Trapping performance improvement of submicron particles in electrostatic cyclone by the applied magnetic field

Abstract

Aiming at improving the trapping performance of submicron particles, the magnetic field was introduced into the outer vortex electrostatic cyclone (ESC), and the dust-removal mechanism under the action of electromagnetic field was investigated. Besides, the theoretical model was established to analyze the interaction between fluid flow field, electromagnetic field and particle dynamic field, and the influences of magnetic field on submicron particles collection efficiency at different working voltages and gas velocities were simulated and discussed. The results indicate that the introduction of magnetic field obviously enhances the ESC trapping performance for submicron particles. High working voltage and low gas velocity at a given magnetic flux density are both more favorable for trapping submicron particles, but the magnetic field effect is more obvious at high gas velocity, as well as at low working voltage. Furthermore, at the same working voltage and gas velocity, the contribution of magnetic field to collection efficiency increases with the applied magnetic flux density increased, but the increment gradually decreases, which can lay significant foundation for optimal design of submicron particles removal in ESC.

Keywords

Applied magnetic field electrostatic cyclone submicron particles removal mechanism trapping performance

1. Introduction

Cyclones are suitable tools for removing particulates from flue gas, without the use of filter elements [1]. For particles greater than 8 $\mu$ m, the modern cyclone can remove full of them basically, and for particles more than 5 $\mu$ m, the cyclone also has better trapping efficiency, so it can be widely used in the industry [2]. Compared with the electrostatic precipitator and the bag filter, the obvious advantage of the cyclone is low consumption and small occupation [3], but the disadvantage is inefficient for particles smaller than 5 $\mu$ m [4, 5]. Therefore, how to improve the trapping performance for fine particles in the cyclone is a hot research, and the idea of combining different separation techniques has been promoted [6].

In order to improve the trapping efficiency of fine particles, an electrostatic cyclone has been developed. In this respect, the main researches focused on the aspects of tests, and a good effect had been achieved. The earliest example of the application of ESC comes from America, and the design is to add a discharge electrode at the center of the exhaust pipe in the cyclone to restrain the escaping of dust with the airflow. Dietz [7] demonstrated that the separation performance of a cyclone can be enhanced if electrical forces were employed to supplement the inertial forces, and moreover, the effect of electrostatics on trapping performance was more significant for small particles and at low gas velocities [8, 9]. Lim et al. [10] found that an increase in applied voltage and a decrease in wire diameter both boost collection efficiency, particularly at low flow rates for small particles. Yoshida et al. [11] analyzed the effect of conical section length on the performance of particle separation using an electrical hydro-cyclone. Lin et al. [12] designed a wet electrocyclone with high efficiency for long-term operation, and the experimental results showed that the collection efficiency decreased with an increasing air flow rate. Lv and Gan [13] obtained the relationship between the sediment characteristics and the collecting efficiency of electrostatic cyclonic precipitator using Kompton back scatter method. Titov [14] proved that the re-entrainment existed in the electrocyclone, and it decreased the collecting efficiency by 5–30% at aerosol velocity in range 14–27 m/s and concentration in range 2–30 g/m ${}^{3}$ . The earthed atomizing corona discharge was applied to the cyclone precipitator, and the grade efficiency increased 15% than the traditional cyclone [15]. Mazyan et al. [16] investigated the feasibility of using electro-hydrodynamic (EH) forces to enhance the efficiency of solid-gas separation in cyclone separators, and found that the use of an additional EH forces enhanced the efficiency by 33% for the particle sizes of 4 $\mu$ m.

In summary, cyclone separators are popular in today’s particle-handling industry, and the enhancement of fine particle collection is still a demanding topic [17]. Although adding electrode to the cyclone can improve the collection efficiency of fine particles, the removal performance for submicron particles is still far from meeting the requirements. At present, magnetron electrostatic precipitation is a breakthrough to develop new dust removal equipments [18]. The flocculation of paramagnetic particles under the influence of a strong magnetic field was reported, and particle size and magnetic susceptibility each played an important role in the selective flocculation of particles of different properties [19]. Prakash and Pratim [20] proposed a calculation analytical expression of particle coagulation factor in uniform magnetic field on the basis of the Brownian diffusion. Ukai et al. [21] investigated the cluster-cluster aggregations of superparamagnetic particles in a rotational magnetic field numerically by Brownian dynamics method. Park et al. [22] found that when the vertical magnetic field was applied to the electrostatic precipitator, the precipitation efficiency was improved about 5% more than the case of non-magnetized ferrite plate. Zhang et al. [23] discussed the main principle of wire-pipe electrostatic precipitators subjected to the external magnetic field, which can improve the dust collection efficiency.

