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Flow simulation and performance analysis of a cyclone–granular bed filter
PTEC-14648; No of Pages 10 Powder Technology xxx (2019) xxx
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Flow simulation and performance analysis of a cyclone–granular bed filter Minghao You a,1, Zhaoyang Li b,c,d,1, Minshu Zhan b,c,⁎⁎, Meili Liu a,⁎, Guogang Sun e, Jiaqing Chen a a
School of Mechanical Engineering, Beijing Institute of Petrochemical Technology, Beijing 102617, China JITRI Institute for Process Modelling and Optimization, Suzhou 215123, China Center for Simulation and Modelling of Particulate Systems, Southeast University - Monash University Joint Research Institute, Suzhou 215123, China d Shandong Iron and Steel Group Co., Ltd., Jinan 250101, China e Beijing Key Laboratory of Process Fluid Filtration and Separation, China University of Petroleum, Beijing 102249, China b c
a r t i c l e
i n f o
Article history: Received 16 May 2019 Received in revised form 19 August 2019 Accepted 28 August 2019 Available online xxxx Keywords: Cyclone Granular bed filter Flow field Separation performance
a b s t r a c t The rapid and efficient filtration of particles from high temperature pyrolysis vapors is of crucial importance for enhancing yields and quality of pyrolysis oil. In this work, an integrated dust removal technology of cyclonegranular bed filter (C-GBF) was designed. A computational fluid dynamics (CFD) simulation of the flow pattern of the C-GBF was carried out. The Reynolds stress model (RSM) and discrete phase model (DPM) were used to describe the gas-solid flow behavior in the C-GBF. The simulated results demonstrated that the flow pattern characterized by a free vortex in the C-GBF was observed. The location of maximum tangential velocity was found to be at the inlet section and the maximum value was about 1.2 times larger than the inlet gas velocity. The pressure drop of the C-GBF was mainly affected by the granular bed with the free vortex playing a trivial role. Based on the understanding of flow characteristics of the free vortex, the effects of the inlet gas velocity and filtration gas velocity on separation performance of the C-GBF were analyzed. The feasibility of the C-GBF was further examined by laboratory experiments under a constant-velocity filtration condition. The matching condition of the C-GBF was obtained with an inlet gas velocity of 30 m/s and the corresponding filtration gas velocity of 0.4 m/s. © 2019 Elsevier B.V. All rights reserved.
1. Introduction The removal of flying char particles from high temperature pyrolysis vapors is a common challenge in thermal conversion processing such as biomass, coal or oil shale. The pyrolysis vapors present a high concentration of char particles (particle size less than 10 μm) in a corrosive, viscous and high-temperature (above 400 °C) gases stream. The filtration performance of char particles directly affects the yields and quality of pyrolysis oil as well as the emission of particulate pollutants. In view of this, several attempts have been made to remove char particles from the high temperature and high viscosity pyrolysis vapors. Cyclones in series were used to separate particle matter from the pyrolysis vapors [1–3]. However, the collection efficiency of cyclone deteriorates drastically for small char particles less than 10 μm in size. A granular bed filter (GBF), using silica sand as filter media, makes a good filtration performance of removing char particles. Liang [4,5], Xu [6,7] and Zhan [8] developed different types of GBF for filtration of particles in coal pyrolysis. ⁎ Corresponding author. ⁎⁎ Corresponding author at: JITRI Institute for Process Modelling and Optimization, Suzhou 215123, China. E-mail addresses: [email protected] (M. Zhan), [email protected] (M. Liu). 1 Mr. You and Dr. Li contribute equally to this work.
Hsiau [9–11] and Brown [12,13] analyzed the filtration performance of moving granular bed filter (MGBF) in biomass pyrolysis. In these experiments, a cyclone followed by a GBF was used in the filtration system. By far, the combination of a GBF with a cyclone is considered to be one of the most promising solution to pyrolysis vapor streams filtration. Locating the GBF inside the cyclone has become an important development direction. Therefore, an integrated dust removal technology of cyclone-granular bed filter (C-GBF) is developed. Compared to a cyclone and a GBF in series, the C-GBF is expected to minimize the resistance time of high temperature pyrolysis vapors and reduce the risk of secondary reactions. Some applications of the C-GBF have been performed by a number of researchers. Brown [12,13] developed a C-GBF with a tangential inlet to induce the cyclonic flow. The coarse particles were separated in the cyclonic chamber while the fine particles were collected by the counter-current flow in the GBF. In order to obtain a uniform distribution of gas flow, several fins were installed inside the cyclonic chamber. However, the gas flow in the outer vortex was not fully developed with such a design. Lv [14,15] developed a C-GBF with a similar structure. The difference was the cross flow GBF used in their studies. A combination of C-GBF has been used by Xu [16]. A spiral vane was used to direct a downward swirling flow. The pressure drop increased correspondingly. Gao [17–19] proposed a combination of a cyclone with a built-in circulating granular bed filter (C-CGBF).
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Please cite this article as: M. You, Z. Li, M. Zhan, et al., Flow simulation and performance analysis of a cyclone–granular bed filter, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.088
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The CGBF was a cross flow filter inherent. Then, the pressure drop characteristics and separation performance were analyzed in the C-CGBF. However, most of these previous studies did not utilized the centrifugal separation in the outer vortex effectively. Moreover, these studies only characterized the performance of the C-GBF. There are limited published investigations on the flow pattern and separation characteristics in the outer vortex of the C-GBF. The performance of the C-GBF not only relies on the combination of the two separating stages, but also comes from the match of operational parameters. The velocity of the gas flow is considered as an important factor to determine the C-GBF performance. For a cyclone, an optimal inlet gas velocity yields the maximum separation efficiency. Many studies [20,21] have confirmed that the optimal inlet gas velocity ranges from 15 m/s to 30 m/s. Similarly, there also exits an optimal filtration gas velocity in a GBF. The value is from about 0.2 m/s to 1 m/s. Therefore, there should be an optimum combination of the gas flow velocity in the cyclone and the GBF in order to increase the collection efficiency while decrease the pressure drop. However, few studies have been carried out in this area, focusing on the matching between the inlet gas velocity and filtration gas velocity. It should be noted that the granular bed filtration is a process in unsteady state. The accumulation of deposited particles in the GBF increases with time. Accordingly, the pressure drop increases while the filtration gas velocity decreases. Therefore, the inlet gas velocity and separation performance in the first stage will also be affected. Especially in the combination of filters or filters in series, the optimal filtration gas velocity could be obtained by a constant-velocity filtration condition. Therefore, a constant-velocity filtration is important to the C-GBF study. However, most of the previous studies are conducted under a constant-pressure drop filtration condition. In this study, the authors designed a C-GBF, which aims at utilizing the full separation potential of the outer vortex. A cold model experimental system of the C-GBF under a constant-velocity filtration condition was also built. The flow pattern and separation characteristics in the cyclonic separation chamber were analyzed by using numerical simulations. Based on the understanding of the flow flied in the outer vortex of the C-GBF, the experiments of separation performance and matching conditions of the operational parameters were studied and identified. 2. The design of the C-GBF In a traditional reverse-flow cyclone with a tangential entry, the global flow pattern in the separation chamber is usually a double swirling flow. The gas flow moves downward in the outer vortex and upward in the inner vortex. In the bottom of the cyclone, the outer vortex weakens and turns to the inner vortex. The centrifugal separation is caused by the downward flow in the outer vortex. Meanwhile, the existence of particles in the inner vortex is unfavorable. Fig. 1 is the schematic illusion of the newly designed C-GBF. It has three parts, including a tangential gas inlet, a cyclone shell and a granular bed. The cyclone shell is a cylinder-cone structure. And, the granular bed is a coaxial cylinder-cone vessel filled with granules. The height of the cylinder section and angle of the cone section for the cyclone shell and the granular bed are identical, respectively. The cyclone chamber is an annular space between the cyclone shell and the granular bed. The granular bed is located between the outer part of the vortex and the inner part. The dust-laden gas flow enters the C-GBF through a tangential inlet. Initially, the gas flow movies downward in the outer vortex. Most of the coarse particles are separated by the cyclonic motion. In the bottom of the cyclone, the gas flow enters the granular bed from the entrance of the GBF. Then, the gas flows upward through the granular bed and the fine particles are collected by the GBF. Finally, the clean gas flow is obtained in the gas exit. The C-GBF is a compacted design, in which two stages of separation proceeds. The coarse and fine particles are collected separately, hence
Fig. 1. Schematic representation of the C-GBF.
reducing the risk of re-entrainment. Additionally, the centrifugal separation could be made an efficient utilization by the fully developed outer vortex. It is suitable for removal particles from high temperature pyrolysis vapors. 3. Model description Granular filtration is a complicated gas-solid two-phase flow process due to the interaction between the two solid phases (consists of granule and dust that are with different properties) and one fluid phase in the complex geometry of a real GBF. Few numerical studies have been conducted, concerned about the coupled macroscopic fluid flow and microscopic particle deposition in a full scale GBF. Because of the difficulty to simulate such a complex process, a simplified numerical simulation considering merely the gas-solid flow in the cyclonic separation chamber of the C-GBF was attempted by using ANSYS-FLUENT. 3.1. Gas-solid flow model The Eulerian–Lagrangian method is adopted in this work to simulate the gas phase (air) and solid phase (dust) flow in the cyclonic separation chamber of the C-GBF. [22,23] For the governing equations of each phase, the conservation of mass and momentum are considered. The continuity and momentum conservation equations are expressed as Eqs. (1) and (2) under the Cartesian coordinate: ∂ρ ! þ div ρ v ¼ 0 ∂t
ð1Þ
∂ðρuÞ ∂p ! þ div ρu v ¼ divðμgraduÞ− þ Su ∂t ∂x
ð2:aÞ
∂ðρvÞ ∂p ! þ div ρv v ¼ divðμgradvÞ− þ Sv ∂t ∂y
ð2:bÞ
∂ðρwÞ ∂p ! þ div ρw v ¼ divðμgradwÞ− þ Sw ∂t ∂z
ð2:cÞ
∂u ∂v ∂w ∂ð Þ ∂ð Þ ∂ð Þ ! þ þ , gradð Þ ¼ þ þ , ρ is the fluid where divð v Þ ¼ ∂x ∂y ∂z ∂x ∂y ∂z density, t is the time, μ is the fluid viscosity coefficient, p is the hydro! static pressure, v is the velocity vector, u, v and w are the velocity com! ponents of the velocity vector v in the x, y and z directions, respectively, Su, Sv and Sw are the generalized source term of the equations. The flow field is significantly influenced by the turbulence model. The Reynolds stress model (RSM) has been proved to reasonably predict the anisotropic turbulence and the strong swirling flow in the cyclone
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[24]. The Reynolds stress transport Eq. [21] is expressed as Eq. (3). ∂ 0 0 ∂ ρvk v0i v0j ¼ Dij þ P ij þ Φij −εij ρvi v j þ ∂t ∂xk
3
Table 1 Geometrical dimensions of the C-GBF (m).
