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Investigation on dust collection and particle classification performance of cyclones by airflow control for design of cyclones
Powder Technology 277 (2015) 22–35
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Investigation on dust collection and particle classification performance of cyclones by airflow control for design of cyclones Yuhei Kosaki a,⁎, Takayuki Hirai b, Yoshinari Yamanaka a, Keishi Takeshima b a b
Kanematsu Engineering Co., Ltd., 3981-7, Nunoshida, Kochi City, Kochi 781-5101, Japan Kochi National College of Technology, 200-1, Otsu, Monobe, Nankoku City, Kochi 783-8508, Japan
a r t i c l e
i n f o
Article history: Received 10 October 2014 Received in revised form 11 December 2014 Accepted 25 February 2015 Available online 5 March 2015 Keywords: Cyclone Large eddy simulation Particle separation Apex cone Stabilizer
a b s t r a c t We investigated the design of relatively large cyclones with large amounts of airflow containing dust that are used in actual dust collection plants. In order to obtain basic data on the design of conical cyclones with a Reynolds number of approximately 8.9 × 105, we compared the fluid analysis results with the experimental results on dust collection and particle classification performance for conical cyclones to which apex cones and stabilizers were attached. Then, we elucidated the relationship between the flow conditions inside the conical cyclone with a Reynolds number of 8.9 × 105 and dust collection and particle classification performance. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The separation and collection of particles at dust collection plants using pneumatic conveying generally involve the installation of a receiver tank (settling tank) for the conveying process where particles with relatively large diameters and high densities are separated and collected via the gravitational force that acts on them. Particles with smaller diameters and lower densities, which cannot be separated and collected easily with a receiver tank (for cases where Stokes' law applies to the aerodynamic force acting on particles), are partially separated and collected by the cyclone in the subsequent process, by utilizing the centrifugal force acting on the particles. However, the particles that cannot be collected by the cyclone are separated and collected using a filter in the following process. Subsequently, the airflow is usually guided into a suction machine (blower) installed at the very end of the conveying line and then discharged into the atmosphere. In order to reduce the load on the filter during such dust collection processes, it is necessary to improve the dust collection and particle classification performance of cyclones. Particle separation in a cyclone is based on the principle wherein particles are accumulated in a dust collection section after being separated outward by the centrifugal force originating from a swirling
Abbreviations: CFD, computational fluid dynamics; LES, large eddy simulation; PIV, particle image velocity; SGS, sub-grid scale; WALE, wall-adapting local eddy-viscosity; SST, shear-stress transport. ⁎ Corresponding author. Tel.: +81 088 845 5511; fax: +81 088 845 5255. E-mail address: [email protected] (Y. Kosaki).
http://dx.doi.org/10.1016/j.powtec.2015.02.051 0032-5910/© 2015 Elsevier B.V. All rights reserved.
flow and trickling into the dust collection section along the cyclone wall surface. The swirling flow inside the cyclone is a combination of a free vortex and forced vortex (hereinafter referred to as the Rankin vortex). This combined vortex also has descending and ascending flows, causing a downward reverse flow at times as negative pressure occurs around the central region. Therefore, it is known as an unsteady flow because the inclination angle of the flow to the tangential direction changes constantly owing to the eccentricity of the swirling flow center and the shape center [1,2]. Thus, in order to design a cyclone with high particle classification performance, it is necessary to have an appropriate design that takes the unsteady flow into consideration. However, it is not practical to create a prototype in advance and take measurements using a Pitot tube current meter, hot-wire anemometer, or particle image velocity (PIV) for the estimation of the flow field inside a cyclone during design, from the standpoint of the time and cost required for the measurements and prototyping. However, the high processing speeds and decreased prices of computers in recent years have made it possible to apply the analysis of the fluid dynamic phenomenon by computational fluid dynamics (CFD) to engineering as well. Using CFD, Yoshida et al. [3–6] calculated the flow inside cyclones and the particle trajectory in a three-dimensional simulation by the direct method. They discussed the particle classification and dust collection performance of the cyclones by comparing the results of dust collection and classification experiments. With regard to the prediction of unsteady flow fields inside cyclones, further progress in CFD, especially in recent years, allowed Akiyama
Y. Kosaki et al. / Powder Technology 277 (2015) 22–35
et al. [7,8] to confirm the feasibility of reproducing the unsteady flow inside cyclones based on the comparison between the experimental values in the flow field and the analysis results obtained by employing CFD with large eddy simulation (LES), which targets a compact cyclone (Reynolds number of approximately 3 × 104 to 4 × 104) with a low flow rate at its inlet. Additionally, they discussed the dust collection and particle classification performance by comparing dust collection and particle classification experiment results. We clarified the validity of the analysis conditions (e.g., the mesh and Courant number) by comparing the CFD calculation results obtained by employing LES with the experiment results for the flow fields inside a relatively large cyclone (Reynolds number of approximately 8.9 × 105) with large amounts of airflow containing dust, which is used in actual dust collection plants; we also considered a design target for this study. Then, we reported that the distinctive flow inside the cyclone [1,2] can be reproduced in a conical cyclone [9]. The purpose of this paper is to report the useful knowledge gained by conducting an investigation on the relationship between the flow conditions inside a cyclone and the dust collection and particle classification performance of the cyclone. This task was carried out by conducting dust collection and particle classification experiments, implementing LES analyses for cases when using an apex cone and a stabilizer [6,8]—a structure and configuration intended to improve dust collection and particle classification performance reported in the past studies on conical and cylindrical cyclones—and performing comparative analyses on the obtained results. The investigation aimed to gather basic data on the design of relatively large conical cyclones (Reynolds number of approximately 8.9 × 105) with large amounts of airflow containing dust, which are used in actual dust collection plants. 2. Dust collection and particle classification experiments 2.1. Experiment device Fig. 1 shows a schematic diagram of the experiment device. While air is allowed to flow into the cyclone by maintaining the average flow rate at the inlet of the cyclone ① constant with an inverter driven suction blower ②, a constant amount of powder is supplied by the feeder ⑦ from the cyclone inlet. Before supplying the powder, the average flow rate at the inlet of the cyclone Uin is defined by the following equation, based on values
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measured using a vortex flow meter ③, a pressure gauge ④, a thermometer ⑤ installed in the downstream side of the cyclone and a barometer and pressure gauge ⑥ installed in the upstream side from the inlet of the cyclone.
U in ¼
p f TaQ pa T f Ain
ð1Þ
where pf is the static pressure in the vortex flow meter section, pa is the atmospheric pressure, Ta is the atmospheric temperature, Tf is the temperature of the vortex flow meter section, Q is the volumetric flow rate measured using a vortex flow meter, and Ain is the cross-sectional area of the pipe at the inlet of the cyclone. 2.2. Trial cyclones Fig. 2 shows four types of conical cyclones. The origin of the coordinate system was set at the center of the bottom surface of the cyclone. The central axis of the cyclone was defined as the y-axis, and the direction of flow into the cyclone was defined as the z-axis. Type-A cyclone is a standard conical cyclone comprising a cylindrical section with an internal diameter D of 385 mm, a conical section, and a dust collection section. Type-B cyclone inhibits the re-scattering of particles that enter the dust collection section by reducing the airflow rate inside the dust collection section. Therefore, an apex cone was installed at the inlet of the dust collection section of a Type-A cyclone [6]. For Type-C and Type-D cyclones, a core bar with a circular cross section (hereinafter referred to as the stabilizer) was installed at the central axis of the Type-A and Type-B cyclones in order to confirm the dust collection and particle classification performance when inhibiting the eccentricity of the swirling flow center and the shape center in Type-A and Type-B cyclones [8]. 2.3. Experiment method The dust collection and particle classification experiments of the cyclones were performed at an average flow rate of Uin = 35 m/s at
Fig. 1. Experiment device.
