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Study on the cut size of a turbo air classifier
Powder Technology 237 (2013) 520–528
Contents lists available at SciVerse ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
Study on the cut size of a turbo air classifier Liping Gao a, Yuan Yu b, Jiaxiang Liu a,⁎ a b
College of Materials Science and Engineering, Beijing University of Chemical Technology, Beijing 100029, China College of Mechanical and Electrical Engineering Beijing University of Chemical Technology, Beijing 100029, China
a r t i c l e
i n f o
Article history: Received 7 May 2012 Received in revised form 14 December 2012 Accepted 20 December 2012 Available online 28 December 2012 Keywords: Turbo air classifier Cut size Discrete phase model Particle trajectory Numerical simulation
a b s t r a c t Cut size is regarded as an important indicator for evaluating the classification performance of turbo air classifiers. However, traditional methods of cut size calculation by theoretical analysis have some deviations. In this paper, a new strategy was introduced to determine the cut size using the FLUENT discrete phase model (DPM) coupled with material experiments. The simulation results revealed that: the closer the feeding point position approached the inner edge of annular region, the shorter the time the particle moved into the area between the two neighboring blades of the rotor. The same small diameter particles which were fed at three different positions in annular region could all enter into the area between the two neighboring blades of the rotor, and ultimately were discharged by the fine powder outlet. When air inlet velocity was 8 m/s, rotor cage rotary speed was 800 r/min, the cut size of talcum powder could be calculated as 30–40 μm, and the cut size of quartz sand powder could be calculated as 40–50 μm. When rotor cage rotary speed was 1200 r/min, the cut size of talcum powder could be calculated as 20–30 μm, and the cut size of quartz sand powder could be calculated as 30–40 μm. The contrastive experiments of material classification were in good agreement with simulation results. Simulation method provides a new method to determine the cut size of a turbo air classifier, as well as provides a reference method to study the cut size of various types of classifier. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The dynamic classification of ultra-fines with a certain particle size distribution has been a subject of great interest over the past decade due to the potential applications in various industries, including chemical engineering, mining, and industrial pharmacy. As one of the most important indicators to evaluate the classification effect, the cut size of classifiers draws considerable concern. To date, a number of methods have been developed to calculate cut size in theory [1,2]. Different size particles have different moments of inertia and withstand different forces from air in gas–solid flows. Based on this phenomenon, different particle sizes in the turbo air classifier can be effectively separated from one another. Cut size d50 is usually defined as the diameter of a spherical particle for which the inertial centrifugal force offsets the radial viscous force, keeping a serial movement on a certain cylinder theoretically. Liu et al. conducted particle force analysis in turbo air classifiers and calculated the cut size of turbo air classifiers using the following equation [3]: 2
2
d50 ¼ 3C D ρa Rvr =4vθ ρP
ð1Þ
Where CD is the drag coefficient, R is the external semidiameter of the rotor cage, vr is the radial velocity of airflow, vθ is the tangential ⁎ Corresponding author. Tel./fax: +86 10 64446432. E-mail address: [email protected] (J. Liu). 0032-5910/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.powtec.2012.12.043
velocity of airflow, ρa is the density of airflow and ρP is the density of particles. Based on a systematic analysis of calculation formulas obtained under different assumptions for finding the cut size of turbo air classifiers, Liu et al. [2] obtained a simplified equation as follows: d50 ¼ k
Qε nδ
ð2Þ
where Q is airflow rate and n is rotor cage rotary speed, ε, δ, and k are the parameters related to the property of materials, the temperature, humidity, and pressure of air, and the structure of classifiers. However, these methods suffer from a serious deficiency: the theoretical results deviate from the actual values. Zhang et al. [4] showed that theoretical values of d50 are larger than the actual ones under different rotor cage rotary speeds. They said that maybe the theoretical air flow is greater than the actual air flow. Literature [5] showed that rotor cage rotary speed played an important part on d50. The deviation of d50 increased to 42.5% when Q was 500 m3/min and rotor cage rotary speed decreased to 165 r/min from 265 r/min. In view of this shortcoming, new methods with sufficient accuracy and precision are highly desirable to determine the cut size of classifiers. Computational Fluid Dynamics (CFD) technology has become a promising tool to solve complex flow problems [6–9]. For example, FLUENT, the dedicated CFD software for fluid flow problems in complex geometric regions has been widely used in analyzing flow field characteristics
L. Gao et al. / Powder Technology 237 (2013) 520–528
521
Fine powder outlet
Guide blade
Rotor cage blade
Annular region Air inlet
Volute
Cone Coarse powder outlet Fig. 1. Schematic diagram of the turbo air classifier.
