Mechanism study of electrostatic precipitation in a compact hybrid particulate collector

Powder Technology 328 (2018) 84–94

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Mechanism study of electrostatic precipitation in a compact hybrid particulate collector Gongming Tu, Qiang Song ⁎, Qiang Yao Key Laboratory of Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, 100084 Beijing, China

a r t i c l e

i n f o

Article history: Received 21 August 2017 Received in revised form 20 December 2017 Accepted 9 January 2018 Available online 12 January 2018 Keywords: Particle Electrostatic precipitation Electric field Charging Hybrid particulate collector

a b s t r a c t Hybrid structure significantly affects the collection mechanism and performance of a hybrid particulate collector. The electrostatic precipitation of particles in the wire-perforated plate structure of a full-scale compact hybrid particulate collector is numerically simulated in this study. The distributions of electric and flow fields and the charging, motion, and precipitation of particles in this specific structure are studied. The results show that the distribution of electric field in the final stage is asymmetrical because of the baffle plate at the end of the channel. The field distributions of other stages are identical to that of wire-plate electrostatic precipitator. The openings increase the electric field strength in the region adjacent to the perforated plate. The electric field passes through the openings, which is then distributed to the back side of the perforated plate. The aerosol cross flow rate along the perforated plate varies periodically under the effect of electric body force. Whereas, the overall cross flow rate of each stage is the same, except the first stage. Two counter-rotating eddies are formed behind the perforated plate between every two openings. Particle charge exceeds 80% of the final charge when the particles move to the position of the first wire. The 10 μm particles finish their charging processes faster than 1 μm particles with a final charge of approximately 100 times that of 1 μm particles. The charge acquired by a particle under the wire-perforated plate structure is 3% higher than that under the wire-plate structure. Particle trajectory result shows three modes of electrostatic precipitation in a compact hybrid particulate collector, namely, collection on the front, flank, and back sides of the perforated plate. Particle transport by eddies on the back of the perforated plate plays an important role in particle deposition on the back side. Variation in the capture probability of particles released from different positions corresponds to the opening structure. High and low probability areas separate with each other. The collection efficiency of 10 μm particle is higher than that of the 1 μm particle. The results can explain hybrid mechanism and optimize hybrid structure. © 2018 Elsevier B.V. All rights reserved.

1. Introduction Particulate matter has become the principal atmospheric pollutant in China. Studies and statistics showed that industrial emissions are the main source of primary particles [1]. The development of high efficient and low-cost particle removal technology is the fundamental solution to this problem. The most widely used particle removal methods include electrostatic precipitator (ESP) and fabric filter (FF) [2, 3]. Both methods are extremely expensive to satisfy the new ultralow emission standard for coal-fired power plants. Hybrid particulate collector, which integrates ESP and FF in series, was developed within this context [4]. Hybrid particulate collectors combine the advantages of the two traditional techniques. ESP removes most of the particles at low cost, whereas FF catches the remaining particles with high efficiency. In addition, fabric filtration is enhanced by particle charging. Thus, hybrid particulate collectors were rapidly adopted in recent years [5, 6]. The University ⁎ Corresponding author. E-mail address: [email protected] (Q. Song).

https://doi.org/10.1016/j.powtec.2018.01.016 0032-5910/© 2018 Elsevier B.V. All rights reserved.

of North Dakota developed a compact type of hybrid particulate collector [7]. This type of hybrid particulate collector adopts perforated plates as collection plates in the ESP zone. The unique structure has the same advantage as the previous hybrid device and solves the problems of re-entrainment and re-collection in conventional FF. A full-scale proto device was installed in Big Stone Plant, USA in 2002. This device provides ultrahigh collection efficiency at the initial stage, but fails to maintain high efficiency during long-term operation [8] due to the unreasonable dust load distribution. This limitation is attributed to the lack of electrostatic precipitation on perforated collection plates related to unreasonable design. Thus, the collection mechanism in wireperforated plate structure must be examined. The most commonly used configuration in industrial ESPs is wireplate type. The principles of the wire-plate ESPs are well described in literature [9–11]. Particle transport in ESPs is a result of the interactive coupling of corona electric field, gas flow field, particle charging, and particle motion. These results provide physical and mathematical models to study wire-perforated plate ESP. Long et al. [12, 13] calculated the corona electric field under the wire-perforated plate structure. Their