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Fig. 2. Schematic diagrams for each cyclone.
the inlet of the cyclone based on the assumption that a cyclone with large amounts of airflow containing dust is used. The Reynolds number Re is defined by the following equation:
Re ¼
U in D 5 ¼ 8:9 10 ν
ð2Þ
where Uin is the average flow rate at the inlet of the cyclone, D is the diameter of the cylindrical section of the cyclone, and ν is the kinematic viscosity of air. As Fig. 3 shows, acrylic spherical particles (EXM-5 manufactured by Sekisui Plastics Co., Ltd.) were used as the test powder; they had a density of ρp = 1200 kg/m3, with the distribution of particle diameters ranging from Dp = 1 to 10 μm and a mass median diameter of Dp = 5 μm. This selection was based on the assumption of the presence of low-density particles with relatively small particle diameters that are difficult to separate and collect using a receiver tank in the preliminary process of cyclone operation in a dust collection plant. Moreover, the particle volume fraction φ in the airflow containing dust was set at approximately 7.5 × 10−7 based on the current values of the cyclones considered for our design, and the mass flow rate of the powder was set at 25 g/min. Past studies have reported that the effects of the collision between particles and particle motions on the flow can be disregarded when the particle volume fraction is of the order of 10−7 [10].
After supplying the dust-containing air to the cyclone for 2 h under the conditions described above, the increase in the mass of the cyclone was measured. Then, the particle size distribution was measured by sampling the dust collected by the cyclone and the filter. The dust collection performance and classification performance of each cyclone were evaluated by calculating the dust collection efficiency η, partial separation efficiency Δη, and classification accuracy κ defined by the following equation based on the measured mass and particle size distribution. A laser diffraction particle size analyzer (SALD-2200 manufactured by Shimadzu Corporation) was used to measure the particle size distribution of the powder.
η¼
mc 100 m
ð3Þ
where m is the mass of the powder supplied to the cyclone and mc is the mass of the powder collected by the cyclone (=the amount of increase in the mass of the cyclone).
Δη ¼
mc f c 100 mc f c þ ðm−mc Þf f
ð4Þ
where fc is the abundance ratio of each particle diameter of the powder collected by the cyclone, and ff is the abundance ratio of each particle diameter of the powder collected by the filter.
Fig. 3. Particle size distribution and the SEM photograph of the test powder.
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κ1 ¼
Dp75 Dp25
ð5Þ
κ2 ¼
Dp90 Dp10
ð6Þ
25
where Dpx is the particle diameter at a partial separation efficiency of x%. 2.4. Experiment results Table 1 shows the dust collection efficiency η of each cyclone. The dust collection efficiency for the Type-A cyclone, which was the standard conical cyclone, was 90.1%. Compared to the dust collection efficiency of the Type-A cyclone, the dust collection efficiency for the Type-B cyclone with an apex cone was higher, whereas that for the Type-C cyclone with a stabilizer was lower. However, it was confirmed that the dust collection efficiency of the Type-D cyclone, which was designed by adding an apex cone to the Type-C cyclone, was higher compared to the Type-C cyclone. These differences in the dust collection efficiencies of each cyclone can reveal the relationship between the structure and configuration and the dust collection performance of each cyclone by comparing the partial separation efficiency of the cyclones shown in Fig. 4. Compared to the Type-A cyclone, the Type-B cyclone with an apex cone attached showed a decrease in the diameters of the separable particles and an increase in the partial separation efficiency for each particle diameter. Moreover, the partial separation efficiency decreased over a wide range of particle diameters for the Type-C cyclone with a stabilizer attached. However, it was confirmed that the partial separation efficiency for each particle diameter increased and the diameters of the particles that can be separated decreased for the Type-D cyclone compared to the Type-C cyclone. These findings revealed that the dust collection performance of conical cyclones improves by attaching an apex cone but declines by attaching a stabilizer. Additionally, the decline in the dust collection performance due to the stabilizer can be eliminated by adding an apex cone while leaving the stabilizer attached. Moreover, the highest dust collection performance can be achieved when an apex cone is attached without installing a stabilizer. Table 2 shows the classification accuracy κ of each cyclone. The classification accuracy was obtained from the partial separation efficiency results shown in Fig. 4 and the classification performance improves as the classification accuracy nears 1. Compared to the classification accuracy of the Type-A cyclone, both κ1 and κ2 of the Type-B cyclone approached 1, improving the particle classification performance, whereas the particle classification performance decreased for the Type-C cyclone. Yet, κ2 of the Type-D cyclone was confirmed to be near 1 compared to the Type-C cyclone. These findings show that the particle classification performance of conical cyclones improves when an apex cone is attached but declines when a stabilizer is attached as is the case for the dust collection performance. Moreover, the classification accuracy of the Type-B cyclone was closest to 1, indicating that the cyclone had the highest particle classification performance. Thus, the dust collection performance and particle classification performance of conical cyclones (Reynolds number of 8.9 × 105), which
process large amounts of airflow containing dust, improve by adding an apex cone and decline by adding a stabilizer. Additionally, it was revealed that the cyclone with an apex cone but without a stabilizer has the highest dust collection and particle classification performance. It was also found that attaching a stabilizer is not a useful way to improve dust collection and particle classification performance. 3. Fluid analysis and discussion 3.1. Method Fluid analysis was performed on four types of cyclones with shapes identical to those in the experiments shown in Fig. 2, to investigate the relationship between the flow conditions inside the cyclone and the dust collection and particle classification performance. 3.2. Analysis conditions SCRYU/Tetra for Windows (manufactured by Software Cradle Co., Ltd.) was used to conduct the fluid analysis. The mass conservation Eq. (7) and the Navier–Stokes Eq. (8), which are the equations described by orthogonal coordinates and averaged by the grid filter, were used as fundamental equations to perform the LES analysis.
∂ui ¼0 ∂xi
ð7Þ
! ∂ρτ i j ∂ρui ∂ρui u j ∂p ∂ ∂ui ∂u j ¼− þ μ þ þ − ∂t ∂x j ∂x j ∂xi ∂x j ∂xi ∂x j
ð8Þ
where ūi is the xi direction component of the flow rate averaged by the grid filter, p is the static pressure averaged by the grid filter, ρ is the density of fluid, μ is the viscosity of fluid, and τij is the sub-grid scale (SGS) stress. The density ρ of the fluid, in other words air, was set to 1.206 kg/m3 and the viscosity μ was set to 1.83 × 10−5 Pa·s.
Table 2 Accuracy of classification for each cyclone.
Table 1 Dust collection efficiency for each cyclone.
η [%]
Fig. 4. Partial separation efficiency of each cyclone.
Type-A
Type-B
Type-C
Type-D
90.1
98.6
84.6
96.9
κ1 [−] κ2 [−]
Type-A
Type-B
Type-C
Type-D
1.12 1.26
1.09 1.19
1.14 1.34
1.14 1.30
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Model constant Cw was set to 0.316 suggested by Temmerman et al. [12]. Furthermore, the grid filter size Δ was defined using the following equation:
Δ¼V
Fig. 5. Mesh of Type-A cyclone.
The wall-adapting local eddy viscosity (WALE) model [11] was adopted as the SGS model. In other words, the following expressions were used: τi j ¼ ui u j −ui u j ¼ −2νSGS Si j 3=2 Sdij Sdij 5=2 5=4 Si j Si j þ Sdij Sdij
ν SGS
2 ¼ Cw Δ
Si j ¼
1 g þ g ji 2 ij
ð11Þ
Si j ¼
1 1 2 2 2 g i j þ g ji − δi j gkk 2 3
ð12Þ
gi j ¼
∂ui ∂xi
ð13Þ
d
2
ð9Þ
g i j ¼ g ik g k j
ð10Þ
ð14Þ
where νSGS is SGS kinematic eddy viscosity, Si j is the strain rate tensor averaged by the grid filter, g i j is the velocity gradient tensor averaged by the grid filter, δij is the Kronecker delta, Cw is the model constant, and Δ is the grid filter size.