Seen from the current research situation, applying magnetic field to ESC for improving the trapping performance has not been reported. Therefore, in this work, the removal mechanism of ESC under the applied magnetic field was analyzed, and the influences of magnetic field on trapping performance for submicron particles at different working voltages and gas velocities were investigated and discussed.

2. Mechanism analysis

2.1 Magnetic field mechanism

The magnetic field application in the ESC forces the charged particles under the action of Lorentz force to deflect, which is expected to be one of important measures to improve collection efficiency of ESC so far. The dust particles are charged when they enter charged area of ESC, and then the charged particles with a muzzle velocity move toward the dust collection plate due to electric field force and the movement trajectory is parabolic. Eventually, charged particles are absorbed on the surface of the dust collection plate, but at the same time, part of particles with too large muzzle velocity escape from the dust collection area. When the magnetic field is introduced, the charged particles only affected by Lorenz force will perform circular movement [23]. Actually, charged particles make more complex spiral movement under the combined action of Lorentz force and electric field force. Thus the residence time of charged particles in the dust channel is prolonged, and particles are charged more fully, which makes charged particles easily trapped to achieve the purpose of improving collection efficiency.

2.2 Multi-field coupling mechanism

There exist three physical fields including fluid field, electromagnetic field and particle dynamic field which are coupled with each other inside ESC. The electrical field influences the fluid field by the means of electric wind, and the electromagnetic field affects the particle dynamic field by Lorenz force and electric field force produced by field charging and diffusion charging. Meanwhile, the fluid field reacts on the particle dynamic field by aerodynamic drag, and the particle dynamic field influences distribution of electrical field by space charging and affects the fluid field by particle-gas coupling effect. In this workï¼Œthe specific coupling relationship can be seen in Fig. 1.

Figure 1.

Multi-field coupling effect inside ESC under applied magnetic field.

3. Theoretical model

3.1 Flow field

The density of flue gas can be regarded as a constant under the condition that the flue gas is assumed to be incompressible in ESC. Meanwhile, considering that the generalized source term is substituted by the sum of the aerodynamic drag and the electric body force in Navier-Stokes equations, the mass conservation equation and the momentum conservation equations can be expressed as

$\displaystyle\frac{\partial}{\partial x_{i}}(\rho_{g}u_{i})=0$ (1) $\displaystyle\rho_{g}\frac{\partial}{\partial t}(u_{j})+\frac{\partial}{% \partial x_{i}}(\rho_{g}u_{j}u_{i})=-\frac{\partial P}{\partial x_{j}}+(\mu+% \mu_{t})\frac{\partial^{2}u_{j}}{\partial x^{2}_{i}}+F_{Dj}+\rho E_{j}$ (2)

where $\rho_{g}$ is density of air (kg/m ${}^{3}$ ), $u_{i}$ and $u_{j}$ are gas velocities (m $\cdot$ s ${}^{-1}$ ), and $P$ is average static pressure of gas (Pa). $\mu$ is dynamic viscosity coefficient of gas, and $\mu_{t}$ denotes turbulent dynamic viscosity coefficient, $\mu_{t}=\rho_{g}C_{\mu}k^{2}/\varepsilon$ , (kg/(m $\cdot$ s)), where $C_{\mu}=$ 0.09, $k$ is turbulent kinetic energy, and $\varepsilon$ is the dissipation rate of the turbulent energy. $F_{Dj}$ and $E_{j}$ are separately drag force of particles (N), and electric field intensity (V/m). The subscripts of “ $i$ ” and “ $j$ ” represent $x$ , $y$ and $z$ directions, respectively.

3.2 Electromagnetic field

Electromagnetic field in the ESC consists of the electrostatic field and steady magnetic field. In this study, the magnetic field applied in the ESC can be considered to be uniformly distributed and doesn’t change with time, which doesn’t involve solving Maxwell equations. The magnetic field makes the charged particles generate the Lorentz force, which is loaded into the dynamic control equation of particles.

Due to the symmetry of ESC structure and application way of corona wire, the electric field in the coordinates is constant along the axial and the circular direction, and only changes in the radial direction. Thus, the electric field strength $E$ can be obtained as [23]

$\displaystyle E=-\sqrt{\frac{I}{2\pi b_{\textit{eff}}\varepsilon_{0}}+\frac{C^% {2}}{r^{2}}}$ (3)

in which, $I$ denotes the current per unit of corona wire (A/m), and $r$ is the radial distance from a point in the space to the corona wire (m). $\varepsilon_{0}$ and $C$ represent the permittivity of free space and integration constant. The effective mobility $b_{\textit{eff}}$ is composed of dust particles mobility $b_{pc}$ and ions mobility $b_{\textit{ion}}$ , $b_{\textit{ion}}=$ 2.2 $\times$ 10 ${}^{-4}$ (m ${}^{2}$ /(V $\cdot$ s)), $b_{pc}=$ 5 $\times$ 10 ${}^{-7}$ (m ${}^{2}$ /(V $\cdot$ s)). Compared with $b_{\textit{ion}}$ , $b_{pc}$ can be ignored, so $b_{\textit{eff}}$ is actually the ion mobility $b_{\textit{ion}}$ .

