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Numerical study on fine-particle charging and transport behaviour in electrostatic precipitators
Accepted Manuscript Numerical study on fine-particle charging and transport behaviour in electrostatic precipitators
Ming Dong, Fei Zhou, Yuxuan Zhang, Yan Shang, Sufen Li PII: DOI: Reference:
S0032-5910(18)30159-1 doi:10.1016/j.powtec.2018.02.038 PTEC 13214
To appear in:
Powder Technology
Received date: Revised date: Accepted date:
3 August 2017 24 January 2018 12 February 2018
Please cite this article as: Ming Dong, Fei Zhou, Yuxuan Zhang, Yan Shang, Sufen Li , Numerical study on fine-particle charging and transport behaviour in electrostatic precipitators. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Ptec(2017), doi:10.1016/j.powtec.2018.02.038
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ACCEPTED MANUSCRIPT Numerical study on fine-particle charging and transport behaviour in electrostatic precipitators Ming Dong*, Fei Zhou, Yuxuan Zhang, Yan Shang, Sufen Li Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of
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Technology, Dalian 116024, China; Corresponding author: Ming Dong, School of Energy and Power Engineering, Dalian University
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of Technology, No. 2 Linggong Road, Ganjingzi District, Dalian, Liaoning, 116024, People’s
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Republic of China, Tel:+86-0411-84762312， Fax:+86-0411-84708460
E-Mails: [email protected]; [email protected]; [email protected]; [email protected]; [email protected];
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Abstract
In this work, a numerical study on the charging and transport of fine particles has been
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carried out based on wire-plate electrostatic precipitators (ESPs) with multiple wire electrodes. The effect of the applied wire voltage, inlet height, and wire spacing on particle charging and
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transport, and the influence of the precipitator structure on particle trapping are analysed in detail.
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Results indicate that a voltage increase in the high voltage range improves the particle-trapping efficiency. However, the Brownian diffusion causes the particle fluctuation, but it doesn’t change the direction of main movement. Particles injected into the precipitator at the channel centre are
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influenced most intensively, whereas particles injected at approximately 5 mm from the centre of the precipitator exhibit the poorest particle-trapping ability. An increased wire spacing enhances
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particle trapping, within a certain range, and a larger particle size causes an even more obvious enhancement. Furthermore, changing the discharge-electrode arrangement shows a much greater effect on the charging and transport behaviour of particles in the model of M3, which has the highest trapping efficiency. Keywords：Electrostatic precipitators (ESPs); Electrostatic precipitators structure; Particle trapping; Wire spacing.
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NOMENCLATURE electric potential
space-charge density
E
electric field intensity
0
permittivity of free space
J
current density
K
ion mobility
D u
diffusion coefficient of ions
up
particle velocity
gas-flow velocity
p
f
fluid density
particle density
dynamic viscosity of the fluid
dp
particle diameter
Re
relative Reynolds number
v w
non-dimensional particle charge non-dimensional electric field
p
rc
radius of the corona wire
t
CD
drag force coefficient
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relative permittivity of the particles
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charging time
the Gaussian random number
the fluid kinematic viscosity
Kn
the Knudsen number
the particle mass
S0
the spectral intensity of the noise
P kB
the absolute pressure the Boltzmann constant
the molecular mean free path
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mp
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i
D
the Cunningham slip correction factor
Introduction
non-dimensional particle-charging time
Ep Peek’s electric field intensity
Cc
1.
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Electrostatic precipitators (ESPs) are major air pollution control devices to remove particles
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from treated gas. Extensive research has been done on several aspects of this process, such as electrostatics, fluid dynamics, charging mechanism, and particle dynamics [1-5]. The overall particle-collection efficiency of a modern industrial wire-plate ESPs exceeds 99%. However, the removal efficiency of submicron particles by conventional ESPs is as low as 70–80% owing to the low charge carried by fine particles and the decreased size particles are more inclined to travel with the surrounding fluid [2-3]. Submicron particles possess a high superficial area, thus favouring toxic heavy metals and other pollutants. Therefore, fine particles are collected with much lower efficiency and further research is required to improve this aspect [5]. The basic working process in ESPs involves several complicated and interrelated physical
ACCEPTED MANUSCRIPT mechanisms. The particles are given electric charge by forcing them to pass through a corona discharge, a region in which gaseous ions flow. Charged particles are then deflected from the main gas stream by an electric field to be precipitated onto the collecting plates [6]. The particle trajectories are influenced by the interacting electrostatic, fluid field, and the particle transport factors. These factors are mutually coupled, although some couplings are weaker than others and
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can be neglected. The electrohydrodynamic (EHD) flow is generated owing to momentum transfer from moving charged species (ions and particles) to neutral molecules, in addition to the primary
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flow and electric field. Some researchers believe that the particle collection efficiency could be significantly improved if the EHD flow were eliminated [7]. Soldati showed that the EHD flow
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not only contributes to re-entrainment of particles in the central region of the channel, but also to sweeping the particles to the collecting plates, thus having a negligible influence on the overall
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collection efficiency [8]. He also pointed out that this effect is only significant at low flow velocities. In the present paper, the fluid-flow velocity is higher than 1 m/s and the EHD flow has
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a negligible effect on the collection efficiency of the particles. The particle-charging rate is a function of the ease of electrical charge acceptance, which is
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described by the classical Deutsch model using resistivity as the characteristic material property
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[9-10]. However, the Deutsch model, its derivatives, and other theoretical correlations fail to give an accurate estimate of the charge level under a wide range of operating variables [9]. Numerous studies have been devoted to the numerical modelling of the complex and coupled physical
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phenomena involved in the precipitation process. McDonald et al. developed a numerical method that can be used to calculate the electric potential and space-charge density in electrostatic
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precipitation [11]. Lami et al. developed the coupled system of the Poisson equation and the space-charge drift formula considering the statistical size distribution of particles and the corresponding charging processes with a finite-difference scheme [12]. Kim presented a modified model for considering simultaneously the convection force, electrostatic force, and diffusion to predict the wire-plate ESP performance for collecting polydisperse particles [10]. Later, the strong coupling between the fluid flow and electric field have been extensively examined with the model developed by Schmid et al. [13,14]. The use of CFD in the description of ESP operations was introduced by Fletcher and his collaborators [15]. In this model, the turbulent gas flow and particle motion under electrostatic forces are calculated using FLUENT, linked to a finite-volume solver
ACCEPTED MANUSCRIPT for the electric field and ion charge. The charge density and velocity of the particles are averaged over a control volume to use the Lagrangian formulation of the particle motion for the calculation of the gas and electric fields. Nikas et al. and Skodras et al. have developed a CFD model considering gas flow, particulate flow, particle charging, electric field, and current-flow equations and analysed the collection performances of ESPs under certain conditions [16,17]. Recently,
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Adamiak et al. presented a coupled numerical model on the simulation of secondary EHD flow caused by corona discharge and charged particles [18]. Moreover, they performed detailed
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investigations on the effects of charged particles and EHD turbulent flow on the gas-flow patterns in a spike-plate ESP [19,20].
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However, previous works focused on the collection efficiencies of relatively large particles, as well as the apparent effects of secondary EHD flow on the collection performance of ESPs.
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Nonetheless, a better knowledge of the detailed charging and transport behaviour of fine particles in the ESPs, especially those with a diameter of less than 1 μm, is extremely important. The
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numerical simulation results of Liang and Lin indicated that, if the main flow velocity is higher than 0.6m/s, the effect of EHD is insignificant [21]. As the main flow velocity is higher than 1 m/s,
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the effect of electrohydrodynamic flow is minimal [22]. Therefore, the main flow velocity is
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higher than 1 m/s in this study and the EHD flow has a negligible. An understanding of electrical and geometric effects on the particle trapping is critical during design and operation of wire-plate ESPs. Present work presents the results of numerical investigations of the corona-electrostatic
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field, and the charging and transport behaviour of fine particles in a simple two-dimensional model of an ESP. The 2-D numerical model involves electric field, space-charge density, gas flow,
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and particle trajectories. The electric field and gas flow are calculated using the finite-volume method. The flow simulation is done using the commercial software FLUENT with other parts coded as user-defined functions. A Lagrangian approach for particle transport is used to track the trajectories of individual particles by solving their motion equation. 2.
Mathematical model
The computational model of the ESP includes corona discharge, gas flow, particle charging, and transport. Consequently, the governing equations consist of the electric field and space charge, fluid dynamics, particle trajectory, and charging equation, respectively. 2.1 Electric field and space charge
ACCEPTED MANUSCRIPT The charge density and the electric potential distribution of the ions inside the ESP model are obtained from the numerical solution of the Poisson and charge-conservation equations. They are expressed as follows:
2
0
(1) (2)
J (KE u) D
(3)
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E
J 0
(V) is the electric potential, ρ(C ·m-3) the space-charge density, 0 (F ·m-1) the
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permittivity of free space,
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where,
(4)
E (V ·m-1) the electric field intensity, J (A ·m-2) the current density,
K (m2 ·V-1s-1) the ion mobility, and D (m2 ·s-1) the diffusion coefficient of the ions. As the drift
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velocity of ions is usually about two orders of magnitude faster than the typical velocity of the gas flow, the convective component in equation (3) can be neglected. Hence, the charge-conservation equation can be expressed as
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(K E D) 0 2.2. Fluid dynamics
(5)
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In the present study, the EHD flow can be neglected as the inlet-flow velocity is 1 m/s [3].
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Therefore, the influence of the electric field on the flow field is neglected in the numerical simulation. The air flow through the ESP channel was modelled as steady and turbulent while assuming constant density and viscosity. This was done by solving the continuity and the NS
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equations using the FLUENT. The particulate two-phase turbulence requires solutions to both the fluid field and particulate phase. The focus of present study is Lagrangian particle tracking with
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large-eddy simulation (LES). LES considers modelling of subgrid scale (SGS) effects on particles. The larger turbulent motions are solved for the smaller turbulent scales modelled in LES. For instance, turbulence effects were introduced using the LES turbulence model [23]. 2.3. Particle dynamics Due to relatively low concentration of the particles, the particle space charge was assumed to be negligible, and one-way coupling in which the dispersed phase had no influence on the fluid flow or the electrostatics, was assumed [23]. The particle dynamics was modelled using the discrete phase model (DPM) in FLUENT, based on a Lagrangian approach. The particle
ACCEPTED MANUSCRIPT trajectories in ESP are affected by the following factors: the electric field force acting on the
Fd represents the drag force due to the relative velocity of the particle and
charged particle ( FE ), the fluid.