and particle trajectories [10–13]. In the present study, a novel, convenient, and accurate strategy for calculating the cut size of classifiers was developed using a FLUENT-based simulation of particle trajectories in turbo air classifiers. The proposed strategy was the first example using the simulation of particle trajectories to determine cut size. Simulation and material experimental results revealed that the developed method held great potential as a convenient and precise platform for determining the cut size of classifiers. 2. Model descriptions The schematic diagram of the turbo air classifier used in the present study is shown in Fig. 1. The main geometric dimensions of
the classifier are as follows: (1) the outer and inner semidiameters of the rotor cage are 106 and 76 mm respectively; 24 blades are radially installed and evenly distributed across the circumference of the rotor cage; (2) the air inlet is 95 mm in height and 62 mm in width; and (3) 24 guide blades (95 × 30 × 3 mm) are distributed uniformly along the circumference of a circle with a radius of 136 mm. The discrete phase model (DPM) used by FLUENT requires the discrete phase to be present at a fairly low volume fraction, usually less than 10%–12%. Particle volume fraction in the turbo air classifier was measured about 0.039% at a feed rate of 35 kg/h, air inlet velocity of 8 m/s, talcum powder material density of 2800 kg/m 3, and quartz sand powder material density of 2650 kg/·m 3, meeting the requirement of DPM. Thus, particle trajectories in the turbo air classifier
c—125mm b—120mm a—115mm
Fig. 2. Trajectories of 20 μm talcum particle.
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L. Gao et al. / Powder Technology 237 (2013) 520–528
could be calculated using DPM by simulating the continuous phase flow field at first. 2.1. Continuous phase governing equations Flows within the turbo air classifier are usually turbulence of moderate strength. The present study utilized the RNG k–ε turbulence
model, which is mostly used for the treatment of strong swirling flows or high-strain rate flows, to accurately describe the flow field in turbo air classifiers [14–16]. The governing equations of the RNG k-ε model for incompressible turbulent flow are written as follows: ∂ ∂ ∂ ðρkui Þ ¼ ðρkÞ þ ∂t ∂xi ∂xj
α k μ eff
∂k ∂xj
! þ Gk þ Gb −ρε þ Sk
ð3Þ
Fig. 3. Trajectories of 30 μm talcum particle (a) Feed particle at a point in the annulus; (b) Feed particle at b point in the annulus; and (c) Feed particle at c point in the annulus.
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523
Fig. 3 (continued).
∂ ∂ ∂ ðρεui Þ ¼ ðρε Þ þ ∂t ∂xi ∂xj
α ε μ eff
∂ε ∂xj
!
ε ε2 þ c1 ðGk þ c3 Gb Þ−c2 ρ −Rε þ Sε : k k
ð4Þ
In these equations, Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients, Gb is the generation of turbulence kinetic energy due to buoyancy, αk and αε are the inverse
effective Prandtl numbers for k and ε respectively, Sk and Sε are the user-defined source terms for k and ε respectively, and Rε is defined as 3 C μ ρη 1−η=η0 ε2 Rε ¼ k 1 þ βη3
ð5Þ
where η = Sk/ε, η0 = 4.38, β = 0.012, Cμ = 0.0845 and S is the modulus of the mean rate-of-strain tensor.
10µm 20µm 30µm
Fig. 4. Particle trajectories of different talcum particle sizes fed at b point.
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2.2. Discrete phase governing equations
FD ¼
Through the DPM of FLUENT, the trajectory of a discrete phase particle can be calculated in a Lagrangian reference frame by integrating the force balance on the particle. This force balance equation can be written in Cartesian coordinates: g x ρp −ρ ¼ F D ν−νp þ þ Fx ρp dt
dup
ð6Þ
18μ C D Re ρp d2p 24
ð7Þ
where FD (ν − νp) is the drag force per unit particle mass, ν is the fluid phase velocity, νp is the particle velocity, μ is the kinematic viscosity of fluids, ρ is the fluid density, ρp is the particle density, dp is the particle diameter, Re is the relative Reynolds number, CD is the drag coefficient, and Fx is an additional acceleration (force/unit particle mass) term.
Fig. 5. Particle trajectories of different talcum particle sizes fed at b point (a) d = 30 μm; and (b) d = 40 μm.
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2.3. Boundary conditions
525
cut size of turbo air classifiers can be calculated as 20–30 μm when particles are fed at b point in the annular region.