G. Tu et al. / Powder Technology 328 (2018) 84–94

results showed that the openings change the electric field distribution on the plate surface. The curve of the field strength distribution reached its peak values at non-open areas, whereas valley values were achieved at open areas. The ratio of mean electric field strength in the opening areas to the other areas is approximately 0.67. Space charge density distribution is not significantly affected by the openings. They also noticed that the electric field passes through the plate openings and distributes on the filter surface. This mechanism may cause sparks on the bags. Different opening structures were evaluated to protect the bags from electrical damage [14]. Their valuable results provided an insight into the special electric field distribution under the wire-perforated plate structure. Tu et al. [15] built a laboratory-scale hybrid particulate collector to investigate the effect of opening structure on dust collection performance. They found that total collection efficiency change little when the percentage of open area is increased from 0.19 to 0.45 due to complementary effect. The opening type exhibits a minimal effect on the total collection efficiency. These results provided the preferred opening structures for the design of perforated plate in a hybrid particulate collector. Another important factor that influences particle motion is the distribution of flow field. Industrial ESPs usually operate at an inlet velocity of 1 m/s with turbulent flow. The air ions in the ESP migrate toward the grounded electrode under Coulomb force. These ions transfer their momentum to neutral gas molecules upon collision, which results in macro gas flow called electrohydrodynamic (EHD) flow [16]. Research shows that the Coulomb force on the ions acts as a body force on the gas. The body force is equal to the product of the electric field vector and space charge density [17]. The main flow and EHD flow interact to form a complex flow state in the ESP. EHD flow in wire-plate ESPs was numerically calculated in previous studies [18–22]. Results showed that the flow state is characterized by a dimensionless EHD number, which is defined as the ratio of electric body force to fluid inertia [23]. When the EHD number is low, the main flow is barely affected by the electric field. When the EHD number is high, the electric effect is strong, which creates a vortex in the channel. Some studies focused on the effect of EHD flow on particle motion. Results showed that EHD flow facilitates the capture of micron particles [24, 25]. Only a few studies examined the flow field under the wire-perforated plate structure. The main flow significantly differs from traditional ESPs because of the openings on the plate. The openings also change the electric field and the body force on the gas. Both elements significantly affect particle motion. A particle begins to acquire charge and migrate toward the plates under the effect of electrostatic force after entering ESP. The rate of particle charging and the amount of charge acquired are crucial in the design of ESPs given that the electrostatic force on a particle is

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proportional to its charge. The two classical models used to predict the particle charging process include field charging theory [26] and diffusion charging theory [27]. Ion diffusion is neglected in the field theory, whereas the external field is neglected in the diffusion theory. A combined field and diffusion charging approach is employed in ESP particle charging. The sum of field theory and diffusion theory is not theoretically justified, but it is often used to predict particle charging in ESPs as if other mechanisms were not present. Attempts have been exerted to develop a combined theory for particle charging in ESPs [28, 29]. Long and Yao [30] developed a complete summary of all these particle charging theories. Although various theories were developed based on different assumptions, it is accepted that the charge on particles increases with residence time, and charging rate increases with electric field strength and ion concentration. The openings of the plate change the distribution of the electric field, whereas the particles leave the ESP zone through the openings, thereby reducing particle residence time. These conditions affect the particle charging processes and may result in insufficient particle charge. The unique structure of the ESP zone in the compact hybrid particulate collector leads to the distinctive distribution of electric and flow fields. The particle collection of perforated plates also differs from that of traditional wire-plate ESPs. Deep research on the collection mechanism with a perforated collection plate remains lacking. Therefore, the current study developed a numerical model to simulate the electrostatic precipitation in a compact hybrid particulate collector. The distributions of electric and flow fields under the perforated plate structure were calculated. Particle charging and deposition processes were simulated and analyzed based on field distributions. The results provide guidance to the development of compact hybrid particulate removal techniques.

2. Numerical 2.1. Precipitator geometry The structure of a compact hybrid particulate collector can be divided into an ESP zone followed by a FF zone. An industrial-scale collector is composed of a plurality of ESP zones and FF zones with identical structures in parallel to handle the large flow of gas. Given its symmetry, the two-dimensional feature structure was examined from the overall structure of the compact hybrid particulate collector. Fig. 1 shows the structure of a compact hybrid particulate collector with a five-wire ESP zone. Boundaries y = 0 mm and y = 1125 mm are symmetrical boundaries. The aerosols initially move into the ESP zone, and the perforated plates capture most of the particles. The aerosols simultaneously

Fig. 1. Structure of the five-stage compact hybrid particulate collector.