ð3Þ
The left two terms of Eq. (3) are the transient term and the convection term respectively. The four terms on the right side are the turbulent diffusion term Dij, the shear stress generation term Pij, the pressure strain term Φij and the viscous dissipation term εij. The superscript “-” represents the average value of time, and the superscript “’” represents the pulsation value. As for the solid phase, the discrete phase model (DPM) based on the Lagrangian method is used to obtain the spatial distribution of particles. 3.2. Geometry and mesh generation The geometrical dimensions of the C-GBF are illustrated in Fig. 2. It is a cylinder-on-cone structure. The cylinder diameter D is 0.2 m with a rectangular inlet of 0.02 × 0.06 m2. The origin of the coordinates is located at the center of the top plate on the annular space. The specific dimensions are listed in Table 1. In order to investigate the variations of the flow field, a cyclone with the similar geometrical structure is studied (see Fig. 2a). Non-uniform structured hexahedral mesh is adopted in the numerical simulation. Because of the significant variation of pressure drop and velocity gradients at the tangential inlet and annular entrance of the GBF, grids are intentionally refined in these regions to accurately capture the local simulation phenomena. Fig. 2c shows the structure diagram and generated meshes in the grid system. The conditions for a case in this study were inlet gas velocity of vi = 15 m/s and filtration gas velocity of vf = 0.4 m/s. A number of numerical simulations were performed to ensure that the grid size was fine enough to produce grid-independent results (see Fig. 3). It was found that a grid number larger than 462,126 produced acceptable results by comparing the distribution of tangential and axial velocity in the region of Z = −0.2 m. Therefore, the mesh number of 462,126 was used in the simulations in this work. 3.3. Boundary conditions and solution methodology The inlet of the C-GBF is defined as a velocity inlet, where the velocity magnitude is calculated according to the flow rates and the cross-sectional area. The inlet gas is air under standard conditions, i.e., ρ = 1.225 kg/m3 and μ = 1.789 × 10−5 Pa·s. The top outlet is
D
D1
D2
A
B
H1
H2
S
0.2
0.15
0.1
0.06
0.02
0.4
0.6
0.1
defined as a velocity outlet while the bottom outlet is assumed to be fully developed. The walls are considered as the non-slip boundary conditions, where the standard wall function is used to determine the flow near the walls. The talcum powder with a true density of 2700 kg/m3 is used as the discrete phase of particles. The particles are continuously injected to the inlet surface with a velocity equal to the inlet gas velocity. The governing equations of fluid are solved by the commercial CFD code of ANSYS FLUENT. The SIMPLEC algorithm is employed to solve the coupling relationship between pressure and velocity, while the QUICK scheme is chosen for solving the convection term. The solution is considered to be converged when the scaled residual of the continuity is below 1 × 10−5. 4. Experimental setup and methodology 4.1. Experimental system Fig. 4 is the schematic illustration of the cold model experimental apparatus used in this work. It consists of three parts, including an air flow control system, a filter system (C-GBF), and a measurement system. To investigate the C-GBF, two centrifugal blowers are used to control the air flow system. The blower 1 generates the main gas flow in the top outlet of the C-GBF. It is controlled by a variable frequency drive (VFD), which adjusts the flow rate (filtration gas velocity). Dust-laden gas enters the C-GBF through a square tangential inlet. A large number of coarse particles are separated by the cyclonic flow while the rest fine particles is collected by the GBF. The blower 2 controlled by a VFD generates a bypass gas flow in the bottom outlet of the C-GBF. The matching conditions of the filtration gas velocity and inlet gas velocity are obtained by adjusting the two gas flows. The granules enter the GBF from a sealed feed hopper above the filter. The GBF with a fixed bed is studied in these experiments. The dirty granules are augered into a sealed catch hopper located at the bottom of the filter. The specific dimension is given in Table 1. The velocity distributions in the cross section of the pipe are measured by a hot-wire anemometer. The pressure drop caused by the filter is measured by the differential pressure gauge. In order to measure the pressure drop for
Fig. 2. Geometrical dimensions and the mesh topology.
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13 12 (a) 11 10 9 8 7 6 5 4 3 2 1 0 -1 -0.10
280929 354680 401326 462126 537834
-0.05
0.00
axial-velocity (m/s)
tangential-velocity (m/s)
4
0.05
0.10
x-coordinate (m)
4.5 4.0 (b) 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -0.10
280929 354680 401326 462126 537834
-0.05
0.00
0.05
0.10
x-coordinate (m)
Fig. 3. Comparisons of (a) tangential and (b) axial velocity with different grids.
the vortex space, two pressure probes (P0 and P1) are located at the tangential inlet of the C-GBF and the entrance of the C-GBF (see Fig. 4). The pressure probes are connected with a differential pressure gauge. So, the pressure drop of the vortex space could be obtained. Similarly, the pressure drop of the GBF could also be measured. The concentration and particle size distributions of the dust are measured by an aerosol spectrometer (Welas® digital 3000, Palas Gmbn, Germany). During the unsteady state of granular filtration in the C-GBF, the controlling of the filtration gas velocity and inlet gas velocity as constants becomes very important for the operation. Obviously, the constant velocity condition determines the performance of the C-GBF. In order to obtain this condition, an automatic control program based on PID controller is developed. The velocity is measured by the hot-wire anemometer. The velocity output signal is converted to an electrical signal which feeds back to the VFD by using this automatic control program. Then, the blower controlled by the VFD generates the desired velocity. It can
make the gas velocity generated by the blower slightly fluctuates around the certain value in a very narrow range. 4.2. Materials and method The talcum powder with a similar particle size of flying char particles was used as the dust particles. The size distribution of talcum powder was ranging from 1 μm to 100 μm, whcih is shown in Fig. 5. The median size of dust particles is 10.6 μm, while the true density of the particles is 2700 kg/m3. The quartz sands with high hardness and heat resistance was used as the granular materials. The size and the true density of quartz sands were 1 mm and 2650 kg/m3, respectively. To obtain a constant-velocity condition, the two centrifugal blowers were started before the filtration experiments. The filtration gas velocity and inlet gas velocity were held as steady as possible. Then, a screw-feeder was initiated to generate the dust-laden gas flow. In the
Fig. 4. Experimental setup for the cold flow testing.
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6
0.8
4 0.6 3 0.4 2 0.2
1
0.0 1
10 Particulate size (mm)
α¼
ð5Þ
3:5 ð1−εÞ Dp ε 3
ð6Þ
C2 ¼
0 100
Fig. 5. Particle size distribution of the talcum powder.
meantime, the aerosol spectrometer was started to measure the concentration and size distributions of the dust particles at the C-GBF top outlet. The data of pressure drop in the C-GBF was recorded at every 5 s interval. The mass concentration of the dust at the outlet, cout, was used to express the ability to collect particulate matter by the C-GBF. A number of filtration experiments were performed with different filtration gas velocities, inlet gas velocities, and dust mass concentrations. The experimental conditions were listed in Table 2. In tests 1 to 4, experiments were carried out under low inlet gas velocity, moderate dust mass concentration with different filtration gas velocities. In tests 5 and 6, experiments were carried out under high dust mass concentration, moderate filtration gas velocity with different inlet gas flows. 5. Results and discussions To get an understanding of the cyclonic separation processes occurring within the systems, numerical simulations were performed to obtain the characteristics of the flow filed. The effects of the key operational parameters on flow field in the C-GBF were investigated. Then, the validation of separation performance and the match of operational parameters were studied by laboratory experiments. 5.1. Model validation The porous media model in FLUENT was employed for modelling the region of granule in the C-GBF. The flow resistance in the region of the GBF could be obtained by using this model. For the process of turbulent flow in a packed bed, the permeability and the inertial loss coefficient are key parameters to represent the porous zone. Based on the Ergun Equation (Eq. (4)), the appropriate constants for porous media are identified as Eqs. (5) and (6).
