Analysis of PM2.5 collection efficiency in a wire-cylinder ESP with ionic wind effect under multi-field coupling

Abstract

In order to investigate the PM2.5 collection efficiency of a wire-cylinder electrostatic precipitator (ESP) under the action of ionic wind, PM2.5 removal mechanism was studied, and an ESP mathematic model including the multi-field coupling between gas flow field, electric field and particle dynamical field was built. By applying Deutsch-Anderson Equation to process and analyze the numerical solution after compiling user-defined function (UDF) program and linking it to Fluent, grade collection efficiency and overall collection efficiency for PM2.5 were obtained. Numerical results indicate that PM2.5 removal performance under the consideration of ionic wind is better, and the contribution of ionic wind to PM2.5 removal performance is different by changing operating voltage and gas velocity. The research results can provide references for researchers to design a novel wire-cylinder ESP.

Keywords

Multi-field coupling wire-cylinder ESP ionic wind PM2.5 removal performance

1. Introduction

With social development, people’s attention to the living environment and their own health has been more and more prominent [1]. The control problem of the fine particulate pollutants, especially the emission of PM2.5 with the particle size less than 2.5 μm, has become the focus of attention of the international community [2]. Even treated by electrostatic precipitator, the dust from thermal power plant still causes serious environmental pollution. According to the experimental results [3], PM2.5 percentage of overall dust in the pulverized coal fired boiler of thermal power plant increases from 2.42% to 35.56% before and after ESP, which shows that PM2.5 removal efficiency is low. Therefore, it is worth further research on the electrostatic dust removal mechanism.

Researchers found that the electro hydrodynamic field (EHD) plays an important role in the fine particle trapping. The working principle is that the charged particles can be effectively transported to the electrostatic field area of the collecting plate by the ionic wind to affect dust removal efficiency. In the discharge space, the electro hydrodynamic field makes the particle collection process more complex [4].

Kang et al. [5] solved the current continuity equation and electric field governing equation, and drew the conclusion that the effect of ionic wind on gas flow was not negligible by simulating the internal space charge density and the volt-ampere characteristic curve of the electrostatic precipitator. Li et al. [6] measured velocity distribution, analyzed its principle of ionic wind on different positions of collection electrode of wire-to-plate type ESP using the method of subarea and point distribution on collection electrode in the situation of ESP without gas inlet, and exhibited that ionic wind deduced from corona discharge in wire-to-plate type electrostatic precipitator (ESP) enhanced particle migration velocity. Defoort et al. [7] found the best geometrical configuration of wire-to-plate dielectric barrier discharges through the experiment, and in the case, the ionic wind velocity could reach up to 3.3 m/s. Li et al. [8] explored experimentally needle cylinder electrodes designed to generate ionic wind and drew the conclusion that electrode arrangement was very important to maximize the ionic wind velocity. Yuan et al. [9] obtained the ionic wind speed field images of discharges in air of tine-plate electrodes, investigated the characteristics of ionic wind speed and the distribution of flow field under power supplies, having uniform voltage, of the positive polarity DC, negative polarity DC and power frequency AC, and analyzed EHD (Electrohydro-dynamic) effect and hydrokinetics by using the theories of particle collision. Niewulis et al. [10] investigated the EHD secondary flow measured through 2-dimensional particle image velocimetry (PIV) method, and found the similarities and differences of the particle flow in the wire-cylinder type ESP for a negative and a positive DC voltage polarity. Yamamoto et al. [11] invented a new electrohydrodynamically assisted plasma electrostatic precipitator (plasma ESP), which is not only to collect low resistive particles generated from diesel engine but also to incinerate captured particulates within the same reactor. Podliński et al. [12] measured the secondary flow in a spike-plate type electrostatic precipitator (ESP) through PIV experiment, and considered that the collection efficiency of submicron dust particles depended on the generated EHD secondary flow.