3.3 Particle dynamic field

When the forces acting on dust particles are analyzed, some relatively low secondary forces can be neglected, and there are only electric field force $F_{e}$ , Lorentz force $F_{m}$ , and the drag force $F_{D}$ worthy of consideration [18]. In this case, the mass conservation equation and the momentum conservation equation of particles are respectively given as follows [24]

$\displaystyle\frac{\partial n_{p}}{\partial t}+\frac{\partial}{\partial x}(u_{% j}\cdot n_{p})=0$ (4) $\displaystyle m_{p}\frac{du_{j}}{dt}=F_{m}+F_{e}+F_{Dj}$ (5)

where, $n_{p}$ and $m_{p}$ are separately unit volume of particle number concentration (L/m ${}^{3}$ ) and the particle mass (kg), and $u_{j}$ denotes the particle velocities (m/s) in $j$ direction ( $j=$ 1, 2, 3 represents the direction of $x, y, z$ ).

4. CFD model

4.1 Boundary conditions

The boundary of solution domain in the outer vortex ESC includes inlet and outlet of flue gas, ash export, corona wire surface and axis of corona line. No slip is used at ash export surface, and the wall roughness is set as the default value. The wall is the main source of vortex, so setting the wall boundary condition has a great influence on the numerical calculation. In the vicinity of the wall, due to the enhancing viscosity action and the weakening turbulent diffusion effect, the standard wall function method is adopted to calculate the surfaces of collection electrode and corona wire. The above settings are shown in Table 1, where $\bar{T}_{i}$ and $D_{q}$ are respectively the turbulence intensity and the equivalent diameter of the ESC inlet. The boundary conditions of dispersed phase of dust particles are also listed in Table 1. In addition, the space charge density can be regarded as a constant, so $\nabla\rho=$ 0 is set on the boundaries of inlet, outlet and corona wire surface.

Table 1
Boundary conditions of outer vortex ESC

	$x$ -velocity	$y$ -velocity	$z$ -velocity	$U$	$k$	$\varepsilon$	Particle
Inlet	$u=u_{0}$	$v=$ 0	$w=$ 0	$\nabla U=$ 0	$3\bar{T}_{i}^{2}u_{i}^{2}$ /2	0.05 $k^{1.5}D_{q}$	Escape
Outlet	Pressure	Pressure	Pressure	$\nabla U=$ 0	$\partial k/\partial x=$ 0	$\partial\varepsilon/\partial x=$ 0	Escape
Corona wire	No slip	No slip	No slip	$U=U_{0}$	wall-function	wall-function	Reflect
Collection plate	No slip	No slip	No slip	$U=0$	wall-function	wall-function	Trap

5. Results and discussion

5.1 Optimized design of physical model

Combined with the principle of ‘trajectories of charged particles can be effectively controlled due to electromagnetic field’, four corona wires with a length of 190 mm are evenly arranged along the circumference at a half position between the central channel and the cylinder wall. Then the magnetic field is exerted in the direction parallel to the axis of ESC and perpendicular to the direction of electric field, which makes particles charged more fully so as to achieve the optimum design of ESC model.

Figure 2.

Schematic diagram of dust-removal mechanism in electromagnetic field.

As shown in Fig. 2a, when the negative high voltage is applied to the electrode wire, the direction of electric field strength $E$ points to corona lines along the radius. Meanwhile, the downward magnetic flux density $B$ is applied in the direction parallel to the axis of ESC and perpendicular to $E$ . When the positive high voltage is applied to the electrode wire in Fig. 2b, $E$ and $B$ directions are opposite to those in Fig. 2a.

Figure 3.

Reliability verification curves.

5.2 Reliability verification of calculation

Figure 4.

Grade efficiency with different working voltages.

Figure 5.

Overall efficiency varying with magnetic flux density at different working voltages.

Figure 6.

Grade efficiency with different gas velocities.

Aiming at verifying the reliability of calculation results, the simulated data in this work is compared with the experimental one in reference [25]. Under the same working condition, contrast curves of collection efficiency varying with gas velocities are displayed in Fig. 3. It can be found that the two curves are in good agreement with each other, which implies that the theoretical and numerical models in this study can accurately simulate the trapping performance of particles in outer vortex ESC.

5.3 Effects of magnetic field on trapping performance

5.3.1 Collection efficiency at different working voltages

To explore the trapping performance of outer vortex ESC under different magnetic flux densities, set the gas velocity at inlet as 4 m/s and the temperature as 200 ${}^{\circ}$ C, respectively, and then variation curves of grade efficiency for submicron particles with working voltage are given in Fig. 4. The following can be concluded.

