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Abstract—Numerical analysis of flow characteristics and separation efficiency in a high-efficiency cyclone has been performed. Several models based on the experimental observation for a design purpose were proposed. However, the model is only estimated the cyclone's performance under the limited environments; it is difficult to obtain a general model for all types of cyclones. The purpose of this study is to find out the flow characteristics and separation efficiency numerically. The Reynolds stress model (RSM) was employed instead of a standard k-ε or a k-ω model which was suitable for isotropic turbulence and it could predict the pressure drop and the Rankine vortex very well. For small particles, there were three significant components (entrance of vortex finder, cone, and dust collector) for the particle separation. In the present work, the particle re-entraining phenomenon from the dust collector to the cyclone body was observed after considerable time. This re-entrainment degraded the separation efficiency and was one of the significant factors for the separation efficiency of the cyclone. Keywords—CFD, High-efficiency cyclone, Pressure drop, Rankine vortex, Reynolds stress model (RSM), Separation efficiency. I. INTRODUCTION YCOLNES, which can separate the particles from an air stream, have been widely used in many industrial processes, such as air pollution control and environmental cleaning processes due to their well adaptability to harsh conditions, simplicity to design, and low costs to operate and maintain. The cyclone designs are generally classified into straight-through, uni-flow, and reverse-flow cyclones according to the purpose in use. Among them, it is known that the use of tangential inlet and reverse-flow is the most common way for cyclone design. Because of the above mentioned many merits of cyclone, much attention have been paid on predicting the flow fields in cyclones both by experimental and numerical methods for last few decades [1-3]. The performance of a cyclone separator is generally characterized by the collection efficiency of particles and the pressure drop through the cyclone. According to the many researches, the cyclone height, diameter, and shape (i.e., cylinder or rectangular), the shape and diameter of vortex finder, and the inlet geometry can influence considerably the performance of the cyclones. Kyoungwoo Park is with the Department of Mechanical Engineering, Hoseo University, Asan 336-795, Rep. of Korea (phone:+82-41-540-5804; fax: +82-41-540-5808; e-mail: kpark@hoseo.edu). Chol Ho Hong is with the Department of System Control Engineering, Hoseo University, Asan 336-795, Rep. of Korea (e-mail: chhong@hoseo. edu). Ji Won Han is with the Department of Mechanical Engineering, Hoseo University, Asan 336-795, Rep. of Korea (e-mail: jwhan@ hoseo. edu). Byeong Sam Kim is with the Department of Automotive Engineering, Hoseo University, Asan 336-795, Rep. of Korea (e-mail: kbs@ hoseo. edu). Oh Kyung Kwon is with the KITECH, Cheonan 330-825, Rep. of Korea (e-mail: kwonok@kitech.re.kr) In 2006, [4] analyzed the influence of the shape of the cyclone cylinder on the flow characteristics and collection performance by using the commercial package, FLUENT. They observed that the long-cone cyclone has an unstable flow fields and these characteristics results in the short circulating flow at the vortex finder opening and affects adversely the particle collection efficiency. [5] evaluated the effect of vortex finder shape and diameter on cyclone performance and flow field numerically. In order to predict particles tracking in the cyclone, the Eulerian- Lagrangian procedure was used. They found that the tangential velocity and separation efficiency are decreased when the cyclone vortex finder diameter is increased. Recently, [6] studied numerically the effect of cyclone inlet dimension on the flow pattern and performance using the Reynolds stress turbulence model (RSM) for five cyclone separators. They showed that the tangential velocity in the cyclone decreases with increasing the cyclone inlet dimensions. They also found that the effect of changing the inlet width is more significant than that of the inlet height for the cut-off diameter and the optimal ratio of inlet width to height, b/a, is from 0.5 to 0.7. The interaction of gas-solid plays an important role in the flow field and performance in cyclones. There are two kinds of methods to predict it, that is, one-way and two-way coupling approaches. An one-way coupling method is base on the assumption that the presence of the particles doses not affect the flow field because the particle loading in a cyclone separator is small [7]. On the contrary, a two-way coupling effect [8] is considered the effect of the particles on the gas flow. In this model, the particle source-in cell (PSIC) model is generally used to solve the momentum equation of a particle in the two-phase flow. In the present study, the effects of the cyclone dimensions, the particle size, and the presence of dust collector on the flow characteristics and performance of the cyclone are investigated numerically. The turbulent flow is analyzed by using the Reynolds stress model (RSM) and the Eulerian-Lagrangian approach is implemented for predicting the particle motion. A one-way coupling effect, which the gas flow is not affected by the presence of the particles, is employed to estimate the gas-solid interaction. The computational model can