Environ Eng Res > Volume 28(4); 2023 > Article
Zhang, Lu, Zhao, Zhang, Hu, Zhang, and Ren: Influences of magnetic field on the removal of submicron particles in electrostatic cyclone at different temperatures

### Abstract

Aiming at improving the capture performance of inner vortex electrostatic cyclone (ESC), which is widely used in the field of flue gas purification, magnetic field is introduced to remove submicron particles. The theoretical and physical models of electromagnetic dust removal were established, and the dust-removal efficiency of submicron particles under different temperatures and magnetic fields was numerically simulated by FLUENT. The results show that a rise in temperature leads to a reduction in the grade efficiency of submicron particles of ESC, a decrease in the number of escaped particles at lower temperature, and the differences of the rising amplitude in overall efficiency corresponding to the traditional cyclone, which were 36.7%, 34.8%, 33.8%, and 31.9% at four temperatures. The contribution of temperature to the capture of submicron particles decreases continuously with the increasing temperature, but that of magnetic field progressively increases at this time. The magnetic field environment is conducive to the capture of submicron particles, the removal effect is more obvious with the increase of magnetic flux density, but the ascended ranges of magnetic field and temperature both decrease when it reaches 0.5 T. These results can provide a theoretical basis and a technical reference for the design of ESC.

### 1. Introduction

In recent years, with the continuous occurrence of haze in major cities in China [12], air quality has become increasingly worse. More and more attention has been paid to the harm caused by fine particles, with the emission of vehicle exhaust being of the main sources of pollution [35]. Submicron particles refer to particles whose aerodynamic equivalent size is less than 1 μm in atmospheric dust inhalation [68], and they can easily enter human alveolar and cause serious harm to human health [910]. As an economic, energy-saving and efficient power system, diesel engines are widely configured in high-power transportation vehicles [1112]. The main components of diesel engine exhaust are submicron particles and nitrogen oxides [1314]. The exhaust pipe of a diesel engine emits a large number of submicron particles due to the incomplete combustion of most engine cylinders, which has a serious impact on human health and the environment [15].
Some achievements have been made in the exploration of submicron particles capture in diesel engine exhaust. In order to improve the overall performance of these diesel particulate filter (DPF), a multidisciplinary design optimization (MDO) model was established based on objective functions such as pressure drop, regeneration performance, microwave energy consumption, and thermal shock resistance [16]. The DPF performance was investigated, and it was demonstrated that it was not convenient for the removal of large-diameter particles when the regeneration temperature was higher than 525°C, but the increase of flow rate had a negative impact on the maximum temperature [17]. Subsequently, real-time particle emission data onto a heavy-duty chassis dynamometer during steady-state driven DPF regeneration was analyzed, and it was found that the application of more modern passive regeneration technology could reduce the emission of total particles and ultrafine particles on the road [18]. Cyclone is widely applied to the treatment of flue gas from fossil energy combustion, but it has the problem of low separation efficiency of fine particles [1921]. A novel cartridge-filtering cyclone combining a cyclone separator with a cartridge filter was put forward, and the experimental results showed that it had a better dust-removal properties [22]. Since the introduction of electric fields can improve the dust-removal performance of electrostatic cyclone, more researchers have conducted some experimental research on the electrostatic cyclone (ESC) and obtained good results. The earliest application example of inner vortex ESC came from the United States, in which a linear discharge electrode was attached to the exhaust pipe center of the cyclone to prevent dust from escaping from the airflow. The effect of electrostatic force in ESC was more significant at a lower flue gas flow rate and could substantially reduce the escape of fine particles [23]. The swirl vanes and vortex stabilizer played an important role in the optimization of the catch efficiency of the gas and liquid phases, and the velocity field inside the cyclone separator was investigated to explain the separate effects of the two internal components [24]. The magnetic field can effectively improve the collection efficiency of electrostatic precipitator for particles, which is a method of using the magnetic field to create Lorentz force on charged moving particles to change their movement paths [2526]. The development of magnetically controlled ESC based on this principle will be a breakthrough for the effective removal of submicron particulate matter.
In summary, it is uncommon to study the collection efficiency at different temperatures by introducing magnetic field to analyze the dust-removal mechanism of ESC. Therefore, the influences of magnetic field on the capture performance of submicron particles in an inner vortex ESC at different temperatures were simulated and analyzed with the diffusion charge effect considered in this work. The research results can provide theoretical and technical references for the design of a novel ESC aimed at economic and environment protection.

