Analysis of Flow Field in Optimal Cyclone Separators with Hexagonal

Article pubs.acs.org/IECR

Analysis of Flow Field in Optimal Cyclone Separators with Hexagonal Structure Using Mathematical Models and Computational Fluid Dynamics Simulation Ting Zhang, Chunjiang Liu,* Kai Guo, Hui Liu, and Zhengchao Wang School of Chemical Engineering and Technology and State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, P.R. China S Supporting Information *

ABSTRACT: This paper presents a series of hexagonal cyclones with hexahedral outer tube and outer cone parts. By comparison with Hoffmann cyclone and square cyclone, we confirm the submicrometer particle separation performance of the hexagonal cyclone separator based on the computational fluid dynamics method. The Reynolds stress turbulence model combined with the discrete phase model is used to simulate the three-dimensional gas cyclone separator. The simulation results of the hexagonal cyclone demonstrate an excellent balance of transient separation and swirling flow separation. Two types of optimized hexagonal cyclones are designed, and three parameters are introduced. The results indicate that increasing the hexagonal twist angle and hexagonal outer body round corner diameter leads to higher overall pressure drop and lower collection efficiency in the hexagonal cyclone. The particle residence time in unit volume of the hexagonal cyclone is shorter, and the wall wear rate was lower as well. This represents a substantial potential savings in energy and costs. performance.38 However, the effect of the body appearance configuration of the cyclone separator has not been studied adequately because of the incomplete understanding of the flow fluid separators mechanism of cyclone separators. In practice, cyclone designers would settle a double-objective decision problem, maximizing separation efficiency (η) while minimizing the overall pressure drop (Δp) to obtain the satisfactory performance of cyclone separation.14 However, in

1. INTRODUCTION A gas cyclone separator is a widely applied separation device using centrifugal force to remove particles from a gas stream.1−3 Cyclones have effective application in a variety of industrial process, such as chemical engineering, food engineering, pharmaceutical engineering, and so on.4−9 The fact that they are easy to manufacture and contain no moving parts distinguishes them from other separation technologies. Despite their outstanding advantages, cyclones are complicated to design and difficult to optimize because the flow field within them is extremely complex.11,12 For a long time, the design and optimization targets of the cyclone focused on the separation of large-diameter particles. The separation efficiency of these cyclone separators could reach up to 99% for particles larger than 5 μm, but the efficiency is extremely lower for submicometer and smaller particles. Recently, with improvements in the dimensions of various components of cyclones, high-precision separation of micrometer particles has become possible.42−44 Qiu et al.15 designed a divergent cyclone that has strong capability to trap the particles with small diameters (d < 5 μm), and the inlet velocity range is restricted to be 14−18 ms−1. Many authors have demonstrated that both design dimensions and operating parameters influence the comprehensive performance of cyclones.10,18 Thus, many researchers focused on cyclone parts and components design.16 Wakizono et al. optimized a ring attached gas cyclone and assumed that a Dc ring cyclone could obtain minimum pressure drop.19 Xiong et al.20 designed a cyclone with reflux cone and gaps (straight and spiral) in a vortex finder that could improve separation performance of the cyclone separator through reducing the pressure drop and increasing the overall separation efficiency and grade efficiency. Cyclone body structural configuration and dimension have a significant effect on cyclone separator © 2015 American Chemical Society

Figure 1. Configuration of conventional cyclones: (A) inlet, (B) gas exit pipe,(C) cyclone outer tube, (D) cyclone outer cone parts, and (E) underflow dust exit. Received: Revised: Accepted: Published: 351

July 31, 2015 October 26, 2015 December 14, 2015 December 23, 2015 DOI: 10.1021/acs.iecr.5b02813 Ind. Eng. Chem. Res. 2016, 55, 351−365

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Industrial & Engineering Chemistry Research

Figure 2. Schematic diagram for the cyclone geometry and coordinate definition (measuremens are in millimeters).

