The Influence of Electrohydrodynamic Secondary Flow on the Collection Efficiency and Deposition Pattern in ESP

Electrostatic precipitator (ESP) is widely used for dust removal from flue gas in industry. In the electrostatic precipitation, the electrohydrodynamic secondary flow (EHD) produced by corona ionization has an important influence on the characteristics of particletransportandthecollectionefficiencyofESP.Inthiswork,acomprehensiveESPmodelwithinteractionofmultiplephysicalfieldsisestablishedtostudytheEHDeffectinESP.ThenumericalresultsshowthattheEHDgenerallycanincreasethestreamwisevelocityofairflownearthecollectionplate,whichmakestheremovalperformanceofESPworsen.Meanwhile,theEHDhasasignificanteffectontheparticledepositionpattern,especiallyatlowerfluegasvelocity.Whentheneedletipofdischargeelectrodepointstothecollectionplate,theEHDcanpromotethecirculationofairflownearthecoronawire,increasetheprobabilityofparticlecharging,andthenimprovethecollectionefficiencyofESP.


Introduction
Electrostatic precipitator (ESP) is widely used to purify the flue gas in the thermal power plants. In electrostatic precipitation, the force driving gas-solid separation just acts on the solid particles; hence the ESP has the advantages of less energy cost and pressure loss, high collection efficiency, and good applicability for particles with different physical characteristics. Furthermore, high collection efficiency can be achieved under conditions of high temperature and pressure [1][2][3][4]. Nevertheless, the low removal efficiency on particles less than 10 m in ESP still exists. And it is necessary to improve the removal performance of ESP for conforming the strict flue gas emission standards.
Massive free ions resulting from the corona discharge move along the electric line and collide with neutral molecules in the air, which transfers the momentum from ions to neutral molecules, known as electrohydrodynamic secondary flow (EHD) [5][6][7][8][9]. The significant effect of EHD on the transport of particles, especially fine particles, has been confirmed in previous studies [10][11][12][13]. And the particle transport is closely related to the collection efficiency used for assessing removal performance of ESP. Therefore, the effect of EHD should be considered in optimal design of ESP.
Some scholars characterized the EHD phenomenon of ESP experimentally. Leonard et al. performed the laseranemometry experiments and demonstrated that a 2-D positive corona discharge has an interaction with the flow of a wire-plate ESP by a nonturbulent secondary flow in a plane perpendicular to the discharge wires. A basic conclusion was verified that negative-corona-discharge nonuniformities are responsible for producing both secondary flows in a plane parallel to the discharge wire [14]. Davidson et al. explained the EHD flow by measured current-voltage relationships, turbulence intensities, integral length scales, and eddy diffusivities. And by comparison with gas flow in the wire-plate precipitator, they found that increases in turbulence intensity in the barbed plate geometry are offset by reductions in the scale of the electrically induced flow [15]. Kallio   laser-Doppler anemometry (LDA). And the measurement result of streamwise velocity showed that flow acceleration zones occurred upstream of each wire and also between wires near the collecting plate [16].
In experimenting, the accuracy of Laser Doppler Anemometer and hot wire probe can be interfered by the external electric field. Taking this into account, numerical simulation has been favored by more researchers. Bernstein et al. adopted a fundamental model being laid on the coupled effects of the fluid dynamics and electrostatics and found that the interactions between fluid dynamics and electrostatics have a significant role in altering the flow in the precipitator [17]. Zhao et al. employed a hybrid finite-element methodmethod of characteristics numerical algorithm to study the interaction between the electric and the flow fields. And they found that the EHD flow plays an important role in the channel at very low Reynolds number and high EHD characteristic number [18]. Heng et al. studied the EHD in wire-plate ESP of five shaped collecting electrodes with the aid of a user defined function (UDF) and drew the conclusion that the EHD induced in the C-type plate is the strongest among the five channels [8]. Mantach et al. investigated the effect of EHD in the point-plane configuration in air at atmospheric pressure and room temperature and predicted the existence of an additional small vortex in the ionization layer by calculation [19]. Zheng et al. studied the electrical characteristics of a wire-plate electrostatic precipitator and the particle transport behavior with consideration of EHD and particle space charge by numerical simulation and the results indicate that the ionic wind in the electrostatic field weakened in the condition that the movement of ions is restricted for corona suppression [20]. Feng et al. utilized a hybrid method comprising of the Finite Element Method (FEM) for the simulation of the ionized electric field and the Finite Volume Method (FVM) for the prediction of the EHD flow in ESP simulation and analyzed quantitatively the corona induced EHD flow analyzed by the Qkubo-Weiss index [21].
In summary, the research on EHD at home and abroad mainly focuses on the coupling analysis of particle transport and flow field. This means that the influence of EHD on collection efficiency of ESP is obtained indirectly by the analysis on flow field distribution. Few studies have focused on the deposition pattern induced by EHD, which can provide valuable data for the optimal design of the structure and size of ESP, especially for the shape of the collection plate. In our work, a comprehensive multifield coupling model of wire-plate ESP was established by self-defined programming. The effects of EHD on collection efficiency of ESP and particle deposition pattern were studied, and the EHD behavior in a special needle-plate arrangement was analyzed. Relevant research results can provide reliable theoretical reference for the design and modification of large ESP in industry.