Assumptions and settings were made as follows: (1) The fluid was incompressible [17]. (2) The rotor cage area was the kinematical frame of reference in a rotating coordinate system. (3) Pressure–velocity coupling was provided by the SIMPLEC method. (4) The non-equilibrium wall function was used for near-wall treatments while the second-order upwind scheme was used for discretization. (5) The air inlet was defined in FLUENT as an air inlet velocity of 8 m/s. The rotor cage rotary speeds were set as 800 r/min and 1200 r/min. The outlet was defined as a pressure outlet. (6) Heat/mass transfer of particles was ignored when performing discrete phase calculation. (7) Talcum particles with a density of 2800 kg/m3 and quartz sand particles with a density of 2650 kg/m 3 were fed from different points of the classifiers' main separating ribbon, the annular region, 115 mm, 120 mm, and 125 mm radial distances away from the axis, while assuming the radial velocity of the fluid at the feeding point to be the particles' initial radial velocity, and the tangential velocity of the fluid at the feeding point to be the initial tangential velocity. (8) Collision between particles and walls was considered to be a case of a fully elastic collision with an elastic coefficient of 1 and equal amounts of incident/reflected angles.
3. Calculation results and experimental analysis of talcum material 3.1. Talcum particle trajectories in the annular region 3.1.1. Particle trajectories when the ratio of air inlet velocity and rotor cage rotary speed is 8–1200 Particle in the annulus not only has the trend of a rotary movement under the flow viscous force, but also has the inertia of a linear motion along the radial. In the trajectory of particle distribution diagrams, different colors represent different particle residence times. As seen in Fig. 2, when the particle size is 20 μm, particles are fed at three different positions of annular region, and all particles can enter into the area between neighboring blades of the rotor. The running time is different when the feeding position is different. In contrast three feeding positions, a, b, c feeding at a point use the shortest time. Small diameter particles with small inertia force can be taken out of the fine powder outlet. While large diameter particles moved outside the annular region, spiral down, and eventually are gathered into the coarse powder-collecting cone at the base. As seen in Fig. 3, when the particle size is 30 μm, all particles cannot enter into the area between neighboring blades of the rotor and spiral down in the annular region when particles are fed at three different positions of annular region. In an ideal classification system, particles with a diameter of cut size d50 have the same probability of going into the fine and the coarse particles, whereas particles with a diameter less or larger than d50 should have full access to the fine or the coarse particles, respectively. Particles with different diameters have different trajectories. As shown in Fig. 4, when different size particles are fed at b point, small diameter particles are carried inside the rotor cage together with the air flow, collide with the auxiliary blade through the rotor, and finally are taken out of the fine powder outlet. Meanwhile, large diameter particles move outside the annular region. Simulation results reveal that particles with diameter less than 20 μm fully come into the fine powder outlet, whereas particles with a diameter larger than 30 μm completely come into the coarse powder outlet. Thus, the
3.1.2. Particle trajectories when the ratio of air inlet velocity and rotor cage rotary speed is 8–800 Fig. 5 shows talcum powder particle trajectories of different size which are fed at b point in the annular region. When the particle size is 30 μm, particles quickly enter into the area between neighboring blades of the rotor under the joint action of the centrifugal force and air drag force. The centrifugal force of particle is greater than the air drag force when the particle size is 40 μm, so the particle cannot enter into the area between neighboring blades of the rotor, spiral in the annular region. Through the above analysis, the cut size of turbo air classifier can be calculated as 30–40 μm. 3.2. Talcum powder material experiments Material experiment were conducted at the rotor cage rotary speeds of 800 r/min and 1200 r/min when the air inlet velocity is 8 m/s and the feeding speed is 35 kg/m 3. Talcum powder's density is 2800 kg/m 3. The obtained Tromp curve of the turbo air classifier is shown in Fig. 6. In the actual classification process, the cut size d50 is defined as the diameter of a particle whose partial classification efficiency is 50%. As shown in Fig. 6, the cut size d50 obtained by material experiments is around 37 μm when the rotor cage rotary speed is 800 r/min, and the cut size d50 is around 25 μm when rotor cage rotary speed is 1200 r/min. Comparing the experiment and simulation results, the cut sizes calculated are closer to the actual cut size. Moreover, the reliability of the cut size of the air turbo classifier obtained by numerical simulation is verified. 4. Calculation results and experimental analysis of quartz sand material Quartz sand particle trajectories are shown in Fig. 7 when the ratio of air inlet velocity and rotor cage rotary speed is 8–1200. Quartz sand particle trajectories are shown in Fig. 8 when the ratio of air inlet velocity and rotor cage rotary speed is 8–800. Figs. 7 and 8 are similar to Fig. 5. When different size of quartz sand particles are fed at the same point, smaller diameter particles move along the inner edge of the annular region, and enter into the area between neighboring blades of the rotor. Meanwhile, larger diameter particles move outside the annular region, spiral down, and are gathered into the coarse powder-collecting cone at the base.