1=3
ð15Þ
where V is the volume of the mesh element. The fundamental equations were discretized by the finite volume method. The second-order central difference scheme was applied to the advection term and the diffusion term. On the other hand, secondorder implicit scheme was applied to the time term. The mesh of Type-A cyclone is shown in Fig. 5 as an example of the mesh. The inlet boundary and the outlet boundary were secured by a piping section immediately adjacent to the main unit, and the mesh comprised a prism-shaped pentahedral unstructured mesh for the three layers from the wall surface and a tetrahedral unstructured mesh for the rest of the layers. However, in order to determine the Rankin vortex with good accuracy, the meshes at the central area of the cyclone were reduced to half the size of the surrounding meshes. Furthermore, the meshes of Type B, Type C and Type D also had configurations that were similar to that of Type A. The number of elements in each cyclone was 22,274,926 in the Type-A cyclone, 21,886,136 in the Type-B cyclone, 21,632,693 in the Type-C cyclone, and 21,593,363 in the Type-D cyclone. The boundary conditions consist of a steady inflow flow rate of Uin = 35 m/s at the inlet of the cyclone and static pressure of pout = 0 Pa at the outlet of the cyclone. The wall boundary conditions were set to expand the dual layer model of the Werner and Wengle type to a triple layer model in the LES [13]. With regard to the analysis, to first of all performed 1000 steps of steady state analysis, the existing shear-stress transport (SST) k-ω turbulence model [14] and the calculation results thereof were used as initial values to perform unsteady analysis with the LES. The Courant number C was set at 4, with the time advancement occurring at the minimum value Δt of the time increment Δti defined by Eq. (16) based on each element width ΔLi and the flow rate at each element ui. The averaging process was conducted when the average pressure value at the inlet of the cyclone started to stabilize to obtain the flow field.
Δt i ¼ C
ΔLi ΔL ¼ 4 i ; i ¼ 1; 2; :::; n ui ui
ð16Þ
where Δti is the time increment calculated for each element, ΔLi is the width of each element, ui is the flow rate of each element, C is the Courant number, and n is the number of elements.
Fig. 6. Comparison of the calculation results and experiment results on the inner wall surface static pressure of Type-A cyclone.
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3.3. Validity of analysis conditions The validity of the analysis conditions has already been verified by comparing calculation results with experiment results on the inner wall surface static pressure of the cyclone, using the cyclone (Reynolds number of approximately 8.9 × 105) with large amounts of airflow containing dust, as shown in our previous study [9]. A case where the cyclone shape was Type-A is shown in Fig. 6, as an example for the comparison of the calculation results derived with the CFD using the LES of the inner wall surface static pressure of the cyclone with experiment results. The analysis conditions are same as the analysis conditions described earlier in Section 3.2. The horizontal axis shown in the figure represents the dimensionless distance L/D along the wall surface from the center of the upper surface on the cylindrical section in the cyclone with a cyclone internal diameter of D, while the vertical axis represents the pressure coefficient Cp defined by the following equation: Cp ¼
p−pin ρa U in2 =2
ð17Þ
where p is the respective inner wall surface static pressure, pin is the static pressure at the cyclone inlet, and ρa is the atmospheric density. The pressure difference in the cylindrical section was small, while the pressure declined in the conical section, then the pressure recovered in the dust collection section. The pressure distribution was typical for conical cyclone associated with acceleration of flow and the calculation results were confirmed to be quantitatively matching experiment results. 3.4. Analysis results and discussions Figs. 7, 8 and 9 show the calculation results for the tangential velocity uθ, axial velocity uy, and radial velocity ur inside each cyclone, respectively. The velocity in each direction becomes non-dimensional with the average flow rate of Uin at the inlet of the cyclone, showing changes in the velocity over time. The calculation results were obtained by averaging the velocity for every 500 steps during the time in which the inlet pressure of the cyclone was sufficiently stabilized. With regard to the tangential velocity uθ, Fig. 7 confirms the presence of the distinctive Rankin vortex with a forced vortex in the central part and a free vortex in the periphery for all the cyclones. Furthermore, the tangential velocity uθ also decreased in all regions of the dust collection section in Type-B and Type-D cyclones with an apex cone regardless of whether a stabilizer was attached. With regard to axial velocity uy, Fig. 8 shows no significant changes over time in any of the cyclones. The figure also confirms the presence of a descending flow in the periphery and an ascending flow in the central part of the cylindrical and conical sections. Additionally, the line graph in Fig. 8 indicates that the absolute value of the axial velocity uy in the dust collection section was smaller and uniform for Type-B and Type-D cyclones with apex cones compared to Type-A and Type-C cyclones without apex cones regardless of whether a stabilizer was attached. With regard to the radial velocity ur, Fig. 9 confirms that there were larger fluctuations between the positive and negative sides at the central part of the Type-A cyclone only. Compared to the Type-A cyclone, the Type-B cyclone with an apex cone as well as the Type-C and Type-D cyclones with stabilizers had smaller fluctuations in the radial velocity ur at the central part of the cyclone. Furthermore, in order to clarify this point, Figs. 10 and 11 show the distributions of flow rate vectors of each cyclone in the x–y section. The length of the vectors is represented as fixed-length for making the flow direction clearly understandable.
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Figs. 10 and 11 confirm the presence of a descending flow in the periphery and an ascending flow in the central part of the cylindrical and conical sections in any of the cyclones, as described above. In the Type-A cyclone, the ascending flow direction significantly changed with the time within the range from the direction toward the center of the cyclone to the opposite direction at each position within the area where the ascending flow appeared in the central part of the conical section, whereas, in the Type-B cyclone with an apex cone, the ascending flow direction became smaller with the temporal fluctuations getting closer to a direction parallel to the axial direction at the same time. Additionally, in the Type-C and Type-D cyclones with stabilizers, the ascending flow direction became significantly smaller temporal fluctuations resulting in an almost parallel direction to the axial direction. As the degree of temporal fluctuations in the ascending flow direction which varied within the range from the direction toward the center of the cyclone to the opposite direction corresponded with the temporal fluctuations of the radial velocity ur, the degree of temporal fluctuations of the radial velocity ur clearly decreased by attaching an apex cone or a stabilizer in the area the ascending flow appeared in the central part of the conical section. The diminished fluctuation in the radial velocity ur at the central part of the cyclone may be attributed to the decrease in the inclination angle of the flow to the tangential direction because of a reduction in the eccentricity of the swirling flow center and the shape center of the cyclone caused by attaching an apex cone or a stabilizer. In order to clarify this point, Fig. 12 shows the distributions of flow rate vectors at the central part of each cyclone in the x–z section (y = 2.20D). The swirling flow can be confirmed to have been flowing in the circumferential direction on the surface of the stabilizer in Type-C and Type-D cyclones, as opposed to the flow of the Type-A cyclone. This implies that the swirling flow center and the shape center mostly corresponded with one another and that the inclination angle of the swirling flow to the tangential direction decreased. It can also be confirmed that the eccentricity of the swirling flow center and the shape center was clearly smaller for the Type-B cyclone, which had an apex cone but no stabilizer, compared to the Type-A cyclone. For the Type-A cyclone, the presence of a swirling flow that appears to cut across the shape center of the cyclone can be confirmed at the central part of the cyclone. These findings revealed that attaching an apex cone impacts the flow condition as the inclination angle to the tangential direction of the swirling flow decreases at the central part of the cyclone owing to the inhibited eccentricity of the swirling center and the shape center in the conical section, while the swirling flow which cuts across the shape center of the cyclone is inhibited. Moreover, these findings showed that the ascending and descending swirling airflow rates decrease in the dust collection section. Furthermore, we discovered that attaching the stabilizer affected the flow conditions, in that the swirling flow moved along the circumferential direction on the stabilizer surface. This resulted in a flow in which the swirling flow center and the shape center mostly corresponded with one another, leading to the smaller inclination angle to the tangential direction of the swirling flow. In other words, this implied that the reason for the improvement or decline in dust collection and particle classification performance of the cyclones by attaching an apex cone or a stabilizer in the experiments can be attributed to the impact of the flow conditions arising from the aforementioned differences in the structure and configuration of the cyclones on the particle motions. The following two areas can be considered factors that led to the improvement in the dust collection and particle classification performance of cyclones by attaching an apex cone: (1) The decrease in the airflow rate of the descending and ascending swirling flows in the dust collection section may have reduced
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the frequency of discharging the particles that are separated in the conical section and collected in the dust collection section from the cyclone as they are once again whirled up and ascended by the swirling flow. (2) There is a flow cutting across the shape center of the cyclone when the eccentricity of the swirling flow center in the conical section and the shape center of the cyclone exists. Thus, the particles that are included in that flow at times are discharged by the
ascending flow at the center of the cyclone without being separated. However, when no eccentricity of the swirling flow center and the shape center of the cyclone exists, the frequency of a flow cutting across the shape center of the cyclone decreases, inhibiting the discharge of particles from the cyclone. Moreover, the decline in the dust collection and particle classification performance by attaching a stabilizer can be explained based on
Fig. 7. Computed tangential velocity inside each cyclone in the x–y section.