predict the two-phase flow in cyclones accurately and provide the design concept for the presence of the dust collector. Kyoungwoo Park, Chol-Ho Hong, Ji-Won Han, Byeong-Sam Kim, Cha-Sik Park, and Oh Kyung Kwon The Effect of Cyclone Shape and Dust Collector on Gas-Solid Flow and Performance C World Academy of Science, Engineering and Technology 61 2012 252 Fig. 1 Schematics of the cyclone and its grid system II. PHYSICAL MODEL The schematic of the cyclone separator and the generated grid system considered in the present work is given in Fig. 1 and the geometrical dimensions are depicted in Table 1. As can be seen in Table 1, all dimensions are normalized by using the diameter of cyclone body (D = 290 mm). According to the cyclone’s height, it can be divided into three parts such as vortex finder (annular space), separation space and dust collection part. The inlet pipe is mounted tangentially onto the side of the cylindrical part of the cyclone body and the working fluid (gas and particles) is incoming through this section with the uniform velocity such as v in = 25 m/s. The exit tube, called the vortex finder, is fixed on the top of the cyclone. III. THEORETICAL ANALYSIS A. Governing Equations The flow in cyclones is assumed to be turbulent swirl flow with incompressible fluid and it can be reasonably predicted by the Reynolds stress model (RSM). The turbulent flow for gas can be described by the Reynolds-Average Navier-Stokes (RANS) equation and the equation of continuity for the mean motion. They are expressed in tensor notation as follows: TABLE I GEOMETRICAL DIMENSIONS FOR THE CYCLONE Dimension Values/ D (mm) Cyclone diameter (D) Gas outlet diameter (D e) Dust collector inlet diameter (D id ) Dust collector diameter (D d) Exit length (L e) Vortex finder length (S) Cylinder length (h) Cyclone length (H) Dust collector length (L d) Inlet width (a) Inlet height (b) Inlet length (l) 1.0D (290 mm) 0.5D (145 mm) 3/8D (108 mm) 1.0D (290 mm) 2.0D (580 mm) 0.5D (1245mm) 0.5D (145 mm) 4.0D (1160 mm) 1.7D (493 mm) 0.2D (58 mm) 0.5D (145 mm) 1.0D (290 mm) ( ) 0 i i U x ? = ? (1) ( ) ( ) 2 1 i i i j i j j i i j j U U P U U u u t x x x x x n r ? ? ? ? ? ￠ ￠ + = - + - ? ? ? ? ? ? (2) Where i U is the mean velocity, i x the coordinate system, t the time, P the mean pressure, r the gas density, and n the kinematic viscosity. i j u u ￠ ￠ (= ij R ) represents the Reynolds stress tensor and i i i u u U ￠ = - is the i-th fluid fluctuation velocity component. As shown in Eq.(2), the Reynolds stresses should be modeled using various assumptions. In the present work, the Reynolds stress terms are directly calculated by RSTM. B. Turbulent Modeling The accurate prediction of a strong turbulent swirl flow is generally dependent on the turbulent model used. In the present work, the Reynolds stress turbulent model (RSTM) which solves the individual Reynolds stress term ( i j u u ￠ ￠ - ) by using differential transport equations is used. The transport equations of Reynolds stresses can be written as ( ) ( ) i j k i j ij ij ij ij k u u U u u D P E t x P ? ? ￠ ￠ ￠ ￠ + = + + + ? ? (3) Where the individual terms in the right hand side stand for stress diffusion, stress production, pressure strain, and dissipation terms, respectively, and defined as follows; ( ) t ij i j k k k D u u x x n s ? ? ? ? ￠ ￠ = ? ? ? ? ? ? (4) 1 , 2 j i ij i k j k ij k k U U P u u u u P P x x ? ? ? ? ￠ ￠ ￠ ￠ = - + = ? ? ? ? ? ? (5) 1 2 2 2 3 3 ij i k ij ij ij C u u k C P P k e P d d ? ? ? ? ? ? ￠ ￠ = - - + - ? ? ? ? ? ? ? ? ? ? ? ? (6) 2 3 ij ij E d e = - (7) Here t n is the turbulent viscosity, P the fluctuation kinetic energy production, k the turbulent kinetic energy ( (1/ 2) i j u u ￠ ￠ = ), and e the dissipation rate of k, respectively. The empirical constants are 1 k s = , 1 1.8 C = , and 2 0.6 C = [9]. The transport equation for the turbulent dissipation rate ( e ) is expressed as ( ) 2 1 2 t i j i j j j j j U U C u u C t x x x k x k e e e n e e e e e n s ? ? ? ? ? ? ? ? ? ￠ ￠ + = + - - ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? (8) The values of constants are 1.3 e s = , 1 1.44 C e = and 2 1.92 C e = . C. Particle Motion Equations The basic assumptions employed in the present work to model the particle motion are as follows; the solid (particle) has a fully spherical shape and disperses dilutely in the gas phase so that the gas-solid interactions and the influence of the dispersed particle volume fraction on the gas phase are negligibly small. Exit (Vortex finder) Dust collector Inlet D S h H L e L d a b L i D e D id D d D e World Academy of Science, Engineering and Technology 61 2012 253 Generally, the particle loading in a cyclone is small (3 - 5%), and therefore, it can be assumed that the presence of the particles does not affect the flow field (i.e., one-way coupling). Additionally, collisions between particles and the walls of the cyclone are assumed to be perfectly elastic and the interaction between particles is neglected because of dilute flow. In order to simulate the particle motion in the cyclone, the discrete phase model (DPM) was used by defining the initial position, velocity and size of individual particles. The trajectory of particles was obtained by integrating the force balance on the particle. The equation of motion of a small particle, which is included the effects of nonlinear drag and gravitational forces, in terms of the Eulerian-Lagrangian approach is given by [10]. ( ) , , 2 18 Re 1 24 p i D r i p i i p p p du C u u g dt d m r r r ? ? = - +