Fig. 6. Tromp curve of talcum powder material in air turbo classifier.
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L. Gao et al. / Powder Technology 237 (2013) 520–528
As seen in Figs. 7 and 8, when the ratio of air inlet velocity and rotor cage rotary speed is 8–1200, the cut size can be calculated as 30–40 μm. When the ratio of air inlet velocity and rotor cage rotary speed is 8–800, the cut size can be calculated as 40–50 μm. Quartz sand was selected as experimental material, and its density is 2650 kg/m 3. The experiment were conducted at the rotor cage rotary speed of 800 r/min and 1200 r/min, at an air inlet velocity of
8 m/s, and at the feeding speed of 35 kg/h. Table 1 is the comparison of quartz sand cutting size obtained at different rotor cage rotary speeds. It can be seen from Table 1, the cut sizes of quartz sand obtained through experiment are in the scope of simulation results, which verify the reliability of the cut size of turbo air classifier obtained by numerical simulation.
Fig. 7. Particle trajectories of different quartz sand particle sizes fed at b point (a) d = 30 μm; and (b) d = 40 μm.
L. Gao et al. / Powder Technology 237 (2013) 520–528
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Fig. 8. Particle trajectories of different quartz sand particle sizes fed at b point (a) d = 40 μm; and (b) d = 50 μm.
5. Conclusions In summary, the present study proposed a novel method for cut size determination based on simulation via FLUENT and validation through material experiments. Compared with traditional methods, the proposed strategy can be very accurately and easily performed. Furthermore, several conclusions can be obtained as follows:
(1) By establishing a model, we observed the trajectories of the particles in a turbo air classifier. The trajectories were different when different size particles were fed at the same position. Smaller diameter particles moved into the annular region, larger diameter particles rotated in the annular region, and eventually were gathered into the coarse powder-collecting cone at the base.
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Table 1 Comparison of quartz sand cutting size obtained at different rotor cage rotary speeds. The ratio of air inlet velocity and rotor cage rotary speed (m/s–r/min)
Cut size (μm)
8–800 8–1200
47 32
(2) Simulation results showed: when the air inlet velocity was 8 m/s, rotor cage rotary speed was 800 r/min, the cut size of talcum powder material could be calculated as 30–40 μm, and the cut size of quartz sand material could be calculated as 40–50 μm. When rotor cage rotary speed was 1200 r/min, the cut size of talcum powder material could be calculated as 20–30 μm, and the cut size of quartz sand material could be calculated as 30–40 μm. (3) The material experiment was done to verify the simulation results. The simulation method provides a new method to determine the cut size of a turbo air classifier, as well as provides a reference method to study the cut size of various types of classifier. Acknowledgments This project was supported financially by the National Natural Science Foundation of China (no. 51074012). References [1] Tao Ye, Xu. Ning, Zhichu Huang, et al., Experimental investigation on classified particles cut size of turbo air classifier, Mining & Processing Equipment 34 (2006) 62–63. [2] Shengzhao Liu, Jiaxiang Liu, Lijie Guo, Study on theoretical cut size of turbo air classifier, Non-Ferrous Mining and Metallurgy 22 (2006) 138–140.
[3] Jiaxiang Liu, Jingbo Xia, Tingshu He, Air flow field characteristics analyzing and classification process of the turbo classifier, Journal of the Chinese Ceramic Society 31 (2003) 485–489. [4] Yifei Zhang, Wu. Tieming, Study on the critical grading size of pulverizer with vertical axes, Food and Machinery 5 (1999) 40–41. [5] Youlin Zhang, Xuan Wang, Guohua Li, et al., Calculation and analysis of classified particles cut size in O-Sepa classifier, Cement Guide for New Epoch 4 (1998) 29–31. [6] E. Heinl, M. Bohnet, Calculation of particle-wall adhesion in horizontal gas-solids flow using CFD, Powder Technology 159 (2005) 95–104. [7] Rodrigo J.G. Lopes, Rosa M. Quinta-Ferreira, CFD modelling of multiphase flow distribution in trickle beds, Chemical Engineering Journal 147 (2009) 342–355. [8] R. Vuthaluru, H.B. Vuthaluru, Modelling of a wall fired furnace for different operating conditions using FLUENT, Fuel Processing Technology 87 (2006) 633–639. [9] J. Schmidt, J. Werther, Simulation and optimization of a centrifugal fluidized bed classifier in the micrometer range, Chemical Engineering and Processing 45 (2006) 488–499. [10] A. Mainza, M. Narasimha, M.S. Powell, et al., Study of flow behaviour in a three-product cyclone using computational fluid dynamics, Minerals Engineering 19 (2006) 1048–1058. [11] Shuangyue Li, Hong Li, Chaofu Ren, Jiguang Liu, Jinchun