Mathematical Model
The gas flow, electric field, and particle transport inside ESP exert an influence on each other [22][23][24][25]. The interaction between them is shown in Figure 1. The EHD induced by electric field affects the particle transport by changing flow field first.
. . Electric Field. The electric field intensity in the wire-plate ESP can be described by Poisson equation [26].
where V is potential; is space charge density; 0 is vacuum dielectric constant; E is electric field intensity. The charge density can be expressed as current continuity equation.
where J is current density; b is ionic mobility; u is gas velocity; D is ionic diffusion coefficient.
Mathematical Problems in Engineering 3 C ol le ct io n pl at e C or on a el ec tr od e C or on a sp ac in g C o l l e c t i o n p l a t e s p a c i n g . . Particle Transport. Momentum conservation equation of particles is as follows: where x p is the spatial position of particles; u p is the particle velocity; is the particle density; C D is the drag coefficient; F EP is electric field force acting on particles and can be expressed as ; m p is the mass of single particle.
. . Gas Flow. Mass conservation equation of gas phase is as follows: where u k is gas velocity; is gas density.
In view of the fact that the average random range of ion motion is small relative to the characteristic scale of ESP, the influence of EHD on flow field is assumed to be instantaneous and can be embodied by adding a volume force term of in the gas phase momentum equation [27,28].
Momentum conservation equation of gas phase is as follows: where is the dynamic coefficient of viscosity; is the turbulent viscosity; is the resistance force due to the relative motion between the gas and particles.

Geometric Structure
The geometric model of 3D ESP is shown in Figure 2  field and particle transport and the randomness of particle phase, the coupling between them is carried out by a small underrelaxation factor. The 2D-ESP model adopted in this work includes four corona electrodes to exhibit the ionic wind effect evidently; a detailed illustration is omitted here.

Model Verification
To validate the corona model which is related to the EHD characteristics, the simulation results of electric field without gas flow effect in 2D case are compared with the experimental data of wire-plate ESP [29], as shown in Figure 3. It can be seen from the graph that the simulated current density on the plate is in good agreement with experimental data, indicating that the corona model adopted in our work is in line with reality.