2
jΔP j 150μ ð1−εÞ 1:75ρ ð1−ε Þ 2 ¼ v∞ þ v∞ L Dp ε3 ε3 Dp 2
Dp 2 ε 3 150 ð1−εÞ2
ð4Þ
Table 2 Conditions of the experiments. Test
Inlet gas velocity (vi/m·s−1)
Filtration gas velocity (vf/m·s−1)
Dust concentration (cin/g·m−3)
Filtration time (t/s)
1 2 3 4 5 6
15 15 15 15 15 30
0.2 0.4 0.6 0.8 0.4 0.4
10 10 10 10 20 20
3600 3600 3600 3600 3600 3600
In these equations, μ is the viscosity, Dp is the mean particle diameter of granule, L is the bed depth, ε is the void fraction of the bed or granule, v∞ is fluid velocity in the porous media, α is the permeability, C2 is the inertial resistance factor. To evaluate the validity of the model, a comparison of the pressure drop of the GBF was performed between the experimental results and those obtained from the numerical simulations. Since the porous media model is a simplified model, the blockage of the GBF due to the dust deposition was not taken into account during the filtration. Several filtration experiments without dust were conducted with the variations of the filtration gas velocity. The pressure drop of the clean GBF was recorded. Fig. 6 shows that the predicted results by the model (lines) displayed a good agreement with the experimental data (dispersed symbols). The pressure drop increased with the increasing of the filtration gas velocity. It was proved that the numerical method was able to describe the process of the C-GBF. 5.2. Flow characteristics of the C-GBF Fig. 7 shows the tangential velocity contours in the longitudinal section and different cross sections of the C-GBF. It indicated that there was an asymmetrical tangential velocity distribution in the C-GBF, especially in the inlet section. When the gas flow moved into the C-GBF, the fluid gained a rotating momentum under the action of the tangential inlet, resulting in an increase of the velocity magnitude. As the gas flow moved into the cyclone cylinder section, a uniform tangential velocity distribution was observed. In order to keep the same angular momentum, a gradual increase of the rotating velocity was observed in the cone section. The GBF filtration would be benefited because of the uniform tangential velocity distribution obtained in the inlet of the GBF. The quantitative distribution of the tangential velocity in the C-GBF is shown in Fig. 8. The rotating flow generated a swirling flow in the cyclone chamber while the gas flow near the wall spiraled downward along the cylinder. The maximum tangential velocity was observed in the inlet section of Z = -0.03 m. The value of the maximum tangential velocity was about 36 m/s. The existence of the GBF was beneficial to the flow field. The symmetrical tangential velocity distribution was obtained in the cyclonic chamber (see Fig. 8b and c). In the radial range of r/R = (0.75–1), where the tangential velocity decreased with r/R, the flow pattern of a free vortex was observed (see Fig. 8b and c). Fig. 8 also compares the flow patterns of the cyclone and C-GBF. In the radial range of r/R = (0.75–1), the similar distributions of the
pressure drop (DP/ Pa)
5
Differential distribution (%)
Cumulative distribution (%)
1.0
5
2200 2000 1800 1600 1400 1200 1000 800 600 400
experiments simulation
0.2
0.3
0.4
0.5
0.6
0.7
0.8
filtration gas velocity (m/s) Fig. 6. Comparison of the GBF pressure drop between the experimental and numerical simulations.
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Fig. 7. The tangential velocity distributions in the C-GBF (vi=30 m/s、vf=0.4 m/s).
-40 -35 -30 -25 -20 -15 -10 -5 0 5 -1.0
(a)
Cyclone C-GBF
tangential velocity (m/s)
-40 -35 -30 -25 -20 -15 -10 -5 0 5 -1.0
Z=-0.03 m
-0.5
0.0 r/R
0.5
1.0
(c)
Cyclone C-GBF
Z=-0.4 m
-0.5
0.0 r/R
with a diameter of 5 μm, most of the particles were separated by the cyclonic motion and a small part of particles would be collected by the GBF. With the decrease of particle diameter, the particle trajectories became more complicated. Small particles which follow the gas flow well, were little affected by the action of the centrifugal force. However, the entrained fine particles would be further captured by the GBF. The coarse particles were separated in the cyclonic chamber, while the fine particles would be collected by the counter-current flow GBF. Therefore, both of the coarse particles and fine particles were collected in the C-GBF. These results manifested that the collecting mechanisms based on the centrifugal separation and porous media filtration worked well in the C-GBF.
tangential velocity (m/s)
tangential velocity (m/s)
tangential velocity (m/s)
tangential velocity were observed. The rotation intensity was not diminished by the GBF. The same position and values of the maximum tangential velocity in the range of r/R = (0.75–1) were found. It was indicated that the same separation performance was obtained in the cyclonic chamber. As shown in Fig. 8, a double swirling was generated by the rotating flow in the cyclone. The tangential velocity distribution contained both the rigid vortex and free vortex [24]. However, only the free vortex could be obtained in the C-GBF. Fig. 9 shows the particle trajectories in the C-GBF with different particle diameters (vi=30 m/s, vf=0.4 m/s, cin=10 g/m3). For the particles with a diameter of 10 μm, all the particles were separated in the cyclonic chamber and few particles were entrained into the GBF. For the particles
0.5
1.0
-40 -35 -30 -25 -20 -15 -10 -5 0 5 -1.0 -40 -35 -30 -25 -20 -15 -10 -5 0 5 -1.0
(b)
Cyclone C-GBF
Z=-0.2 m
-0.5
0.0 r/R
0.5
1.0
(d)
Cyclone C-GBF
Z=-0.435 m
-0.5
0.0 r/R
0.5
1.0
Fig. 8. The tangential velocity comparisons of the Cyclone and C-GBF (vi=30 m/s, vf=0.4 m/s).
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7
the swirl separation space with the filtration gas velocity of vf = 0.4 m/s. The similar profiles of the tangential velocity distribution curves were obtained. It was indicated that the inlet gas velocity only affected the magnitude of the tangential velocity. The symmetrical tangential velocity distribution was observed in the cyclonic chamber. The tangential velocity increased with the increasing of the inlet gas velocity. The maximum tangential velocity was about 1.2 times larger than the inlet gas velocity. The effect of the inlet gas velocity on the pressure drop was illustrated in Fig. 11. It was revealed that the pressure drop caused by the cyclonic motion increased with the increasing of the inlet gas velocity. However, the total pressure drop was little affected by the variations of the inlet gas velocity. Fig. 12 depicts the effects of the filtration gas velocity on the tangential velocity of the swirl separation space with the inlet gas velocity of vi = 30 m/s. The same tangential velocity distribution curves were obtained. The separating ability of the cyclonic motion was little influenced by the filtration gas velocity. In order to obtain a stable cyclonic separation performance, the filtration gas velocity should be kept as a constant in the C-GBF. The effects of the filtration gas velocity on the pressure drop was shown in Fig. 13. It was obvious that the GBF contributed to the most of the total pressure drop. The deposition formed by flying char particles offered a more significant increase in the pressure drop. 5.4. Performance examined by experiments
Fig. 9. Particle trajectories in the C-GBF.
5.3. Effects of the operational parameters on flow flied
40 35 30 25 20 15 10 5 0 -5 -1.0
(a)
Z= −0.03 m
tangential velocity (m/s)
40 35 30 25 20 15 10 5 0 -5 -1.0
15m/s 20m/s 25m/s 30m/s
-0.5
0.0 r/R
0.5
1.0
(c)
Z=-0.4 m
tangential velocity (m/s)
tangential velocity (m/s)
tangential velocity (m/s)
The tangential velocity dominates the swirling motion of the fluid and the centrifugal action on particles. The magnitude of the inlet gas velocity directly causes the variation of the tangential velocity. Fig. 10 shows the effects of the inlet gas velocity on the tangential velocity in
15m/s 20m/s 25m/s 30m/s
-0.5
0.0 r/R
To further examine the feasibility of the C-GBF, the experiments to observe the effects of the inlet gas velocity and filtration gas velocity on separation performance were examined. The outlet dust concentration cout was used to represent the overall separation efficiency. A low cout value indicated a good separation performance. Fig. 14 depicts the effects of the inlet gas velocity on separation performance. In test 5 (with the inlet gas velocity of vi=15 m/s), the outlet dust concentration cout was less than 1 mg/m3 and did not vary with time from the beginning to 30 min. It should be attributed to the fact that most of the particles was captured by the surface of the GBF.
0.5
1.0
40 35 30 25 20 15 10 5 0 -5 -1.0
40 35 30 25 20 15 10 5 0 -5 -1.0
(b)
Z=-0.2 m 15m/s 20m/s 25m/s 30m/s
-0.5
0.0 r/R
0.5
1.0
(d)
Z=-0.435 m 15m/s 20m/s 25m/s 30m/s
-0.5
0.0 r/R
0.5
1.0
Fig. 10. Effect of the inlet gas velocity on the tangential velocity (vf = 0.4 m/s).
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M. You et al. / Powder Technology xxx (2019) xxx
4500 4000 3500 3000 2500 2000 1500 1000 500 0 10
8000 7000
pressure drop (DP/Pa)
pressure drop (DP/ Pa)
8
Total Pressure drop Vortex space pressure drop
15
20 25 30 inlet gas velocity (m/s)
Total pressure drop Vortex space pressure drop
6000 5000 4000 3000 2000 1000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 filtration gas velocity (m/s)
35
Fig. 13. Effect of the filtration gas velocity on the pressure drop (vi = 30 m/s).
From 30 min to 60 min, the outlet dust concentration cout increased, which might be due to the deposited particles on the surface that was entrained into the deeper part of the GBF. The total pressure drop was found to be increased with time, which revealed that the particles were collected by the GBF while the porosity of the filter media was decreased. The same tendency of both the outlet dust concentration and total pressure drop was observed in test 6. The difference in the outlet dust concentration between the tests 5 and 6 might be due to the different inlet gas velocities. Figs. 10 and 11 show the effects of the inlet gas velocity on the distributions of the tangential velocity and the pressure drop, respectively. The simulations indicated that the tangential velocity was increased and the corresponding centrifugal separation efficiency was improved with the increasing of the inlet gas velocity. The C-GBF in test 6 (with a inlet gas velocity of vi=30 m/s) might obtain a higher tangential velocity of the cyclonic motion than that of test 5 (with a inlet gas velocity of vi=15 m/s). More dust particles were separated by the strong cyclonic motion and little dust particles were entrained in the GBF. The simulations also demonstrated that the total pressure drop was little affected by the variations of the inlet gas velocity.