Fg is
the gravitational force acting only in the vertical direction.
Fb is
the buoyancy
force acting only in the vertical direction. Fv is the virtual mass force accounting for the relative
FB
is the Basset history force due to the transient
FS
the acceleration of the fluid flow field.
Fp
is the pressure gradient force due to
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formation of a boundary layer near the particle surface.
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acceleration of the particle and the fluid.
is the Saffman lift force acting on the particle moving
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through the stream with a velocity gradient. Hong Lei et al. showed that the electric field and drag forces are the key forces acting on particles in the ESP [24]. This rule can be applied under a
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condition that the distance for a particle to enter the channel is greater than a quarter of separation distance. Under the influence of gas flow and electric field, particles were mainly subjected to
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drag force, electric forces, and Brownian force in the presents study. Therefore, the particle motion equation can be written as
dup 18 CD Re Eq S0 (u up ) p i 2 dt p d p 24 mp t
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D
(6)
where u p (m·s-1) is the particle velocity, u ( m·s-1) is the gas-flow velocity,
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kg·m-3) is the fluid density, and
f (
p ( kg·m-3) is the particle density, (Pa·s) is the
dynamic viscosity of the fluid, d p (μm) is the particle diameter, CD is the drag force
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coefficient, Re is the relative Reynolds number( Re electric field force, E is
particle mas, i
) ,
Eq p is the mp
the electric field intensity, qp is the particle charge, mp is the
S0 t
f d p up u
is the Brownian force, i is a Gaussian random number
chosen from a normal distribution with a zero mean and a unit variance. S0 is the
ACCEPTED MANUSCRIPT corresponding spectral intensity of the noise given by ( S0
216kBT )[25]， 2 2 d p5 p Cc f
is the fluid kinematic viscosity, kB is the Boltzmann constant. The Cunningham slip correction factor Cc can be can be expressed as ( Cc 1 Kn[1.257 0.4exp(
2 ), is the molecular mean free path. dp
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[26], Kn the Knudsen number ( Kn
1.1 )] ) Kn
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2.4. Particle-charging model
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The neutral submicron particles with a spherical shape are injected at the entrance of the precipitator and become charged as they move along the ESP channel and across the ionic
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space-charge zone. Affected by the electrostatic and aerodynamic forces, some particles are trapped on the collecting walls while others manage to escape. The calculation of the particle charge in this work is based on Lawless᾽ model [27]:
(7)
1 , w 0.525 f (w) (w 0.475)0.575 1, w 0.525
(8)
v qe / 20d pkBT
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where
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D
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3w f (w) , 3w exp( 3w) 1 d 3w (1 )2 f (w), 3w 3w and d 4 3w 3w 3w f (w) exp( 3w) 1,
is the non-dimensional particle charge,
non-dimensional particle-charging time, electric field,
= Dt / 0
the
w= p / p 2 Ed pe / 2kBT the non-dimensional
f (w) the non-dimensional electric field (fraction of the surface covered by the
diffusive band), and
p
the relative permittivity of the particles. Therefore, the charging level
depends on the size and shape of the particles, unipolar ion density, particle residence time, and the electric field intensity. 3.
ESP model and numerical procedure
The ESP consists of two grounded parallel collecting plates and three wire electrodes located
ACCEPTED MANUSCRIPT between the plates and supplied with a high negative potential. The duct length is L = 800 mm and its width w = 100 mm. The structure comprising three wire electrodes with a diameter of 1 mm each is mounted along the X-axis. The centre of the wire electrode is located at the central plane of the ESP (X = 400 mm, Y = 0 mm), as shown in Fig.1. Take in Figure 1.
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The values of the supply voltage, gas flow velocity, pressure, gas temperature, and particle diameter are given in Table 1. The gas flow has had a turbulence intensity of 5.4 % at the inlet,
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which was replicated in the present CFD simulations in which the gas density and viscosity were set equal to 1.185 kg/m3 and 1.8×10-5 kg/m·s, respectively. The fine particles were introduced into
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the computational domain at the inlet of the ESP channel and had a mass density of 2100 kg/m3. The fine particles had a uniform diameter that was varied between 0.2-1.0 μm, and the inlet
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velocity was 1 m/s.
Take in Table 1.
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The computational domain was discretized into quadrilateral cells. The mesh conditions for the discharge electrodes were set separately owing to their small diameter. Therefore, the mesh
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was much finer near the discharge electrodes to maximize the accuracy of the calculated gradients
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within the higher current density regions, as shown in Fig. 2.
Take in Figure 2.
The LES turbulence model was solved with FLUENT, with the given pressure and gas
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velocity distribution in the whole ESP channel. The electric field, space-charge distributions, electrical force, and particle charge must be determined using the so-called user-defined functions
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(UDF). All particle trajectories are tracked until the particles are trapped or they escape the ESP channel. Particle injection from the inlet of the ESP used the DPM when the residuals stabilized. The two collecting plates and the wire electrode surfaces act as stationary walls where all velocity vector components vanish. The effect of collecting plates on electric field is neglected. Therefore, image force has negligible. The left boundary is defined as the velocity inlet, and right boundary is defined as the outflow. The summary of boundary conditions for the proposed model is given in Table 2.
Take in Table 2. The corona discharge in an ESP is governed by a set of four partial differential equations
ACCEPTED MANUSCRIPT (Eqs. (1), (2), (4) and (5)) with two unknown distributions: potential
and space-charge density ρ.
The iterative method used to obtain and ρ is as follows [19]: (1) Set an initial guess for the space-charge density (ρ ≠ 0) for the entire computational domains. (2) Make an initial guess for the space-charge density on the wire surface (ρc).
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(3) Solve Eq. (1) and Eq.(2) for . (4) Solve the conservation of current (Eqs.( 4 ) and(5)) for the space charge density.
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(5) Return to step (3) until the solution becomes self-consistent.
(6) Update the charge density on the wire surface by comparing the actual electric field intensity with
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Peek’s value.
surface.
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(7) Rescale the whole charge within the domain considering the new charge density on the wire
(8) Return to step (3) and repeat the procedures until the average electric field magnitude on the wire
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surface is sufficiently close to Peek’s value.
The Kaptzov’s hypothesis is adopted that suggests the electric field intensity increases with
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increasing voltage before the corona phenomenon occurs. However, the electric field intensity no
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longer increases after the corona is initiated. Peek’s formula is used to determine the threshold strength of electric field for the corona onset at the corona electrode [28]:
rc （cm）is the radius of the corona wire.
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where
(9)
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0.308 Ep 3.1106 (kV / cm) 1 rc
The numerical procedure can be summarized as follows: (1) Evaluate the electric potential and space-charge density distribution in the whole ESP channel by using the above method until the whole residual decreases to 10-8. (2) Solve the gas flow with the LES until the whole residual decreases to 10-6. (3) Inject particles into the computational domains and determine the coupled motion and particle-charge equations of the particulate phase using DPM in FLUENT. 4. Results and discussion
4.1. Comparison with previous experimental results
ACCEPTED MANUSCRIPT For quantitative comparison of the CFD results with the measured results of Penney and Matick [29], the electric potential distribution was measured along 0-114.3 mm in the Y-direction at distances of 228.6, 266.7, and 304.8 mm in the X-direction. The selection of 228.6 mm in the X-direction was done to enable a comparison with the experimental measurements of Penney and Matick. The electric potential distribution on the vicinity of wire electrodes for three grid cells is
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shown in Fig. 3. It is shown that the electric potential distribution doesn’t change when the number of cells exceeds 53206 and the simulated electric potential distribution is agreement with
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the experimental results. Therefore, the mesh consisting 53206 cells was adopted for numerical
Take in Figure 3.
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analysis.
4.2. Distribution of the ionized electrostatic field in the ESP
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To further investigate the characteristics of the ionized electrostatic field in the ESP, the simulation procedure was performed for an applied voltage of 45 kV. The electric potential
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distribution is shown in Fig. 4 (a). It is clear from that figure that the shape of the electric potential distribution is elliptical in the vicinity of the wire electrodes. As the value of the electric potential
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near the wire electrodes is larger than in other regions of the simulation domain, it forms
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high-potential regions around the wire electrodes. However, the electric potential quickly decreases between the wire electrodes and the collecting plates and remains comparatively stable. Further, owing to the same polarity of adjacent discharge electrodes, the electric potential is
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reduced between the wire electrodes.
However, the distribution of charge density is quite different from that of the electric
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potential, as shown in Fig. 4 (b). As the charge density gradually increases between the inlet and the discharging zone, it also forms several high-density regions around the electrodes, reaching the peak value of 2×10-5 C/m3 on the surface of the wire electrode. The area of the high-density regions gradually extends, reaching the collecting plates, unlike the rapid decrease of the electric potential. Therefore, the high-density region provides adequate charging ions for diffusion charging of fine particles in the entire discharging zone.
Take in Figure 4. 4.3. Particle-charging characteristics In this analysis, the particle charging characteristics for different particle sizes and voltages
ACCEPTED MANUSCRIPT were determined. By introducing a known number and the injection position of particles into the computational domain, the particle charge could be determined. The particles were released at the centre line of the channel (X = 0 mm, Y = 0 mm) into the computational domain, at initial velocities equal to the inlet-gas velocity. The charging of particles with diameters of 0.2, 0.4, 0.6, 0.8, and 1.0 μm at applied voltages of 30, 45, and 60 kV with a gas
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velocity of 1 m/s are shown in Fig. 5. It is apparent from the results of Fig. 5 that the particle charge increases with increasing particle diameter and, therefore, larger particles are easily
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collected as compared to smaller particles. A particle with a diameter of 0.2 μm has a charge less than 40 unit charges, which implies a weak charging ability. The number of elementary charges on
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a particle grows rapidly within a narrow diameter interval when the particles have a diameter larger than 0.4 μm. As the particle surface area and diameter have an exponential relationship of
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order two, the particle surface area rapidly increases with increasing diameter. For the particles of the same material, the number of elementary charges on a particle improves with the increment in
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surface area. Furthermore, diffusion charging takes the lead for particle diameters less than 1 μm. Therefore, the number of elementary charges on a particle rapidly grows with increasing diameter.