Figure 3. Configuration of hexagon cyclone I.

many design targets of the cyclone separator, wall friction and particle residence time (PRT) are two indispensable and important factors that are related to cyclone running period and lifetime.13 Taking into account of the above four objectives has the best effects on reach a trade-off between device endurance and centrifugal separation. 1.1. Cyclone Configurations. In 1951, Stairmand presented one of the most popular design guidelines for high-efficiency cyclone separators, including inlet, gas exit pipe, cyclone outer tube, cyclone outer cone parts, and underflow dust exit (Figure 1). The cyclone outer body includes cyclone outer tube and cyclone outer cone parts. Hoffmann et al. presented the geometrical ratios for these parts, and these values became the basis for the design of the Stairmand model, which suffers from many shortcomings.21−24

Although the structure of the cyclone separator is simple, the fluid dynamics and separation principles inside the cyclone are rather complex and unclear. To improve cyclone performance, researchers have made great efforts during the past decades. These efforts can be traced to two considerations. First, cyclones are designed to large monoscale and small multiscale.25,34 Large monoscale cyclones are used in the filtration separation industry and circulating fluidized bed (CFB) industries and small integrated scale cyclones are used for separating very fine particles in integrated cyclone scrubbers, which guarantee overall system integration effectiveness.26 The other design consideration for cyclones is based on cyclone configuration and its flow field characteristics. To date, there are two main body appearance configurations of cyclones in a wide range of industrial applications, cylinder and square cyclone (showed in Figure 1). 352

DOI: 10.1021/acs.iecr.5b02813 Ind. Eng. Chem. Res. 2016, 55, 351−365

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Figure 4. Schematic of experimental equipment setup.

Safikhani27 tested two small square cyclones, and the results showed that the pressure drop in a small square cyclone is less than that in a small cylindrical cyclone. Cylindrical cyclones are characterized by huge volume and long start−stop times, whereas square cyclones are appropriate for high flow rate and remove large particles (particles size range is greater than 5 μm). The separation principle of cylindrical cyclones is based on centrifugal separation, but that of square cyclones is characterized by instantaneous separation and centrifugal separation.17,47 Raoufi et al. studied the separation mechanism of two square cyclones using a computational fluid dynamics (CFD) method, and it is observed that different outer shapes could affect the pressure drop.28 However, optimized cyclone separators still could not meet the requirements of fine particle separation. Thus, some researchers began to seek an effective approach by introducing computational fluid dynamics as an important tool to analyze the flow field inside these cyclone separators. 1.2. CFD Analysis. With the rapid development of the computer and CFD techniques, the use of numerical simulations to predict the performance of the cyclone separators has received intensive development and achieved much success.29−31 For the turbulent flow in a cyclone separator, the key to CFD is accurate descriptions of swirling turbulent flow. There are a number of turbulence models available in FLUENT, from standard k−ε model to time-consuming large eddy simulation (LES).32 Elsayed and Lacor studied three cyclones with different cone tip diameters using LES.33 Contrary to LES, the Reynolds stress model (RSM) is validated and can give reasonable predictions58,59 on the mean flow fields in cyclone simulations in contrast to test results.47 Azadi studied the effect of turbulent modeling inside cyclones with different sizes and particle trajectories calculated via a discrete phase model (DPM) based on an Eulerian−Lagranrian approach.35 Consequently, accurate turbulence modeling is the foundation of swirling flows simulation. The Eulerian−Eulerian approach and Eulerian−Lagranrian approach are two powerful methods to

Figure 5. Comparisons of the collection efficiency between experiment and numerical solution.

describe particle trajectories and flow.34 The stochastic Lagrangian multiphase flow model is suitable for describing the particle motion, and the discrete random walk (DRW) model is suited to showing the turbulent dispersion of particles, especially for the lower particle diameters.36,37 Considering that the hexagonal structure can be easily integrated into a parallel multiscale unit like a honeycomb and the discovery of a high-speed hexagonal cyclonic vortex on Saturn’s north polar,39 the objective of the present work is an attempt to study a novel hexagonal cyclone separator and to optimize the novel hexagonal cyclone separator based on CFD and mathematic models. We also include some experimental validations of models to predict and optimize the performance of these modified structures of hexagonal cyclones.

2. MATHEMATICAL MODEL 2.1. Cyclone Geometry. The geometry parameters of cyclone separators are shown in Figure 2 and Table S1. 353


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Figure 6. Hexagon cyclone I optimization flowchart.

describe the particle-tracking percentage of cyclones in a specific particle diameter range, and the formulation of x90 and x75 of hexagonal cyclone are defined as