Li, Research on flow-guided characteristics of plane vortex classifier based on FLUENT, China Powder Science and Technology 1 (2008) 20–23. [12] Qingliang Yang, Jiaxiang Liu, Analysis of flow field in turbo air classifier and improvement of rotor cage structure, Chemical Engineering (China) 38 (2010) 79–83. [13] Du. Yanchen, Yulin Wang, Study to motion track of particle in vortex classifier, Mining & Processing Equipment 35 (2007) 84–87. [14] Hongfei Zhang, Hongsong Cao, Handong Zhao, Jizhi Zhu, The choice of turbulence model in numerical simulation, Journal of Projectiles, Rockets, Missiles and Guidance 26 (2006) 242–244. [15] Qingguang Chen, Xu Zhong, Yongjian Zhang, Application of RNG κ–ε models in numerical simulations of engineering turbulent flows, Chinese Quarterly of Mechanics 24 (2003) 88–95. [16] Jiangyun Wang, Yu Mao, Meili Liu, Juan Wang, Numerical simulation of strongly swirling flow in cyclone separator by using an advanced RNG κ–ε model, Acta Petrolei Sinica (Petroleum Processing Section) 26 (2010) 8–13. [17] Qingliang Yang, Jiaxiang Liu, Numerical simulation and measurement of three-dimensional flow field in turbo air classifier, Chemical Engineering (China) 37 (2009) 24–27.
Contents lists available at SciVerse ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
Study on the cut size of a turbo air classifier Liping Gao a, Yuan Yu b, Jiaxiang Liu a,⁎ a b
College of Materials Science and Engineering, Beijing University of Chemical Technology, Beijing 100029, China College of Mechanical and Electrical Engineering Beijing University of Chemical Technology, Beijing 100029, China
a r t i c l e
i n f o
Article history: Received 7 May 2012 Received in revised form 14 December 2012 Accepted 20 December 2012 Available online 28 December 2012 Keywords: Turbo air classifier Cut size Discrete phase model Particle trajectory Numerical simulation
a b s t r a c t Cut size is regarded as an important indicator for evaluating the classification performance of turbo air classifiers. However, traditional methods of cut size calculation by theoretical analysis have some deviations. In this paper, a new strategy was introduced to determine the cut size using the FLUENT discrete phase model (DPM) coupled with material experiments. The simulation results revealed that: the closer the feeding point position approached the inner edge of annular region, the shorter the time the particle moved into the area between the two neighboring blades of the rotor. The same small diameter particles which were fed at three different positions in annular region could all enter into the area between the two neighboring blades of the rotor, and ultimately were discharged by the fine powder outlet. When air inlet velocity was 8 m/s, rotor cage rotary speed was 800 r/min, the cut size of talcum powder could be calculated as 30–40 μm, and the cut size of quartz sand powder could be calculated as 40–50 μm. When rotor cage rotary speed was 1200 r/min, the cut size of talcum powder could be calculated as 20–30 μm, and the cut size of quartz sand powder could be calculated as 30–40 μm. The contrastive experiments of material classification were in good agreement with simulation results. Simulation method provides a new method to determine the cut size of a turbo air classifier, as well as provides a reference method to study the cut size of various types of classifier. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The dynamic classification of ultra-fines with a certain particle size distribution has been a subject of great interest over the past decade due to the potential applications in various industries, including chemical engineering, mining, and industrial pharmacy. As one of the most important indicators to evaluate the classification effect, the cut size of classifiers draws considerable concern. To date, a number of methods have been developed to calculate cut size in theory [1,2]. Different size particles have different moments of inertia and withstand different forces from air in gas–solid flows. Based on this phenomenon, different particle sizes in the turbo air classifier can be effectively separated from one another. Cut size d50 is usually defined as the diameter of a spherical particle for which the inertial centrifugal force offsets the radial viscous force, keeping a serial movement on a certain cylinder theoretically. Liu et al. conducted particle force analysis in turbo air classifiers and calculated the cut size of turbo air classifiers using the following equation [3]: 2
2
d50 ¼ 3C D ρa Rvr =4vθ ρP
ð1Þ
Where CD is the drag coefficient, R is the external semidiameter of the rotor cage, vr is the radial velocity of airflow, vθ is the tangential ⁎ Corresponding author. Tel./fax: +86 10 64446432. E-mail address: [email protected] (J. Liu). 0032-5910/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.powtec.2012.12.043