### 2.1. Gas Flow Field

It is generally believed the complexity of turbulent motion does not affect the applicability of unsteady continuum equations and Navier-Stokes equations for common turbulent transient motion [2728]. The flue gas can be regarded as an incompressible fluid, so its density can be taken as a constant, and the flow of flue gas in the ESC satisfies the mass conservation equation and the momentum conservation equation, which can be expressed as follows:
##### (1)
$∂∂xi(ρgui)=0$
##### (2)
$∂∂xi(ρgujui)=-∂P∂xj+(μ+μt)∂2uj∂xi2+FDj+ρEj$
where ρg is the flue gas density, kg/m3; μ is the dynamic viscosity coefficient of gas, kg/(m·s); ui and uj are the gas velocities, m/s; μt is the turbulent dynamic viscosity coefficient, kg/(m·s); P is the average static pressure of gas, Pa; FDj is the aerodynamic drag force, N; ρ is the electric charge, C; Ej is the electric field intensity, V/m. The subscripts of i, j denote variables, and i, j = 1,2.3 respectively represent x, y, and z direction.

### 2.2. Electric and Magnetic Fields

By exerting a certain voltage between the dust collector and the corona electrode, an electric field can be applied in the dust removal area. The actual distribution of the electric field in ESC is not uniform. In view of the complex structure of ESC, it is quite difficult to deduce the analytical solution of electric field distribution in theory [29]. There are two main ways to calculate the electric field and compared with the method of considering the electric field generated by corona discharge as a simple superposition of electrostatic field and the space charge electric field, the coupled solution of potential Poisson equation and current continuity equation is adopted in this work, which is more realistic and more widely used.
According to the structural symmetry and the voltage application way, the electric field in the ESC in cylindrical coordinates remains constant along the axial and the annular directions, and changes its magnitude only along the radial direction, so the calculation of electric field can be simplified as one-dimensional problem. Poisson equation of the electric field in cylindrical coordinates can be written as [30]:
##### (3)
$d2Udr2+1rdUdr+ρɛ0=0$
here r is the radial distance to the corona wire, m; U is the potential, V; ɛ0 is the vacuum dielectric constant; ρ is the space charge density, C/m3. The electric field strength E can be expressed as:
##### (4)
$E=-dUdr$
There exists both an electric field and a magnetic field around the moving charge and charged particles in an applied external magnetic field are subjected to Lorentz force. The magnetic field given in this work is uniformly distributed among ESC space, and its magnitude and direction do not change with time, which does not involve the solution and calculation of Maxwell equations.

### 2.3. Particle Dynamic Field

In the numerical model of ESC with external magnetic field, the governing equations of particle dynamic field are the same as that without consideration [31]. In two-phase gas-solid flow, the density of the gas is far lower than that of the particle, and the buoyant, pressure gradient, additional mass, and gravitational forces are very small compared with the inertia force of the particle itself. Hence, these forces can be neglected. Considering that electric field force, Lorentz force and drag force acting on the particles are obvious, the form of particle force balance equation in two-dimensional coordinates is obtained as:
##### (5)
$mpd vjdt=Fmj+Fej+FDj$
in which, mp is the particle mass, kg; vj is the particle velocity, m/s; magnetic field force Fmj = Qp vj B, N; Qp is the particle charge, C; B is the applied magnetic flux density, T; electric field force Fej = QpE, N; drag force FDj = 1/2mp Ap ρg CD (ujvj)|ujvj|, N; Ap is the area of approach stream of particles, m2; CD is the drag coefficient between airflow and dust particles. The subscripts of i, j denote variables, and i, j = 1,2.3 respectively represent x, y, and z direction.

### 3.1. Layout of Inner Vortex ESC Corona Line

A structure schematic diagram of the ESC two-dimensional central exhaust tube is illustrated in Fig. 1. The corona wire is often installed in the center of the exhaust tube in circular or star shape. The dusty air flows through the channel in the tube from bottom to top. In Fig. 1, d represents the distance from the outer surface of the corona line to the inside of the central tube with radius R and can be replaced by the radius R in the calculation since the corona line of M0 in length is thin, and N denotes the height of the central tube.
The structural parameters of the model are: center tube height N = 150 mm, corona wire length M0 = 190 mm and its radius rw = 1.0 mm. The flue gas flows upwards at the vertical inlet of the central channel, and one can set the ρ-axis and the z-axis as the directions of flue gas perpendicular and parallel to the dust collector pole respectively, so the dust concentration around the concentric circle centered on the axis is considered to remain constant. In view of the simplicity of calculating ESC electric field in column coordinates, it is assumed that the variation of electric field intensity in ρ-direction is only taken into account, and that the electric field intensity in z-direction is neglected.