In order to compare the performance of new hexagonal cyclones with conventional ones, the design and geometry characteristics of a set of new hexagonal cyclone separators have been described (Figure3 and Table S1). Several geometry variables were collected and eight-plotting sections were used to investigate the effect of cyclone outer tube and cone parts on the velocity profiles as given by Table S2. 2.2. Model Description. The modeling procedure was performed in the following steps: Step 1: establish design variables. Step 2: design sample, optimizing geometry parameters. Step 3: CFD testing simulation and evaluate cyclone performance. The new geometry and parameters may suffer from flowchart optimization loops.57 x90 and x75 are introduced based on x50 of the Muschelknautz method (MM) from Hoffmann and Stein40 traced back to an early work performed by Barth.41 x90 and x75 are used to

x 90 = x′90

′ x 75 = x 75

18μ(0.9Q) 2π (ρp − ρ)(H − S)vtangential 2

(1)

18μ(0.9Q ) 2π (ρp − ρ)(H − S)vtangential 2

(2)

Where vtangential is the tangential velocity of gas flow; x75 represents the particle size that corresponds to 75% collection efficiency; x90 represents the particle size that corresponds to 90% collection efficiency; and x90 ′ and x75 ′ are the corresponding constants. ′ = f (vin , ρp , ρ , μ , Dex , Dc , B , β′, β , a , b , H , S) x 90 354

(3)


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Industrial & Engineering Chemistry Research ′ = f (vin , ρp , ρ , μ , Dex , Dc , B , β′, β , a , b , H , S) x 75

(4)

We could also get the relative right deviation degree Xr (the right collection diameter distribution deviation of particles), which is defined as x X r = 75 x 90 (5) Xr is a dimensionless constant and is used to describe the efficiency curve deviation and gradient trend. Because of gravity force, x90 is normally bigger than x75 in cyclone working time. Therefore, Xr is smaller than 1 in most cases, and then the separation curve increases. The efficiency−particle diameter curve of a cyclone tends to smooth when Xr is close to one. On the other hand, the curve tends to be steeper when Xr is closer to zero. The wall shear stress τw is a dominant factor of wall friction, which has a prominent effect on the total pressure drop across cyclones. E is defined as the wear rate, and it is a crucial factor in the measure of wall durability and service life. Normally, τw is related to β and β′, the cyclone outer tube shape factor ξshape, and the geometrical parameter of the cyclone Dz. ξshape is a dimensionless constant, and it is less than 1; when the cyclone outer tube is close to cylindrical, the constant is close to 1; conversely, if the cyclone outer tube is close to triangular, then ξshape is close to 0. In eq 6, E is inversely proportional to the diameter of cone parts, Dz65, and proportional to the product of ξshape. In eq 7, E is proportional to τw, and τw is also proportional to inlet gas velocity.66 E = 0.1993ξshapeDz −2.1971

(6)

E ∝ τw

(7)

Figure 7. Optimized hexagonal cyclone separators.

For an incompressible fluid flow, the continuity and momentum equation given as

∂ ui =0 ∂xi

(10)

∂ ui ∂u ∂ 2 ui 1 ∂p ̅ ∂ + uj i = − +v − R ij ∂t ∂xj ρ ∂xi ∂xi ∂xj ∂xj

(11)

To describe the trajectories of particles in cyclone separator, several parameters are introduced in the paper. PRT is used to describe particles trajectories inside the cyclone separator. When compared cyclones are calibrated, a volume correction coefficient is given to reduce the error caused by the volume difference. γ is the volume correction coefficient, and it is equal to the ratio of the volume of Hoffmann cyclone and the volume of the compared cyclone. Moreover, PRT′ in unit volume is equal to the product of γ and PRT. The particle tracking time, tt, and escaping time, te, are introduced in this work. Moreover, tδ is the ratio of tt and te, and it is also a parameter used to describe particles motion trajectories. If tδ is greater than 1, most particles experience a long operating time; if tδ is less than 1, there is a greater possibility of transient separation and short circuit flow. t tδ = t te (8)

where ui is the mean velocity, xi the position, t the time, p̅ the mean pressure, ρ the constant gas density, v the kinematics viscosity, and Rij = ui′u′j the Reynolds stress tensor. Here, u′i = ui − ui is the ith fluid fluctuation velocity component. The turbulence model of RSM provided differential transport equations for evaluation of the turbulence stress components, i.e., the turbulence production terms defined with P being the fluctuation kinetic energy production. vt is the turbulent (eddy) viscosity; σk = 1, C1 = 1.8, and C2 = 0.6 are empirical constants.49