velocity of airflow, ρa is the density of airflow and ρP is the density of particles. Based on a systematic analysis of calculation formulas obtained under different assumptions for finding the cut size of turbo air classifiers, Liu et al. [2] obtained a simplified equation as follows: d50 ¼ k
Qε nδ
ð2Þ
where Q is airflow rate and n is rotor cage rotary speed, ε, δ, and k are the parameters related to the property of materials, the temperature, humidity, and pressure of air, and the structure of classifiers. However, these methods suffer from a serious deficiency: the theoretical results deviate from the actual values. Zhang et al. [4] showed that theoretical values of d50 are larger than the actual ones under different rotor cage rotary speeds. They said that maybe the theoretical air flow is greater than the actual air flow. Literature [5] showed that rotor cage rotary speed played an important part on d50. The deviation of d50 increased to 42.5% when Q was 500 m3/min and rotor cage rotary speed decreased to 165 r/min from 265 r/min. In view of this shortcoming, new methods with sufficient accuracy and precision are highly desirable to determine the cut size of classifiers. Computational Fluid Dynamics (CFD) technology has become a promising tool to solve complex flow problems [6–9]. For example, FLUENT, the dedicated CFD software for fluid flow problems in complex geometric regions has been widely used in analyzing flow field characteristics
L. Gao et al. / Powder Technology 237 (2013) 520–528
521
Fine powder outlet
Guide blade
Rotor cage blade
Annular region Air inlet
Volute
Cone Coarse powder outlet Fig. 1. Schematic diagram of the turbo air classifier.
and particle trajectories [10–13]. In the present study, a novel, convenient, and accurate strategy for calculating the cut size of classifiers was developed using a FLUENT-based simulation of particle trajectories in turbo air classifiers. The proposed strategy was the first example using the simulation of particle trajectories to determine cut size. Simulation and material experimental results revealed that the developed method held great potential as a convenient and precise platform for determining the cut size of classifiers. 2. Model descriptions The schematic diagram of the turbo air classifier used in the present study is shown in Fig. 1. The main geometric dimensions of
the classifier are as follows: (1) the outer and inner semidiameters of the rotor cage are 106 and 76 mm respectively; 24 blades are radially installed and evenly distributed across the circumference of the rotor cage; (2) the air inlet is 95 mm in height and 62 mm in width; and (3) 24 guide blades (95 × 30 × 3 mm) are distributed uniformly along the circumference of a circle with a radius of 136 mm. The discrete phase model (DPM) used by FLUENT requires the discrete phase to be present at a fairly low volume fraction, usually less than 10%–12%. Particle volume fraction in the turbo air classifier was measured about 0.039% at a feed rate of 35 kg/h, air inlet velocity of 8 m/s, talcum powder material density of 2800 kg/m 3, and quartz sand powder material density of 2650 kg/·m 3, meeting the requirement of DPM. Thus, particle trajectories in the turbo air classifier
c—125mm b—120mm a—115mm
Fig. 2. Trajectories of 20 μm talcum particle.
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L. Gao et al. / Powder Technology 237 (2013) 520–528
could be calculated using DPM by simulating the continuous phase flow field at first. 2.1. Continuous phase governing equations Flows within the turbo air classifier are usually turbulence of moderate strength. The present study utilized the RNG k–ε turbulence
model, which is mostly used for the treatment of strong swirling flows or high-strain rate flows, to accurately describe the flow field in turbo air classifiers [14–16]. The governing equations of the RNG k-ε model for incompressible turbulent flow are written as follows: ∂ ∂ ∂ ðρkui Þ ¼ ðρkÞ þ ∂t ∂xi ∂xj
α k μ eff
∂k ∂xj
! þ Gk þ Gb −ρε þ Sk
ð3Þ
Fig. 3. Trajectories of 30 μm talcum particle (a) Feed particle at a point in the annulus; (b) Feed particle at b point in the annulus; and (c) Feed particle at c point in the annulus.
L. Gao et al. / Powder Technology 237 (2013) 520–528
523
Fig. 3 (continued).
∂ ∂ ∂ ðρεui Þ ¼ ðρε Þ þ ∂t ∂xi ∂xj
α ε μ eff
∂ε ∂xj
!
ε ε2 þ c1 ðGk þ c3 Gb Þ−c2 ρ −Rε þ Sε : k k
ð4Þ
In these equations, Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients, Gb is the generation of turbulence kinetic energy due to buoyancy, αk and αε are the inverse
effective Prandtl numbers for k and ε respectively, Sk and Sε are the user-defined source terms for k and ε respectively, and Rε is defined as 3 C μ ρη 1−η=η0 ε2 Rε ¼ k 1 þ βη3
ð5Þ
where η = Sk/ε, η0 = 4.38, β = 0.012, Cμ = 0.0845 and S is the modulus of the mean rate-of-strain tensor.
