and gas exit tube diameter, the cyclone height can influence considerably the separation efficiency of the cyclones. Xiang and Lee [21], obtained detailed flow information by CFD simulation within those cyclones tested by Zhu and Lee and compared the flow pattern in cyclones of different height. Lim et al. [22] depicted the performance of a cyclone, with different vortex finders, was evaluated to examine the effect of the vortex finder shape on the characteristics of the collection efficiency. Four cylinder-shaped and six cone-shaped vortex finders were designed and employed to compare the collection efficiencies of the cyclone, at flow rates of 30, 50 and 70 l/min. The cylinder-shaped vortex finders had different diameters, i.e. 15, 11 and 7 mm, and the cone-shaped vortex finders had different cone lengths, i.e. 10, 25 and 45 mm, with 7 and 15 mm diameters at both ends of the cone. Lim et al. [22] have conducted detailed experiments on the effects of the vortex finder shapes and dimensions, at different flow rates, on the cyclone performance. However, they did not provide any information about the fluid flow in the cyclones and their explanation for the efficiency results could not be adequate. This study is intended to obtain detailed flow information by CFD simulation within those cyclones tested by Lim et al. Subsequently, comparison of the flow pattern in the cyclones with the different vortex finder shapes and dimensions is made to reveal how the vortex finder shape and dimension influence its performance. 2. Configuration of cyclone and vortex finders (cyclone dimension) As mentioned earlier in Section 1, the simulations were performed on 10 cyclones with different vortex finder shapes and diameters, which have been tested for separation efficiency and pressure drop by Lim et al. [22]. These cyclones had a reversed flow tangential inlet. The dimensions of cyclones are shown in Fig. 1(a) and Table 1. Fig. 2 shows the vortex finders with different shapes. Four cylinder-shaped and six cone-shaped vortex finders were shown. The cylinder-shaped vortex finders have different diameters, i.e. 15, 11 and 7 mm, and the cone-shaped vortex finders have different cone length, i.e. 10, 25 and 45 mm, with 7 and 15 mm diameters at both ends of the cone. The particles size range is 0.5–3 ␮m. In the simulations, the flow rates through the cyclone was 30, 50, 70 l/min.

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Fig. 1. (a) Definition of the cyclone dimensional parameters; (b) CFD Mesh for the cyclone.

The RSTM provides for differential transport equations for evaluation of the turbulence stress components, i.e.

3. Flow simulation For an incompressible fluid flow, the equations of continuity and balance of momentum for the mean motion are given as ∂u¯ i =0 ∂xi

(1)

∂u¯ i ∂u¯ i 1 ∂p¯ ∂2 u¯ i ∂ =− +ν = Rij + u¯ j ∂t ∂xj ρ ∂xi ∂xj ∂xj ∂xj

(2)

where u¯ i is the mean velocity, xi the position, t the time, p¯ the mean pressure, ρ the constant gas density, v the kinematics viscosity, and Rij = ui uj is the Reynolds stress tensor. Here, ui = ui − u¯ i is the ith fluid fluctuation velocity component. Table 1 Dimensions of the cyclones Dimensions and operating conditions

Values

Cyclone diameter, D (mm) Outlet diameter, De (mm) Inlet height, a (mm) Inlet width, b (mm) Outlet height, S (mm) Cyclone height, H (mm) Cyclone body height, h (mm) Dust outlet diameter, B (mm) Flow rate (l/min) Temperature

30 15, 11, 7 12 6 45 122 45 15 30, 50 293

∂ ∂ Rij + u¯ k Rij ∂t ∂xk     νt ∂ ∂ ∂u¯ j ∂u¯ i − R = R + R ij ik jk ∂xk σ k ∂xk ∂xk ∂xk     ε 2 2 2 − C1 Rij − δij k − C2 Pij − δij P − δij ε k 3 3 3

(3)

where the turbulence production terms are defined as Pij = −Rik

∂u¯ j ∂u¯ i − Rjk , ∂xk ∂xk

P=

1 Pij 2

(4)

with P being the fluctuation kinetic energy production. Here vt is the turbulent (eddy) viscosity; σ k = 1, C1 = 1.8 and C2 = 0.6 are empirical constants [23]. The transport equation for the turbulence dissipation rate, e, is given as   νt  ∂ε ∂ε ∂ε ε ∂u¯ i ε2 ∂  ν+ ε − Cε1 Rij + u¯ j = − Cε2 ∂t ∂xj ∂xj σ ∂xj k ∂xj k (5) In Eq. (5), k = (1/2)ui ui is the fluctuation kinetic energy and ε is the turbulence dissipation rate. The values of constants are σ ε = 1.3, Cε1 = 1.44 and Cε2 = 1.92.