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Moreover, it can be concluded that the number of elementary charges on a particle increases with
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increasing voltage because of the higher electric field intensity of the discharge electrodes. Take in Figure 5.
To investigate the effect of the particle-inlet location on the particle maximum charge for 60
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kV, the inlet velocity was set to 1 m/s. The results are shown in Fig. 6. Fig. 6 (a) shows that the nearer a particle is released to the centre line, the larger is the maximum charge of the particle. The
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development of the charge at various release locations is more obvious with an increasing particle size. Fig. 6(b) shows the charging history for a particle with a diameter of 1 μm released at various inlet heights. The particle inlet location is one of the key factors affecting the particle-charging process. The nearer the particle is released to the centre line, the larger the charge. For a distance of 10 mm between the release location and centre line, the increase in the particle-inlet height is not obvious after it passes the first corona wire. In addition, during the particle-charging process in the above-mentioned domain, the acquired particle charges along the trajectories were obtained. At the inlet (0 < x < 0.25 m), particles were charged at near-constant rates. However, when they approached the vicinity of the first electrode (0.25 < x < 0.3 m), the particles were rapidly charged
ACCEPTED MANUSCRIPT to much higher values. In the following region (x > 0.3 m), when the highly-charged particles were travelling between the electrodes, the acquired particle charges remained stable until the particles approached the precipitator outlet. Take in Figure 6. 4.4. Particle trajectory characteristics In present work, the particle trajectories for different particle sizes and voltages were
computational domain, the particle trajectories could be determined.
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computed. By introducing a known number of particles and their injection position into the
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To ensure that the Brownian diffusion subroutine has been correctly implemented in Fluent,
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we compared the particle trajectories for particle size of 1 µm with and without the Brownian diffusion at different voltages in Fig.7. Fig. 7(b) shows that the particles trajectories are very
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smooth without Brownian diffusion, and the opposite with Brownian diffusion. In addition, with Brownian diffusion the particle trajectories became very rough when the particle moved far away
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from wire electrodes. This phenomenon occurs because the random directions of Brownian force breaks down the balance between electric and drag forces. Moreover, the Brownian force was much smaller compared the other forces. Therefore, the Brownian diffusion caused the particle
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fluctuation, but it didn’t affect the main movement direction.
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Fig.7 shows that the particles hardly move towards the collecting plate at the inlet stage of the precipitator since the electric field intensity and the charge level are low there. Later, in the
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vicinity of the first corona wire, the electric field intensity is larger and the migration velocities are higher. In between two wire electrodes the particles are slowed down due to a lower field strength.
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When the particles enter the vicinity of the next corona wire they gain a larger migration speed again. The outlet heights of the particles are 22.33, 39.23, and 50.00mm at voltages of 30, 45, and 60 kV, respectively. With an increase of voltage, the increment of height measures 16.90 and 10.77 mm. Evidently, the efficiency of particles moving to the collecting plate is better at voltages of 45 and 60 kV. Thus, enhancing the applied voltage leads to much greater effects on the transport behaviour of larger particles, whereas higher ion migration may help to improve trapping of particles. Take in Figure 7. The influence of the particle injection position on particle trapping was significant. In order to
ACCEPTED MANUSCRIPT further study this impact, the particle injection Y-positions were assumed to be equal 0mm, 1mm, 2mm, 3mm, 4mm, 5 mm and 10 mm, 15 mm, 20 mm, 25 mm, 30 mm and 35 mm. Due to the Brownian diffusion of particles acting up and down at the outlet position, the average exit height was used to determine the particle outlet Y-position. The particle was injected into the computational domain at the inlet (X = 0 mm), at initial velocities equal to the inlet-gas velocity.
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Fig.8 (a) shows that the particles injected from Y=0mm have the highest particle outlet Y-position and can trap 0.8 and 1.0 µm particles; 0.2, 0.4 and 0.6 µm particles are higher than other injection
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position. For the injection heights of 3mm-5mm, the particle outlet Y-position does not change much. The reason for this phenomenon is that the particles obtained a smaller charge amount and
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the electric field force was small. Fig. 8 (b) clearly shows that for the same injection position the particle outlet Y-position increases with the particle size. Because a larger particle size has a larger
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surface area, thus it obtains a greater charge. The larger particles of 0.6, 0.8 and 1.0 µm can be trapped at 35 mm injection position since if the collecting plate is closer, the particles can move to
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it and be trapped, even for a small charge. Therefore, the injected particles are more conducive to the particle trapping in the centre of the ESP channel and the vicinity of the collecting plates.
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Take in Figure 8.
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4.5 Influence of discharge-electrode spacing on particle trapping To study the effect of the discharge-electrode spacing on particle trapping, the spacings between the corona wires were set to 100, 150, and 200 mm. The central position was at (X = 400
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mm, Y = 0 mm), and the particle-injection position was set to (X = 0 mm, Y = 0 mm). The trajectories of particles with sizes of 0.2, 0.4, 0.6, 0.8, and 1 μm were calculated.
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Fig.9 shows tthe outlet height of particles with different diameters at different discharge-electrode spacings. The outlet height of the particles increases with increasing particle size since larger particle sizes lead to greater acquired particle charges. The resulting greater field forces then lead to higher outlet heights. When compared with the three discharge-electrode spacings, it is evident that the outlet height increases significantly between the discharge-electrode spacings of 100 and 150 mm. Since the discharge-electrodes are loaded with the same polarity of applied voltages at the same time and the potential difference between the adjacent electrode is zero, the potential gradient is very low and the electric field intensity is very weak in this region. With the discharge-electrodes spacing increases, the outlet height of the particles increases as the
ACCEPTED MANUSCRIPT electric field screening effect is reduced. However, there is a minimal and insignificant variation in outlet height between 150 and 200 mm. As it can be seen in Fig.9, a larger than 150 mm discharge-electrode spacing leads to no obvious improvement of the particle-trapping effect. Because the electric field screening effect is not the main factor. Further, an increase of the discharge-electrode spacing will increase the precipitator size. Thus, choosing the appropriate
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discharge-electrode spacing for the precipitator design is also important. Take in Figure 9.
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The discharge-electrode spacing plays an important role in the improvement of particle trapping. To further investigate the effect of the discharge-electrode spacing on particle trapping,
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the computed trajectories for three particle sizes at wire distances of 100 and 150 mm are shown in Fig.10. It is apparent from the results that for equal particle diameters the displacement of the
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particles in the Y-direction for a discharge-electrode spacing of 150 mm is higher than that for a spacing of 100 mm. The larger the particle size, the more obvious is the difference in the final
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outlet height. As the electric field intensity is relatively weak between the discharge electrodes, closer discharge electrodes lead to a stronger electrostatic shielding. Thus, the total electric field
D
intensity is much lower. The enhancement of the distance was beneficial in enhancing the electric
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field intensity of the whole region, including the area between the discharge electrodes, inlet, and outlet. A stronger electric field intensity leads to higher charged particles. Thus, the stronger the
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electric field force, the better the particle-trapping effect in the precipitator. Take in Figure 10
4.6. Effect of discharge electrode arrangement on particle trapping
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As mentioned above, the discharge electrode spacing of 150 mm was very efficient and led to a relatively high performance. On this basis, the structure of the electrode arrangement was adjusted to achieve better particle trapping in the precipitator. Fig. 11 shows three types of discharge-electrode arrangement, which are referred to as cases M1, M2, and M3. The distance of wire collecting is 100mm. Particles are mainly distributed in the centre of the square channel of ESP. In order to better study the effect of wire electrodes arrangement on the particle trapping, we assumed that particles with diameters of 0.2, 0.4, 0.6, 0.8 and 1.0 μm were injected at the simulation domain of X = 0 mm, Y = 0 mm. Take in Figure 11
ACCEPTED MANUSCRIPT Fig. 12 shows the particle trajectories from injection position Y=0mm for three models. From the figure, firstly, it is noticeable that in three models the particles with diameters of 0.6, 0.8 and 1.0μm are well trapped. Furthermore, the slop of particle trajectories for M3 is bigger than for M1 and M2, which means that the transverse velocity is largest. Therefore, the particles were sooner reached the collecting plate. Secondly, the trajectory of particles with a diameter of 0.4μm near the
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collecting plate is greatly fluctuated in model M3. This is because the electric field intensity near the collecting plate is relatively small, leading to a decreased electric field force. In addition, the
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drag force also decreases near the collecting plate. The Brownian diffusion becomes dominant and leads to longer trapping time of particles. Finally, the outlet height decreases from 9.55 to 5.23
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mm for M3 when the particle diameter is 0.2μm. This is because the particle passes the second electrode at the Y-position similar to that of the electrode. This causes the particle to have an
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oppositely-directed transverse velocity.
Take in Figure 12.
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As mentioned in the previous discussion, the precipitator had the poorest collection efficiency at an inlet height of approximately 5 mm. Therefore, a change in the
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discharge-electrode arrangement was investigated to study the transport behaviour for inlet heights
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of 5 and 10 mm. Particle collection is depended on the particle outlet Y –position; the particle outlet Y-position of M1, M2, and M3 are shown in Fig.13. Particles with a diameter of 0.8 and 1 μm enter the precipitator at inlet heights of 5 and 10 mm. Fig.13 shows a significantly improved
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outlet height in the model M3. The lowest outlet Y-position occurs in the case of injection at Y-position at 5mm for M3 with the particle diameter of 0.2μm, which was similar to the above
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analysis. Except for this particle size, the M3 had the highest outlet Y-position compared the other models for the same particle size and injection position. Therefore, the model M3 was the best for particle trapping. Thus, changing the discharge-electrode arrangement shows a much greater effect on the charging and transport behaviour of particles, while a higher ion migration may help improve the collecting performance for submicron particles. Take in Figure 13. 5. Conclusions
In this paper, the charging and transport behaviour of fine particles in a wire-plate ESP were studied in detail. Some detailed conclusions can be formulated as follows:
ACCEPTED MANUSCRIPT Firstly, the influence of the particle injection position on particle trapping was significant. The injection particles can be trapped easier when they were injected at the centre of the ESP channel or in the vicinity of the collecting plates. The larger the particle size, the higher the Y-displacement of particles because larger particle sizes improve both the particle charging level and electric field strength.
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Secondly, to study the effect of the discharge-electrode spacing on particle trapping, the spacings between the corona wires were set to 100, 150, and 200 mm. It was observed that a
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discharge-electrode spacing larger than 150 mm leads to no obvious improvement of the particle-trapping. Thus, choosing the appropriate discharge-electrode spacing for the precipitator
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design is important.