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flow through the openings to the FF zone. Clean gas is then discharged into the atmosphere after filtering residual particles. Most dimensions are selected to match those of the commonly used industrial ESPs and FFs. The wire-to- perforated plate spacing is 200 mm, and the wire-to-wire spacing is 400 mm. The 2 mm thick perforated plates are grounded electrically. The diameter of the corona wires is 1 mm. The percentage of open area of the perforated plate is a key parameter of the ESP zone. Previous studies showed that the plates with opening diameter less than 25 mm and the percentage of open area in the range of 0.4 to 0.45 have better performance [15]. The strength of electric field on the bag surface increases with the percentage of open area, which may cause sparks and damage the bags [14]. The percentage of open area in this study is 0.4 after considering collection efficiency and bag safety. Each wire faces a 400 mm long plate with eight 20 mm openings. This configuration is called one stage hereafter. The opening position is selected, where the perforated plate in every stage is identical and symmetrical about the wire. The configuration of the last stage is different from others with a grounded baffle plate at the end of the channel. All grounded plates are illustrated with red lines in Fig. 1. The three surfaces of the perforated plate are the front side (surfaces facing the wires), back side (surfaces facing the bags), and flank side (surfaces created by opening). Boundary y = 380 mm is considered the outer surface of the computational domain of electric field given that the field strength is extremely weak in the region beyond y = 380 mm. Eighteen bags with 200 mm diameter are arranged behind the perforated plate. The bag-to-bag spacing is between 250 mm and 280 mm. In the design of industrial ESP, the appropriate length of the collecting plate should be selected according to the required efficiency. Compact hybrid particulate collectors with perforated plates of various length were studied. They were constructed by varying the number of ESP stages, whereas maintaining the bag number and spacing. Four to twenty three stage compact hybrid particulate collectors were studied. The corresponding perforated plate length is 1.6 m to 9.2 m. The electric field, flow field distribution, and the particle charging and trajectory of the collectors with various stages have similar characteristics. The results of the five-stage compact hybrid particulate collector are illustrated in the next section as an example.

The physical models, which are involved in the electrostatic collection of particles, are the corona electric field, flow field, particle charging, and particle motion models. Based on the analysis, the mathematical model established in this study ignores the effect of the flow field on the electric field and considers EHD flow. The effects of particle charge and motion on the electric and flow fields can be neglected without causing substantial errors. The prediction of the collection efficiency of a perforated plate by the present model was validated with experimental results in our previous study [15]. The corona electric field adopts a simplified single-species stationary model. In addition, a steady state model is used without any changes with time. The convective component in the ionic current density can be neglected, whereas the drift and diffusion components are included given that the drift velocity of ions is approximately two orders of magnitude faster than the typical velocity of the gas flow. The governing equations are as follows:

Zi

ρ ε0

ρ2 −Z i ∇φ  ∇ρ−Di ∇2 ρ ¼ 0 ε0

Di ¼

ð1Þ

ð2Þ 3

where φ is the electric potential (V); ρ is the space charge density (C/m ); ε0 is the air permittivity (8.85 × 10−12 F/m); and Zi is the mobility of negative ions in air. Lawless' measurements indicate a Zi of 2.02 ×

kB TZ i ni e

ð3Þ

where kB is the Boltzmann constant (1.38 × 10−23 J/K); T is the air temperature (K); ni is the number of elementary charges carried by an ion (i.e., 1); and e is the elementary charge (1.60 × 10−19 C). This equation provides a Di of 5.19 × 10−6 m2/s. Boundary conditions were provided to solve these equations. The electric potential of the wires is equal to the applied voltage. The electric potential of the grounded plates is zero. Another boundary condition on the wires is determined by Katpzov hypothesis, which suggests that electric field strength increases in proportional to the voltage below the corona onset. However, a constant value is preserved after the corona is initiated [32]. This constant value can be predicted using Peek's formula [33]. The normal gradients of the electric potential and space charge density at the other boundaries are prescribed as zero. The flow in the electrostatic zone is steady turbulence. The standard k-ε model is adopted similar to other numerical studies [9, 34, 35]. The detailed equations are provided by Launder and Spalding [36]. The electric body force on the air, which is the product of the electric field and space charge density, is considered in the momentum equation. The boundary condition of the wall surface is non-slip. The inlet is the velocity inlet, and the outlet is the pressure outlet. The filter is considered as a boundary with some resistance. The resistance coefficient is determined so that pressure drop across the filter is 900 Pa, which is the typical pressure drop of industrial FFs. Particle charging processes are described by the Lawless model [29]. Long et al. [30] recommended utilizing the Lawless model to simulate particle charging in ESPs from the aspects of accuracy and computational efficiency. The Lagrange approach is adopted to describe particle motion. The main forces that act on a particle in the electrostatic zone are the electrostatic and drag forces. The motion equation of a particle can be written as: m