### 3.2. Mesh Division

As the pre-processing meshing software of FLUENT, GAMBIT can be used to establish the ESC simplified model and divide the mesh cells, where the mesh profile is adopted as a hexahedral mesh. The grid system established by the above method has better adaptability, and the mesh orthogonality is better. Meanwhile, the refined mesh technique is employed to the inlet and outlet of exhaust tube, thereby the precision of regenerated grids is improved. The final mesh profile result is shown in Fig. 2.

### 3.3. Grid Independence Verification

For numerical simulation research, grid-independent verification is essential to ensure the accuracy of the numerical simulation, and the quality and the density of grid system have a significant influence on the numerical accuracy [32]. The relative errors of overall efficiency for different grid cell numbers are shown in Fig. 3, and it can be seen that the relative error decreases and flattens out with the increase of grid cell numbers. When the number of grid cells reaches 128357, the relative error is only 1.55%, so this grid cell value is chosen to ensure both the speed

### 3.4. Numerical Reliability Verification

To ensure the reliability of calculated results from the inner vortex ESC, the simulations were performed for an electrostatic cyclone dust collector under the same operating conditions (inlet airspeed is 2 m/s, emitter tube diameter is 10 mm) as those in the literature [33]. The comparison curves of airflow tangential speed variation along radial direction are plotted, as shown in Fig. 4. It is very clear that the numerical simulation result in this study is in good agreement with the data from the literature, showing that the numerical model of inner vortex ESC in this work can accurately simulate the dust-removal efficiency of particles.

### 4.1. Temperature Effect

R-R distribution particles are used as incident ones in ESC. Fig. 5 shows the grade efficiency variation of submicron particles with particle sizes at different temperatures when working voltage and flue gas velocity are separately set to 50 kV and 4 m/s. It can be observed that:
1. At any temperature, the grade efficiency of ESC decreases continuously, and the reduction range is more obvious at small particle sizes with the increase of particle size, suggesting that ESC has a more effective removal effect for smaller particles.

2. The graded efficiency increases uninterruptedly with the decrease of temperature, and the rising amplitude is more obvious at lower temperature, indicating that the low-temperature environment is conducive to the capture of submicron particles, but the dust-removal efficiency at this time is only below 75%, which needs the introduction of new dust-removal technologies to improve the trapping performance of ESC.

For the sake of investigating the influence of temperature on overall efficiency of particles in ESC and comparing it with the dust-removal performance of the traditional cyclone, the histogram of the overall efficiency of traditional cyclone and ESC under the same condition with Fig. 5 is presented in Fig. 6, and some details can be clarified as follows:
1. The overall efficiency of submicron particles in ESC is much higher than that in traditional cyclone regardless of the temperature, showing that the impact of charging effect on improving the removal of fine particles is remarkable, and the trapping effect of ESC on dust particles is much better than that of traditional cyclone.

2. Regardless of whether there is charging effect or not, the overall efficiency of submicron particles decreases continuously with the rise of temperature, further giving evidence that the low-temperature environment is more favorable for the removal of fine particles in ESC.

3. In the four cases with constantly increasing temperature, the difference between overall efficiencies with and without charging effect was 36.7%, 34.8%, 33.8% and 31.9% respectively, showing a significant decreasing trend, which implies that the influence of charging effect on the dust-removal efficiency of ESC gradually weakens with the rise of temperature.

### 4.2. Magnetic Field Effect

In magnetic field environment, working voltage and flue gas velocity are separately set to 50 kV and 4 m/s, and the capture performance of particles with a particle size of 1 μm in ESC is investigated. Fig. 7 plots the influence curves of external magnetic flux density on the particle overall efficiency at different temperatures, and it is found that:
1. At the same temperature, the overall efficiency rises nonlinearly with the increase of magnetic flux density. Under the condition of temperature of T = 200°C, the overall efficiency for inner vortex ESC without the effect of magnetic field is the largest, which is about 65.5%, and when the applied magnetic flux density reaches 0.625 T, the overall efficiency is increased to about 15%. The results showing that the magnetic field has a promoting effect on the removal of particles in ESC, and the stronger the magnetic field, the more obvious the promotion effect.

