Research on electrostatic shielding characteristics of electrostatic precipitator

Figures & data

Table 1. Governing equation

Equation name	Governing equation	Remarks
Poisson equation	$\mathrm{\nabla }E=\rho /{\epsilon }_0$	Electric field equation
Current continuity Equation	$\begin{array}{rl}& \mathrm{\nabla }J=0\\ & J=Z_{\mathrm{i}\mathrm{o}\mathrm{n}}\rho E-D\mathrm{\nabla }\rho \end{array}$
Peek formula	$E_0=3.1\times {10}^6(1+\frac{0.308}{\sqrt{r_c}})$
Momentum conservation equation	$\begin{array}{rl}& {\rho }_f(u_f\cdot \mathrm{\nabla })=\mathrm{\nabla }\left[-pI+(\mu +{\mu }_T)\left(\mathrm{\nabla }{u}_f+{(\mathrm{\nabla }{u}_f)}^T\right)I\right.\\ & \left.-\frac{2}{3}\rho kI\right]+\rho (-\mathrm{\nabla }\phi )\end{array}$	Flow field equation
Turbulence energy governing equation	${\rho }_f(u_f\cdot \mathrm{\nabla })k=\mathrm{\nabla }\left[(\mu +{\mu }_T{\sigma }_k^{\ast })\mathrm{\nabla }k\right]+P_k-{\beta }_0^{\ast }{\rho }_f\omega k$
Specific dissipation rate equation	${\rho }_f(u_f\cdot \mathrm{\nabla })\omega =\mathrm{\nabla }\left[(\mu +{\mu }_T{\sigma }_k^{\ast })\mathrm{\nabla }\omega \right]+{\alpha }_{\frac{\omega }{k}}{P}_k-{\rho }_f{\beta }_0{\omega }^2$
Charge equation	$\frac{d{Q}_p}{dt}=\left\{\begin{array}{c}\frac{Q_p}{t_q}(1-\frac{Q_p}{Q_s}{)}^2+\frac{2\pi \alpha {\rho }_{ion}{Z}_{ion}{k}_B{d}_{par}}{e},Q_p\le Q_s\\ \frac{\alpha }{4t_q}(Q_p-Q_s)exp(\frac{e(Q_p-Q_s)}{2\pi {\epsilon }_0{k}_B{d}_{par}}),Q_p>Q_s\end{array}\right.$	Particle charge and motion equation
Equation of motion	$\frac{d(m_{par}{u}_{par})}{dt}=eZE+\frac{m_{par}}{{\tau }_{par}}(u_f-u_{par})+m_{par}g\frac{{\rho }_{par}-{\rho }_f}{{\rho }_{par}}$

Table 2. Boundary conditions

Position	Voltage	Space charge density	Particles
Discharge Electrode surface	V = V0	$-n\cdot \mathrm{\nabla }V=E_0$ ($\rho$ is constantly adjust)	rebound
Dust collector	$\frac{\mathrm{\partial }V}{\mathrm{\partial }n}=0$	$\mathrm{\partial }{\rho }_i=0$	capture
Import	$\frac{\mathrm{\partial }V}{\mathrm{\partial }n}=0$	$\mathrm{\partial }{\rho }_i=0$	freed
Exit	$V=0$	$\mathrm{\partial }{\rho }_i=0$	escape

Table 3. Main parameters of ESP

Parameter Type	Value and unit
Dust collection board length	0.5 m
Height of dust collector	0.1 m
Number of discharge electrodes	3–8 pieces
Radius of discharge electrode	1–2 mm
Wire-to-plate distance	0.05–0.1 m
Wire-to-wire distance	0.05–0.1 m
Corona voltage	30–50kV
Airflow velocity	1 m/s
Pressure	1 atm
Ion mobility	2.2E-04 m^2V^−1s^−1
Air mobility	8.85E-12 C^2N^−1m^−2
Particle size	$1\mu m$

Figure 1. Three-dimensional diagram of ESP.

Figure 2. Schematic diagram of the grid map of the computational domain and the grid map around the discharge electrode line.

Figure 3. Diagram of experimental setup.

Figure 4. BS barbed discharge electrode.

Figure 5. Current density distribution corresponding to the tip of BS discharge.

Figure 6. Comparison between this study and Kasdi V–I characteristic experiment.

Figure 7. Comparison between this study and Kasdi current density experiment.

Figure 8. Cloud map of space charge density distribution (voltage).

Figure 9. Space charge density distribution curve under different voltages.

Table 4. Electrostatic shielding degree under different voltages

Voltage (kV)	30	40	50
Space charge density ratio	1.055	1.027	1.019

Figure 10. Cloud map of space charge density distribution (wire-to-wire distance).

Table 5. Electrostatic shielding degree under three wire-to-wire distances

Wire-to-wire distance (m)	0.05	0.075	0.1
Space charge density ratio	1.147	1.063	1.027

Figure 11. The distribution curve of space charge density under three wire-to-wire distances.

Figure 12. Cloud map of space charge density distribution (wire-to-plate distance).

Table 6. Electrostatic shielding degree under three wire-to-plate distances

Wire-to-plate distance (m)	0.05	0.075	0.1
Space charge density ratio	1.027	1.095	1.201

Figure 13. Space charge density distribution curve under three wire-to-plate distances.

Table 7. Electrostatic shielding degree under different discharge electrode radius

Discharge electrode radius (mm)	1	1.5	2
Space charge density ratio	1.027	1.035	1.069

Figure 14. Cloud map of space charge density distribution (discharge electrode radius).

Figure 15. Space charge density distribution curve under different discharge electrode radius.

Table 8. Electrostatic shielding degree under different number of discharge electrodes

Number of discharge electrodes (pieces)	3	4	5
Space charge density ratio	1.027	1.106	1.202

Figure 16. Cloud map of space charge density distribution (number of discharge electrodes).

Figure 17. Space charge density distribution curve under different number of discharge electrodes.

Table 9. The level table that affects the degree of electrostatic shielding

Level	A Voltage (kV)	B Wire-to-wire distance (m)	C Wire-to-plate distance (m)	D Discharge electrode radius (mm)
1	30	0.05	0.05	1
2	40	0.075	0.075	1.5
3	50	0.1	0.1	2

Table 10. Orthogonal test analysis

Factor Test number	A	B	C	D	Space charge density ratio
1	1	1	1	1	1.371
2	1	2	2	2	1.978
3	1	3	3	3	2.156
4	2	1	2	3	2.744
5	2	2	3	1	1.575
6	2	3	1	2	1.035
7	3	1	3	2	1.567
8	3	2	1	3	1.074
9	3	3	2	1	1.088
k1	1.835	1.894	1.160	1.345
k2	1.785	1.542	1.937	1.527
k3	1.243	1.426	1.766	1.991
R	0.592	0.468	0.777	0.646
R3> R4> R1> R2

Figure 18. Particle charging and dust removal efficiency under different number of discharge electrodes.

Figure 19. The relationship between the number of electrodes at different voltages and the dust removal efficiency.

Data availability statement

Available on request (https://doi.org/ 10.1080/10962247.2021.2017374).