2.2. Mathematical model

∇2 φ ¼ −

10−4 m2/(V·s) [31]. Di is the ion diffusion coefficient given by the Einstein equation:

! ! dup ! ¼ FD þ FE dt

ð4Þ

! ! where m is particle mass (kg); u p is the particle velocity (m/s); F D is ! the drag force (N); and F E is the electrostatic force (N). Particles are assumed spherical. The particle Reynolds number is lower than 1. Hence, the drag force on the particles can be expressed by the Stokes law:
 ! !0 ! 3πμdp u þ u − u p ! FD ¼ Cc ! ! F E ¼ E qp

ð5Þ ð6Þ

where μ is the dynamic viscosity of air (Pa·s); dp is the particle diameter ! (m); E is the electric field vector (V/m); and qp is the particle charge (C). Turbulence in the electrostatic zone is strong. Thus, the turbulent diffusion of particles is considered by adjusting the fluid velocity employed ! in the drag force. u is the mean velocity from the Reynolds-averaged !0 Navier–Stokes equations. u is the turbulent fluctuation velocity defined pffiffiffiffiffiffiffiffiffiffiffi as ζ 2k=3 in each direction. ζ is a normally distributed random number with zero mean and unit standard deviation. Cc is the Cunningham slip correction factor [37]: Cc ¼ 1 þ

   λg dp 2:284 þ 1:116 exp −0:4995 dp λg

where λg is the mean free pass of the air molecules (m).

ð7Þ

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Fig. 2. Comparison of the electric field of the wire-plate ESP (left) and the wire-perforated plate ESP (right).

Particles are considered trapped upon collision with walls, plates or filter bags. 2.3. Solution method The main tool for the numerical calculations in this study is COMSOL MULTIPHYSICS, which is based on the finite element method. The partial differential equation module was utilized to solve the electric field by inputting the equations and boundary conditions into the software. The CFD module was applied to resolve the fluid dynamic equations. Particle motion was solved using the particle tracing module. Particle charging equations were added to the particle tracing module. The electric field was calculated first, and the results were utilized to calculate the electric body force. The fluid field was then calculated considering the electric body force. Finally, the results of the electric and flow fields were passed to the particle tracing module to calculate the charging and motion processes of the particles. Each time step calculates the charging rate of a particle according to particle position and then updates the particle charge. The geometry was discretized with triangular mesh elements to resolve the complicated structure in the ESP and FF zones. The mesh adjacent to the wires, perforated plate, and bags was refined to obtain a maximum element size of 0.1 mm, 2 mm, and 1 mm, respectively, on each surface. The maximum element size in the computational domain is 4 mm. A discretized five-stage compact hybrid particulate collector (Fig. 1) consists of 485,892 elements. Convergence tests were conducted to confirm that the mesh was sufficiently fine to obtain meshindependent solutions.

The motion of 1 μm and 10 μm particles were simulated to investigate the effect of particle size. The density of the particles was 2000 kg/m3. The particles were injected into the gas at the inlet of the ESP zone with the same velocity as the gas. The time step in solving the particle motion equations is 0.5 ms. Convergence tests confirmed that this time step is sufficiently small. 3. Results and discussion 3.1. The electric field Fig. 2 shows the electric field distribution in the ESP zone of the compact hybrid particulate collector. The results of the traditional wireplate ESP with the same wire-to-wire and wire-to-plate spacing are

2.4. Model parameters The operational parameters of the compact hybrid particulate collector were selected to match common operation conditions of industrial ESPs and FFs. The voltage on the wires is −70 kV. Inlet gas velocity is 1 m/s. Mean filtration velocity is 1.06 m/min. The electric potential and space charge density in the following results are absolute values for convenience.

Fig. 3. Sketch map of the cut line position.

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(b) 400 Plate

Wire

20

400 Plate

Wire

Ex (kV/m)

Space charge density (μC/m3)

(a) 30

300

300

200

200

100

100

Ey (kV/m)

88

10

0 0.0

0.1

0.2 y coordinate (m)

0.3

0 0.0

0 0.1

0.2 y coordinate (m)

0.3

Fig. 4. Comparison of the electric field along cut line 1 of the wire-plate ESP (dash lines) and the wire-perforated plate ESP (solid lines): (a) space charge density, (b) field strength.