The ratio of the average escaping particles Z position, ze, and the height of cyclone, H, defined as Ψ is used to describe the escaping particles’ trajectories. When Ψ is close to S/H, it shows that most particles escaped rapidly and the possibility of short circuit flow is high. Conversely, when Ψ is close to 0.5, it shows that the separation is moderate and stable. Normally, the larger diameter particles have larger Ψ value and Ψ is greater than S/H (the ratio of length of gas exit tube to cyclone height; in this paper, S/H = 1/8). z Ψ= e (9) H

(13)

⎞ ⎡ ∂ uj ∂u ⎤ ∂ ⎛ vt ∂ ∂ ∂ + R jk i ⎥ R ij + uk R ij = R ij⎟ − ⎢R ij· ⎜ k· ∂xk ⎦ ∂xk ⎝ σ ∂xk ⎠ ⎣ ∂xk ∂xk ∂t ⎤ ⎡ 2 2 ⎤ 2 ε⎡ − C1 ⎢R ij − δijK ⎥ − C 2⎢Pij − δijP ⎥ − δijε ⎦ ⎣ 3 3 ⎦ 3 k⎣

⎡ ∂ uj ∂u ⎤ + R jk i ⎥ , Pij = −⎢R ij ∂xk ⎦ ⎣ ∂xk

P=

1 Pij 2

(12)

The transport equation for the turbulence dissipation rate, ε, is given by v ⎞ ∂ε ⎤ ∂ε ε ∂u ε2 ∂ε ∂ ⎡⎢⎛ + uj = ⎜v + t ⎟ ⎥ − C ε1 R ij i − C ε2 ∂t σk ⎠ ∂xj ⎥⎦ ∂xj K ∂xj K ∂xj ⎢⎣⎝ (14)

In eq 14, K = (1/2) ui′u′j is the fluctuation kinetic energy and ε is the turbulence dissipation rate. The values of the constants are σε = 1.3, Cε1 = 1.44, and Cε2 = 1.92. 355


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Figure 8. Computational radial profile for the static pressure at different sections on the X−Z plane (Y = 0) at section S1−S6 (cone to inlet crosssection). From top to bottom: sections S1−S3 (left column) and sections S4−S6 (right column).

Figure 9. Relationship between inlet gas velocity and the total pressure drop (CFD) from inlet to gas exit tube of five compared cyclones.

dxpi

The particle loading in a cyclone separator is typically small, so it is assumed that the particles in the cyclone do not affect the flow field. In this study, the motion of solid particles in a flow field is simulated using the Eulerian−Lagrangian approach with a discrete phase method (DPM) based on Newton’s second law. Because the particle material density is nearly 2300 times the gas density, forces such as Saffman’s, Basset, and virtual force have been neglected. The equation of particle motion is given by40 du pi dt

= FD(ui − u pi) +

dt

= u pi

where the term FD(ui − upi) is the drag force per unit particle mass:40 FD =

gi(ρp − ρ) ρp

(16)

Re p =

(15) 356

18μC DRe p ρp d p2 24

(17)

ρp d p|u − u p| μ

(18) DOI: 10.1021/acs.iecr.5b02813 Ind. Eng. Chem. Res. 2016, 55, 351−365

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Figure 10. Flow in the y = 0 plane in terms of velocity vectors and flow velocity contours in the z = 0.05 m cross section: (a) Hoffmann cyclone, (b) hexagon cyclone II, and (c) square cyclone.

10 to 20 ms−1. The total pressure drop, Δp, is detected and compared with the results from CFD and Hoffmann.48,50 Figure 4 shows a comparative experiment flow diagram and photograph of experimental setup. The estimation of the total pressure drop (static pressure plus dynamic pressure) is more accurate because it takes into account the change in the flow kinetic energy between the inlet and outlet sections.45 A particle concentration−separation efficiency model and a corresponding experience formula revealed

In FLUENT, the gas phase is treated as a continuum by solving Navier−Stokes equations and the solid phase is calculated by tracking particles because the solid-phase flow and gas-phase flow cannot be calculated simultaneously.63,64 Collection efficiency statistics are obtained by releasing a specified number of monodispersed particles at the inlet and by calculating the number trapping through the underflow dust exit tube. A discrete random walk is used to model the instantaneous velocity fluctuations. In addition, particle− particle collision is negligible. 2.3. Model Validation. 2.3.1. Pressure Drop Validation. This experiment was used to validate the pressure drop Δp of CFD and CFD-Exp of Hoffmann. Four continuous variables were detected by pitot tubes: inlet static pressure, inlet total pressure, gas exit tube static pressure, and gas exit tube total pressure. In the experiment, inlet gas velocities varied from

Δp(c in) = (1 − αc in β) Δp0

(19)

In eq 19, Δp0 is the pure air pressure drop of the cyclone and Cin is inlet particle concentration (g/m3); constants α and β are equal to 0.02 and 0.6, respectively.46 357


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Figure 11. Radial profile for the time-averaged axial velocity at different sections on the X−Z plane (Y = 0) at section S1−S6 (cone to inlet cross section). From top to bottom: sections S1−S3 (lines 1−3) and sections S4−S6 (lines 4−6), respectively.