Therefore, lower outlet dust concentration and total pressure drop were obtained with a high inlet gas velocity. The dust load in the GBF was also decreased by a high inlet gas velocity. The results revealed that the proper operational condition for the C-GBF should be a high inlet gas velocity of vi=30 m/s. Fig. 15 shows the effect of the filtration gas velocity on separation performance. The simulations revealed that the tangential velocity and the corresponding centrifugal separation efficiency did not vary with the filtration gas velocity (see Fig. 12). The overall separation efficiency was only affected by the filtration gas velocity. As shown in Fig. 15a, when the filtration gas velocity was in the range of 0.2–0.4 m/s, those outlet dust concentrations did not vary with time and the values were less than 1 mg/m3. When the filtration gas velocity exceeded 0.6 m/s, the outlet dust concentrations increased. The outlet dust concentration for the filtration gas velocity of 0.8 m/s would reach a value in the vicinity of 8 mg/m3. It might be contribute to the effects of the inertial impaction. The inertial impaction played an important role in capturing particles with a low filtration gas velocity. When the velocity exceeded 0.6 m/s, the mechanism of the inertial impaction was ineffective and the re-
40 35 30 25 20 15 10 5 0 -5 -1.0
(a)
Z=-0.03m
tangential velocity (m/s)
40 35 30 25 20 15 10 5 0 -5 -1.0
0.2 m/s 0.4 m/s 0.6 m/s 0.8 m/s
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0.0 r/R
0.5
1.0
(c)
Z=-0.4 m
tangential velocity (m/s)
tangential velocity (m/s)
tangential velocity (m/s)
Fig. 11. Effect of the inlet gas velocity on the pressure drop (vf = 0.4 m/s).
0.2 m/s 0.4 m/s 0.6 m/s 0.8 m/s
-0.5
0.0 r/R
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1.0
40 35 30 25 20 15 10 5 0 -5 -1.0
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(b)
Z=-0.2m 0.2 m/s 0.4 m/s 0.6 m/s 0.8 m/s
-0.5
0.0 r/R
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(d)
Z=-0.435 m 0.2 m/s 0.4 m/s 0.6 m/s 0.8 m/s
-0.5
0.0 r/R
1.0
0.5
1.0
Fig. 12. Effect of the filtration gas velocity on the tangential velocity (vi = 30 m/s).
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M. You et al. / Powder Technology xxx (2019) xxx
4.00 3.00
cout(15 m/s) L=70mm cout(30 m/s) c =20g/m3
6000
in
P (15 m/s) v =0.4m/s P (30 m/s) f
4000
2.00 1.00 0.00 0
1000
2000
3000
P (Pa)
2000
pressure drop
-3 concentration (cout/ mg· m )
5.00
0
time (t / s) Fig. 14. Effect of the inlet gas velocity on the outlet dust concentration and total pressure drop.
entrainment of deposited particles would lead to a higher outlet dust concentration. Fig. 15b shows that the curves of total pressure drop increased with time. When the filtration gas velocity increased from 0.2 m/s to 0.8 m/s, the total pressure drop increased significantly. The simulation results indicated that the GBF contributed to the major part of the total pressure drop. The pressure drop of the GBF was linearly increased with the increasing of the filtration gas velocity. In general, the simulation results agreed well with those obtained from the experiments. It is also shows that, when the filtration gas velocity was less than 0.4 m/s, the total pressure drop was less than 4 kPa. Considering the
Fig. 15. Effect of the filtration velocity on the outlet dust concentration and total pressure drop.
9
strict environmental emission standards and the economic aspect, the outlet dust concentration less than 10 mg/m3 and the total pressure drop less than 4 kPa should be acceptable for application in industry. The results showed that the proper filtration gas velocity should be 0.4 m/s. 6. Conclusions An integrated dust removal technology of cyclone-granular bed filter (C-GBF) was developed. CFD simulations of the flow pattern and separation performance of the C-GBF were carried out with a basic understanding of the flow field in the C-GBF, which will facilitate the better design of the equipment. The experiments of the separation performance and matching relations of the operational parameters were studied. The following conclusions have been found: (1) The results showed that the flow pattern of a free vortex was observed in the C-GBF. The location of maximum tangential velocity was at the inlet and the maximum value was found to be about 1.2 times larger than the inlet gas velocity. The pressure drop of the C-GBF was mainly due to the effects of the granular bed and insignificantly affected by the free vortex. (2) The effects of the inlet gas velocity and filtration gas velocity on separation performance of the C-GBF were analyzed based on the understanding of flow behaviors of the free vortex. The tangential velocity was increased and the corresponding separation performance was improved with the increasing of the inlet gas velocity. The centrifugal separation efficiency was little affected by the variations of the filtration gas velocity. The GBF contributed to the most of the total pressure drop in the whole equipment. (3) The desired performance of the C-GBF was obtained and the outlet dust concentration was less than 10 mg/m3. The matching conditions of the C-GBF were identified, where the inlet gas velocity was vi=30 m/s and the filtration gas velocity was vf= 0.4 m/s.
Nomenclature A width of the inlet cross section (m) B length of the inlet cross section (m) C2 inertial resistance factor (m−1) cin inlet particle mass concentrations (g/m3) cout outlet particle mass concentrations (mg/m3) Dij turbulent diffusion term D cyclone cylinder diameter (m) D1 granular bed filter diameter (m) D2 dust discharge pipe diameter (m) Dp mean particle diameter (m) H1 cyclone cylinder height (m) H2 dust discharge pipe height (m) L bed depth (m) Pij shear stress generation term P static pressure (Pa) ΔP pressure drop (Pa) r radial position (m) R cyclone cylinder radius (m) S length of the exhaust pipe (m) Su, Sv, Sw generalized source term of the equation t time (s) u, v, w Cartesian components of the velocity vector (m/s) ! v velocity vector (m/s) vi inlet gas velocity (m/s) vf filtration gas velocity (m/s) v∞ fluid velocity in the porous media x, y, z Cartesian coordinates (m)
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Greek symbols μ dynamic viscosity of the fluid (Pa·s) ρ density of the fluid (kg/m3) Φij pressure strain term εij viscous dissipation term α permeability (m2) ε porosity of the clean granular bed filter, dimensionless Subscripts represents the average value of time ′ represents the pulsation value. i, j, k
Cartesian base vectors
Acknowledgement The authors acknowledge the financial support by National Natural Science Foundation of China (Grant No. 21606022), the National Basic Research Program of China (973 Program, Grant No. 2014CB744304), the Scientific Research Project of Beijing Municipal Commission of Education (Grant No. KM201910017009) and Natural Science Foundation of Jiangsu Province (Grant No. BK20180287). Author information Corresponding author: Dr. Minshu Zhan, [email protected], Dr. Meili Liu, [email protected]. References [1] B. Wang, Y. Liu, J. Liu, G. Sun, Experimental study on separation performance of a cyclone separator for oil shale processes, Petro. Process. Petrochem. 42 (2011) 59–62. [2] W. Wang, Y. Wang, Q. Ma, G. Sun, Contrast experiments on cyclone separator performances of shale ash and FCC fine catalysts, CN, Powder Sci. Technol. 18 (2012) 70–72. [3] F.A. Agblevor, S. Besler, Inorganic compounds in biomass feedstocks. 1. Effect on the quality of fast pyrolysis oils, Energy Fuel 10 (1996) 293–298. [4] P. Liang, X. Qu, J. Bi, Study on the low temperature coal pyrolysis by solid heat carrier in a moving bed pyrolyzer, J. Fuel Chem. Technol. 36 (2008) 401–405. [5] P. Liang, Z. Wang, Z. Dong, J. Bi, Hot dust removal in the process of low temperature coal pyrolysis, J. Fuel Chem. Technol. 34 (2006) 25–29.