2. The ascended range of overall efficiency gradually decreases with the increase of magnetic flux density, and the trend tends to be flat until B= 0.5 T. When the magnetic flux density changes from 0 T to 0.125 T, the overall efficiency is increased by about 4%–6%, and when it ranges from 0.5 T to 0.625 T, the one is increased by about 1%, which proves that magnetic field effect is weaker at higher magnetic flux density.

3. Under the same magnetic field environment, the overall efficiency gradually decreases with the rise of temperature, and the dropped amplitude reduces constantly, stating that the temperature increase has an opposite effect on raising the overall efficiency of ESC, that is, the temperature effect is more evident when the temperature is lower.

4. With the increase of magnetic flux density, the difference of overall efficiency between two adjacent curves gradually reduces, proving that the effect of temperature on trapping particles constantly declines when magnetic flux density enhances.

It can be obtained from Fig. 7 that the variation curves of contribution rate of particle overall efficiency with temperature under different magnetic field environments, as shown in Fig. 8. It is very clear that:
1. The contribution rate of magnetic field to the overall efficiency of submicron particles increases with the rise of temperature, and the growth trend gradually slows down.

2. With the rise of temperature, the difference between adjacent curves gradually widens, indicating that the higher the temperature is, the more obvious the contribution rate of magnetic field to promoting dust-removal performance is.

3. At the same temperature, the augmented range of contribution rate of the magnetic field to trapping submicron particles in ESC flattens out with the increase of external magnetic flux density, proving that the increased speed of magnetic field on particle removal effect drops continuously when the magnetic flux density strengthens.

### 5. Conclusions

This study mainly focuses on the influence of temperature and magnetic flux density on the separation performance of inner vortex ESC and compares the overall efficiency of ESC with that of traditional cyclone. The final conclusions are as follows:
1. No matter under any operating condition, ESC has better performance trapping submicron particles than traditional cyclone, but the existing gap between them decreases with increasing temperature.

2. The grade efficiency of submicron particles in inner vortex ESC at different temperatures shows a non-linear decrease with the increase of particle size until it tends to be flat, and the grade efficiency and the overall efficiency both rise constantly with the reduction of temperature.

3. With the increase of magnetic induction intensity, the overall efficiency of submicron particles rises continuously, but the improvement range of magnetic field on overall efficiency decreases progressively, while the influence of temperature on particle capture performance weakens gradually.

4. The contribution of magnetic field to the overall efficiency of submicron particles is more significant at higher temperatures, while the contribution of temperature is lower. Meanwhile, the ascended range of magnetic field or temperature for the overall efficiency is more obvious at weaker magnetic flux density.

### Acknowledgements

This research is supported by National Natural Science Foundation of China (12172228, 11572187), Natural Science Foundation of Shanghai (22ZR1444400), and the Program of Foundation of Science and Technology Commission of Shanghai Municipality (22DZ1206005, 22DZ1204202).

### Notes

Conflict-of-Interest

The authors declare that they have no conflict of interest.

Authorship Contributions

J.Z. (Professor) Data curation, Conceptualization, Methodology, Visualization. X.L. (M.S. student) Visualization, Software, Writing-original draft. D.Z. (Senior engineer) Visualization, Funding acquisition. P.Z. (Professor) Data curation, Funding acquisition, Resources. J.H. (engineer) Software. Z.Z. (engineer) Visualization. B.R. (M.S. student) Validation.

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##### Fig. 1
Corona wire arrangement of inner vortex ESC
##### Fig. 2
Three-dimensional mesh model of ESC
##### Fig. 3
Grid independence verification of ESC
##### Fig. 4
Variation curves of tangential velocity along radial direction and the precision of the calculation.
##### Fig. 5
Grade efficiency change at different temperatures
##### Fig. 6
Overall efficiency change of submicron particles under R-R distribution
##### Fig. 7
Variation of overall efficiency with magnetic flux density
##### Fig. 8
Contribution rate of overall efficiency under different magnetic flux density
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