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Fig. 8. Computed axial velocity inside each cyclone in the x–y section.
the results obtained from comparing different flows when a stabilizer was attached and when it was not attached at the center of the cyclone in the x–y section (y = 2.20D), as shown in Fig. 13. Fig. 13(a) shows no significant changes in the axial velocity for the Type-C cyclone with a stabilizer compared to the Type-A cyclone even though a decline in the tangential velocity can be observed near the stabilizer surface. Additionally, comparative results between the
Type-B and Type-D cyclones in Fig. 13(b) reveal that the flow conditions that vary depending on whether or not a stabilizer was attached were similar to those in situations when an apex cone was attached. This indicates that the decline in the dust collection and particle classification performance occurs because the velocity of the swirling flow near the stabilizer surface decreases with the presence of a stabilizer, causing the particles to mix near the stabilizer surface in the conical
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Fig. 9. Computed radial velocity inside each cyclone in the x–y section.
section to remain unseparated and be discharged with the ascending flow from the cyclone without gaining sufficient centrifugal force. The above mentioned eccentricity of the swirling flow center and the shape center can be observed in Fig. 13. The temporal changes in the eccentricity of the swirling flow center and the shape center cause changes in the oscillation of the forced vortex over time in the Type-A cyclone. However, changes in the oscillation of the
forced vortex over time are not observed in the Type-B cyclone with a stabilizer because the eccentricity of the swirling flow center and the shape center is inhibited. Moreover, in the case of the TypeC and Type-D cyclones, which have stabilizers, changes in the oscillation of the forced vortex over time are not observed, and the swirling flow center and the shape center mostly correspond with one another.
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Fig. 10. Computed fluid velocity distributions of Type-A and Type-B cyclones in the x–y section.
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Fig. 11. Computed fluid velocity distributions of Type-C and Type-D cyclones in the x–y section.
Y. Kosaki et al. / Powder Technology 277 (2015) 22–35
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Fig. 12. Computed fluid velocity distributions at the central part of each cyclone in the x–z section (y = 2.20D).
4. Conclusion This study conducted dust collection and particle classification experiments and LES analysis for cases where an apex cone or a stabilizer—a structure and configuration intended to improve dust collection and classification performance reported in past studies on conical or cylindrical cyclones—was attached to a relatively large conical cyclone with a Reynolds number of 8.9 × 105, which processes large amounts of airflow containing dust and is used in an actual dust collection plant [6,8]. The relationship between the flow conditions in the cyclones and the dust collection and particle classification performance was investigated by comparing and examining the experiment and analysis results. The findings led us to the following conclusions. (1) With regard to the structure and configuration intended to improve the dust collection and particle classification performance, this study revealed that the best collection and particle classification performance can be achieved by having no stabilizer attached, but having an apex cone attached when considering the experiment conditions used in this study.
(2) The apex cone attached to the conical cyclone decreases the airflow rate of the descending and ascending swirling flows in the dust collection section, which reduces the frequency of the particles collected in the dust collection section being whirled up by the swirling flow in the dust collection section. This phenomenon inhibits the discharge of particles from the cyclone. Furthermore, because the eccentricity of the swirling flow center and the shape center is inhibited in the conical section, the frequency of a flow cutting across the shape center decreases, causing the frequency of particles in such flows being discharged by the ascending flow at the center to decrease. This, in turn, is effective in inhibiting the discharge of particles from the cyclone. (3) The stabilizer attached to the conical cyclone causes the swirling flow to move along its surface. Therefore, there is no flow cutting across the shape center because the swirling flow center and the shape center mostly correspond with one another. However, the velocity of the swirling flow near the surface of this stabilizer decreases. Hence, the particles mixed near the stabilizer surface in the conical section do not gain sufficient centrifugal force and
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Fig. 13. a. Comparisons of the computed fluid velocity distributions in the central parts of each cyclone without apex cone in the x–y section (y = 2.20D). b. Comparisons of the computed fluid velocity distributions in the central part of each cyclone with apex cone in the x–y section (y = 2.20D).
are discharged with the ascending flow from the cyclone without being separated. (4) Conducting a simulation on the flow field (swirling flow, ascending flow, and descending flow) inside the cyclone with CFD using LES under appropriate analysis conditions made it possible to compare the dust collection and particle classification performance for different structures and configurations of cyclones qualitatively. Thus, with regard to the design of a conical cyclone, we believe that it would be possible to design a cyclone with improved dust collection and particle classification performance by examining the structures and configurations of the cyclone that inhibit the eccentricity of the swirling flow center and shape center in the conical section of the cyclone without stabilizers, and also by examining the structures and configurations that reduce the velocity of the ascending and descending swirling flows in the dust collection section, with CFD using LES.
The investigation on a conical cyclone in this study showed that a stabilizer did not play a part in improving the dust collection and particle classification performance. On the other hand, it has been reported that a stabilizer does improve the dust collection and particle classification performance when attached to a cylindrical cyclone [8]. Therefore,
our future task is to investigate the relationship between the flow field inside the cyclone and the dust collection and particle classification performance of a cylindrical cyclone. Disclosure statement The authors declare that they do not have any conflicts of interest. Source of funding No specific source of funding received. References [1] K. Iinoya, Syujin Sochi (New Edition), Nikkan Kogyo Shimbunsya, Tokyo, 1972. 128. [2] K. Iinoya, On the air flow of a cyclone dust separator: study on a cyclone separator, the 2nd report, Trans. Jpn. Soc. Mech. Eng. 18 (1952) 42–48. [3] H. Yoshida, K. Fukui, K. Yoshida, E. Shinoda, Particle separation by Iinoya's type gas cyclone, Powder Technol. 118 (2001) 16–23. [4] H. Yoshida, K. Ono, K. Fukui, The effect of a new method of fluid flow control on submicron particle classification in gas-cyclones, Powder Technol. 149 (2005) 139–147. [5] H. Yoshida, Y. Inada, K. Fukui, T. Yamamoto, Improvement of gas-cyclone performance by use of local fluid flow control method, Powder Technol. 193 (2009) 6–14. [6] H. Yoshida, Y. Nishimura, K. Fukui, T. Yamamoto, Effect of apex cone shape on fine particle classification of gas-cyclone, Powder Technol. 204 (2010) 54–62.