[6] S. Gao, S. Xu, S. Wei, J. Xia, Y. Ren, Experimental study on moving granular bed filter for removing particulate at ambient temperature and high pressure, J. Fuel Chem. Technol. 29 (2001) 532–536. [7] J. Xia, S. Xu, S. Gao, Y. Ren, Experimental research on moving granular bed filter for hot gas cleanup, Power Eng. 23 (2003) 2337–2341. [8] M. Zhan, G. Sun, S. Yan, J. Chen, M. You, Filtration performance of coal pyrolysis flying char particles in a granular bed filter, Energy Fuel 32 (2018) 1070–1079. [9] C.-J. Hsu, S.-S. Hsiau, A study of filtration performance in a cross-flow moving granular bed filter: the influence of gas flow uniformity, Powder Technol. 274 (2015) 20–27. [10] Y.-S. Chen, C.-J. Hsu, S.-S. Hsiau, S.-M. Ma, Clean coal technology for removal dust using moving granular bed filter, Energy 120 (2017) 441–449. [11] Y.-S. Chen, S.-S. Hsiau, J. Smid, J.-F. Wu, S.-M. Ma, Removal of dust particles from fuel gas using a moving granular bed filter, Fuel 182 (2016) 174–187. [12] R.C. Brown, H. Shi, G. Colver, S.-C. Soo, Similitude study of a moving bed granular filter, Powder Technol. 138 (2003) 201–210. [13] I.A. El-Hedok, L. Whitmer, R.C. Brown, The influence of granular flow rate on the performance of a moving bed granular filter, Powder Technol. 214 (2011) 69–76. [14] B. Lv, C. Liu, Modeling for the optimum design of cyclone-filtrating removable grain bed dust collector, CN. Saf. Sci. J. 16 (2006) 59. [15] B. Lv, Research and application of LX type moving granular bed dust collector, Build. Therm. Venti. Air Cond. 3 (1998) 46–48. [16] Y. Xu, The inertia tornado body moves the bed pellet dust remover the design research, Modern Manuf. Eng. 7 (2006) 117–118. [17] S. Gao, D. Zhang, Y. Fan, C. Lu, Pressure drop characteristics of dry gas purification process in a coupled apparatus of cyclone and granular bed filter/absorber, CIESC J. 69 (2018) 1873–1883. [18] S. Gao, D. Zhang, Y. Fan, C. Lu, Separation performance in a novel coupled cyclone with built-in circulating granular bed filter (C-CGBF), Ind. Eng. Chem. Res. 57 (2018) 12192–12201. [19] S. Gao, D. Zhang, Y. Fan, C. Lu, A novel gas-solids separator scheme of coupling cyclone with circulating granular bed filter (C-CGBF), J. Hazard. Mater. 362 (2019) 403–411. [20] J. Yang, G. Sun, M. Zhan, Prediction of the maximum-efficiency inlet velocity in cyclones, Powder Technol. 286 (2015) 124–131. [21] G. Wan, G. Sun, X. Xue, M. Shi, Solids concentration simulation of different size particles in a cyclone separator, Powder Technol. 183 (2008) 94–104. [22] H. Zhang, B. Xiong, X. An, C. Ke, G. Wei, Prediction on drag force and heat transfer of spheroids in supercritical water: a PR-DNS study, Powder Technol. 342 (2019) 99–107. [23] H. Zhang, B. Xiong, X. An, C. Ke, G. Wei, Numerical investigation on the effect of the incident angle on momentum and heat transfer of spheroids in supercritical water, Comput. Fluids 179 (2019) 533–542. [24] S. Liu, Y. Guo, G. Sun, L. Weng, Flow simulation and performance comparison of rough-cut cyclones with different structures in dilute phase, Chem. Eng. Technol. 38 (2015) 1809–1816.
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Powder Technology journal homepage: www.elsevier.com/locate/powtec
Flow simulation and performance analysis of a cyclone–granular bed filter Minghao You a,1, Zhaoyang Li b,c,d,1, Minshu Zhan b,c,⁎⁎, Meili Liu a,⁎, Guogang Sun e, Jiaqing Chen a a
School of Mechanical Engineering, Beijing Institute of Petrochemical Technology, Beijing 102617, China JITRI Institute for Process Modelling and Optimization, Suzhou 215123, China Center for Simulation and Modelling of Particulate Systems, Southeast University - Monash University Joint Research Institute, Suzhou 215123, China d Shandong Iron and Steel Group Co., Ltd., Jinan 250101, China e Beijing Key Laboratory of Process Fluid Filtration and Separation, China University of Petroleum, Beijing 102249, China b c
a r t i c l e
i n f o
Article history: Received 16 May 2019 Received in revised form 19 August 2019 Accepted 28 August 2019 Available online xxxx Keywords: Cyclone Granular bed filter Flow field Separation performance
a b s t r a c t The rapid and efficient filtration of particles from high temperature pyrolysis vapors is of crucial importance for enhancing yields and quality of pyrolysis oil. In this work, an integrated dust removal technology of cyclonegranular bed filter (C-GBF) was designed. A computational fluid dynamics (CFD) simulation of the flow pattern of the C-GBF was carried out. The Reynolds stress model (RSM) and discrete phase model (DPM) were used to describe the gas-solid flow behavior in the C-GBF. The simulated results demonstrated that the flow pattern characterized by a free vortex in the C-GBF was observed. The location of maximum tangential velocity was found to be at the inlet section and the maximum value was about 1.2 times larger than the inlet gas velocity. The pressure drop of the C-GBF was mainly affected by the granular bed with the free vortex playing a trivial role. Based on the understanding of flow characteristics of the free vortex, the effects of the inlet gas velocity and filtration gas velocity on separation performance of the C-GBF were analyzed. The feasibility of the C-GBF was further examined by laboratory experiments under a constant-velocity filtration condition. The matching condition of the C-GBF was obtained with an inlet gas velocity of 30 m/s and the corresponding filtration gas velocity of 0.4 m/s. © 2019 Elsevier B.V. All rights reserved.
1. Introduction The removal of flying char particles from high temperature pyrolysis vapors is a common challenge in thermal conversion processing such as biomass, coal or oil shale. The pyrolysis vapors present a high concentration of char particles (particle size less than 10 μm) in a corrosive, viscous and high-temperature (above 400 °C) gases stream. The filtration performance of char particles directly affects the yields and quality of pyrolysis oil as well as the emission of particulate pollutants. In view of this, several attempts have been made to remove char particles from the high temperature and high viscosity pyrolysis vapors. Cyclones in series were used to separate particle matter from the pyrolysis vapors [1–3]. However, the collection efficiency of cyclone deteriorates drastically for small char particles less than 10 μm in size. A granular bed filter (GBF), using silica sand as filter media, makes a good filtration performance of removing char particles. Liang [4,5], Xu [6,7] and Zhan [8] developed different types of GBF for filtration of particles in coal pyrolysis. ⁎ Corresponding author. ⁎⁎ Corresponding author at: JITRI Institute for Process Modelling and Optimization, Suzhou 215123, China. E-mail addresses: [email protected] (M. Zhan), [email protected] (M. Liu). 1 Mr. You and Dr. Li contribute equally to this work.
Hsiau [9–11] and Brown [12,13] analyzed the filtration performance of moving granular bed filter (MGBF) in biomass pyrolysis. In these experiments, a cyclone followed by a GBF was used in the filtration system. By far, the combination of a GBF with a cyclone is considered to be one of the most promising solution to pyrolysis vapor streams filtration. Locating the GBF inside the cyclone has become an important development direction. Therefore, an integrated dust removal technology of cyclone-granular bed filter (C-GBF) is developed. Compared to a cyclone and a GBF in series, the C-GBF is expected to minimize the resistance time of high temperature pyrolysis vapors and reduce the risk of secondary reactions. Some applications of the C-GBF have been performed by a number of researchers. Brown [12,13] developed a C-GBF with a tangential inlet to induce the cyclonic flow. The coarse particles were separated in the cyclonic chamber while the fine particles were collected by the counter-current flow in the GBF. In order to obtain a uniform distribution of gas flow, several fins were installed inside the cyclonic chamber. However, the gas flow in the outer vortex was not fully developed with such a design. Lv [14,15] developed a C-GBF with a similar structure. The difference was the cross flow GBF used in their studies. A combination of C-GBF has been used by Xu [16]. A spiral vane was used to direct a downward swirling flow. The pressure drop increased correspondingly. Gao [17–19] proposed a combination of a cyclone with a built-in circulating granular bed filter (C-CGBF).
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Please cite this article as: M. You, Z. Li, M. Zhan, et al., Flow simulation and performance analysis of a cyclone–granular bed filter, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.088
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The CGBF was a cross flow filter inherent. Then, the pressure drop characteristics and separation performance were analyzed in the C-CGBF. However, most of these previous studies did not utilized the centrifugal separation in the outer vortex effectively. Moreover, these studies only characterized the performance of the C-GBF. There are limited published investigations on the flow pattern and separation characteristics in the outer vortex of the C-GBF. The performance of the C-GBF not only relies on the combination of the two separating stages, but also comes from the match of operational parameters. The velocity of the gas flow is considered as an important factor to determine the C-GBF performance. For a cyclone, an optimal inlet gas velocity yields the maximum separation efficiency. Many studies [20,21] have confirmed that the optimal inlet gas velocity ranges from 15 m/s to 30 m/s. Similarly, there also exits an optimal filtration gas velocity in a GBF. The value is from about 0.2 m/s to 1 m/s. Therefore, there should be an optimum combination of the gas flow velocity in the cyclone and the GBF in order to increase the collection efficiency while decrease the pressure drop. However, few studies have been carried out in this area, focusing on the matching between the inlet gas velocity and filtration gas velocity. It should be noted that the granular bed filtration is a process in unsteady state. The accumulation of deposited particles in the GBF increases with time. Accordingly, the pressure drop increases while the filtration gas velocity decreases. Therefore, the inlet gas velocity and separation performance in the first stage will also be affected. Especially in the combination of filters or filters in series, the optimal filtration gas velocity could be obtained by a constant-velocity filtration condition. Therefore, a constant-velocity filtration is important to the C-GBF study. However, most of the previous studies are conducted under a constant-pressure drop filtration condition. In this study, the authors designed a C-GBF, which aims at utilizing the full separation potential of the outer vortex. A cold model experimental system of the C-GBF under a constant-velocity filtration condition was also built. The flow pattern and separation characteristics in the cyclonic separation chamber were analyzed by using numerical simulations. Based on the understanding of the flow flied in the outer vortex of the C-GBF, the experiments of separation performance and matching conditions of the operational parameters were studied and identified. 2. The design of the C-GBF In a traditional reverse-flow cyclone with a tangential entry, the global flow pattern in the separation chamber is usually a double swirling flow. The gas flow moves downward in the outer vortex and upward in the inner vortex. In the bottom of the cyclone, the outer vortex weakens and turns to the inner vortex. The centrifugal separation is caused by the downward flow in the outer vortex. Meanwhile, the existence of particles in the inner vortex is unfavorable. Fig. 1 is the schematic illusion of the newly designed C-GBF. It has three parts, including a tangential gas inlet, a cyclone shell and a granular bed. The cyclone shell is a cylinder-cone structure. And, the granular bed is a coaxial cylinder-cone vessel filled with granules. The height of the cylinder section and angle of the cone section for the cyclone shell and the granular bed are identical, respectively. The cyclone chamber is an annular space between the cyclone shell and the granular bed. The granular bed is located between the outer part of the vortex and the inner part. The dust-laden gas flow enters the C-GBF through a tangential inlet. Initially, the gas flow movies downward in the outer vortex. Most of the coarse particles are separated by the cyclonic motion. In the bottom of the cyclone, the gas flow enters the granular bed from the entrance of the GBF. Then, the gas flows upward through the granular bed and the fine particles are collected by the GBF. Finally, the clean gas flow is obtained in the gas exit. The C-GBF is a compacted design, in which two stages of separation proceeds. The coarse and fine particles are collected separately, hence
Fig. 1. Schematic representation of the C-GBF.