10µm 20µm 30µm
Fig. 4. Particle trajectories of different talcum particle sizes fed at b point.
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2.2. Discrete phase governing equations
FD ¼
Through the DPM of FLUENT, the trajectory of a discrete phase particle can be calculated in a Lagrangian reference frame by integrating the force balance on the particle. This force balance equation can be written in Cartesian coordinates: g x ρp −ρ ¼ F D ν−νp þ þ Fx ρp dt
dup
ð6Þ
18μ C D Re ρp d2p 24
ð7Þ
where FD (ν − νp) is the drag force per unit particle mass, ν is the fluid phase velocity, νp is the particle velocity, μ is the kinematic viscosity of fluids, ρ is the fluid density, ρp is the particle density, dp is the particle diameter, Re is the relative Reynolds number, CD is the drag coefficient, and Fx is an additional acceleration (force/unit particle mass) term.
Fig. 5. Particle trajectories of different talcum particle sizes fed at b point (a) d = 30 μm; and (b) d = 40 μm.
L. Gao et al. / Powder Technology 237 (2013) 520–528
2.3. Boundary conditions
525
cut size of turbo air classifiers can be calculated as 20–30 μm when particles are fed at b point in the annular region.
Assumptions and settings were made as follows: (1) The fluid was incompressible [17]. (2) The rotor cage area was the kinematical frame of reference in a rotating coordinate system. (3) Pressure–velocity coupling was provided by the SIMPLEC method. (4) The non-equilibrium wall function was used for near-wall treatments while the second-order upwind scheme was used for discretization. (5) The air inlet was defined in FLUENT as an air inlet velocity of 8 m/s. The rotor cage rotary speeds were set as 800 r/min and 1200 r/min. The outlet was defined as a pressure outlet. (6) Heat/mass transfer of particles was ignored when performing discrete phase calculation. (7) Talcum particles with a density of 2800 kg/m3 and quartz sand particles with a density of 2650 kg/m 3 were fed from different points of the classifiers' main separating ribbon, the annular region, 115 mm, 120 mm, and 125 mm radial distances away from the axis, while assuming the radial velocity of the fluid at the feeding point to be the particles' initial radial velocity, and the tangential velocity of the fluid at the feeding point to be the initial tangential velocity. (8) Collision between particles and walls was considered to be a case of a fully elastic collision with an elastic coefficient of 1 and equal amounts of incident/reflected angles.
3. Calculation results and experimental analysis of talcum material 3.1. Talcum particle trajectories in the annular region 3.1.1. Particle trajectories when the ratio of air inlet velocity and rotor cage rotary speed is 8–1200 Particle in the annulus not only has the trend of a rotary movement under the flow viscous force, but also has the inertia of a linear motion along the radial. In the trajectory of particle distribution diagrams, different colors represent different particle residence times. As seen in Fig. 2, when the particle size is 20 μm, particles are fed at three different positions of annular region, and all particles can enter into the area between neighboring blades of the rotor. The running time is different when the feeding position is different. In contrast three feeding positions, a, b, c feeding at a point use the shortest time. Small diameter particles with small inertia force can be taken out of the fine powder outlet. While large diameter particles moved outside the annular region, spiral down, and eventually are gathered into the coarse powder-collecting cone at the base. As seen in Fig. 3, when the particle size is 30 μm, all particles cannot enter into the area between neighboring blades of the rotor and spiral down in the annular region when particles are fed at three different positions of annular region. In an ideal classification system, particles with a diameter of cut size d50 have the same probability of going into the fine and the coarse particles, whereas particles with a diameter less or larger than d50 should have full access to the fine or the coarse particles, respectively. Particles with different diameters have different trajectories. As shown in Fig. 4, when different size particles are fed at b point, small diameter particles are carried inside the rotor cage together with the air flow, collide with the auxiliary blade through the rotor, and finally are taken out of the fine powder outlet. Meanwhile, large diameter particles move outside the annular region. Simulation results reveal that particles with diameter less than 20 μm fully come into the fine powder outlet, whereas particles with a diameter larger than 30 μm completely come into the coarse powder outlet. Thus, the