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Fig. 2. Shape and dimensions of vortex finders.

is reached, a new value of the instantaneous velocity is obtained by introducing a ζ new value of f in Eq. (6).

4. Simulation of fluctuating velocities The dispersion of small particles is strongly affected by the instantaneous fluctuation fluid velocity. The turbulence fluctuations are random functions of space and time. Here, a discrete random walk (DRW) model is used for evaluating the instantaneous velocity fluctuations. The values of that prevail during the lifetime of the turbulent eddy, Te , are sampled by assuming that they obey a Gaussian probability distribution. That is, the instantaneous velocity in the ith direction is given as   ui = ζ ui ui (6) In Eq. (6), ζ is a zero-mean, unit-variance, normally distributed,  ui ui

random number; is the local root mean-square (RMS) fluctuation velocity in the ith direction; and the summation convention on i is suspended. The characteristic lifetime of the eddy is defined as a constant given by Te = 2TL

(7)

where TL is the eddy turnover time given as Te = 0.15(k/ε). The other option allows for a log-normal random variation of eddy lifetime that is given by Te = −TL log(r)

(8)

where r is a uniform random number between 0 and 1. The particle is assumed to interact with the fluid fluctuation field, which stays fixed over the eddy lifetime. When the eddy lifetime

5. Particle equation of motion To calculate the trajectories of particles in the flow, the discrete phase model (DPM) was used to track individual particles through the continuum fluid. The particle loading in a cyclone separator is typically small, and therefore, it can be safely assumed that the presence of the particles does not affect the flow field. The equation of motion of a small particle, including the effects of nonlinear drag and gravitational forces, is given by 3vCD Rep duPi = (ui − uPi ) + gi dt 4d 2 S dxi = uPi dt

(9) (10)

Here, uPi is the velocity of the particle and xi its position, d the particle diameter, S the ratio of particle density to fluid density, and gi is the acceleration of gravity. The buoyancy, virtual mass and Basset forces are negligible because of the small fluid-toparticle density ratio. The first term on the right-hand side (RHS) of Eq. (9) is the drag force due to the relative slip between the particle and the fluid. The drag force is, generally, the dominating force. According to Hinds [24], the drag coefficient, CD , is given as CD =

24 , ReP

for ReP < 1

(11)

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CD =

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24 ReP





1 2/3 1 + ReP , 6

for 1 < ReP < 400

(12)

where ReP is the particle Reynolds number defined as ReP =

d|uj − uPj | ν

(13)

The particle equation of motion requires the instantaneous turbulent fluid velocity values at particles location. The mean liquid velocity was evaluated by the use of the Reynolds stress transport turbulence model (RSTM) and the fluctuation velocity components were calculated form Eq. (6). The drag coefficient for spherical particles is calculated by using the correlations developed by Morsi and Alexander [25]. The ordinary differential equation (Eq. (10)) is integrated along the trajectory of an individual particle. Collection efficiency statistics are obtained by releasing a specified number of mono dispersed particles at the inlet of the cyclone and by monitoring the number escaping through the underflow. Collisions between particles and the walls of the cyclone were assumed to be perfectly elastic (coefficient of restitution is equal to 1) [26]. Particle–particle collision is negligible. 6. Results A number of 60,000–100,000 hexahedral cells are generated with the Gambit code for analyzing the flow in the cyclone. Fig. 1(b) shows the details of the computational grid for the cyclone model. The hexahedral computational grids are generated by dividing the whole cyclone geometry into a number of blocks and then meshing each block separately. A “velocity inlet” boundary condition is used at the cyclone inlet, which means that a velocity normal to the inlet is specified. A fully developed boundary condition is used at the outlet. Grid refinement tests are conducted in order to make sure that the solution is not grid dependent. To attain the confidence about the simulation, it is necessary to compare the simulation result with the available experimental data. The finite volume methods have been used to discrete the partial differential equations of the model using the simple method for pressure–velocity coupling and the second-order upwind scheme to interpolate the variables on the surface of the control volume. The RSTM is used in the simulation, and the computation is continued until the solution converged with a total relative error of less than 0.0005. The dimensions of cyclones are shown in Fig. 1(a). Fig. 2 shows the vortex finders geometry and shapes. Four cylindershaped and six cone-shaped vortex finders are shown. The cylinder-shaped vortex finders have different diameters, i.e. 15, 11 and 7 mm, and the cone-shaped vortex finders have different cone length, i.e. 10, 25 and 45 mm, with 7 and 15 mm diameters at both ends of the cone. The calculated static pressure drop of the cyclone between inlet and outlet for different vortex finder and at different flow rates is shown in Fig. 3. The numerical results agree well with the experimental data. Pressure drop in the low flow rates are the same for 7-B, 15-B and 11-A, as indicated in Fig. 3. But with