presented for comparison. The potential, space charge density, and electric field strength distribution of the wire-plate structure in each stage are identical. In each stage, the distribution is bilaterally symmetrical about the wire. The electric potential and the space charge density are the highest at wire surface, but decrease away from the wire. The electric field strength is highest at wire surface, which reaches 7.39 × 106 V/ m. The strength of the electric field decreases and then increases slowly from the wire to the plate. The electric field strength on plate surface increases with the decrease of the distance to the wire. For the wire-

perforated plate structure, the electric field distribution characteristics of the first four stages are similar to that of the wire-plate structure. The field distribution in the fifth stage is different from the first four stages because of baffle plate in the channel end. Field distribution is no longer bilaterally symmetrical about the wire. The field distribution on the left side of the wire is the same as that of the first four stages, whereas, the right side of the wire is affected by the baffle plate. The electric field, starting from the wire, changes at the same speed in the positive x and y directions. The openings on the plate only affect the

Fig. 5. Comparison of the electric field along cut line 2 of the wire-plate ESP (dash lines) and the wire-perforated plate ESP (solid lines): (a) space charge density, (b) field strength.

Fig. 6. Flow field in the compact hybrid particulate collector (arrows indicate flow direction).

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Fig. 7. Flow rate of the openings (dots) and the main flow velocity (solid line).

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electric field distribution near the perforated plate. The enlarged view near the perforated plate shows that the distribution of the electric field strength on the perforated plate surface is related to the location of the wires and openings. The strength of electric field reaches maximum values at opening edges. The electric field then passes through the openings to distribute in the back side region of the perforated plate. The potential, space charge density, and electric field strength in the back side region decrease rapidly away from the perforated plate. The values in most regions far from the perforated plate are close to zero. The quantitative analysis of the electric field strength shows that the influence of the asymmetry of the last stage on the previous stages is less than 1%. The electric field distribution in each stage is the same except for the last stage. For the wire-perforated plate ESPs with more stages, the electric field distribution at all stages except the last stage can be described by the first stage shown in Fig. 2. The electric field along two cut lines was examined to explore the effect of opening on electric field distribution, as shown in Fig. 3. Cut line 1

Fig. 8. Motion and charging processes of particles: (a) and (b) are particle trajectories and field strength, (c) and (d) are the charging processes of 1 μm and 10 μm particles, respectively.

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is located at x = 0.28 m, which passes through the opening at a distance of 5 mm from the right side edge. Cut line 2 is located at y = 0.195 m, which is located 5 mm from the perforated plate surface. Fig. 4 compares the electric field distribution along cut line 1 of the wire-plate ESP and the wire-perforated plate ESP. The space charge density distribution curves of the two structures coincide in the region between the wire and the plate. After the plate is opened, the ions pass through the openings and migrate to the back side of the perforated plate. The space charge density decreases rapidly to zero after passing through the openings. Two components of the electric field vector can be distinguished as parallel to the perforated plate (Ex) and perpendicular to the perforated plate (Ey). The Ex and Ey curves along cut line 1 of the two structures coincide in most areas, but diverge near the plate. The opening affects the electric field strength in a region approximately one-tenth the wire-plate spacing adjacent to the perforated plate. The openings lead the Ey to decrease, and the Ex to increases. Ex of the wire-perforated plate ESP presents a maximum at the perforated plate position and rapidly decreases to zero in the back side of the perforated plate. Fig. 5 compares the electric field distribution along cut line 2 of the wire-plate ESP and the wire-perforated plate ESP. It still can be seen that the openings have little effect on the space charge density distribution, but they greatly affects the electric field strength. Ex is close to zero under the wire-plate structure. By contrast, Ex shows a periodical fluctuation with a period of the opening-to-opening spacing and an amplitude around 80 kV/m under the wire-perforated plate structure. The amplitude increases when approaching the wire. The fluctuation reaches the minimum values at the left edges of the openings, the maximum values at the right edges of the openings, and zero at the center of the openings and the solid sections. The change in the sign of Ex indicates the change of the direction. Ex changes direction when passing by the center positions of the solid sections or the opening center positions. Direction always points to the nearest center position of the solid section. Analysis shows that Ex exhibits the same characteristics in the region adjacent to the perforated plate, which contributes to particle deposition on the three sides of the perforated plate. Under the wire-plate structure, Ey reaches its maximum at the position opposite to the wire, and gradually decreases away from the wire with an average value of 340 kV/m. After the plate is opened, Ey at the opening positions decreases, whereas Ey at the solid sections increases. The average value 336 kV/m slightly changes. Considering the relative magnitude of the two electric field vector components, the electric field strength near the perforated plate slightly increased because of the openings. 3.2. The flow field Fig. 6 shows the flow field in the compact hybrid particulate collector. Gas flows along the perforated plate and enters into the bag zone through the openings at the same time. The velocity of main flow decreases gradually. In the first four stages, the action of electric body force is weak, and the main flow is not greatly affected. The electric body force only changes the velocity distribution on the transverse section. Main flow velocity in the last stage is small. The vortex caused by the electric body force is superimposed with the main flow, thereby deflecting it toward the wire to the end of the ESP zone. The vortex then flows out through the openings at the end of the perforated plate. The enlarged view of the flow field near the perforated plate shows that eddies are formed at the back side of the solid sections due to the expansion of the flow area. Two counter-rotating eddies are in the vortex zone between two openings. The left eddy is clockwise, and the right eddy is counterclockwise. These eddies carry the particles through the openings to the vicinity of the perforated plate, thereby promoting particle deposition. Fig. 7 shows the flow rate of the gas through the openings from the ESP zone to the bag zone. The flow velocity in x direction along the line y = 0.1 m is also shown. The flow rate of the gas in the first stage is low,