In summary, the effect of ionic wind on ESP collection efficiency can not be negligible. However, researchers don’t explore the influence law of ionic wind on ESP particle trapping. Therefore, based on in-depth understanding of the multi-field coupling between gas flow field, electromagnetic field and particle dynamic field, the PM2.5 removal mechanism by ionic wind was analyzed, and the solid modeling of wire-cylinder ESP and numerical simulation of PM2.5 dust removal performance were carried out, which can provide a technical reference for the optimal design of PM2.5 trapping in a novel ESP.

2. Action mechanism of ionic wind

In the corona area, the movement of various ions, accompanied by the formation of electron avalanche, will form an additional fluid flow known as ionic wind [13].

The corona outer zone refers to the space from the corona area to the collecting electrodes. In the space, the field strength decays to a small value and tends towards stability, which makes air molecules unable to be ionized. The electrons generated from corona area collide with air molecules in corona outer space, charge them and move together, which is equivalent to form a wind source at the junction between corona area and corona outer zone. The current state inside the corona space is rather complex. Accompanied by the formation of electron avalanche, the electrons collide with air molecules and make them ionized, which forms positive ions and negative ions. The ions under the force of electric field move in the direction, contrary to its polarity, which means that positive (negative) ions move to the corona electrode (collecting plate) direction, so the collision and ionization still exist during the ion movement.

Through the above analysis, it is found that the charged fluid formed during corona discharge accord with the basic law of fluid motion.

Ionic wind speed near the corona wire and working voltage has the following relation [14] $\begin{eqnarray}\displaystyle v_{i}=(0.126-0.0217U_{0}+9.418\times 10^{-4}U_{0}^{2})\times 23.3 & & \displaystyle\end{eqnarray}$ (1) where v _i is the ionic wind speed, m/s; U ₀ is the working voltage, kV.

Equation (1) describes the relationship between the ionic wind speed and working voltage, as shown in Fig. 1. It can be clearly seen that the relationship between them is a parabola going upward. Normally, the working voltage of electrostatic precipitator is greater or equal to 20 kV. Therefore, for the electrostatic precipitator under practical operating conditions, the ionic wind speed increases nonlinearly with working voltage.

Fig. 1.

Varying curves of ion velocity with working voltage.

3. Mathematical model

3.1. Multi-field coupling relationship

Gas flow field, electric field and particle dynamic field are included in ESP. The three fields are connected and coupled with each other essentially, which is shown in Fig. 2 in detail.

Fig. 2.

Multi-field coupling diagram in ESP.

3.2. Gas flow field

Considering that the flow gas is incompressible in 2-D ESP model, one can regard the density of flue gas as a constant. Instead of generalized source term in Navier-Stokes equation by the sum of aerodynamic drag force and electric volume force [15,16], mass conservation equation and momentum conservation equation are written as $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \frac{\partial (u_{g})}{\partial x}+\frac{\partial (w_{g})}{\partial y}=0\end{eqnarray}$ (2) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \frac{\partial ({\rho}_{g}u_{g})}{\partial t}+\frac{\partial ({\rho}_{g}u_{g}u_{g})}{\partial x}+\frac{\partial ({\rho}_{g}u_{g}w_{g})}{\partial y}=-\frac{\partial p}{\partial x}+({\mu}+{\mu}_{t})\left(\frac{\partial ^{2}u_{g}}{\partial x^{2}}+\frac{\partial ^{2}u_{g}}{\partial y^{2}}\right)+F_{Dx}+{\rho}E_{x}\end{eqnarray}$ (3) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \frac{\partial ({\rho}_{g}w_{g})}{\partial t}+\frac{\partial ({\rho}_{g}u_{g}w_{g})}{\partial x}+\frac{\partial ({\rho}_{g}w_{g}w_{g})}{\partial y}=-\frac{\partial p}{\partial y}+({\mu}+{\mu}_{t})\left(\frac{\partial ^{2}w_{g}}{\partial x^{2}}+\frac{\partial ^{2}w_{g}}{\partial y^{2}}\right)+F_{Dy}+{\rho}E_{y}\end{eqnarray}$ (4) where 𝜌_g is the air density, kg ⋅ m⁻³; u _g and w _g are the gas velocity components in x direction and y direction, respectively, m ⋅ s⁻¹; P is the gas mean pressure, Pa; F _D is the aerodynamic drag force, N; E _x and E _y are the electric field intensity components in x direction and y direction, respectively, V/m; x and y represent being perpendicular to the dust collector and being parallel to the dust collector, respectively. $\rho$ is the space charge density, C/m³; 𝜇 is the gas dynamic viscosity coefficient, kg/(m ⋅ s); the turbulent viscosity 𝜇_t is expressed as a function of k and $\varepsilon$ using ${\mu}_{t}={\rho}_{g}C_{{\mu}}\frac{k^{2}}{{\varepsilon}}$ with the eddy viscosity concept built by Boussinesq, kg/(m ⋅ s); the empirical constant C _𝜇 equals 0.09 in general.