3. BOUNDARY CONDITIONS AND COMPUTATION GRID INDEPENDENCE STUDY

A comparison between total pressure drops obtained, the experimental data of Hoffmann,40 and CFD predicted total pressure drop are shown in Table S3. Table S3 indicates a good agreement between the measured and the predicted results. 2.3.2. Efficiency Validation. The present simulations were compared with the measured collection efficiency profiles at particle diameters ranging from 0.5 to 5 μm in the cyclone separator. Collisions between particles are negligible, and collisions between particles and the walls of the cyclone are assumed to be perfectly elastic.54 Figure 5 and Table S4 indicate a good agreement between the measured and the predicted results of collection efficiencies.

A velocity inlet boundary condition was used at the cyclone inlet based on a round cornered hexagonal cyclone. An outflow boundary condition was used at the outlets. The turbulent intensity equals 5%, and the characteristic length equals 0.07 times the inlet width.51 To calculate the cutoff particle size of these cyclones, 6400 particles are injected from the inlet surface and inlet particle feed rate mp′ of 0.001 kg/s. Table S5 shows that the boundary conditions of the tested cyclones cover the above range. In swirling flow trajectory computation, the swirl number of particles with different diameters usually characterizes the 358


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Figure 12. Radial profile for the time-averaged tangential velocity at different sections on the X−Z plane (Y = 0) at section S1−S6 (cone to inlet cross-section). In the first line, from left to right, sections S1 and S2; in the second line, from left to right, sections S3 and S4; and in the bottom line, from left to right, sections S5 and S6.

degree of swirl.52 Swirling flow is characterized by the number of particles per unit time Nṗ , which results from the total particle mass flow ṁ pand the total number of the trajectories, NS.62 The geometric swirl time, TS, determined by the total number of the trajectories, NS, is a measure for the ratio of tangential to axial momentum.

Nṗ =

ṁ p N

π

ρp ∑ j =T1 6 d p3

3Dex Dc Ns = ξshape 2π 3 A in

Ts =

where Dex is the average vortex diameter; Dc the cyclone body diameter; Ain the inlet cross sectional area; vin the inlet velocity; and kd the residence time constant, which relates to particle diameter. In the simulation, the unsteady RSM used a transient time step of 0.0001s. The residence times tres (cyclone volume/gas volume flow rate) of these cyclones are close to 0.175 s.33 Table S6 shows the computational details of five tested cyclones.

DN 3 3 · kd· c s 2 vin

(20)

tres =

Q in Vcyclone

(23)

The finite volume method has been used in the discretization of the partial differential equations of the model using the semiimplicit method for pressure-linked equations-consistent methods (SIMPLEC) for pressure−velocity coupling and second-order upwind scheme to interpolate the variables on

(21)

(22) 359


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Industrial & Engineering Chemistry Research the surface of the control volume. The implicit coupled solution algorithm used in the simulation and the numerical setting for the current simulations are shown in Table S7. The computational grids are generated using GAMBIT grid generator. The grid independence study was also performed. Three levels of grid made the obtained grid independence obvious (Table S8). The total CPU running time is about 180 h for each case on 4nodes CPU X64 using FLUENT 14.0 commercial solver. All transient simulations have been converged with the designed time step of 1 × 10−4 s, and the numerical results are given in the following descriptions.