3.1.2. Particle trajectories when the ratio of air inlet velocity and rotor cage rotary speed is 8–800 Fig. 5 shows talcum powder particle trajectories of different size which are fed at b point in the annular region. When the particle size is 30 μm, particles quickly enter into the area between neighboring blades of the rotor under the joint action of the centrifugal force and air drag force. The centrifugal force of particle is greater than the air drag force when the particle size is 40 μm, so the particle cannot enter into the area between neighboring blades of the rotor, spiral in the annular region. Through the above analysis, the cut size of turbo air classifier can be calculated as 30–40 μm. 3.2. Talcum powder material experiments Material experiment were conducted at the rotor cage rotary speeds of 800 r/min and 1200 r/min when the air inlet velocity is 8 m/s and the feeding speed is 35 kg/m 3. Talcum powder's density is 2800 kg/m 3. The obtained Tromp curve of the turbo air classifier is shown in Fig. 6. In the actual classification process, the cut size d50 is defined as the diameter of a particle whose partial classification efficiency is 50%. As shown in Fig. 6, the cut size d50 obtained by material experiments is around 37 μm when the rotor cage rotary speed is 800 r/min, and the cut size d50 is around 25 μm when rotor cage rotary speed is 1200 r/min. Comparing the experiment and simulation results, the cut sizes calculated are closer to the actual cut size. Moreover, the reliability of the cut size of the air turbo classifier obtained by numerical simulation is verified. 4. Calculation results and experimental analysis of quartz sand material Quartz sand particle trajectories are shown in Fig. 7 when the ratio of air inlet velocity and rotor cage rotary speed is 8–1200. Quartz sand particle trajectories are shown in Fig. 8 when the ratio of air inlet velocity and rotor cage rotary speed is 8–800. Figs. 7 and 8 are similar to Fig. 5. When different size of quartz sand particles are fed at the same point, smaller diameter particles move along the inner edge of the annular region, and enter into the area between neighboring blades of the rotor. Meanwhile, larger diameter particles move outside the annular region, spiral down, and are gathered into the coarse powder-collecting cone at the base.
Fig. 6. Tromp curve of talcum powder material in air turbo classifier.
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As seen in Figs. 7 and 8, when the ratio of air inlet velocity and rotor cage rotary speed is 8–1200, the cut size can be calculated as 30–40 μm. When the ratio of air inlet velocity and rotor cage rotary speed is 8–800, the cut size can be calculated as 40–50 μm. Quartz sand was selected as experimental material, and its density is 2650 kg/m 3. The experiment were conducted at the rotor cage rotary speed of 800 r/min and 1200 r/min, at an air inlet velocity of
8 m/s, and at the feeding speed of 35 kg/h. Table 1 is the comparison of quartz sand cutting size obtained at different rotor cage rotary speeds. It can be seen from Table 1, the cut sizes of quartz sand obtained through experiment are in the scope of simulation results, which verify the reliability of the cut size of turbo air classifier obtained by numerical simulation.
Fig. 7. Particle trajectories of different quartz sand particle sizes fed at b point (a) d = 30 μm; and (b) d = 40 μm.
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Fig. 8. Particle trajectories of different quartz sand particle sizes fed at b point (a) d = 40 μm; and (b) d = 50 μm.
5. Conclusions In summary, the present study proposed a novel method for cut size determination based on simulation via FLUENT and validation through material experiments. Compared with traditional methods, the proposed strategy can be very accurately and easily performed. Furthermore, several conclusions can be obtained as follows:
(1) By establishing a model, we observed the trajectories of the particles in a turbo air classifier. The trajectories were different when different size particles were fed at the same position. Smaller diameter particles moved into the annular region, larger diameter particles rotated in the annular region, and eventually were gathered into the coarse powder-collecting cone at the base.
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Table 1 Comparison of quartz sand cutting size obtained at different rotor cage rotary speeds. The ratio of air inlet velocity and rotor cage rotary speed (m/s–r/min)
Cut size (μm)
8–800 8–1200
47 32
(2) Simulation results showed: when the air inlet velocity was 8 m/s, rotor cage rotary speed was 800 r/min, the cut size of talcum powder material could be calculated as 30–40 μm, and the cut size of quartz sand material could be calculated as 40–50 μm. When rotor cage rotary speed was 1200 r/min, the cut size of talcum powder material could be calculated as 20–30 μm, and the cut size of quartz sand material could be calculated as 30–40 μm. (3) The material experiment was done to verify the simulation results. The simulation method provides a new method to determine the cut size of a turbo air classifier, as well as provides a reference method to study the cut size of various types of classifier. Acknowledgments This project was supported financially by the National Natural Science Foundation of China (no. 51074012). References [1] Tao Ye, Xu. Ning, Zhichu Huang, et al., Experimental investigation on classified particles cut size of turbo air classifier, Mining & Processing Equipment 34 (2006) 62–63. [2] Shengzhao Liu, Jiaxiang Liu, Lijie Guo, Study on theoretical cut size of turbo air classifier, Non-Ferrous Mining and Metallurgy 22 (2006) 138–140.
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