3.3. Electric field

Due to the axial symmetry and the neglect of the end effect [17], the electric field calculation in a wire-cylinder ESP can usually be simplified as a one-dimensional problem (x-direction), which implies that the calculation of y-direction is neglected. When the space charge of ions and charged dust exists in electric field, the Poisson equation in cylindrical coordinates can be written by the following formula $\begin{eqnarray}\displaystyle \frac{d^{2}U}{dr^{2}}+\frac{1}{r}\frac{dU}{dr}+\frac{{\rho}}{{\varepsilon}_{0}}=0 & & \displaystyle\end{eqnarray}$ (5) where U is the potential at the radial distance r from a space point to corona wire, V; ϵ₀ is the vacuum dielectric constant, which is generally taken as 8.854 × 10⁻¹² F/m.

Combining with current density and electric field strength, one can obtain $\begin{eqnarray}\displaystyle E\frac{dE}{dr}+\frac{E^{2}}{r}-\frac{I}{2{\pi}r{\varepsilon}_{0}b_{\text{eff}}}=0 & & \displaystyle\end{eqnarray}$ (6) where I is the current of corona line in unit length, A/m; b _eff is the effective mobility, which is composed of dust particles mobility b _pc and ions mobility b _ion [18].

3.4. Particle dynamic field

The Fluent software is used to numerically solve the particle dynamic field by integrating the force balance equation acting on particles in a two-dimensional plane. The force balance equation can be expressed in the form of “the inertia force on particles is equal to the sum of the forces acting on the particle”, the specific expression is as follows $\begin{eqnarray}\displaystyle m_{p}\frac{du_{p}}{dt}=Q_{p}E+F_{D}+F_{i} & & \displaystyle\end{eqnarray}$ (7) where m _p is the quality of particulate matter, kg; u _p is the particle velocity in x-direction and y-direction; Q _p is the total particle charge, including the particle charge Q _sat by field charging and the particle charge Q _diff by diffusion charging [19]; Q _p E is the electric field force acting on charged particles, N; F _D = m _p F _d, and the unit mass drag force F _d on single particle in flow field can be expressed as $\begin{eqnarray}\displaystyle F_{d}=\frac{1}{2}A_{p}{\rho}_{g}C_{D}(u_{g}-u_{p})|u_{g}-u_{p}| & & \displaystyle\end{eqnarray}$ (8) where A _p is the cross-sectional area of particles, and $A_{p}={\pi}D_{i}^{2}/4$ ; D _i is the particle diameter, m; u _g and u _p are the mean velocity of flue gas and the mean velocity of particles, respectively, m/s; C _D is the drag coefficient between gas flow and particles.

In addition, the ionic wind force F _i near the corona wire can be written as $\begin{eqnarray}\displaystyle F_{i}=\frac{1}{8}{\pi}{\rho}_{g}v_{i}^{2}D_{i}^{2}. & & \displaystyle\end{eqnarray}$ (9)

3.5. Calculation of collection efficiency

In the case that the numerical solution of the particle dynamic field is simulated by Fluent, Deutsch-Anderson semi-empirical formula is employed to calculate the grade collection efficiency and the overall collection efficiency of PM2.5 particles. The collection electrode length is divided into sections, and all particles are divided into 34 types of diameters. The PM2.5 grade efficiency 𝜂_i of the ith diameter can be expressed as $\begin{eqnarray}\displaystyle {\eta}_{i}=\frac{\mathop{\sum }_{j}{\eta}_{i,j}N_{i,j}}{N_{i,1}} & & \displaystyle\end{eqnarray}$ (10) where 𝜂_{i, j} is the collection efficiency of the ith diameter in the jth section of collection electrode; N _{i, j} is the concentration of the ith diameter in the area over against the jth section of collection electrode. When j = 1, N _{i, j} = N _i,1, representing the concentration of the ith diameter at the inlet of ESP.