reducing the risk of re-entrainment. Additionally, the centrifugal separation could be made an efficient utilization by the fully developed outer vortex. It is suitable for removal particles from high temperature pyrolysis vapors. 3. Model description Granular filtration is a complicated gas-solid two-phase flow process due to the interaction between the two solid phases (consists of granule and dust that are with different properties) and one fluid phase in the complex geometry of a real GBF. Few numerical studies have been conducted, concerned about the coupled macroscopic fluid flow and microscopic particle deposition in a full scale GBF. Because of the difficulty to simulate such a complex process, a simplified numerical simulation considering merely the gas-solid flow in the cyclonic separation chamber of the C-GBF was attempted by using ANSYS-FLUENT. 3.1. Gas-solid flow model The Eulerian–Lagrangian method is adopted in this work to simulate the gas phase (air) and solid phase (dust) flow in the cyclonic separation chamber of the C-GBF. [22,23] For the governing equations of each phase, the conservation of mass and momentum are considered. The continuity and momentum conservation equations are expressed as Eqs. (1) and (2) under the Cartesian coordinate: ∂ρ ! þ div ρ v ¼ 0 ∂t
ð1Þ
∂ðρuÞ ∂p ! þ div ρu v ¼ divðμgraduÞ− þ Su ∂t ∂x
ð2:aÞ
∂ðρvÞ ∂p ! þ div ρv v ¼ divðμgradvÞ− þ Sv ∂t ∂y
ð2:bÞ
∂ðρwÞ ∂p ! þ div ρw v ¼ divðμgradwÞ− þ Sw ∂t ∂z
ð2:cÞ
∂u ∂v ∂w ∂ð Þ ∂ð Þ ∂ð Þ ! þ þ , gradð Þ ¼ þ þ , ρ is the fluid where divð v Þ ¼ ∂x ∂y ∂z ∂x ∂y ∂z density, t is the time, μ is the fluid viscosity coefficient, p is the hydro! static pressure, v is the velocity vector, u, v and w are the velocity com! ponents of the velocity vector v in the x, y and z directions, respectively, Su, Sv and Sw are the generalized source term of the equations. The flow field is significantly influenced by the turbulence model. The Reynolds stress model (RSM) has been proved to reasonably predict the anisotropic turbulence and the strong swirling flow in the cyclone
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[24]. The Reynolds stress transport Eq. [21] is expressed as Eq. (3). ∂ 0 0 ∂ ρvk v0i v0j ¼ Dij þ P ij þ Φij −εij ρvi v j þ ∂t ∂xk
3
Table 1 Geometrical dimensions of the C-GBF (m).
ð3Þ
The left two terms of Eq. (3) are the transient term and the convection term respectively. The four terms on the right side are the turbulent diffusion term Dij, the shear stress generation term Pij, the pressure strain term Φij and the viscous dissipation term εij. The superscript “-” represents the average value of time, and the superscript “’” represents the pulsation value. As for the solid phase, the discrete phase model (DPM) based on the Lagrangian method is used to obtain the spatial distribution of particles. 3.2. Geometry and mesh generation The geometrical dimensions of the C-GBF are illustrated in Fig. 2. It is a cylinder-on-cone structure. The cylinder diameter D is 0.2 m with a rectangular inlet of 0.02 × 0.06 m2. The origin of the coordinates is located at the center of the top plate on the annular space. The specific dimensions are listed in Table 1. In order to investigate the variations of the flow field, a cyclone with the similar geometrical structure is studied (see Fig. 2a). Non-uniform structured hexahedral mesh is adopted in the numerical simulation. Because of the significant variation of pressure drop and velocity gradients at the tangential inlet and annular entrance of the GBF, grids are intentionally refined in these regions to accurately capture the local simulation phenomena. Fig. 2c shows the structure diagram and generated meshes in the grid system. The conditions for a case in this study were inlet gas velocity of vi = 15 m/s and filtration gas velocity of vf = 0.4 m/s. A number of numerical simulations were performed to ensure that the grid size was fine enough to produce grid-independent results (see Fig. 3). It was found that a grid number larger than 462,126 produced acceptable results by comparing the distribution of tangential and axial velocity in the region of Z = −0.2 m. Therefore, the mesh number of 462,126 was used in the simulations in this work. 3.3. Boundary conditions and solution methodology The inlet of the C-GBF is defined as a velocity inlet, where the velocity magnitude is calculated according to the flow rates and the cross-sectional area. The inlet gas is air under standard conditions, i.e., ρ = 1.225 kg/m3 and μ = 1.789 × 10−5 Pa·s. The top outlet is
D
D1
D2
A
B
H1
H2
S
0.2
0.15
0.1
0.06
0.02
0.4
0.6
0.1
defined as a velocity outlet while the bottom outlet is assumed to be fully developed. The walls are considered as the non-slip boundary conditions, where the standard wall function is used to determine the flow near the walls. The talcum powder with a true density of 2700 kg/m3 is used as the discrete phase of particles. The particles are continuously injected to the inlet surface with a velocity equal to the inlet gas velocity. The governing equations of fluid are solved by the commercial CFD code of ANSYS FLUENT. The SIMPLEC algorithm is employed to solve the coupling relationship between pressure and velocity, while the QUICK scheme is chosen for solving the convection term. The solution is considered to be converged when the scaled residual of the continuity is below 1 × 10−5. 4. Experimental setup and methodology 4.1. Experimental system Fig. 4 is the schematic illustration of the cold model experimental apparatus used in this work. It consists of three parts, including an air flow control system, a filter system (C-GBF), and a measurement system. To investigate the C-GBF, two centrifugal blowers are used to control the air flow system. The blower 1 generates the main gas flow in the top outlet of the C-GBF. It is controlled by a variable frequency drive (VFD), which adjusts the flow rate (filtration gas velocity). Dust-laden gas enters the C-GBF through a square tangential inlet. A large number of coarse particles are separated by the cyclonic flow while the rest fine particles is collected by the GBF. The blower 2 controlled by a VFD generates a bypass gas flow in the bottom outlet of the C-GBF. The matching conditions of the filtration gas velocity and inlet gas velocity are obtained by adjusting the two gas flows. The granules enter the GBF from a sealed feed hopper above the filter. The GBF with a fixed bed is studied in these experiments. The dirty granules are augered into a sealed catch hopper located at the bottom of the filter. The specific dimension is given in Table 1. The velocity distributions in the cross section of the pipe are measured by a hot-wire anemometer. The pressure drop caused by the filter is measured by the differential pressure gauge. In order to measure the pressure drop for
Fig. 2. Geometrical dimensions and the mesh topology.
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13 12 (a) 11 10 9 8 7 6 5 4 3 2 1 0 -1 -0.10
280929 354680 401326 462126 537834
-0.05
0.00
axial-velocity (m/s)
tangential-velocity (m/s)
4
0.05
0.10
x-coordinate (m)
4.5 4.0 (b) 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -0.10
280929 354680 401326 462126 537834
-0.05
0.00
0.05
0.10
x-coordinate (m)
Fig. 3. Comparisons of (a) tangential and (b) axial velocity with different grids.
the vortex space, two pressure probes (P0 and P1) are located at the tangential inlet of the C-GBF and the entrance of the C-GBF (see Fig. 4). The pressure probes are connected with a differential pressure gauge. So, the pressure drop of the vortex space could be obtained. Similarly, the pressure drop of the GBF could also be measured. The concentration and particle size distributions of the dust are measured by an aerosol spectrometer (Welas® digital 3000, Palas Gmbn, Germany). During the unsteady state of granular filtration in the C-GBF, the controlling of the filtration gas velocity and inlet gas velocity as constants becomes very important for the operation. Obviously, the constant velocity condition determines the performance of the C-GBF. In order to obtain this condition, an automatic control program based on PID controller is developed. The velocity is measured by the hot-wire anemometer. The velocity output signal is converted to an electrical signal which feeds back to the VFD by using this automatic control program. Then, the blower controlled by the VFD generates the desired velocity. It can
make the gas velocity generated by the blower slightly fluctuates around the certain value in a very narrow range. 4.2. Materials and method The talcum powder with a similar particle size of flying char particles was used as the dust particles. The size distribution of talcum powder was ranging from 1 μm to 100 μm, whcih is shown in Fig. 5. The median size of dust particles is 10.6 μm, while the true density of the particles is 2700 kg/m3. The quartz sands with high hardness and heat resistance was used as the granular materials. The size and the true density of quartz sands were 1 mm and 2650 kg/m3, respectively. To obtain a constant-velocity condition, the two centrifugal blowers were started before the filtration experiments. The filtration gas velocity and inlet gas velocity were held as steady as possible. Then, a screw-feeder was initiated to generate the dust-laden gas flow. In the
Fig. 4. Experimental setup for the cold flow testing.