Y. Kosaki et al. / Powder Technology 277 (2015) 22–35 [7] O. Akiyama, C. Kato, D. Kawate, Mechanism of particle collection in a cylindrical cyclone separator: 1st report, validation of large eddy simulation and investigation on detailed flow structures, Trans. Jpn. Soc. Mech. Eng. B 78 (2012) 1886–1902. [8] O. Akiyama, C. Kato, D. Kawate, Mechanism of particle collection in a cylindrical cyclone separator: 2nd report, validation of large eddy simulation and investigation on detailed flow structures, Trans. Jpn. Soc. Mech. Eng. B 78 (2012) 1903–1918. [9] Y. Kosaki, Y. Yamanaka, K. Takeshima, Investigative study on cyclone design, 1st report, investigation of flow field inside the cyclone by fluid analysis, Jpn. Soc. Des. Eng. 49 (2015) 589–596. [10] S. Elgobashi, Particle-laden turbulent flows: direct simulation and closure models, Appl. Sci. Res. 48 (1991) 301–314.
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[11] F. Nicoud, F. Ducros, Subgrid-scale stress modeling based on the square of the velocity gradient tensor, Flow Turbul. Combust. 62 (1999) 183–200. [12] L. Temmerman, M.A. Leschziner, C.P. Mellen, J. Frohlich, Investigation of wallfunction approximations and subgrid-scale models in large eddy simulation of separated flow in a channel with streamwise periodic constrictions, Int. J. Heat Fluid Flow 24 (2003) 157–180. [13] M. Inagaki, O. Murata, K. Abe, T. Kondoh, Numerical prediction of fluid-resonant oscillations at low Mach number, Trans. Jpn. Soc. Mech. Eng. B 66 (2000) 2274–2281. [14] F. Menter, Zonal Two Equation k-ω Turbulence Models for Aerodynamic Flows, AIAA 93-2906, 1993.
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Powder Technology journal homepage: www.elsevier.com/locate/powtec
Investigation on dust collection and particle classification performance of cyclones by airflow control for design of cyclones Yuhei Kosaki a,⁎, Takayuki Hirai b, Yoshinari Yamanaka a, Keishi Takeshima b a b
Kanematsu Engineering Co., Ltd., 3981-7, Nunoshida, Kochi City, Kochi 781-5101, Japan Kochi National College of Technology, 200-1, Otsu, Monobe, Nankoku City, Kochi 783-8508, Japan
a r t i c l e
i n f o
Article history: Received 10 October 2014 Received in revised form 11 December 2014 Accepted 25 February 2015 Available online 5 March 2015 Keywords: Cyclone Large eddy simulation Particle separation Apex cone Stabilizer
a b s t r a c t We investigated the design of relatively large cyclones with large amounts of airflow containing dust that are used in actual dust collection plants. In order to obtain basic data on the design of conical cyclones with a Reynolds number of approximately 8.9 × 105, we compared the fluid analysis results with the experimental results on dust collection and particle classification performance for conical cyclones to which apex cones and stabilizers were attached. Then, we elucidated the relationship between the flow conditions inside the conical cyclone with a Reynolds number of 8.9 × 105 and dust collection and particle classification performance. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The separation and collection of particles at dust collection plants using pneumatic conveying generally involve the installation of a receiver tank (settling tank) for the conveying process where particles with relatively large diameters and high densities are separated and collected via the gravitational force that acts on them. Particles with smaller diameters and lower densities, which cannot be separated and collected easily with a receiver tank (for cases where Stokes' law applies to the aerodynamic force acting on particles), are partially separated and collected by the cyclone in the subsequent process, by utilizing the centrifugal force acting on the particles. However, the particles that cannot be collected by the cyclone are separated and collected using a filter in the following process. Subsequently, the airflow is usually guided into a suction machine (blower) installed at the very end of the conveying line and then discharged into the atmosphere. In order to reduce the load on the filter during such dust collection processes, it is necessary to improve the dust collection and particle classification performance of cyclones. Particle separation in a cyclone is based on the principle wherein particles are accumulated in a dust collection section after being separated outward by the centrifugal force originating from a swirling
Abbreviations: CFD, computational fluid dynamics; LES, large eddy simulation; PIV, particle image velocity; SGS, sub-grid scale; WALE, wall-adapting local eddy-viscosity; SST, shear-stress transport. ⁎ Corresponding author. Tel.: +81 088 845 5511; fax: +81 088 845 5255. E-mail address: [email protected] (Y. Kosaki).
http://dx.doi.org/10.1016/j.powtec.2015.02.051 0032-5910/© 2015 Elsevier B.V. All rights reserved.
flow and trickling into the dust collection section along the cyclone wall surface. The swirling flow inside the cyclone is a combination of a free vortex and forced vortex (hereinafter referred to as the Rankin vortex). This combined vortex also has descending and ascending flows, causing a downward reverse flow at times as negative pressure occurs around the central region. Therefore, it is known as an unsteady flow because the inclination angle of the flow to the tangential direction changes constantly owing to the eccentricity of the swirling flow center and the shape center [1,2]. Thus, in order to design a cyclone with high particle classification performance, it is necessary to have an appropriate design that takes the unsteady flow into consideration. However, it is not practical to create a prototype in advance and take measurements using a Pitot tube current meter, hot-wire anemometer, or particle image velocity (PIV) for the estimation of the flow field inside a cyclone during design, from the standpoint of the time and cost required for the measurements and prototyping. However, the high processing speeds and decreased prices of computers in recent years have made it possible to apply the analysis of the fluid dynamic phenomenon by computational fluid dynamics (CFD) to engineering as well. Using CFD, Yoshida et al. [3–6] calculated the flow inside cyclones and the particle trajectory in a three-dimensional simulation by the direct method. They discussed the particle classification and dust collection performance of the cyclones by comparing the results of dust collection and classification experiments. With regard to the prediction of unsteady flow fields inside cyclones, further progress in CFD, especially in recent years, allowed Akiyama
Y. Kosaki et al. / Powder Technology 277 (2015) 22–35
et al. [7,8] to confirm the feasibility of reproducing the unsteady flow inside cyclones based on the comparison between the experimental values in the flow field and the analysis results obtained by employing CFD with large eddy simulation (LES), which targets a compact cyclone (Reynolds number of approximately 3 × 104 to 4 × 104) with a low flow rate at its inlet. Additionally, they discussed the dust collection and particle classification performance by comparing dust collection and particle classification experiment results. We clarified the validity of the analysis conditions (e.g., the mesh and Courant number) by comparing the CFD calculation results obtained by employing LES with the experiment results for the flow fields inside a relatively large cyclone (Reynolds number of approximately 8.9 × 105) with large amounts of airflow containing dust, which is used in actual dust collection plants; we also considered a design target for this study. Then, we reported that the distinctive flow inside the cyclone [1,2] can be reproduced in a conical cyclone [9]. The purpose of this paper is to report the useful knowledge gained by conducting an investigation on the relationship between the flow conditions inside a cyclone and the dust collection and particle classification performance of the cyclone. This task was carried out by conducting dust collection and particle classification experiments, implementing LES analyses for cases when using an apex cone and a stabilizer [6,8]—a structure and configuration intended to improve dust collection and particle classification performance reported in the past studies on conical and cylindrical cyclones—and performing comparative analyses on the obtained results. The investigation aimed to gather basic data on the design of relatively large conical cyclones (Reynolds number of approximately 8.9 × 105) with large amounts of airflow containing dust, which are used in actual dust collection plants. 2. Dust collection and particle classification experiments 2.1. Experiment device Fig. 1 shows a schematic diagram of the experiment device. While air is allowed to flow into the cyclone by maintaining the average flow rate at the inlet of the cyclone ① constant with an inverter driven suction blower ②, a constant amount of powder is supplied by the feeder ⑦ from the cyclone inlet. Before supplying the powder, the average flow rate at the inlet of the cyclone Uin is defined by the following equation, based on values
23
measured using a vortex flow meter ③, a pressure gauge ④, a thermometer ⑤ installed in the downstream side of the cyclone and a barometer and pressure gauge ⑥ installed in the upstream side from the inlet of the cyclone.