Finally, the ESP models M1, M2 and M3 were used to investigate their influence on the
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particles trapping. Changing the discharge-electrode arrangement shows a much greater effect on the charging and transport behaviour of particles and the model of M3 was found to be the best for
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particle trapping, while a higher ion migration may help improve the collecting performance for submicron particles.
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Acknowledgments
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The authors would like to acknowledge the support of the National Key Research and Development Program of China (No.2016YFB0600602), the National Natural Science Foundation of China (NSFC Grant No. 51576030) and the Fundamental Research Funds for the Central
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Universities (No. DUT16ZD202). The authors give special thanks to Professor Kazimierz Adamiak of the Department of Electrical and Computer Engineering in Western University for his
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help with the English language. Reference [1] K. Adamiak, G.S.P. Castle, I.I. Inculet, E. Pierz, Numerical simulation of the electric field distribution in tribo-powder coating of conducting cylindrical objects, IEEE Trans. Ind. Appl. 30 (1) (1994) 215-221. [2] Y. Zhuang, Y.J. Kim, T.G. Lee, P. Biswas, Experimental and theoretical studies of ultra-fine particle behavior in electrostatic precipitators, J. Electrostatics, 48(2000) 245-260. [3] N. Farnoosh, K. Adamiak and G.S. Peter Castle, 3-D numerical simulation of particle concentration effect on a single-wire ESP performance for collecting poly-dispersed particles, IEEE Trans. Dielectr. Electr. Insul. 18(2011) 211-220. [4] Z.Y. Ning, J. Podlinski, X.J. Shen, S.R. Li, S.L. Wang, P. Han, K.P. Yan, Electrode geometry
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optimization in wire-plate electrostatic precipitator and its impact on collection efficiency, J. Electrostatics, 80(2016) 76-84. S. Arif, D.J. Branken, R.C. Everson, H.W.J.P. Neomagus, L.A. le Grange, A. Arif, CFD modeling of particle charging and collection in electrostatic precipitators, J. Electrostatics, 84(2016) 10-12. S.H. Huang, C.C. Chen, Loading characteristics of a miniature wire-plate electrostatic precipitator, Aerosol Sci. Tech. 37(2003)109-121. U. Kogelschatz, W. Egli, E.A. Gerteisen, Advanced computational tools for electrostatic precipitators, ABB Rev. 4 (1999) 33-42. A. Soldati, On the effects of electro-hydrodynamic flows and turbulence on aerosol transport and collection in wire-plate electrostatic precipitators, J. Aerosol Sci. 31 (2000) 293-305. S. Kim, K. Lee, Experimental study of electrostatic precipitator performance and comparison with existing theoretical prediction models, J. Electrostat. 48 (1999) 3-25. S.H. Kim, H.S. Park, K.W. Lee, Theoretical model of electrostatic precipitator performance for collecting polydisperse particles, J. Electrostat. 50 (2001) 177-190. J.R. McDonald, W.B. Smith, H.W. Spencer Iii, L.E. Sparks, A mathematical model for calculating electrical conditions in wire-duct electrostatic precipitation devices, J. Appl. Phys. 48 (1977) 2231-2243. E. Lami, F.Mattachini, I. Gallimberti, R. Turri, U. Tromboni, A numerical procedure for computing the voltage–current characteristics in electrostatic precipitator configurations, J. Electrost. 34 (4) (1995) 385-399. H.J. Schmid, L. Vogel, On the modelling of the particle dynamics in electrohydrodynamic flow-fields: I. Comparison of Eulerian and Lagrangian modeling approach, Powder Technol. 135 (S1) (2003) 118-135. H.J. Schmid, On the modelling of the particle dynamics in electro-hydrodvnamic flow fields: II. Influences of in homogeneities on electrostatic precipitation, Powder Technol. 135 (S1) (2003) 136-149. B.S. Choi, C.A.J. Fletcher, Turbulent particle dispersion in an electrostatic precipitator, Appl Math Model 22 (1998) 1009-102. K.S.P. Nikas, A.A. Varonos, G.C. Bergeles, Numerical simulation of the flow and the collection mechanisms inside a laboratory scale electrostatic precipitator, J. Electrostat. 63 (2005) 423-443. G. Skodras, S.P. Kaldis, D. Sofialidis, O. Faltsi, P. Grammelis, G.P. Sakellaropoulos, Particulate removal via electrostatic precipitators-CFD simulation, Fuel Process. Technol. 87 (2006) 623-631. K. Adamiak, P. Atten, Numerical simulation of the 2-D gas flow modified by the action of charged fine particles in a single-wire ESP, IEEE Trans. Dielectr. Electr. Insul. 16 (2009) 608-614. N. Farnoosh, K. Adamiak, G. Castle, 3-D numerical analysis of EHD turbulent flow and mono-disperse charged particle transport and collection in a wireplate ESP, J. Electrostat. 68 (2010) 513-522. N. Farnoosh, K. Adamiak, G. Castle, Three-dimensional analysis of electrohydrodynamic flow in a spiked electrode-plate electrostatic precipitator, J. Electrostat. 69 (2011) 419-428. W.-J. Liang and T. H. Lin, The characteristics of ionic wind and its effect on electrostatic
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precipitators, Aerosol Sci. Technol. 20(1994) 330-344. S. Arif, D.J. Branken, R.C. Everson, H.W.J.P. Neomagus, L.A. le Grange, A. Arif, CFD modeling of particle charging and collection in electrostatic precipitators, J. Electrostat. 84 (2016) 10-22. M.J. Cernick, S.W. Tullis, M.F. Lightstone, Particle subgrid scale modeling in large-eddy simulation of particle laden turbulence, J. Turbul.16 (2014) 101-135. Hong Lei, Lian-Ze Wang, Zi-Niu Wu, EHD turbulent flow and Monte-Carlo simulation for particle charging and tracing in a wire-plate electrostatic precipitator, J. Electrostat.66 (2008) 130-141. A. Li, G. Ahmadi, Dispersion and deposition of spherical-particles from point sources in a turbulent chemical flow, J.Aerosol Sci. Technol. 16 (1992)209-226. H. Ounis, G. Ahmadi, J. B. McLaughlin, Brownian diffusion of submicrometer particles in the viscous sublayer, J. Colloid Interface Sci. 143(1)(1991)266-277. P.A. Lawless, Particle charging bounds, symmetry relations, and an analytic charging rate model for the continuum regime, J. Aerosol Sci. 27(2) ( 1996) 191-215. A.M. Meroth, T. Gerber, C.D. Munz, P.L. Levin, A.J. Schwab, Numerical solution of nonstationary charge coupled problems, J. Electrost. 45 (3) (1999 )177-198. G.W. Penney and R.E. Matick, Potentials in D-C corona fields,J. American Institute of Electrical Engineers Part I Communication & Electronics Transactions of the.79(2)(1960) 91-99.
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TABLE CAPTIONS Table 1. Basic parameters of ESP Table 2. Boundary conditions for two-dimensional analysis of processes in ESP.
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FIGURE CAPTIONS Figure 1. Schematic of a ESP Figure 2. Mesh near the wire electrodes. Figure 3. Comparison of numerical results with experimental results of Penney and Matick at X=228.6 mm. Figure 4. Distribution of potential and charge density in the ESP. Figure 5. Effect of particle diameter on particle charge at different voltages. Figure 6. Effect of particle-inlet location on particle charge. (a) Effect of particle-inlet position on maximum particle charge at V = 60 kV and (b) Charging history for a particle with diameter of 1 µm released at various inlet heights. Figure 7. Particle trajectories for particle size of 1 µm with (a) and without (b) the Brownian diffusion at different voltages. Figure 8. Comparison of particle-outlet height for different particle diameters and different injection Y-positions. Figure 9. Comparison of particle-outlet height for different particle diameters and different wire distances. Figure 10. Comparison of particle trajectories for different diameters and wire distances. Figure 11. Schematic of a three ESPs with different wire arrangements. Figure 12. Particle trajectories in an ESP with different wire arrangements. Figure 13. Comparison of particle outlet Y-position for different injection heights in three types of ESPs.
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Figures Figure 1. Schematic of a ESP
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Figure 2. Schematic of refined mesh near the wire electrodes.
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Figure 3. Comparison of numerical results with experimental results of Penney and Matick at X = 228.6 mm.
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（a）Electric potential distribution (V).
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（b）Space-charge density distribution (C/m3).
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Figure 5. Effect of particle diameter on particle charge at different voltages.
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Figure 6. Effect of particle-inlet location on particle charge. (a) Effect of particle-inlet position on maximum particle charge at V = 60 kV and (b) Charging history for a particle with diameter of 1 µm released at various inlet heights.
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Figure 7. Compared the particle trajectories with particle size of 1 µm with (a) and without (b) the Brownian diffusion at different voltages
(b)
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Figure 8. Comparison of particle-outlet height in dependence of particle diameter at different injection Y-positions.
(b)
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Figure 9. Comparison of particle-outlet height in dependence of particle diameter at different wire distances.
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Figure 10. Comparison of particle trajectories with different diameters and wire distances.
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Figure 12. Particle trajectories in an ESP with different wire arrangement.
(b) M2
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(a) M1
(c) M3
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Figure 13. Comparison of particle outlet Y-position with different injection heights in three types of ESPs.
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Gas
Gas
Gas
Particle
Particle
Particle
velocity
permittivity
density
density
diameter
/kV
/K
/kg·m-3
/μm
30~60
1
298.5
1.185
0.2~1
/kg·m-3 2
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temperature
/m·s-1
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Particle
Potential
Space charge density
Inlet
ux = 1 m·s-1, uy = 0
Escape
0 n
0 n
Outlet
Outflow, pressure=0
Escape
0 n
0 n
Collecting plates
Stationary walls
Trap
0
0 n
Wire electrodes
Stationary walls
Reflect
φ = 30–60 kV
ρ = ρc
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Surface
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(e) M2
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(d) M1
(f) M3
Figure 12. Particle trajectories in an ESP with different wire arrangement. Graphical abstract
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(i) The voltage increase in the high voltage range is better for improving the particle-trapping. (ii) Particles injected at central height into the precipitator are influenced most intensively.
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(iii) The model of M3 was best for particle trapped.