For a wire-cylinder ESP, PM2.5 overall efficiency 𝜂 can be calculated by the following formula $\begin{eqnarray}\displaystyle {\eta}=\mathop{\sum }_{i}{\eta}_{i}P_{i} & & \displaystyle\end{eqnarray}$ (11) where P _i is the mass flow of the ith diameter at ESP inlet.

4. CFD model setting

4.1. Setting of gas-solid phase parameters and boundary conditions

In the process of ESP numerical simulation, reasonable setting on the physical parameters of particle phase and gas phase according to practical situation is a prerequisite to truly reflect the actual working conditions.

PM2.5 generated by coal-fired power plant is considered as the object in this work. The particle is assumed to be spherical, and its material property is anthracite. Based on the flue gas data [20], the physical parameters are set as shown in Table 1. The particle diameters ranging from 0.1 μm to 2.5 μm follow Rosin-Rammler distribution where the distribution index n = 1.64, the mean diameter D _m = 0.5D _max, and the maximum diameter D _max = 2.5 μm.

Table 1
Physical parameter setting of incident particles

Density (kg/m³) Constant-pressure specific heat (J/kg ⋅ K) Thermal conductivity (W/m ⋅ K)

2100 1680 0.0454

Density (kg/m³)	Constant-pressure specific heat (J/kg ⋅ K)	Thermal conductivity (W/m ⋅ K)
2100	1680	0.0454

Table 2

Boundary conditions of wire-cylinder ESP

	x-velocity	y-velocity	U	k	ϵ	Particle
Inlet	u _g = 0	w _g = v ₀	𝛻U = 0	$3T_{i}^{2}u_{i}^{2}/2$	0.05k ^1.5 D	Escape
Outlet	Pressure	Pressure	𝛻U = 0	∂k∕∂x = 0	∂ϵ∕∂x = 0	Escape
Corona wire	No slip	No slip	U = U ₀	Wall-function	Wall-function	Reflect
Collection plate	No slip	No slip	U = 0	Wall-function	Wall-function	Trap

The gas-phase substance in gas-solid flow can be viewed as continuous medium in Fluent. Due to no chemical interaction between flue gas and particles, the flue gas is simplified as air, and its pressure is regarded to be atmospheric pressure, that is, P = 1.01 × 10⁵ Pa. It is considered that the inlet gas evenly distributes at the entrance of ESP and is perpendicular to the inlet section. According to thermal physical property table of standard flue gas under atmospheric pressure [21], the flue gas density, specific heat and thermal conductivity at 450 K can be gained by linear interpolation.

The specific boundary conditions of wire-cylinder ESP are listed in Table 2, where T _i and D are the turbulence intensity and equivalent diameter at the inlet, respectively. The inlet and the outlet boundaries of the flue gas are, respectively, set as the velocity and the pressure conditions. The potential of corona wire surface is given as U ₀, and that of collection electrode surface is set as zero. The calculation on the surface of corona wire and collection electrode employs standard wall function, which connects physical quantities of wall with those of the turbulent core area.

4.2. Numerical iterative process

In this work, the finite volume method (FVM) is used to discretize the equations of fluid domain, and the nonlinear problem resulted from pressure velocity correction and multi-field coupling can be carried out by iterative calculation. The specific steps are shown in Fig. 3.

Fig. 3.

Flow chart of the numerical calculation for wire-cylinder ESP.