whereas the flow rates in the other stages are basically the same. The flow rate of the openings varies periodically. The flow rate in each stage reaches maximum value at openings opposite to wires, except for the last stage. This result is attributed to the strong electric body force near the wire, which drives the gas toward the perforated plate. The distribution of electric field in the last stage is different from the previous stages, thereby causing the maximum flow rate to appear at the end of the perforated plate. The main flow velocity decreases almost linearly along the perforated plate. Results showed that the resistance of the system is mainly caused by the bags. The pressure drop across the bags is two orders of magnitude higher than the pressure difference of the other positions. Although the electric body force affects the flow field, the flow rate of each stage remains relatively uniform because of the bags. The flow field distributions in compact hybrid particulate collectors of different stages show the same characteristics. 3.3. Particle charging Particles were released from y = 0.178 m, 0.1 m, and 0.01 m at the inlet to illustrate particle charging processes, as shown in Fig. 8. Similarities were observed for particles with different sizes and released from different positions. The amount of charge acquired by a particle increases gradually and remains constant after a certain period. Within the first 0.2 s when the particles enter the ESP zone and move to the position of the first wire, the particles acquire most of the charges, and particle charge exceeds 80% of the final value. The particles then maintain their charge when they move away from the wires or the perforated plate, and start charging again when they move close to the wires or the perforated plate, which is related to the charging mechanisms. When the particles come close to the wires or the perforated plate, the electric field strength increases, and the particles start charging due to field charging. The strength of the electric field decreases when the particles move away from the wires or the perforated plate. Particle charge exceeds the saturation charge that corresponds to the field strength at that position. Field charging stops and the particle continues to acquire charge by diffusion charging. However, the particle charge is high so that the Coulomb repulsion force between the ions and the particle is large. The ions can hardly diffuse to the particle surface. Therefore, particle charge remains unchanged. The 10 μm particle deflects to the perforated plate much earlier than the 1 μm particle. The final charge of the 10 μm particle is approximately 100 times the value of the 1 μm particle. A total of 10,000 particles are uniformly injected at the entrance of the ESP zone, and the charging processes of these particles are simulated. The 1 μm particles take 2.32 s on average to reach the final charge of

Fig. 9. Final charge on a particle vs. particle initial position.

G. Tu et al. / Powder Technology 328 (2018) 84–94

182.7 electrons. When the 1 μm particles move to the position of the first wire, the average charge on a particle is 150 electrons, which is 82% of the final charge. The 10 μm particles take 0.93 s on average to reach the final charge of 12,311 electrons. When the 10 μm particles move to the position of the first wire, the average charge on a particle is 10,799 electrons, which is 88% of the final charge. Fig. 9 shows the relationship between the final charge on a particle and the initial position of the particle when it enters the ESP zone. The results of the five-stage wire-plate ESP are presented for comparison. The final charge is the highest at the position near the wire, and lowest at the position near the plate. Particles released from positions in-between are charged to a moderate state. This result is caused by the difference in the electric field strength along the trajectories of the particles released from different positions. The final charge increases with the maximum

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electric field strength along a particle trajectory. The curves of the two structures coincide. The average final charge on a 1 μm particle is 178 for wire-plate ESP and 183 for wire-perforated plate ESP. The average final charge on a 10 μm particle is 12,257 for wire-plate ESP and 12,304 for wire-perforated plate ESP. The charge acquired by a particle under the wire-perforated plate structure is 3% higher than that under the wire-plate structure. This finding is attributed to the similarity of electric field distribution in most regions of the two structures, and the increase in electric field strength near the perforated plate caused by the openings. 3.4. Particle motion Fig. 10 shows the trajectories of 1000 particles uniformly injected at the entrance. The trajectories of the particles captured in the ESP zone