Ming Dong, Fei Zhou, Yuxuan Zhang, Yan Shang, Sufen Li PII: DOI: Reference:
S0032-5910(18)30159-1 doi:10.1016/j.powtec.2018.02.038 PTEC 13214
To appear in:
Powder Technology
Received date: Revised date: Accepted date:
3 August 2017 24 January 2018 12 February 2018
Please cite this article as: Ming Dong, Fei Zhou, Yuxuan Zhang, Yan Shang, Sufen Li , Numerical study on fine-particle charging and transport behaviour in electrostatic precipitators. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Ptec(2017), doi:10.1016/j.powtec.2018.02.038
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ACCEPTED MANUSCRIPT Numerical study on fine-particle charging and transport behaviour in electrostatic precipitators Ming Dong*, Fei Zhou, Yuxuan Zhang, Yan Shang, Sufen Li Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of
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Technology, Dalian 116024, China; Corresponding author: Ming Dong, School of Energy and Power Engineering, Dalian University
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of Technology, No. 2 Linggong Road, Ganjingzi District, Dalian, Liaoning, 116024, People’s
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Republic of China, Tel:+86-0411-84762312， Fax:+86-0411-84708460
E-Mails: [email protected]; [email protected]; [email protected]; [email protected]; [email protected];
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Abstract
In this work, a numerical study on the charging and transport of fine particles has been
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carried out based on wire-plate electrostatic precipitators (ESPs) with multiple wire electrodes. The effect of the applied wire voltage, inlet height, and wire spacing on particle charging and
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transport, and the influence of the precipitator structure on particle trapping are analysed in detail.
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Results indicate that a voltage increase in the high voltage range improves the particle-trapping efficiency. However, the Brownian diffusion causes the particle fluctuation, but it doesn’t change the direction of main movement. Particles injected into the precipitator at the channel centre are
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influenced most intensively, whereas particles injected at approximately 5 mm from the centre of the precipitator exhibit the poorest particle-trapping ability. An increased wire spacing enhances
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particle trapping, within a certain range, and a larger particle size causes an even more obvious enhancement. Furthermore, changing the discharge-electrode arrangement shows a much greater effect on the charging and transport behaviour of particles in the model of M3, which has the highest trapping efficiency. Keywords：Electrostatic precipitators (ESPs); Electrostatic precipitators structure; Particle trapping; Wire spacing.
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NOMENCLATURE electric potential
space-charge density
E
electric field intensity
0
permittivity of free space
J
current density
K
ion mobility
D u
diffusion coefficient of ions
up
particle velocity
gas-flow velocity
p
f
fluid density
particle density
dynamic viscosity of the fluid
dp
particle diameter
Re
relative Reynolds number
v w
non-dimensional particle charge non-dimensional electric field
p
rc
radius of the corona wire
t
CD
drag force coefficient
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relative permittivity of the particles
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charging time
the Gaussian random number
the fluid kinematic viscosity
Kn
the Knudsen number
the particle mass
S0
the spectral intensity of the noise
P kB
the absolute pressure the Boltzmann constant
the molecular mean free path
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mp
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i
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the Cunningham slip correction factor
Introduction
non-dimensional particle-charging time
Ep Peek’s electric field intensity
Cc
1.
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Electrostatic precipitators (ESPs) are major air pollution control devices to remove particles
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from treated gas. Extensive research has been done on several aspects of this process, such as electrostatics, fluid dynamics, charging mechanism, and particle dynamics [1-5]. The overall particle-collection efficiency of a modern industrial wire-plate ESPs exceeds 99%. However, the removal efficiency of submicron particles by conventional ESPs is as low as 70–80% owing to the low charge carried by fine particles and the decreased size particles are more inclined to travel with the surrounding fluid [2-3]. Submicron particles possess a high superficial area, thus favouring toxic heavy metals and other pollutants. Therefore, fine particles are collected with much lower efficiency and further research is required to improve this aspect [5]. The basic working process in ESPs involves several complicated and interrelated physical
ACCEPTED MANUSCRIPT mechanisms. The particles are given electric charge by forcing them to pass through a corona discharge, a region in which gaseous ions flow. Charged particles are then deflected from the main gas stream by an electric field to be precipitated onto the collecting plates [6]. The particle trajectories are influenced by the interacting electrostatic, fluid field, and the particle transport factors. These factors are mutually coupled, although some couplings are weaker than others and
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can be neglected. The electrohydrodynamic (EHD) flow is generated owing to momentum transfer from moving charged species (ions and particles) to neutral molecules, in addition to the primary
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flow and electric field. Some researchers believe that the particle collection efficiency could be significantly improved if the EHD flow were eliminated [7]. Soldati showed that the EHD flow
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not only contributes to re-entrainment of particles in the central region of the channel, but also to sweeping the particles to the collecting plates, thus having a negligible influence on the overall
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collection efficiency [8]. He also pointed out that this effect is only significant at low flow velocities. In the present paper, the fluid-flow velocity is higher than 1 m/s and the EHD flow has
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a negligible effect on the collection efficiency of the particles. The particle-charging rate is a function of the ease of electrical charge acceptance, which is
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described by the classical Deutsch model using resistivity as the characteristic material property
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[9-10]. However, the Deutsch model, its derivatives, and other theoretical correlations fail to give an accurate estimate of the charge level under a wide range of operating variables [9]. Numerous studies have been devoted to the numerical modelling of the complex and coupled physical
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phenomena involved in the precipitation process. McDonald et al. developed a numerical method that can be used to calculate the electric potential and space-charge density in electrostatic
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precipitation [11]. Lami et al. developed the coupled system of the Poisson equation and the space-charge drift formula considering the statistical size distribution of particles and the corresponding charging processes with a finite-difference scheme [12]. Kim presented a modified model for considering simultaneously the convection force, electrostatic force, and diffusion to predict the wire-plate ESP performance for collecting polydisperse particles [10]. Later, the strong coupling between the fluid flow and electric field have been extensively examined with the model developed by Schmid et al. [13,14]. The use of CFD in the description of ESP operations was introduced by Fletcher and his collaborators [15]. In this model, the turbulent gas flow and particle motion under electrostatic forces are calculated using FLUENT, linked to a finite-volume solver
ACCEPTED MANUSCRIPT for the electric field and ion charge. The charge density and velocity of the particles are averaged over a control volume to use the Lagrangian formulation of the particle motion for the calculation of the gas and electric fields. Nikas et al. and Skodras et al. have developed a CFD model considering gas flow, particulate flow, particle charging, electric field, and current-flow equations and analysed the collection performances of ESPs under certain conditions [16,17]. Recently,
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Adamiak et al. presented a coupled numerical model on the simulation of secondary EHD flow caused by corona discharge and charged particles [18]. Moreover, they performed detailed
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investigations on the effects of charged particles and EHD turbulent flow on the gas-flow patterns in a spike-plate ESP [19,20].
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However, previous works focused on the collection efficiencies of relatively large particles, as well as the apparent effects of secondary EHD flow on the collection performance of ESPs.
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Nonetheless, a better knowledge of the detailed charging and transport behaviour of fine particles in the ESPs, especially those with a diameter of less than 1 μm, is extremely important. The
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numerical simulation results of Liang and Lin indicated that, if the main flow velocity is higher than 0.6m/s, the effect of EHD is insignificant [21]. As the main flow velocity is higher than 1 m/s,
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the effect of electrohydrodynamic flow is minimal [22]. Therefore, the main flow velocity is
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higher than 1 m/s in this study and the EHD flow has a negligible. An understanding of electrical and geometric effects on the particle trapping is critical during design and operation of wire-plate ESPs. Present work presents the results of numerical investigations of the corona-electrostatic
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field, and the charging and transport behaviour of fine particles in a simple two-dimensional model of an ESP. The 2-D numerical model involves electric field, space-charge density, gas flow,
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and particle trajectories. The electric field and gas flow are calculated using the finite-volume method. The flow simulation is done using the commercial software FLUENT with other parts coded as user-defined functions. A Lagrangian approach for particle transport is used to track the trajectories of individual particles by solving their motion equation. 2.
Mathematical model
The computational model of the ESP includes corona discharge, gas flow, particle charging, and transport. Consequently, the governing equations consist of the electric field and space charge, fluid dynamics, particle trajectory, and charging equation, respectively. 2.1 Electric field and space charge
ACCEPTED MANUSCRIPT The charge density and the electric potential distribution of the ions inside the ESP model are obtained from the numerical solution of the Poisson and charge-conservation equations. They are expressed as follows:
2
0
(1) (2)
J (KE u) D
(3)
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J 0
(V) is the electric potential, ρ(C ·m-3) the space-charge density, 0 (F ·m-1) the
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permittivity of free space,
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where,
(4)
E (V ·m-1) the electric field intensity, J (A ·m-2) the current density,
K (m2 ·V-1s-1) the ion mobility, and D (m2 ·s-1) the diffusion coefficient of the ions. As the drift
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velocity of ions is usually about two orders of magnitude faster than the typical velocity of the gas flow, the convective component in equation (3) can be neglected. Hence, the charge-conservation equation can be expressed as
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(K E D) 0 2.2. Fluid dynamics
(5)
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In the present study, the EHD flow can be neglected as the inlet-flow velocity is 1 m/s [3].
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Therefore, the influence of the electric field on the flow field is neglected in the numerical simulation. The air flow through the ESP channel was modelled as steady and turbulent while assuming constant density and viscosity. This was done by solving the continuity and the NS
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equations using the FLUENT. The particulate two-phase turbulence requires solutions to both the fluid field and particulate phase. The focus of present study is Lagrangian particle tracking with
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large-eddy simulation (LES). LES considers modelling of subgrid scale (SGS) effects on particles. The larger turbulent motions are solved for the smaller turbulent scales modelled in LES. For instance, turbulence effects were introduced using the LES turbulence model [23]. 2.3. Particle dynamics Due to relatively low concentration of the particles, the particle space charge was assumed to be negligible, and one-way coupling in which the dispersed phase had no influence on the fluid flow or the electrostatics, was assumed [23]. The particle dynamics was modelled using the discrete phase model (DPM) in FLUENT, based on a Lagrangian approach. The particle
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Fd represents the drag force due to the relative velocity of the particle and
charged particle ( FE ), the fluid.
Fg is
the gravitational force acting only in the vertical direction.