U in ¼
p f TaQ pa T f Ain
ð1Þ
where pf is the static pressure in the vortex flow meter section, pa is the atmospheric pressure, Ta is the atmospheric temperature, Tf is the temperature of the vortex flow meter section, Q is the volumetric flow rate measured using a vortex flow meter, and Ain is the cross-sectional area of the pipe at the inlet of the cyclone. 2.2. Trial cyclones Fig. 2 shows four types of conical cyclones. The origin of the coordinate system was set at the center of the bottom surface of the cyclone. The central axis of the cyclone was defined as the y-axis, and the direction of flow into the cyclone was defined as the z-axis. Type-A cyclone is a standard conical cyclone comprising a cylindrical section with an internal diameter D of 385 mm, a conical section, and a dust collection section. Type-B cyclone inhibits the re-scattering of particles that enter the dust collection section by reducing the airflow rate inside the dust collection section. Therefore, an apex cone was installed at the inlet of the dust collection section of a Type-A cyclone [6]. For Type-C and Type-D cyclones, a core bar with a circular cross section (hereinafter referred to as the stabilizer) was installed at the central axis of the Type-A and Type-B cyclones in order to confirm the dust collection and particle classification performance when inhibiting the eccentricity of the swirling flow center and the shape center in Type-A and Type-B cyclones [8]. 2.3. Experiment method The dust collection and particle classification experiments of the cyclones were performed at an average flow rate of Uin = 35 m/s at
Fig. 1. Experiment device.
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Y. Kosaki et al. / Powder Technology 277 (2015) 22–35
Fig. 2. Schematic diagrams for each cyclone.
the inlet of the cyclone based on the assumption that a cyclone with large amounts of airflow containing dust is used. The Reynolds number Re is defined by the following equation:
Re ¼
U in D 5 ¼ 8:9 10 ν
ð2Þ
where Uin is the average flow rate at the inlet of the cyclone, D is the diameter of the cylindrical section of the cyclone, and ν is the kinematic viscosity of air. As Fig. 3 shows, acrylic spherical particles (EXM-5 manufactured by Sekisui Plastics Co., Ltd.) were used as the test powder; they had a density of ρp = 1200 kg/m3, with the distribution of particle diameters ranging from Dp = 1 to 10 μm and a mass median diameter of Dp = 5 μm. This selection was based on the assumption of the presence of low-density particles with relatively small particle diameters that are difficult to separate and collect using a receiver tank in the preliminary process of cyclone operation in a dust collection plant. Moreover, the particle volume fraction φ in the airflow containing dust was set at approximately 7.5 × 10−7 based on the current values of the cyclones considered for our design, and the mass flow rate of the powder was set at 25 g/min. Past studies have reported that the effects of the collision between particles and particle motions on the flow can be disregarded when the particle volume fraction is of the order of 10−7 [10].
After supplying the dust-containing air to the cyclone for 2 h under the conditions described above, the increase in the mass of the cyclone was measured. Then, the particle size distribution was measured by sampling the dust collected by the cyclone and the filter. The dust collection performance and classification performance of each cyclone were evaluated by calculating the dust collection efficiency η, partial separation efficiency Δη, and classification accuracy κ defined by the following equation based on the measured mass and particle size distribution. A laser diffraction particle size analyzer (SALD-2200 manufactured by Shimadzu Corporation) was used to measure the particle size distribution of the powder.
η¼
mc 100 m
ð3Þ
where m is the mass of the powder supplied to the cyclone and mc is the mass of the powder collected by the cyclone (=the amount of increase in the mass of the cyclone).
Δη ¼
mc f c 100 mc f c þ ðm−mc Þf f
ð4Þ
where fc is the abundance ratio of each particle diameter of the powder collected by the cyclone, and ff is the abundance ratio of each particle diameter of the powder collected by the filter.
Fig. 3. Particle size distribution and the SEM photograph of the test powder.
Y. Kosaki et al. / Powder Technology 277 (2015) 22–35
κ1 ¼
Dp75 Dp25
ð5Þ
κ2 ¼
Dp90 Dp10
ð6Þ
25
where Dpx is the particle diameter at a partial separation efficiency of x%. 2.4. Experiment results Table 1 shows the dust collection efficiency η of each cyclone. The dust collection efficiency for the Type-A cyclone, which was the standard conical cyclone, was 90.1%. Compared to the dust collection efficiency of the Type-A cyclone, the dust collection efficiency for the Type-B cyclone with an apex cone was higher, whereas that for the Type-C cyclone with a stabilizer was lower. However, it was confirmed that the dust collection efficiency of the Type-D cyclone, which was designed by adding an apex cone to the Type-C cyclone, was higher compared to the Type-C cyclone. These differences in the dust collection efficiencies of each cyclone can reveal the relationship between the structure and configuration and the dust collection performance of each cyclone by comparing the partial separation efficiency of the cyclones shown in Fig. 4. Compared to the Type-A cyclone, the Type-B cyclone with an apex cone attached showed a decrease in the diameters of the separable particles and an increase in the partial separation efficiency for each particle diameter. Moreover, the partial separation efficiency decreased over a wide range of particle diameters for the Type-C cyclone with a stabilizer attached. However, it was confirmed that the partial separation efficiency for each particle diameter increased and the diameters of the particles that can be separated decreased for the Type-D cyclone compared to the Type-C cyclone. These findings revealed that the dust collection performance of conical cyclones improves by attaching an apex cone but declines by attaching a stabilizer. Additionally, the decline in the dust collection performance due to the stabilizer can be eliminated by adding an apex cone while leaving the stabilizer attached. Moreover, the highest dust collection performance can be achieved when an apex cone is attached without installing a stabilizer. Table 2 shows the classification accuracy κ of each cyclone. The classification accuracy was obtained from the partial separation efficiency results shown in Fig. 4 and the classification performance improves as the classification accuracy nears 1. Compared to the classification accuracy of the Type-A cyclone, both κ1 and κ2 of the Type-B cyclone approached 1, improving the particle classification performance, whereas the particle classification performance decreased for the Type-C cyclone. Yet, κ2 of the Type-D cyclone was confirmed to be near 1 compared to the Type-C cyclone. These findings show that the particle classification performance of conical cyclones improves when an apex cone is attached but declines when a stabilizer is attached as is the case for the dust collection performance. Moreover, the classification accuracy of the Type-B cyclone was closest to 1, indicating that the cyclone had the highest particle classification performance. Thus, the dust collection performance and particle classification performance of conical cyclones (Reynolds number of 8.9 × 105), which
process large amounts of airflow containing dust, improve by adding an apex cone and decline by adding a stabilizer. Additionally, it was revealed that the cyclone with an apex cone but without a stabilizer has the highest dust collection and particle classification performance. It was also found that attaching a stabilizer is not a useful way to improve dust collection and particle classification performance. 3. Fluid analysis and discussion 3.1. Method Fluid analysis was performed on four types of cyclones with shapes identical to those in the experiments shown in Fig. 2, to investigate the relationship between the flow conditions inside the cyclone and the dust collection and particle classification performance. 3.2. Analysis conditions SCRYU/Tetra for Windows (manufactured by Software Cradle Co., Ltd.) was used to conduct the fluid analysis. The mass conservation Eq. (7) and the Navier–Stokes Eq. (8), which are the equations described by orthogonal coordinates and averaged by the grid filter, were used as fundamental equations to perform the LES analysis.
∂ui ¼0 ∂xi
ð7Þ
! ∂ρτ i j ∂ρui ∂ρui u j ∂p ∂ ∂ui ∂u j ¼− þ μ þ þ − ∂t ∂x j ∂x j ∂xi ∂x j ∂xi ∂x j
ð8Þ
where ūi is the xi direction component of the flow rate averaged by the grid filter, p is the static pressure averaged by the grid filter, ρ is the density of fluid, μ is the viscosity of fluid, and τij is the sub-grid scale (SGS) stress. The density ρ of the fluid, in other words air, was set to 1.206 kg/m3 and the viscosity μ was set to 1.83 × 10−5 Pa·s.
Table 2 Accuracy of classification for each cyclone.
Table 1 Dust collection efficiency for each cyclone.
η [%]
Fig. 4. Partial separation efficiency of each cyclone.