Fig. 10. trajectories of the particles collected by the plate (red) and the particles that escaped from the ESP zone (green): (a) 1 μm particle, (b) 10 μm particle. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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are marked as red, and the trajectories of the escaping particles are marked as green. The particles move with the gas toward the end of the perforated plate and deflect with the gas toward the perforated plate. The particle charge increases along the course, and the electric force drives the particles toward the perforated plate, which causes the particles to deflect faster than the gas. When the particles move to the vicinity of the perforated plate, the particles near the openings are likely to escape, whereas the particles near the solid sections are likely to be trapped. The trajectories of the two colors are distributed separately, thereby forming distinct partitions. The opening position corresponds to an escaping particle track, whereas the solid position corresponds to a trapping particle track. The starting position of a particle determines the position where the particle will deposit on. Thus, the possibility of a particle to be trapped by the perforated plate is directly related to its initial position. The enlarged graph shows that the particles released from some locations are more likely to be captured by the perforated plate, whereas particles starting from other locations are more likely to escape. However, no definite boundary is observed between the trapped particles and the escaping particles because of turbulent diffusion of the particles. The 10 μm particles acquire more charge than the 1 μm particles. Thus, they migrate faster toward the perforated plate and reach the perforated plate earlier. The collection efficiency of 10 μm particles is higher than that of the 1 μm particles as shown by the proportion of the red trajectories. A total of 10,000 particles are uniformly injected at the entrance of the ESP zone to illustrate the relationship between particle initial position and their capture probability by the perforated plate. The inlet is divided into 200 groups at intervals of 1 mm. The capture probability of the particles in each group is shown in Fig. 11 by the black line. The capture probability fluctuates between 0 and 1, which shows periodicity that corresponds to the opening position. The peak and valley values correspond to the position of the solid sections and the openings, respectively. The curve would be a step function if there were no diffusion at all. Turbulent diffusion causes a certain random fluctuation of the particle trajectory to obtain a smooth probability distribution curve. A 10 μm particle is more likely to be captured than a 1 μm particle because of high electric mobility. The blue curves in the figure were obtained by averaging the black curves. The particles, which were released near the wire position or the perforated plate position, are more likely to be captured. Particles released close to the perforated plate move to the first stage. The gas flow rate of the openings in the first stage is low, which is in favor of particle capture. The capture probability of particles, which were released close to the wire is high because they acquire more charges than average. Periodicity corresponds to the wire distribution is not observed in the probability distribution curve. This finding is attributed to the fact that the electric field strength is high at the wire position, whereas the flow rate through openings at the wire position is also high. The two

4. Conclusions The electric field, flow field, particle charging, and motion behavior in a compact hybrid particulate collector are simulated. The main conclusions are as follows. The electric field distribution in the last stage is asymmetrical because of the baffle plate in the channel end. The field distributions in the other stages are identical and bilaterally symmetrical about the wire. The potential, space charge density, and electric field strength are the highest at wire surface in each stage. The openings barely affect the space charge

(b) 1.0

Average

Collection probability in ESP

Collection probability in ESP

(a) 1.0

effects cancel each other. Thus, different in collection efficiency in each stage is small. Fig. 12 shows the particle trajectories at the vicinity of the perforated plate and the particle deposition processes. The particle trajectories of green, blue, red, and gray represent particle final deposition on the front side, flank side, back side, and bag surface, respectively. When the particles move to the vicinity of the perforated plate, the particles facing the solid sections are deposited on the front and left flank sides of the perforated plate. Particles that face the openings pass through the openings with gas. During this process, a small fraction of the particles near the vortex zone first migrate into the vortex under the action of electric force that is parallel to the perforated plate, and then deposit on the back and right flank sides of the perforated plate. Particles far from the vortex zone cannot enter the vortex and escape from the ESP zone. Two counter-rotating eddies are located in the vortex zone between two openings. The particles near the left edge of the solid section enter the clockwise eddy on the left, whereas the particles near the right edge of the solid section enter the counterclockwise eddy on the right. The electric field strength at the back side of the perforated plate is lower than that at the front side. Therefore, the influence of turbulence on the particle motion at the back side is large, and the trajectories show randomness. The behavior of particles varies greatly with particle size due to the difference in particle charge. A larger fraction of 10 μm particles are captured in the front side and enters the vortex zone, compared with 1 μm particles. All the 10 μm particles that enter the vortex zone are eventually deposited on the perforated plate. By contrast, some 1 μm particles that enter the vortex zone escape and move to the bag zone. The electric force on a 1 μm particle is weak. So a 1 μm particle completely follows the gas flow after it enters the vortex zone. The particle is captured by the perforated plate when it moves with the eddy to the vicinity of the perforated plate where the electric field strength is sufficiently strong. Otherwise, the particle continues to rotate with the eddy. When the particle moves close to the outer boundary of the vortex zone during this rotation, it is possible for the particle to leave the vortex zone under the action of turbulence. Most 1 μm particles that enter the vortex zone are eventually deposited on the perforated plate, and the rest ones move to the bags.