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6
0.8
4 0.6 3 0.4 2 0.2
1
0.0 1
10 Particulate size (mm)
α¼
ð5Þ
3:5 ð1−εÞ Dp ε 3
ð6Þ
C2 ¼
0 100
Fig. 5. Particle size distribution of the talcum powder.
meantime, the aerosol spectrometer was started to measure the concentration and size distributions of the dust particles at the C-GBF top outlet. The data of pressure drop in the C-GBF was recorded at every 5 s interval. The mass concentration of the dust at the outlet, cout, was used to express the ability to collect particulate matter by the C-GBF. A number of filtration experiments were performed with different filtration gas velocities, inlet gas velocities, and dust mass concentrations. The experimental conditions were listed in Table 2. In tests 1 to 4, experiments were carried out under low inlet gas velocity, moderate dust mass concentration with different filtration gas velocities. In tests 5 and 6, experiments were carried out under high dust mass concentration, moderate filtration gas velocity with different inlet gas flows. 5. Results and discussions To get an understanding of the cyclonic separation processes occurring within the systems, numerical simulations were performed to obtain the characteristics of the flow filed. The effects of the key operational parameters on flow field in the C-GBF were investigated. Then, the validation of separation performance and the match of operational parameters were studied by laboratory experiments. 5.1. Model validation The porous media model in FLUENT was employed for modelling the region of granule in the C-GBF. The flow resistance in the region of the GBF could be obtained by using this model. For the process of turbulent flow in a packed bed, the permeability and the inertial loss coefficient are key parameters to represent the porous zone. Based on the Ergun Equation (Eq. (4)), the appropriate constants for porous media are identified as Eqs. (5) and (6).
2
jΔP j 150μ ð1−εÞ 1:75ρ ð1−ε Þ 2 ¼ v∞ þ v∞ L Dp ε3 ε3 Dp 2
Dp 2 ε 3 150 ð1−εÞ2
ð4Þ
Table 2 Conditions of the experiments. Test
Inlet gas velocity (vi/m·s−1)
Filtration gas velocity (vf/m·s−1)
Dust concentration (cin/g·m−3)
Filtration time (t/s)
1 2 3 4 5 6
15 15 15 15 15 30
0.2 0.4 0.6 0.8 0.4 0.4
10 10 10 10 20 20
3600 3600 3600 3600 3600 3600
In these equations, μ is the viscosity, Dp is the mean particle diameter of granule, L is the bed depth, ε is the void fraction of the bed or granule, v∞ is fluid velocity in the porous media, α is the permeability, C2 is the inertial resistance factor. To evaluate the validity of the model, a comparison of the pressure drop of the GBF was performed between the experimental results and those obtained from the numerical simulations. Since the porous media model is a simplified model, the blockage of the GBF due to the dust deposition was not taken into account during the filtration. Several filtration experiments without dust were conducted with the variations of the filtration gas velocity. The pressure drop of the clean GBF was recorded. Fig. 6 shows that the predicted results by the model (lines) displayed a good agreement with the experimental data (dispersed symbols). The pressure drop increased with the increasing of the filtration gas velocity. It was proved that the numerical method was able to describe the process of the C-GBF. 5.2. Flow characteristics of the C-GBF Fig. 7 shows the tangential velocity contours in the longitudinal section and different cross sections of the C-GBF. It indicated that there was an asymmetrical tangential velocity distribution in the C-GBF, especially in the inlet section. When the gas flow moved into the C-GBF, the fluid gained a rotating momentum under the action of the tangential inlet, resulting in an increase of the velocity magnitude. As the gas flow moved into the cyclone cylinder section, a uniform tangential velocity distribution was observed. In order to keep the same angular momentum, a gradual increase of the rotating velocity was observed in the cone section. The GBF filtration would be benefited because of the uniform tangential velocity distribution obtained in the inlet of the GBF. The quantitative distribution of the tangential velocity in the C-GBF is shown in Fig. 8. The rotating flow generated a swirling flow in the cyclone chamber while the gas flow near the wall spiraled downward along the cylinder. The maximum tangential velocity was observed in the inlet section of Z = -0.03 m. The value of the maximum tangential velocity was about 36 m/s. The existence of the GBF was beneficial to the flow field. The symmetrical tangential velocity distribution was obtained in the cyclonic chamber (see Fig. 8b and c). In the radial range of r/R = (0.75–1), where the tangential velocity decreased with r/R, the flow pattern of a free vortex was observed (see Fig. 8b and c). Fig. 8 also compares the flow patterns of the cyclone and C-GBF. In the radial range of r/R = (0.75–1), the similar distributions of the
pressure drop (DP/ Pa)
5
Differential distribution (%)
Cumulative distribution (%)
1.0
5
2200 2000 1800 1600 1400 1200 1000 800 600 400
experiments simulation
0.2
0.3
0.4
0.5
0.6
0.7
0.8
filtration gas velocity (m/s) Fig. 6. Comparison of the GBF pressure drop between the experimental and numerical simulations.
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M. You et al. / Powder Technology xxx (2019) xxx
Fig. 7. The tangential velocity distributions in the C-GBF (vi=30 m/s、vf=0.4 m/s).
-40 -35 -30 -25 -20 -15 -10 -5 0 5 -1.0
(a)
Cyclone C-GBF
tangential velocity (m/s)
-40 -35 -30 -25 -20 -15 -10 -5 0 5 -1.0
Z=-0.03 m
-0.5
0.0 r/R
0.5
1.0
(c)
Cyclone C-GBF
Z=-0.4 m
-0.5
0.0 r/R
with a diameter of 5 μm, most of the particles were separated by the cyclonic motion and a small part of particles would be collected by the GBF. With the decrease of particle diameter, the particle trajectories became more complicated. Small particles which follow the gas flow well, were little affected by the action of the centrifugal force. However, the entrained fine particles would be further captured by the GBF. The coarse particles were separated in the cyclonic chamber, while the fine particles would be collected by the counter-current flow GBF. Therefore, both of the coarse particles and fine particles were collected in the C-GBF. These results manifested that the collecting mechanisms based on the centrifugal separation and porous media filtration worked well in the C-GBF.
tangential velocity (m/s)
tangential velocity (m/s)
tangential velocity (m/s)
tangential velocity were observed. The rotation intensity was not diminished by the GBF. The same position and values of the maximum tangential velocity in the range of r/R = (0.75–1) were found. It was indicated that the same separation performance was obtained in the cyclonic chamber. As shown in Fig. 8, a double swirling was generated by the rotating flow in the cyclone. The tangential velocity distribution contained both the rigid vortex and free vortex [24]. However, only the free vortex could be obtained in the C-GBF. Fig. 9 shows the particle trajectories in the C-GBF with different particle diameters (vi=30 m/s, vf=0.4 m/s, cin=10 g/m3). For the particles with a diameter of 10 μm, all the particles were separated in the cyclonic chamber and few particles were entrained into the GBF. For the particles
0.5
1.0
-40 -35 -30 -25 -20 -15 -10 -5 0 5 -1.0 -40 -35 -30 -25 -20 -15 -10 -5 0 5 -1.0
(b)
Cyclone C-GBF
Z=-0.2 m
-0.5
0.0 r/R
0.5
1.0
(d)
Cyclone C-GBF
Z=-0.435 m
-0.5
0.0 r/R
0.5
1.0
Fig. 8. The tangential velocity comparisons of the Cyclone and C-GBF (vi=30 m/s, vf=0.4 m/s).
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7
the swirl separation space with the filtration gas velocity of vf = 0.4 m/s. The similar profiles of the tangential velocity distribution curves were obtained. It was indicated that the inlet gas velocity only affected the magnitude of the tangential velocity. The symmetrical tangential velocity distribution was observed in the cyclonic chamber. The tangential velocity increased with the increasing of the inlet gas velocity. The maximum tangential velocity was about 1.2 times larger than the inlet gas velocity. The effect of the inlet gas velocity on the pressure drop was illustrated in Fig. 11. It was revealed that the pressure drop caused by the cyclonic motion increased with the increasing of the inlet gas velocity. However, the total pressure drop was little affected by the variations of the inlet gas velocity. Fig. 12 depicts the effects of the filtration gas velocity on the tangential velocity of the swirl separation space with the inlet gas velocity of vi = 30 m/s. The same tangential velocity distribution curves were obtained. The separating ability of the cyclonic motion was little influenced by the filtration gas velocity. In order to obtain a stable cyclonic separation performance, the filtration gas velocity should be kept as a constant in the C-GBF. The effects of the filtration gas velocity on the pressure drop was shown in Fig. 13. It was obvious that the GBF contributed to the most of the total pressure drop. The deposition formed by flying char particles offered a more significant increase in the pressure drop. 5.4. Performance examined by experiments
Fig. 9. Particle trajectories in the C-GBF.
5.3. Effects of the operational parameters on flow flied
40 35 30 25 20 15 10 5 0 -5 -1.0
(a)
Z= −0.03 m
tangential velocity (m/s)
40 35 30 25 20 15 10 5 0 -5 -1.0
15m/s 20m/s 25m/s 30m/s
-0.5
0.0 r/R
0.5
1.0
(c)
Z=-0.4 m
tangential velocity (m/s)
tangential velocity (m/s)
tangential velocity (m/s)
The tangential velocity dominates the swirling motion of the fluid and the centrifugal action on particles. The magnitude of the inlet gas velocity directly causes the variation of the tangential velocity. Fig. 10 shows the effects of the inlet gas velocity on the tangential velocity in
15m/s 20m/s 25m/s 30m/s
-0.5
0.0 r/R
To further examine the feasibility of the C-GBF, the experiments to observe the effects of the inlet gas velocity and filtration gas velocity on separation performance were examined. The outlet dust concentration cout was used to represent the overall separation efficiency. A low cout value indicated a good separation performance. Fig. 14 depicts the effects of the inlet gas velocity on separation performance. In test 5 (with the inlet gas velocity of vi=15 m/s), the outlet dust concentration cout was less than 1 mg/m3 and did not vary with time from the beginning to 30 min. It should be attributed to the fact that most of the particles was captured by the surface of the GBF.