Results and Discussion
. . EHD Effect on Collection Efficiency. EHD primarily affects the gas flow, and the particle transport is influenced through gas-solid coupling. The residence time of particles in ESP depends on the streamwise velocity, which has a direct impact on collection efficiency of ESP. Figure 4 shows the streamwise velocity of airflow with or without EHD in 2D case where the voltage and velocity are fixed. As seen in Figure 4, the airflow velocity near the wall is small and keeps constant with no EHD effect, which contributes to the particle deposition on the collection plate. When considering the EHD effect, the airflow velocity near the wall becomes unstable, and velocity in local space becomes very large. This is because the electric force effect of EHD drives the gas moving from the corona wire towards the collection plate and makes the gas circulate in local space of ESP, resulting in a decrease of the airflow area, and thus the airflow velocity near the collection plate increases.
The collection efficiency of particles with different diameters in the presence or absence of EHD is shown in Figure 5. It can be obtained from the graph that the collection efficiency with EHD effect is lower than that without EHD effect; this is because the airflow circulation caused by EHD increases the airflow velocity near the wall and causes the particles to escape faster from ESP, which is not conducive to the particle deposition; the negative effect of EHD on collection efficiency of small particles is greater than that of big particles. This is due to the fact that the EHD affects particle transport through gas-solid coupling, and the small particles have small inertia and good airflow following, which makes them more sensitive to airflow variation.
. . EHD Effect on Particle Deposition. The particle deposition pattern has three-dimensional characteristics. Therefore, the 3D-ESP structure is built to characterize the particle deposition process with or without EHD.
The trajectory of particles with uniform diameter of 2.5 m in the presence or absence of EHD in 3D-ESP is shown in Figure 6, colored by the particle charge. It can be concluded from the figure that when EHD is not available, the particle trajectory is basically straight, and certain regularity shows up. When EHD is considered, the particle motion becomes irregular and the turbulence intensity increases. Figures 7 and 8 are the particle deposition rate when v=0.25m/s or 0.5m/s, respectively. It can be found from the figures that EHD has a significant effect on particle deposition no matter what the flow velocity is. And the effect of EHD on particle deposition rate is greater at low airflow velocity.
. . EHD Effect in the Case of Needle Pointing Plate. When the needle tip points to the plate, the trajectory of particles with uniform diameter of 2.5 m is shown in Figure 9, colored by particle charge. Because the needle tip is oriented towards the collection plate, the ions produced by corona discharge cannot reach the tip root, i.e., the symmetrical axis in streamwise direction of ESP. Therefore, a region without free ions appears near the symmetrical axis. From Figure 9, one can obtain that, when EHD is switched off, the charge of particles passing through the nonionic region is very small, which indicates that particles cannot obtain enough charge in the region. When EHD effect is considered, the particle trajectory changes significantly and the particles charge more when passing near the corona wire. This is because EHD makes the airflow circulate locally near the corona wire and reduces the number of particles passing through the nonionic region. Due to the airflow circulation, some particles move from the nonionic region to the collection plate and are then charged. Figure 10 shows the collection efficiency of 2.5 m particles with or without EHD effect when the needle points to the plate. As can be seen from the figure, the collection efficiency with EHD is slightly higher than that without EHD. This is because the existence of EHD reduces the number of particles passing through the nonionic region and increases the number of fully charged particles in the case of needle pointing to the plate. Under the influence of electric field, fully charged particles move towards the plate and are trapped by collection plate, thus improving the collection efficiency. And with the decrease of flue gas velocity, the enhancement of collection efficiency due to ionic wind is greater.

Conclusions
On the basis of self-defined programming, a comprehensive multifield coupling model of ESP was established, and the influence of EHD on particle transport and deposition pattern was analyzed. The conclusions are as follows: Generally, when the EHD is switched on, the airflow area of the airflow decreases, the streamwise velocity of airflow near the collection plate obviously increases, and the residence time of particles in ESP is shortened, which results in a decline of the collection efficiency of ESP; the effect of EHD on particle deposition pattern cannot be ignored and is more obvious at lower flue gas velocity; in the case of needle tip pointing to the collection plate, the EHD contributes to the improvement of collection efficiency of ESP by the transportation of particles in nonionic region to the ionic region.

Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
The authors declare that they have no conflicts of interest.