0.8 0.6 0.4 0.2 0.0 0.00

0.05

0.10

0.15

Particle initial y coordinate (m)

0.20

Average

0.8 0.6 0.4 0.2 0.0 0.00

0.05

0.10

0.15

Particle initial y coordinate (m)

Fig. 11. Capture probability of the particles in the ESP zone and their initial positions: (a) 1 μm particle, (b) 10 μm particle.

0.20

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Fig. 12. Particle trajectories at the vicinity of the plate: (a)1 μm particle, (b)10 μm particle.

density and electric field strength near the wire, but significantly affect the electric field strength in the region of approximately onetenth the wire-plate spacing adjacent to the perforated plate. In this region, the electric field strength perpendicular to the perforated plate decreases at the opening positions and increases at solid sections with the average value slightly changing. The electric field strength parallel to the perforated plate is increased and always points to the nearest center position of the solid section, which facilitates particle deposition on the flank and back sides. In addition, the openings on the plate cause the electric field to distribute to the back side of the perforated plate. Gas flows along the perforated plate and enters into the bag zone through the openings at the same time. The cross flow rate in the first stage is the lowest, whereas the flow rates of the other stages are the same. The flow rate of the openings varies periodically under the effect of electric body force. Flow rate through the openings opposite to the wires is increased. The cross flow through the openings creates eddies behind the solid sections, which promote particle deposition on the back side. Particle charge increases gradually and finally maintains a constant value after entering the ESP zone. Most of the charging processes are completed when the particles move to the position of the first wire. The 1 μm particles reach 82% of their final charge, whereas the 10 μm particles reach 88% of their final charge. The 10 μm particles complete their charging processes much faster than the 1 μm particles with the final charge of approximately 100 times that of the 1 μm particles. The final charge on a particle is related to its initial position. Particles released close to the wire are charged to the highest level, whereas those released close to the perforated plate are charged to the lowest level. The effect of opening on particle charging is small. The charge acquired by a particle under the wireperforated plate structure is 3% higher than that under the wireplate structure. After entering the ESP zone, the particles move with the gas toward the end of the channel and deflect toward the perforated plate under the effect of electric and flow fields. When the particles move to the vicinity of the perforated plate, the particles near the solid sections are deposited on the front side. Particles near the vortex zone enter the vortex under electric force and then move toward the back side of the perforated plate. All 10 μm particles that enter the vortex zone are eventually deposited on the perforated plate. Some 1 μm particles that enter the vortex zone escape because of turbulence. Particle capture probability by the perforated plate is related to its initial position. The peak and valley values correspond to the position of the solid sections and the openings, respectively. The particles released near the wire position or the

perforated plate position are more likely to be captured than the particles released in-between. The collection efficiency of the 10 μm particle is higher than that of the 1 μm particle. Nomenclature Cunningham slip correction factor Cc particle diameter, m dp ion diffusion coefficient, m2/s Di e elementary charge, 1.602 × 10−19 C ! E ,E electric field vector, V/m ! drag force, N FD ! electrostatic force, N FE k turbulent kinetic energy, m2/s2 kB Boltzmann constant, 1.38 × 10−23 J/K m particle mass, kg particle charge, C qp t time, s T temperature, K ! u mean velocity of air, m/s !0 turbulent fluctuation velocity, m/s u ! particle velocity, m/s up x x coordinate, m y y coordinate, m ion mobility, m2/(V·s) Zi Greek letters ε ε0 λg μ ζ ρ φ

turbulent dissipation rate, m2/s3 permittivity of air, 8.85 × 10−12 F/m mean free pass of air molecules, m dynamic viscosity of air, Pa·s random number space charge density, C/m3 electric potential, V

Particle charging and motion in the compact hybrid particulate collector. Acknowledgements This work was supported by the fund from the National Key Technologies R&D Program of China (2015BAA05B01) and the National Basic Research Program of China (2013CB228506).

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