Fig. 3. Numerical and experimental results for pressure drops for the cyclones: (a) 7-A, 7-B, 7-C, 7-D and 11-A; (b) 15-A, 15-B, 15-C, 15-D and 15-7-A.

increasing the flow rate, discrepancy of pressure drop between the different vortex finder shapes increases. It is also shown that differences of numerical prediction and experimental data are distinguished with increasing the flow rate. This numerical error could be contributed to the increase of flow complexity in high flow rates. Figs. 4 and 5 show the CFD prediction of collection efficiency on the cyclones of a different vortex finder diameter and shape. The CFD predicts the effect of the different vortex finder to the cyclone collection efficiency with the acceptable deviation from Lim et al. [22] experimental data. It is obvious that numerical simulation can properly adapt with pattern of experimental efficiency curve. CFD is a very useful tool to obtain details of the flow inside a cyclone. The flow field inside a cyclone is affected by vortex finder shape. Figs. 6–8 show variation of flow parameters in vicinity of the different vortex finder.

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Fig. 4. Comparisons between the experimental data with CFD results for the cyclones: (a) 7-A, 7-B, 7-C, 7-D and 11-A; (b) 15-A, 15-B, 15-C, 15-D and 15-7-A efficiency at 30 l/min.

Fig. 5. Comparisons between the experimental data with CFD results for the cyclones: (a) 7-A, 7-B, 7-C, 7-D and 11-A; (b) 15-A, 15-B, 15-C, 15-D and 15-7-A efficiency at 50 l/min.

Fig. 6 shows the velocity vectors in the vortex finder inlets of cyclones 15-B, 15-C and 15-D at different flow rates. The shape of vortex finder affects the flow pattern. The velocity vectors are influenced by the flow rates in the cyclone 15-B

for the case of 70 l/min. The velocity vector that is influenced by the cyclone inlet, is asymmetric at low flow rate, but by increasing the flow rate to 70 l/min, the velocity vectors is symmetric.

Fig. 6. Velocity vectors in the cyclone 15-B at flow rates: (a) 30 l/min; (b) 50 l/min; (c) 70 l/min.

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Fig. 7. Velocity vector at flow rate 70 l/min in the cyclones: (a) 15-B; (b) 15-C; (c) 15-D.

Velocity vector at flow rate 70 l/min for different shapes of entrance is shown in Fig. 7. This figure shows that decreasing slop of the, the vortex in the cyclone 15-B disappears. Fig. 8 shows the turbulence intensity contours in 11-A cyclone in different flow rates. The maximum turbulence intensity occurs at the flow rate 70 l/min. The contours of pressure are shown in Figs. 9 and 10. Fig. 9 presents the contours of pressure at the flow rate 70 l/min in cyclones 7-A, 7-B, 7-C and 7-D. By decreasing the vortex finder divergence angle, the low-pressure zone in the middle of cyclones expands. More particles are trapped in this zone and transported to the vortex finder outlet. Therefore, the collection efficiency is diminished. This pattern conforms to the experimental and numerical results shown in Figs. 4(a) and 5(a). This behavior is also similar to that of converging vortex finders. As indicated in Fig. 10, decreas-

ing the convergence angle leads to more slight low-pressure region and decreases the collection efficiency, as illustrated in Figs. 4(b) and 5(b). Velocity profiles are measured along the cyclone radius at three axial stations in the cyclone. The Sections 1–3 are at 30, 50 and 70 mm from bottom of cyclone, respectively. Fig. 11 presents the radial profiles of tangential velocity at three axial stations in cyclone 15-A. The tangential velocity profiles at three heights clearly show that the swirling flow inside the cyclone chamber consists of two parts, an outer free vortex and an inner solid rotation in the center. The tangential velocity distribution in the inner region is rather similar at different height. In the outer region, due to the sharp drop in velocity magnitude in the near wall region, the distribution is different. Overall, the tangential velocity distribution varies only slightly with axial positions.