4. RESULTS AND DISCUSSION 4.1. Body Structural Configurations and Optimization. Based on the flowchart optimization loop, this work found key design variables; then, first, second, third, etc modified shapes of the cyclone could be presented and simulated (Figure 6). This work introduces hexagon cyclone II and hexagon cyclone III, which are optimal structural type of hexagon cyclone I based on CFD (Figure 7 and Table S9). Three parameters are introduced simultaneously. The parameters including the twist angle of outer tube (β) and outer cone parts (β′) and hexagonal cyclone outer body round corner diameter (drc) are varied. The characteristics of hexagon cyclone II and III, square cyclone, cylindrical cyclone with the same external diameter, one square, one cylinder, and one hexagonal cyclone (β = β′ = 0°) are numerically compared with two optimum hexagonal cyclones (hexagon cyclone II and hexagon cyclone III). Table S10 shows the influence of cyclone outer body tube when the inlet gas velocity is 10 m/s. The RSM predicted a 4.91% decrease in micrometer particle separation and resulted in a 27.01% reduction in total pressure drop, Δp. The x75 and x90 for the hexagonal cyclone corresponding to the Hoffmann cyclone with the same hydraulic diameter and volumetric airflow are indicated in Table S9. As shown in Table S10, the predicted results of Xr decreased 5.6% for the novel hexagon cyclone II compared with that of Hoffmann cyclone. Figure 8 shows the static pressure contours of the cyclones (lines 1−6 are located on S1−S6, respectively, and Y = 0) and axial section of S6 (at the middle of the inlet section, Table S2), and Figure 4 indicates the static and dynamic pressure from S1−S6 (designated as lines 1−6, respectively). In the compared cyclones, the time-averaged static pressure decreased from wall to center. The corner of swirl flow field is one of the major regions to cause pressure drop because the suspension at the corners consumed more energy of flow. However, a negative pressure zone appears in the axial direction of the gas exit tube because of the outstanding swirling flow phenomenon. Figure 9 shows the relationship between the inlet gas velocity and the total pressure drop of five compared cyclones. It can be seen that the total pressure drop based on area-weighted average principle of computational fluid dynamics (from inlet to gas exit tube) increases with the increase of inlet gas velocity. Flow field impression in the following description is based on inlet velocity of 10 m/s (Qin = 0.04 m3/s) in Figures 10−19. In Figure 10, an axially oriented plane (S1−S6 in the x−z plane with y = 0, as defined in Table S2) is given. The core has a swirl shape flow that extends into the underflow dust exit tube, making the flow nonasymmetric, and the vortex finder has a negative pressure zone, making particles separate significantly. The swirling flow inside the square cyclone showed the vortex

Figure 13. Relationship between the separation grade efficiency and particle diameter.

Figure 14. Relationship between the separation efficiency and inlet gas velocity.

characteristics, i.e., strong swirling vortex at the central region of the cross section and weak swirling quasi-free vortex near the wall.55 Figure 10 shows the time-averaged tangential velocity and axial velocity contours, and the profiles at sections S1−S6 are shown in Figures 11 and 12, leading to the following conclusions. The axial velocity profiles exhibit an M shape, and part of the flow in the central region moves downward in the zero line of measuring. From Figure 11, we can see that the axial velocity of hexagon cyclone II is higher than that of the Hoffmann design in outer vortex and inner vortex as the centrifugal force is the main driving force for particle collection in the cyclone separator. The tangential velocity profile at any section is composed of two regions, an inner and an outer one. Moreover, the tangential velocity of the hexagonal cyclone is lower than that of the Hoffmann design in both outer and inner one in Figure 12. This profile is a so-called Rankine type vortex including a quasiforced vortex in the central region and a quasi-free vortex in the outer region. These tangential velocity flow fields maybe caused lower total pressure drop, higher fine particle collection efficiency, and low wall erosion. Lower tangential velocity maybe results in appreciably lower separation efficiency of 2.5−5 μm particles. 360


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Figure 15. PRT of single particle trajectory (d = 2.5 μm) in Hoffmann cyclone (top), hexagonal cyclone (middle), and square cyclone (bottom) when the particle enters the separator at the top, middle, and the bottom of the inlet (from left to right).

Specific particle efficiency profiles of representative hexagon cyclone II, cylindrical cyclone, and square cyclone are shown in Figure 13. As seen from Figure 13, the particles with 0.5 μm diameter escape in the compared cyclones significantly; on the other hand, the particles with diameters of 2.5 and 5 μm are easily trapped in the cylindrical cyclone and hexagonal cyclone and escaped from the gas exit pipe. Moreover, it is obvious that hexagon cyclone II is the predominant one in overall particle grading efficiency. Figure 14 depicts the relationship between the separation efficiency (η, %) and inlet velocity in a specific particle diameter range. Moreover, the separation efficiency of micrometer particles increases with the increase of inlet gas velocity. When the inlet gas velocity is lower than 10 m/s, the separation

efficiency maintains a high level while the pressure drop maintains a relatively decrease, as shown in Figure 14. Thus, it is economical to obtain high separation efficiency by using hexagon cyclone II at low inlet velocity. 4.2. Discrete Phase Modeling Results. Figure 15 shows a series of particle trajectories (d = 2.5 μm) from the top, center, and bottom of the inlet at an air volume flow rate of 0.04 m3/s. It is obvious that PRT of the hexagonal cyclone is smaller than that of the Hoffmann cyclone and square cyclone. The total number of the trajectories, NS, and the geometric swirl time, TS, of the hexagonal cyclone are less than those of the Hoffmann design and square design. The trajectories, Ns, of hexagonal cyclone are longer than those of square cyclone because the efficient swirl flow separation (centrifugal separation) is not the 361