At the same working voltage, the grade efficiency of submicron particles under applied magnetic field slowly decreases with the increasing particle diameter, and then flattens out.

As magnetic flux density increases with the same increment, the grade efficiency rises, but the increment decreases, showing that the magnetic field is beneficial to enhance the collection efficiency of outer vortex ESC, but the increment constantly becomes smaller.

Regardless of magnetic flux density, the grade efficiency progressively increases with the increase of working voltage.

Combined with Fig. 4, overall efficiency under the same working condition is given in Fig. 5, and it is clear that:

At the same working voltage, overvall efficiency of submicron particles shows a gradually rising trend with the increasing magnetic flux density, until to be flat, which demonstrates that the enhancement of magnetic flux density results in the gradual increase of the contribution of the magnetic field to removing submicron particles, but the increment decreases progressively.

Under the same magnetic flux density, the overall efficiency constantly increases with the increase of working voltage, but the increased extent becomes smaller, proving that the high working voltage is more beneficial for trapping particles in the outer vortex ESC.

With the increase of working voltage, the curve slope of overall efficiency gradually drops, that is, the magnetic field at low working voltage promotes the trapping efficiency of submicron particles more significantly, which indicates that the effect of magnetic field on the collection efficiency at low working voltage is more obvious than that at high working voltage.

Figure 7.

Overall efficiency varying with magnetic flux density at different gas velocities.

5.3.2 Collection efficiency at different gas velocities

Under the condition that working voltage and temperature are separately set to 50 kV and 200 ${}^{\circ}$ C, Fig. 6 exhibits the grade efficiency of outer vortex ESC subjected to the applied magnetic field at different gas velocities. It can be found that:

At the same gas velocity, the grade efficiency has the same varying tendency with that in Fig. 4.

Under the same magnetic field condition, the grade efficiency is constantly decreasing with the increasing gas velocity, implying that low gas velocity improves the trapping performance for submicron particles.

For a given gas velocity, as the magnetic flux density increases uniformly, the grade efficiency basically presents the same changing trend with the one in Fig. 4, which indicates that the magnetic field can effectively improve the trapping performance. Meanwhile, the bigger the magnetic flux density becomes, the smaller the ascended amplitude of the grade efficiency is.

Under the same condition with Fig. 6, variation curves of the overvall efficiency with magnetic flux density at different gas velocities are plotted in Fig. 7, and it is apparent that:

At the same gas velocity, the overvall efficiency has the same varying tendency with the grade efficiency in Fig. 6, which evidently shows that the increase of magnetic flux density improves the contribution of magnetic field to the trapping performance.

With the increase of gas velocity, the overvall efficiency at the same magnetic flux density continually decreases, and the slope of curves also rises, which implies that at the high gas velocity, the magnetic field effect on improving the trapping performance of outer vortex ESC is greater.

6. Conclusion

Under different working voltages and gas velocities, the influences of magnetic field on collection efficiency of the outer vortex ESC were investigated by optimized design and numerical simulation. The conclusions are summarized as follows:

An optimization ESC model is developed by applying magnetic field to the outer vortex ESC, and the dust-removal mechanism under multi-field coupling effect is revealed, making that the trapping performance for submicron particles is dramatically improved.

On the premise of the same magnetic field environment, the improvement of collection efficiency results from the increasing working voltage and the decreasing gas velocity. Furthermore, the constant amplitude increase of magnetic flux density increases the collection efficiency, but the increment becomes flat.

As the working voltage decreases and the gas velocity increases, the curve slope of overall efficiency varying with magnetic flux density gradually rises, showing that the magnetic field effect on improving the trapping performance of ESC is more significant in case of low working voltage and high gas velocity.

The ESC model optimized by introducing an external magnetic field can provide a new strategy for enhancing trapping performance of industrial fine particles.

Footnotes

Acknowledgments

This work is supported by National Natural Science Foundation of China (11572187); Foundation of Science and Technology Commission of Shanghai Municipality (15110501000, 11DZ2281700).

Nomenclature

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Trapping performance improvement of submicron particles in electrostatic cyclone by the applied magnetic field

Abstract

Keywords

1. Introduction

2. Mechanism analysis

2.1 Magnetic field mechanism

2.2 Multi-field coupling mechanism

3.1 Flow field

4.1 Boundary conditions

Table 1 Boundary conditions of outer vortex ESC

5.1 Optimized design of physical model

5.3.1 Collection efficiency at different working voltages

6. Conclusion

Footnotes

Acknowledgments

Nomenclature

References

Table 1
Boundary conditions of outer vortex ESC