5. Results and discussion

5.1. Simplified model of wire-cylinder ESP

Figure 4 gives the 2-D simplified model of wire-cylinder ESP, and r axis and z axis are perpendicular and parallel to the collection electrode, respectively. The gas flows up axially at ESP inlet and has a uniform distribution, thus the dust concentration can be assumed to be constant on concentric circles centered on axis. Specific structure parameters of the model are as follows: the tube length of collection electrode L = 7.6 m, the radius of corona wire r _w = 1.0 mm and the inner diameter of collection electrode R = 0.3 m [22].

Fig. 4.

2-D simplified model of electric field for wire-cylinder ESP.

5.2. Grid independence verification

The collection efficiency and relative error of 1 μm particles in different mesh numbers are shown in Table 3. It can be seen that the relative error of collection efficiency is progressively reduced with the increase of grid number. The calculation accuracy can be ensured when the grid number reaches 34850, which is selected to carry out the calculation in this work.

Table 3
Grid independence verification of wire-cylinder ESP

Mesh number Grid growth Collection efficiency Relative error

22800 — 20.00% —

26250 15.13% 18.33% 8.35%

30000 14.29% 17.33% 5.46%

34850 15.27% 16.47% 4.96%

Mesh number	Grid growth	Collection efficiency	Relative error
22800	—	20.00%	—
26250	15.13%	18.33%	8.35%
30000	14.29%	17.33%	5.46%
34850	15.27%	16.47%	4.96%

5.3. Numerical reliability verification

To verify numerical reliability, the computational results in this work are compared with the data of reference paper [23] by setting the same working condition (v ₀ = 0.5 m/s, U ₀ = 60 kV), and the contrast curves are plotted in Fig. 5. It can be found that the numerical results agree well with literature data, which indicates that the theory and numerical model of wire-cylinder ESP in this study can objectively simulate the particle trapping performance.

Fig. 5.

Contrast curves of collection efficiency in wire-cyclinder ESP.

5.4. Effect of ionic wind under different operating voltages

When v ₀ = 1 m/s, the ionic wind effect on PM2.5 grade efficiency at different operating voltages is displayed in Fig. 6. As can be seen from Fig. 6, whether or not the ionic wind is considered, the PM2.5 grade efficiency is gradually increasing with the operating voltage, and the amplitude is decreasing. The grade efficiency in the presence of ionic wind is higher than that in the absence of ionic wind, and the amplitude under the action of ionic wind is increasing with particle diameter, which implies that ionic wind effect on large particle trapping is obvious. In the diameter range from 0.1 μm to 2.5 μm, the grade efficiency of wire-cylinder ESP without the consideration of ionic wind presents nonlinearly decreasing trend with the increasing particle diameter. Meanwhile, the grade efficiency with the consideration of ionic wind decreases with the increase of particle diameter firstly, and then increases. With the increasing operating voltage, the difference of PM2.5 grade efficiency with and without ionic wind effect is decreasing, showing that the contribution of ionic wind to particle trapping performance increases with the decrease of operating voltage.

Fig. 6.

PM2.5 grade efficiency vs. particle diameter with and without ionic wind effect.

The PM2.5 overall collection efficiency under different operating voltages is given in Fig. 7. It is clear that the overall efficiency with ionic wind is higher than that without ionic wind under the same operating voltage. With the constant amplitude increase of operating voltage, the overall efficiency increments with ionic wind ignored are 9.4% and 4.6%, respectively, while the ones with ionic wind considered are 7% and 4.5%, respectively, both keeping falling. When the operating voltage constantly increases, the differences between the overall efficiency with and without ionic wind are 3.8%, 1.4% and 1.3%, respectively, all keeping decreasing. The results show that the contribution of ionic wind to PM2.5 trapping gradually reduces with the increase of operating voltage.

Fig. 7.

PM2.5 overall efficiency with and without ionic wind under different operating voltages.

Fig. 8.

PM2.5 grade efficiency with and without ionic wind (U ₀ = 30 kV).