0.5
1.0
40 35 30 25 20 15 10 5 0 -5 -1.0
40 35 30 25 20 15 10 5 0 -5 -1.0
(b)
Z=-0.2 m 15m/s 20m/s 25m/s 30m/s
-0.5
0.0 r/R
0.5
1.0
(d)
Z=-0.435 m 15m/s 20m/s 25m/s 30m/s
-0.5
0.0 r/R
0.5
1.0
Fig. 10. Effect of the inlet gas velocity on the tangential velocity (vf = 0.4 m/s).
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4500 4000 3500 3000 2500 2000 1500 1000 500 0 10
8000 7000
pressure drop (DP/Pa)
pressure drop (DP/ Pa)
8
Total Pressure drop Vortex space pressure drop
15
20 25 30 inlet gas velocity (m/s)
Total pressure drop Vortex space pressure drop
6000 5000 4000 3000 2000 1000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 filtration gas velocity (m/s)
35
Fig. 13. Effect of the filtration gas velocity on the pressure drop (vi = 30 m/s).
From 30 min to 60 min, the outlet dust concentration cout increased, which might be due to the deposited particles on the surface that was entrained into the deeper part of the GBF. The total pressure drop was found to be increased with time, which revealed that the particles were collected by the GBF while the porosity of the filter media was decreased. The same tendency of both the outlet dust concentration and total pressure drop was observed in test 6. The difference in the outlet dust concentration between the tests 5 and 6 might be due to the different inlet gas velocities. Figs. 10 and 11 show the effects of the inlet gas velocity on the distributions of the tangential velocity and the pressure drop, respectively. The simulations indicated that the tangential velocity was increased and the corresponding centrifugal separation efficiency was improved with the increasing of the inlet gas velocity. The C-GBF in test 6 (with a inlet gas velocity of vi=30 m/s) might obtain a higher tangential velocity of the cyclonic motion than that of test 5 (with a inlet gas velocity of vi=15 m/s). More dust particles were separated by the strong cyclonic motion and little dust particles were entrained in the GBF. The simulations also demonstrated that the total pressure drop was little affected by the variations of the inlet gas velocity.
Therefore, lower outlet dust concentration and total pressure drop were obtained with a high inlet gas velocity. The dust load in the GBF was also decreased by a high inlet gas velocity. The results revealed that the proper operational condition for the C-GBF should be a high inlet gas velocity of vi=30 m/s. Fig. 15 shows the effect of the filtration gas velocity on separation performance. The simulations revealed that the tangential velocity and the corresponding centrifugal separation efficiency did not vary with the filtration gas velocity (see Fig. 12). The overall separation efficiency was only affected by the filtration gas velocity. As shown in Fig. 15a, when the filtration gas velocity was in the range of 0.2–0.4 m/s, those outlet dust concentrations did not vary with time and the values were less than 1 mg/m3. When the filtration gas velocity exceeded 0.6 m/s, the outlet dust concentrations increased. The outlet dust concentration for the filtration gas velocity of 0.8 m/s would reach a value in the vicinity of 8 mg/m3. It might be contribute to the effects of the inertial impaction. The inertial impaction played an important role in capturing particles with a low filtration gas velocity. When the velocity exceeded 0.6 m/s, the mechanism of the inertial impaction was ineffective and the re-
40 35 30 25 20 15 10 5 0 -5 -1.0
(a)
Z=-0.03m
tangential velocity (m/s)
40 35 30 25 20 15 10 5 0 -5 -1.0
0.2 m/s 0.4 m/s 0.6 m/s 0.8 m/s
-0.5
0.0 r/R
0.5
1.0
(c)
Z=-0.4 m
tangential velocity (m/s)
tangential velocity (m/s)
tangential velocity (m/s)
Fig. 11. Effect of the inlet gas velocity on the pressure drop (vf = 0.4 m/s).
0.2 m/s 0.4 m/s 0.6 m/s 0.8 m/s
-0.5
0.0 r/R
0.5
1.0
40 35 30 25 20 15 10 5 0 -5 -1.0
40 35 30 25 20 15 10 5 0 -5 -1.0
(b)
Z=-0.2m 0.2 m/s 0.4 m/s 0.6 m/s 0.8 m/s
-0.5
0.0 r/R
0.5
(d)
Z=-0.435 m 0.2 m/s 0.4 m/s 0.6 m/s 0.8 m/s
-0.5
0.0 r/R
1.0
0.5
1.0
Fig. 12. Effect of the filtration gas velocity on the tangential velocity (vi = 30 m/s).
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4.00 3.00
cout(15 m/s) L=70mm cout(30 m/s) c =20g/m3
6000
in
P (15 m/s) v =0.4m/s P (30 m/s) f
4000
2.00 1.00 0.00 0
1000
2000
3000
P (Pa)
2000
pressure drop
-3 concentration (cout/ mg· m )
5.00
0
time (t / s) Fig. 14. Effect of the inlet gas velocity on the outlet dust concentration and total pressure drop.
entrainment of deposited particles would lead to a higher outlet dust concentration. Fig. 15b shows that the curves of total pressure drop increased with time. When the filtration gas velocity increased from 0.2 m/s to 0.8 m/s, the total pressure drop increased significantly. The simulation results indicated that the GBF contributed to the major part of the total pressure drop. The pressure drop of the GBF was linearly increased with the increasing of the filtration gas velocity. In general, the simulation results agreed well with those obtained from the experiments. It is also shows that, when the filtration gas velocity was less than 0.4 m/s, the total pressure drop was less than 4 kPa. Considering the
Fig. 15. Effect of the filtration velocity on the outlet dust concentration and total pressure drop.
9
strict environmental emission standards and the economic aspect, the outlet dust concentration less than 10 mg/m3 and the total pressure drop less than 4 kPa should be acceptable for application in industry. The results showed that the proper filtration gas velocity should be 0.4 m/s. 6. Conclusions An integrated dust removal technology of cyclone-granular bed filter (C-GBF) was developed. CFD simulations of the flow pattern and separation performance of the C-GBF were carried out with a basic understanding of the flow field in the C-GBF, which will facilitate the better design of the equipment. The experiments of the separation performance and matching relations of the operational parameters were studied. The following conclusions have been found: (1) The results showed that the flow pattern of a free vortex was observed in the C-GBF. The location of maximum tangential velocity was at the inlet and the maximum value was found to be about 1.2 times larger than the inlet gas velocity. The pressure drop of the C-GBF was mainly due to the effects of the granular bed and insignificantly affected by the free vortex. (2) The effects of the inlet gas velocity and filtration gas velocity on separation performance of the C-GBF were analyzed based on the understanding of flow behaviors of the free vortex. The tangential velocity was increased and the corresponding separation performance was improved with the increasing of the inlet gas velocity. The centrifugal separation efficiency was little affected by the variations of the filtration gas velocity. The GBF contributed to the most of the total pressure drop in the whole equipment. (3) The desired performance of the C-GBF was obtained and the outlet dust concentration was less than 10 mg/m3. The matching conditions of the C-GBF were identified, where the inlet gas velocity was vi=30 m/s and the filtration gas velocity was vf= 0.4 m/s.
Nomenclature A width of the inlet cross section (m) B length of the inlet cross section (m) C2 inertial resistance factor (m−1) cin inlet particle mass concentrations (g/m3) cout outlet particle mass concentrations (mg/m3) Dij turbulent diffusion term D cyclone cylinder diameter (m) D1 granular bed filter diameter (m) D2 dust discharge pipe diameter (m) Dp mean particle diameter (m) H1 cyclone cylinder height (m) H2 dust discharge pipe height (m) L bed depth (m) Pij shear stress generation term P static pressure (Pa) ΔP pressure drop (Pa) r radial position (m) R cyclone cylinder radius (m) S length of the exhaust pipe (m) Su, Sv, Sw generalized source term of the equation t time (s) u, v, w Cartesian components of the velocity vector (m/s) ! v velocity vector (m/s) vi inlet gas velocity (m/s) vf filtration gas velocity (m/s) v∞ fluid velocity in the porous media x, y, z Cartesian coordinates (m)
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Greek symbols μ dynamic viscosity of the fluid (Pa·s) ρ density of the fluid (kg/m3) Φij pressure strain term εij viscous dissipation term α permeability (m2) ε porosity of the clean granular bed filter, dimensionless Subscripts represents the average value of time ′ represents the pulsation value. i, j, k
Cartesian base vectors
Acknowledgement The authors acknowledge the financial support by National Natural Science Foundation of China (Grant No. 21606022), the National Basic Research Program of China (973 Program, Grant No. 2014CB744304), the Scientific Research Project of Beijing Municipal Commission of Education (Grant No. KM201910017009) and Natural Science Foundation of Jiangsu Province (Grant No. BK20180287). Author information Corresponding author: Dr. Minshu Zhan, [email protected], Dr. Meili Liu, [email protected]. References [1] B. Wang, Y. Liu, J. Liu, G. Sun, Experimental study on separation performance of a cyclone separator for oil shale processes, Petro. Process. Petrochem. 42 (2011) 59–62. [2] W. Wang, Y. Wang, Q. Ma, G. Sun, Contrast experiments on cyclone separator performances of shale ash and FCC fine catalysts, CN, Powder Sci. Technol. 18 (2012) 70–72. [3] F.A. Agblevor, S. Besler, Inorganic compounds in biomass feedstocks. 1. Effect on the quality of fast pyrolysis oils, Energy Fuel 10 (1996) 293–298. [4] P. Liang, X. Qu, J. Bi, Study on the low temperature coal pyrolysis by solid heat carrier in a moving bed pyrolyzer, J. Fuel Chem. Technol. 36 (2008) 401–405. [5] P. Liang, Z. Wang, Z. Dong, J. Bi, Hot dust removal in the process of low temperature coal pyrolysis, J. Fuel Chem. Technol. 34 (2006) 25–29.
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