Fb is
the buoyancy
force acting only in the vertical direction. Fv is the virtual mass force accounting for the relative
FB
is the Basset history force due to the transient
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the acceleration of the fluid flow field.
Fp
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acceleration of the particle and the fluid.
is the Saffman lift force acting on the particle moving
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through the stream with a velocity gradient. Hong Lei et al. showed that the electric field and drag forces are the key forces acting on particles in the ESP [24]. This rule can be applied under a
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condition that the distance for a particle to enter the channel is greater than a quarter of separation distance. Under the influence of gas flow and electric field, particles were mainly subjected to
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drag force, electric forces, and Brownian force in the presents study. Therefore, the particle motion equation can be written as
dup 18 CD Re Eq S0 (u up ) p i 2 dt p d p 24 mp t
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D
(6)
where u p (m·s-1) is the particle velocity, u ( m·s-1) is the gas-flow velocity,
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kg·m-3) is the fluid density, and
f (
p ( kg·m-3) is the particle density, (Pa·s) is the
dynamic viscosity of the fluid, d p (μm) is the particle diameter, CD is the drag force
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coefficient, Re is the relative Reynolds number( Re electric field force, E is
particle mas, i
) ,
Eq p is the mp
the electric field intensity, qp is the particle charge, mp is the
S0 t
f d p up u
is the Brownian force, i is a Gaussian random number
chosen from a normal distribution with a zero mean and a unit variance. S0 is the
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216kBT )[25]， 2 2 d p5 p Cc f
is the fluid kinematic viscosity, kB is the Boltzmann constant. The Cunningham slip correction factor Cc can be can be expressed as ( Cc 1 Kn[1.257 0.4exp(
2 ), is the molecular mean free path. dp
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[26], Kn the Knudsen number ( Kn
1.1 )] ) Kn
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2.4. Particle-charging model
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The neutral submicron particles with a spherical shape are injected at the entrance of the precipitator and become charged as they move along the ESP channel and across the ionic
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space-charge zone. Affected by the electrostatic and aerodynamic forces, some particles are trapped on the collecting walls while others manage to escape. The calculation of the particle charge in this work is based on Lawless᾽ model [27]:
(7)
1 , w 0.525 f (w) (w 0.475)0.575 1, w 0.525
(8)
v qe / 20d pkBT
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where
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D
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3w f (w) , 3w exp( 3w) 1 d 3w (1 )2 f (w), 3w 3w and d 4 3w 3w 3w f (w) exp( 3w) 1,
is the non-dimensional particle charge,
non-dimensional particle-charging time, electric field,
= Dt / 0
the
w= p / p 2 Ed pe / 2kBT the non-dimensional
f (w) the non-dimensional electric field (fraction of the surface covered by the
diffusive band), and
p
the relative permittivity of the particles. Therefore, the charging level
depends on the size and shape of the particles, unipolar ion density, particle residence time, and the electric field intensity. 3.
ESP model and numerical procedure
The ESP consists of two grounded parallel collecting plates and three wire electrodes located
ACCEPTED MANUSCRIPT between the plates and supplied with a high negative potential. The duct length is L = 800 mm and its width w = 100 mm. The structure comprising three wire electrodes with a diameter of 1 mm each is mounted along the X-axis. The centre of the wire electrode is located at the central plane of the ESP (X = 400 mm, Y = 0 mm), as shown in Fig.1. Take in Figure 1.
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The values of the supply voltage, gas flow velocity, pressure, gas temperature, and particle diameter are given in Table 1. The gas flow has had a turbulence intensity of 5.4 % at the inlet,
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which was replicated in the present CFD simulations in which the gas density and viscosity were set equal to 1.185 kg/m3 and 1.8×10-5 kg/m·s, respectively. The fine particles were introduced into
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the computational domain at the inlet of the ESP channel and had a mass density of 2100 kg/m3. The fine particles had a uniform diameter that was varied between 0.2-1.0 μm, and the inlet
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velocity was 1 m/s.
Take in Table 1.
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The computational domain was discretized into quadrilateral cells. The mesh conditions for the discharge electrodes were set separately owing to their small diameter. Therefore, the mesh
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was much finer near the discharge electrodes to maximize the accuracy of the calculated gradients
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within the higher current density regions, as shown in Fig. 2.
Take in Figure 2.
The LES turbulence model was solved with FLUENT, with the given pressure and gas
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velocity distribution in the whole ESP channel. The electric field, space-charge distributions, electrical force, and particle charge must be determined using the so-called user-defined functions
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(UDF). All particle trajectories are tracked until the particles are trapped or they escape the ESP channel. Particle injection from the inlet of the ESP used the DPM when the residuals stabilized. The two collecting plates and the wire electrode surfaces act as stationary walls where all velocity vector components vanish. The effect of collecting plates on electric field is neglected. Therefore, image force has negligible. The left boundary is defined as the velocity inlet, and right boundary is defined as the outflow. The summary of boundary conditions for the proposed model is given in Table 2.
Take in Table 2. The corona discharge in an ESP is governed by a set of four partial differential equations
ACCEPTED MANUSCRIPT (Eqs. (1), (2), (4) and (5)) with two unknown distributions: potential
and space-charge density ρ.
The iterative method used to obtain and ρ is as follows [19]: (1) Set an initial guess for the space-charge density (ρ ≠ 0) for the entire computational domains. (2) Make an initial guess for the space-charge density on the wire surface (ρc).
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(3) Solve Eq. (1) and Eq.(2) for . (4) Solve the conservation of current (Eqs.( 4 ) and(5)) for the space charge density.
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(5) Return to step (3) until the solution becomes self-consistent.
(6) Update the charge density on the wire surface by comparing the actual electric field intensity with
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Peek’s value.
surface.
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(7) Rescale the whole charge within the domain considering the new charge density on the wire
(8) Return to step (3) and repeat the procedures until the average electric field magnitude on the wire
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surface is sufficiently close to Peek’s value.
The Kaptzov’s hypothesis is adopted that suggests the electric field intensity increases with
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increasing voltage before the corona phenomenon occurs. However, the electric field intensity no
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longer increases after the corona is initiated. Peek’s formula is used to determine the threshold strength of electric field for the corona onset at the corona electrode [28]:
rc （cm）is the radius of the corona wire.
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where
(9)
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0.308 Ep 3.1106 (kV / cm) 1 rc
The numerical procedure can be summarized as follows: (1) Evaluate the electric potential and space-charge density distribution in the whole ESP channel by using the above method until the whole residual decreases to 10-8. (2) Solve the gas flow with the LES until the whole residual decreases to 10-6. (3) Inject particles into the computational domains and determine the coupled motion and particle-charge equations of the particulate phase using DPM in FLUENT. 4. Results and discussion
4.1. Comparison with previous experimental results
ACCEPTED MANUSCRIPT For quantitative comparison of the CFD results with the measured results of Penney and Matick [29], the electric potential distribution was measured along 0-114.3 mm in the Y-direction at distances of 228.6, 266.7, and 304.8 mm in the X-direction. The selection of 228.6 mm in the X-direction was done to enable a comparison with the experimental measurements of Penney and Matick. The electric potential distribution on the vicinity of wire electrodes for three grid cells is
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shown in Fig. 3. It is shown that the electric potential distribution doesn’t change when the number of cells exceeds 53206 and the simulated electric potential distribution is agreement with
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the experimental results. Therefore, the mesh consisting 53206 cells was adopted for numerical
Take in Figure 3.
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analysis.
4.2. Distribution of the ionized electrostatic field in the ESP
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To further investigate the characteristics of the ionized electrostatic field in the ESP, the simulation procedure was performed for an applied voltage of 45 kV. The electric potential
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distribution is shown in Fig. 4 (a). It is clear from that figure that the shape of the electric potential distribution is elliptical in the vicinity of the wire electrodes. As the value of the electric potential
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near the wire electrodes is larger than in other regions of the simulation domain, it forms
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high-potential regions around the wire electrodes. However, the electric potential quickly decreases between the wire electrodes and the collecting plates and remains comparatively stable. Further, owing to the same polarity of adjacent discharge electrodes, the electric potential is
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reduced between the wire electrodes.
However, the distribution of charge density is quite different from that of the electric
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potential, as shown in Fig. 4 (b). As the charge density gradually increases between the inlet and the discharging zone, it also forms several high-density regions around the electrodes, reaching the peak value of 2×10-5 C/m3 on the surface of the wire electrode. The area of the high-density regions gradually extends, reaching the collecting plates, unlike the rapid decrease of the electric potential. Therefore, the high-density region provides adequate charging ions for diffusion charging of fine particles in the entire discharging zone.
Take in Figure 4. 4.3. Particle-charging characteristics In this analysis, the particle charging characteristics for different particle sizes and voltages
ACCEPTED MANUSCRIPT were determined. By introducing a known number and the injection position of particles into the computational domain, the particle charge could be determined. The particles were released at the centre line of the channel (X = 0 mm, Y = 0 mm) into the computational domain, at initial velocities equal to the inlet-gas velocity. The charging of particles with diameters of 0.2, 0.4, 0.6, 0.8, and 1.0 μm at applied voltages of 30, 45, and 60 kV with a gas
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velocity of 1 m/s are shown in Fig. 5. It is apparent from the results of Fig. 5 that the particle charge increases with increasing particle diameter and, therefore, larger particles are easily
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collected as compared to smaller particles. A particle with a diameter of 0.2 μm has a charge less than 40 unit charges, which implies a weak charging ability. The number of elementary charges on
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a particle grows rapidly within a narrow diameter interval when the particles have a diameter larger than 0.4 μm. As the particle surface area and diameter have an exponential relationship of
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order two, the particle surface area rapidly increases with increasing diameter. For the particles of the same material, the number of elementary charges on a particle improves with the increment in
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surface area. Furthermore, diffusion charging takes the lead for particle diameters less than 1 μm. Therefore, the number of elementary charges on a particle rapidly grows with increasing diameter.
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Moreover, it can be concluded that the number of elementary charges on a particle increases with
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increasing voltage because of the higher electric field intensity of the discharge electrodes. Take in Figure 5.