Type-A
Type-B
Type-C
Type-D
90.1
98.6
84.6
96.9
κ1 [−] κ2 [−]
Type-A
Type-B
Type-C
Type-D
1.12 1.26
1.09 1.19
1.14 1.34
1.14 1.30
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Y. Kosaki et al. / Powder Technology 277 (2015) 22–35
Model constant Cw was set to 0.316 suggested by Temmerman et al. [12]. Furthermore, the grid filter size Δ was defined using the following equation:
Δ¼V
Fig. 5. Mesh of Type-A cyclone.
The wall-adapting local eddy viscosity (WALE) model [11] was adopted as the SGS model. In other words, the following expressions were used: τi j ¼ ui u j −ui u j ¼ −2νSGS Si j 3=2 Sdij Sdij 5=2 5=4 Si j Si j þ Sdij Sdij
ν SGS
2 ¼ Cw Δ
Si j ¼
1 g þ g ji 2 ij
ð11Þ
Si j ¼
1 1 2 2 2 g i j þ g ji − δi j gkk 2 3
ð12Þ
gi j ¼
∂ui ∂xi
ð13Þ
d
2
ð9Þ
g i j ¼ g ik g k j
ð10Þ
ð14Þ
where νSGS is SGS kinematic eddy viscosity, Si j is the strain rate tensor averaged by the grid filter, g i j is the velocity gradient tensor averaged by the grid filter, δij is the Kronecker delta, Cw is the model constant, and Δ is the grid filter size.
1=3
ð15Þ
where V is the volume of the mesh element. The fundamental equations were discretized by the finite volume method. The second-order central difference scheme was applied to the advection term and the diffusion term. On the other hand, secondorder implicit scheme was applied to the time term. The mesh of Type-A cyclone is shown in Fig. 5 as an example of the mesh. The inlet boundary and the outlet boundary were secured by a piping section immediately adjacent to the main unit, and the mesh comprised a prism-shaped pentahedral unstructured mesh for the three layers from the wall surface and a tetrahedral unstructured mesh for the rest of the layers. However, in order to determine the Rankin vortex with good accuracy, the meshes at the central area of the cyclone were reduced to half the size of the surrounding meshes. Furthermore, the meshes of Type B, Type C and Type D also had configurations that were similar to that of Type A. The number of elements in each cyclone was 22,274,926 in the Type-A cyclone, 21,886,136 in the Type-B cyclone, 21,632,693 in the Type-C cyclone, and 21,593,363 in the Type-D cyclone. The boundary conditions consist of a steady inflow flow rate of Uin = 35 m/s at the inlet of the cyclone and static pressure of pout = 0 Pa at the outlet of the cyclone. The wall boundary conditions were set to expand the dual layer model of the Werner and Wengle type to a triple layer model in the LES [13]. With regard to the analysis, to first of all performed 1000 steps of steady state analysis, the existing shear-stress transport (SST) k-ω turbulence model [14] and the calculation results thereof were used as initial values to perform unsteady analysis with the LES. The Courant number C was set at 4, with the time advancement occurring at the minimum value Δt of the time increment Δti defined by Eq. (16) based on each element width ΔLi and the flow rate at each element ui. The averaging process was conducted when the average pressure value at the inlet of the cyclone started to stabilize to obtain the flow field.
Δt i ¼ C
ΔLi ΔL ¼ 4 i ; i ¼ 1; 2; :::; n ui ui
ð16Þ
where Δti is the time increment calculated for each element, ΔLi is the width of each element, ui is the flow rate of each element, C is the Courant number, and n is the number of elements.
Fig. 6. Comparison of the calculation results and experiment results on the inner wall surface static pressure of Type-A cyclone.
Y. Kosaki et al. / Powder Technology 277 (2015) 22–35
3.3. Validity of analysis conditions The validity of the analysis conditions has already been verified by comparing calculation results with experiment results on the inner wall surface static pressure of the cyclone, using the cyclone (Reynolds number of approximately 8.9 × 105) with large amounts of airflow containing dust, as shown in our previous study [9]. A case where the cyclone shape was Type-A is shown in Fig. 6, as an example for the comparison of the calculation results derived with the CFD using the LES of the inner wall surface static pressure of the cyclone with experiment results. The analysis conditions are same as the analysis conditions described earlier in Section 3.2. The horizontal axis shown in the figure represents the dimensionless distance L/D along the wall surface from the center of the upper surface on the cylindrical section in the cyclone with a cyclone internal diameter of D, while the vertical axis represents the pressure coefficient Cp defined by the following equation: Cp ¼
p−pin ρa U in2 =2
ð17Þ
where p is the respective inner wall surface static pressure, pin is the static pressure at the cyclone inlet, and ρa is the atmospheric density. The pressure difference in the cylindrical section was small, while the pressure declined in the conical section, then the pressure recovered in the dust collection section. The pressure distribution was typical for conical cyclone associated with acceleration of flow and the calculation results were confirmed to be quantitatively matching experiment results. 3.4. Analysis results and discussions Figs. 7, 8 and 9 show the calculation results for the tangential velocity uθ, axial velocity uy, and radial velocity ur inside each cyclone, respectively. The velocity in each direction becomes non-dimensional with the average flow rate of Uin at the inlet of the cyclone, showing changes in the velocity over time. The calculation results were obtained by averaging the velocity for every 500 steps during the time in which the inlet pressure of the cyclone was sufficiently stabilized. With regard to the tangential velocity uθ, Fig. 7 confirms the presence of the distinctive Rankin vortex with a forced vortex in the central part and a free vortex in the periphery for all the cyclones. Furthermore, the tangential velocity uθ also decreased in all regions of the dust collection section in Type-B and Type-D cyclones with an apex cone regardless of whether a stabilizer was attached. With regard to axial velocity uy, Fig. 8 shows no significant changes over time in any of the cyclones. The figure also confirms the presence of a descending flow in the periphery and an ascending flow in the central part of the cylindrical and conical sections. Additionally, the line graph in Fig. 8 indicates that the absolute value of the axial velocity uy in the dust collection section was smaller and uniform for Type-B and Type-D cyclones with apex cones compared to Type-A and Type-C cyclones without apex cones regardless of whether a stabilizer was attached. With regard to the radial velocity ur, Fig. 9 confirms that there were larger fluctuations between the positive and negative sides at the central part of the Type-A cyclone only. Compared to the Type-A cyclone, the Type-B cyclone with an apex cone as well as the Type-C and Type-D cyclones with stabilizers had smaller fluctuations in the radial velocity ur at the central part of the cyclone. Furthermore, in order to clarify this point, Figs. 10 and 11 show the distributions of flow rate vectors of each cyclone in the x–y section. The length of the vectors is represented as fixed-length for making the flow direction clearly understandable.