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Figure 16. Profile of the particle residence time PRT and PRT′.

instant separation and short circuit flow. A lower level of energy would be sure to maintain the gas−solid flow inside the hexagonal cyclones. This phenomenon may be the reason for the wide range of inlet velocity and the reduction in total pressure drop obtained when the hexagonal cyclone is applied here. Figure 16 shows the ratio of particle tracking time and particle escaping time, and the particle diameter range is from 0.5 to 5 μm. In the hexagonal cyclone, the bigger particles trend to shorter PRT and PRT′ and the smaller particles trend to longer PRT and PRT′, but the PRT and PRT′ profile of the compared cyclones fluctuate, which shows that the hexagonal cyclone is characterized by an excellent particle classification feature. In Figure 17, the curve of the hexagonal cyclone is smooth; the ratio of escaping time and tracking time is smaller than that of Hoffmann design and bigger than that of the square design. However, tδ (tt/te) of the hexagon decreases slightly with increasing particle diameter in Figure 17. In addition, we observed that the escaping time of square cyclone particles is shorter than that of hexagon cyclone II, and it is close to the ratio of length of gas exit tube to the height of the cyclone, H. The particle escaping phenomenon is mainly due to the force imbalance of particles, rather than short circuit flow and large dead regions. In Figure 18, we can see that the hexagonal cyclone is characterized by outstanding transient separation performance and satisfactory swirl flow separation results. Compared to the square cyclone and Hoffmann cyclone, the Ψ of hexagon cyclone II is moderate and stable, and the bigger diameter particles have smaller Ψ, but the average Z position/H ratio, Ψ, is greater than 1/8 (the ratio of length of gas exit tube and cyclone height) and less than 1. 4.3. Wear Regularity. Figure 19 shows the profile of wall shear stress. We obtained that the hexagonal cyclone has longer service life than that of the others and excellent durability degree. Wall wear rate can be divided into three parts: part I, the upper gas exit tube (from −0.1236 to 0 m of Z position); part II, cyclone outer tube (from 0 to 0.3 m of Z position); and part III, the cone parts (from 0.3 to 0.8 m of Z position). In part I, the wall shear stress curve is smooth. In part II, the curve has a peak value for the existence of gas exit pipe. Part III is related to the cone parts wear rate, E, and the kinetic energy of swirling particles in cyclone cone parts. In part III, the wall shear stress of the hexagon is significantly lower than that of the

Figure 17. Profiles of tδ.

Figure 18. Profiles of Ψ.

Hoffmann design and slightly higher than that of the square cyclone. In Figure 19, we can see that the wall shear stress τw is proportional to the product of ξshape and diameter of Dz; the phenomenon is obvious in part III. From Figure 19, the three kinds of cyclone separators tend to analogous wear conditions in part I, and the wall shear stress curve of hexagon cyclone II is 362


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Figure 19. Evolution of wall shear stress of three cyclones.

(5) At a specific inlet solid concentration, separation efficiency of a hexagonal cyclone obtained satisfactory instantaneous separation and rotational speeds; PRT′ is shorter than that of conventional cyclones. This represents a substantial potential savings in energy and costs.

similar to that of Hoffmann cyclone in part II but lower that of square cyclone in part III. The phenomenon of hexagonal cyclone separator II probably results from obvious centrifugal separation56 in part II and predominant transient separation in part III.