To investigate the effect of the particle-inlet location on the particle maximum charge for 60
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kV, the inlet velocity was set to 1 m/s. The results are shown in Fig. 6. Fig. 6 (a) shows that the nearer a particle is released to the centre line, the larger is the maximum charge of the particle. The
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development of the charge at various release locations is more obvious with an increasing particle size. Fig. 6(b) shows the charging history for a particle with a diameter of 1 μm released at various inlet heights. The particle inlet location is one of the key factors affecting the particle-charging process. The nearer the particle is released to the centre line, the larger the charge. For a distance of 10 mm between the release location and centre line, the increase in the particle-inlet height is not obvious after it passes the first corona wire. In addition, during the particle-charging process in the above-mentioned domain, the acquired particle charges along the trajectories were obtained. At the inlet (0 < x < 0.25 m), particles were charged at near-constant rates. However, when they approached the vicinity of the first electrode (0.25 < x < 0.3 m), the particles were rapidly charged
ACCEPTED MANUSCRIPT to much higher values. In the following region (x > 0.3 m), when the highly-charged particles were travelling between the electrodes, the acquired particle charges remained stable until the particles approached the precipitator outlet. Take in Figure 6. 4.4. Particle trajectory characteristics In present work, the particle trajectories for different particle sizes and voltages were
computational domain, the particle trajectories could be determined.
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computed. By introducing a known number of particles and their injection position into the
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To ensure that the Brownian diffusion subroutine has been correctly implemented in Fluent,
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we compared the particle trajectories for particle size of 1 µm with and without the Brownian diffusion at different voltages in Fig.7. Fig. 7(b) shows that the particles trajectories are very
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smooth without Brownian diffusion, and the opposite with Brownian diffusion. In addition, with Brownian diffusion the particle trajectories became very rough when the particle moved far away
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from wire electrodes. This phenomenon occurs because the random directions of Brownian force breaks down the balance between electric and drag forces. Moreover, the Brownian force was much smaller compared the other forces. Therefore, the Brownian diffusion caused the particle
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fluctuation, but it didn’t affect the main movement direction.
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Fig.7 shows that the particles hardly move towards the collecting plate at the inlet stage of the precipitator since the electric field intensity and the charge level are low there. Later, in the
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vicinity of the first corona wire, the electric field intensity is larger and the migration velocities are higher. In between two wire electrodes the particles are slowed down due to a lower field strength.
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When the particles enter the vicinity of the next corona wire they gain a larger migration speed again. The outlet heights of the particles are 22.33, 39.23, and 50.00mm at voltages of 30, 45, and 60 kV, respectively. With an increase of voltage, the increment of height measures 16.90 and 10.77 mm. Evidently, the efficiency of particles moving to the collecting plate is better at voltages of 45 and 60 kV. Thus, enhancing the applied voltage leads to much greater effects on the transport behaviour of larger particles, whereas higher ion migration may help to improve trapping of particles. Take in Figure 7. The influence of the particle injection position on particle trapping was significant. In order to
ACCEPTED MANUSCRIPT further study this impact, the particle injection Y-positions were assumed to be equal 0mm, 1mm, 2mm, 3mm, 4mm, 5 mm and 10 mm, 15 mm, 20 mm, 25 mm, 30 mm and 35 mm. Due to the Brownian diffusion of particles acting up and down at the outlet position, the average exit height was used to determine the particle outlet Y-position. The particle was injected into the computational domain at the inlet (X = 0 mm), at initial velocities equal to the inlet-gas velocity.
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Fig.8 (a) shows that the particles injected from Y=0mm have the highest particle outlet Y-position and can trap 0.8 and 1.0 µm particles; 0.2, 0.4 and 0.6 µm particles are higher than other injection
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position. For the injection heights of 3mm-5mm, the particle outlet Y-position does not change much. The reason for this phenomenon is that the particles obtained a smaller charge amount and
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the electric field force was small. Fig. 8 (b) clearly shows that for the same injection position the particle outlet Y-position increases with the particle size. Because a larger particle size has a larger
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surface area, thus it obtains a greater charge. The larger particles of 0.6, 0.8 and 1.0 µm can be trapped at 35 mm injection position since if the collecting plate is closer, the particles can move to
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it and be trapped, even for a small charge. Therefore, the injected particles are more conducive to the particle trapping in the centre of the ESP channel and the vicinity of the collecting plates.
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Take in Figure 8.
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4.5 Influence of discharge-electrode spacing on particle trapping To study the effect of the discharge-electrode spacing on particle trapping, the spacings between the corona wires were set to 100, 150, and 200 mm. The central position was at (X = 400
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mm, Y = 0 mm), and the particle-injection position was set to (X = 0 mm, Y = 0 mm). The trajectories of particles with sizes of 0.2, 0.4, 0.6, 0.8, and 1 μm were calculated.
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Fig.9 shows tthe outlet height of particles with different diameters at different discharge-electrode spacings. The outlet height of the particles increases with increasing particle size since larger particle sizes lead to greater acquired particle charges. The resulting greater field forces then lead to higher outlet heights. When compared with the three discharge-electrode spacings, it is evident that the outlet height increases significantly between the discharge-electrode spacings of 100 and 150 mm. Since the discharge-electrodes are loaded with the same polarity of applied voltages at the same time and the potential difference between the adjacent electrode is zero, the potential gradient is very low and the electric field intensity is very weak in this region. With the discharge-electrodes spacing increases, the outlet height of the particles increases as the
ACCEPTED MANUSCRIPT electric field screening effect is reduced. However, there is a minimal and insignificant variation in outlet height between 150 and 200 mm. As it can be seen in Fig.9, a larger than 150 mm discharge-electrode spacing leads to no obvious improvement of the particle-trapping effect. Because the electric field screening effect is not the main factor. Further, an increase of the discharge-electrode spacing will increase the precipitator size. Thus, choosing the appropriate
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discharge-electrode spacing for the precipitator design is also important. Take in Figure 9.
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The discharge-electrode spacing plays an important role in the improvement of particle trapping. To further investigate the effect of the discharge-electrode spacing on particle trapping,
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the computed trajectories for three particle sizes at wire distances of 100 and 150 mm are shown in Fig.10. It is apparent from the results that for equal particle diameters the displacement of the
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particles in the Y-direction for a discharge-electrode spacing of 150 mm is higher than that for a spacing of 100 mm. The larger the particle size, the more obvious is the difference in the final
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outlet height. As the electric field intensity is relatively weak between the discharge electrodes, closer discharge electrodes lead to a stronger electrostatic shielding. Thus, the total electric field
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intensity is much lower. The enhancement of the distance was beneficial in enhancing the electric
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field intensity of the whole region, including the area between the discharge electrodes, inlet, and outlet. A stronger electric field intensity leads to higher charged particles. Thus, the stronger the
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electric field force, the better the particle-trapping effect in the precipitator. Take in Figure 10
4.6. Effect of discharge electrode arrangement on particle trapping
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As mentioned above, the discharge electrode spacing of 150 mm was very efficient and led to a relatively high performance. On this basis, the structure of the electrode arrangement was adjusted to achieve better particle trapping in the precipitator. Fig. 11 shows three types of discharge-electrode arrangement, which are referred to as cases M1, M2, and M3. The distance of wire collecting is 100mm. Particles are mainly distributed in the centre of the square channel of ESP. In order to better study the effect of wire electrodes arrangement on the particle trapping, we assumed that particles with diameters of 0.2, 0.4, 0.6, 0.8 and 1.0 μm were injected at the simulation domain of X = 0 mm, Y = 0 mm. Take in Figure 11
ACCEPTED MANUSCRIPT Fig. 12 shows the particle trajectories from injection position Y=0mm for three models. From the figure, firstly, it is noticeable that in three models the particles with diameters of 0.6, 0.8 and 1.0μm are well trapped. Furthermore, the slop of particle trajectories for M3 is bigger than for M1 and M2, which means that the transverse velocity is largest. Therefore, the particles were sooner reached the collecting plate. Secondly, the trajectory of particles with a diameter of 0.4μm near the
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collecting plate is greatly fluctuated in model M3. This is because the electric field intensity near the collecting plate is relatively small, leading to a decreased electric field force. In addition, the
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drag force also decreases near the collecting plate. The Brownian diffusion becomes dominant and leads to longer trapping time of particles. Finally, the outlet height decreases from 9.55 to 5.23
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mm for M3 when the particle diameter is 0.2μm. This is because the particle passes the second electrode at the Y-position similar to that of the electrode. This causes the particle to have an
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oppositely-directed transverse velocity.
Take in Figure 12.
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As mentioned in the previous discussion, the precipitator had the poorest collection efficiency at an inlet height of approximately 5 mm. Therefore, a change in the
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discharge-electrode arrangement was investigated to study the transport behaviour for inlet heights
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of 5 and 10 mm. Particle collection is depended on the particle outlet Y –position; the particle outlet Y-position of M1, M2, and M3 are shown in Fig.13. Particles with a diameter of 0.8 and 1 μm enter the precipitator at inlet heights of 5 and 10 mm. Fig.13 shows a significantly improved
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outlet height in the model M3. The lowest outlet Y-position occurs in the case of injection at Y-position at 5mm for M3 with the particle diameter of 0.2μm, which was similar to the above
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analysis. Except for this particle size, the M3 had the highest outlet Y-position compared the other models for the same particle size and injection position. Therefore, the model M3 was the best for particle trapping. Thus, changing the discharge-electrode arrangement shows a much greater effect on the charging and transport behaviour of particles, while a higher ion migration may help improve the collecting performance for submicron particles. Take in Figure 13. 5. Conclusions
In this paper, the charging and transport behaviour of fine particles in a wire-plate ESP were studied in detail. Some detailed conclusions can be formulated as follows:
ACCEPTED MANUSCRIPT Firstly, the influence of the particle injection position on particle trapping was significant. The injection particles can be trapped easier when they were injected at the centre of the ESP channel or in the vicinity of the collecting plates. The larger the particle size, the higher the Y-displacement of particles because larger particle sizes improve both the particle charging level and electric field strength.
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Secondly, to study the effect of the discharge-electrode spacing on particle trapping, the spacings between the corona wires were set to 100, 150, and 200 mm. It was observed that a
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discharge-electrode spacing larger than 150 mm leads to no obvious improvement of the particle-trapping. Thus, choosing the appropriate discharge-electrode spacing for the precipitator
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design is important.
Finally, the ESP models M1, M2 and M3 were used to investigate their influence on the
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particles trapping. Changing the discharge-electrode arrangement shows a much greater effect on the charging and transport behaviour of particles and the model of M3 was found to be the best for
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particle trapping, while a higher ion migration may help improve the collecting performance for submicron particles.