27
Figs. 10 and 11 confirm the presence of a descending flow in the periphery and an ascending flow in the central part of the cylindrical and conical sections in any of the cyclones, as described above. In the Type-A cyclone, the ascending flow direction significantly changed with the time within the range from the direction toward the center of the cyclone to the opposite direction at each position within the area where the ascending flow appeared in the central part of the conical section, whereas, in the Type-B cyclone with an apex cone, the ascending flow direction became smaller with the temporal fluctuations getting closer to a direction parallel to the axial direction at the same time. Additionally, in the Type-C and Type-D cyclones with stabilizers, the ascending flow direction became significantly smaller temporal fluctuations resulting in an almost parallel direction to the axial direction. As the degree of temporal fluctuations in the ascending flow direction which varied within the range from the direction toward the center of the cyclone to the opposite direction corresponded with the temporal fluctuations of the radial velocity ur, the degree of temporal fluctuations of the radial velocity ur clearly decreased by attaching an apex cone or a stabilizer in the area the ascending flow appeared in the central part of the conical section. The diminished fluctuation in the radial velocity ur at the central part of the cyclone may be attributed to the decrease in the inclination angle of the flow to the tangential direction because of a reduction in the eccentricity of the swirling flow center and the shape center of the cyclone caused by attaching an apex cone or a stabilizer. In order to clarify this point, Fig. 12 shows the distributions of flow rate vectors at the central part of each cyclone in the x–z section (y = 2.20D). The swirling flow can be confirmed to have been flowing in the circumferential direction on the surface of the stabilizer in Type-C and Type-D cyclones, as opposed to the flow of the Type-A cyclone. This implies that the swirling flow center and the shape center mostly corresponded with one another and that the inclination angle of the swirling flow to the tangential direction decreased. It can also be confirmed that the eccentricity of the swirling flow center and the shape center was clearly smaller for the Type-B cyclone, which had an apex cone but no stabilizer, compared to the Type-A cyclone. For the Type-A cyclone, the presence of a swirling flow that appears to cut across the shape center of the cyclone can be confirmed at the central part of the cyclone. These findings revealed that attaching an apex cone impacts the flow condition as the inclination angle to the tangential direction of the swirling flow decreases at the central part of the cyclone owing to the inhibited eccentricity of the swirling center and the shape center in the conical section, while the swirling flow which cuts across the shape center of the cyclone is inhibited. Moreover, these findings showed that the ascending and descending swirling airflow rates decrease in the dust collection section. Furthermore, we discovered that attaching the stabilizer affected the flow conditions, in that the swirling flow moved along the circumferential direction on the stabilizer surface. This resulted in a flow in which the swirling flow center and the shape center mostly corresponded with one another, leading to the smaller inclination angle to the tangential direction of the swirling flow. In other words, this implied that the reason for the improvement or decline in dust collection and particle classification performance of the cyclones by attaching an apex cone or a stabilizer in the experiments can be attributed to the impact of the flow conditions arising from the aforementioned differences in the structure and configuration of the cyclones on the particle motions. The following two areas can be considered factors that led to the improvement in the dust collection and particle classification performance of cyclones by attaching an apex cone: (1) The decrease in the airflow rate of the descending and ascending swirling flows in the dust collection section may have reduced
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Y. Kosaki et al. / Powder Technology 277 (2015) 22–35
the frequency of discharging the particles that are separated in the conical section and collected in the dust collection section from the cyclone as they are once again whirled up and ascended by the swirling flow. (2) There is a flow cutting across the shape center of the cyclone when the eccentricity of the swirling flow center in the conical section and the shape center of the cyclone exists. Thus, the particles that are included in that flow at times are discharged by the
ascending flow at the center of the cyclone without being separated. However, when no eccentricity of the swirling flow center and the shape center of the cyclone exists, the frequency of a flow cutting across the shape center of the cyclone decreases, inhibiting the discharge of particles from the cyclone. Moreover, the decline in the dust collection and particle classification performance by attaching a stabilizer can be explained based on
Fig. 7. Computed tangential velocity inside each cyclone in the x–y section.
Y. Kosaki et al. / Powder Technology 277 (2015) 22–35
29
Fig. 8. Computed axial velocity inside each cyclone in the x–y section.
the results obtained from comparing different flows when a stabilizer was attached and when it was not attached at the center of the cyclone in the x–y section (y = 2.20D), as shown in Fig. 13. Fig. 13(a) shows no significant changes in the axial velocity for the Type-C cyclone with a stabilizer compared to the Type-A cyclone even though a decline in the tangential velocity can be observed near the stabilizer surface. Additionally, comparative results between the
Type-B and Type-D cyclones in Fig. 13(b) reveal that the flow conditions that vary depending on whether or not a stabilizer was attached were similar to those in situations when an apex cone was attached. This indicates that the decline in the dust collection and particle classification performance occurs because the velocity of the swirling flow near the stabilizer surface decreases with the presence of a stabilizer, causing the particles to mix near the stabilizer surface in the conical
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Y. Kosaki et al. / Powder Technology 277 (2015) 22–35
Fig. 9. Computed radial velocity inside each cyclone in the x–y section.
section to remain unseparated and be discharged with the ascending flow from the cyclone without gaining sufficient centrifugal force. The above mentioned eccentricity of the swirling flow center and the shape center can be observed in Fig. 13. The temporal changes in the eccentricity of the swirling flow center and the shape center cause changes in the oscillation of the forced vortex over time in the Type-A cyclone. However, changes in the oscillation of the
forced vortex over time are not observed in the Type-B cyclone with a stabilizer because the eccentricity of the swirling flow center and the shape center is inhibited. Moreover, in the case of the TypeC and Type-D cyclones, which have stabilizers, changes in the oscillation of the forced vortex over time are not observed, and the swirling flow center and the shape center mostly correspond with one another.
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Fig. 10. Computed fluid velocity distributions of Type-A and Type-B cyclones in the x–y section.
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Fig. 11. Computed fluid velocity distributions of Type-C and Type-D cyclones in the x–y section.
Y. Kosaki et al. / Powder Technology 277 (2015) 22–35
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Fig. 12. Computed fluid velocity distributions at the central part of each cyclone in the x–z section (y = 2.20D).
4. Conclusion This study conducted dust collection and particle classification experiments and LES analysis for cases where an apex cone or a stabilizer—a structure and configuration intended to improve dust collection and classification performance reported in past studies on conical or cylindrical cyclones—was attached to a relatively large conical cyclone with a Reynolds number of 8.9 × 105, which processes large amounts of airflow containing dust and is used in an actual dust collection plant [6,8]. The relationship between the flow conditions in the cyclones and the dust collection and particle classification performance was investigated by comparing and examining the experiment and analysis results. The findings led us to the following conclusions. (1) With regard to the structure and configuration intended to improve the dust collection and particle classification performance, this study revealed that the best collection and particle classification performance can be achieved by having no stabilizer attached, but having an apex cone attached when considering the experiment conditions used in this study.
(2) The apex cone attached to the conical cyclone decreases the airflow rate of the descending and ascending swirling flows in the dust collection section, which reduces the frequency of the particles collected in the dust collection section being whirled up by the swirling flow in the dust collection section. This phenomenon inhibits the discharge of particles from the cyclone. Furthermore, because the eccentricity of the swirling flow center and the shape center is inhibited in the conical section, the frequency of a flow cutting across the shape center decreases, causing the frequency of particles in such flows being discharged by the ascending flow at the center to decrease. This, in turn, is effective in inhibiting the discharge of particles from the cyclone. (3) The stabilizer attached to the conical cyclone causes the swirling flow to move along its surface. Therefore, there is no flow cutting across the shape center because the swirling flow center and the shape center mostly correspond with one another. However, the velocity of the swirling flow near the surface of this stabilizer decreases. Hence, the particles mixed near the stabilizer surface in the conical section do not gain sufficient centrifugal force and
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Fig. 13. a. Comparisons of the computed fluid velocity distributions in the central parts of each cyclone without apex cone in the x–y section (y = 2.20D). b. Comparisons of the computed fluid velocity distributions in the central part of each cyclone with apex cone in the x–y section (y = 2.20D).
are discharged with the ascending flow from the cyclone without being separated. (4) Conducting a simulation on the flow field (swirling flow, ascending flow, and descending flow) inside the cyclone with CFD using LES under appropriate analysis conditions made it possible to compare the dust collection and particle classification performance for different structures and configurations of cyclones qualitatively. Thus, with regard to the design of a conical cyclone, we believe that it would be possible to design a cyclone with improved dust collection and particle classification performance by examining the structures and configurations of the cyclone that inhibit the eccentricity of the swirling flow center and shape center in the conical section of the cyclone without stabilizers, and also by examining the structures and configurations that reduce the velocity of the ascending and descending swirling flows in the dust collection section, with CFD using LES.
The investigation on a conical cyclone in this study showed that a stabilizer did not play a part in improving the dust collection and particle classification performance. On the other hand, it has been reported that a stabilizer does improve the dust collection and particle classification performance when attached to a cylindrical cyclone [8]. Therefore,
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