Fig. 8. The turbulence intensity (%) contours in 11-A cyclone at flow rates: (a) 30 l/min; (b) 50 l/min; (c) 70 l/min.

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Fig. 9. The pressure contours (Pa) at flow rate 70 l/min in cyclone: (a) 7-A; (b) 7-B; (c) 7-C; (d) 7-D.

In order to find out why separation efficiency increases with decreasing cyclone vortex finder diameter as observed experimentally by Lim et al. [22], it is necessary to compare the flow pattern within the cyclones of different vortex finder. Tangential velocity is the dominant component of the gas flow in the cyclones, which results in the centrifugal force for particle separation. Therefore, our discussion will be focused on the tangential velocity distribution in cyclones. It is difficult to understand the cyclone separation behavior without information about the flow field. Fig. 12 compares the tangential velocity dis-

tribution at axial station of h = 70 mm in the three cyclones of 7-A, 11-A and 15-A at different flow rates. Although the tangential velocity profiles in these three cyclones have similar shape, the magnitude of the tangential velocity is different. The tangential velocity in the inner region of cyclones decreases when the cyclone vortex finder diameter is increased from 7 mm for cyclone 7-A to 15 mm for 15-A. Higher tangential velocity results in larger centrifugal force in the inner region, which in turn leads to higher separation efficiency. This explains well why the separation efficiency

Fig. 10. The pressure contours (Pa) at flow rate 70 l/min in cyclone: (a) 15-B; (b) 15-C; (c) 15-D.

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increases from cyclone 15-A to 7-A when cyclone vortex finder diameter is decreased. 7. Conclusions A numerical approach is employed to study flow in cyclones with different vortex finder. The presented numerical results for pressure drop and collection efficiency are compared with the experimental data and good agreement is obtained. The flow field parameters at the different vortex finder are numerically investigated. The contour of pressure is used to explain variation of collection efficiency with different shapes of vortex finder. The radial profiles of tangential velocity at three axial stations in different cyclones are investigated. Based on the presented results, the following conclusions may be drawn: Fig. 11. Tangential velocity distribution at different heights on a vertical plane Y = 0 in cyclone 15-A.

1. Variations of the flow rate will influence the shape of velocity vectors in the vortex finder.

Fig. 12. The tangential velocity at axial station of h = 70 mm in cyclones of 7-A, 11-A and 15-A at: (a) 30 l/min; (b) 50 l/min; (c) 70 l/min.

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2. By decreasing the vortex finder divergence angle, lowpressure zone in the middle of cyclones expands. More particles are trapped in this zone and transported to the vortex finder outlet, and the collection efficiency is decreased. In the converging vortex finders, decreasing the convergence angle decreases the pressure. 3. In a certain cyclone, the tangential velocity distribution does not vary significantly with axial stations. 4. Tangential velocity in the inner region of cyclones decreases when the cyclone vortex finder diameter is increased, and this would lead to the lower separation efficiency observed in cyclones with bigger vortex finder. References [1] C.J. Stairmand, The design and performance of cyclone separators, Trans. Inst. Chem. Eng. 29 (1951) 356–383. [2] A.C. Hoffmann, L.E. Stein, Gas Cyclones and Swirl Tubes, SpringerVerlag, Berlin, 2002. [3] D. Leith, W. Licht, The collection efficiency of cyclone type particle collectors—a new theoretical approach, AIChE Symp. Ser. 68 (126) (1972) 196–206. [4] P.W. Dietz, Collection efficiency of cyclone separators, AIChE J. 27 (6) (1981) 888–892. [5] H.S. Bryant, R.W. Silverman, F.A. Zenz, How dust in gas affects cyclone pressure drop, Hydrocarb. Process. 62 (1983) 87–90. [6] J. Dirgo, D. Leith, Performance of theoretically optimized cyclones, Filtr. Sep. 22 (1985) 199–225. [7] M.U. Bhatia, P.N. Cheremisinoff, Cyclones, in: P.N. Cheremisinoff (Ed.), Air Pollution Control and Design for Industry, Marcel Dekker, New York, 1993. [8] S.H. Rongbiao, K.W. Xiang, K.W. Park, K.W. Lee, Effects of cone dimension on cyclone performance, Aerosol Sci. 32 (2001) 549–561. [9] M. Bohnet, Cyclone separation for fine particles and difficult operating conditions, KONA Powder Part. 12 (1994) 69–76. [10] C.H. Kim, J.W. Lee, A new collection efficiency model for small cyclones considering the boundary layer effect, Aerosol Sci. 32 (2000).

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