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Acknowledgments
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The authors would like to acknowledge the support of the National Key Research and Development Program of China (No.2016YFB0600602), the National Natural Science Foundation of China (NSFC Grant No. 51576030) and the Fundamental Research Funds for the Central
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Universities (No. DUT16ZD202). The authors give special thanks to Professor Kazimierz Adamiak of the Department of Electrical and Computer Engineering in Western University for his
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help with the English language. Reference [1] K. Adamiak, G.S.P. Castle, I.I. Inculet, E. Pierz, Numerical simulation of the electric field distribution in tribo-powder coating of conducting cylindrical objects, IEEE Trans. Ind. Appl. 30 (1) (1994) 215-221. [2] Y. Zhuang, Y.J. Kim, T.G. Lee, P. Biswas, Experimental and theoretical studies of ultra-fine particle behavior in electrostatic precipitators, J. Electrostatics, 48(2000) 245-260. [3] N. Farnoosh, K. Adamiak and G.S. Peter Castle, 3-D numerical simulation of particle concentration effect on a single-wire ESP performance for collecting poly-dispersed particles, IEEE Trans. Dielectr. Electr. Insul. 18(2011) 211-220. [4] Z.Y. Ning, J. Podlinski, X.J. Shen, S.R. Li, S.L. Wang, P. Han, K.P. Yan, Electrode geometry
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optimization in wire-plate electrostatic precipitator and its impact on collection efficiency, J. Electrostatics, 80(2016) 76-84. S. Arif, D.J. Branken, R.C. Everson, H.W.J.P. Neomagus, L.A. le Grange, A. Arif, CFD modeling of particle charging and collection in electrostatic precipitators, J. Electrostatics, 84(2016) 10-12. S.H. Huang, C.C. Chen, Loading characteristics of a miniature wire-plate electrostatic precipitator, Aerosol Sci. Tech. 37(2003)109-121. U. Kogelschatz, W. Egli, E.A. Gerteisen, Advanced computational tools for electrostatic precipitators, ABB Rev. 4 (1999) 33-42. A. Soldati, On the effects of electro-hydrodynamic flows and turbulence on aerosol transport and collection in wire-plate electrostatic precipitators, J. Aerosol Sci. 31 (2000) 293-305. S. Kim, K. Lee, Experimental study of electrostatic precipitator performance and comparison with existing theoretical prediction models, J. Electrostat. 48 (1999) 3-25. S.H. Kim, H.S. Park, K.W. Lee, Theoretical model of electrostatic precipitator performance for collecting polydisperse particles, J. Electrostat. 50 (2001) 177-190. J.R. McDonald, W.B. Smith, H.W. Spencer Iii, L.E. Sparks, A mathematical model for calculating electrical conditions in wire-duct electrostatic precipitation devices, J. Appl. Phys. 48 (1977) 2231-2243. E. Lami, F.Mattachini, I. Gallimberti, R. Turri, U. Tromboni, A numerical procedure for computing the voltage–current characteristics in electrostatic precipitator configurations, J. Electrost. 34 (4) (1995) 385-399. H.J. Schmid, L. Vogel, On the modelling of the particle dynamics in electrohydrodynamic flow-fields: I. Comparison of Eulerian and Lagrangian modeling approach, Powder Technol. 135 (S1) (2003) 118-135. H.J. Schmid, On the modelling of the particle dynamics in electro-hydrodvnamic flow fields: II. Influences of in homogeneities on electrostatic precipitation, Powder Technol. 135 (S1) (2003) 136-149. B.S. Choi, C.A.J. Fletcher, Turbulent particle dispersion in an electrostatic precipitator, Appl Math Model 22 (1998) 1009-102. K.S.P. Nikas, A.A. Varonos, G.C. Bergeles, Numerical simulation of the flow and the collection mechanisms inside a laboratory scale electrostatic precipitator, J. Electrostat. 63 (2005) 423-443. G. Skodras, S.P. Kaldis, D. Sofialidis, O. Faltsi, P. Grammelis, G.P. Sakellaropoulos, Particulate removal via electrostatic precipitators-CFD simulation, Fuel Process. Technol. 87 (2006) 623-631. K. Adamiak, P. Atten, Numerical simulation of the 2-D gas flow modified by the action of charged fine particles in a single-wire ESP, IEEE Trans. Dielectr. Electr. Insul. 16 (2009) 608-614. N. Farnoosh, K. Adamiak, G. Castle, 3-D numerical analysis of EHD turbulent flow and mono-disperse charged particle transport and collection in a wireplate ESP, J. Electrostat. 68 (2010) 513-522. N. Farnoosh, K. Adamiak, G. Castle, Three-dimensional analysis of electrohydrodynamic flow in a spiked electrode-plate electrostatic precipitator, J. Electrostat. 69 (2011) 419-428. W.-J. Liang and T. H. Lin, The characteristics of ionic wind and its effect on electrostatic
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precipitators, Aerosol Sci. Technol. 20(1994) 330-344. S. Arif, D.J. Branken, R.C. Everson, H.W.J.P. Neomagus, L.A. le Grange, A. Arif, CFD modeling of particle charging and collection in electrostatic precipitators, J. Electrostat. 84 (2016) 10-22. M.J. Cernick, S.W. Tullis, M.F. Lightstone, Particle subgrid scale modeling in large-eddy simulation of particle laden turbulence, J. Turbul.16 (2014) 101-135. Hong Lei, Lian-Ze Wang, Zi-Niu Wu, EHD turbulent flow and Monte-Carlo simulation for particle charging and tracing in a wire-plate electrostatic precipitator, J. Electrostat.66 (2008) 130-141. A. Li, G. Ahmadi, Dispersion and deposition of spherical-particles from point sources in a turbulent chemical flow, J.Aerosol Sci. Technol. 16 (1992)209-226. H. Ounis, G. Ahmadi, J. B. McLaughlin, Brownian diffusion of submicrometer particles in the viscous sublayer, J. Colloid Interface Sci. 143(1)(1991)266-277. P.A. Lawless, Particle charging bounds, symmetry relations, and an analytic charging rate model for the continuum regime, J. Aerosol Sci. 27(2) ( 1996) 191-215. A.M. Meroth, T. Gerber, C.D. Munz, P.L. Levin, A.J. Schwab, Numerical solution of nonstationary charge coupled problems, J. Electrost. 45 (3) (1999 )177-198. G.W. Penney and R.E. Matick, Potentials in D-C corona fields,J. American Institute of Electrical Engineers Part I Communication & Electronics Transactions of the.79(2)(1960) 91-99.
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TABLE CAPTIONS Table 1. Basic parameters of ESP Table 2. Boundary conditions for two-dimensional analysis of processes in ESP.
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FIGURE CAPTIONS Figure 1. Schematic of a ESP Figure 2. Mesh near the wire electrodes. Figure 3. Comparison of numerical results with experimental results of Penney and Matick at X=228.6 mm. Figure 4. Distribution of potential and charge density in the ESP. Figure 5. Effect of particle diameter on particle charge at different voltages. Figure 6. Effect of particle-inlet location on particle charge. (a) Effect of particle-inlet position on maximum particle charge at V = 60 kV and (b) Charging history for a particle with diameter of 1 µm released at various inlet heights. Figure 7. Particle trajectories for particle size of 1 µm with (a) and without (b) the Brownian diffusion at different voltages. Figure 8. Comparison of particle-outlet height for different particle diameters and different injection Y-positions. Figure 9. Comparison of particle-outlet height for different particle diameters and different wire distances. Figure 10. Comparison of particle trajectories for different diameters and wire distances. Figure 11. Schematic of a three ESPs with different wire arrangements. Figure 12. Particle trajectories in an ESP with different wire arrangements. Figure 13. Comparison of particle outlet Y-position for different injection heights in three types of ESPs.
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Figures Figure 1. Schematic of a ESP
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Figure 2. Schematic of refined mesh near the wire electrodes.
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Figure 3. Comparison of numerical results with experimental results of Penney and Matick at X = 228.6 mm.
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（a）Electric potential distribution (V).
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（b）Space-charge density distribution (C/m3).
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Figure 5. Effect of particle diameter on particle charge at different voltages.
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Figure 6. Effect of particle-inlet location on particle charge. (a) Effect of particle-inlet position on maximum particle charge at V = 60 kV and (b) Charging history for a particle with diameter of 1 µm released at various inlet heights.
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Figure 7. Compared the particle trajectories with particle size of 1 µm with (a) and without (b) the Brownian diffusion at different voltages
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Figure 8. Comparison of particle-outlet height in dependence of particle diameter at different injection Y-positions.
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Figure 9. Comparison of particle-outlet height in dependence of particle diameter at different wire distances.
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Figure 10. Comparison of particle trajectories with different diameters and wire distances.
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Figure 12. Particle trajectories in an ESP with different wire arrangement.
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(a) M1
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Figure 13. Comparison of particle outlet Y-position with different injection heights in three types of ESPs.
ACCEPTED MANUSCRIPT Tables Table 1 Basic parameters of ESP Voltage
Gas
Gas
Gas
Particle
Particle
Particle
velocity
permittivity
density
density
diameter
/kV
/K
/kg·m-3
/μm
30~60
1
298.5
1.185
0.2~1
/kg·m-3 2
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SC
RI
PT
temperature
/m·s-1
2100
ACCEPTED MANUSCRIPT Table2 Boundary conditions for two-dimensional analysis of processes in ESP. Airflow
Particle
Potential
Space charge density
Inlet
ux = 1 m·s-1, uy = 0
Escape
0 n
0 n
Outlet
Outflow, pressure=0
Escape
0 n
0 n
Collecting plates
Stationary walls
Trap
0
0 n
Wire electrodes
Stationary walls
Reflect
φ = 30–60 kV
ρ = ρc
AC
CE
PT E
D
MA
NU
SC
RI
PT
Surface
RI
PT
ACCEPTED MANUSCRIPT
(e) M2
AC
CE
PT E
D
MA
NU
SC
(d) M1
(f) M3
Figure 12. Particle trajectories in an ESP with different wire arrangement. Graphical abstract
ACCEPTED MANUSCRIPT Highlights
(i) The voltage increase in the high voltage range is better for improving the particle-trapping. (ii) Particles injected at central height into the precipitator are influenced most intensively.
AC
CE
PT E
D
MA
NU
SC
RI
PT
(iii) The model of M3 was best for particle trapped.