5.5. Ionic wind effect at different flue gas velocities

With the change of flue gas velocity, the ionic wind also has a certain effect on PM2.5 trapping, as shown Fig. 8. It is identified that the grade efficiency varying with diameter has a downward trend tending to be stable whether the ionic wind effect is considered or not. With the increase of flue gas velocity, the grade efficiency in a small diameter range has a more and more obvious decline, while the one in a big diameter range shows a steady trend, which indicates that the effect of gas velocity on small particles is more evident. The grade efficiency with ionic wind is higher than that without ionic wind, and the difference between them increases with flue gas velocity, which states that the higher the flue gas velocity is, the better the promoting effect of ionic wind on PM2.5 trapping efficiency is.

Combining with Fig. 8, one can apply histogram to exhibit PM2.5 overall collection efficiency with and without ionic wind at different gas velocities, as shown in Fig. 9. It is found that the overall efficiency with ionic wind is higher than that without ionic wind under the same gas velocity. Whether the ionic wind is considered or not, PM2.5 overall efficiency is decreasing with the increase of flue gas velocity, showing that PM2.5 collection efficiency is higher when the flue gas velocity is lower. With the constant amplitude increase of the gas velocity, the PM2.5 overall efficiency ignoring ionic wind decreases by 15.6% and 13.6% respectively, while the one considering ionic wind decreases by 13.6% and 11.8%, respectively, showing that with the increase of velocity, although the collection efficiency is decreasing, the ionic wind effect is increasing. Furthermore, when the gas velocity constantly increases, the difference of PM2.5 overall efficiency with and without ionic wind is 3.8%, 6.2% and 8.0%, respectively, all being increasing, stating that the effect of ionic wind on particle trapping at higher gas velocity is more obvious.

Fig. 9.

PM2.5 overall efficiency with and without ionic wind at different gas velocities.

6. Conclusions

The PM2.5 removal mechanism of ionic wind was explored, the mathematical model of 2-D wire-cylinder ESP under multi-field coupling was built, and the numerical analysis of PM2.5 collection efficiency was carried out by editing self-defining function loaded into Fluent software. The conclusions can be drawn as follows:

Ionic wind can effectively inhibit the weakening effect of increasing velocity on PM2.5 collection efficiency. With the decrease of operating voltage, the improvement of ionic wind on PM2.5 collection efficiency is more obvious.

No matter whether the ionic wind effect is considered or not, the curves of PM2.5 grade efficiency are gradually decreasing with the increasing of particle diameter.

Despite of the existence of ionic wind, PM2.5 collection efficiency increases with operating voltage and decreases with gas velocity.

The effect of ionic wind on PM2.5 collection performance is more and more obvious with the increase of gas velocity or the decrease of operating voltage.

Footnotes

Acknowledgements

This work is supported by National Natural Science Foundation of China (11572187); Foundation of Science and Technology Commission of Shanghai Municipality (18DZ1202105, 18DZ1202302).

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Analysis of PM2.5 collection efficiency in a wire-cylinder ESP with ionic wind effect under multi-field coupling

Abstract

Keywords

1. Introduction

2. Action mechanism of ionic wind

3.1. Multi-field coupling relationship

4.1. Setting of gas-solid phase parameters and boundary conditions

Table 1 Physical parameter setting of incident particles Density (kg/m3) Constant-pressure specific heat (J/kg ⋅ K) Thermal conductivity (W/m ⋅ K) 2100 1680 0.0454

5.1. Simplified model of wire-cylinder ESP

Table 3 Grid independence verification of wire-cylinder ESP Mesh number Grid growth Collection efficiency Relative error 22800 — 20.00% — 26250 15.13% 18.33% 8.35% 30000 14.29% 17.33% 5.46% 34850 15.27% 16.47% 4.96%

Footnotes

Acknowledgements

References

Table 1
Physical parameter setting of incident particles

Density (kg/m³) Constant-pressure specific heat (J/kg ⋅ K) Thermal conductivity (W/m ⋅ K)

2100 1680 0.0454

Table 3
Grid independence verification of wire-cylinder ESP

Mesh number Grid growth Collection efficiency Relative error

22800 — 20.00% —

26250 15.13% 18.33% 8.35%

30000 14.29% 17.33% 5.46%

34850 15.27% 16.47% 4.96%