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5. CONCLUSION This study introduces a novel design of hexagonal cyclone separators based on a four-objective optimization loop. The new cyclone design has a hexagonal outer tube and hexagonal outer cone parts instead of a cylindrical or square body seen in conventional cyclones. The performance parameters of the new cyclone is investigated by using CFD and mathematic models. The models are validated with experimental data on pressure drop and collection efficiency. Moreover, the effect of hexagon twist angle, β and β′, and hexagon outer body round corner diameter, drc, are clearly seen in the results of the novel cyclones. Moreover, the following conclusions could be obtained from the present study: (1) In the separation space and the vortex finder, there exists a velocity vortex: the gas stream rotates around the vortex center spontaneously but not around the gas exit tube outside or cyclone outer body inside, which may be caused by the special hexagonal body appearance configuration. (2) The particle separation efficiency increased with particle diameter. The hexagonal cyclone is more suitable for fine particle separation than the conventional cyclone for higher axial velocity. It also is characterized by satisfactory particle separation gradient efficiency, and the value of the RSM indicates the Xr decreased 5.6% for the novel hexagon cyclone II compared with that of the Hoffmann cyclone. However, the separation efficiencies of the hexagonal cyclone are appreciably lower than that of the conventional cyclone; this phenomenon may be caused by lower tangential velocity in the outer vortex. (3) A hexagonal cyclone obtained low overall pressure drop (Δp decreases 27.01% at 10 m/s inlet velocity compared with Hoffmann cyclone40), low operation noise, moderate wall shear stress, and compact integration. These advantages may be caused by higher axial velocity and higher tangential velocity in the inner vortex. (4) A high operating flexibility could be achieved in a hexagonal cyclone. At low inlet velocity, a hexagonal cyclone could still keep excellent separation performance that almost excludes the ratio of other cyclone separators.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b02813. Data and validation tables of the geometrical cyclone parameters values and different plotting sections descriptions; additional validation of the computational pressure drop of the Hoffmann cyclone; additional comparison of numerical and experimental collection efficiency of Hoffmann cyclone, hexagon cyclone I, and square cyclone; and additional details of the operating and geometric conditions in the computational fluid dynamics simulation (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel.:+86 22 23502063. Fax:+86 22 27404496. E-mail: cjliu@ tju.edu.cn. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge financial support by the National Basic Research Program of China (2012CB720500) and the National Natural Science Foundation of China (Project 21406157).

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NOMENCLATURE

Roman Letters

a = inlet height, mm AR = total inside area of the cyclone contributing to frictional drag, m2 Ain = inlet cross sectional area, m2 b = inlet width, mm B = diameter of underflow dust exit, mm C = perimeter of cyclone outer tube, m C0 = inlet particle and air mass ratio Cin = inlet particle concentration, g/m3 Dc = cyclone diameter, mm 363


Article

Industrial & Engineering Chemistry Research Dex = vortex finder diameter, mm drc = hexagon outer tube round corner diameter, mm dp = particle diameter, m Dh = hydraulic diameter, m Dz = cone parts diameter of any axial position, m E = erosion percentage, kg/kg gi = gravitational acceleration in i direction m′p = particle feed rate, kg/s ṁ p = the total particle mass flow, kg/s Ṅ p = the number of particles per unit time Ns = geometric swirl number of swirling flow Qin = air volume flow rate, m3/s Sc = section area, m2 tres = cyclone volume/gas volume flow rate tt = particle tracking time, s te = particle escaping time, s tδ = ratio of particle tracking time and particle escaping time ui = gas velocity in i direction, m/s upi = particle velocity in i direction, m/s vin = inlet velocity, m/s vtangential = tangential velocity of the gas at the inner core radius, m/s vaxial = average axial velocity through the vortex finder, m/s Vcyclone = volume of cyclone, m3 x75 = particle diameter of 75% cutoff separation efficiency, μm x90 = particle diameter of 90% cutoff separation efficiency, μm Xr = right deviation degree index (right diameter distribution deviation of particles collection)

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Greek Letters

ρp = density of particles, kg/m3 ρ = gas density, kg/m3 θ = hexagonal cyclone two sides intersection angle β = hexagonal cyclone outer tube twist angle β′ = hexagonal cyclone outer cone parts twist angle η = cyclone efficiency, % μ = dynamic viscosity of air, kg/m·s γ = volume correction coefficient τw = Wall shear stress, pa ξshape = cyclone outer tube shape factor Ψ = ratio of the average particles escaping Z position and height of cyclone

Abbreviations

CFD = computational fluid dynamics DPM = discrete phase modeling DRW = discrete random walk LES = large eddy simulation MM = Muschelknautz method of modeling RSM = Reynolds stress turbulence model PRT = particle residence time, s PRT′ = particle residence time in unit cyclone volume, s CFB = circulating fluidized bed

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Analysis of Flow Field in Optimal Cyclone Separators with Hexagonal

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